Solve the following inequation, write down the solution set and represent it on the real number line: −3 + x ≤ + 2 < 8 + 2x, x ∈ I.

Solve the inequation, write the solution set and represent it on the real number line:2x − < + 10 ≤ + 11, x ∈ R.

The solution set for the inequation 2x + 4 ≤ 14, x ∈ W is: (a) {1, 2, 3, 4, 5} (b) {0, 1, 2, 3, 4, 5} (c) {1, 2, 3, 4} (d) {0, 1, 2, 3, 4}

Solve the following inequation. Write down the solution set and represent it on the real number line. − 5(x − 9) ≥ 17 − 9x > x + 2, x ∈ R.

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 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)

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

For the following frequency distribution, find:(a) the mean, to the nearest whole number.(b) the median.x10111213141516f3226353

Solve the quadratic equation 2x² − 5x − 4 = 0. Give your answers correct to three significant figures.

A man bought ₹200 shares of a company at 25% premium. He received a return of 5% on his investment. Find:(a) the market value of one share.(b) the dividend percentage declared.(c) the number of shares purchased if the annual dividend is ₹1,000.