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

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)

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.

Prove that:

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

If A = , then A² is equal to: (a) (b) (c) (d)

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.

(x + 3), 1, (3x − 7) and −5 are in proportion. The value of x is : (a) −1 (b) 1 (c) −5 (d) 5

If A = and B = , then the order of AB is: (a) 2 × 2 (b) 2 × 1 (c) 1 × 2 (d) AB is not possible

Assertion (A): The probability of getting a number greater than 6 on throwing a die is . Reason (R): The possible outcomes on throwing a die are 1, 2, 3, 4, 5 and 6. (a) A is true and R is false. (b) A is false and R is true. (c) Both A and R are true and R is the correct explanation of A. (d) Both A and R are true but R is not the correct explanation of A.

The marked price of a refrigerator is ₹ 12,000 and GST paid by the customer is ₹ 2,160. The rate of GST is: (a) 5% (b) 12% (c) 18% (d) 28%

Mr Anuj deposits ₹500 per month for 18 months in a recurring deposit account at a certain rate. If he earns ₹570 as interest at the time of maturity, then his matured amount is: (a) ₹(500 × 18 + 570) (b) ₹(500 × 19 + 570) (c) ₹(500 × 18 × 19 + 570) (d) ₹(500 × 9 × 19 + 570)