{"subject":"further_mathematics","questions":[{"q":"Differentiate y = 2x^3 + 5x^2 + 4x with respect to x.","o":["6x² + 10x + 4","2x² + 10x + 4","6x² + 5x + 4","6x² + 10x"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 4x^3 + 8x^2 − 4x with respect to x.","o":["12x² + 16x − 4","12x² + 16x","4x² + 16x − 4","12x² + 8x − 4"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 3x^3 + 5x^2 − 7x with respect to x.","o":["9x² + 10x − 7","9x² + 10x","3x² + 10x − 7","9x² + 5x − 7"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 4x^3 + 5x^2 + 5x with respect to x.","o":["4x² + 10x + 5","12x² + 5x + 5","12x² + 10x + 5","12x² + 10x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 − 5x^2 + 2x with respect to x.","o":["18x² − 10x + 2","6x² − 10x + 2","18x² − 10x","18x² − 5x + 2"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = x^3 − 8x^2 + 5x with respect to x.","o":["1x² − 16x + 5","3x² − 16x + 5","3x² − 8x + 5","3x² − 16x"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 3x^2 − 8x with respect to x.","o":["6x² − 6x − 8","6x² − 6x","2x² − 6x − 8","6x² − 3x − 8"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 6x^2 − 6x with respect to x.","o":["2x² − 12x − 6","6x² − 6x − 6","6x² − 12x","6x² − 12x − 6"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 + 2x^2 − 5x with respect to x.","o":["2x² + 4x − 5","6x² + 4x","6x² + 2x − 5","6x² + 4x − 5"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 4x^3 + 8x^2 + 3x with respect to x.","o":["4x² + 16x + 3","12x² + 16x","12x² + 8x + 3","12x² + 16x + 3"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = x^3 − 6x^2 − 4x with respect to x.","o":["3x² − 12x","3x² − 6x − 4","1x² − 12x − 4","3x² − 12x − 4"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = x^3 + 8x^2 − 2x with respect to x.","o":["3x² + 8x − 2","1x² + 16x − 2","3x² + 16x − 2","3x² + 16x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 3x^2 + 2x with respect to x.","o":["2x² − 6x + 2","6x² − 3x + 2","6x² − 6x + 2","6x² − 6x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 5x^2 − 4x with respect to x.","o":["2x² − 10x − 4","6x² − 10x","6x² − 10x − 4","6x² − 5x − 4"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 7x^2 + 7x with respect to x.","o":["6x² − 14x","2x² − 14x + 7","6x² − 14x + 7","6x² − 7x + 7"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 − 8x^2 + 2x with respect to x.","o":["18x² − 8x + 2","6x² − 16x + 2","18x² − 16x","18x² − 16x + 2"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 3x^2 + 8x with respect to x.","o":["2x² − 6x + 8","6x² − 6x","6x² − 3x + 8","6x² − 6x + 8"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = x^3 + x^2 − 8x with respect to x.","o":["3x² + 2x − 8","3x² + 1x − 8","1x² + 2x − 8","3x² + 2x"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 3x^2 + 3x with respect to x.","o":["6x² − 3x + 3","2x² − 6x + 3","6x² − 6x + 3","6x² − 6x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 + 7x^2 − 8x with respect to x.","o":["2x² + 14x − 8","6x² + 14x − 8","6x² + 14x","6x² + 7x − 8"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = x^3 − 2x^2 + 2x with respect to x.","o":["1x² − 4x + 2","3x² − 2x + 2","3x² − 4x + 2","3x² − 4x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 4x^3 + 7x^2 with respect to x.","o":["12x² + 7x + 0","12x² + 14x + 0","4x² + 14x + 0","12x² + 14x"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 4x^3 − 4x^2 − 9x with respect to x.","o":["12x² − 4x − 9","4x² − 8x − 9","12x² − 8x − 9","12x² − 8x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 5x^3 + 5x^2 − x with respect to x.","o":["15x² + 5x − 1","15x² + 10x","5x² + 10x − 1","15x² + 10x − 1"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 5x^2 + 3x with respect to x.","o":["6x² − 10x","6x² − 10x + 3","2x² − 10x + 3","6x² − 5x + 3"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 3x^3 − 4x^2 with respect to x.","o":["3x² − 8x + 0","9x² − 8x + 0","9x² − 4x + 0","9x² − 8x"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 3x^2 − 4x with respect to x.","o":["6x² − 3x − 4","6x² − 6x","2x² − 6x − 4","6x² − 6x − 4"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 5x^3 + 8x^2 − 8x with respect to x.","o":["15x² + 16x","5x² + 16x − 8","15x² + 8x − 8","15x² + 16x − 8"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 4x^3 − 3x^2 − 2x with respect to x.","o":["12x² − 3x − 2","4x² − 6x − 2","12x² − 6x − 2","12x² − 6x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 + 4x^2 − 5x with respect to x.","o":["2x² + 8x − 5","6x² + 4x − 5","6x² + 8x − 5","6x² + 8x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 5x^3 − 5x^2 + 8x with respect to x.","o":["15x² − 10x + 8","15x² − 5x + 8","15x² − 10x","5x² − 10x + 8"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 5x^3 + x^2 with respect to x.","o":["15x² + 2x","15x² + 2x + 0","5x² + 2x + 0","15x² + 1x + 0"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 + 3x^2 − 7x with respect to x.","o":["6x² + 3x − 7","6x² + 6x","2x² + 6x − 7","6x² + 6x − 7"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 − 6x^2 + 5x with respect to x.","o":["18x² − 12x + 5","18x² − 6x + 5","18x² − 12x","6x² − 12x + 5"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 4x^3 + 8x^2 + 7x with respect to x.","o":["12x² + 8x + 7","12x² + 16x","4x² + 16x + 7","12x² + 16x + 7"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = x^3 − 7x^2 + 4x with respect to x.","o":["1x² − 14x + 4","3x² − 14x","3x² − 14x + 4","3x² − 7x + 4"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 + 5x^2 + 5x with respect to x.","o":["6x² + 10x + 5","18x² + 10x","18x² + 5x + 5","18x² + 10x + 5"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 4x^3 − x^2 − 7x with respect to x.","o":["12x² − 2x","12x² − 1x − 7","4x² − 2x − 7","12x² − 2x − 7"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 3x^3 − 2x^2 + 5x with respect to x.","o":["9x² − 4x + 5","9x² − 2x + 5","3x² − 4x + 5","9x² − 4x"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 4x^3 + 4x^2 with respect to x.","o":["12x² + 4x + 0","4x² + 8x + 0","12x² + 8x","12x² + 8x + 0"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 + 2x^2 − 3x with respect to x.","o":["6x² + 2x − 3","2x² + 4x − 3","6x² + 4x","6x² + 4x − 3"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = x^3 − 3x^2 − 7x with respect to x.","o":["1x² − 6x − 7","3x² − 3x − 7","3x² − 6x − 7","3x² − 6x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 + 6x^2 − 6x with respect to x.","o":["18x² + 12x","18x² + 6x − 6","6x² + 12x − 6","18x² + 12x − 6"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 3x^3 − 2x^2 − x with respect to x.","o":["9x² − 4x − 1","9x² − 4x","9x² − 2x − 1","3x² − 4x − 1"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 + 8x^2 − 3x with respect to x.","o":["2x² + 16x − 3","6x² + 8x − 3","6x² + 16x − 3","6x² + 16x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 + 4x^2 + 5x with respect to x.","o":["2x² + 8x + 5","6x² + 8x","6x² + 4x + 5","6x² + 8x + 5"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 − 3x^2 + 3x with respect to x.","o":["18x² − 3x + 3","18x² − 6x + 3","6x² − 6x + 3","18x² − 6x"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 7x^2 + 2x with respect to x.","o":["6x² − 7x + 2","6x² − 14x + 2","2x² − 14x + 2","6x² − 14x"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 5x^3 − 7x^2 + 3x with respect to x.","o":["5x² − 14x + 3","15x² − 7x + 3","15x² − 14x","15x² − 14x + 3"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 8x^2 + 8x with respect to x.","o":["6x² − 16x","6x² − 16x + 8","6x² − 8x + 8","2x² − 16x + 8"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 4x^3 + 3x^2 − 9x with respect to x.","o":["12x² + 6x","12x² + 6x − 9","4x² + 6x − 9","12x² + 3x − 9"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 5x^3 − 7x^2 with respect to x.","o":["15x² − 14x","5x² − 14x + 0","15x² − 7x + 0","15x² − 14x + 0"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 + 6x^2 − 9x with respect to x.","o":["6x² + 12x","6x² + 6x − 9","6x² + 12x − 9","2x² + 12x − 9"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 − 2x^2 − 5x with respect to x.","o":["6x² − 4x − 5","18x² − 2x − 5","18x² − 4x","18x² − 4x − 5"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 4x^3 + 2x^2 − 5x with respect to x.","o":["4x² + 4x − 5","12x² + 4x","12x² + 4x − 5","12x² + 2x − 5"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 3x^3 − 8x^2 − 7x with respect to x.","o":["9x² − 8x − 7","9x² − 16x","9x² − 16x − 7","3x² − 16x − 7"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 − 2x^2 + 2x with respect to x.","o":["18x² − 2x + 2","18x² − 4x + 2","6x² − 4x + 2","18x² − 4x"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = x^3 + 7x^2 − x with respect to x.","o":["3x² + 7x − 1","3x² + 14x","1x² + 14x − 1","3x² + 14x − 1"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = x^3 − x^2 + 2x with respect to x.","o":["3x² − 2x + 2","1x² − 2x + 2","3x² − 1x + 2","3x² − 2x"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 − 2x^2 + 7x with respect to x.","o":["18x² − 4x","18x² − 4x + 7","18x² − 2x + 7","6x² − 4x + 7"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 + 8x^2 − 8x with respect to x.","o":["6x² + 8x − 8","2x² + 16x − 8","6x² + 16x − 8","6x² + 16x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = x^3 + 3x^2 + 6x with respect to x.","o":["3x² + 6x","1x² + 6x + 6","3x² + 6x + 6","3x² + 3x + 6"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 3x^3 − 7x^2 − 3x with respect to x.","o":["9x² − 14x − 3","9x² − 14x","9x² − 7x − 3","3x² − 14x − 3"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 + 6x^2 + 2x with respect to x.","o":["6x² + 12x + 2","6x² + 6x + 2","2x² + 12x + 2","6x² + 12x"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 5x^3 − 8x^2 + 3x with respect to x.","o":["15x² − 16x","15x² − 16x + 3","5x² − 16x + 3","15x² − 8x + 3"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − x^2 + 7x with respect to x.","o":["2x² − 2x + 7","6x² − 2x + 7","6x² − 1x + 7","6x² − 2x"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = x^3 − x^2 + 3x with respect to x.","o":["1x² − 2x + 3","3x² − 2x","3x² − 2x + 3","3x² − 1x + 3"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 5x^3 − 4x^2 − 9x with respect to x.","o":["15x² − 4x − 9","15x² − 8x − 9","15x² − 8x","5x² − 8x − 9"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 − 5x^2 − 3x with respect to x.","o":["6x² − 10x − 3","18x² − 5x − 3","18x² − 10x − 3","18x² − 10x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = x^3 − 3x^2 − 2x with respect to x.","o":["1x² − 6x − 2","3x² − 3x − 2","3x² − 6x","3x² − 6x − 2"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 4x^3 − 2x^2 − 3x with respect to x.","o":["4x² − 4x − 3","12x² − 4x","12x² − 4x − 3","12x² − 2x − 3"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 + 7x^2 + 6x with respect to x.","o":["6x² + 14x + 6","6x² + 7x + 6","6x² + 14x","2x² + 14x + 6"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 7x^2 + x with respect to x.","o":["6x² − 14x","2x² − 14x + 1","6x² − 7x + 1","6x² − 14x + 1"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 − x^2 − 4x with respect to x.","o":["18x² − 2x","6x² − 2x − 4","18x² − 2x − 4","18x² − 1x − 4"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = x^3 + x^2 + 9x with respect to x.","o":["3x² + 2x","1x² + 2x + 9","3x² + 2x + 9","3x² + 1x + 9"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 + 7x^2 − 8x with respect to x.","o":["18x² + 14x − 8","18x² + 7x − 8","6x² + 14x − 8","18x² + 14x"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 3x^3 + 6x^2 + 2x with respect to x.","o":["9x² + 6x + 2","3x² + 12x + 2","9x² + 12x","9x² + 12x + 2"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 3x^3 − 5x^2 + 2x with respect to x.","o":["3x² − 10x + 2","9x² − 5x + 2","9x² − 10x + 2","9x² − 10x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = x^3 − 2x^2 + x with respect to x.","o":["3x² − 2x + 1","3x² − 4x + 1","1x² − 4x + 1","3x² − 4x"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 6x with respect to x.","o":["6x² + 0x","2x² + 0x − 6","6x² + 0x − 6","2x⁴ + 0x³ − 6x²"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 5x^3 − 2x^2 − 5x with respect to x.","o":["15x² − 2x − 5","15x² − 4x","5x² − 4x − 5","15x² − 4x − 5"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 + 2x^2 + 7x with respect to x.","o":["18x² + 2x + 7","18x² + 4x","18x² + 4x + 7","6x² + 4x + 7"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 3x^3 − 7x^2 − x with respect to x.","o":["9x² − 7x − 1","9x² − 14x","3x² − 14x − 1","9x² − 14x − 1"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 5x^3 + 8x^2 − 9x with respect to x.","o":["5x² + 16x − 9","15x² + 16x − 9","15x² + 16x","15x² + 8x − 9"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 4x^3 + 8x^2 + 8x with respect to x.","o":["12x² + 16x + 8","4x² + 16x + 8","12x² + 8x + 8","12x² + 16x"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 + 3x^2 − 5x with respect to x.","o":["6x² + 6x − 5","18x² + 6x","18x² + 3x − 5","18x² + 6x − 5"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 + 8x^2 + 9x with respect to x.","o":["18x² + 8x + 9","18x² + 16x","6x² + 16x + 9","18x² + 16x + 9"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 + 6x^2 − 2x with respect to x.","o":["18x² + 12x − 2","18x² + 12x","18x² + 6x − 2","6x² + 12x − 2"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 3x^2 − 9x with respect to x.","o":["2x² − 6x − 9","6x² − 3x − 9","6x² − 6x − 9","6x² − 6x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 3x^3 − 2x^2 − 8x with respect to x.","o":["9x² − 4x − 8","9x² − 4x","3x² − 4x − 8","9x² − 2x − 8"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = x^3 − 3x^2 − 5x with respect to x.","o":["3x² − 3x − 5","3x² − 6x","3x² − 6x − 5","1x² − 6x − 5"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 + 4x^2 − 6x with respect to x.","o":["18x² + 8x − 6","6x² + 8x − 6","18x² + 8x","18x² + 4x − 6"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 5x^3 − 8x^2 − 7x with respect to x.","o":["15x² − 16x − 7","5x² − 16x − 7","15x² − 16x","15x² − 8x − 7"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 2x^2 + 4x with respect to x.","o":["6x² − 4x + 4","6x² − 4x","6x² − 2x + 4","2x² − 4x + 4"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 3x^3 + 3x^2 + 4x with respect to x.","o":["9x² + 6x","9x² + 3x + 4","3x² + 6x + 4","9x² + 6x + 4"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 5x^3 + 7x^2 − 4x with respect to x.","o":["15x² + 14x − 4","15x² + 14x","15x² + 7x − 4","5x² + 14x − 4"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 + 7x with respect to x.","o":["6x² + 0x + 7","18x² + 0x + 7","18x² + 0x","6x⁴ + 0x³ + 7x²"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 + 7x^2 − x with respect to x.","o":["18x² + 7x − 1","18x² + 14x − 1","6x² + 14x − 1","18x² + 14x"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 3x^3 − 6x^2 + 6x with respect to x.","o":["9x² − 12x + 6","3x² − 12x + 6","9x² − 12x","9x² − 6x + 6"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 3x^3 + x^2 + 3x with respect to x.","o":["3x² + 2x + 3","9x² + 1x + 3","9x² + 2x + 3","9x² + 2x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 4x^3 + 8x^2 − 6x with respect to x.","o":["12x² + 16x","12x² + 8x − 6","4x² + 16x − 6","12x² + 16x − 6"],"a":3,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 − 2x^2 − 8x with respect to x.","o":["6x² − 4x − 8","18x² − 2x − 8","18x² − 4x − 8","18x² − 4x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 4x^3 − 3x^2 − 9x with respect to x.","o":["12x² − 6x − 9","12x² − 6x","4x² − 6x − 9","12x² − 3x − 9"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 − 2x^2 − 4x with respect to x.","o":["6x² − 2x − 4","6x² − 4x − 4","6x² − 4x","2x² − 4x − 4"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 3x^3 + 8x^2 + 3x with respect to x.","o":["9x² + 8x + 3","3x² + 16x + 3","9x² + 16x + 3","9x² + 16x"],"a":2,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 6x^3 + 3x^2 + 6x with respect to x.","o":["18x² + 6x + 6","6x² + 6x + 6","18x² + 3x + 6","18x² + 6x"],"a":0,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 3x^3 − 6x^2 − 8x with respect to x.","o":["3x² − 12x − 8","9x² − 12x − 8","9x² − 6x − 8","9x² − 12x"],"a":1,"t":"Calculus","d":"Medium"},{"q":"Differentiate y = 2x^3 + 4x^2 − 9x with respect to x.","o":["6x² + 8x − 9","2x² + 8x − 9","6x² + 4x − 9","6x² + 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9]].","o":["-20","5","52","-52"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-2, 8], [6, 8]].","o":["32","64","-76","-64"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[6, -1], [2, 9]].","o":["21","56","52","-56"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-1, 9], [8, 2]].","o":["-74","-26","74","70"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[8, -3], [7, 6]].","o":["27","69","74","-69"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[4, -6], [3, 3]].","o":["-30","30","7","-6"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-5, -1], [0, 7]].","o":["2","-35","35","7"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[4, -2], [1, -1]].","o":["3","-2","2","-6"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-6, -1], [6, 3]].","o":["-12","12","-24","-33"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[6, -2], [-2, -1]].","o":["-10","-2","-14","10"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[3, 0], [7, 9]].","o":["27","12","-27","21"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-4, -3], [6, -4]].","o":["34","-36","-2","-34"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[7, -2], [6, 2]].","o":["2","-26","26","46"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-1, 5], [9, -3]].","o":["6","48","42","-42"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-5, 9], [-3, -1]].","o":["24","32","-22","-32"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[3, -6], [1, -1]].","o":["2","-9","-3","3"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[1, 5], [-3, 2]].","o":["-17","17","3","-13"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-5, 5], [3, 4]].","o":["-35","35","-5","-1"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[8, 0], [9, -4]].","o":["32","4","72","-32"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[3, -6], [-2, -3]].","o":["3","-21","21","-24"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[9, -6], [6, 1]].","o":["-27","45","60","-45"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-5, 1], [1, -6]].","o":["29","-29","1","31"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-4, 9], [3, 5]].","o":["47","-57","-47","7"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-4, 9], [3, 2]].","o":["-30","35","19","-35"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[7, -6], [6, -1]].","o":["-29","29","36","-43"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[8, 2], [5, 0]].","o":["8","40","10","-10"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-1, 8], [3, -4]].","o":["29","28","-20","20"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[6, 7], [6, 9]].","o":["-27","-12","96","12"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-2, -2], [7, 9]].","o":["4","-4","7","-32"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[3, 8], [-4, -3]].","o":["23","-23","-41","12"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[2, 6], [1, 1]].","o":["-4","8","3","4"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-5, 5], [7, 1]].","o":["30","-40","-4","40"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[1, -5], [-3, 6]].","o":["27","-9","9","21"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[5, -4], [1, -3]].","o":["-19","11","-7","-11"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[1, 7], [6, -2]].","o":["-44","40","20","44"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[3, -5], [8, 6]].","o":["58","-58","-22","54"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-6, 9], [-6, 7]].","o":["-27","-12","12","-96"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-3, 3], [-3, -2]].","o":["-3","-15","-5","15"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-5, -4], [3, -2]].","o":["22","-22","-23","-2"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[9, -3], [-4, 0]].","o":["-36","12","9","-12"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[2, 9], [1, 7]].","o":["-5","5","-61","23"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[4, 1], [1, -3]].","o":["-11","-13","13","7"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[9, 7], [8, -1]].","o":["65","47","79","-65"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-3, 4], [0, 6]].","o":["-18","3","-24","18"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[5, -3], [0, -6]].","o":["30","-30","-18","-1"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[3, 4], [-3, 5]].","o":["-27","27","-29","3"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[6, 9], [4, -4]].","o":["60","12","2","-60"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[3, -1], [-1, 4]].","o":["11","1","13","-11"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[5, -1], [3, -1]].","o":["-8","2","14","-2"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-3, 4], [-1, -3]].","o":["5","13","15","-13"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[2, -1], [6, 5]].","o":["17","4","16","-16"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-2, -4], [-5, -6]].","o":["32","-8","8","-14"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[7, -1], [8, 8]].","o":["-64","48","64","15"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-3, -4], [3, -4]].","o":["-25","0","-24","24"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[7, 9], [6, 8]].","o":["-2","-30","110","2"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[1, 6], [1, 9]].","o":["-53","15","-3","3"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-4, 0], [-3, -5]].","o":["20","12","-9","-20"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-3, -4], [1, 3]].","o":["9","-13","-5","5"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[8, 1], [-4, 8]].","o":["-68","68","-40","60"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-4, 4], [2, 8]].","o":["4","-24","-40","40"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[6, 7], [1, -6]].","o":["43","-29","48","-43"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[2, -3], [0, -5]].","o":["-3","10","-10","-15"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[9, 5], [-1, 9]].","o":["86","-86","76","-54"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[6, -2], [3, 2]].","o":["18","22","-18","6"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-5, 4], [9, 5]].","o":["11","61","-65","-61"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-1, 1], [9, 7]].","o":["6","-16","16","2"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[4, -3], [6, 3]].","o":["30","33","-30","-6"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[7, 9], [2, 8]].","o":["-38","38","-58","74"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-1, 4], [8, 0]].","o":["-8","-32","32","-1"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-1, 2], [7, 8]].","o":["-23","-22","22","6"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[9, -4], [8, -5]].","o":["52","-77","13","-13"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[8, -1], [2, 2]].","o":["-18","14","10","18"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-4, 3], [1, -3]].","o":["9","5","15","-9"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[3, 5], [9, -1]].","o":["32","-48","48","42"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[5, -6], [1, -2]].","o":["-16","-7","4","-4"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[7, 2], [-6, 6]].","o":["30","-54","54","13"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-3, 6], [7, -4]].","o":["54","3","30","-30"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-4, 7], [9, 4]].","o":["47","-79","79","-64"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[0, 9], [-2, -6]].","o":["18","-18","-6","54"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[1, -5], [-4, 6]].","o":["14","7","26","-14"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-2, 4], [9, 5]].","o":["-38","-46","26","46"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[3, -1], [-1, 0]].","o":["1","3","-1","-3"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-1, -2], [5, -4]].","o":["-13","-6","-14","14"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[3, 8], [1, 1]].","o":["5","-5","11","4"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[9, 8], [7, -1]].","o":["-65","71","65","47"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[3, -2], [7, 9]].","o":["39","41","13","-41"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[7, 6], [7, -6]].","o":["0","-84","84","85"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[8, -4], [-4, 0]].","o":["16","8","-16","-32"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-4, 2], [-3, 9]].","o":["-6","30","-30","-42"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[9, 3], [-5, 9]].","o":["66","-72","96","-96"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[1, 4], [6, 6]].","o":["7","30","-18","18"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[7, -6], [8, 7]].","o":["97","98","-97","1"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[8, 7], [-5, -1]].","o":["27","-43","-27","-33"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[9, -2], [0, -4]].","o":["-8","-36","5","36"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-6, 4], [7, 9]].","o":["-82","-26","-78","82"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-4, -1], [6, 3]].","o":["-18","6","-21","-6"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[4, -3], [-2, 3]].","o":["6","18","-6","1"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-5, 9], [0, 9]].","o":["4","-81","-45","45"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[6, 0], [5, 7]].","o":["13","42","30","-42"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-5, -5], [-5, 6]].","o":["55","-5","1","-55"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-3, -5], [6, 9]].","o":["27","3","-57","-3"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[9, -6], [9, -2]].","o":["36","-72","69","-36"],"a":0,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[3, 3], [9, 1]].","o":["4","30","24","-24"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-6, -1], [9, 2]].","o":["-52","3","-3","-21"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[1, -6], [-2, -1]].","o":["-8","13","-13","11"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[4, 4], [5, 1]].","o":["5","16","24","-16"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-6, -6], [2, -2]].","o":["-24","-8","0","24"],"a":3,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[1, -4], [7, 5]].","o":["-33","-23","33","27"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[-5, 1], [3, 6]].","o":["-27","33","-33","-21"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[7, -5], [0, 6]].","o":["-42","13","42","30"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[9, 1], [-5, -3]].","o":["22","-32","-22","-42"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[0, 6], [1, -5]].","o":["-5","30","-6","6"],"a":2,"t":"Matrices","d":"Medium"},{"q":"Find the determinant of the matrix [[9, 3], [5, -1]].","o":["6","24","-24","48"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[1, 2], [2, -4]] and Q = [[-2, -1], [-4, 4]], find the element in the first row, first column of PQ.","o":["-3","6","-10","7"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-4, 3], [5, 1]] and Q = [[5, -1], [1, 1]], find the element in the first row, first column of PQ.","o":["-17","-23","-15","5"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[-2, -3], [0, -2]] and Q = [[-1, -4], [-3, 3]], find the element in the first row, first column of PQ.","o":["2","-9","-7","11"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[4, 2], [-4, 6]] and Q = [[2, 1], [-4, 2]], find the element in the first row, first column of PQ.","o":["16","0","4","24"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[0, 3], [6, -1]] and Q = [[3, -2], [-3, -2]], find the element in the first row, first column of PQ.","o":["3","-18","9","-9"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[2, -1], [-4, 6]] and Q = [[-1, 2], [1, 4]], find the element in the first row, first column of PQ.","o":["-3","-6","1","-1"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[4, -1], [-4, 1]] and Q = [[-4, -4], [-3, 2]], find the element in the first row, first column of PQ.","o":["-13","-4","-19","-18"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[-1, 4], [-1, -2]] and Q = [[2, 3], [2, 2]], find the element in the first row, first column of PQ.","o":["-4","7","6","-10"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[4, 0], [2, 4]] and Q = [[3, -4], [-2, -4]], find the element in the first row, first column of PQ.","o":["8","5","12","-16"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-1, 5], [4, 6]] and Q = [[1, -4], [6, -3]], find the element in the first row, first column of PQ.","o":["29","23","-31","11"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[1, 0], [-1, 1]] and Q = [[-3, 2], [-2, 2]], find the element in the first row, first column of PQ.","o":["2","-1","-3","-4"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[1, 5], [-4, 6]] and Q = [[-4, 1], [-3, 5]], find the element in the first row, first column of PQ.","o":["-19","-1","8","11"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[6, -1], [2, 5]] and Q = [[0, 1], [5, 5]], find the element in the first row, first column of PQ.","o":["5","1","10","-5"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[0, 1], [-1, 6]] and Q = [[2, 1], [4, 3]], find the element in the first row, first column of PQ.","o":["-4","3","7","4"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[-1, 3], [4, -1]] and Q = [[6, 6], [-3, 3]], find the element in the first row, first column of PQ.","o":["3","5","-15","-18"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[1, -2], [-3, 6]] and Q = [[5, -3], [-2, -4]], find the element in the first row, first column of PQ.","o":["11","1","2","9"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[1, -4], [0, 6]] and Q = [[-4, 1], [-2, -2]], find the element in the first row, first column of PQ.","o":["-12","-4","4","-9"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[2, -1], [3, 6]] and Q = [[2, -3], [2, -1]], find the element in the first row, first column of PQ.","o":["6","10","2","5"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-2, -4], [0, -4]] and Q = [[6, -3], [3, -2]], find the element in the first row, first column of PQ.","o":["3","0","-12","-24"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[-3, 3], [-3, 0]] and Q = [[6, -1], [5, 6]], find the element in the first row, first column of PQ.","o":["-33","-3","21","11"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[6, -1], [-2, 6]] and Q = [[6, -1], [6, -2]], find the element in the first row, first column of PQ.","o":["42","17","30","24"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[3, 1], [-2, -2]] and Q = [[-3, 5], [-4, 6]], find the element in the first row, first column of PQ.","o":["-3","-5","-1","-13"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[6, 2], [1, -4]] and Q = [[2, -4], [3, 6]], find the element in the first row, first column of PQ.","o":["13","6","15","18"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[5, 6], [5, -3]] and Q = [[-1, 1], [5, 5]], find the element in the first row, first column of PQ.","o":["-35","25","20","15"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[-4, 1], [3, -4]] and Q = [[6, 0], [1, 1]], find the element in the first row, first column of PQ.","o":["-21","-23","4","-25"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[-2, -4], [-4, -1]] and Q = [[5, 0], [6, 3]], find the element in the first row, first column of PQ.","o":["14","-12","5","-34"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[5, -2], [-2, 3]] and Q = [[-3, 0], [-3, 1]], find the element in the first row, first column of PQ.","o":["-9","-3","-2","-21"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[1, -4], [-2, 5]] and Q = [[-4, 1], [5, 6]], find the element in the first row, first column of PQ.","o":["-2","-14","-24","16"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[5, -3], [0, 0]] and Q = [[4, 0], [6, 5]], find the element in the first row, first column of PQ.","o":["12","2","38","20"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[2, -2], [4, 4]] and Q = [[-1, 3], [6, 5]], find the element in the first row, first column of PQ.","o":["-14","5","10","22"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[3, -2], [3, 0]] and Q = [[4, -4], [-2, 3]], find the element in the first row, first column of PQ.","o":["3","8","16","6"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-2, 4], [-3, -1]] and Q = [[2, 2], [6, -3]], find the element in the first row, first column of PQ.","o":["10","-28","-22","20"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[4, 1], [4, -1]] and Q = [[0, 2], [2, 2]], find the element in the first row, first column of PQ.","o":["2","7","8","-2"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[6, -1], [6, -2]] and Q = [[3, -3], [4, -4]], find the element in the first row, first column of PQ.","o":["22","14","12","42"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[-3, 1], [5, 0]] and Q = [[-2, 0], [6, -3]], find the element in the first row, first column of PQ.","o":["36","2","12","0"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[0, -2], [4, -1]] and Q = [[4, -4], [-3, -4]], find the element in the first row, first column of PQ.","o":["6","-6","-1","-12"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[6, 4], [3, 6]] and Q = [[2, -4], [-3, 1]], find the element in the first row, first column of PQ.","o":["9","0","3","24"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[1, 6], [4, 3]] and Q = [[4, -3], [-2, 2]], find the element in the first row, first column of PQ.","o":["16","-8","-4","9"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[4, 1], [2, -1]] and Q = [[2, -3], [2, -2]], find the element in the first row, first column of PQ.","o":["6","10","9","12"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[1, 1], [6, 2]] and Q = [[0, 5], [5, 2]], find the element in the first row, first column of PQ.","o":["7","5","-5","30"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[0, -2], [2, 3]] and Q = [[5, -4], [-4, 5]], find the element in the first row, first column of PQ.","o":["-8","-1","-10","8"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[0, 2], [5, 3]] and Q = [[5, 6], [5, -1]], find the element in the first row, first column of PQ.","o":["-10","25","12","10"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[-1, 4], [1, 1]] and Q = [[-3, -2], [-2, 0]], find the element in the first row, first column of PQ.","o":["-5","1","-2","11"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[2, -1], [1, 4]] and Q = [[0, 2], [-3, -3]], find the element in the first row, first column of PQ.","o":["3","-3","-2","7"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[4, -1], [5, 1]] and Q = [[-1, -3], [-3, 6]], find the element in the first row, first column of PQ.","o":["-18","-1","-19","-7"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[4, 4], [-4, -2]] and Q = [[-2, -2], [2, 1]], find the element in the first row, first column of PQ.","o":["-4","8","0","-16"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-3, 2], [-1, 4]] and Q = [[-4, -4], [-2, -4]], find the element in the first row, first column of PQ.","o":["14","16","-7","8"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[-4, -1], [4, -2]] and Q = [[0, 3], [3, -2]], find the element in the first row, first column of PQ.","o":["-2","3","12","-3"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[5, -2], [4, 1]] and Q = [[-4, -2], [-2, 6]], find the element in the first row, first column of PQ.","o":["-28","-24","-3","-16"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[0, 5], [1, 4]] and Q = [[4, -4], [-3, 6]], find the element in the first row, first column of PQ.","o":["-3","15","6","-15"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[-4, 0], [-4, 0]] and Q = [[5, 4], [-3, 0]], find the element in the first row, first column of PQ.","o":["-16","-2","-20","-8"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[3, -4], [-2, -1]] and Q = [[1, 1], [-3, 3]], find the element in the first row, first column of PQ.","o":["-9","-3","15","9"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[2, 3], [1, 1]] and Q = [[6, 0], [4, 6]], find the element in the first row, first column of PQ.","o":["0","15","24","16"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-1, -4], [2, 4]] and Q = [[5, 2], [3, 6]], find the element in the first row, first column of PQ.","o":["3","7","1","-17"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[3, -2], [-2, -3]] and Q = [[3, 4], [1, 6]], find the element in the first row, first column of PQ.","o":["5","7","0","11"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[1, 3], [6, 5]] and Q = [[5, 1], [-4, -4]], find the element in the first row, first column of PQ.","o":["17","-19","-7","5"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[5, -3], [-4, -2]] and Q = [[1, 0], [-3, 2]], find the element in the first row, first column of PQ.","o":["14","-4","0","17"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[3, -3], [-2, 2]] and Q = [[1, 4], [-4, 6]], find the element in the first row, first column of PQ.","o":["15","-3","11","-9"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[-3, 3], [1, -3]] and Q = [[-3, 1], [-1, 2]], find the element in the first row, first column of PQ.","o":["12","6","8","-4"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[-3, 3], [-4, 3]] and Q = [[6, 6], [-3, -3]], find the element in the first row, first column of PQ.","o":["-9","-6","3","-27"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[4, 6], [-1, 0]] and Q = [[-2, 2], [-2, -1]], find the element in the first row, first column of PQ.","o":["-6","6","-20","4"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-3, -1], [2, 2]] and Q = [[5, 2], [2, -3]], find the element in the first row, first column of PQ.","o":["-13","-17","3","-11"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[5, -1], [-3, 0]] and Q = [[4, -2], [5, -3]], find the element in the first row, first column of PQ.","o":["15","25","5","13"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[-4, -4], [-1, 2]] and Q = [[-2, -4], [-2, 3]], find the element in the first row, first column of PQ.","o":["0","10","16","-12"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-4, 3], [-1, 4]] and Q = [[6, -3], [6, -4]], find the element in the first row, first column of PQ.","o":["-30","-42","-6","11"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-2, 1], [0, 5]] and Q = [[-1, 5], [-1, 0]], find the element in the first row, first column of PQ.","o":["-3","2","1","3"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[4, 0], [4, 5]] and Q = [[0, -4], [1, 2]], find the element in the first row, first column of PQ.","o":["0","5","4","-16"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[4, -1], [4, -4]] and Q = [[5, -4], [-3, 6]], find the element in the first row, first column of PQ.","o":["23","17","5","8"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[5, 6], [0, -2]] and Q = [[6, 0], [5, 4]], find the element in the first row, first column of PQ.","o":["22","30","60","0"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-1, -4], [-1, -3]] and Q = [[-4, 1], [6, -2]], find the element in the first row, first column of PQ.","o":["-20","28","-3","-2"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[5, 2], [5, 0]] and Q = [[-2, -3], [-2, -4]], find the element in the first row, first column of PQ.","o":["-14","-6","3","-20"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[1, -4], [5, -4]] and Q = [[5, 3], [2, -1]], find the element in the first row, first column of PQ.","o":["13","4","15","-3"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[4, 5], [6, 1]] and Q = [[2, -3], [3, 2]], find the element in the first row, first column of PQ.","o":["-7","14","26","23"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[2, -1], [5, 1]] and Q = [[0, -4], [4, -2]], find the element in the first row, first column of PQ.","o":["5","-4","20","4"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[6, -1], [6, -3]] and Q = [[3, -4], [5, 4]], find the element in the first row, first column of PQ.","o":["-28","13","23","48"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[2, 3], [3, 4]] and Q = [[0, 3], [3, 0]], find the element in the first row, first column of PQ.","o":["9","6","8","-9"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[2, -2], [-2, 5]] and Q = [[1, 0], [-3, -3]], find the element in the first row, first column of PQ.","o":["-4","6","-2","8"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[1, 1], [6, 5]] and Q = [[-1, 6], [2, -2]], find the element in the first row, first column of PQ.","o":["-3","3","11","1"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[0, -3], [-1, 5]] and Q = [[1, 3], [-1, 5]], find the element in the first row, first column of PQ.","o":["-3","-15","3","1"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-1, 0], [1, -1]] and Q = [[-1, 5], [1, 2]], find the element in the first row, first column of PQ.","o":["1","-5","-1","2"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[-1, 5], [-1, -4]] and Q = [[0, 0], [4, -3]], find the element in the first row, first column of PQ.","o":["-20","20","8","-4"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[-2, 6], [-3, -3]] and Q = [[-2, 4], [-3, -3]], find the element in the first row, first column of PQ.","o":["13","-1","22","-14"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[1, -3], [2, 2]] and Q = [[-3, 3], [3, 0]], find the element in the first row, first column of PQ.","o":["-2","3","-12","6"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-1, 4], [5, 5]] and Q = [[5, 2], [5, 2]], find the element in the first row, first column of PQ.","o":["20","13","-25","15"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[-4, 5], [3, -1]] and Q = [[3, -2], [-1, 3]], find the element in the first row, first column of PQ.","o":["3","-15","-17","-7"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[3, 4], [1, -1]] and Q = [[-4, -4], [2, 5]], find the element in the first row, first column of PQ.","o":["-20","-10","5","-4"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[4, -1], [-1, 4]] and Q = [[4, 5], [4, 5]], find the element in the first row, first column of PQ.","o":["11","15","12","20"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[5, -1], [5, 1]] and Q = [[5, 4], [6, 1]], find the element in the first row, first column of PQ.","o":["31","19","55","15"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[4, 0], [-1, 3]] and Q = [[-4, 6], [2, 2]], find the element in the first row, first column of PQ.","o":["24","-18","-16","2"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[1, 4], [1, 1]] and Q = [[0, 5], [-1, 6]], find the element in the first row, first column of PQ.","o":["29","4","-1","-4"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[2, -2], [-4, 5]] and Q = [[1, 4], [1, -1]], find the element in the first row, first column of PQ.","o":["-2","4","2","0"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[6, 2], [0, -4]] and Q = [[4, 1], [6, 2]], find the element in the first row, first column of PQ.","o":["18","12","36","24"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-3, -1], [4, 0]] and Q = [[2, 4], [-2, -1]], find the element in the first row, first column of PQ.","o":["-11","-14","-8","-4"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[3, 3], [-1, -1]] and Q = [[1, 4], [6, 6]], find the element in the first row, first column of PQ.","o":["13","-3","-15","21"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[3, -2], [4, 4]] and Q = [[4, 1], [-4, 1]], find the element in the first row, first column of PQ.","o":["1","20","-4","4"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[0, 6], [0, -2]] and Q = [[2, -4], [4, 1]], find the element in the first row, first column of PQ.","o":["12","24","-24","0"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[-3, 6], [2, -4]] and Q = [[-1, 5], [5, 3]], find the element in the first row, first column of PQ.","o":["33","7","13","-27"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[1, 2], [0, -1]] and Q = [[-3, 4], [5, 1]], find the element in the first row, first column of PQ.","o":["5","-3","-13","7"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[5, 0], [6, -2]] and Q = [[-1, 3], [3, 2]], find the element in the first row, first column of PQ.","o":["7","13","-5","15"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[5, -4], [-1, 4]] and Q = [[1, 5], [-3, -3]], find the element in the first row, first column of PQ.","o":["8","-7","17","-1"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[2, 2], [-2, 6]] and Q = [[4, -1], [6, 6]], find the element in the first row, first column of PQ.","o":["-4","14","20","10"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[6, 1], [-2, 0]] and Q = [[5, 3], [-3, 2]], find the element in the first row, first column of PQ.","o":["27","36","33","9"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[6, 1], [5, 6]] and Q = [[3, 0], [-4, 2]], find the element in the first row, first column of PQ.","o":["14","22","6","-2"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[3, 0], [4, -4]] and Q = [[4, 1], [1, 0]], find the element in the first row, first column of PQ.","o":["12","16","8","3"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[1, 1], [-4, 4]] and Q = [[5, 6], [5, 6]], find the element in the first row, first column of PQ.","o":["-15","0","10","12"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-2, 4], [1, 5]] and Q = [[4, 4], [-4, -1]], find the element in the first row, first column of PQ.","o":["-24","2","8","-12"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[5, -4], [-4, 5]] and Q = [[-2, -2], [-1, 0]], find the element in the first row, first column of PQ.","o":["-10","-6","-14","-2"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[-1, -1], [4, 0]] and Q = [[0, 3], [-4, 1]], find the element in the first row, first column of PQ.","o":["-16","-6","4","-4"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-3, 4], [-4, 3]] and Q = [[-3, -4], [6, -1]], find the element in the first row, first column of PQ.","o":["8","33","-15","4"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[4, 3], [6, -1]] and Q = [[1, -2], [-3, 3]], find the element in the first row, first column of PQ.","o":["5","-14","-5","13"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[-1, -4], [4, -2]] and Q = [[6, 5], [-4, 1]], find the element in the first row, first column of PQ.","o":["-3","-9","10","-22"],"a":2,"t":"Matrices","d":"Medium"},{"q":"If P = [[2, -4], [0, 5]] and Q = [[5, 6], [1, 3]], find the element in the first row, first column of PQ.","o":["6","10","14","4"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[-1, 4], [0, 4]] and Q = [[-4, -2], [-2, 0]], find the element in the first row, first column of PQ.","o":["12","-3","4","-4"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[3, -1], [-3, 6]] and Q = [[5, 2], [6, -2]], find the element in the first row, first column of PQ.","o":["13","21","-3","9"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[4, -1], [3, 3]] and Q = [[-3, -3], [-3, 0]], find the element in the first row, first column of PQ.","o":["-21","-9","-15","-3"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[-1, 4], [2, 0]] and Q = [[-3, 4], [-1, 4]], find the element in the first row, first column of PQ.","o":["7","12","1","-1"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[-2, 4], [-3, 1]] and Q = [[-4, -3], [5, 2]], find the element in the first row, first column of PQ.","o":["28","3","-12","-7"],"a":0,"t":"Matrices","d":"Medium"},{"q":"If P = [[-2, 1], [-2, 4]] and Q = [[2, -2], [-3, 5]], find the element in the first row, first column of PQ.","o":["-2","-7","2","-1"],"a":1,"t":"Matrices","d":"Medium"},{"q":"If P = [[-3, 1], [1, 4]] and Q = [[3, -1], [6, 6]], find the element in the first row, first column of PQ.","o":["9","7","-15","-3"],"a":3,"t":"Matrices","d":"Medium"},{"q":"If P = [[0, 2], [6, 1]] and Q = [[4, 0], [3, 3]], find the element in the first row, first column of PQ.","o":["-6","6","9","18"],"a":1,"t":"Matrices","d":"Medium"},{"q":"Find the scalar product of the vectors (-1, 7, 6) and (-4, 2, -1).","o":["9","12","11","15"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (3, 2, -5) and (-5, -2, 0).","o":["-17","-19","-24","-14"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-5, 6, -5) and (6, 6, 1).","o":["1","9","-2","6"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (1, 7, 6) and (-2, 4, -3).","o":["11","5","8","6"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, 7, -1) and (-1, 5, 2).","o":["18","25","29","27"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, 6, -5) and (7, 3, 2).","o":["-24","-16","-26","-20"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (5, 4, -3) and (1, -4, 6).","o":["-39","-35","-31","-29"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (2, -5, 5) and (-3, 5, -5).","o":["-66","-56","-31","-61"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (3, 6, 5) and (7, 1, 5).","o":["52","67","37","27"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-2, -5, -4) and (2, -3, 1).","o":["8","11","6","7"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (3, -1, 3) and (4, -3, 2).","o":["23","27","11","21"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (5, 3, 3) and (6, 5, 7).","o":["29","48","66","96"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, -5, -3) and (-2, 3, -3).","o":["-19","-4","-18","-15"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (7, 6, 7) and (-2, -5, 4).","o":["-16","-14","-13","-19"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (3, -5, 2) and (1, 5, 2).","o":["-22","-23","-18","-19"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (0, 3, -3) and (4, 4, -4).","o":["24","26","18","22"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, 1, 4) and (2, 5, -2).","o":["7","6","9","17"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (3, -1, -5) and (0, -2, 7).","o":["-18","2","-30","-33"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, -1, 1) and (-4, 5, 1).","o":["-26","-28","-30","-34"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (7, -2, 1) and (5, -5, -3).","o":["3","42","22","62"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (3, -1, -2) and (4, -5, -2).","o":["-3","21","19","23"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, -3, -5) and (1, 5, 5).","o":["-40","-44","-48","-19"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-2, -4, -2) and (-4, -5, 0).","o":["32","28","30","38"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (4, 3, 3) and (-2, 4, 5).","o":["19","14","24","21"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-2, 0, 0) and (-5, 1, 0).","o":["13","12","10","7"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (5, 0, -5) and (-1, -4, 1).","o":["-10","-12","-5","-4"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-2, 4, 0) and (4, -5, -5).","o":["-4","-22","-38","-28"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (2, 1, -4) and (0, 1, 0).","o":["0","-1","1","3"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (4, -3, 6) and (6, -2, 4).","o":["69","54","59","64"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, 0, 3) and (5, 3, 2).","o":["-11","-13","-14","-9"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (0, 7, 5) and (3, -5, 5).","o":["-10","-13","-5","-8"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, 7, -3) and (-4, 0, 0).","o":["6","-14","-24","-28"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, 3, 6) and (2, -4, 4).","o":["3","-1","2","4"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (4, -1, 2) and (-2, 0, 4).","o":["0","7","1","2"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (7, 6, -4) and (2, -2, -4).","o":["19","5","18","2"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (0, 4, -5) and (6, 5, 6).","o":["-10","20","-15","-12"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (2, 5, -5) and (-3, -2, 6).","o":["-16","-26","-50","-46"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-1, 0, -4) and (2, 5, 5).","o":["-24","-12","-22","-16"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-5, 7, -4) and (1, -1, -2).","o":["-12","-3","-2","-4"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-1, -1, 0) and (-5, -5, 4).","o":["5","10","8","15"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (1, 5, 1) and (7, 7, 3).","o":["45","42","57","65"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-3, -4, -1) and (-3, 2, 1).","o":["-1","2","0","5"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (2, 1, 1) and (0, 4, 2).","o":["5","11","6","7"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-2, -4, -1) and (1, 0, 6).","o":["-10","-9","-13","-8"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, 6, -2) and (0, 5, -4).","o":["38","53","41","35"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (1, 3, 2) and (-4, 7, 7).","o":["17","31","46","40"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, -3, 2) and (4, 6, 7).","o":["-16","-20","-14","-22"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-2, 6, -2) and (1, 5, 1).","o":["16","9","26","36"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (1, 7, -2) and (-3, 7, 2).","o":["30","22","42","12"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-3, -4, 7) and (6, 1, -2).","o":["-27","-45","-51","-36"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-1, 0, 3) and (-2, -1, 7).","o":["2","23","29","21"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (7, 5, 1) and (3, -3, -2).","o":["2","6","4","-1"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, -4, 2) and (1, 6, 0).","o":["11","-18","-23","-13"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (2, -4, 0) and (-5, 2, -2).","o":["-20","-17","-18","-15"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-2, 5, 2) and (-5, -3, -3).","o":["-11","-6","-9","-10"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (5, -5, -2) and (2, -3, 2).","o":["25","27","17","21"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (3, 0, -3) and (1, 2, -2).","o":["1","6","9","3"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-2, 7, -3) and (-2, -4, -4).","o":["-11","-24","-8","-12"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (5, 0, -1) and (-2, 7, 4).","o":["-14","-13","-17","-11"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, -1, 1) and (1, 5, -3).","o":["1","-3","-2","3"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, -5, 2) and (0, 3, -4).","o":["-23","-33","-17","-21"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (7, 1, -3) and (-5, 6, 5).","o":["-32","-36","-44","-64"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-2, 7, 5) and (-3, 6, 2).","o":["33","73","83","58"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (2, 6, 4) and (-5, 5, -1).","o":["16","18","20","17"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-2, 6, 1) and (4, 7, 1).","o":["29","20","32","35"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-5, -5, -2) and (6, 4, -4).","o":["-46","-38","-42","-6"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, -3, 5) and (2, -2, 3).","o":["24","42","33","48"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (1, 1, 0) and (3, 1, -5).","o":["4","7","-1","5"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (2, 4, 4) and (-4, -5, 4).","o":["-12","-7","-11","-17"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-2, -2, 0) and (5, -3, -3).","o":["-5","-4","-3","-6"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, 0, 3) and (1, 0, 3).","o":["6","-4","0","5"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, 5, 4) and (-3, -2, -2).","o":["-27","-39","-36","-21"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, 5, -3) and (5, 1, 5).","o":["-15","9","-30","-39"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, -2, 4) and (-5, 3, 6).","o":["32","14","35","38"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (7, -3, 0) and (0, 2, -5).","o":["-4","1","-8","-6"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-3, 6, -4) and (-3, -2, 1).","o":["-5","-12","-7","-4"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, -2, 6) and (3, 6, 1).","o":["14","13","17","12"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (3, 7, -2) and (0, -5, 5).","o":["-33","-35","-49","-45"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-5, 5, -1) and (4, 1, 5).","o":["-15","-24","-20","-10"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, 5, -2) and (-2, -2, 3).","o":["-8","-6","-10","-2"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (5, 2, -1) and (4, 0, 1).","o":["18","16","17","19"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (7, -3, -1) and (7, 3, 2).","o":["38","23","35","29"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-5, -5, 4) and (-2, 6, 5).","o":["0","-1","-5","1"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, -2, -1) and (4, 0, 2).","o":["-13","-18","-21","-16"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (3, 5, 3) and (2, 2, -3).","o":["10","9","12","7"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (3, -4, 7) and (5, 0, -2).","o":["1","3","-2","0"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, 3, -2) and (1, -3, 0).","o":["-8","-10","-13","-11"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-2, 0, 4) and (-4, -2, 6).","o":["35","32","47","23"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-3, -5, 3) and (-5, -2, 3).","o":["-9","34","31","19"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, 0, -3) and (7, 0, -1).","o":["9","25","65","45"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (7, 6, 6) and (-2, -4, 0).","o":["-38","-29","-41","-35"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-3, -2, 0) and (2, 0, 5).","o":["2","-3","-1","-6"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (1, 4, -4) and (0, -5, 7).","o":["-40","-48","-28","-56"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (4, 5, -2) and (1, 6, 1).","o":["34","38","32","26"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (5, 1, 1) and (3, -2, 1).","o":["14","12","13","15"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (4, -4, 3) and (7, 2, 1).","o":["29","27","20","23"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-2, -2, 2) and (3, 4, 4).","o":["-5","-6","9","-1"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, 1, 5) and (0, 7, -2).","o":["0","-3","7","-1"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, -4, 5) and (2, 5, 7).","o":["21","33","25","27"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (1, 3, -3) and (3, 0, 5).","o":["-11","-12","-10","-7"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (4, -2, 1) and (4, 7, 5).","o":["12","19","5","7"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (1, 0, -2) and (1, -4, 3).","o":["-7","-5","-6","-1"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-3, 2, -4) and (-3, 5, 2).","o":["11","9","13","19"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (3, -4, -3) and (-2, 1, -2).","o":["-5","-2","-4","-7"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-3, 5, 7) and (-1, -2, 7).","o":["42","-7","54","46"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (3, 0, -4) and (-1, 2, -4).","o":["13","14","18","15"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (3, 5, -2) and (1, 3, 0).","o":["13","21","18","17"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (7, 7, 0) and (-3, -4, -3).","o":["-41","-49","-53","-69"],"a":1,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, -3, 3) and (0, 1, 6).","o":["15","13","20","16"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, 4, -1) and (5, -5, -4).","o":["14","9","5","17"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-5, 4, 6) and (4, -3, 4).","o":["-9","-6","-3","-8"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, 2, 0) and (5, 3, -1).","o":["-9","-12","-14","5"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, 1, 5) and (6, 5, 6).","o":["19","-19","11","14"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-2, 1, 2) and (1, 7, -1).","o":["5","6","3","8"],"a":2,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (7, 2, 3) and (6, -3, 3).","o":["33","36","41","45"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-1, 4, 4) and (-5, 7, 6).","o":["47","82","42","57"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-2, 2, 0) and (4, 6, -4).","o":["2","5","6","4"],"a":3,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (6, 5, -1) and (1, 3, -1).","o":["22","12","13","26"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (-4, 5, 2) and (-5, 3, 5).","o":["45","49","41","6"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the scalar product of the vectors (0, 4, 0) and (-2, 1, -3).","o":["4","2","6","1"],"a":0,"t":"Vectors","d":"Medium"},{"q":"Find the magnitude of the vector 9i + 12j.","o":["21","108","15","16"],"a":2,"t":"Vectors","d":"Easy"},{"q":"Find the magnitude of the vector 6i + 8j.","o":["11","10","48","14"],"a":1,"t":"Vectors","d":"Easy"},{"q":"Find the magnitude of the vector 8i + 15j.","o":["120","18","23","17"],"a":3,"t":"Vectors","d":"Easy"},{"q":"Find the magnitude of the vector 5i + 12j.","o":["13","17","60","14"],"a":0,"t":"Vectors","d":"Easy"},{"q":"Find the magnitude of the vector 3i + 4j.","o":["6","7","5","12"],"a":2,"t":"Vectors","d":"Easy"},{"q":"Simplify (5 + 7i)(-6 − 3i).","o":["-51 − 57i","-9 + 27i","-9 − 57i","-1 + 4i"],"a":2,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (1 − 3i)(7 + 8i).","o":["-17 − 13i","31 − 13i","8 + 5i","31 + 29i"],"a":1,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (-6 − 6i)(-5 + 6i).","o":["66 − 66i","-11 + 0i","66 − 6i","-6 − 6i"],"a":2,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (-2 + 6i)(5 + 2i).","o":["2 + 26i","-22 − 34i","3 + 8i","-22 + 26i"],"a":3,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (4 + 3i)(-4 − 4i).","o":["-4 − 28i","-28 − 28i","-4 − 4i","0 − 1i"],"a":0,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (8 − 4i)(-3 + 6i).","o":["-48 + 60i","5 + 2i","0 + 60i","0 + 36i"],"a":2,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (3 − 3i)(5 − 1i).","o":["12 + 12i","12 − 18i","18 − 18i","8 − 4i"],"a":1,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (-3 + 5i)(2 − 2i).","o":["4 + 16i","4 − 4i","-1 + 3i","-16 + 16i"],"a":0,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (8 + 6i)(5 + 8i).","o":["-8 + 94i","-8 + 34i","88 + 94i","13 + 14i"],"a":0,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (6 − 5i)(-6 + 4i).","o":["0 − 1i","-56 + 54i","-16 + 54i","-16 − 6i"],"a":2,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (-3 + 3i)(4 + 1i).","o":["-9 + 9i","-15 + 9i","-15 − 15i","1 + 4i"],"a":1,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (1 − 4i)(6 − 3i).","o":["7 − 7i","-6 − 27i","18 − 27i","-6 + 21i"],"a":1,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (-1 − 2i)(3 − 1i).","o":["2 − 3i","-1 − 5i","-5 + 7i","-5 − 5i"],"a":3,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (3 + 2i)(6 − 3i).","o":["24 − 21i","12 + 3i","9 − 1i","24 + 3i"],"a":3,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (-3 − 6i)(-4 − 2i).","o":["-7 − 8i","0 + 30i","0 − 18i","24 + 30i"],"a":1,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (2 − 5i)(-6 − 1i).","o":["-17 − 32i","-7 + 28i","-4 − 6i","-17 + 28i"],"a":3,"t":"Complex Numbers","d":"Hard"},{"q":"Simplify (0 + 6i)(-4 + 3i).","o":["18 − 24i","-18 − 24i","-4 + 9i","-18 + 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√−1.","o":["−i","i","1","−1"],"a":1,"t":"Complex Numbers","d":"Medium"},{"q":"Evaluate i^18, where i = √−1.","o":["1","−i","i","−1"],"a":3,"t":"Complex Numbers","d":"Medium"},{"q":"Evaluate i^60, where i = √−1.","o":["−1","i","−i","1"],"a":3,"t":"Complex Numbers","d":"Medium"},{"q":"Evaluate i^55, where i = √−1.","o":["−1","−i","1","i"],"a":1,"t":"Complex Numbers","d":"Medium"},{"q":"Evaluate i^4, where i = √−1.","o":["−i","1","i","−1"],"a":1,"t":"Complex Numbers","d":"Medium"},{"q":"Evaluate i^22, where i = √−1.","o":["1","−1","−i","i"],"a":1,"t":"Complex Numbers","d":"Medium"},{"q":"Evaluate i^33, where i = √−1.","o":["i","−i","−1","1"],"a":0,"t":"Complex Numbers","d":"Medium"},{"q":"Evaluate i^30, where i = √−1.","o":["−i","i","−1","1"],"a":2,"t":"Complex Numbers","d":"Medium"},{"q":"Evaluate i^7, where i = √−1.","o":["−i","i","−1","1"],"a":0,"t":"Complex Numbers","d":"Medium"},{"q":"Evaluate i^31, where i = √−1.","o":["1","i","−i","−1"],"a":2,"t":"Complex Numbers","d":"Medium"},{"q":"Evaluate i^23, where i = √−1.","o":["1","i","−i","−1"],"a":2,"t":"Complex Numbers","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 8 and r = 3 (the number of permutations of 8 things taken 3 at a time).","o":["56","344","512","336"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 9 and r = 4 (the number of permutations of 9 things taken 4 at a time).","o":["126","3033","3024","6561"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 12 and r = 3 (the number of permutations of 12 things taken 3 at a time).","o":["1320","220","1332","1728"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 12 and r = 2 (the number of permutations of 12 things taken 2 at a time).","o":["1320","144","132","66"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 5 and r = 2 (the number of permutations of 5 things taken 2 at a time).","o":["60","10","25","20"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 11 and r = 4 (the number of permutations of 11 things taken 4 at a time).","o":["7931","7920","330","14641"],"a":1,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 9 and r = 3 (the number of permutations of 9 things taken 3 at a time).","o":["729","513","84","504"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 10 and r = 4 (the number of permutations of 10 things taken 4 at a time).","o":["210","5050","10000","5040"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 11 and r = 2 (the number of permutations of 11 things taken 2 at a time).","o":["55","990","110","121"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 7 and r = 4 (the number of permutations of 7 things taken 4 at a time).","o":["2401","840","35","847"],"a":1,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 8 and r = 2 (the number of permutations of 8 things taken 2 at a time).","o":["336","28","56","64"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 8 and r = 4 (the number of permutations of 8 things taken 4 at a time).","o":["1680","70","1688","4096"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 6 and r = 4 (the number of permutations of 6 things taken 4 at a time).","o":["1296","366","360","15"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 6 and r = 3 (the number of permutations of 6 things taken 3 at a time).","o":["126","120","216","20"],"a":1,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 5 and r = 4 (the number of permutations of 5 things taken 4 at a time).","o":["120","125","625","5"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 7 and r = 2 (the number of permutations of 7 things taken 2 at a time).","o":["42","21","49","210"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 5 and r = 3 (the number of permutations of 5 things taken 3 at a time).","o":["125","65","10","60"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 10 and r = 3 (the number of permutations of 10 things taken 3 at a time).","o":["720","1000","120","730"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 10 and r = 2 (the number of permutations of 10 things taken 2 at a time).","o":["720","90","45","100"],"a":1,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 9 and r = 2 (the number of permutations of 9 things taken 2 at a time).","o":["504","81","72","36"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 7 and r = 3 (the number of permutations of 7 things taken 3 at a time).","o":["35","217","343","210"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 6 and r = 2 (the number of permutations of 6 things taken 2 at a time).","o":["36","15","30","120"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 11 and r = 3 (the number of permutations of 11 things taken 3 at a time).","o":["1001","990","1331","165"],"a":1,"t":"Permutation and Combination","d":"Medium"},{"q":"Evaluate ⁿPᵣ with n = 12 and r = 4 (the number of permutations of 12 things taken 4 at a time).","o":["11880","20736","495","11892"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 3 students be chosen from 5 students?","o":["10","5","15","60"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 4 students be chosen from 7 students?","o":["840","28","42","35"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 2 students be chosen from 8 students?","o":["36","16","56","28"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 3 students be chosen from 10 students?","o":["720","130","120","30"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 2 students be chosen from 13 students?","o":["91","156","26","78"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 2 students be chosen from 14 students?","o":["182","28","105","91"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 3 students be chosen from 14 students?","o":["42","378","2184","364"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 3 students be chosen from 6 students?","o":["20","26","120","18"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 4 students be chosen from 13 students?","o":["52","17160","715","728"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 4 students be chosen from 9 students?","o":["36","3024","135","126"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 3 students be chosen from 8 students?","o":["336","24","64","56"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 2 students be chosen from 10 students?","o":["20","55","90","45"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 3 students be chosen from 12 students?","o":["36","220","232","1320"],"a":1,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 3 students be chosen from 9 students?","o":["93","504","27","84"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 2 students be chosen from 11 students?","o":["55","22","66","110"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 3 students be chosen from 13 students?","o":["1716","299","286","39"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 4 students be chosen from 8 students?","o":["1680","32","70","78"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 4 students be chosen from 14 students?","o":["24024","1001","1015","56"],"a":1,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 3 students be chosen from 7 students?","o":["210","21","42","35"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 4 students be chosen from 10 students?","o":["40","5040","210","220"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 2 students be chosen from 6 students?","o":["15","12","21","30"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 2 students be chosen from 9 students?","o":["36","45","18","72"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 4 students be chosen from 6 students?","o":["15","360","24","21"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 4 students be chosen from 11 students?","o":["44","330","341","7920"],"a":1,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 2 students be chosen from 7 students?","o":["42","28","21","14"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 4 students be chosen from 12 students?","o":["495","507","11880","48"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 4 students be chosen from 5 students?","o":["10","120","20","5"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 3 students be chosen from 11 students?","o":["176","33","165","990"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can 2 students be chosen from 12 students?","o":["66","24","132","78"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can the letters of the word SCHOOL be arranged?","o":["360","180","720","5040"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can the letters of the word ABUJA be arranged?","o":["60","240","720","120"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can the letters of the word BOOK be arranged?","o":["24","6","12","120"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can the letters of the word LAGOS be arranged?","o":["120","720","240","60"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can the letters of the word LEVEL be arranged?","o":["60","30","15","720"],"a":1,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can the letters of the word PLANET be arranged?","o":["1440","360","5040","720"],"a":3,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can the letters of the word FRIEND be arranged?","o":["360","720","5040","1440"],"a":1,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can the letters of the word NIGERIA be arranged?","o":["10080","2520","5040","40320"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can the letters of the word STONE be arranged?","o":["120","60","240","720"],"a":0,"t":"Permutation and Combination","d":"Medium"},{"q":"In how many ways can the letters of the word MATHS be arranged?","o":["720","60","120","240"],"a":2,"t":"Permutation and Combination","d":"Medium"},{"q":"What is the coefficient of x^3 in the expansion of (1 + x)^6?","o":["120","20","30","26"],"a":1,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^4 in the expansion of (1 + x)^7?","o":["56","35","42","840"],"a":1,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^5 in the expansion of (1 + x)^7?","o":["28","2520","21","42"],"a":2,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^2 in the expansion of (1 + x)^4?","o":["10","12","6","8"],"a":2,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^4 in the expansion of (1 + x)^9?","o":["210","3024","126","135"],"a":2,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^5 in the expansion of (1 + x)^8?","o":["98","6720","56","64"],"a":2,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^3 in the expansion of (1 + x)^7?","o":["42","56","35","210"],"a":2,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^2 in the expansion of (1 + x)^6?","o":["30","15","21","26"],"a":1,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^3 in the expansion of (1 + x)^8?","o":["98","56","336","64"],"a":1,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^3 in the expansion of (1 + x)^9?","o":["162","84","93","504"],"a":1,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^2 in the expansion of (1 + x)^7?","o":["28","21","42","14"],"a":1,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^7 in the expansion of (1 + x)^9?","o":["36","45","93","181440"],"a":0,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^6 in the expansion of (1 + x)^8?","o":["64","36","20160","28"],"a":3,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^6 in the expansion of (1 + x)^9?","o":["60480","93","162","84"],"a":3,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^5 in the expansion of (1 + x)^9?","o":["126","135","210","15120"],"a":0,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^2 in the expansion of (1 + x)^8?","o":["64","56","36","28"],"a":3,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^4 in the expansion of (1 + x)^8?","o":["70","1680","78","112"],"a":0,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^2 in the expansion of (1 + x)^9?","o":["93","72","36","45"],"a":2,"t":"Binomial Theorem","d":"Medium"},{"q":"What is the coefficient of x^4 in the expansion of (1 + x)^6?","o":["360","21","26","15"],"a":3,"t":"Binomial Theorem","d":"Medium"},{"q":"Find the sum of the first 3 terms of the GP with first term 1 and common ratio 3.","o":["27","12","13","14"],"a":2,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 7 terms of the GP with first term 1 and common ratio 2.","o":["43","127","128","126"],"a":1,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 6 terms of the GP with first term 2 and common ratio 3.","o":["727","730","728","1458"],"a":2,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 4 terms of the GP with first term 3 and common ratio 2.","o":["44","51","45","48"],"a":2,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 3 terms of the GP with first term 4 and common ratio 2.","o":["32","12","28","27"],"a":2,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 7 terms of the GP with first term 4 and common ratio 3.","o":["4371","4372","8748","4376"],"a":1,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 6 terms of the GP with first term 1 and common ratio 3.","o":["729","365","364","363"],"a":2,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 5 terms of the GP with first term 2 and common ratio 3.","o":["241","244","486","242"],"a":3,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 3 terms of the GP with first term 4 and common ratio 3.","o":["108","52","51","56"],"a":1,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 5 terms of the GP with first term 3 and common ratio 3.","o":["362","366","729","363"],"a":3,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 6 terms of the GP with first term 1 and common ratio 2.","o":["63","65","64","62"],"a":0,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 5 terms of the GP with first term 4 and common ratio 3.","o":["488","972","483","484"],"a":3,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 6 terms of the GP with first term 4 and common ratio 2.","o":["252","251","256","260"],"a":0,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 5 terms of the GP with first term 3 and common ratio 2.","o":["93","96","92","33"],"a":0,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 6 terms of the GP with first term 4 and common ratio 3.","o":["1456","1460","1455","2916"],"a":0,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 3 terms of the GP with first term 2 and common ratio 2.","o":["16","14","6","13"],"a":1,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 4 terms of the GP with first term 3 and common ratio 3.","o":["123","119","120","243"],"a":2,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 6 terms of the GP with first term 3 and common ratio 2.","o":["189","192","195","188"],"a":0,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 4 terms of the GP with first term 2 and common ratio 2.","o":["34","29","32","30"],"a":3,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 7 terms of the GP with first term 3 and common ratio 2.","o":["380","129","381","384"],"a":2,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 7 terms of the GP with first term 4 and common ratio 2.","o":["507","508","512","172"],"a":1,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 7 terms of the GP with first term 3 and common ratio 3.","o":["3278","3282","6561","3279"],"a":3,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 4 terms of the GP with first term 4 and common ratio 3.","o":["324","160","159","164"],"a":1,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 3 terms of the GP with first term 3 and common ratio 3.","o":["42","38","39","81"],"a":2,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 4 terms of the GP with first term 2 and common ratio 3.","o":["79","82","80","162"],"a":2,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 5 terms of the GP with first term 2 and common ratio 2.","o":["61","62","22","64"],"a":1,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 4 terms of the GP with first term 1 and common ratio 2.","o":["17","14","16","15"],"a":3,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 5 terms of the GP with first term 1 and common ratio 3.","o":["121","243","120","122"],"a":0,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 4 terms of the GP with first term 1 and common ratio 3.","o":["81","40","39","41"],"a":1,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 3 terms of the GP with first term 2 and common ratio 3.","o":["26","25","54","28"],"a":0,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 4 terms of the GP with first term 4 and common ratio 2.","o":["60","59","64","68"],"a":0,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 3 terms of the GP with first term 1 and common ratio 2.","o":["7","6","8","3"],"a":0,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 7 terms of the GP with first term 2 and common ratio 3.","o":["2186","2185","2188","4374"],"a":0,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 6 terms of the GP with first term 3 and common ratio 3.","o":["1095","2187","1092","1091"],"a":2,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 3 terms of the GP with first term 3 and common ratio 2.","o":["20","24","21","9"],"a":2,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 5 terms of the GP with first term 1 and common ratio 2.","o":["11","32","31","30"],"a":2,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 7 terms of the GP with first term 1 and common ratio 3.","o":["2187","1094","1092","1093"],"a":3,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 5 terms of the GP with first term 4 and common ratio 2.","o":["124","44","128","123"],"a":0,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 6 terms of the GP with first term 2 and common ratio 2.","o":["128","125","130","126"],"a":3,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum of the first 7 terms of the GP with first term 2 and common ratio 2.","o":["254","253","86","256"],"a":0,"t":"Sequence and Series","d":"Medium"},{"q":"Find the sum to infinity of the GP with first term 18 and common ratio 1/2.","o":["18","54","27","36"],"a":3,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 10 and common ratio 1/5.","o":["50","5/2","25/2","12"],"a":2,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 80 and common ratio 1/5.","o":["96","400","100","20"],"a":2,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 105 and common ratio 1/5.","o":["525","105/4","126","525/4"],"a":3,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 135 and common ratio 1/5.","o":["135/4","162","675","675/4"],"a":3,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 4 and common ratio 1/4.","o":["16","4/3","5","16/3"],"a":3,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 5 and common ratio 1/5.","o":["6","25","5/4","25/4"],"a":3,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 45 and common ratio 1/3.","o":["45/2","60","135/2","135"],"a":2,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 36 and common ratio 1/3.","o":["48","54","108","18"],"a":1,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 6 and common ratio 1/3.","o":["9","3","8","18"],"a":0,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 4 and common ratio 1/2.","o":["8","6","12","4"],"a":0,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 15 and common ratio 1/3.","o":["45/2","15/2","20","45"],"a":0,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 14 and common ratio 1/2.","o":["14","21","42","28"],"a":3,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 45 and common ratio 1/5.","o":["45/4","54","225/4","225"],"a":2,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 24 and common ratio 1/2.","o":["72","48","24","36"],"a":1,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 12 and common ratio 1/4.","o":["15","4","48","16"],"a":3,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 9 and common ratio 1/3.","o":["12","27","27/2","9/2"],"a":2,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 36 and common ratio 1/2.","o":["36","108","72","54"],"a":2,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 30 and common ratio 1/5.","o":["15/2","75/2","36","150"],"a":1,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 35 and common ratio 1/5.","o":["35/4","42","175/4","175"],"a":2,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 40 and common ratio 1/5.","o":["10","48","200","50"],"a":3,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 20 and common ratio 1/2.","o":["60","20","40","30"],"a":2,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 8 and common ratio 1/2.","o":["8","12","24","16"],"a":3,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 32 and common ratio 1/4.","o":["128/3","128","40","32/3"],"a":0,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 60 and common ratio 1/4.","o":["80","20","75","240"],"a":0,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 64 and common ratio 1/4.","o":["256/3","80","256","64/3"],"a":0,"t":"Sequence and 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with first term 24 and common ratio 1/3.","o":["12","36","32","72"],"a":1,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 50 and common ratio 1/5.","o":["125/2","25/2","60","250"],"a":0,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 96 and common ratio 1/4.","o":["32","128","384","120"],"a":1,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 42 and common ratio 1/3.","o":["56","21","63","126"],"a":2,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 48 and common ratio 1/2.","o":["48","144","72","96"],"a":3,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 21 and common ratio 1/3.","o":["21/2","63","63/2","28"],"a":2,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 32 and common ratio 1/2.","o":["64","32","48","96"],"a":0,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 84 and common ratio 1/4.","o":["112","28","105","336"],"a":0,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 72 and common ratio 1/3.","o":["216","96","108","36"],"a":2,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 36 and common ratio 1/4.","o":["12","45","144","48"],"a":3,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 90 and common ratio 1/5.","o":["225/2","108","45/2","450"],"a":0,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 20 and common ratio 1/4.","o":["80","80/3","25","20/3"],"a":1,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 75 and common ratio 1/5.","o":["375","375/4","75/4","90"],"a":1,"t":"Sequence and 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term 12 and common ratio 1/2.","o":["12","36","18","24"],"a":3,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 56 and common ratio 1/4.","o":["224/3","56/3","224","70"],"a":0,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 24 and common ratio 1/4.","o":["32","96","8","30"],"a":0,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 54 and common ratio 1/3.","o":["81","27","72","162"],"a":0,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 6 and common ratio 1/2.","o":["12","6","18","9"],"a":0,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 8 and common ratio 1/4.","o":["10","32/3","32","8/3"],"a":1,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 81 and common ratio 1/3.","o":["81/2","243/2","243","108"],"a":1,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 30 and common ratio 1/3.","o":["15","45","40","90"],"a":1,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 18 and common ratio 1/3.","o":["9","54","27","24"],"a":2,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 16 and common ratio 1/4.","o":["16/3","20","64/3","64"],"a":2,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 28 and common ratio 1/2.","o":["42","84","56","28"],"a":2,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 48 and common ratio 1/3.","o":["24","64","144","72"],"a":3,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 63 and common ratio 1/3.","o":["189/2","63/2","84","189"],"a":0,"t":"Sequence and 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term 10 and common ratio 1/2.","o":["10","20","30","15"],"a":1,"t":"Sequence and Series","d":"Hard"},{"q":"Find the sum to infinity of the GP with first term 108 and common ratio 1/4.","o":["36","135","144","432"],"a":2,"t":"Sequence and Series","d":"Hard"},{"q":"The quadratic equation 3x^2 + 2x − 4 = 0 has:","o":["two imaginary roots","equal real roots","no real roots","two distinct real roots"],"a":3,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 2x^2 + 9x + 3 = 0 has:","o":["no real roots","two distinct real roots","equal real roots","two imaginary roots"],"a":1,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 2x^2 − 2x + 3 = 0 has:","o":["two imaginary roots","two distinct real roots","no real roots","equal real roots"],"a":2,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation x^2 − 4x − 5 = 0 has:","o":["two distinct real roots","two imaginary roots","no real roots","equal real roots"],"a":0,"t":"Quadratic 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roots","two distinct real roots"],"a":2,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation x^2 − 4x + 2 = 0 has:","o":["two imaginary roots","equal real roots","two distinct real roots","no real roots"],"a":2,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 4x^2 − 2x − 3 = 0 has:","o":["no real roots","two distinct real roots","two imaginary roots","equal real roots"],"a":1,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 4x^2 + 9x + 6 = 0 has:","o":["two distinct real roots","two imaginary roots","equal real roots","no real roots"],"a":3,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 5x^2 + 5x + 3 = 0 has:","o":["no real roots","two distinct real roots","two imaginary roots","equal real roots"],"a":0,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 5x^2 + 4x + 2 = 0 has:","o":["two distinct real roots","no real roots","equal real roots","two imaginary roots"],"a":1,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 3x^2 − 7x + 5 = 0 has:","o":["equal real roots","two imaginary roots","no real roots","two distinct real roots"],"a":2,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 5x^2 + 4x − 3 = 0 has:","o":["two distinct real roots","two imaginary roots","equal real roots","no real roots"],"a":0,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation x^2 + x − 2 = 0 has:","o":["two imaginary roots","no real roots","two distinct real roots","equal real roots"],"a":2,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 2x^2 − 9x + 5 = 0 has:","o":["equal real roots","two imaginary roots","no real roots","two distinct real roots"],"a":3,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 4x^2 + 3x = 0 has:","o":["two imaginary roots","two distinct real roots","no real roots","equal real roots"],"a":1,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 4x^2 − 8x + 1 = 0 has:","o":["equal real roots","two imaginary roots","no real roots","two distinct real roots"],"a":3,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 5x^2 − 6x = 0 has:","o":["no real roots","two distinct real roots","equal real roots","two imaginary roots"],"a":1,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation x^2 + 2x + 4 = 0 has:","o":["no real roots","two distinct real roots","two imaginary roots","equal real roots"],"a":0,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 2x^2 + 5x − 1 = 0 has:","o":["two distinct real roots","two imaginary roots","equal real roots","no real roots"],"a":0,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 4x^2 + 9x + 3 = 0 has:","o":["two imaginary roots","equal real roots","two distinct real roots","no real roots"],"a":2,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 2x^2 + 3x − 1 = 0 has:","o":["two distinct real roots","equal real roots","two imaginary roots","no real roots"],"a":0,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 5x^2 − 4x + 1 = 0 has:","o":["two distinct real roots","no real roots","equal real roots","two imaginary roots"],"a":1,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 3x^2 − x − 3 = 0 has:","o":["no real roots","two imaginary roots","equal real roots","two distinct real roots"],"a":3,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 3x^2 + 6x + 6 = 0 has:","o":["two imaginary roots","two distinct real roots","equal real roots","no real roots"],"a":3,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 2x^2 + 8x = 0 has:","o":["two distinct real roots","equal real roots","two imaginary roots","no real roots"],"a":0,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 2x^2 − x + 2 = 0 has:","o":["equal real roots","no real roots","two imaginary roots","two distinct real roots"],"a":1,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 3x^2 + 4x − 4 = 0 has:","o":["no real roots","two imaginary roots","two distinct real roots","equal real roots"],"a":2,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 4x^2 − 2x − 5 = 0 has:","o":["equal real roots","no real roots","two imaginary roots","two distinct real roots"],"a":3,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 3x^2 − 8x + 4 = 0 has:","o":["no real roots","two imaginary roots","two distinct real roots","equal real roots"],"a":2,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 4x^2 + 8x + 6 = 0 has:","o":["no real roots","two distinct real roots","two imaginary roots","equal real roots"],"a":0,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 3x^2 + 6x = 0 has:","o":["no real roots","equal real roots","two imaginary roots","two distinct real roots"],"a":3,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 3x^2 + 9x − 1 = 0 has:","o":["equal real roots","two imaginary roots","two distinct real roots","no real roots"],"a":2,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 5x^2 + x + 4 = 0 has:","o":["equal real roots","two distinct real roots","no real roots","two imaginary roots"],"a":2,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 3x^2 + 6x + 3 = 0 has:","o":["no real roots","equal real roots","two imaginary roots","two distinct real roots"],"a":1,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 2x^2 + 5x − 2 = 0 has:","o":["two distinct real roots","two imaginary roots","equal real roots","no real roots"],"a":0,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation x^2 + 5x + 5 = 0 has:","o":["no real roots","two imaginary roots","two distinct real roots","equal real roots"],"a":2,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 5x^2 − 8x + 2 = 0 has:","o":["two imaginary roots","two distinct real roots","no real roots","equal real roots"],"a":1,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 2x^2 − 3 = 0 has:","o":["two distinct real roots","two imaginary roots","equal real roots","no real roots"],"a":0,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation x^2 + 5x − 4 = 0 has:","o":["no real roots","two distinct real roots","two imaginary roots","equal real roots"],"a":1,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 3x^2 − 3x + 1 = 0 has:","o":["no real roots","two imaginary roots","two distinct real roots","equal real roots"],"a":0,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 3x^2 + 8x − 2 = 0 has:","o":["no real roots","two imaginary roots","two distinct real roots","equal real roots"],"a":2,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 2x^2 − 8x + 4 = 0 has:","o":["equal real roots","two distinct real roots","two imaginary roots","no real roots"],"a":1,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation x^2 − 2x + 4 = 0 has:","o":["two imaginary roots","equal real roots","no real roots","two distinct real roots"],"a":2,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 4x^2 − 9x − 2 = 0 has:","o":["two distinct real roots","equal real roots","two imaginary roots","no real roots"],"a":0,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 5x^2 + x + 5 = 0 has:","o":["equal real roots","no real roots","two distinct real roots","two imaginary roots"],"a":1,"t":"Quadratic Equations","d":"Medium"},{"q":"The quadratic equation 3x^2 + 3 = 0 has:","o":["no real roots","two imaginary roots","equal real roots","two distinct real roots"],"a":0,"t":"Quadratic Equations","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 648 in terms of x and y.","o":["3x − 4y","12(x + y)","4x + 3y","3x + 4y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 186624 in terms of x and y.","o":["48(x + y)","6x + 8y","8x − 6y","8x + 6y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 1296 in terms of x and y.","o":["(4+4)(x + y)","4x − 4y","4x + 4y","16(x + y)"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 324 in terms of x and y.","o":["4x + 2y","2x − 4y","2x + 4y","8(x + y)"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 1152 in terms of x and y.","o":["2x + 7y","7x − 2y","7x + 2y","14(x + y)"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 17496 in terms of x and y.","o":["21(x + y)","3x + 7y","7x + 3y","3x − 7y"],"a":1,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 5184 in terms of x and y.","o":["6x − 4y","24(x + y)","4x + 6y","6x + 4y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 629856 in terms of x and y.","o":["5x + 9y","45(x + y)","5x − 9y","9x + 5y"],"a":0,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 23328 in terms of x and y.","o":["5x − 6y","6x + 5y","5x + 6y","30(x + y)"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 2916 in terms of x and y.","o":["12(x + y)","6x + 2y","2x − 6y","2x + 6y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 78732 in terms of x and y.","o":["2x − 9y","18(x + y)","9x + 2y","2x + 9y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 972 in terms of x and y.","o":["5x + 2y","10(x + y)","2x − 5y","2x + 5y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 5832 in terms of x and y.","o":["18(x + y)","3x + 6y","6x + 3y","3x − 6y"],"a":1,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 10077696 in terms of x and y.","o":["81(x + y)","9x + 9y","(9+9)(x + y)","9x − 9y"],"a":1,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 1259712 in terms of x and y.","o":["9x + 6y","6x + 9y","54(x + y)","6x − 9y"],"a":1,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 2592 in terms of x and y.","o":["5x − 4y","4x + 5y","20(x + y)","5x + 4y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 124416 in terms of x and y.","o":["45(x + y)","9x + 5y","5x + 9y","9x − 5y"],"a":1,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 93312 in terms of x and y.","o":["7x − 6y","42(x + y)","7x + 6y","6x + 7y"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 157464 in terms of x and y.","o":["9x + 3y","27(x + y)","3x − 9y","3x + 9y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 69984 in terms of x and y.","o":["5x + 7y","5x − 7y","35(x + y)","7x + 5y"],"a":0,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 139968 in terms of x and y.","o":["42(x + y)","6x + 7y","7x + 6y","6x − 7y"],"a":1,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 11664 in terms of x and y.","o":["4x − 6y","4x + 6y","6x + 4y","24(x + y)"],"a":1,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 6912 in terms of x and y.","o":["8x − 3y","3x + 8y","8x + 3y","24(x + y)"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 3456 in terms of x and y.","o":["3x + 7y","7x + 3y","7x − 3y","21(x + y)"],"a":1,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 2304 in terms of x and y.","o":["2x + 8y","8x − 2y","8x + 2y","16(x + y)"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 419904 in terms of x and y.","o":["8x + 6y","6x + 8y","48(x + y)","6x − 8y"],"a":1,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 1679616 in terms of x and y.","o":["(8+8)(x + y)","64(x + y)","8x − 8y","8x + 8y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 216 in terms of x and y.","o":["9(x + y)","3x − 3y","3x + 3y","(3+3)(x + y)"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 52488 in terms of x and y.","o":["24(x + y)","3x + 8y","8x + 3y","3x − 8y"],"a":1,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 209952 in terms of x and y.","o":["5x − 8y","40(x + y)","8x + 5y","5x + 8y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 46656 in terms of x and y.","o":["(6+6)(x + y)","6x − 6y","6x + 6y","36(x + y)"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 279936 in terms of x and y.","o":["(7+7)(x + y)","49(x + y)","7x − 7y","7x + 7y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 26244 in terms of x and y.","o":["2x + 8y","2x − 8y","16(x + y)","8x + 2y"],"a":0,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 144 in terms of x and y.","o":["2x + 4y","4x + 2y","4x − 2y","8(x + y)"],"a":1,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 4608 in terms of x and y.","o":["2x + 9y","18(x + y)","9x + 2y","9x − 2y"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 62208 in terms of x and y.","o":["40(x + y)","5x + 8y","8x − 5y","8x + 5y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 1728 in terms of x and y.","o":["18(x + y)","6x + 3y","3x + 6y","6x − 3y"],"a":1,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 559872 in terms of x and y.","o":["7x + 8y","56(x + y)","8x − 7y","8x + 7y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 3359232 in terms of x and y.","o":["72(x + y)","9x − 8y","8x + 9y","9x + 8y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 8748 in terms of x and y.","o":["2x + 7y","2x − 7y","7x + 2y","14(x + y)"],"a":0,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 2519424 in terms of x and y.","o":["7x − 9y","9x + 7y","7x + 9y","63(x + y)"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 5038848 in terms of x and y.","o":["9x + 8y","72(x + y)","8x + 9y","8x − 9y"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 104976 in terms of x and y.","o":["8x + 4y","32(x + y)","4x − 8y","4x + 8y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 576 in terms of x and y.","o":["2x + 6y","6x − 2y","12(x + y)","6x + 2y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 20736 in terms of x and y.","o":["8x + 4y","32(x + y)","8x − 4y","4x + 8y"],"a":0,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 432 in terms of x and y.","o":["12(x + y)","3x + 4y","4x − 3y","4x + 3y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 839808 in terms of x and y.","o":["7x + 8y","56(x + y)","8x + 7y","7x − 8y"],"a":0,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 288 in terms of x and y.","o":["2x + 5y","5x − 2y","10(x + y)","5x + 2y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 108 in terms of x and y.","o":["2x − 3y","6(x + y)","2x + 3y","3x + 2y"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 31104 in terms of x and y.","o":["7x + 5y","35(x + y)","7x − 5y","5x + 7y"],"a":0,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 72 in terms of x and y.","o":["3x − 2y","3x + 2y","2x + 3y","6(x + y)"],"a":1,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 15552 in terms of x and y.","o":["6x − 5y","6x + 5y","5x + 6y","30(x + y)"],"a":1,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 36 in terms of x and y.","o":["2x − 2y","4(x + y)","2x + 2y","(2+2)(x + y)"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 864 in terms of x and y.","o":["5x + 3y","3x + 5y","5x − 3y","15(x + y)"],"a":0,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 41472 in terms of x and y.","o":["9x + 4y","4x + 9y","36(x + y)","9x − 4y"],"a":0,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 373248 in terms of x and y.","o":["9x + 6y","54(x + y)","6x + 9y","9x − 6y"],"a":0,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 1119744 in terms of x and y.","o":["9x + 7y","7x + 9y","9x − 7y","63(x + y)"],"a":0,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 13824 in terms of x and y.","o":["9x − 3y","9x + 3y","3x + 9y","27(x + y)"],"a":1,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 314928 in terms of x and y.","o":["4x + 9y","9x + 4y","36(x + y)","4x − 9y"],"a":0,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 3888 in terms of x and y.","o":["4x + 5y","4x − 5y","20(x + y)","5x + 4y"],"a":0,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 7776 in terms of x and y.","o":["25(x + y)","(5+5)(x + y)","5x + 5y","5x − 5y"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 1944 in terms of x and y.","o":["3x + 5y","5x + 3y","3x − 5y","15(x + y)"],"a":0,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 34992 in terms of x and y.","o":["28(x + y)","4x − 7y","7x + 4y","4x + 7y"],"a":3,"t":"Logarithms","d":"Medium"},{"q":"If log 2 = x and log 3 = y, express log 10368 in terms of x and y.","o":["28(x + y)","7x − 4y","7x + 4y","4x + 7y"],"a":2,"t":"Logarithms","d":"Medium"},{"q":"Find the equation of the line through (-3, -7) with gradient 2.","o":["y = 2x − 1","y = 2x + 1","y = -2x − 1","y = 2x − 7"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 26) with gradient 6.","o":["y = -6x + 2","y = 6x + 26","y = 6x + 2","y = 6x − 2"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-2, -8) with gradient 3.","o":["y = 3x + 2","y = 3x − 8","y = 3x − 2","y = -3x − 2"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (3, 16) with gradient 6.","o":["y = 6x − 2","y = -6x − 2","y = 6x + 16","y = 6x + 2"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, -23) with gradient 6.","o":["y = -6x − 5","y = 6x − 5","y = 6x + 5","y = 6x − 23"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-1, -6) with gradient 5.","o":["y = 5x − 6","y = -5x − 1","y = 5x + 1","y = 5x − 1"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 20) with gradient 5.","o":["y = 5x","y = -5x","y = 5x + 20","y = 5x + 1"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (2, 14) with gradient 5.","o":["y = 5x + 14","y = -5x + 4","y = 5x − 4","y = 5x + 4"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (3, 10) with gradient 3.","o":["y = 3x + 10","y = 3x − 1","y = -3x + 1","y = 3x + 1"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (1, -4) with gradient 4.","o":["y = 4x − 4","y = 4x − 8","y = -4x − 8","y = 4x + 8"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (2, 7) with gradient 5.","o":["y = -5x − 3","y = 5x − 3","y = 5x + 3","y = 5x + 7"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, -4) with gradient 2.","o":["y = 2x − 4","y = x − 2","y = -2x − 4","y = 2x + 4"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (1, -1) with gradient 1.","o":["y = 1x + 2","y = -1x − 2","y = 1x − 1","y = 1x − 2"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (3, 23) with gradient 5.","o":["y = 5x + 8","y = -5x + 8","y = 5x − 8","y = 5x + 23"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, -14) with gradient 3.","o":["y = 3x − 14","y = 3x − 5","y = -3x − 5","y = 3x + 5"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-2, 6) with gradient 1.","o":["y = 1x − 8","y = 1x + 6","y = 1x + 8","y = -1x + 8"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-1, -2) with gradient 3.","o":["y = 3x + 1","y = -3x + 1","y = 3x − 1","y = 3x − 2"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, 5) with gradient 2.","o":["y = 2x − 5","y = 2x + 5","y = x + 7","y = -2x + 5"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (2, 15) with gradient 4.","o":["y = 4x + 7","y = 4x − 7","y = -4x + 7","y = 4x + 15"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 23) with gradient 4.","o":["y = -4x + 7","y = 4x − 7","y = 4x + 7","y = 4x + 23"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 6) with gradient 2.","o":["y = 2x + 2","y = -2x − 2","y = 2x − 2","y = 2x + 6"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, -14) with gradient 2.","o":["y = 2x + 8","y = 2x − 14","y = -2x − 8","y = 2x − 8"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-1, 2) with gradient 4.","o":["y = 4x + 2","y = -4x + 6","y = 4x − 6","y = 4x + 6"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, -7) with gradient 4.","o":["y = x − 3","y = -4x − 7","y = 4x + 7","y = 4x − 7"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (1, 0) with gradient 3.","o":["y = 3x + 3","y = -3x − 3","y = 3x − 3","y = 3x + 0"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-2, -6) with gradient 5.","o":["y = 5x − 6","y = -5x + 4","y = 5x − 4","y = 5x + 4"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (1, 11) with gradient 5.","o":["y = 5x + 11","y = 5x − 6","y = 5x + 6","y = -5x + 6"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, -10) with gradient 3.","o":["y = 3x + 1","y = -3x − 1","y = 3x − 1","y = 3x − 10"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, -6) with gradient 2.","o":["y = 2x − 6","y = 2x + 6","y = -2x − 6","y = x − 4"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (3, 5) with gradient 3.","o":["y = -3x − 4","y = 3x + 4","y = 3x − 4","y = 3x + 5"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (3, 3) with gradient 1.","o":["y = 1x + 3","y = 1x + 1","y = -1x","y = 1x"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-1, -3) with gradient 2.","o":["y = 2x + 1","y = -2x − 1","y = 2x − 1","y = 2x − 3"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (1, 1) with gradient 4.","o":["y = -4x − 3","y = 4x + 3","y = 4x + 1","y = 4x − 3"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, 5) with gradient 1.","o":["y = -1x + 5","y = x + 6","y = 1x + 5","y = 1x − 5"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, -3) with gradient 3.","o":["y = 3x + 3","y = -3x − 3","y = x + 0","y = 3x − 3"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-2, -2) with gradient 1.","o":["y = 1x + 1","y = 1x − 2","y = -1x","y = 1x"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (1, -6) with gradient 1.","o":["y = 1x − 6","y = -1x − 7","y = 1x + 7","y = 1x − 7"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (2, 1) with gradient 3.","o":["y = 3x + 1","y = 3x + 5","y = -3x − 5","y = 3x − 5"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (3, 18) with gradient 4.","o":["y = -4x + 6","y = 4x + 6","y = 4x − 6","y = 4x + 18"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-1, -12) with gradient 4.","o":["y = 4x − 12","y = 4x − 8","y = 4x + 8","y = -4x − 8"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, 8) with gradient 6.","o":["y = 6x − 8","y = x + 14","y = 6x + 8","y = -6x + 8"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (1, 5) with gradient 6.","o":["y = 6x − 1","y = 6x + 1","y = -6x − 1","y = 6x + 5"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, 2) with gradient 2.","o":["y = 2x − 8","y = 2x + 8","y = 2x + 2","y = -2x + 8"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, -2) with gradient 3.","o":["y = -3x − 2","y = 3x − 2","y = x + 1","y = 3x + 2"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, -3) with gradient 1.","o":["y = 1x","y = -1x","y = 1x − 3","y = 1x + 1"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-1, 5) with gradient 2.","o":["y = 2x − 7","y = -2x + 7","y = 2x + 7","y = 2x + 5"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-1, -3) with gradient 3.","o":["y = 3x","y = -3x","y = 3x − 3","y = 3x + 1"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (1, 2) with gradient 5.","o":["y = -5x − 3","y = 5x − 3","y = 5x + 3","y = 5x + 2"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, 5) with gradient 5.","o":["y = -5x + 5","y = 5x + 5","y = 5x − 5","y = x + 10"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 8) with gradient 4.","o":["y = x − 4","y = -4x − 8","y = 4x + 8","y = 4x − 8"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 18) with gradient 5.","o":["y = 5x + 2","y = 5x − 2","y = -5x − 2","y = 5x + 18"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-1, 2) with gradient 1.","o":["y = 1x + 3","y = -1x + 3","y = 1x + 2","y = 1x − 3"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, 1) with gradient 2.","o":["y = 2x + 1","y = -2x + 7","y = 2x + 7","y = 2x − 7"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (1, -3) with gradient 2.","o":["y = -2x − 5","y = 2x + 5","y = 2x − 3","y = 2x − 5"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-2, -7) with gradient 1.","o":["y = 1x + 5","y = 1x − 7","y = 1x − 5","y = -1x − 5"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, -13) with gradient 5.","o":["y = 5x − 13","y = 5x + 2","y = 5x − 2","y = -5x + 2"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-2, -10) with gradient 5.","o":["y = 5x","y = 5x − 10","y = -5x","y = 5x + 1"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (1, 5) with gradient 5.","o":["y = 5x + 5","y = 5x","y = -5x","y = 5x + 1"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (3, 12) with gradient 6.","o":["y = 6x − 6","y = 6x + 6","y = -6x − 6","y = 6x + 12"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, 8) with gradient 1.","o":["y = 1x − 8","y = x + 9","y = 1x + 8","y = -1x + 8"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-2, -18) with gradient 6.","o":["y = 6x − 6","y = -6x − 6","y = 6x + 6","y = 6x − 18"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-2, -14) with gradient 4.","o":["y = 4x − 6","y = -4x − 6","y = 4x + 6","y = 4x − 14"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, -8) with gradient 1.","o":["y = -1x − 5","y = 1x − 5","y = 1x − 8","y = 1x + 5"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 5) with gradient 2.","o":["y = 2x + 3","y = 2x − 3","y = 2x + 5","y = -2x − 3"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-1, -10) with gradient 6.","o":["y = 6x − 4","y = -6x − 4","y = 6x − 10","y = 6x + 4"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, -21) with gradient 5.","o":["y = 5x + 6","y = -5x − 6","y = 5x − 6","y = 5x − 21"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (2, 9) with gradient 2.","o":["y = -2x + 5","y = 2x − 5","y = 2x + 5","y = 2x + 9"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-1, -9) with gradient 5.","o":["y = -5x − 4","y = 5x − 9","y = 5x − 4","y = 5x + 4"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-1, -7) with gradient 3.","o":["y = 3x + 4","y = 3x − 4","y = -3x − 4","y = 3x − 7"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 11) with gradient 2.","o":["y = 2x − 3","y = 2x + 3","y = -2x + 3","y = 2x + 11"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (2, 16) with gradient 5.","o":["y = 5x − 6","y = -5x + 6","y = 5x + 16","y = 5x + 6"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, 1) with gradient 3.","o":["y = -3x + 1","y = x + 4","y = 3x − 1","y = 3x + 1"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (1, -5) with gradient 2.","o":["y = 2x + 7","y = 2x − 5","y = 2x − 7","y = -2x − 7"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, 2) with gradient 4.","o":["y = x + 6","y = -4x + 2","y = 4x + 2","y = 4x − 2"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 15) with gradient 3.","o":["y = 3x − 3","y = -3x + 3","y = 3x + 3","y = 3x + 15"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, -3) with gradient 5.","o":["y = x + 2","y = 5x − 3","y = -5x − 3","y = 5x + 3"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-2, -1) with gradient 4.","o":["y = 4x + 7","y = 4x − 1","y = -4x + 7","y = 4x − 7"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-2, 3) with gradient 2.","o":["y = 2x − 7","y = -2x + 7","y = 2x + 7","y = 2x + 3"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 24) with gradient 6.","o":["y = 6x + 24","y = 6x + 1","y = -6x","y = 6x"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, 1) with gradient 4.","o":["y = 4x + 1","y = x + 5","y = 4x − 1","y = -4x + 1"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (3, 8) with gradient 4.","o":["y = -4x − 4","y = 4x − 4","y = 4x + 4","y = 4x + 8"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 17) with gradient 4.","o":["y = 4x + 1","y = 4x + 17","y = -4x + 1","y = 4x − 1"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (1, -3) with gradient 1.","o":["y = 1x + 4","y = -1x − 4","y = 1x − 4","y = 1x − 3"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, 0) with gradient 4.","o":["y = 4x + 1","y = 4x + 0","y = 4x","y = -4x"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-1, 5) with gradient 1.","o":["y = 1x + 6","y = -1x + 6","y = 1x + 5","y = 1x − 6"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (2, 11) with gradient 5.","o":["y = 5x + 1","y = -5x + 1","y = 5x − 1","y = 5x + 11"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (2, 14) with gradient 4.","o":["y = 4x + 6","y = -4x + 6","y = 4x + 14","y = 4x − 6"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, -1) with gradient 2.","o":["y = 2x − 1","y = -2x − 1","y = 2x + 1","y = x + 1"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-1, 4) with gradient 1.","o":["y = -1x + 5","y = 1x + 5","y = 1x + 4","y = 1x − 5"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 31) with gradient 6.","o":["y = 6x − 7","y = 6x + 7","y = 6x + 31","y = -6x + 7"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-2, -9) with gradient 2.","o":["y = -2x − 5","y = 2x − 5","y = 2x − 9","y = 2x + 5"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (1, 10) with gradient 6.","o":["y = 6x + 10","y = 6x − 4","y = -6x + 4","y = 6x + 4"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, 6) with gradient 1.","o":["y = -1x + 6","y = 1x + 6","y = 1x − 6","y = x + 7"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (3, 8) with gradient 1.","o":["y = 1x + 8","y = 1x − 5","y = 1x + 5","y = -1x + 5"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, -5) with gradient 2.","o":["y = -2x + 1","y = 2x − 5","y = 2x − 1","y = 2x + 1"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (2, 12) with gradient 5.","o":["y = 5x + 2","y = 5x − 2","y = -5x + 2","y = 5x + 12"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-1, 3) with gradient 2.","o":["y = 2x − 5","y = 2x + 3","y = 2x + 5","y = -2x + 5"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, -2) with gradient 1.","o":["y = 1x + 6","y = -1x − 6","y = 1x − 6","y = 1x − 2"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (2, 4) with gradient 5.","o":["y = 5x + 4","y = 5x − 6","y = -5x − 6","y = 5x + 6"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, -17) with gradient 6.","o":["y = -6x + 1","y = 6x + 1","y = 6x − 1","y = 6x − 17"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (3, 23) with gradient 6.","o":["y = -6x + 5","y = 6x + 23","y = 6x + 5","y = 6x − 5"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 14) with gradient 5.","o":["y = 5x − 6","y = 5x + 6","y = -5x − 6","y = 5x + 14"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 2) with gradient 1.","o":["y = 1x − 2","y = x − 1","y = -1x − 2","y = 1x + 2"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, -2) with gradient 6.","o":["y = x + 4","y = -6x − 2","y = 6x + 2","y = 6x − 2"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, -6) with gradient 3.","o":["y = 3x − 6","y = -3x − 6","y = x − 3","y = 3x + 6"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, -14) with gradient 5.","o":["y = 5x + 1","y = 5x − 1","y = -5x + 1","y = 5x − 14"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, -1) with gradient 4.","o":["y = 4x + 1","y = x + 3","y = -4x − 1","y = 4x − 1"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 13) with gradient 3.","o":["y = 3x − 1","y = -3x + 1","y = 3x + 1","y = 3x + 13"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, -13) with gradient 4.","o":["y = 4x − 1","y = 4x + 1","y = -4x − 1","y = 4x − 13"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, -20) with gradient 5.","o":["y = -5x − 5","y = 5x + 5","y = 5x − 5","y = 5x − 20"],"a":2,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 30) with gradient 6.","o":["y = -6x + 6","y = 6x + 6","y = 6x + 30","y = 6x − 6"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (0, -3) with gradient 6.","o":["y = 6x − 3","y = -6x − 3","y = x + 3","y = 6x + 3"],"a":0,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 10) with gradient 3.","o":["y = -3x − 2","y = 3x − 2","y = 3x + 10","y = 3x + 2"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (4, 4) with gradient 2.","o":["y = 2x + 4","y = -2x − 4","y = x − 2","y = 2x − 4"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-1, -8) with gradient 1.","o":["y = 1x + 7","y = 1x − 8","y = -1x − 7","y = 1x − 7"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (2, 2) with gradient 5.","o":["y = 5x + 8","y = 5x + 2","y = -5x − 8","y = 5x − 8"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, -11) with gradient 3.","o":["y = 3x + 2","y = -3x − 2","y = 3x − 11","y = 3x − 2"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-3, -22) with gradient 5.","o":["y = 5x + 7","y = 5x − 7","y = -5x − 7","y = 5x − 22"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-2, -3) with gradient 4.","o":["y = 4x − 5","y = 4x − 3","y = -4x + 5","y = 4x + 5"],"a":3,"t":"Coordinate Geometry","d":"Medium"},{"q":"Find the equation of the line through (-2, -11) with gradient 2.","o":["y = 2x − 11","y = 2x − 7","y = -2x − 7","y = 2x + 7"],"a":1,"t":"Coordinate Geometry","d":"Medium"},{"q":"If a = 1i + 2j and b = 4i + 2j, find a + 2b.","o":["9i + 6j","5i + 4j","6i + 6j","-7i + -2j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 4j and b = 1i + 2j, find a + 2b.","o":["4i + 8j","0i + 0j","5i + 10j","3i + 6j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 2j and b = 1i + 4j, find a + 2b.","o":["4i + 10j","3i + 6j","5i + 8j","0i + -6j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 2j and b = 1i + 1j, find a + 2b.","o":["9i + 5j","2i + 0j","5i + 3j","6i + 4j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 1j and b = 4i + 2j, find a + 2b.","o":["-4i + -3j","12i + 4j","8i + 3j","12i + 5j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 1j and b = 2i + 1j, find a + 2b.","o":["7i + 3j","8i + 3j","5i + 2j","-1i + -1j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 4j and b = 1i + 1j, find a + 2b.","o":["5i + 6j","4i + 5j","1i + 2j","7i + 9j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 1j and b = 1i + 2j, find a + 2b.","o":["3i + 4j","-1i + -3j","2i + 3j","3i + 5j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 1j and b = 4i + 1j, find a + 2b.","o":["9i + 3j","-7i + -1j","5i + 2j","6i + 3j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 3j and b = 3i + 4j, find a + 2b.","o":["9i + 11j","6i + 7j","-3i + -5j","9i + 10j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 1j and b = 4i + 2j, find a + 2b.","o":["9i + 5j","-7i + -3j","6i + 4j","5i + 3j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 1j and b = 4i + 4j, find a + 2b.","o":["5i + 5j","6i + 6j","-7i + -7j","9i + 9j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 2j and b = 4i + 3j, find a + 2b.","o":["7i + 5j","10i + 7j","11i + 8j","-5i + -4j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 1j and b = 4i + 4j, find a + 2b.","o":["8i + 6j","-6i + -7j","6i + 5j","10i + 9j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 3j and b = 3i + 1j, find a + 2b.","o":["-5i + 1j","4i + 4j","7i + 5j","5i + 7j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 2j and b = 1i + 2j, find a + 2b.","o":["3i + 4j","4i + 6j","5i + 6j","0i + -2j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 1j and b = 1i + 2j, find a + 2b.","o":["2i + -3j","5i + 3j","6i + 5j","9i + 4j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 1j and b = 3i + 4j, find a + 2b.","o":["9i + 6j","6i + 5j","-3i + -7j","9i + 9j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 4j and b = 1i + 1j, find a + 2b.","o":["5i + 5j","6i + 6j","9i + 9j","2i + 2j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 4j and b = 2i + 3j, find a + 2b.","o":["8i + 11j","-1i + -2j","7i + 10j","5i + 7j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 2j and b = 3i + 1j, find a + 2b.","o":["11i + 5j","7i + 3j","-2i + 0j","10i + 4j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 4j and b = 3i + 1j, find a + 2b.","o":["11i + 9j","7i + 5j","-2i + 2j","10i + 6j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 1j and b = 2i + 4j, find a + 2b.","o":["4i + 5j","6i + 9j","-2i + -7j","6i + 6j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 4j and b = 4i + 1j, find a + 2b.","o":["12i + 9j","12i + 6j","-4i + 2j","8i + 5j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 4j and b = 1i + 4j, find a + 2b.","o":["3i − 12j","2i + 8j","3i + 12j","-1i + -4j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 3j and b = 1i + 2j, find a + 2b.","o":["5i + 5j","9i + 8j","2i + -1j","6i + 7j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 3j and b = 4i + 1j, find a + 2b.","o":["10i + 5j","-6i + 1j","6i + 4j","8i + 7j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 3j and b = 3i + 4j, find a + 2b.","o":["5i + 7j","7i + 10j","-4i + -5j","8i + 11j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 1j and b = 2i + 3j, find a + 2b.","o":["0i + -5j","6i + 4j","10i + 5j","8i + 7j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 2j and b = 4i + 2j, find a + 2b.","o":["-4i + -2j","8i + 4j","12i + 6j","12i − 6j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 4j and b = 2i + 3j, find a + 2b.","o":["6i + 11j","-2i + -2j","6i + 10j","4i + 7j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 1j and b = 3i + 2j, find a + 2b.","o":["9i + 4j","-3i + -3j","9i + 5j","6i + 3j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 1j and b = 1i + 4j, find a + 2b.","o":["0i + -7j","4i + 9j","3i + 5j","5i + 6j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 1j and b = 3i + 3j, find a + 2b.","o":["5i + 4j","-4i + -5j","8i + 7j","7i + 5j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 4j and b = 3i + 2j, find a + 2b.","o":["11i + 10j","7i + 6j","-2i + 0j","10i + 8j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 4j and b = 1i + 3j, find a + 2b.","o":["2i + 7j","-1i + -2j","3i + 11j","3i + 10j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 2j and b = 2i + 1j, find a + 2b.","o":["-3i + 0j","4i + 5j","5i + 4j","3i + 3j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 3j and b = 1i + 2j, find a + 2b.","o":["0i + -1j","4i + 7j","5i + 8j","3i + 5j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 3j and b = 2i + 2j, find a + 2b.","o":["8i + 7j","6i + 5j","10i + 8j","0i + -1j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 3j and b = 1i + 4j, find a + 2b.","o":["3i + 10j","2i + 7j","-1i + -5j","3i + 11j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 2j and b = 4i + 4j, find a + 2b.","o":["11i + 10j","7i + 6j","-5i + -6j","10i + 8j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 3j and b = 3i + 1j, find a + 2b.","o":["7i + 4j","10i + 5j","11i + 7j","-2i + 1j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 2j and b = 2i + 3j, find a + 2b.","o":["6i + 7j","6i + 8j","-2i + -4j","4i + 5j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 3j and b = 3i + 3j, find a + 2b.","o":["-2i + -3j","10i + 9j","7i + 6j","11i + 9j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 4j and b = 3i + 1j, find a + 2b.","o":["5i + 9j","7i + 6j","-5i + 2j","4i + 5j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 2j and b = 2i + 4j, find a + 2b.","o":["7i + 10j","8i + 8j","-1i + -6j","5i + 6j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 3j and b = 3i + 2j, find a + 2b.","o":["8i + 7j","7i + 8j","5i + 5j","-4i + -1j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 3j and b = 3i + 3j, find a + 2b.","o":["5i + 9j","7i + 9j","4i + 6j","-5i + -3j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 4j and b = 3i + 4j, find a + 2b.","o":["-2i + -4j","7i + 8j","10i + 12j","11i + 12j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 3j and b = 2i + 4j, find a + 2b.","o":["3i + 7j","5i + 11j","-3i + -5j","4i + 10j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 2j and b = 4i + 4j, find a + 2b.","o":["6i + 6j","8i + 8j","-6i + -6j","10i + 10j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 4j and b = 2i + 4j, find a + 2b.","o":["6i − 12j","-2i + -4j","4i + 8j","6i + 12j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 1j and b = 4i + 4j, find a + 2b.","o":["12i + 9j","12i + 6j","-4i + -7j","8i + 5j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 3j and b = 4i + 4j, find a + 2b.","o":["6i + 10j","9i + 11j","-7i + -5j","5i + 7j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 4j and b = 4i + 1j, find a + 2b.","o":["10i + 6j","8i + 9j","-6i + 2j","6i + 5j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 1j and b = 3i + 1j, find a + 2b.","o":["9i − 3j","9i + 3j","6i + 2j","-3i + -1j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 2j and b = 1i + 3j, find a + 2b.","o":["2i + 5j","3i + 8j","3i + 7j","-1i + -4j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 1j and b = 1i + 4j, find a + 2b.","o":["5i + 5j","9i + 6j","2i + -7j","6i + 9j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 2j and b = 3i + 1j, find a + 2b.","o":["-3i + 0j","6i + 3j","9i + 5j","9i + 4j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 4j and b = 3i + 1j, find a + 2b.","o":["7i + 9j","8i + 6j","-4i + 2j","5i + 5j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 1j and b = 1i + 3j, find a + 2b.","o":["5i + 7j","4i + 4j","1i + -5j","7i + 5j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 4j and b = 1i + 3j, find a + 2b.","o":["1i + -2j","4i + 7j","5i + 10j","7i + 11j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 4j and b = 3i + 3j, find a + 2b.","o":["8i + 10j","7i + 11j","-4i + -2j","5i + 7j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 4j and b = 4i + 3j, find a + 2b.","o":["12i + 10j","12i + 11j","8i + 7j","-4i + -2j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 4j and b = 1i + 4j, find a + 2b.","o":["4i + 8j","1i + -4j","7i + 12j","5i + 12j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 3j and b = 2i + 3j, find a + 2b.","o":["3i + 6j","-3i + -3j","4i + 9j","5i + 9j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 2j and b = 4i + 3j, find a + 2b.","o":["6i + 7j","-7i + -4j","5i + 5j","9i + 8j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 4j and b = 1i + 1j, find a + 2b.","o":["3i + 5j","4i + 6j","0i + 2j","5i + 9j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 3j and b = 3i + 4j, find a + 2b.","o":["5i + 10j","4i + 7j","7i + 11j","-5i + -5j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 3j and b = 3i + 3j, find a + 2b.","o":["7i + 9j","8i + 9j","5i + 6j","-4i + -3j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 3j and b = 2i + 2j, find a + 2b.","o":["6i + 7j","4i + 5j","6i + 8j","-2i + -1j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 2j and b = 2i + 3j, find a + 2b.","o":["0i + -4j","8i + 8j","10i + 7j","6i + 5j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 4j and b = 3i + 1j, find a + 2b.","o":["9i + 9j","6i + 5j","9i + 6j","-3i + 2j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 2j and b = 3i + 1j, find a + 2b.","o":["8i + 4j","-4i + 0j","7i + 5j","5i + 3j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 1j and b = 2i + 2j, find a + 2b.","o":["6i + 5j","-2i + -3j","4i + 3j","6i + 4j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 2j and b = 2i + 3j, find a + 2b.","o":["7i + 8j","8i + 7j","-1i + -4j","5i + 5j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 1j and b = 3i + 3j, find a + 2b.","o":["4i + 4j","-5i + -5j","5i + 5j","7i + 7j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 2j and b = 3i + 3j, find a + 2b.","o":["-4i + -4j","5i + 5j","7i + 7j","8i + 8j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 1j and b = 2i + 1j, find a + 2b.","o":["-3i + -1j","5i + 3j","4i + 3j","3i + 2j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 1j and b = 1i + 3j, find a + 2b.","o":["5i + 4j","9i + 5j","6i + 7j","2i + -5j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 3j and b = 4i + 3j, find a + 2b.","o":["11i + 9j","10i + 9j","-5i + -3j","7i + 6j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 3j and b = 4i + 3j, find a + 2b.","o":["10i + 9j","6i + 6j","-6i + -3j","8i + 9j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 1j and b = 1i + 3j, find a + 2b.","o":["-1i + -5j","3i + 7j","3i + 5j","2i + 4j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 1j and b = 3i + 3j, find a + 2b.","o":["10i + 7j","-2i + -5j","11i + 5j","7i + 4j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 3j and b = 1i + 3j, find a + 2b.","o":["4i + 6j","7i + 9j","1i + -3j","5i + 9j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 1j and b = 2i + 2j, find a + 2b.","o":["10i + 4j","8i + 5j","0i + -3j","6i + 3j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 2j and b = 3i + 4j, find a + 2b.","o":["-2i + -6j","11i + 8j","7i + 6j","10i + 10j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 2j and b = 1i + 4j, find a + 2b.","o":["7i + 8j","4i + 6j","5i + 10j","1i + -6j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 3j and b = 2i + 3j, find a + 2b.","o":["8i + 9j","7i + 9j","5i + 6j","-1i + -3j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 2j and b = 4i + 4j, find a + 2b.","o":["8i + 6j","-4i + -6j","12i + 10j","12i + 8j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 4j and b = 1i + 1j, find a + 2b.","o":["-1i + 2j","3i + 9j","2i + 5j","3i + 6j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 1j and b = 1i + 4j, find a + 2b.","o":["2i + 5j","3i + 9j","-1i + -7j","3i + 6j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 4j and b = 2i + 1j, find a + 2b.","o":["6i + 9j","4i + 5j","-2i + 2j","6i + 6j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 2j and b = 1i + 2j, find a + 2b.","o":["-1i + -2j","3i + 6j","2i + 4j","3i − 6j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 4j and b = 3i + 3j, find a + 2b.","o":["-3i + -2j","9i + 11j","6i + 7j","9i + 10j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 4j and b = 2i + 3j, find a + 2b.","o":["4i + 11j","3i + 7j","-3i + -2j","5i + 10j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 3j and b = 4i + 2j, find a + 2b.","o":["6i + 5j","8i + 8j","10i + 7j","-6i + -1j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 3j and b = 4i + 2j, find a + 2b.","o":["-4i + -1j","12i + 7j","12i + 8j","8i + 5j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 4j and b = 4i + 1j, find a + 2b.","o":["5i + 5j","6i + 9j","9i + 6j","-7i + 2j"],"a":2,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 4j and b = 2i + 1j, find a + 2b.","o":["-1i + 2j","5i + 5j","8i + 9j","7i + 6j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 3j and b = 2i + 3j, find a + 2b.","o":["0i + -3j","6i + 6j","10i + 9j","8i + 9j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 1j and b = 3i + 1j, find a + 2b.","o":["8i + 3j","5i + 2j","7i + 3j","-4i + -1j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 4j and b = 2i + 2j, find a + 2b.","o":["8i + 10j","5i + 6j","-1i + 0j","7i + 8j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 4j and b = 1i + 2j, find a + 2b.","o":["1i + 0j","5i + 8j","4i + 6j","7i + 10j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 3i + 1j and b = 4i + 4j, find a + 2b.","o":["10i + 6j","11i + 9j","-5i + -7j","7i + 5j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 3j and b = 3i + 1j, find a + 2b.","o":["-4i + 1j","7i + 7j","5i + 4j","8i + 5j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 4j and b = 4i + 2j, find a + 2b.","o":["12i + 10j","8i + 6j","-4i + 0j","12i + 8j"],"a":3,"t":"Vectors","d":"Easy"},{"q":"If a = 2i + 3j and b = 2i + 1j, find a + 2b.","o":["-2i + 1j","6i + 5j","4i + 4j","6i + 7j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 2j and b = 2i + 3j, find a + 2b.","o":["5i + 8j","-3i + -4j","4i + 7j","3i + 5j"],"a":0,"t":"Vectors","d":"Easy"},{"q":"If a = 4i + 3j and b = 2i + 4j, find a + 2b.","o":["6i + 7j","8i + 11j","0i + -5j","10i + 10j"],"a":1,"t":"Vectors","d":"Easy"},{"q":"If a = 1i + 4j and b = 4i + 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