Bihar Board 12th Maths Objective Questions and Answers

## Bihar Board 12th Maths VVI Objective Questions Model Set 2 in English

Question 1.

Answer:

(b) 1

Question 2.

Answer:

(b) 1

Question 3.

Answer:

(b) -2

Question 4.

Answer:

(c) -1

Question 5.

Answer:

(d) -(x^{3} + y^{3})^{2}

Question 6.

Answer:

(c) a + c = -1, b ∈ R

Question 7.

Answer:

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

Question 8.

(a) continuous at every x except x = 0

(b) discontinuous at every x except x = 0

(c) continuous everywhere

(d) discontinuous everywhere

Answer:

(b) discontinuous at every x except x = 0

Question 9.

(a) continuous at x = 1

(b) differentiable at x = 1

(c) continuous at x = -3

(d) All of these

Answer:

(d) All of these

Question 10.

If \(f(x)=\frac{\sqrt{4+x}-2}{x}\), x ≠ 0 be continuous at x = 0, then f(0) =

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

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

(c) 2

(d) \(\frac{3}{2}\)

Answer:

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

Question 11.

Moving along the x-axis there are two points with x = 10 + 6t, x = 3 + t^{2}. The speed with which they are reaching from each other at the time of encounter is (x is an cm and t is in seconds)

(a) 16 cm/s

(b) 20 cm/s

(c) 8 cm/s

(d) 12 cm/s

Answer:

(c) 8 cm/s

Question 12.

A particle is moving along the curve x = at^{2} + bt + c. If ac = b^{2}, then particle would be moving with uniform

(a) rotation

(b) velocity

(c) acceleration

(d) retardation

Answer:

(c) acceleration

Question 13.

The distance ‘s’ metres covered by a body in t seconds, is given by s = 3t^{2} – 8t + 5. The body will stop after

(a) 1 s

(b) \(\frac{3}{4}\) s

(c) \(\frac{4}{3}\) s

(d) 4 s

Answer:

(c) \(\frac{4}{3}\) s

Question 14.

The position of a point in time ‘t’ is given by x = a + bt – ct^{2}, y = at + bt^{2}. Its acceleration at time ‘t’ is

(a) b – c

(b) b + c

(c) 2b – 2c

(d) \(2 \sqrt{b^{2}+c^{2}}\)

Answer:

(d) \(2 \sqrt{b^{2}+c^{2}}\)

Question 15.

The function f(x) = log (1 + x) – \(\frac{2 x}{2+x}\)

(a) (-1, ∞)

(b) (-∞, 0)

(c) (-∞, ∞)

(d) None of these

Answer:

(a) (-1, ∞)

Question 16.

Answer:

(d) log_{e}(10^{x} + x^{10}) + C

Question 17.

Answer:

(a) \(\frac{1}{(\log 2)^{3}} 2^{2^{2^{x}}}+C\)

Question 18.

Answer:

(b) \(-\frac{\cos ^{4} x}{4}+C\)

Question 19.

Answer:

(a) \(\frac{-3}{\sqrt[3]{\sin x}}+C\)

Question 20.

Answer:

(b) \(-\frac{3}{5} \tan ^{5 / 3} x+\frac{3}{11} \tan ^{11 / 3} x+C\)

Question 21.

The area bounded by the curve 2x^{2} + y^{2} = 2 is

(a) π sq. units

(b) √2 π sq. units

(c) \(\frac{\pi}{2}\) sq. units

(d) 2π sq. units

Answer:

(b) √2 π sq. units

Question 22.

Area of the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) is

(a) 4πab sq. units

(b) 2πab sq. units

(c) πab sq. units

(d) \(\frac{\pi a b}{2}\) sq. units

Answer:

(c) πab sq. units

Question 23.

Area of the region bounded by y = |x|, x ≤ 5 in the first quadrant is

(a) \(\frac{11}{2}\) sq. units

(b) \(\frac{17}{2}\) sq. units

(c) \(\frac{25}{2}\) sq. units

(d) \(\frac{27}{2}\) sq. units

Answer:

(c) \(\frac{25}{2}\) sq. units

Question 24.

Determine the area under the curve \(y=\sqrt{a^{2}-x^{2}}\) included between the lines x = 0 and x = a.

(a) \(\frac{\pi a^{a}}{4}\)

(b) \(\frac{\pi a^{3}}{4}\)

(c) \(\frac{\pi a^{2}}{8}\)

(d) None of these

Answer:

(a) \(\frac{\pi a^{a}}{4}\)

Question 25.

The area enclosed by curve \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\) is

(a) 10π sq. units

(b) 20π sq. units

(c) 5π sq. units

(d) 4π sq. units

Answer:

(b) 20π sq. units

Question 26.

The order of the differential equation whose general solution is given by

y = (C_{1} + C_{2}) cos(x + C_{3}) – C_{4}\(e^{x+C_{5}}\)

where C_{1}, C_{2}, C_{3}, C_{4}, C_{5} are arbitrary constant, is

(a) 5

(b) 4

(c) 3

(d) 2

Answer:

(c) 3

Question 27.

The order of the differential equation whose general solution is given by y = (A + B) cos (x + C) + De^{x} is

(a) 4

(b) 3

(c) 2

(d) 1

Answer:

(b) 3

Question 28.

Find the magnitude of vector \(3 \hat{i}+2 \hat{j}+12 \hat{k}\)

(a) √157

(b) 4√11

(c) √213

(d) 9√3

Answer:

(a) √157

Direction (29) : Study the given parallelogram and answer the following questions.

Question 29.

Which of the following represents equal vectors?

(a) a, c

(b) b, d

(c) b, c

(d) m, d

Answer:

(b) b, d

Question 30.

The cosines of the angle between any two diagonals of a cube is

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

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

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

(d) \(\frac{1}{\sqrt{3}}\)

Answer:

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

Question 31.

Which of the following is false?

(a) 30°, 45°, 60° can be the direction angles of a line is space.

(b) 90°, 135°, 45° can be the direction angles of a line is space.

(c) 120°, 60°, 45° can be the direction angles of a line in space.

(d) 60°, 45°, 60° can be the direction angles of a line in space.

Answer:

(a) 30°, 45°, 60° can be the direction angles of a line is space.

Question 32.

The optimal value of the objective function is attained at the points

(a) on X-axis

(b) on Y-axis

(c) which are corner points of the feasible region

(d) none of these

Answer:

(c) which are corner points of the feasible region

Question 33.

Which one of the following is the order of the differential equation \(\frac{d^{2} y}{d x^{2}}+x^{3}\left(\frac{d y}{d x}\right)^{2}=x^{4}\)?

(a) 1

(b) 2

(c) 3

(d) 0

Answer:

(b) 2

Question 34.

If two events A and B area such that P(\(\bar{A}\)) = 0.3, P(b) = 0.4 and \(P(B | A \cup \bar{B})=\)

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

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

(c) \(\frac{2}{5}\)

(d) \(\frac{1}{4}\)

Answer:

(d) \(\frac{1}{4}\)

Question 35.

If E and F are events such that 0 < P(F) < 1, then

(a) P(E|F) + P(\(\bar{E}\)|F) = 1

(b) P(E|F) + P(E|\(\bar{F}\)) = 1

(c) P(\(\bar{E}\)|F)+ P(E|\(\bar{F}\)) = 1

(d) P(E|\(\bar{F}\)) + P(\(\bar{E}\)|F) = 0

Answer:

(a) P(E|F) + P(\(\bar{E}\)|F) = 1

Question 36.

Let R be a relation in N defined by R= {(1 + x, 1 + x^{2}) : x ≤ 5, x ∈ N). Which of the following is false?

(a) R = {(2, 2), (3, 5), (4, 10), (5, 17), (6, 25)}

(b) Domain of R = (2, 3, 4, 5, 6)

(c) Range of R = {2, 5, 10, 17, 26}

(d) None of these

Answer:

(a) R = {(2, 2), (3, 5), (4, 10), (5, 17), (6, 25)}

Question 37.

The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is

(a) Reflexive but not symmetric

(b) Reflexive but not transitive

(c) Symmetric and transitive

(d) Neither symmetric nor transitive

Answer:

(a) Reflexive but not symmetric

Question 38.

Let P = {(x, y) | x^{2} + y^{2} = 1, x, y ∈ R}. Then, P is

(a) Reflexive

(b) Symmetric

(c) Transitive

(d) Anti-symmetric

Answer:

(b) Symmetric

Question 39.

For real numbers x and y. we write xRy ⇔ x – y + √2.

(a) Reflexive

(b) Symmetric

(c) Transitive

(d) None of these

Answer:

(a) Reflexive

Question 40.

Let L denote the set of all straight lines in a plane. Let a relation R be defined by αRβ ⇔ α ⊥ β, α, β ∈ L. Then, R is

(a) Reflexive only

(b) Symmetric only

(c) Transitive only

(d) None of these

Answer:

(b) Symmetric only

Question 41.

Answer:

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

Question 42.

Answer:

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

Question 43.

Answer:

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

Question 44.

Answer:

(b) \(\frac{3 \pi}{4}\)

Question 45.

Answer:

(d) \(\frac{2 \pi}{3}\)

Question 46.

If \(\left[\begin{array}{ll}

x+y & 2 x+z \\

x-y & 2 z+w

\end{array}\right]=\left[\begin{array}{cc}

4 & 7 \\

0 & 10

\end{array}\right]\), then the values of x, y, z and w respectively are

(a) 2, 2, 3, 4

(b) 2, 3, 1, 2

(c) 3, 3, 0, 1

(d) None of these

Answer:

(a) 2, 2, 3, 4

Question 47.

If \(\left[\begin{array}{cc}

a+b & 2 \\

5 & a b

\end{array}\right]=\left[\begin{array}{cc}

6 & 2 \\

5 & 8

\end{array}\right]\), then find the values of a and b respectively

(a) 2, 4

(b) 4, 2

(c) Both (a) & (b)

(d) None of these

Answer:

(c) Both (a) & (b)

Question 48.

For what values of x and y are the following matrices equal?

(a) 2, 3

(b) 3, 4

(c) 2, 2

(d) 3, 3

Answer:

(c) 2, 2

Question 49.

Find the values of a, b, c and d respectively if

(a) 1, 3, 9, 8

(b) 1, 2, 3, 4

(c) 1, 4, 8, 10

(d) 1, 5, 6, 7

Answer:

(b) 1, 2, 3, 4

Question 50.

then find the values of a, b, c, x, y and z respectively.

(a) -2, -7, -1, -3, -5, 2

(b) 2, 7, 1, 3, 5, -2

(c) 1, 3, 4, 2, 8, 9

(d) -1, 3, -2, -7, 4, 5

Answer:

(a) -2, -7, -1, -3, -5, 2