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 limx->0 {(x3 * cotx)/(1-cosx)} is
(A) 0
(B) 1
(C) -1
(D) 2
Answer: 2
2. The expansion of ex is
(A) ex = 1 – x/1! + x2 /2! – x3 /3! + x4 /4! – …………..
(B) ex = 1 + x/1! + x2 /2! + x3 /3! + x4 /4! + …………..
(C) ex = -1 – x/1! – x2 /2! – x3 /3! – x4 /4! – …………..
(D) None of these
Answer: ex = 1 + x/1! + x2 /2! + x3 /3! + x4 /4! + ………….
3. The derivative of x + 1/x is
(A) 1 + 1/x
(B) 1 – 1/x
(C) 1 – 1/x2
(D) 1 + 1/x2
Answer: 1 – 1/x2
4. The value of limit Limx->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 – 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 – ……..
6. Let f(x) = cos x, when x ≥ 0 and f(x) = x + k, when x < 0 Find the value of k given that Limx→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 Limx→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 Limx→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 Limx→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) y20=−240cos4x−240cos2x
(B) y20=240cos4x−240cos2x
(C) y20=240cos4x+240cos2x
(D) y20=240sin4x+240sin2x
Answer: y20=240sin4x+240sin2x
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 x2 + y2 – 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) = ex log x, then f'(x) is ____.
(A) xf'(x) – xf(x) = e-x
(B) ex f'(x) – ex f(x) = 1/x
(C) f1(x) = f(x) + ex/x
(D) f'(x) – f(x) = ex
Answer: f1(x) = f(x) + ex/x
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