Bihar Board 12th Maths Objective Important Questions Part 1 in English

Bihar Board 12th Maths Objective Important Questions Part 1 in English

BSEB 12th Maths Objective Important Questions Part 1 in English

Question 1.
Law ab + = b + a is called.
(a) closure law
(b) Associative law
(c) commutative law
(d) distributive law
Answer:
(c) commutative law

Question 2.
If A is skew symmetric matrix of oder 2 then det (A) is of the form :
(a) a²
(b) a² – 1
(c) a² + 1
(d) None of these
Answer:
(a) a²

Question 3.
If A be a matrix then, (A’)’ equals
(a) A’
(b) A
(c) A^-1
(d) none of these
Answer:
(b) A

Question 4.
If A and B are matrices, compatible for addition then, (A + B)’ equal
(a) A + B
(b) A’ + B
(c) A + B’
(d) A’ + B’
Answer:
(d) A’ + B’

Question 5.
If A and B art- matrices compatible for multiplication then (AB)’ is equal to
(a) A’B’
(b) A’B
(c) B’A
(d) B’A’
Answer:
(d) B’A’

Question 6.
If A be a singular matrix then |Aj-=
(a) 1
(b) -1
(c) 0
(d) none of these
Answer:
(c) 0

Question 7.
For a symmetric matrix A, |A| is equal to
(a) 0
(b) 1
(c) 2A
(d) none of these
Answer:
(c) 2A

Question 8.
For a skew symmetric matrix A, A + A’ is equal to
(a) 0
(b) 1
(c) 2A
(d) none of these
Answer:
(d) none of these

Question 9.
tan^-1 x + tan^-1 y is equal to

Answer:
(c)

Question 10.
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
Answer:
(d) f is neither one-one nor on to

Question 11.
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 12.
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 13.
Let f : R → R be-given bv f(x) = (3 – x³)^1/3 then fof (x) is :
(a) x^1/3
(b) x³
(c) x
(d) (x-x³)
Answer:
(c) x

Question 14.
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 15.
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 16.
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
Answer:
(b) as * commutative but not associative

Question 17.
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 18.
No. of binary operations on the set {a, b} are :
(a) 10
(b) 16
(c) 20
(d) 8
Answer:
(b) 16

Question 19.
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 20.
a = [aij]m x n is a square matrix if:
(a) mn
(c) m = n
(d) None
Answer:
(c) m = n

Question 21.
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 22.
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 23.
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 24.
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 25.
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 26.
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
Answer:
(c) I

Question 27.
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|
Answer:
(c) K³ |A|

Question 28.
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 29.
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 30.
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 31.
sin(tan^-1), |x| < |is equal to :

Answer:
(d)

Question 32.
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 33.
If f(x) – log (logx²) (logx) then f(x) at x = ?
a) 0
b) 1
c) 1/e
d) 1/2e
Answer:
d) 1/2e

Question 34.
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