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1. What is the equation of the parabola whose focus is (2, 0) and the directrix is x + 5 = 0?

A

y2 = 21x – 14

B

y2 = 14x – 21

C

y2 = 14x + 21

D

y2 = 21x + 14

2. If 5p – 7q + r = 11, 6p – 8q – r = 15 and 3p + 2q – 6r = 7, then what is the value of (p + q + r)?

A

–2

B

–3

C

zero

D

–1

3. If y = x2sinx, then what is the value of (dy/dx) at x = π/2?

A

π

B

π/4

C

π/6

D

π/2

4. If the angle between two lines is π/4 and slope of one of the lines is 1/3, then what is the slope of the other line?

A

3

B

1

C

2

D

4

5. ϕ, {1}, {2}, {1, 2} are the subsets of ___

A

{1, 2}

B

{0, 1, 2}

C

{1}, {2}

D

{1, 3}

6. Differentiation of cotx with respect to x is ___

A

–tan2x

B

tan2x

C

cosec2x

D

-cosec2x

7. If y = ex cosx, then what is the value of (dy/dx) at x = 0?

A

zero

B

2

C

-1

D

1

8. Which of the following is a finite set?

A

The set of numbers which are multiple of 3

B

The set of even numbers

C

The set of whole number less than 1

D

The set of negative integers

9. What is the value of the eccentricity of the ellipse 25x2 + 9y2 – 150x – 90y + 225 = 0?

A

2/5

B

3/4

C

3/5

D

4/5

10. Two vertices of a triangle are (3, 2) and (7, 4). If the centroid of the triangle is (8, 9), then what is the coordinates of the third vertex of that triangle?

A

(14, 21)

B

(21, 23)

C

(16, 19)

D

(15, 23)

11. If A and B are two sets such that n(A)= 50, n(B) = 15 and n(A ∪ B) = 60, then what is the value of n(A ∩ B)?

A

5

B

15

C

8

D

10

12. What is the slope of the tangent to the curve f(x) = 2x5 + x3 – 2 at x = 1?

A

13

B

11

C

14

D

12

13. Differentiation of sin(4x + 5) with respect to x is ___

A

4sin(4x + 5)

B

4cos(4x + 5)

C

5cos(4x + 5)

D

5sin(4x + 5)

14. What is the equation of the line which is parallel to 2x – 3y + 10 = 0 and passes through the point (2, 3)?

A

2x – 3y + 5 = 0

B

2x + 3y + 10 = 0

C

2x – 3y + 10 = 0

D

2x + 3y + 5 = 0

15. Which of the following is correct form of De-Morgan`s Law?

A

(A ⋂ B )` = A` ∪ B`

B

(A ⋂ B)` = A` ⋂ B`

C

A ∪ B) = A ⋂ B

D

(A ⋂ B) = A` ⋂ B`

16. The length of the latus-rectum of the ellipse x2 + 4y2 + 2x + 16y + 13 = 0 is __

A

2

B

3

C

4

D

1

17. Which of the following is correct roaster form of set A = {x : x is an integer and –1 ≤ x < 3}?

A

A = {–1, 0, 1, 2}

B

A = {–1, 0, 1, 2, 3}

C

A = {0, 1, 2}

D

A = {0, 1, 2, 3}

18. The set builder form of the set A = {3, 9, 27, 81, 243} is ____

A

{x : x = 3n, n ∈ N and 1 < n < 5}

B

{x : x = 3n, n ∈ N and 1 < n ≤ 5}

C

{x : x = 3n, n ∈ N and 1 ≤ n ≤ 5}

D

{x : x = 3n, n ∈ N and 1 ≤ n < 5}

19. What is the equation of a line passing through (3, 5) and inclined at an angle of 135 degree with the positive direction of x-axis?

A

x + y = 8

B

x – y = –8

C

x + y = –8

D

x – y = 8

20. If f(x) = kx3 + px + 10 and f`(3) = 15 and f`(1) = 10, then what is the value of (k + p)?

A

109/12

B

113/12

C

119/12

D

115/12