These Limits And Derivatives Class 11 Questions and Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Limits And Derivatives Class 11 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 Questions and Answers

1. The displacement of a particle describing a non – linear motion is given by s = (1/6) t^{3} – 8t. Then, the acceleration at the time when velocity vanishes is ____.

(A) 6 units/ s^{2}

(B) 0

(C) 4 units/ s^{2}

(D) 16 units/ s^{2}

**Answer:** 4 units/ s^{2}

2. The mathematical expression x→a means_____

(A) x = a

(B) x ≠ a

(C) x is approaching a

(D) x is greater than a

**Answer:** x is approaching a

3. In the curve y^{2 }= x^{3}, the slope of the tangent at (4, 8) is ____.

(A) 4

(B) 8

(C) 1/2

(D) 3

**Answer:** 3

4. If f(x) = e^{mx} + e^{nx}, then the second derivative f'(x) is ____.

(A) m^{2}e^{mx} + n^{2}e^{nx}

(B) me^{mx} + ne^{nx}

(C) e^{mx }+ e^{nx}

(D) e^{mx} – e^{nx}

**Answer:** m^{2}e^{mx} + n^{2}e^{nx}

5. The deleted neighborhood of a is ____.

(A) (a – δ, a] i.e. left neighborhood

(B) [a, a + δ) i.e. right neighborhood

(C) a sphere of radius ‘a’ with the point ‘a’ deleted

(D) (a – δ, a + δ) – {a}

**Answer:** (a – δ, a + δ) – {a}

6. If y = tan x + sec x, then d^{2}y/dx^{2} is ____.

(A) 0

(B) 1

(C) y

(D) (dy/dx)y

**Answer:** (dy/dx)y

7. If y = x^{2} sin 2x, then the first derivative is ____.

(A) 2(x cos 2x + sin 2x)

(B) (x cos 2x + sin 2x)

(C) 2x (x cos 2x + sin 2x)

(D) x^{2} (x cos 2x + sin 2x)

**Answer:** 2x (x cos 2x + sin 2x)

8. The differential of (sin x + cos x)^{2}is

(A) 0

(B) cos x – sin x

(C) 2 cos 2x

(D) cos^{2} x – sin^{2} x

**Answer:** 2 cos 2x

9. In a real number line, the neighbourhood of positive real number ‘a’ with a very small radius δ>0 will be ____.

(A) (a – δ, a]

(B) [a, a + δ)

(C) (a – δ, a + δ)

(D) a sphere of radius a

**Answer:** (a – δ, a + δ)

10. If fx = 1 + x + x^{2}/2+x^{3}/3, then f’ (x) is ____.

(A) 1/1 – x^{2}

(B) 1+ x + x^{2}

(C) 1 + x

(D) 1 – x

**Answer:** 1+ x + x^{2}

11. The ratio of the rate of change of area and the rate of change of radius with respect to given circle is ____.

(A) radius of the circle

(B) perimeter of the circle

(C) diameter of the circle

(D) area of the circle

**Answer:** perimeter of the circle

12. The limit of a function exists only if the left hand limit and the right hand limit coincide with each other.

(A) True

(B) False

**Answer:** True

13. The value of Lim_{n}_{→}_{∞} (sin x/x) is

(A) 0

(B) 1

(C) -1

(D) None of these

**Answer:** 0

14. The value of lim_{y}_{→}_{0} {(x + y) × sec (x + y) – x × sec x}/y is

(A) x × tan x × sec x

(B) x × tan x × sec x + x × sec x

(C) tan x × sec x + sec x

(D) x × tan x × sec x + sec x

**Answer:** x × tan x × sec x + sec x

15. The value of Lim_{x}_{→}_{01} (1/x) × sin^{-1} {2x/(1 + x²) is

(A) 0

(B) 1

(C) 2

(D) -2

**Answer:** 2

16. The value of Lim_{x}_{→}_{0} ax is

(A) 0

(B) 1

(C) 1/2

(D) 3/2

**Answer:** 1

17. Lim_{x}_{→}_{0} (e^{x²} – cos x)/x² is equals to

(A) 0

(B) 1

(C) 2/3

(D) 3/2

**Answer:** 3/2

18. The value of the limit Lim_{x}_{→}_{0} (cos x)^{cot2 x} is

(A) 1

(B) e

(C) e^{1/2}

(D) e^{-1/2}

**Answer:** e^{-1/2}

19. 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)

20. Lim_{x}_{→}_{-1} [1 + x + x² + ……….+ x^{10}] is

(A) 0

(B) 1

(C) -1

(D) 2

**Answer:** 1