Continuity and Differentiability MCQ Questions for Class 12 Maths Chapter 5 with Answers

Find here the NCERT chapter-wise Multiple Choice Questions from Class 12 Mathematics book Chapter 5 Continuity and Differentiability with Answers Pdf free download. This may assist you to understand and check your knowledge about the chapters. Students also can take a free test of the Multiple Choice Questions of Continuity and Differentiability. Each question has four options followed by the right answer. These MCQ Questions are selected supported by the newest exam pattern as announced by CBSE.

MCQ Questions for Class 12 Mathematics with Answers

Q1. If x² + y² = 1, then

(a) yy” – (2y’)² + 1 = 0
(b) yy” + (y’)² + 1 = 0
(c) yy” – (y’)² – 1 = 0
(d) yy” + (2y’)² + 1 = 0

(b) yy” + (y’)² + 1 = 0

Q2. 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

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

Q3. The function f(x) = [x], where [x] denotes the greatest integer function, is continuous at:

(a) 4
(b)-2
(c) 1
(d) 1.5.

(d) 1.5.

Q4. The value of c in mean value theorem for the function f(x) = (x – 3)(x – 6)(x – 9) in [3, 5] is

(a) 6 ± √(13/3)
(b) 6 + √(13/3)
(c) 6 – √(13/3)
(d) None of these

(c) 6 – √(13/3)

Q5. 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

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

Q6. The value of ‘c’ in Rolle’s Theorem for the function f(x) = x³ – 3x in the interval [0, √3] is

(a) 1
(b) -1
(c) 3/2
(d) 1/3

(a) 1

Q7. The number of discontinuous functions y(x) on [-2, 2] satisfying x² + y² = 4 is

(a) 0
(b) 1
(c) 2
(d) >2

(a) 0

Q8. If y = aex+ be-x + c Where a, b, c are parameters, they y’ is equal to

(a) aex – be-x
(b) aex + be-x
(c) -(aex + be-x)
(d) aex – bex

(a)

Q9. Let f : (- 1, 1) → R be a differentiable function with f(0) = – 1 and f'(0) = 1.
Let g(x) = [f (2f(x) + 2)]². Then g'(0) =

(a) 4
(b) -4
(c) log 2
(d) -log 2.

(b) -4

Q10. The derivative of y = (1 – x)(2 – x) ….. (n – x) at x = 1 is equal to

(a) 0
(b) (-1)(n – 1)!
(c) n! – 1
(d) (-1)n-1(n – 1)!

(b) (-1)(n – 1)!

Q11. For x ∈ R, f(x) = |log 2 – sin x| and g(x) =f(f(x)), then

(a) g is not differentiable at x = 0
(b) g'(0) = cos (log 2)
(c) g'(0) = -cos (log 2)
(d) g is differentiable at x = 0 and g'(0) = – sin (log 2).

(b) g'(0) = cos (log 2)

Q12. What are the kinds of discontinuity?

(a) Minor and major kinds
(b) Increment and decrement kinds
(c) First and second kinds
(d) Zero and one kinds

(c) First and second kinds

Q13. What is/are conditions for a function to be continuous on (a,b)?

(a) The function is continuous at each point of (a,b)
(b) The function is right continuous
(c) The function is left continuous
(d) Right continuous, left continuous, continuous at each point of (a,b)

(d) Right continuous, left continuous, continuous at each point of (a,b)

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MCQ Questions for Class 12 Mathematics Chapter wise with Answers

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