# NCERT Solutions : Class 12 Maths with Answers MCQs Chapter 5

## 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

(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°

(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

(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}}

(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.