MATHEMATICS (Differential Calculus)

SECTION -1 (Only One Option Correct Type)

This Section Contains 5 Single Choice Questions. Each Question Has Four Choices (A), B), (C) And (D) Out

of Which Only One Option Is Correct.

1. The value of is

(a) n (b) (c) (d)

2. for what value of k, f (x) is continuous at x = 0?

(a) k = 0 (b) k = 1 (c) k = e2 (d) k = 2

3. The set of all points where the function is differentiable is

(a) (0, ) (b) (,) (c) (, ) ~ {0} (d) (, )

4. Find the sum of the intercepts on the axes of coordinates by any tangent to the curve,

(a) (b)

(c) (d)

5. (a) one solution (b) two solution

(c) three solution (d) four solution

SECTION 2 (One or More Than One Options Correct Type) This Section Contains 5 Multiple Choice Type Questions. Each Question Has Four Choices (A), (B), (C) and

(D) Out of Which ONE or MORE THAN ONE Are Correct.

6.

(d) None of these

7. Let Q(x) = f (x) + f (1 x) and f (x) < 0 for all

(a) Q increases in [1/2, 1] (b) Q decreases in [1/2, 1]

(c) Q decreases in [0, 1/2] (d) Q increases in [0, 1/2]

8. For the function

(a) Domain is (b) Range is R

(c) Domain is R (d) Range is

9. where {x} denotes the fractional part of x. Then

10. If then

(a) f (x) is increasing in the interval

(b) f {f (x)} is increasing in the interval

(c) f {f (x)} is decreasing in and increasing in

(d) f{f(x)} is invertible in

Section -3 Comprehension Type

This Section Contains 2 Paragraphs Describing Theory, Experiments, Data etc. 6 Questions Relate To The

Paragraphs. Each Question Has Only One Correct Answer Among The Four Given Options (A), (B), (C) And

(D).

Paragraph For Questions 11 & 13

f : A B is said to be injective if distinct elements in A have distinct images in B and surjective if f (A) = B. Now

answer the following,

11. If the function defined by is injective then A can be

12. If the function defined by is surjective then B is

(d) R

13. The functions defined by where [.] is G.I.F. is furjective, then B =

(a) R (b) [0, 1]

(c) [1, 0] (d) {1, 0}

Paragraph For Questions 14 & 16

Now, consider the function y = h(x), where

14.

(a) 1/2 (b) 1/2

(c) 0 (d) 1

15. Domain of the function y = h(x) is

(b) R

(c) (0, 1) (d) [0, 1]

16. Range of the function y = h(x) is

SECTION 4 (One Integer Value Correct Type) This section contains 4 questions. Each question, when worked out will result in one integer from 0 to 9 (both

inclusive).

17. Find the value of if the period of the function

18. A cubic function f (x) vanishes at x = 2 and has relative minimum/maximum at x = 1 and

19. If f is a polynomial such that and f (3) = 28 then the

value of

20. If fe (0) exists equals to 1, f (0) =2, find f (2).