CBSE Class 12 Continuity and Differentiability Multiple Choice Questions with Answers. MCQ Questions Class 12 Continuity and Differentiability with Answers Is Prepared Based on Latest Exam Pattern. Students can solve NCERT MCQ questions Class 12 Continuity and Differentiability with Answers to know their preparation level.
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MCQ Questions Class 12 Continuity and Differentiability with Answers - Set - 3
Question 1:
If y = (1 + x) (1 + x²) (1 + x4) …….. (1 + x2n), then the value of dy/dx at x = 0 is
(a) 0
(b) -1
(c) 1
(d) None of these
Correct Answer – (C)
Question 2:
For the function f(x) = x + (1/x), x ∈ [1, 3] the value of c for mean value theorem is
(a) 1
(b) √3
(c) 2
(d) None of these
Correct Answer – (B)
Question 3:
Let f(x) = |sin x| Then
(a) f is everywhere differentiable
(b) f is everywhere continuous but not differentiable at x = nπ, n ∈ Z
(c) f is everywhere continuous but no differentiable at x = (2n + 1) (π/2) n ∈ Z
(d) None of these
Correct Answer – (B)
Question 4:
The function f(x) = e|x| is
(a) continuous everywhere but not differentiable at x = 0
(b) continuous and differentiable everywhere
(c) not continuous at x = 0
(d) None of these
Correct Answer – (A)
Question 5:
The set of points where the function f given by f (x) =| 2x – 1| sin x is differentiable is
(a) R
(b) R = (1/2)
(c) (0, ∞)
(d) None of these
Correct Answer – (B)
MCQ Questions Class 12 Continuity and Differentiability With Answers
Question 6:
If y = ax² + b, then dy/dx at x = 2 is equal to ax
(a) 4a
(b) 3a
(c) 2a
(d) None of these
Correct Answer – (A)
Question 7:
The value of c in Rolle’s theorem for the function f(x) = x³ – 3x in the interval [o, √3] is
(a) 1
(b) -1
(c) 3/2
(d) 1/3
Correct Answer – (A)
Question 8:
If f(x) = x² sin (1/x), where x ≠ 0, then the value of the function f(x) at x = 0, so that the function is continuous at x = 0 is
(a) 0
(b) -1
(c) 1
(d) None of these
Correct Answer – (A)
Question 9:
The function f(x) = cot x is discontinuous on the set
(a) {x = nπ, n ∈ Z}
(b) {x = 2nπ, n ∈ Z}
(c) {x = (2n + 1) (π/2) n ∈ Z}
(d) {x – (nπ/2) n ∈ Z}
Correct Answer – (A)
Question 10:
The function f(x) = (4−x2)/(4x−x2) is
(a) discontinuous at only one point at x = 0
(b) discontinuous at exactly two points
(c) discontinuous at exactly three points
(d) None of these
Correct Answer – (A)
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