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 lim_x→1 (1+X)⁶ – 1 / (1+X²) – 1     
(a) 20
(b) 21
(c) 15
(d) 17

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

Question. The value of

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

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

Question.The value of

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

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

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

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

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

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

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

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

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

Question. lim_x→1 X^m-1 / Xⁿ-1 is equal to     
(a) 1
(b) m/n
(c) m/n
(d) m²/n²

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

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

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

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

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

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

Question. If value of lim_x→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

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

Question. lim_x→0 sin(πcos²x ) /x² equals
(a) −π
(b) π
(c) π/2
(d) 1

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

Question. Derivative of e^{3 log x} is
(a) e^x
(b) 3x²
(c) 3x
(d) log x

Question. The value of

(a) 2
(b) –2
(c) 0
(d) –1

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

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

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

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

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

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

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

Question. lim_h→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

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

Question. Consider the function g (x) = | x |, x ≠ 0. Then
I. g (0) is not defined.
II. lim_x→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

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

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

Limits Class 11 MCQ has been gathered for students to rehearse. Students can prepare these Limits MCQ Class 11 Questions with Answers. Each question has four choices with answers. Firstly, Solve all these Questions and check your answer with the right answer. If your answers do not match with the right answer, Don’t worry try again because You need to prepare daily to score higher marks in the Class 11 Maths Exam.

We hope you liked MCQ Questions for Class 11 Limits and Derivatives provided above. If you have any questions, please post them in the comments box below. Our teachers will provide a response.

We hope this Limits and Derivatives Class 11 MCQ shared with you will help you to get good marks in your exam. We have also other study material like NCERT Solutions, NCERT Book, Exam Question, and simpler paper of Class 12. If You want to score higher in your exam, So practice all this study material and if you have any problem in regard to the MCQ on Limits Class 11 then, write it in the comment box and we will guide you as much as possible.