NCERT MCQ CLASS-12 CHAPTER-5 | MATH NCERT MCQ | CONTINUITY AND DIFFERENTIABILITY | EDUGROWN

In This Post we are  providing Chapter-5 Continuity And Differentiability NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON CONTINUITY AND DIFFERENTIABILITY

Question 1.
If f (x) = 2x and g (x) = x22 + 1, then which of the following can be a discontinuous function
(a) f(x) + g(x)
(b) f(x) – g(x)
(c) f(x).g(x)
(d) g(x)f(x)

Answer: (d) g(x)f(x)

Question 2.
The function f(x) = 4−x24x−x3 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

Answer: (a) discontinuous at only one point at x = 0

Question 3.
The set of points where the function f given by f (x) =| 2x – 1| sin x is differentiable is
(a) R
(b) R = {12}
(c) (0, ∞)
(d) None of these

Answer: (b) R = {12}

Question 4.
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) π2 n ∈ Z}
(d) {x – nπ2 n ∈ Z}

Answer: (a) {x = nπ, n ∈ Z}

Question 5.
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 theseAnswer

Answer: (a) continuous everywhere but not differentiable at x = 0

Question 6.
If f(x) = x² sin1x, 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

Answer: (a) 0

Question 7.
If f(x) =

is continuous at x = π2, then
(a) m = 1, n = 0
(b) m = nπ2 + 1
(c) n = mπ2
(d) m = n = π2

Answer: (c) n = mπ2

Question 8.
If y = log(1−x21+x2), then dydx is equal to
(a) 4×31−x4
(b) −4×1−x4
(c) 14−x4
(d) −4×31−x4

Answer: (b) −4×1−x4

Question 9.
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) π2 n ∈ Z
(d) None of these

Answer: (b) f is everywhere continuous but not differentiable at x = nπ, n ∈ Z

Question 10.
If y = sinx+y√ then dydx is equal to
(a) cosx2y−1
(b) cosx1−2y
(c) sinx1−xy
(d) sinx2y−1

Answer: (a) cosx2y−1

Question 11.
The derivative of cos^-1 (2x² – 1) w.r.t cos^-1 x is
(a) 2
(b) −121−x2√
(c) 2x
(d) 1 – x²

Answer: (a) 2

Question 12.
If x = t², y = t³, then d2ydx2
(a) 32
(b) 34t
(c) 32t
(d) 34t

Answer: (b) 34t

Question 13.
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) 32
(d) 13

Answer: (a) 1

Question 14.
For the function f(x) = x + 1x, x ∈ [1, 3] the value of c for mean value theorem is
(a) 1
(b) √3
(c) 2
(d) None of these

Answer: (b) √3

Question 15.
Let f be defined on [-5, 5] as
f(x) = {x ,if x is rational−x, if x is irrational Then f(x) is
(a) continuous at every x except x = 0
(b) discontinuous at every x except x = 0
(c) continuous everywhere
(d) discontinuous everywhere

Answer: (b) discontinuous at every x except x = 0

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