## NCERT Solutions for Class 12 Maths Chapter 5 MCQ’s with Answers

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## NCERT **Maths MCQs for Class 12 Question and Answers Chapter 5 Continuity and Differentiability PDF**

### 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

Option b – yy” + (y’)2 + 1 = 0

### Q2. The number of discontinuous functions y(x) on [-2, 2] satisfying x2 + y2 = 4 is

(a) 0

(b) 1

(c) 2

(d) >2

Option a – 0

### Q3. 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)!

Option b – (-1)(n – 1)!

### Q4. Derivative of cot x° with respect to x is

(a) cosec x°

(b) cosec x° cot x°

(c) -1° cosec2 x°

(d) -1° cosec x° cot x°

Option c – -1° cosec2 x°

### Q5. Write the number of points where f(x) = |x + 2| + |x – 3| is not differentiable.

(a) 2

(b) 3

(c) 0

(d) 1

Option a – 2

### Q6. A function /is said to be continuous for x ∈ R, if

(a) it is continuous at x = 0

(b) differentiable at x = 0

(c) continuous at two points

(d) differentiable for x ∈ R

Option d – differentiable for x ∈ R

### Q7. If f(x) = ex and g(x) = loge x, then (gof)’ (x) is

(a) 0

(b) 1

(c) e

(d) 1 + e

Option b – 1

### Q8. The derivative of sin x with respect to log x is

(a) cos x

(b) x cos x

(c)1/xcos x

Option b – x cos x

### Q9. A function f(x) = sin x + cos x is continuous function. State true or false.

Option – True, as sum of two continuous functions is a continuous function.

### Q10. Give an example of a function which is continuous but not differentiable at exactly two points.

Option – We know function f(x)=|x – a| is continuous at x = a but not differentiable at x = a. ∴ functions |x| and |x – 1| are continuous but not differentiable at x = 0 and 1. ∴ function is h(x) = |x| + |x – 1|.

### Q11. If y = sin 3x, find y2

Option – y = sin 3x y1 = 3 cos 3x y2 = -9 sin 3x.

### Q12. Verify the Rolle’s Theorem for the function f(x) = x² in the inverval [-1, 1].

Option – Function f(x) = x² is continuous in [-1,1 ], differentiable in ( -1, 1) and f(-1) = f(1). Hence, Rolle’s Theorem verified. ⇒ f'(c) = 0 ⇒ 2c = 0 ⇒ c = 0 for c ∈ (-1, 1)

### Q13.Verify the Rolle’s Theorem for die functiony(x) = |x| in the inverval [-1, 1].

Option – Not verified, as /(x) =|x| is not derivable at x = 0.

### Q14. 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

Option a – continuous everywhere but not differentiable at x = 0

### Q15. 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

Option a – 0

### Q16. 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) n ∈ Z

(d) None of these

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

### Q17. 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

Option a – aex – be-x

### Q18. Let f (x) = ex, g (x) = sin-1 x and h (x) = f |g(x)|, then \frac{h'(x)}{h(x)} is equal to

(a) esin-1x

(b) \frac{1}{\sqrt{1-x^2}}

(c) sin-1x

(d) \frac{1}{(1-x^2)}

Option b – \frac{1}{\sqrt{1-x^2}}

### Q19. If y = e3x+n, then the value of \frac{dy}{dx}|x=0 is

(a) 1

(b) 0

(c) -1

(d) 3e7

Option d – 3e7

### Q20. If x = exp {tan-1(\frac{y-x^2}{x^2})}, then \frac{dy}{dx} equals

(a) 2x [1 + tan (log x)] + x sec² (log x)

(b) x [1 + tan (log x)] + sec² (log x)

(c) 2x [1 + tan (logx)] + x² sec² (log x)

(d) 2x [1 + tan (log x)] + sec² (log x)

Option a – 2x [1 + tan (log x)] + x sec² (log x)

### Q21. If f(x) = tan-1(\sqrt{\frac{1+sinx}{1-sinx}}), 0 ≤ x ≤ \frac{π}{2}, then f'(\frac{π}{6}) is

(a) –\frac{1}{4}

(b) –\frac{1}{2}

(c) \frac{1}{4}

(d) \frac{1}{2}

Option d – \frac{1}{2}

### Q22. Derivative of the function f (x) = log5 (Iog,x), x > 7 is

(a) \frac{1}{x(log5)(log7)(log7-x)}

(b) \frac{1}{x(log5)(log7)}

(c) \frac{1}{x(logx)}

(d) None of these

Option a – \frac{1}{x(log5)(log7)(log7-x)}

### Q23. If y = log [ex(\frac{x-1}{x-2})^{1/2}], then \frac{dy}{dx} is equal to

(a) 7

(b) \frac{3}{x-2}

(c) \frac{3}{(x-1)}

(d) None of these

Option d – None of these

### Q24. If xx = yy, then \frac{dy}{dx} is equal to

(a) –\frac{y}{x}

(b) –\frac{x}{y}

(c) 1 + log (\frac{x}{y} )

(d) \frac{1+logx}{1+logy}

Option d – \frac{1+logx}{1+logy}

### Q25. 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)!

Option b – (-1) (n – 1)!

We hope that the given** NCERT MCQ** **Questions for Class 12 Mathematics Chapter 5 Continuity and Differentiability** **Free Pdf download** will help you in gaining knowledge on the subject.