# MCQ Questions for Class 11 Limits and Derivatives with Answers

Students can refer to the following Limits and Derivatives MCQ Questions for Class 11 with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here a collection of multiple choice questions for Limits and Derivatives Class 11 covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

## Limits and Derivatives MCQ Questions for Class 11 with Answers

We have provided below Limits and Derivatives MCQ Questions for Class 11 with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As Limits and Derivatives MCQs in Class 11 Mathematics pdf download can be really scoring for students, you should go through all problems provided below so that you are able to get more marks in your exams.

Question. The value of limx→1 (1+X)6 – 1 / (1+X2) – 1
(a) 20
(b) 21
(c) 15
(d) 17

B

Question. The value of limx→1 X7 – 2X5 + 1 / X3 -3X2 + 2
(a) 0
(b) 1
(c) –1
(d) 3

B

Question. The value of

(a)  8/5
(b) 7/5
(c) 8/5
(d) None of these

C

Question. Find n, if limx→2 Xn – 2n / x-2 = 80, n ∈ N.
(a) 5
(b) 6
(c) 4
(d) 7

A

Question.The value of

(a) 7/3
(b) 7/2
(c) 7/3
(d) 7/2

D

Question. The value of limx→0 sin22x / sin24x
(a) 1/2
(b) 1/4
(c) 1/4
(d) 1/2

C

Question. limx→0 1- Cos2x / x2 is equal to
(a) 2
(b) –2
(c) 3
(d) –3

A

Question. limx→π/6 Sinx / x-π is equal to
(a) 1
(b) 2
(c) –1
(d) –2

C

Question. limx→0 2Sinx – Sin2x / X3 is equal to
(a) –1
(b) 1
(c) 2
(d) –2

B

Question.  limx→π/6 Cot2x -3 / Cosecx -2 is equal to
(a) 3
(b) 4
(c) 2
(d) 1

B

Question. limx→a Sinx – Sina /√x -√a is equal to
(a)  a cos a
(b) a cos a
(c) 2a cos a
(d) 2a cos a

D

Question. limx→0 x2 cosx / 1 -cosx is equal to
(a) 2
(b) 3/2
(c) 3/2
(d) 1

A

Question. limx→0 (1+x)n – 1 is equal to
(a) n
(b) 1
(c) n
(d) 0

A

Question. limx→1 Xm-1 / Xn-1 is equal to
(a) 1
(b) m/n
(c) m/n
(d) m2/n2

B

Question. limΘ→0 1 – cos4Θ / 1 – cos6Θ is equal to
(a) 4/9
(b) 1/2
(c) 1/2
(d) –1

A

Question. If f(x) = 1 + x + x2/2 +….. x100 / 100 then f ‘(1) is equal to
(a) 1 /100
(b) 100
(c) does not exist
(d) 0

B

Question. If f x = x- 4 / 2√x then f’ (1) is
(a) 5/4
(b) 4/5
(c) 1
(d) 0

A

Question.  limx→0 cosecx -cotx /x is equal to
(a) 1 /2
(b) 1
(c) 1/2
(d) 1

C

Question. If y = sinx + cosx / sinx – cosx , then dy/dx at x=0 is
(a) –2
(b) 0
(c) 1/2
(d) does not exist

A

Question. If value of limx→0 √2+x −√2/x is equal to 1/a√2 then ‘a’ equals
(a) 1
(b) 2
(c) 3
(d) 4

B

Question. If value of limx→π/44√2 −(cosx + sin x)5/1−sin 2x is a√2, then the value of ‘a’ is
(a) 2
(b) 3
(c) 4
(d) 5

D

Question. The value of limx→0 cosx/π − x is
(a) π
(b) –π
(c) 1/π
(d) − 1/π

C

Question. limx→0 sin(πcos2x ) /xequals
(a) −π
(b) π
(c) π/2
(d) 1

B

Question. Match the terms given in column-I with the terms given in column-II and choose the correct option from the codes given below.

Codes
A B C D
(a) 4 1 3 2
(b) 1 4 3 2
(c) 4 1 2 3
(d) 4 3 1 2

A

Question. Derivative of e3 log x is
(a) ex
(b) 3x2
(c) 3x
(d) log x

B

Question. The value of

(a) 2
(b) –2
(c) 0
(d) –1

B

Question. As x a, f (x) l, then l is called ………… of the function f (x),
(a) limit
(b) value
(c) absolute value
(d) None of these

A

Question. Derivative of f at x = a is denoted by

D

Question. If f(x) + f (y) = f (x+y/1−xy) for all x, y ∈ R (xy ≠ 1) and limx→0f(x)/x = 2. Then, f ‘(1/√3) is
(a) 3/4
(b) 4/3
(c) 3/6
(d) 3/2

D

Question. The derivative of 1+1/x / 1−1/x is
(a) 2/(1+ x)2
(b) −2/(1−x)2
(c) −1/(1−x)2
(d) 3/(1−x)2

B

STATEMENT TYPE QUESTIONS

Question. Consider the following limits which holds for function f and g:

Which of the above are true ?
(a) Only I
(b) Only II
(c) Only III
(d) All of the above

D

Question. Which of the following is/are true?

(a) Both I and II are true
(b) Only I is true
(c) Only II is true
(d) Both I and II are false

A

Question. Which of the following is/are true?
I. The derivative of f (x) = x3 is x2
II. The derivative of f (x) = 1/x3 is −1/x2
(a) Both I and II are true
(b) Only I is true
(c) Only II is true
(d) Both I and II are false

D

Question. limh→0 (a+h)2sin(a+h)−a2sin a/h is equal to
I. a2 sin a + 2a cos a
II. a2 cos a + 2a sin a
(a) Both I and II are true
(b) Only I is true
(c) Only II is true
(d) Both I and II are false

C

Question. Which of the following is/are true?
I. The derivative of x2 – 2at x = 10 is 18.
II. The derivative of 99x at x = 100 is 99.
III. The derivative of x at x = 1 is 1.
(a) I, II and III are true
(b) I and II are true
(c) II and III are true
(d) I and III are true

C

Question. Consider the function g (x) = | x |, x ≠ 0. Then
I. g (0) is not defined.
II. limx→0 g(x) is not defined.
Which of the following is/are true?
(a) Both I and II are true
(b) Only I is true
(c) Only II is true
(d) Both I and II are false

B

Question. Which of the following is/are true?
I. The derivative of sin (x + a) is cos (x + a), where a is a fixed non-zero constant.
II. The derivative of cosec x cot x is cosec3 x – cot2 x cosec x
(a) Both I and II are true
(b) Only I is true
(c) Only II is true
(d) Borh I and II are false

B

Question. Consider the following derivatives which holds for function u and v.
I. (u ± v)’ = u’ ± v’
II. (uv)’ = uv’ + vu’
III. (u/v)’ = u’v−uv’/v2
Which of the above holds are true ?
(a) Only I
(b) Only II
(c) Only III
(d) All of these