## Bihar Board 12th Maths Objective Important Questions Part 4

Question 1.

The order of the differential equation \(2 x^{2} \frac{d^{2} y}{d x^{2}}+3 \frac{d y}{d x}+y=0\) is ’

(a) 3

(b) 2

(c) 1

(d) not defined

Answer:

(a) 3

Question 2.

The number of arbitrary constants in the general solution of a differential equation of fourth order are.

(a) 0

(b) 2

(c) 3

(d) 4

Answer:

(d) 4

Question 3.

The number of arbitrary constants in the particular solution of a differential equation of third order are :

(a) 3

(b) 2

(c) 1

(d) 0

Answer:

(d) 0

Question 4.

Which of the following differential equations hasy = c1e^{x} + c2e^{-x} as the general solution?

(a) \(\frac{d^{2} y}{d x^{2}}\) + y = 0

(b) \(\frac{d^{2} y}{d x^{2}}\) – y = 0

(c) \(\frac{d^{2} y}{d x^{2}}\) + 1 = 0

(d) \(\frac{d^{2} y}{d x^{2}}\) – 1 = 0

Answer:

(b) \(\frac{d^{2} y}{d x^{2}}\) – y = 0

Question 5.

Which of the following differential equations has y =x as one crits particular solution ?

Answer:

(c)

Our free handy Double Integral Calculator tool is aimed at giving the double integral of a function within fraction of seconds.

Question 6.

The general solution of the differential equation \(\frac{d y}{d x}\) = e^{x+y} is ;

(a) e^{x} + e^{-x}y = c

(b) e^{x} + e^{y} = c

(c) e^{-x} + e^{y} = c

(d) e^{-x} + e^{-y} = c

Answer:

(a) e^{x} + e^{-x}y = c

Question 7.

A homogeneous differential equation of the front \(\frac{d x}{d y}=h\left(\frac{x}{y}\right)\) can be solved by marking the substitution : .

(a) y = Vx

(b) V = yx

(c) x = Vy

(d) x = V

Answer:

(c) x = Vy

Question 8.

Which of the following is a homogeneous differential equation :

(a) (4x + 6y + 5) dy – |3y + 2x + 4| dx = 0

(b) (xy) dx – (x^{3} + y^{3}) dy = 0

(c) (x^{3} + 2y^{2})dx + 2xydy = 0

(d) y^{2}dx + (x^{2} – xy – y^{3})dy = 0

Answer:

(d) y^{2}dx + (x^{2} – xy – y^{3})dy = 0

Question 9.

The integrating factor of the differential equation \(x \frac{d y}{d x}-y=2 x^{2}\) is :

(a) e^{-x}

(b) e^{-y}

(c) 1/x

(d) x

Answer:

(c) 1/x

Question 10.

The general solution of a differential equation of the type \(\frac{d x}{d y}+P_{1} x=Q_{1}\) is :

Answer:

(c)

Question 11.

The integrating factor of the differential equation

(a-y^{2})\(\frac{d x}{d y}\)

Answer:

(d) \(\frac{1}{\sqrt{1-y^{2}}}\)

Question 12.

In triangle ABC, which of the following is not true :

Answer:

(c)

Question 13.

If \(\vec{a}\) and \(\vec{b}\) are two colliner vectors, then which of the following are incorrect:

(a) \(\vec{b}\) = λ \(\vec{a}\), for some scalar λ

(b) \(\vec{a}\) = ±\(\vec{b}\)

(c) The respective compounds of \(\vec{a}\) and \(\vec{b}\) are proportional

(d) Both the vectors \(\vec{a}\) and \(\vec{b}\) have some direction, but different magnitudes.

Answer:

(d) Both the vectors \(\vec{a}\) and \(\vec{b}\) have some direction, but different magnitudes.

Question 14.

Let the vectors \(\vec{a}\) and \(\vec{b}\) be such that |\(\vec{a}\)| = 3 and |\(\vec{a}\)|= \(\frac{\sqrt{2}}{3}\), then \(\overrightarrow{a} \times \overrightarrow{b}\) is a unit vector, If the angle between \(\vec{a}\) and \(\vec{b}\) is :

(a) \(\frac{\pi}{6}\)

(b) \(\frac{\pi}{4}\)

(c) \(\frac{\pi}{3}\)

(d) \(\frac{\pi}{2}\)

Answer:

(b) \(\frac{\pi}{4}\)

Question 15.

Area of a rectangle having vertics A, B, C and D with position :

Vectors \(-\hat{i}+\frac{1}{2} \hat{j}+4 \hat{k}, \hat{i}+\frac{1}{2} \hat{j}+4 \hat{k}, \hat{i}-\frac{1}{2} \hat{j}+4 \hat{k}\) and \(-\hat{i}-\frac{1}{2} \hat{j}+4 \hat{k}\) respectively is:

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

(b) 1

(c) 2

(d) 4

Answer:

(c) 2

Question 16.

If \(\vec{a}\) is a nonzero vector of magnitude ‘a’ and λ nonzero scalar, then λ\(\vec{a}\) is unit vector If,

(a) λ = 1

(b) λ = -1

(c) a = |λ|

(d) a = \(\frac{1}{|\lambda|}\)

Answer:

(d) a = \(\frac{1}{|\lambda|}\)

Question 17.

The general solution of the differential equation

e^{x}dy + (ye^{x} +2x)dx = 0 is :

(a) xe^{x} + x^{2} = c

(b) xe^{y} + y^{2} = c

(c) ye^{x} + x^{2} = c

(d) ye^{y} + x^{2} = c

Answer:

(c) ye^{x} + x^{2} = c

Question 18.

If θ is the angle between two vectors \(\vec{a}\) and \(\vec{b}\), the \(\vec{b}\), \(\vec{a}\), \(\vec{b}\) ≥ 0 only when :

(a) 0 < θ < \(\frac{\pi}{2}\)

(b) 0 ≤ θ ≤ \(\frac{\pi}{2}\)

(c) 0 < θ < π

(d) 0 ≤ θ ≤ π

Answer:

(b) 0 ≤ θ ≤ \(\frac{\pi}{2}\)

Question 19.

Let \(\vec{a}\) and \(\vec{b}\) be two unit vectors and θ is the angle between them; Then \(\vec{a}\) + \(\vec{b}\) is a unit vector if:

(a) θ = \(\frac{\pi}{4}\)

(b) θ = \(\frac{\pi}{3}\)

(c) θ = \(\frac{\pi}{2}\)

(d) θ = \(\frac{2\pi}{3}\)

Answer:

(d) θ = \(\frac{2\pi}{3}\)

Question 20.

The value of \(\hat{i}(\hat{j} \times \hat{k})+\hat{j}(\hat{i}+\hat{k})+\hat{k}(\hat{i}+\hat{j})\) is :

(a) 0

(b) -1

(c) 1

(d) 3

Answer:

(c) 1

Question 21.

If θ is the angle between any two vectors \(\vec{a}\) and \(\vec{b}\) the \(|\vec{a} \cdot \vec{b}| \vec{a} \cdot \vec{b}|=| \vec{a} \times \vec{b} \mid\) when θ, is equal to

(a) 0

(b) \(\frac{\pi}{4}\)

(c) \(\frac{\pi}{2}\)

(d) π

Answer:

(b) \(\frac{\pi}{4}\)

Question 22.

The planes 2x – y + 4z = 5 and Sx – 2.5y + 10z = 6 are :

(a) perpendicular

(b) parallel

(c) intersect y-axis

(d) passes through (0, 0, \(\frac{5}{4}\)

Answer:

(b) parallel

Question 23.

Distance between the two planes 2x + 3 y +-4z = 4 and 4x + 6y + 8x = 12 is

(a) 2 units

(b) 4 units

(c) 8 units

(d) 9 units

Answer:

(d) 9 units

Question 24.

The solution set of the in equation 2x + y > 5 is :

(a) half plane that contains the origin

(b) open half plane not containing the origin

(c) when xy-plane except the reints lying on the live 2x + y = 5

(d) none of these

Answer:

(b) open half plane not containing the origin

Question 25.

Which of the following is not a convex set ?

(a) {(x, y)/2x + 5y < 7}

(b) {(x,y)/x^{2} + y^{2} ≤ 4} .

(c) {x/ |x| = 5}

(d) {(x,y)/3x^{2} + 2y ≤ b

Answer:

(c) {x/ |x| = 5}

Question 26.

The reints of which the maximum value of x + y. Subject to the constraints x + 2y ≤ 70, 2x + y ≤ 95,x,y ≥ 0 is obtained is :

(a) (30,25)

(b) (20,35)

(c) (35,20)

(d) (40,15)

Answer:

(d) (40,15)

Question 27.

Objective function of a LPP is :

(a) a constraint

(b) a function to be optimized

(c) a relation b/w the variables

(d) none of these

Answer:

(b) a function to be optimized

Question 28.

The Probability of obtaining an even prime number on each die, when a pair of dice is rolled is :

(a) 0

(b) \(\frac { 1 }{ 3 }\)

(c) \(\frac { 1 }{ 12 }\)

(d) \(\frac { 1 }{ 36 }\)

Answer:

(d) \(\frac { 1 }{ 36 }\)

Question 29.

If P (A) = \(\frac { 1 }{ 2 }\) P(B) = 0 then P(A/B) is :

(a) 0

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

(c) not defined

(d) 1

Answer:

(c) not defined

Question 30.

If Aand B are two events such that P(A) ≠ 0 and P(B/A) = then :

(a ) A⊂B

(b ) B⊂A

(c) B = Φ

(d) A = Φ

Answer”

(a ) A⊂B

Question 31.

If P(B/A)>P(A) then which of the following is correct:

(a) P(B / A) < P(B)

(b) P(AnB)<P(A) P(B) (c) P(B/ A) > P(B)

(d) P(B/A) = P(B)

Answer:

(c) P(B/ A) > P(B)

Question 32.

Two events A and B will be independent, if:

(a) A and B are mutually exclusive

(b) P(A’B’)=[1-P(A)][1-P(B)]

(c )P(A) = P(B)

(d) P(A) + P(B) = 1

Answer:

(b) P(A’B’)=[1-P(A)][1-P(B)]

Question 33.

If A and B are any two events such that P(A) + P(B) – P (A and B) = P(A), the ;

(a) P(B/A) = 1

(b) P(A/B) = 1

(c) P(B/A) = 0

(d) P(A/B) = 0

Answer:

(b) P(A/B) = 1

Question 34.

Suppose that two cards are drown at random from a deck of cards. Let X be the number of aces obtained. Then the. value of E(X) is :

(a) \(\frac{37}{221}\)

(b) \(\frac{9}{13}\)

(c) \(\frac{1}{13}\)

(d) \(\frac{2}{13}\)

Answer:

(d) \(\frac{2}{13}\)

Question 35.

In a box containing 100 bulbs. 10 are defective. The probability that out of a sample of 5 bulbs, none in defective is :

(a) 10^{-1}

(b) \(\left(\frac{1}{2}\right)^{5}\)

(c) \(\left(\frac{9}{10}\right)^{5}\)

(d) \(\frac{9}{10}\)

Answer:

(c) \(\left(\frac{9}{10}\right)^{5}\)

Question 36.

The probability that a student Is not a swimmer is \(\frac{1}{5}\) then the probability that mat of five students four are swimmers is:

(a) \({ }^{5} C_{4}\left(\frac{4}{5}\right)^{4} \frac{1}{5}\)

(b) \(\left(\frac{4}{5}\right)^{4} \frac{1}{5}\)

(c) \({ }^{5} C_{1} \frac{1}{5}\left(\frac{4}{5}\right)^{4}\)

(d) None of these

Answer:

(a) \({ }^{5} C_{4}\left(\frac{4}{5}\right)^{4} \frac{1}{5}\)

Question 37.

The mean of the numbers of obtained on throwing a die having written. I on three facems, 2 on two faces and 5 on one face is :

(a) 1

(b) 2

(c) 5

(d) \(\frac { 8 }{ 3 }\)

Answer:

(b) 2

Question 38.

If y = log x then \(\frac{d^{2} y}{d x^{2}}\) =

(a) log x

(b) \(\frac{1}{x}\)

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

(d) \(\frac{1}{x^{2}}\)

Answer:

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

Question 39.

\(\frac{d}{d x}\left[\frac{d}{d x}(\sin x)\right]=\)

(a) sin x

(b) cos x

(c) -sin x

(d) -cos x

Answer:

(c) -sin x

Question 40.

\(\int_{a}^{b}\left[\frac{d}{d x}(\log x)\right]=\)

(a) log \(\frac{b}{a}\)

(b) log \(\frac{a}{b}\)

(c) log(a-b)

(d) log(b-a)

Answer:

(b) log \(\frac{a}{b}\)

Question 41.

dy – dx = y – x hindi

(a) y + x = k

(b) y – x = k

(c) y/x = k

(d) xy = k

Answer:

(b) y – x = k

Question 42.

\(|2 \vec{i}+3 \vec{j}+5 \vec{k}|\)

(a) 10

(b) \(\sqrt{10}\)

(c) 38

(d) \(\sqrt{38}\)

Answer:

(d) 0

Question 43.

\((5 \vec{i}+2 \vec{j}-\vec{k}) \cdot(\vec{i}-2 \vec{j}-\vec{k})=\)

(a) 13

(b) 8

(c) 6

(d) 0

Answer:

(d) 0

Question 44.

\(\frac{d}{d x}\) [(sin^{-1}x + cos^{-1}x)] =

(a) \(\frac{\pi}{2}\)

(b) 0

(c) \(\frac{\pi^{2}}{2}\)

(d) 1

Answer:

(b) 0

Bihar Board 12th Maths Important Questions