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

Bihar Board 12th Maths Objective Questions and Answers

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) \(-\frac{1}{2}\)

Question 5.

Answer:
(b) \(\frac{1}{4}\)

Question 6.

Answer:
(c) \(\frac{-1}{(1+x)^{2}}\)

Question 7.
If y = (1 + x)(1 + x²)(1 + x⁴)…..(1 + x²ⁿ), then the value of \(\frac{d y}{d x}\) at x = 0 is
(a) 0
(b) -1
(c) 1
(d) None of these
Answer:
(c) 1

Question 8.

Answer:
(d) \(\frac{1}{\sqrt{24}}\)

Question 9.
If y = ax² + b, then \(\frac{d y}{d x}\) at x = 2 is equal to
(a) 4a
(b) 3a
(c) 2a
(d) None of these
Answer:
(a) 4a

Question 10.

Answer:
(b) \(\frac{2 y \sqrt{y^{2}-1}\left(x^{2}+x-1\right)}{\left(x^{2}+1\right)^{2}}\)

Question 11.

Answer:
(b) \(-\sqrt{\frac{\pi}{6}}\)

Question 12.

Answer:
(a) \(\frac{\sqrt{(x+y)}-\sqrt{y-x}}{\sqrt{y-x}+\sqrt{x+y}}\)

Question 13.

Answer:
(b) \(\frac{2 a x+b y-y^{2}}{2 x y-b x-2 y}\)

Question 14.

Answer:
(d) 1

Question 15.

Answer:
(c) \(\frac{1}{2 \sqrt{1-x^{2}}}\)

Question 16.

Answer:
(d) \(\frac{1}{2}\)

Question 17.

Answer:
(c) \(\frac{2\left(1-x^{2}\right)}{\left(1+x^{2}\right)\left|1-x^{2}\right|}, x \neq\pm 1,0\)

Question 18.

Answer:
(b) 0

Question 19.

Answer:
(c) sec x tan x

Question 20.

Answer:
(d) 3e⁷

Question 21.

Answer:
(a) \(\frac{1}{2}\)

Question 22.

Answer:
(c) \(\frac{\log _{10} e}{x}\left(\frac{y}{y-1}\right)\)

Question 23.

Answer:
(d) None of these

Question 24.

Answer:
(d) \([latex]\frac{y}{x}\)[/latex]

Question 25.
If Rolle’s theorem holds for the function f(x) = x³ + bx² + ax + 5 on [1, 3] with c = (2 + \(\frac{1}{\sqrt{3}}\)), 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 \(\frac{d y}{d x}\) 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) \(\frac{\log x}{(1+\log x)^{2}}\)

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 x^y . y^x = 16, then the value of \(\frac{d y}{d x}\) at (2, 2) is
(a) -1
(b) 0
(c) 1
(d) none of these
Answer:
(a) -1

Question 30.

Answer:
(c) \(\frac{y}{1-y}\)

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

Question 32.

Answer:
(c) \(\frac{2}{3}\)

Question 33.

Answer:
(b) 1

Question 34.

Answer:
(c) \(\frac{5}{16 t^{6}}\)

Question 35.

Answer:
(a) n²y

Question 36.

Answer:
(d) \(-\frac{b}{a^{2}} \sec ^{3} \theta\)

Question 37.

Answer:
(c) y. (log ab²)²

Question 38.

Answer:
(d) \(-\frac{1}{e^{2}}\)

Question 39.

Answer:
(a) \(\frac{\sec ^{3} \theta}{a \theta}\)

Question 40.

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, \(\frac{\pi}{2}\)] is
(a) \(\frac{\pi}{2}\)
(b) \(\frac{\pi}{4}\)
(c) \(\frac{\pi}{3}\)
(d) \(\frac{\pi}{6}\)
Answer:
(b) \(\frac{\pi}{4}\)

Question 44.
The value of c in Rolle’s Theorem for the function f(x) = e^x sin x, x ∈ [0, π] is
(a) \(\frac{\pi}{6}\)
(b) \(\frac{\pi}{4}\)
(c) \(\frac{\pi}{2}\)
(d) \(\frac{3 \pi}{4}\)
Answer:
(d) \(\frac{3 \pi}{4}\)

Question 45.
A value of c for which the Mean value theorem holds for the function f(x) = log_ex on the interval [1, 3] is
(a) 2log₃e
(b) \(\frac{1}{2} \log _{e} 3\)
(c) log₃e
(d) log_e3
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) \(\frac{3}{2}\)
(b) \(\frac{2}{3}\)
(c) \(\frac{1}{2}\)
(d) \(\frac{5}{2}\)
Answer:
(a) \(\frac{3}{2}\)