Matrices & Determinants MCQs Part V

1) The coefficient of x in the determinant
a) 1
b) 0
c) 2
d) none of these

2) If A is any m x n matrix such that AB and BA are both defined, then B
is an

a) m x n matrix
b) n x m matrix
c) n x n matrix
d) m x m matrix

3) If and
and differ by an odd multiple
of , then is
a

a) null matrix
b) unit matrix
c) diagonal matrix
d) none of these

4) If A = and B =
are two matrices such that the product AB is the null matrix, then

a) 0
b)
c)
d) none of these

5) If A is a symmetric matrix and
a) symmetric
b) skew- symmetric
c) a diagonal matrix
d) none of these

6) If A, B are symmetric matrices of the same order then AB-BA is
a) symmetric matrix
b) skew-symmetric matrix
c) null matrix
d) unit matrix

7) If
then
for

a) x = 2
b) all real x
c) x = 0
d) none of these

8) If the
A-1 is equal to

a)
b) A
c) adj A
d) none of these

9)
a) 1
b) 0
c) 2
d) None of the given

10)
a) 626
b) -124
c) 624
d) 126

11)
a) 4
b) 3
c) 1
d) 0

12) If the system of equations x = cy = bz, y = az+ cx and z = bx + ay has a non-trival solution, then a, b and c are connected by the relation
a)

a2 + b2 + c2
3 abc = 0

b)

a2 + b2 + c2
ab -bc – ca = 0

c)

a2 + b2 + c2 +
2 abc = 1

d) None of the given

13)
a) 0
b) 1
c) 2
d) None of the given

14)
a)

x (2a + 3x )

b)

ax ( 2a + 3X )

c)

a2 x  + (2a + 3x)

d)

ax2  (2a + 3x )

15)
a) 0
b) 1
c) 2
d) None of the given

16)
a) abc
b) 1
c) 0
d) None of the given

17)
a) 2
b)
c)
d) None of the given

18)
a) 1
b) 0
c) 2
d) 10

19)
a)

a b g

b)

a .  2n
b. 3n
g .4n</f
c)

2 a
+ 3 b + 4
g

d) None of the given

20)
a) 3 x 1
b) 1 x 1
c) 1 x 3
d) 3 x 3

21)

If  A  and  B are two matrices
such that AB = B and  BA = A,  then  A2 + B2

a) 2 AB
b) 2 BA
c) A + B
d) AB

22)
a)
b)
c)
d)

23)
a)
b)
c)
d)

24)
a)
b)
c)
d) None of the given

25)
a) 3
b) 5
c) 2
d) 4

26)
a) no solution
b) unique solution
c) infinitely many solutions
d) finitely many solutions

27) The system of linear equations x + y + z = 2 , 2x + y – z = 3, 3x + 2y + kz = 4 has a unique solution if
a)

k ยน  0

b) -1 < k < 1
c) -2 < k < 2
d) k = 0

28)
a) 0
b)
c)

multiple of p

d) None of the given

29)
a) unit matrix
b) null matrix
c) diagonal matrix
d) None of the given

30)

If  A  is a skew-symmetric
matrix,  then  Bl AB  is

a) symmetric
b) 0
c) I
d) skew-symmetric

31) If A is a square matrix of order n x n then adj ( adj A) is equal to
a)

| A |n -1   A

b)

| A |n  A

c)

| A | n -2   A

d) None of the given

32)
a) 0
b) 1
c) -1
d)

33) The solutions to the system of equations x + y + z = 6 , 2x – y + z = 3 , x – 2y + 3z = 6 is
a) (1,2,3)
b) (2,1,3)
c) (3,1,2)
d) None of the given

34)

If A is a skew-symmetric matrix of order n and
X is a column vector of order n
x
1, then  X l AX is equal to

a) a non-zero numbers
b) 0
c) I
d) a column matrix

35)
a) x, y, z are in A. P
b) x, y, z are in G. P
c) x, y, z are in H. P
d) xy, yz, zx are in A. P

36)
a) 1
b) 0
c) 3
d) a + b + c

37)
a)

a2 + b2 + c2

b)

1 + a2 + b2 + c2

c)

1- a2 – b2 + c2

d) None of the given

Answers

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