Math Problem Solver

If for the matrix A = [

tanx 1

−1 tanx

], A + A

′ = 2√3I, then the value of x ∈ [0,

π

2

] is:

(A) 0 (B) π

4

(C) π

3

(D) π

6

1

5. For what value of k, the function given below is continuous at x = 0?

f(x) = {

√4 + x − 2

x

, x ≠ 0

k, x = 0

(A) 0 (B) 1

4

(C) 1 (D) 4

1

6. If P(A) =

1

2

, P(B) = 0, then P(A|B) is

(A) 0 (B) 1

2

(C) not defined (D) 1

1

7. Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3),

(3, 2)}. Choose the correct answer.

(A) R is reflexive and symmetric but not transitive.

(B) R is reflexive and transitive but not symmetric.

(C) R is symmetric and transitive but not reflexive.

(D) R is an equivalence relation.

1

8. The total revenue in Rupees received from the sale of x units of a product is given by

R(x) = 3x

2 + 36x + 5. The marginal revenue, when x = 15 is

(A) 116 (B) 96 (C) 90 (D) 126

1

9. Area lying in the first quadrant and bounded by the circle x

2 + y

2 = 4 and the lines

x = 0 and x = 2 is

(A) π (B) π

2

(C) π

3

(D) π

4

1

10. The degree and order of differential equation y = px + √1 + p2, where p =

dy

dx

respectively are:

(A) 1, 2 (B) 1

2

, 2 (C) 2, 1

2

(D) 2, 1

1

11.

If aij and Aij represent the (ij)

th element and its cofactor of [

1 2 5

6 −3 −2

0 5 7

] respectively, then

the value of a11A21 + a12A22 + a13A23 is :

(A) 0 (B) – 28 (C) 114 (D) – 114