BSEB Bihar Board 12th Maths Important Questions Objective Type Part 2 are the best resource for students which helps in revision.

## Bihar Board 12th Maths Objective Important Questions Part 2

Question 1.

\(\int_{a}^{b} x d x=\)

Answer:

(a)

Question 2.

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

(a) 2π

(b) π

(c) π/2

(d) π/4

Answer:

(d) π/4

Question 3.

\(\left|\begin{array}{lll}

a & 0 & 0 \\

0 & b & 0 \\

0 & 0 & c

\end{array}\right|\)

(a) a + b + c

(b) abc

(c) 2abc

(d) a^{2} + b^{2} + c^{2}

Answer:

(b) abc

Question 4.

Let f: R → R be defined by f(x) = x^{4}. Choose the correct answer :

(a) f is one-one on to

(b) f is many are on to .

(c) f is one-one but

(d) f is neither one-one nor on to

Answer:

(d) f is neither one-one nor on to

Question 5.

Let R be the relations in the set {1, 2,3,4} given by R – {1,2), (2, 2). (1,1). (4, 4), (1, 3), (3, 2) Choose the correct answer :

(a) R is reflexive & symmetric but not transitive

(b) R is reflexive & transitive but not symmetric

(c) R is symmetric & transitive but not reflexive

(d) R is on equivalence relation.

Answer:

(b) R is reflexive & transitive but not symmetric

Question 6.

Let R be the relation in they set N given by R = {a, b): a = b – 2. b > 6. Choose the correct answer :

(a) (2,4) ∈ R

(b) (3, 8) ∈ R

(c) (6,8) ∈ R

(d) (8,7)∈ R

Answer:

(c) (6,8) ∈ R

Question 7.

Let f : R → R be-given bv f(x) = (3 – x^{3})^{1/3} then fof (x) is :

(a) x^{1/3}

(b) x^{3}

(c) x

(d) (x-x^{3})

Answer:

(c) x

Question 8.

Let f: R – {\(-\frac{4}{5}\)} → R be a function defined as f(x) = \(\frac{4 x}{3 x+4}\) Inverse of f is the map g : Rege f → R – {\(-\frac{4}{3}\)} given by :

(a) g(y) = \(\frac{3 y}{3-4 y}\)

(b) g(y) = \(\frac{4 y}{4-3 y}\)

(c) g(y) = \(\frac{4 y}{3-4 y}\)

(d) g(y) = \(\frac{3 y}{4-3 y}\)

Answer:

(b) g(y) = \(\frac{4 y}{4-3 y}\)

Question 9.

Let f: R → R be defined by f(x) = 3x then

(a) f is one-one on to

(b) f is many-many-one on to

(c) f is one-one but not on to

(d) f is neither one-one nor on to

Answer:

(d) f is neither one-one nor on to

Question 10.

Let A = {1,2,3), Then no of equivalence relations contaning (1,2) is and (1,2, 3), Then of equivalence relations contaning (1,2) is ‘:

(a) 1

(b) 2

(3) 3

(d) 4

Answer:

(a) 1

Question 11.

Consider a hinery operation *on N defined as a * b = a^{3} + b^{3}, choose the correct answer :

(a) as * both associative & commutative

(b) as * commutative but not associative

(c) as * associative but not commutative

(d) as * neither commutative noT associative

Answer:

(b) as * commutative but not associative

Question 12.

Let A = {1,2,3), Then number of relations containing (1,2) and (1,3) which are reflexive and symmetric but not transitive is :

(a) 1

(b) 2

(c) 3

(d) 4

Answer:

(a) 1

Question 13.

No. of binary operations on the set {a, b} are :

(a) 10

(b) 16

(c) 20

(d) 8

Answer:

(b) 16

Question 14.

The No. of possible matrics of order 3 x 3 with each entry 0 or 1 is :

(a) 27

(b) 18

(c) 81

(d) 512

Answer:

(d) 512

Question 15.

a = [aij]m x n is a square matrix if:

(a) mn

(c) m = n

(d) None

Answer:

(c) m = n

Question 16.

Which of the given values of x and y make the following pair of matrics equal : \(\left[\begin{array}{ll}

3 x+7 & 5 \\

y+1 & 2-3 x

\end{array}\right],\left[\begin{array}{ll}

0 & y-2 \\

8 & 4

\end{array}\right]\)

a) x = \(\frac{-2}{3}\), y = 7

(b) not possible to find

(c) y = 7, x = \(\frac{-2}{3}\)

(d) x = \(\frac{-1}{3}\), y = \(\frac{-2}{3}\)

Answer:

(b) not possible to find

Question 17.

The restriction on n, k and P so that PY + WY will be defined are :

(a) K = 3, P = n

(b) K is arbitrary, P = 2

(c) P is arbitrary, K = 3

(d) K = 2, P = 3

Answer:

(a) K = 3, P = n

Question 18.

If n = p, then the order of the matrix 7 x – 5Z is ;

(a) P x 2

(b) 2 x n

(c) n x 3

(d) p x n

Answer:

(b) 2 x n

Question 19.

If A, B are symmetric matrices of same order, then AB – BA is a :

(a) Skew symmetric matrix

(b) symmetric matrix

(c) Zero matrix ;

(d) Identity matrix

Answer:

(a) Skew symmetric matrix

Question 20.

If A = \(\left[\begin{array}{c}

\cos \alpha-\sin \alpha \\

\sin \alpha \cos \alpha

\end{array}\right]\) then a + A’ = I, If then value of α is :

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

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

(c) π

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

Answer:

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

Question 21.

Mat rices A and B will be inverse of each other only If:

(a) AB = BA

(b) AB = BA = 0

(c) AB = 0, BA = I

(d) AB = BA = I

Answer:

(d) AB = BA = I

Question 22.

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

\alpha & \beta \\

\gamma & -\alpha

\end{array}\right]\) is such that A^{2} = 1 then :

(a) 1 + α^{2} + βγ = 0

(b) 1 – α^{2} + βγ = 0

(c) 1 – α^{2} – βγ = 0

(d) 1 + α^{2} – βγ = 0

Answer:

(c) 1 – α^{2} – βγ = 0

Question 23.

If the matrix A is both symmetric and skew symmetric, then :

(a) A is a diagonal matrix

(b) A is a zero matrix

(c) A is a square matrix

(d) None

Answer:

(b) A is a zero matrix

Question 24.

If A is square matrix such that A^{2} = A, then (1 + A)^{2} – 7A is equal to :

(a) A

(b) I – A

(c) I

(d) 3A

Answer:

(c) I

Question 25.

Let A be a square matrix of order 3 x 3, than |KA| is equal to :

(a) K|A|

(b) K_{2}|A|

(c) K^{3} |A|

(d) 3K |A|

Answer:

(c) K^{3} |A|

Question 26.

Which of the following is correct:

(a) Determinant is a square matrix

(b) Determinant a number associated to a matrix

(c) Determinant is a number associated to square matrix

(d) None of these]

Answer:

(c) Determinant is a number associated to square matrix

Question 27.

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

x & 2 \\

18 & x

\end{array}\right|=\left|\begin{array}{cc}

6 & 2 \\

18 & 6

\end{array}\right|\) then x is equal to :

(a) 6

(b) ± 6

(c) – 6

(d) 0

Answer:

(a) 6

Question 28.

If area of triangle is 35 sq. units with vertices (2, – 6), (5,4) & (k, 4) then k is:

(a) 12

(b) -2

(c) – 12, -2

(d) 12, -2

Answer:

(d) 12, -2

Question 29.

Let A be nonsingular square matrix of order 3 x 3 then |AdjA| is equal to:

(a) |A|

(b)|A|^{2}

(c) |A|^{3}

(d) 3|A|

Answer:

(b)|A|^{2}

Question 30.

If A is an inversible matrix of order 2 than det (A^{-1}) is equal to :

(a) det (A)

(b) \(\frac{1}{dat}(A)}\)

(c) 1

(d) 0

Answer:

(b) \(\frac{1}{\operatorname{dat}(A)}\)

Question 31.

If sin^{-1}x = y then :

(a) 0 ≤ y ≤ π

(b) \(-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}\)

(c) 0 < y < π

(d) \(-\frac{\pi}{2}<y<\frac{\pi}{2}\)

Question 32.

tan^{-1}√3 – sec^{-1}(-2) is equal to :

(a) π

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

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

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

Answer:

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

Question 33.

sin(\(\frac{\pi}{3}\) – sin^{-1} ( \(-\frac{1}{2}\) )) is equal to :

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

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

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

(d) 1

Answer:

(d) 1

Question 34.

tan^{-1}√3 – cot^{-1}(-√3) is equal to :

(a) π

(b) \(\frac{-\pi}{2}\)

(c) 0

(d) \(\sqrt{2 / 3}\)

Answer:

(b) \(\frac{-\pi}{2}\)

Question 35.

sin(tan^{-1}), |x| < |is equal to :

Answer:

(d)

Question 36.

sin^{-1}(1 – n) – 2sin^{-1}x = \(\frac{\pi}{2}\) then x is equal to :

(a) 0, \(\frac { 1 }{ 2 }\)

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

(c) 0

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

Answer:

(c) 0

Question 37.

tan ^{-1}(x/y) – tan^{-1}\(\frac{x-y}{x+y}\) is equal to :

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

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

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

(d) \(\frac{-3\pi}{4}\)

Answer:

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

Question 38.

f(x) = (1 n)^{cot n} be continuous at x = 0 then f(0) is equal to :

(a) 0

(b) 1/e

(c) e

(d) none of these

Answer:

(c) e

Question 39.

If f(x) = \(\left\{\begin{array}{c}

\frac{1-\cos x}{x \sin x}, x \neq 0 \\

\frac{1}{2} ; x=0

\end{array}\right.\) then at x = 0 f(x) is :

(a) continuous and differentiable

(b) differentiable but not continuous

(c) continuous but the differeantiable

(d) neither continuous nor differential

Answer:

(a) continuous and differentiable

Question 40.

If f(x) – log (logx^{2}) (logx) then f(x) at x = ?

a) 0

b) 1

c) 1/e

d) 1/2e

Answer:

d) 1/2e

Question 41.

Given f(x) = 4x^{8} then :

Answer:

(c)

Question 42.

If sin y = x cos (a+y) then \(\frac{d y}{d x}\) is equal to :

Answer:

(b)

Question 43.

If y = \(\tan ^{-1}\left(\frac{\sin x+\cos x}{\cos x-\sin x}\right)\) then \(\frac{d y}{d x}\) is equal to :

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

(b) 0

(c) 1

(d) none

Answer:

(c) 1

Question 44.

If y = log\(\left(\frac{1+x^{2}}{1+x^{2}}\right)\) then \(\frac{d y}{d x}\) =

Answer:

(b) \(\frac{-4 x}{1-x^{4}}\)

Question 45.

If y = \(\log \sqrt{\tan x}\) then the value of \(\frac{d y}{d x}\) at x = \(\frac{\pi}{4}\) is given by :

(a) ∞

(b) 1

(c) 1

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

Answer:

(b) 1

Question 46.

The rate of change of the area of a circle with respect to its radius r at γ cm is :

(a) 10π

(b) 12π

(c) 8π

(d) 11π

Answer:

(b) 12π