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1. The radius of the circle having centre at (3, –4) and touching the line 3x + 4y – 8 = 0 is

A

3

B

2

C

4

D

5

2. If f(x) = 5x4 – 7 and f(0) = 5, then what is the anti-derivative of f(x)?

A

x4 – 7x + 2

B

x5 – 7x + 6

C

x4 – 7x + 5

D

x5 – 7x + 5

3. If A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6}, then what is the value of A ∩ B?

A

{1, 2, 3, 4, 5, 6}

B

{2, 4, 6}

C

{2, 4}

D

ϕ

4. What is the length of latus-rectum of the parabola y2 = 16x?

A

16

B

12

C

20

D

8

5. Which of the following pairs of sets are equal?

A

A = {1, 2, 3, 4, 5, 6, 7, 8}, B = {x : x is a natural number and x < 8}

B

A = {3, 6, 9, 12}, B = {x : x = 3n and 1 ≤ n ≤ 4}

C

A = {2, 4, 6, 8}, B = {8, 6, 4, 1}

D

A = {a, e, i, o, v}, B = {e, a, u, i, o}

6. Differentiation of e-x with respect to x is ______.

A

-e-x

B

-ex

C

ex

D

e-x

7. The roster form of the set P = {x : x is an integer and x2 – 81 = 0} is ______.

A

{49, –81}

B

{9, –9}

C

{81, –81}

D

{8, –8}

8. The equation of the directrix of the parabola y2 = 4x + 4y is ______.

A

x + 6 = 0

B

x + 3 = 0

C

x + 5 = 0

D

x + 2 = 0

9. If the circles x2+ y2 = K and x2 + y2 – 8x – 6y + 9 = 0 touches externally, then what is the value of K?

A

1

B

2

C

3

D

4

10. If P and Q are the two sets containing 3 and 6 elements respectively, then what can be the maximum number of elements in P ⋃ Q?

A

10

B

9

C

12

D

11

11. If the coordinates of the mid-points of the sides of a triangle are (1, 2), (2, 4) and (3, 5), then what is the value of coordinates of its centroid?

A

2, (11/3)

B

5, (11/6)

C

3, (11/4)

D

4, (9/4)

12. Differentiation of logtanx with respect to x is ___

A

2cosec2x

B

2sec2x

C

2sin2x

D

2cos2x

13. What is the equation of the circle whose coordinates of centre is (2, 3) and radius is 4?

A

x2 + y2 – 4x – 6y – 3 = 0

B

x2 + y2 + 4x – 6y – 3 = 0

C

x2 + y2 – 4x + 6y + 3 = 0

D

x2 + y2 – 4x – 6y + 3 = 0

14. A rod having length of √5 metre slides with its ends on two perpendicular lines. What is the locus of the mid-point of rod?

A

4x2 + 4y2 = √5

B

4x2 – 4y2 = 5

C

4x2 + 4y2 = 5

D

4x2 – 4y2 = √5

15. The roster form of the set of all letters in the word “MATHEMATICS” is ___

A

{M, A, T, H, E, M, A, T, C, S}

B

{M, A, T, H, E, I, S}

C

{M, A, T, E, H, I}

D

{M, A, T, H, E, I, C, S}

16. If A = {1, 2, 3, 4, 5, 6}, then which of the following statements is correct?

A

{1, 2, 3} ∈ A

B

{3, 4} ∈ A

C

{3, 4} ⊂ A

D

1 ⊂ A

17. A circle of radius 2 units touches the coordinate axes in the first quadrant. What is the equation of its image in the line y = 0?

A

x2 + y2 – 4x + 4y + 4 = 0

B

x2 + y2 + 4x – 4y + 8 = 0

C

x2 + y2 + 4x + 4y + 8 = 0

D

x2 + y2 + 4x – 4y + 4 = 0

18. Which of the following states that A = B?

A

A = {2, 7, 9} and B = {7, 9, 2}

B

A = {a, e, f} and B = {f, e}

C

A = {2, 4, 6, 8} and B = {4, 8}

D

A = {a, b, c, d, e} and B = {e, c, b, a}

19. Set builder form of the set {1, 8, 27, 64, 125} is ___

A

{x : x = n3 and 1 ≤ n ≤ 15}

B

{x : x = n3 and 1 ≤ n ≤ 5}

C

{x : x = 3n and 1 < n ≤ 15}

D

{x : x = 3n and 1 ≤ n ≤ 505}

20. Differentiation of 4x + x5 + 31 with respect to x is ___

A

4x log2 + 5x5

B

5x log4 + 5x4

C

4x log4 + 5x4

D

4x log2 + 4x5