Bihar Board 12th Maths VVI Objective Questions Model Set 1 in English

Bihar Board 12th Maths Objective Questions and Answers

Bihar Board 12th Maths VVI Objective Questions Model Set 1 in English

Question 1.
Let A = {5, 6}; how many binary operations can be defined on this set?
(a) 8
(b) 10
(c) 16
(d) 20
Answer:
(c) 16

Question 2.
Let A = {1, 2, 3}, which of the following functions f : A → A does not have an inverse function?
(a) {(1, 1), (2, 2), (3, 3)}
(b) {(1, 2), (2, 1), (3, 1)}
(c) {(1, 3), (3, 2), (2, 1)}
(d) {(1, 2), (2, 3), (3, 1)}
Answer:
(b) {(1, 2), (2, 1), (3, 1)}

Question 3.
If A = {1, 2, 3}, B = {6, 7, 8} and f : A → B is a function such that f(x) = x + 5 then what type of a function is f?
(a) into
(b) one-one onto
(c) many-one onto
(d) Constant function
Answer:
(b) one-one onto

Question 4.
What type of a relation is “Less than” in the set of real numbers?
(a) only symmetric
(b) only transitive
(c) only reflexive
(d) equivalence relation
Answer:
(b) only transitive

Question 5.

Answer:
(a) \(\frac{8 \pi}{5}\)

Question 6.
cos^-1(2x – 1) =
(a) 2cos^-1 x
(b) cos^-1 √x
(c) 2cos^-1 √x
(d) None of these
Answer:
(c) 2cos^-1 √x

Question 7.
2cot^-1 3 + cot^-1 7 =
(a) \(\frac{\pi}{2}\)
(b) π
(c) \(\frac{\pi}{4}\)
(d) \(\frac{\pi}{6}\)
Answer:
(b) π

Question 8.

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

Question 9.

Answer:
(a) \(\left|\begin{array}{ll}
\lambda a & \lambda b \\
\lambda c & \lambda d
\end{array}\right|\)

Question 10.
If a, b, c are in A.P. then :
\(\left|\begin{array}{ccc}
x+1 & x+2 & x+a \\
x+2 & x+3 & x+b \\
x+3 & x+4 & x+c
\end{array}\right|=\)
(a) 3
(b) -3
(c) 0
(d) 1
Answer:
(c) 0

Question 11.
If 7 and 2 are two roots of the equation \(\left|\begin{array}{lll}
x & 3 & 7 \\
2 & x & 2 \\
7 & 6 & x
\end{array}\right|=0\) then the third root is :
(a) -9
(b) 14
(c) \(\frac{1}{2}\)
(d) None of these
Answer:
(a) -9

Question 12.

Answer:
(d) 0

Question 13.

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

Question 14.
If A be a square matrix. Then A + A’ will be a _________
(a) Symmetric matrix
(b) Skew symmetric matrix
(c) Null matrix
(d) Unit matrix
Answer:
(a) Symmetric matrix

Question 15.
If A is a matrix of order 3 × 3, such that A² = A then (A + I₃)³ – 7A is equal to?
(a) I₃
(b) A
(c) 3A
(d) I₃ – A
Answer:
(a) I₃

Question 16.
Let A be a non-singular matrix of the order 2 × 2 then |adj A| = ________
(a) 2|A|
(b) |A|
(c) |A|²
(d) |A|³
Answer:
(b) |A|

Question 17.
\(\frac{d}{d x}\)[log(sec x + tan x)] =
(a) \(\frac{1}{\sec x+\tan x}\)
(b) sec x
(c) tan x
(d) sec x + tan x
Answer:
(b) sec x

Question 18.
If x²y³ = (x + y)⁵ then \(\frac{d y}{d x}=\)
(a) \(\frac{x}{y}\)
(b) \(\frac{y}{x}\)
(c) \(\frac{-y}{x}\)
(d) \(\frac{-x}{y}\)
Answer:
(b) \(\frac{y}{x}\)

Question 19.

Answer:
(c) 0

Question 20.

Answer:
(c) \(\left(\frac{2}{3}\right)^{x} \log _{3} 2\)

Question 21.
f(x) = √3 sin x + cos x is maximum then value of x = ______
(a) \(\frac{\pi}{6}\)
(b) \(\frac{\pi}{2}\)
(c) \(\frac{\pi}{3}\)
(d) \(\frac{\pi}{4}\)
Answer:
(c) \(\frac{\pi}{3}\)

Question 22.
If y = log cos x², then x = √π at \(\frac{d y}{d x}\) has the value :
(a) 1
(b) \(\frac{\pi}{4}\)
(c) 0
(d) √π
Answer:
(c) 0

Question 23.
Equation of the tangent to the curve x² + y² = a² at (x₁, y₁) is :
(a) xx₁ – yy₁ = 0
(b) xx₁ + yy₁ = 0
(c) xx₁ – yy₁ = a²
(d) xx₁ + yy₁ = a²
Answer:
(d) xx₁ + yy₁ = a²

Question 24.
\(\frac{d}{d x}\left[\lim _{x \rightarrow a} \frac{x^{5}-a^{5}}{x-a}\right]=\)
(a) 5a⁴
(b) 5x⁴
(c) 1
(d) 0
Answer:
(a) 5a⁴

Question 25.

Answer:
(b) √2 sin x + c

Question 26.

Answer:
(b) \(\frac{1}{3} e^{x^{3}}+c\)

Question 27.

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

Question 28.

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

Question 29.

Answer:
(b) 0

Question 30.

Answer:
(d) 0

Question 31.
Area between the x-axis and the curve y = sin x, from x = 0 to x = \(\frac{\pi}{2}\) is :
(a) 2
(b) -1
(c) 1
(d) None of these
Answer:
(c) 1

Question 32.
\(\int_{0}^{1}(x) d x=\dots\)
(a) 0
(b) 1
(c) 2
(d) \(\frac{1}{2}\)
Answer:
(d) \(\frac{1}{2}\)

Question 33.
The differential equation \(1+\left(\frac{d y}{d x}\right)^{2}=\left(\frac{d^{2} y}{d x^{2}}\right)^{3}\) is of order = _______ and degree = _______
(a) order = 2, degree = 3
(b) order = 1, degree = 2
(c) order = 2, degree = 2
(d) None of these
Answer:
(a) order = 2, degree = 3

Question 34.
Solution of the differential equation y dx – x dy = xy dx is
(a) \(\frac{y^{2}}{2}-\frac{x^{2}}{2}=x y+c\)
(b) x = kye^x
(c) x = kye^y
(d) None of these
Answer:
(b) x = kye^x

Question 35.
Integrating factor (I.F.) of differential equation \(\frac{d y}{d x}+\frac{y}{x}=\frac{y^{2}}{x^{2}}\) is
(a) log x
(b) x
(c) \(\frac{1}{x}\)
(d) None of these
Answer:
(c) \(\frac{1}{x}\)

Question 36.

Answer:
(b) \(\frac{x^{2}}{2}+\tan ^{-1} \frac{y}{x}=k\)

Question 37.

Answer:
(b) \(\frac{\vec{i}+\vec{j}+2 \vec{k}}{\sqrt{6}}\)

Question 38.

Answer:
(b) \(\frac{3}{13}, \frac{-4}{13}, \frac{12}{13}\)

Question 39.
\(x \vec{i}-3 \vec{j}+5 \vec{k},-x \vec{i}+x \vec{j}+2 \vec{k}\) are perpendicular to each other then value of x =
(a) -2, 5
(b) 2, 5
(c) -2, -5
(d) 2, -5
Answer:
(d) 2, -5

Question 40.

Answer:
(b) 0

Question 41.
The direction Cosines of y axis are :
(a) (1, 0, 1)
(b) (0, 1, 0)
(c) \(\left(\frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}}\right)\)
(d) None of these
Answer:
(b) (0, 1, 0)

Question 42.
The equation of the xy plane is :
(a) x = 0, y = 0
(b) z = 0
(c) x = y ≠ 0
(d) None of these
Answer:
(b) z = 0

Question 43.
If two planes 2x – 4y + 3z = 5 and x + 2y + λz = 12 are perpendicular to each other, then a =
(a) -2
(b) 2
(c) 3
(d) None of these
Answer:
(b) 2

Question 44.
The distance bewteen (4, 3, 7) and (1, -1, 5) is :
(a) 13
(b) 15
(c) 12
(d) 5
Answer:
(a) 13

Question 45.
If A’ and B’ are independent events then :
(a) P(A’B’) = P(a) . P(b)
(b) P(A’B’) = P(A’) + P(B’)
(c) P(A’B’) = P(A’) . P(B’)
(d) P(A’B’)= P(AP) – P(B’)
Answer:
(c) P(A’B’) = P(A’) . P(B’)

Question 46.
If events A and B are mutually exclusive then :
(a) P(A∩B) = P(a) . P(b)
(b) P(A∩B) = 0
(c) P(A∩B) = 1
(d) P(A∪B) = 0
Answer:
(b) P(A∩B) = 0

Question 47.

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

Question 48.
If A and B are two events such that P(A) ≠ 0 and \(\mathbf{P}\left(\frac{\mathbf{B}}{\mathbf{A}}\right)=\mathbf{1}\)
(a) B ⊂ A
(b) A ⊂ B
(c) B = φ
(d) A∩B = φ
Answer:
(b) A ⊂ B

Question 49.
\(\int \frac{d x}{x+\sqrt{x}} d x\)
(a) log x + log(1 + √x) + C
(b) 2log(1 + √x) + C
(c) log(1 + √x) + C
(d) log√x + C
Answer:
(b) 2log(1 + √x) + C

Question 50.

Answer:
(b) e – 1