These Limits And Derivatives Class 11 NCERT Questions and Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Limits And Derivatives Class 11 NCERT Questions and Answers will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.

## Limits And Derivatives Class 11 NCERT Questions and Answers

1. Lim_{y}_{→}_{∞} {(x + 6)/(x + 1)}^{(x+4)} equals

(A) e

(B) e³

(C) e^{5}

(D) e^{6}

**Answer:** e^{5}

2. The value of Lim_{n}_{→}_{∞} {1² + 2² + 3² + …… + n²}/n³ is

(A) 0

(B) 1

(C) -1

(D) n

**Answer:** 0

3. The value of Lim_{x}_{→}_{0} (1/x) × sin^{-1} {2x/(1 + x²) is

(A) 0

(B) 1

(C) 2

(D) -2

**Answer:** 2

4. Lim_{x}_{→}_{0} sin (ax)/bx is

(A) 0

(B) v

(C) a/b

(D) b/a

**Answer:** a/b

5. Lim_{x}_{→}_{0} log(1 – x) is equals to

(A) 0

(B) 1

(C) 1/2

(D) None of these

**Answer:** 0

6. Lim_{x->0} {(a^{x} – b^{x} )/ x} is equal to

(A) log a

(B) log b

(C) log (a/b)

(D) log (a*b)

**Answer:** log (a/b)

7. The value of Lim_{x->∞} (sin x/x) is

(A) 0

(B) 1

(C) -1

(D) None of these

**Answer:** 0

8. Lim_{x->-1} [1 + x + x^{2} + ……….+ x^{10} ] is

(A) 0

(B) 1

(C) -1

(D) 2

**Answer:** 1

9. The value of Lim_{x->a} (a*sin x – x*sin a)/(ax^{2} – xa^{2} ) is

(A) (a*cos a + sin a)/a^{2}

(B) (a*cos a – sin a)/a^{2}

(C) (a*cos a + sin a)/a

(D) (a*cos a – sin a)/a

**Answer:** (a*cos a – sin a)/a^{2}

10. The value of Lim_{x->0} (sin ax/sin bx) is

(A) a+b

(B) a-b

(C) a*b

(D) a/b

**Answer:** a/b

11. The value of Lim_{x->0} (1 + x)^{n} is equal to

(A) 0

(B) 1

(C) 1/2

(D) None of these

**Answer:** 1

12. The value of the limit Lim_{n->0} (1 + an)b/n is

(A) e^{a}

(B) e^{b}

(C) e^{ab}

(D) e^{a/b}

**Answer:** e^{ab}

13. The expansion of a^{x} is

(A) a^{x} = 1 + x/1! * (log a) + x^{2} /2! * (log a)^{2} + x^{3} /3! * (log a)^{3} + ………..

(B) a^{x} = 1 – x/1! * (log a) + x^{2} /2! * (log a)^{2} – x^{3} /3! * (log a)^{3} + ………..

(C) a^{x} = 1 + x/1 * (log a) + x^{2} /2 * (log a)^{2} + x^{3} /3 * (log a)^{3} + ………..

(D) a^{x} = 1 – x/1 * (log a) + x^{2} /2 * (log a)^{2} – x^{3} /3 * (log a)^{3} + ………..

**Answer:** a^{x} = 1 + x/1! * (log a) + x^{2} /2! * (log a)^{2} + x^{3} /3! * (log a)^{3} + ………..

14. Lim_{x->∞} {(x + 6)/(x + 1)}^{(x + 4)} equals

(A) e

(B) e^{3}

(C) e^{5}

(D) e^{6}

**Answer:** e^{5}

15. Lim_{x->0} (1 – cos x)/x is

(A) 0

(B) 1

(C) 1/2

(D) Limit does not exist

**Answer:** 0

16. Lim_{x->0} sin (ax)/bx is

(A) 0

(B) 1

(C) a/b

(D) b/a

**Answer:** a/b

17. Then value of Lim_{x->0} {e^{x} – (1 + x)}/x^{2} is

(A) 0

(B) 2

(C) 1/2

(D) e

**Answer:** 1/2

18. The value of the limit Lim_{n->∞} (1 + 1/n)^{n+5} is

(A) 0

(B) 1

(C) e

(D) 1/e

**Answer:** e

19. The value of the limit Lim_{x->0} {log(1 + ax)}/x is

(A) 0

(B) 1

(C) a

(D) 1/a

**Answer:** a

20. The derivative of [1+(1/x)] /[1-(1/x)] is

(A) 1/(x-1)^{2}

(B) -1/(x-1)^{2}

(C) 2/(x-1)^{2}

(D) -2/(x-1)^{2}

**Answer:** -2/(x-1)^{2}