# 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)

Q. 14. If

Ans.

Q. 15.

Ans.

Q. 16.

Ans.

Q. 17.

Ans.

Q. 18.

Q. 19.

Ans.

Q. 20. f : [ 0, 1] --> [0, 1] be defined by f(x) = g : [0, 1] --> [0, 1] be defined by g(x) = 4x (1 - x) find fog and gof

Ans.

Q. 21. Differentiate log

Ans.

Q. 22. y =

Ans. 1/2