**MCQs Questions for Class 12 Maths Chapter 5 Continuity and Differentiability**

In this 21^{st} century, Multiple Choice Questions (MCQs) play a vital role to prepare for a competitive examination. CBSE board has also brought a major change in its board exam patterns.

In most of the competitive examinations, only MCQ questions are asked. So, for getting ready for the competitive examinations, we have to practice for MCQ questions to solve. It strengthens the critical thinking and problem solving skills.

In future, if you want to prepare for competitive examination and to crack it, then you should more focus on the MCQ questions. Thus, from the board examinations point of view and competitive examinations point of view, you should practice more on multiple choice questions.

Thus, let’s solve these MCQs Questions to make our foundation very strong.

**MCQs Questions for Class 12 Maths Chapter 5 Continuity and
Differentiability**

**1.** The derivative of f(tan
x) with respect to g(sec x) at x = Ï€/4, where f'(1) = 2 and g'(√2) = 4, is

(a) 1

(b) √2

(c) 1/√2

(d) 0

**Answer: c**

** **

**2.** What is the
mathematical expression for the definition of continuity?

(a) lim_{x→c }f(x) = f(c) ∀ c ∈ a

(b) lim_{x→c }f(x) = f(c) ∀ c ∈ (a, b)

(c) lim_{x→c }f(x) = f(c) ∀ c ∈ b

(d) lim_{x→a }f(x) = f(c) ∀ c ∈ (a, b)

**Answer:**** b**

**3. **If f(x) = 2x and g(x) = x^{2}/2 + 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**

**4.** 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

**Answer:**** b**

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

(a) 6 ±
√(13/3)

(b) 6 +
√(13/3)

(c) 6 –
√(13/3)

(d) None of
these

**Answer:**** c**

**6. **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

**Answer:**** a**

**7. **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

**Answer:**** c**

**8. **If f(x) = |sin x|, then

(a) f is
everywhere differentiable

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

(c) f is
everywhere continuous but no differentiable at x = (2n + 1) Ï€/2, n ∈ Z

(d) None of
these

**Answer:**** b**

**9. **The derivative of f(x) = sin(x^{2}) is

(a) -sin (x^{2})

(b) 2x cos(x^{2})

(c) -2x cos(x^{2})

(d) -2x sin(x^{2})

**Answer:**** b**

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

(a) 1/3

(b) -1

(c) 3/2

(d) 1

**Answer:**** d**

**11. **The differentiation of cos (sin x) is

(a) sin
(sin x).cos x

(b) -sin (sin
x).cos x

(c) sin
(sin x)

(d) sin
(cos x).cos x

**Answer:**** b**

**12. **If y = ax² + b, then y’ at x = 2 is equal to

(a) 4a

(b) 3a

(c) 2a

(d) None of
these

**Answer:**** a**

**13. **The differentiation of 8e^{-x }+ 2e^{x} with respect to x is

(a) 2e^{-x }+ 8e^{x}

(b) 2e^{x }+ 8e^{-x}

(c) 2e^{-x }- 8e^{x}

(d) 2e^{x }- 8e^{-x}^{}

**Answer:**** d**

**14. **If sin y + e^{-x cos y} = e, then y’ at (1, Ï€) is equal to

(a) sin y

(b) -x cos
y

(c) e

(d) sin y –
x cos y

**Answer:**** c**

**15. **Find dy/dx, if x = 2t^{2} and y = 6t^{6}.

(a) -9t^{4}

(b) 9t^{4}

(c) t^{4}

(d) 9t^{3}^{}

**Answer:**** b**

**16. **Find the second order derivative of y = e^{2x2}.

(a) 4e^{2x2} (4x^{2 }+ 3)

(b) 4e^{2x2} (4x^{2 }- 1)

(c) 4e^{2x2} (4x^{2 }+ 1)

(d) e^{2x2} (4x^{2 }+ 1)

**Answer:**** c**