If x − 2 is a factor of x3 − kx − 12, then the value of k is: (a) 3 (b) 2 (c) −2 (d) −3

Find the value of ‘a’ if x − a is a factor of the polynomial 3x3 + x2 − ax − 81.

Factorize completely using the Factor Theorem: 2x³ − x² − 13x − 6.

The polynomial 3x³ + 8x² − 15x + k has (x − 1) as a factor. Find the value of k. Hence, factorize the resulting polynomial completely.

The factor common to the two polynomials x² − 4 and x³ − x² − 4x + 4 is: (a) (x + 1) (b) (x − 1) (c) (x − 2) (d) (x − 4)

The following observations are arranged in ascending order: 27, 31, 46, 52, x, x + 4, 71, 79, 85, 90 If the median is 64, then the value of x is: (a) 60 (b) 61 (c) 62 (d) 66

The sum invested to purchase 15 shares of nominal value ₹75 each at a discount of 20% is: (a) ₹60 (b) ₹90 (c) ₹1350 (d) ₹900

The 7th term of the A.P. is: (a) (b) (c) (d)

Assertion (A): A die is thrown once and the probability of getting an even number is 2/3. Reason (R): The sample space for even numbers on a die is {2, 4, 6}. (a) A is true, R is false. (b) A is false, R is true. (c) Both A and R are true. (d) Both A and R are false.

If A = and A² = , then the value of x is: (a) 2 (b) 4 (c) 8 (d) 10

The roots of the equation px² − qx + r = 0 are real and equal if: (a) p² = 4qr (b) q² = 4pr (c) −q² = 4pr (d) p² > 4qr

Statement 1: The point which is equidistant from three non-collinear points D, E and F is the circumcentre of △DEF. Statement 2: The incentre of a triangle is the point where the bisectors of the angles intersect. (a) Both statements are true. (b) Both statements are false. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.