CBSE Important Questions class XII mathematics 2008 4

Q. 1. If sin y = xcos(a + y) and find k (3 marks)

Q. 2. If f(x) = find f’(o) (3marks)

Q. 3. Verify the mean value theorem for f(x) = in [1,3] (4 marks)

Q. 4. If x = a ( + ) y = (1 + cos ) find (4 marks)

Q. 5. If x^py^q = (x + y) ^p+^q prove that

Or

(4 marks)

Q. 6. Consider the function defined as follows for . In each case ,what choice (if any) of f(0) will make the function continuous at x = 0.

(4 marks)

Q. 7. If x = acos + bsin y = asin - bcos(4 marks)

Q. 8.

Or

(4 marks)

1. Construct a3 x 3 matrix A = [aij]whose elements are given by aij = ( 3 marks)
2. Solve the matrix equation for x (3 marks)
3. Solve the following equation for x (3 marks)
4. Prove that = a + b + c (3 marks)
5. Solve the following equations for using matrices x - y + z = 4 2x + y -3z = 0 x + y + z = 2 ( 6 marks)
6. Determinant of a skew symmetrix matrix of odd orderis always ( 1 marks)
   a) zero
   b) one
   c) negative one
   d) none
7. If A is a square matrix of order 3 then A.Adj (A) is (1 marks) a) | A | I₃
   b) | A | I₂
   C) | A | I
   d) none
   

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)

CBSE Important Questions class XII mathematics 2008 2

Q. 1. Let f:R -> Range of f given by f(x)= (x+1)² - 1 and The set S = {x: f(x) = f ^-1(x)} is

1. {0, -1}
2. {0, 1}
3. {-1, 1}
4. {1, 1}.

Q. 2. The minimum number of elements that must be added to the relation R = { (1,2), (2,3) } on the set of natural numbers so that it is an equivalence is

1. 4
2. 7
3. 6
4. 5

Q. 3. Let ‘R’ be a reflexive relation on a finite set ‘A’ having ‘n’ elements and let there be ‘m’ ordered pairs in ‘R’. Then

1. 
2. 
3. 
4. none of these.

Q. 4. Let ‘X’ be a family of sets and ‘R’ be a relation defined by ‘A is disjoint from B’ .Then R is

1. Reflexive
2. Symmetric
3. Anti symmetric
4. Transitive

Q. 5. The number of surjections from A = {1, 2, 3, ….. n} on to B = {a, b} is

1. ⁿP₂
2. 2ⁿ - 2
3. 2ⁿ - 1
4. none

Q. 6. If a function defined by f(x) = x² - 4x + 5 is a bijection, then B =

1. R
2. 
3. 
4. 

Q. 7. Let be two functions given by f(x) = 2x - 3, g (x) = x³ + 5. fog^-1(x) is equal to

1. 
2. 
3. 
4. 

Q . 8. If A = { a, b} then the number of binary operations that can be defined on A is

1. 4
2. 2
3. 16
4. 1

Q. 9. Let f(x) = [x] and g(x) = x - [x] then which of the following function is the zero function

1. (f+g) (x)
2. (fg) (x)
3. (f-g) (x)
4. fog (x)

Q. 10. Let ‘A’ be a nonempty set and be a binary operator on defined by Identity element of the operator * is

1. 
2. A
3. P(A)
4. none

Q. 11.

1. 
2. 
3. 
4. none

Q. 12. Let f : R --> R be the signum function. g: R -> R g(x) = [x]. fog and gof coincides on [0, 1]. True/False?