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Limits and Derivatives MCQs

Class 11 Maths — questions with answers and worked explanations.

20 free questions Class 11 Maths Answers + explanations No sign-up

These questions are drawn from the Pariksha Sutra question bank for Limits and Derivatives, part of the Class 11 Maths syllabus. Each one shows the correct answer and, where a method helps, the working behind it.

Read the question, decide your answer before looking, then check the explanation — that is what turns practice into marks. If a question catches you out, the explanation is the part worth re-reading.

Questions

Question 1
Evaluate lim x->3 (2x + 1).
  1. 5
  2. 6
  3. 8
  4. 7
Answer: 7
Question 2
Evaluate lim x->0 sin(3x)/sin(5x).
  1. 5/3
  2. 3/5
  3. 1
  4. 0
Answer: 3/5
Question 3
Evaluate lim x->0 (1 - cos x)/x.
  1. 1/2
  2. 0
  3. -1
  4. 1
Answer: 0
Question 4
Find d/dx (2x^3 - 3x).
  1. 6x^2
  2. 6x^2 - 3
  3. 2x^2 - 3
  4. 6x - 3
Answer: 6x^2 - 3
Question 5
Find d/dx of (x^2 + 1)(x + 1).
  1. 3x^2 + 2x + 1
  2. 3x^2 + 1
  3. 3x^2 + 2x
  4. 2x + 1
Answer: 3x^2 + 2x + 1
Question 6
Evaluate lim x->0 sin(5x)/x.
  1. 5
  2. 1
  3. 5x
  4. 0
Answer: 5
Question 7
Evaluate lim x->0 sin(x)/(2x).
  1. 1/2
  2. 0
  3. 1
  4. 2
Answer: 1/2
Question 8
Evaluate lim x->1 (x^2 - 1)/(x - 1).
  1. 1
  2. 0
  3. 2
  4. -2
Answer: 2
Question 9
Evaluate lim x->0 sin(7x)/sin(4x).
  1. 7/4
  2. 7
  3. 1
  4. 4/7
Answer: 7/4
Question 10
Find d/dx (sin x cos x).
  1. sin 2x
  2. 1
  3. cos 2x
  4. -cos 2x
Answer: cos 2x
Question 11
Evaluate lim x->2 (x^2 - 4)/(x - 2).
  1. 6
  2. 0
  3. 2
  4. 4
Answer: 4
Question 12
Evaluate lim x->2 (x^2 - 5x + 6)/(x - 2).
  1. 1
  2. -1
  3. 0
  4. 5
Answer: -1
Question 13
Find d/dx (1/x).
  1. -1/x
  2. ln x
  3. 1/x^2
  4. -1/x^2
Answer: -1/x^2
Question 14
Evaluate lim x->0 (x^2 + 5x)/x.
  1. 1
  2. 5
  3. 0
  4. infinity
Answer: 5
Question 15
Evaluate lim x->0 sin(x)/x.
  1. 0
  2. x
  3. infinity
  4. 1
Answer: 1
Question 16
Find d/dx (x^5).
  1. 5x^4
  2. 5x^5
  3. x^4
  4. 4x^5
Answer: 5x^4
Question 17
Find d/dx (sqrt(x)).
  1. 1/(2 sqrt(x))
  2. 2 sqrt(x)
  3. 1/sqrt(x)
  4. sqrt(x)/2
Answer: 1/(2 sqrt(x))
Question 18
Evaluate lim x->0 cos x.
  1. 1
  2. -1
  3. infinity
  4. 0
Answer: 1
Question 19
By first principle, the derivative of f(x) = 7x^2 is:
  1. 7x
  2. 14x
  3. 7x^2
  4. 14
Answer: 14x
Question 20
Evaluate lim x->0 (1 - cos x)/x^2.
  1. 2
  2. 0
  3. 1
  4. 1/2
Answer: 1/2

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