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Maths MCQ Class 12 Ch- 3 | Matrices
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Multiple Choice Questions (MCQ)
MCQ | Class 12 | Chapter 3 MATRICES
MCQ | CHAPTER 3 | CLASS 12
If A and B are symmetric matrices of the same order, thena) AB is a symmetric matrix
b) A – B is a skew-symmetric matrix
c) AB + BA is a symmetric matrix
d) AB
– BA is a symmetric matrix
If a matrix A is
symmetric as well as skew symmetric then
a) A is a diagonal
matrix
b) A is a null matrix
c) A is a unit matrix
d) A is a triangular
matrix
If A = is a symmetric matrix, then x =
a) 4 b) 3 c) -4 d) -3
Answer: cIf A is a square matrix, then A – A’ is a
a)
diagonal matrix
b) skew-symmetric matrix
c)
symmetric matrix
d) none of these
If A
is any square matrix, then which of the following is skew - symmetric?
a) A + AT b) A
– AT c) AAT d) ATA
If A = then
(A – 2I)(A – 3I) =
a) A b) I c) O d) 5I
Answer cIf A = and A2
=
, then
c) α = a2 + b2, β = a2 – b2
If A = and B =
and AB
= I3, then x + y equals
a) 0 b) -1 c) 2 d) None of these
Answer aIf A = and f(x) = (1 + x)(1 - x), then f(A) is
Question: 10
Total number of possible matrices of order 2 X 3 with each entry 1 or 0 is
a) 6 b) 36 c) 32 d) 64
Answer: dIf A = and A2 – KA – 5I = 0, then k =
a) 5 b) 3 c) 7 d) None of these
Answer: a
If matrix A =
where a, b, c are real positive numbers, abc = 1 and ATA = I, then the value of a3 + b3 + c3 is
a) 1 b) 2 c) 3 d) 4
Answer d
Solution Hint: A’A = I ⇒ A2 = I
Comparing these two matrices we get
a2 + b2 + c2 =
1,
ab + bc + ca = 0,
ac + ba + bc = 0,
bc + ac + ab = 0
Now using
(a + b + c)2 and find the value of (a + b + c) we get (a + b
+ c) = 1
The
order of the matrix A is 3 x 5 and that
of matrix B is 2 x 3. Then order of the
matrix BA is
a) 2 x 3 b) 3 x 2 c) 2 x 5 d) 5 x 2
Answer: cIf a matrix A is
both symmetric and skew symmetric then
matrix A is
a) a scalar matrix
b) a diagonal matrix
c) a zero matrix of
order n x n
d) a rectangular
matrix.
If A = and A2
– 4A + 10 I = A, then k =
a) – 4 b) 0 c) 1 or 4 d) 4 and not 1
Answer: da) - 7 b) - 11 c) - 2 d) 14
Answer: c
Question:19
If A = and A-1
=
, then x equals
a) 2 b) -1/2 c) 1 d) 1/2
Answer: d
Question:20
For any square matrix A,
AAT is a
a) unit
matrix
b) symmetric matrix
c)
skew-symmetric matrix
d) diagonal matrix
Answer: b
If the matrix A = is a symmetric matrix, then find the value of
x, y and t respectively
a) 4, 2, 3 b) 4, 2, -3 c) 4, 2, -7 d) 2, 4, -7
Answer: b
Question:22
If a 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
scalar matrix
d) A is a square matrix
Answer: b
Question:23
The matrix A = is a
a) unit matrix
b) diagonal matrix
c) symmetric matrix
d) skew-symmetric
matrix
Answer: d
Question: 24
If A2 –
A + I = O, then the inverse of A is
a) I – A b) A
– I c) A d) A
+ I
Answer: a
Question: 25
If then the value of x, y, z are respectively
a) 5, 2, 2
b) 1, -2, 3
c) 0, -3, 3
d) 11, 8, 3
Answer: b
Question: 26
Total
number of possible matrices of order 3 × 3 with each entry 2 or 0 is
a) 9 b) 27 c) 81 d)
512
Answer: d
Question: 27
The matrix is a
a)
diagonal matrix
b) symmetric matrix
c) skew symmetric
matrix
d) scalar matrix
Answer: c
Question: 28
If A
is a matrix of order m × n and B is a matrix such that AB’ and B’A are both
defined, then the order of matrix B is
a) m × m b) n
× n c) n
× m d) m
× n
Answer: d
Question: 29
If A
and B are matrices of the same order, then (AB’ – BA’) is a
a) skew-symmetric matrix b)
null matrix
c) symmetric matrix d) unit matrix
Answer a
Question: 30
If A is a square matrix
such that A2 = I, then (A – I)3 + (A + I)3 –
7A is equal to
a) A b) I – A c) I + A d) 3A
Answer: a
Question: 31
If A2 = A,
then (I + A)4 is equal to
a) I + A b) I + 4A c) I + 15 A d) None of these
Answer: c
Question: 32
If A is an m × n matrix
such that AB and BA are both defined, then B is a
a) m × n
matrix b) n × m matrix
c) n × n matrix d) m × n matrix
Answer: b
Question: 33
Which of the given values of x and y make the following pairs of matrices equal
a) x = -1/ 3, y = 7
b) Not possible to find
c) y = 7,
x = -2/ 3
d) x = -1/ 3, y = -2/ 3
Answer: b
Question 34
If A
is a symmetric matrix then, then A2 is a
a) symmetric matrix
b)
Identity matrix
c)
skew symmetric matrix
d)
null matrix
Answer: a
Question: 35
Suppose
P and Q are two different matrices of order
3 x n and n x p, then the order of the matrix P x Q is
?
a) 3 x p b) p x 3 c) n x n d) 3 x 3
Answer: a
Question: 36
Find the order of the following
a) 2 x 3 b) 2 x 2 c) 3 x 2 d) 3 x 3
Answer: d
Question: 37
Matrices A and
B will be inverse of each other only if
a) AB = BA
b) AB = BA = 0
c) AB = 0, BA = 1
d) AB
= BA = I
Answer: d
Question: 38
Total number of
possible matrices of order 2 X 3 with each entry 1 or 0 is
a) 6 b) 36 c) 32 d) 64
Answer: d
Question: 39
If a matrix A is
both symmetric and skew symmetric then
matrix A is
a) a scalar matrix
b) a diagonal matrix
c) a zero matrix of
order n x n
d) a rectangular
matrix.
Answer: c
Question: 40
Then find AB + XY
a) [28] b) [24] c) [32] d) None of these
Answer: a
Question: 41
If A = then A100 is equal to
a) 2100A b) 299 A c) 100A d) 299 A
Answer:
b
Solution Hint
We have, A =
A2 = A x A = = 2
= 2A
A4 = A2 . A2 = 2A . 2A = 4 A2
= 4 x 2A = 8A = 23A
Similarly A8 = 27A ⇒ A100 = 299 A
Question: 42
The
matrix is a
a) Identity Matrix b) Symmetric Matrix
c) Skew – Symmetric Matrix d) None of these
Answer: b
Question: 43
Each
diagonal element of a skew symmetric matrix is
a) zero b) positive c) non-real d) negative
Answer: a
Question: 44
If A
and B are symmetric matrix of same order, then
AB – BA is a :
a)
Skew – Symmetric Matrix
b) Symmetric
Matrix
c)
Zero Matrix
d)
Identity Matrix
Answer: a
Question: 45
If A
is a square matrix such that A2
= I, then (A – I)3 + (A + I)3
– 7A is equal to
a) A b) I – A c) I + A d) 3 A
Answer a
Then
the values of x are
a) 1, 5 b) -1, -5 c) 1,6 d) -1, -6
Answer: dIf A = is upper triangular matrix, then x + y is
a) 3 b) -3 c) 0 d) 1
Answer: cSum of
two symmetric matrix is always
a) symmetric matrix b) Identity matrix
c) skew symmetric matrix d) None of these
Answer aWhich
of the following matrices both symmetric
and skew symmetric matrix ?
a) Identity matrix b) Unit matrix
c) Null matrix d) None of these
Answer: cIf A = and B
=
,
then find the value of x for which A2
= B
a) 1 b) -1 c) 4 d) None of these
Answer: d- Get link
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