CBSE Important Questions class XII mathematics 2008 3

Q. 1.

Ans. x = 1, z = 4, y = 3

Q. 2.

Ans. -1

Q. 3. Using the method of matrices solve

Ans.

Q. 4. Using properties of determinants solve for x

Ans.

Q. 5. If

Q. 6. If

Q. 7.

Ans. a = 1, b = -1

Q. 8.

Ans. a = 1/2

Q. 9. Solve for x : 2tan^-1 (cosx) = tan^-1 (2cosx)

Ans. x = 2n P ± P /2

Q. 10. (a) If tan^-1 x + tan^-1 y + tan^-1 z = P /2 .Evaluate xy + yz + xz

Ans. 1

(b) If tan^-1 x + tan^-1 y + tan^-1 z = P Evaluate

Q. 11. Show that

1. sin.cot ^-1 tan cos ^-1 x = x
2. sec² (tan^-1 2)+cosec² (cot^-13) = 15

Q. 12. Prove that the function f : R -> {x E R –1 is one –one and onto function and hence find its inverse.

Q. 13. Let A=QxQ.Let * be a binary operation on A defined by (a,b) * (c,d)=(ac,ad+b).

1. Find the identity element
2. Find the invertible element .

Ans. (i) (1,0) (ii) (1/a,-b/a)