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Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability

  

Continuity and Differentiability Class 12 Maths MCQs Pdf

Continuity And Differentiability Class 12 MCQ Question 1.
The derivative of f(tan x) w.r.t. g(sec x) at x = Ï€4, where f'(1) = 2 and g'(√2) = 4, is
(a) 12
(b) √2
(c) 1
(d) 0
Answer:
(a) 12

Continuity And Differentiability MCQ Class 12 Question 2.
    
Answer:
(c) 23

Differentiation MCQ Class 12 Question 3.
    
Answer:
(b) 1

MCQ On Continuity And Differentiability Class 12 Question 4.
Answer:
(c) 516t6

Class 12 Maths Chapter 5 MCQ Question 5.
    
Answer:
(a) n2y

MCQ Questions On Differentiation Class 12 Question 6.
    
Answer:
(d) ba2sec3θ

MCQ On Differentiation Class 12 Question 7.
    
Answer:
(c) y. (log ab2)2

MCQ Of Continuity And Differentiability Class 12 Question 8.
    
Answer:
(d) 1e2

MCQ Of Differentiation Class 12 Question 9.
    
Answer:
(a) sec3θ

Continuity And Differentiability Class 12 MCQ With Answers Question 10.
    
Answer:
(d) 0

MCQ Of Chapter 5 Maths Class 12 Question 11.
    
Answer:
(b) Ï€6

Question 12.
    
Answer:
(a) (x+y)yxyx+x+y

Question 13.
    
Answer:
(b) 2ax+byy22xybx2y

Question 14.
    
Answer:
(d) 1

Question 15.
    
Answer:
(c) 121x2

Question 16.
    
Answer:
(d) 12

Question 17.
    
Answer:
(c) 2(1x2)(1+x2)|1x2|,x±1,0

Question 18.
    
Answer:
(b) 0

Question 19.
    
Answer:
(c) sec x tan x

Question 20.
    
Answer:
(d) 3e7

Question 21.
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
Answer:
(b) yy” + (y’)2 + 1 = 0

Question 22.
    
Answer:
(c) -9y

Question 23.
The value of c in Rolle’s theorem for the function, f(x) = sin 2x in [0, Ï€2] is
(a) Ï€2
(b) Ï€4
(c) Ï€3
(d) Ï€6
Answer:
(b) Ï€4

Question 24.
The value of c in Rolle’s Theorem for the function f(x) = ex sin x, x ∈ [0, Ï€] is
(a) Ï€6
(b) Ï€4
(c) Ï€2
(d) 3Ï€4
Answer:
(d) 3Ï€4

Question 25.
A value of c for which the Mean value theorem holds for the function f(x) = logex on the interval [1, 3] is
(a) 2log3e
(b) 12loge3
(c) log3e
(d) loge3
Answer:
(a) 2log3e

Question 26.
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
Answer:
(c) 6 – √(13/3)

Question 27.
The value of c in Mean value theorem for the function f(x) = x(x – 2), x ∈ [1, 2] is
(a) 32
(b) 23
(c) 12
(d) 52
Answer:
(a) 32

Question 28.
    
Answer:
(b) ln a + ln b

Question 29.
    
Answer:
(c) 8

Question 30.
The number of discontinuous functions y(x) on [-2, 2] satisfying x2 + y2 = 4 is
(a) 0
(b) 1
(c) 2
(d) >2
Answer:
(a) 0

Question 31.
    
Answer:
(c) 12

Question 32.
    
Answer:
(b) 14

Question 33.
    
Answer:
(c) 1(1+x)2

Question 34.
If y = (1 + x)(1 + x2)(1 + x4)…..(1 + x2n), then the value of dydx at x = 0 is
(a) 0
(b) -1
(c) 1
(d) None of these
Answer:
(c) 1

Question 35.
    
Answer:
(d) 124

Question 36.
If y = ax2 + b, then dydx at x = 2 is equal to
(a) 4a
(b) 3a
(c) 2a
(d) None of these
Answer:
(a) 4a

Question 37.
    
Answer:
(b) 2yy21(x2+x1)(x2+1)2

Question 38.
    
Answer:
(a) 12

Question 39.
    
Answer:
(c) log10ex(yy1)

Question 40.
    
Answer:
(d) None of these

Question 41.
    
Answer:
(d) [latex]yx[/latex]

Question 42.
If Rolle’s theorem holds for the function f(x) = x3 + bx2 + ax + 5 on [1, 3] with c = (2 + 13), find the value of a and b.
(a) a = 11, b = -6
(b) a = 10, b = 6
(c) a = -11, b = 6
(d) a = 11, b = 6
Answer:
(a) a = 11, b = -6

Question 43.
If y = (tan x)sin x, then dydx is equal to
(a) sec x + cos x
(b) sec x + log tan x
(c) (tan x)sin x
(d) None of these
Answer:
(d) None of these

Question 44.
    
Answer:
(d) logx

Question 45.
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)!
Answer:
(b) (-1)(n – 1)!

Question 46.
If xy . yx = 16, then the value of dydx at (2, 2) is
(a) -1
(b) 0
(c) 1
(d) none of these
Answer:
(a) -1

Question 47.
    
Answer:
(c) 

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