It is given that (x − 2) is a factor of 2x³ − 7x² + kx − 2. (a) Find k. (b) Hence, factorise the resulting polynomial completely.

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

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

What must be subtracted from the polynomial x³ + x² − 2x + 1 so that the resulting polynomial is exactly divisible by (x − 3)? (a) −31 (b) −30 (c) 30 (d) 31

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.

Assertion (A): If sin² A + sin A = 1, then cos⁴ A + cos² A = 1. Reason (R): 1 − sin² A = cos² A. (a) A is true, R is false. (b) A is false, R is true. (c) Both A and R are true, and R is the correct reason for A. (d) Both A and R are true, and R is not the correct reason for A.

In the given diagram, chords AC and BC are equal. If ∠ACD = 120°, then ∠AEC is: (a) 30° (b) 60° (c) 90° (d) 120°

A man invested in a company paying 12% dividend on its shares. If the percentage return on his investment is 10%, then the shares are: (a) at par (b) below par (c) above par (d) cannot be determined

The solution set for 0 < − < 2, x ∈ Z is: (a) {−5, −4, −3, −2, −1} (b) {−6, −5, −4, −3, −2, −1} (c) {−5, −4, −3, −2, −1, 0} (d) {−6, −5, −4, −3, −2, −1, 0} bb

In the given diagram, △ABC ∼ △EFG. If ∠ABC = ∠EFG = 60°, then the length of side FG is: (a) 15 cm (b) 20 cm (c) 25 cm (d) 30 cm

The quadratic equation 3x² + √7x + 2 = 0 has: (a) two equal real roots. (b) two distinct real roots. (c) more than two real roots. (d) no real roots.