# Bihar Board 12th Maths Objective Important Questions Part 3

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## Bihar Board 12th Maths Objective Important Questions Part 3

Question 1.
The total revenue in rupees Received from the sale of u unit of a product is given by R(x) = 3x2 + 36x + 5, the marginal revenue, when x = 15 is :
(a) 115
(b) 96
(c) 90
(d) 126
(d) 126 Question 2.
The interval in which y = x2 . e-x is increasing is :
(a) (-∞, ∞)
(b) (-2,0)
(c) (2 ∞)
(d) (0,2)
(d) (0,2)

Question 3.
Slope of the normal to the carve y = 2×2 + 3 sin x at x = 0 is :
(a) 3
(b) $$\frac { 1 }{ 3 }$$
(c) -3
(d) $$-\frac { 1 }{ 3 }$$
(d) $$-\frac { 1 }{ 3 }$$

Question 4.
The liney – x + 1 is a tangent to the curve y2 = 4x at the point:
(a) (1,2)
(b) (2, 1)
(c) (1, -2)
(d) (-1, 2)
(a) (1,2)

Question 5.
If f(x) = 3x2 + 15x + 5, then the approximate value of f(3.02) is :
(a) 47.66
(b) 57.66
(c) 67.66
(d) 77.66
(d) 77.66

Question 6.
The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is :
(a) 0.06 x3m3
(b) 0.6 x3m3
(c) 0.09 x3m3
(d) 0.9 x3m3
(c) 0.09 x3m3 Question 7.
The point on the curve x2 = 2y which is nearest to the point (0,5) is : V
(a) (2√2,4)
(b) (2√2,0)
(c) (0,0)
(d) (2,2)
(a) (2√2,4)

Question 8.
For all real values of x the minimum value of $$\frac{1-x+x^{2}}{1+x+x^{2}}$$ is:
(a) 0
(b) 1
(c) 3
(d) 1/3
(d) 1/3

Question 9.
The maximum value of [x (x – 1) + 1]1/3,0 ≤ x ≤ is :
(a) $$\left(\frac{1}{3}\right)^{1 / 3}$$
(b) 1/2
(c) 1
(d) ∞
(c) 1

Question 10.
Cylindrical thank of radius 10m is being filled with what at the rate of 314 cubic metre pertions. Then the depth of the sheat is increasing at of the role of:
(a) 1 m3/h
(b) 0.1 m3/m
(c) 1.1
(d) 5 cdt
(a) 1 m3/h

Question 11.
The slope of the tangent to the curve x = t2 + 3t y = 2t2 – 2t – 5 at the point (2,1) is :
(a) $$\frac{22}{7}$$
(b) $$\frac{6}{7}$$
(c) $$\frac{7}{6}$$
(d) $$\frac{-6}{7}$$
(b) $$\frac{6}{7}$$

Question 12.
The lihe y = mx + I is a tangent to the curve y2 = 4x in the value of m is:
(a) 1
(b) 2
(c) 3
(d) 1/2
(a) 1 Question 13.
The normal at the point (1,1) on the curve 2y + x2 = 3 is :
(a) x + y = 0
(b) x – y = 0
(c) x + y + 1 = 0
(d) x – y = 0
(b) x – y = 0

Question 14.
The normal to the curve x2 = 4y passing (1,2) is :
(a) x + y = 3
(b) x – t = 3
(c) y ÷ y = 1
(d) x – y = 1
(a) x + y = 3

Question 15.
The points on the curve 9y2 = x3, where the normal to the curve makes equation intercepts with the axes are :
(a) (4, ±$$\frac{8}{3}$$)
(b) (4, $$\frac{-8}{3}$$)
(c) (4, $$\frac{-8}{3}$$)
(d) (÷4, $$\frac{3}{8}$$)
(a) (4, ±$$\frac{8}{3}$$)

Question 16.
On which of the following intervals is the function f given by f(x) = x100 + sin x – 1 Strictly decreasing ?
(a) (0,1)
(b) (π/2, π)
(c) (0, π/2)
(d) None
(d) None

Question 17.
The antiderivative of ( $$\sqrt{x}+\frac{1}{\sqrt{x}}$$ ) equals:
(a) $$\frac { 1 }{ 3 }$$x1/2 + 21/2 + C
(b) $$\frac { 2 }{ 3 }$$x2/3 + $$\frac { 1 }{ 2 }$$x2 + C
(c) $$\frac { 2 }{ 3 }$$ x3/2 + 2x1/2 + C
(d) $$\frac { 3 }{ 2 }$$x3/2 + $$\frac { 1 }{ 2 }$$x1/2 + C
(c) $$\frac { 2 }{ 3 }$$ x3/2 + 2x1/2 + C

Question 18.
If $$\frac{d}{d x}$$ f(x) = 4x3 – $$\frac{3}{x}$$ such that f(2) = 0, then f(x) is : (a)

Question 19.
$$\int \frac{e^{x}(1+x)}{\cdot \cos ^{2}\left(e^{x} x\right)} d x$$ equals.
(a) -cot(xex) + c
(b) tan(xex) + c
(c) cot ex + c
(d) cot(xex) + c
(b) tan(xex) + c Question 20.
equal to $$\int \frac{10 x^{9}+10^{x} \log _{10}}{x^{10}+10^{x}} e d x$$ equals:
(a) 10x – x10 + c
(b) 10x + x10 + c
(c) (10x – x10)-1 + c
(d) log (10x + x 10) + c
(d) log (10x + x 10) + c

Question 21.
$$\int \frac{d x}{\sin ^{2} x \cdot \cos ^{2} x}$$ equals :
(a) tan x + cot x + c
(b) tan x – cot x + c
(c) tan x – cot x + c
(b) tan x – cot 2x + c
(b) tan x – cot x + c

Question 22.
$$\int \sqrt{1+x^{2}} d x$$ is equal to : (a)

Question 23.
$$\int \frac{\cos 2 x}{(\sin x+\cos x)^{2}} d x$$ is equal to:
(a) $$\frac{-1}{\sin x+\cos x}+c$$
(b) log|sinx + cosx| + c
(c) log|sinx – cos x| + c
(d) $$\frac{1}{(\sin x+\cos x)^{2}}$$
(b) log|sinx + cosx| + c

Question 24.
$$\int \sqrt{x^{2}-8 x+7} d x$$ is equal to : (a)

Question 25.
$$\int \frac{d x}{e^{x}+e^{-x}}$$ is equal to :
(a) tan-1(ex) + c
(b) tan-1(e-x) + c
(c) log(ex – cx) + c
(d) log (ex – e-x) + c
(a) tan-1(ex) + c Question 26.
If f(a + b -x) = f(x), thenf x f(x) dx is equal to : (d)

Question 27.
The value of $$\int_{0}^{1} {tan}^{-1}\left(\frac{2 x-1}{1+x-x^{2}}\right) d x$$ is :
(a) 1
(b) 0
(c) -1
(d) $$\frac{\pi}{4}$$
(b) 0

Question 28.
$$\int \frac{d x}{x^{2}+2 x+2}$$ equals :
(a) x + tan-1 (x + 1) + c
(b) tan-1 (x + 1) + c
(c) (x + 1) tan-1 x + c
(d) tan-1 x + c
(b) tan-1 (x + 1) + c

Question 29.
$$\int \frac{d x}{\sqrt{9 x-4 x^{2}}}$$ equals: (b)

Question 30.
$$\int \frac{d x}{x\left(x^{2}+1\right)}$$ equals :
(a) log|x| – $$\frac { 1 }{ 2 }$$ log (x2 + 1) + c
(b) log|x| + $$\frac { 1 }{ 2 }$$ log (x2 + 1) + c
(c) -log|x| + $$\frac { 1 }{ 2 }$$ log (x2 + 1) + c
(d) $$\frac { 1 }{ 2 }$$ log|x| + log (x2 + 1) + c
(a) log|x| – $$\frac { 1 }{ 2 }$$ log (x2 + 1) + c Question 31.
∫ exsec x (1 + tan x)dx equals :
(a) ex cosx + c
(b) exsecx + c
(c) exsinx + c
(d) ex + tanx + c
(b) exsecx + c

Question 32.
∫ x2ex3 dx equals to :
(a) $$\frac { 1 }{ 3 }$$ex3 + c
(b) $$\frac { 1 }{ 3 }$$ex3 + c
(c) $$\frac { 1 }{ 2 }$$ex3 + c
(d) $$\frac { 1 }{ 2 }$$ex2
(a) $$\frac { 1 }{ 3 }$$ex3 + c

Question 33.
$$\int_{1}^{\sqrt{3}} \frac{d x}{1+x^{2}}$$ equals :
(a) $$\frac{\pi}{3}$$
(b) $$\frac{2\pi}{3}$$
(c) $$\frac{\pi}{6}$$
(d) $$\frac{\pi}{12}$$
(d) $$\frac{\pi}{12}$$

Question 34.
$$\int_{0}^{2 / 3} \frac{d x}{4+9 x^{2}}$$ equals :
(a) $$\frac{\pi}{6}$$
(b) $$\frac{\pi}{12}$$
(c) $$\frac{\pi}{24}$$
(d) $$\frac{\pi}{4}$$
(c) $$\frac{\pi}{24}$$

Question 35.
If f(x) = $$\int_{0}^{x}$$ +sin t dt, then f(x) is :
(a) cos x + x sin x
(b) x sin x
(c) x cos x
(d) sin x + x cos x
(b) x sin x Question 36.
The value of the intergral $$\int_{1 / 3}^{1} \frac{\left(x-x^{3}\right)^{1 / 3}}{x^{4}} d x$$ :
(a) 6
(b) 0
(c) 3
(d) 4
(d) 4

Question 37.
The value $$\int_{-\pi / 2}^{\pi / 2} x^{3}+x \cos x+\tan ^{t} n+1 d x$$ is :
(a) 0
(b) 2
(c) π
(d) 1
(c) π

Question 38.
The value of $$\int_{0}^{\pi / 2} \log \left(\frac{4 x+3 \sin x}{4+3 \cos x} d x\right)$$ is
(a) 2
(b) $$\frac{3}{4}$$
(c) 0
(d) -2
(c) 0

Question 39.
Area lying in the first quaotrant and bounded by the circle x2 + y2 = 4 and the lines (x = 0) and x = 2 is to :
(a) π
(b) $$\frac{\pi}{2}$$
(c) $$\frac{\pi}{3}$$
(d) $$\frac{\pi}{4}$$
(a) π

Question 40.
Area of the region bounded by the curve y2 = 4r,y-axis and the line y = 3 is :
(a) 2
(b) $$\frac{9}{4}$$
(c) $$\frac{9}{3}$$
(d) $$\frac{9}{4}$$
(b) $$\frac{9}{4}$$

Question 41.
Area lying between the curves y2 = 4x and y – lx is :
(a) -9
(b) $$\frac{-15}{4}$$
(c) $$\frac{15}{4}$$
(d) $$\frac{17}{4}$$
(b) $$\frac{-15}{4}$$

Question 42.
Area bounded by the curve y = x3, the x-axis and the cordinates x = -2 and x = 1 is :
(a) -9
(b) $$\frac{-15}{4}$$
(c) $$\frac{15}{4}$$
(d) $$\frac{17}{4}$$
(d) $$\frac{17}{4}$$

Question 43.
The area bounded by the curve y = x|x|, x-axis and the cordinates x = -1 is given by :
(a) 0
(b) $$\frac{1}{3}$$
(c) $$\frac{2}{3}$$
(d) $$\frac{4}{3}$$
(c) $$\frac{2}{3}$$

Question 44.
The area of the circle x2 + y2 = 16 exterier of the parabola y2 = 6x is :
(a) $$\frac{4}{3}$$ (4π+√3)
(b) $$\frac{4}{3}$$ (4π+√3)
(c) $$\frac{4}{3}$$ (8π-√3)
(d) $$\frac{4}{3}$$ (8π+√3)
(c) $$\frac{4}{3}$$ (8π-√3) Question 45.
Smaller area enclosed by the circle x2 + y2 = 4 and the line x +y = 2 is;
(a) 2(π-2)
(b) π – 2
(c) 2π – 1
(d) 2(π + 2)
$$\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d y}{d x}\right)^{2}+\sin \left(\frac{d y}{d x}\right)+1=0$$ is