Prove the following identity: (sin2 θ − 1)(tan2 θ + 1) + 1 = 0

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.

Statement (i): sin² θ + cos² θ = 1 Statement (ii): cosec² θ + cot² θ = 1 Which of the following is valid? (a) Only (i) (b) Only (ii) (c) Both (i) and (ii) (d) Neither (i) nor (ii)

Prove that:

Factorize: sin³ θ + cos³ θ. Hence, prove the identity:

Which of the following cannot be determined graphically for a grouped frequency distribution? (a) Median (b) Mode (c) Quartiles (d) Mean

Naveen deposits ₹800 every month in a recurring deposit account for 6 months. If he receives ₹4884 at the time of maturity, then the interest he earns is: (a) ₹84 (b) ₹42 (c) ₹24 (d) ₹284

The volume of a cylinder of height 3 cm is 48π cm3. The radius of the cylinder is: (a) 48 cm (b) 16 cm (c) 4 cm (d) 24 cm

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}

What number must be added to each of the numbers 4, 6, 8 and 11 so that the resulting four numbers are in proportion?

A bag contains 25 cards numbered from 1 to 25. A card is drawn at random. Find the probability that the number on the card drawn is: (a) a multiple of 5 (b) a perfect square (c) a prime number.

The following distribution gives the daily wages of 60 workers of a factory: Daily income (₹) Number of workers 200–300 6 300–400 10 400–500 14 500–600 16 600–700 10 700–800 4 Use graph paper. Take 2 cm = ₹100 along one axis and 2 cm = 2 workers along the other axis. Draw a histogram and hence find the mode of the distribution.