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

1. The value of lim_{x->0} {(x^{3} * cotx)/(1-cosx)} is

(A) 0

(B) 1

(C) -1

(D) 2

**Answer:** 2

2. The expansion of e^{x} is

(A) e^{x} = 1 – x/1! + x^{2} /2! – x^{3} /3! + x^{4} /4! – …………..

(B) e^{x} = 1 + x/1! + x^{2} /2! + x^{3} /3! + x^{4} /4! + …………..

(C) e^{x} = -1 – x/1! – x^{2} /2! – x^{3} /3! – x^{4} /4! – …………..

(D) None of these

**Answer:** e^{x} = 1 + x/1! + x^{2} /2! + x^{3} /3! + x^{4} /4! + ………….

3. The derivative of x + 1/x is

(A) 1 + 1/x

(B) 1 – 1/x

(C) 1 – 1/x^{2}

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

**Answer:** 1 – 1/x^{2}

4. The value of limit Lim_{x->0} {sin (a + x) – sin (a – x)}/x is

(A) 0

(B) 1

(C) 2 cos a

(D) 2 sin a

**Answer:** 2 cos a

5. The expansion of log(1 – x) is

(A) x – x^{2} /2 + x^{3} /3 – ……..

(B) x + x^{2} /2 + x^{3} /3 + ……..

(C) -x + x^{2} /2 – x^{3} /3 + ……..

(D) -x – x^{2} /2 – x^{3} /3 – ……..

**Answer:** -x – x^{2} /2 – x^{3} /3 – ……..

6. Let f(x) = cos x, when x ≥ 0 and f(x) = x + k, when x < 0 Find the value of k given that Lim_{x}_{→}_{0} f(x) exists

(A) 0

(B) 1

(C) -1

(D) None of these

**Answer:** 1

7. The expansion of log(1 – x) is

(A) x – x²/2 + x³/3 – ……..

(B) x + x²/2 + x³/3 + ……..

(C) -x + x²/2 – x³/3 + ……..

(D) -x – x²/2 – x³/3 – ……..

**Answer:** -x – x²/2 – x³/3 – ……..

8. The value of limit Lim_{x}_{→}_{0} {sin (a + x) – sin (a – x)}/x is

(A) 0

(B) 1

(C) 2 cos a

(D) 2 sin a

**Answer:** 2 cos a

9. 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:** 1/(x-1)²

10. The value of the limit Lim_{x}_{→}_{0} {log(1 + ax)}/x is

(A) 0

(B) 1

(C) a

(D) 1/a

**Answer:** 0

11. If f(x) = x × sin(1/x), x ≠ 0, then Lim_{x}_{→}_{0} f(x) is

(A) 1

(B) 0

(C) -1

(D) does not exist

**Answer:** 0

12. If f(x) = (x + 1)/x then df(x)/dx is

(A) 1/x

(B) -1/x

(C) -1/x²

(D) 1/x²

**Answer:** -1/x²

13. The derivative of f(x) = |x| at x = 0 is ____.

(A) -1

(B) 1

(C) 0

(D) does not exist

**Answer:** does not exist

14. If y = 2 sin 3x cos x, then d20y/dx20 is ____.

(A) y^{20}=−2^{40}cos4x−2^{40}cos2x

(B) y^{20}=2^{40}cos4x−2^{40}cos2x

(C) y^{20}=2^{40}cos4x+2^{40}cos2x

(D) y^{20}=2^{40}sin4x+2^{40}sin2x

**Answer:** y^{20}=2^{40}sin4x+2^{40}sin2x

15. The displacement time relating to a speeding vehicle is given by D(t) = 5 t2- 3t + 30. Then, its speed at the end of 5 seconds is given by ____.

(A) 50 units/ sec

(B) 115 units/ sec

(C) 47 units/ sec

(D) 30 units/ sec

**Answer:** 47 units/ sec

16. The point on the curve x^{2} + y^{2} – 2x + 1 = 0, at which the tangent is parallel to Y axis is given by ____.

(A) (0, -1)

(B) (0, 1)

(C) (1, 0)

(D) (-1, 0)

**Answer:** (1, 0)

17. The degree of a polynomial function is 5. Then, the degree of it’s third derivative is ____.

(A) 2

(B) 3

(C) 0

(D) 5

**Answer:** 2

18. The number of points in (1, 2) where f(x) = a^{[x2]},a > 1 is not differentiable is ____.

(A) 0

(B) 2

(C) at least 5 points

(D) 3 points

**Answer:** 2

19. The slope of the normal at the point θ=π/4 of the curve sin θ – cos θ is ____.

(A) 2

(B) -1/2

(C) 1/2

(D) -2

**Answer:** -1/2

20. If f(x) = e^{x }log x, then f'(x) is ____.

(A) xf'(x) – xf(x) = e^{-x}

(B) ex f'(x) – e^{x} f(x) = 1/x

(C) f^{1}(x) = f(x) + e^{x}/x

(D) f'(x) – f(x) = e^{x}

**Answer:** f^{1}(x) = f(x) + e^{x}/x