NCERT Solutions : Class 12 Maths with Answers MCQs Chapter 5

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

NCERT Books are textbooks which are issued & distributed by the National Council of Educational Research and Training (NCERT). NCERT books are important for the schooling system. NCERT Books are available in E-Books. If you are searching for MCQs (Multiple Choice Questions) with Answers of for NCERT Class 12 Mathematics then you have came to right way. CBSE students can also solve NCERT Class 12 Maths 5 Continuity and Differentiability PDF Download w their preparation level. MCQs are Prepared Based on Latest Exam Patterns. MCQs Questions with Answers for Class 12 Maths Chapter 5 Continuity and Differentiability are prepared to help students to understand concepts very well. Objective wise Questions 12th class Maths Chapter 5 Continuity and Differentiability wise PDF over here are available in the following links. Score maximum marks in the exam.

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.

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