Class 11 Maths Chapter 13, “Limits and Derivatives,” includes MCQs to help students prepare for their 2025-25 exams. These questions cover key topics from the CBSE syllabus and include explanations for the correct answers.
The MCQs are designed to help students practice, check their solutions, and strengthen their problem-solving and application skills. By solving these questions, students can better understand the concepts and improve their performance in exams.
MCQs for Class 11 Maths Chapter 13 Limits and Derivatives with Answers
1. The limit of \( \lim_{x \to 2} (x^2 – 4) \) is:
- a) 0
- b) 2
- c) 4
- d) -4
Answer: a
2. The value of \( \lim_{x \to 0} \frac{\sin x}{x} \) is:
- a) 0
- b) 1
- c) Infinity
- d) Undefined
Answer: b
3. The limit of \( \lim_{x \to \infty} \frac{1}{x} \) is:
- a) 0
- b) 1
- c) Infinity
- d) Undefined
Answer: a
4. The value of \( \lim_{x \to 0} (1 + x)^n \) is:
- a) 1
- b) \( n \)
- c) \( n + 1 \)
- d) Undefined
Answer: a
5. \( \lim_{x \to \pi} \cos x \) equals:
- a) 1
- b) -1
- c) 0
- d) Undefined
Answer: b
6. \( \lim_{x \to 0} \frac{\tan x}{x} \) equals:
- a) 0
- b) 1
- c) Infinity
- d) Undefined
Answer: b
7. \( \lim_{x \to 0} \frac{1 – \cos x}{x^2} \) equals:
- a) 0
- b) \( \frac{1}{2} \)
- c) 1
- d) Undefined
Answer: b
8. The value of \( \lim_{x \to \infty} \frac{2x + 1}{3x – 4} \) is:
- a) \( \frac{2}{3} \)
- b) 1
- c) Infinity
- d) 0
Answer: a
9. \( \lim_{x \to 0} \frac{\ln(1 + x)}{x} \) equals:
- a) 1
- b) 0
- c) Infinity
- d) Undefined
Answer: a
10. \( \lim_{x \to 0} \frac{\sqrt{1 + x} – 1}{x} \) equals:
- a) 0
- b) \( \frac{1}{2} \)
- c) 1
- d) Undefined
Answer: b
11. A function is continuous at \( x = a \) if:
- a) \( f(a) \) is defined
- b) \( \lim_{x \to a} f(x) = f(a) \)
- c) \( \lim_{x \to a} f(x) \) exists
- d) All of the above
Answer: d
12. The derivative of \( f(x) = x^2 \) is:
- a) \( 2x \)
- b) \( x^2 \)
- c) \( x \)
- d) 2
Answer: a
13. The derivative of \( f(x) = \sin x \) is:
- a) \( \cos x \)
- b) \( \sin x \)
- c) 1
- d) 0
Answer: a
14. The derivative of \( f(x) = e^x \) is:
- a) \( e^x \)
- b) \( x e^x \)
- c) 1
- d) 0
Answer: a
15. The derivative of \( f(x) = \ln x \) is:
- a) \( \frac{1}{x} \)
- b) \( \ln x \)
- c) \( x \ln x \)
- d) 0
Answer: a
16. The slope of the tangent to the curve \( y = x^2 \) at \( x = 1 \) is:
- a) 1
- b) 2
- c) 0
- d) Undefined
Answer: b
17. The equation of the tangent to the curve \( y = x^2 \) at \( x = 1 \) is:
- a) \( y = 2x – 1 \)
- b) \( y = x^2 + 1 \)
- c) \( y = 2x \)
- d) \( y = x – 1 \)
Answer: a
18. The second derivative of \( f(x) = x^3 \) is:
- a) \( 6x \)
- b) \( 3x^2 \)
- c) \( 3 \)
- d) \( 0 \)
Answer: a
19. The derivative of \( f(x) = \tan x \) is:
- a) \( \sec^2 x \)
- b) \( \cos^2 x \)
- c) \( \sin x \)
- d) \( -\sin x \)
Answer: a
20. The derivative of \( f(x) = \cos x \) is:
- a) \( -\sin x \)
- b) \( \cos x \)
- c) \( \sin x \)
- d) 0
Answer: a
