# Bihar Board 12th Maths VVI Objective Questions Model Set 3 in English

Bihar Board 12th Maths Objective Questions and Answers

## Bihar Board 12th Maths VVI Objective Questions Model Set 3 in English

Question 1.

Answer:
(a) $$\frac{\pi}{4}$$

Question 2.
The slope of the tangent to the curve X = t2 + 3t – 8, Y = 2t2 – 2t – 5 at the point (2, -1) is
(a) $$\frac{12}{7}$$
(b) $$\frac{-6}{7}$$
(c) $$\frac{6}{7}$$
(d) $$\frac{-12}{7}$$
Answer:
(c) $$\frac{6}{7}$$

Question 3.
The modulus of the vector $$19 \overrightarrow{1}+5 \vec{J}-6 \vec{k}$$ is
(a) √322
(b) √420
(c) √421
(d) √422
Answer:
(d) √422

Question 4.
$$\int_{0}^{\frac{\pi}{2}} \cos x d x=?$$
(a) -1
(b) 1
(c) $$\frac{\pi}{2}$$
(d) 0
Answer:
(a) -1

Question 5.
The direction cosines of z-axis are
(a) (0, 0, 0)
(b) (1, 0, 0)
(c) (0, 1, 0)
(d) (0, 0, 1)
Answer:
(d) (0, 0, 1)

Question 6.

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

Question 7.
$$\vec{K} \times \vec{K}=?$$
(a) 1
(b) -1
(c) K2
(d) 0
Answer:
(d) 0

Question 8.
Integrating factor of the differential equation $$\frac{d y}{d x}$$ + Y sec x = tan x is
(a) sec x + tan x
(b) sec x – tan x
(c) sec x
(d) tan x sec x
Answer:
(c) sec x

Question 9.
Intergrating factor (I.F) of the differential equation $$\frac{d y}{d x}$$ + Y cos x = sin x cos x is
(a) e-sin x
(b) esin x
(c) e-cos x
(d) ecos x
Answer:
(c) ecos x

Question 10.

Answer:
(a) $$\sin ^{-1} \frac{2 x}{1+x^{2}}$$

Question 11.

Answer:
(d) $$\frac{5}{8}$$

Question 12.
If f(x1) = f(x2) ⇒ x1 = x2 ∀ x1, x2 ∈ A, then what type of a function is f : A → B ?
(a) One-one
(b) Constant
(c) Onto
(d) Many one
Answer:
(a) One-one

Question 13.
$$(\vec{a} \times \vec{a}) \cdot \vec{b}=?$$
(a) 1
(b) -1
(c) 2
(d) 0
Answer:
(d) 0

Question 14.

Answer:
(a) 0

Question 15.
P(A) + P(A’) = ?
(a) 0
(b) 1
(c) -1
(d) P(E)
Answer:
(b) 1

Question 16.
$$\vec{a} \cdot \vec{b}=?$$
(a) $$-\vec{b} \cdot \vec{a}$$
(b) 1
(c) -1
(d) $$\vec{b} \cdot \vec{a}$$
Answer:
(d) $$\vec{b} \cdot \vec{a}$$

Question 17.
$$\sin ^{-1} \frac{1}{x}=?$$
(a) sex-1 x
(b) cosec-1 x
(c) tan-1 x
(d) sin x
Answer:
(b) cosec-1 x

Question 18.

Answer:
(b) $$\frac{x^{n+1}}{n+1}+k$$

Question 19.
$$\frac{d}{d x}$$ [tan x] = ?
(a) sec2 x
(b) sec x
(c) cot x
(d) -sec2 x
Answer:
(a) sec2 x

Question 20.

Answer:
(a) $$\frac{1}{x}$$

Question 21.

Answer:
(b) $$\frac{\pi}{4}$$

Question 22.

Answer:
(c) $$\left[\begin{array}{ll} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{array}\right]$$

Question 23.
P(A∪B) = ?
(a) P(A) + P(B) + P(A∩B)
(b) P(A) – P(B) – P(A∩B)
(c) P(A) + P(B) – P(A∩B)
(d) P(A) – P(B) + P(A∩B)
Answer:
(c) P(A) + P(B) – P(A∩B)

Question 24.
The value of x when $$\left[\begin{array}{cc} x & 15 \\ 4 & 4 \end{array}\right]=0$$ is
(a) 15
(b) -15
(c) 4
(d) 4x
Answer:
(a) 15

Question 25.
∫cosec2 x dx = ?
(a) tan x + c
(b) -cot x + c
(c) 2cosec x + c
(d) -cosec x + 2
Answer:
(b) -cot x + c

Question 26.
$$\frac{d}{d x}$$ [sin2 x] = ?
(a) 2 sin x cos x
(b) 2 sin x
(c) cos2 x
(d) sin x cos x
Answer:
(a) 2 sin x cos x

Question 27.
The distance of the point (3, 4, 5) from x-axis is
(a) 3
(b) 5
(c) √41
(d) None of these
Answer:
(c) √41

Question 28.
In the set of all straight lines in a plane, the relation R to be Perpendicular is
(a) Reflexive and transitive
(b) Symmetric and transitive
(c) Symmetric
(d) None of these
Answer:
(c) Symmetric

Question 29.
Which of the following is a homogenous differential equation?
(a) x2y dx – (x3 + y3) dy = 0
(b) (xy) dx – (x4 + y4) dy = 0
(c) (2x + y – 3) dy – (x + 2y – 3) dx = 0
(d) (x – y) dy = (x2 + y + 1) dx
Answer:
(c) (2x + y – 3) dy – (x + 2y – 3) dx = 0

Question 30.
Evaluate $$\left[\begin{array}{cc} 1 & -1 \\ y & x \end{array}\right]$$
(a) x + y
(b) x – y
(c) -y – x
(d) 1 – x
Answer:
(d) 1 – x

Question 31.
The value of the determinant $$\left[\begin{array}{lll} 1 & 2 & 4 \\ 1 & 3 & 6 \\ 1 & 4 & 9 \end{array}\right]$$ is
(a) 1
(b) -1
(c) 0
(d) 2
Answer:
(a) 1

Question 32.
The operation * is defined as a * b = 2a + b, then (2 * 3) * 4 is
(a) 18
(b) 17
(c) 19
(d) 21
Answer:
(d) 21

Question 33.
Which of the following is the unit matrix of order 3 × 3?

Answer:
(b) $$\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]$$

Question 34.
$$\int \frac{d x}{1+x^{2}}=?$$
(a) tan x + c
(b) tan2 x + c
(c) cot x + c
(d) -cot-1 x + c
Answer:
(c) cot x + c

Question 35.
$$\int \frac{d x}{1+x^{2}}=?$$
(a) tan x + c
(b) tan2 x + c
(c) cot x + c
(d) -cot-1 x + c
Answer:
(a) tan x + c

Question 36.
P(E) = ?
(a) n(E) + n(s)
(b) $$\frac{n(s)}{n(E)}$$
(c) n(E) – n(s)
(d) $$\frac{n(E)}{n(s)}$$
Answer:
(a) n(E) + n(s)

Question 37.

Answer:
(a) 1

Question 38.

Answer:
(b) 0

Question 39.
∫sec x dx = ?
(a) log|sec x| + c
(b) log |sec x + tan x| + c
(c) log |sec x -tan x| + c
(d) sec x tan x + c
Answer:
(b) log |sec x + tan x| + c

Question 40.
The order of the differential equation $$\frac{d^{2} y}{d x^{2}}+x^{3}\left(\frac{d y}{d x}\right)^{3}=x^{4}$$ is
(a) 1
(b) 2
(c) 4
(d) 3
Answer:
(b) 2

Question 41.

Answer:
(c) $$\log \frac{1}{2}$$

Question 42.
f: A → B will be an onto function of
(a) f(A) ⊂ B
(b) f(A) = B
(c) f(A) ⊃ B
(d) f(A) ≠ B
Answer:
(b) f(A) = B

Question 43.

Answer:
(a) $$\frac{b^{3}-a^{3}}{3}$$

Question 44.

Answer:
(b) $$\frac{1}{4} \tan -^{-1} \frac{x}{4}+k$$

Question 45.

Answer:
(d) -15

Question 46.

Answer:
(b) $$\left[\begin{array}{ll} 27 & 36 \\ 25 & 10 \end{array}\right]$$

Question 47.
tan-1 x + cot-1 x = ?
(A) 0
(B) 1
(c) $$\frac{\pi}{2}$$
(d) $$-\frac{\pi}{2}$$
Answer:
(c) $$\frac{\pi}{2}$$

Question 48.

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

Question 49.
The position vector of the point (x, y, z) is

Answer:
(d) $$x \vec{i}+y \vec{j}+z \vec{k}$$

Question 50.

(a) (x = -2, y = 8)
(b) (x = 2, y = n – 8)
(c) (x = 3, y = -6)
(d) (x = -3, y = 6)
Answer:
(b) (x = 2, y = n – 8)