Bihar Board 12th Maths Objective Important Questions Part 2

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Bihar Board 12th Maths Objective Important Questions Part 2

Question 1.
$$\int_{a}^{b} x d x=$$

(a)

Question 2.
$$\int_{0}^{1} \frac{d x}{1+x^{2}}=$$
(a) 2π
(b) π
(c) π/2
(d) π/4
(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) a2 + b2 + c2
(b) abc

Question 4.
Let f: R → R be defined by f(x) = x4. 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
(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.
(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
(c) (6,8) ∈ R

Question 7.
Let f : R → R be-given bv f(x) = (3 – x3)1/3 then fof (x) is :
(a) x1/3
(b) x3
(c) x
(d) (x-x3)
(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) = $$\frac{3 y}{4-3 y}$$
(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
(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
(a) 1

Question 11.
Consider a hinery operation *on N defined as a * b = a3 + b3, 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
(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
(a) 1

Question 13.
No. of binary operations on the set {a, b} are :
(a) 10
(b) 16
(c) 20
(d) 8
(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
(d) 512

Question 15.
a = [aij]m x n is a square matrix if:
(a) mn
(c) m = n
(d) None
(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 = $$\frac{-2}{3}$$
(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
(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
(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
(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) $$\frac{3\pi}{2}$$
(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
(d) AB = BA = I

Question 22.
If A = $$\left[\begin{array}{cc} \alpha & \beta \\ \gamma & -\alpha \end{array}\right]$$ is such that A2 = 1 then :
(a) 1 + α2 + βγ = 0
(b) 1 – α2 + βγ = 0
(c) 1 – α2 – βγ = 0
(d) 1 + α2 – βγ = 0
(c) 1 – α2 – 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
(b) A is a zero matrix

Question 24.
If A is square matrix such that A2 = A, then (1 + A)2 – 7A is equal to :
(a) A
(b) I – A
(c) I
(d) 3A
(c) I

Question 25.
Let A be a square matrix of order 3 x 3, than |KA| is equal to :
(a) K|A|
(b) K2|A|
(c) K3 |A|
(d) 3K |A|
(c) K3 |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]
(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
(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
(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|
(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
(b) $$\frac{1}{\operatorname{dat}(A)}$$

Question 31.
If sin-1x = 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) $$\frac{2\pi}{2}$$
(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
(d) 1

Question 34.
tan-1√3 – cot-1(-√3) is equal to :
(a) π
(b) $$\frac{-\pi}{2}$$
(c) 0
(d) $$\sqrt{2 / 3}$$
(b) $$\frac{-\pi}{2}$$

Question 35.
sin(tan-1), |x| < |is equal to :

(d)

Question 36.
sin-1(1 – n) – 2sin-1x = $$\frac{\pi}{2}$$ then x is equal to :
(a) 0, $$\frac { 1 }{ 2 }$$
(b) 1, $$\frac { 1 }{ 2 }$$
(c) 0
(d) $$\frac { 1 }{ 2 }$$
(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) $$\frac{-3\pi}{4}$$
(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
(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
(a) continuous and differentiable

Question 40.
If f(x) – log (logx2) (logx) then f(x) at x = ?
a) 0
b) 1
c) 1/e
d) 1/2e
d) 1/2e

Question 41.
Given f(x) = 4x8 then :

(c)

Question 42.
If sin y = x cos (a+y) then $$\frac{d y}{d x}$$ is equal to :

(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
(c) 1

Question 44.
If y = log$$\left(\frac{1+x^{2}}{1+x^{2}}\right)$$ then $$\frac{d y}{d x}$$ =

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