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 Bihar Board 12th Maths Objective Answers Chapter 5 Continuity and Differentiability

Bihar Board 12th Maths Objective Answers Chapter 5 Continuity and Differentiability

Question 1.

Answer:
(b) ln a + ln b

Question 2.

Answer:
(c) 8

Question 3.
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 4.

Answer:
(c) −12

Question 5.

Answer:
(c) −1(1+x)2

Question 7.
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 8.

Answer:
(d) 124√

Question 9.
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 10.

Answer:
(b) −π6−−√

Question 12.

Answer:
(a) (x+y)√−y−x√y−x√+x+y√

Question 13.

Answer:
(b) 2ax+by−y22xy−bx−2y

Question 14.

Answer:
(c) 121−x2√

Question 16.

Answer:
(c) 2(1−x2)(1+x2)|1−x2|,x≠±1,0

Question 18.

Answer:
(b) 0

Question 19.

Answer:
(d) 3e7

Question 21.

Answer:
(c) log10ex(yy−1)

Question 23.

Answer:
(d) [latex]yx[/latex]

Question 25.
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 26.
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 27.

Answer:
(d) logx

Question 28.
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 29.
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 30.

Answer:
(c) y1−y

Question 31.
The derivative of f(tan x) w.r.t. g(sec x) at x = π4, where f'(1) = 2 and g'(√2) = 4, is
(a) 12√
(b) √2
(c) 1
(d) 0
Answer:
(a) 12√

Question 32.

Answer:
(c) 23

Question 33.

Answer:
(c) 516t6

Question 35.

Answer:
(d) −ba2sec3θ

Question 37.

Answer:
(d) −1e2

Question 39.

Answer:
(d) 0

Question 41.
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 42.

Answer:
(c) -9y

Question 43.
The value of c in Rolle’s theorem for the function, f(x) = sin 2x in [0, π2] is
(a) π2
(b) π4
(c) π3
(d) π6
Answer:
(b) π4

Question 44.
The value of c in Rolle’s Theorem for the function f(x) = ex sin x, x ∈ [0, π] is
(a) π6
(b) π4
(c) π2
(d) 3π4
Answer:
(d) 3π4

Question 45.
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 46.
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 47.
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