# Matrices & Determinants MCQs Part III

1) The value of the determinant
a)
b)
c)
d)

2) The solution set of the equation
a)
b)
c)
d)

3) If A is square matrix such that
then for any +ve integer n,
is equal to

a) 0
b)
c)
d)

4) The multiplicative inverse of
a)
b)
c)
d)

5) The multiplicative inverse of the matrix
a)
b)
c)
d)

6) If a, b, c are non-zero real numbers, then the inverse of the matrix
a)
b)
c)
d)

7) For any
matrix A, if A (Adj A)

a) 0
b) 10
c) 20
d) 100

8) If
a)
b)
c)
d)

9) If
then the value of

a)
b)
c)
d)

10) For a
matrix A, if det A = 4, then det (Adj A) equals

a) -4
b) 4
c) 16
d) 64

11) If
the entries in a
determinant
are either 0 or 1, then the greatest value of this determinant is

a) 1
b) 2
c) 3
d) 9

12) The inverse of the matrix
a) A
b)
c)
d)

13) If a + b + c = 0, one root of
a) x = 1
b) x = 2
c)
d) x = 0

14) The factors of
a) x – a, x – b and x + a + b
b) x + a, x +b and x +a + b
c) x + a, x + b and x- a- b
d) x – a, x – b and x – a – b

15) If
a)
b)
c)
d)

16) If one of the roots of the equation
a) (2,6)
b) (3,6)
c) (2,7)
d) (3,7)

17) One root of the equation
a)
b)
c)
d)

18) If
then the value of

a) 0
b)
c)
d)

19) If (1 2 3 ) A = (4 5), what is the order of matrix A ?
a)
b)
c)
d)

20) If
a)
b)
c)
d)

21) The value of the determinant
a) n
b) a
c) x
d) none of these

22) If a, b, and c are all different from zero and
then the value of

a) abc
b)
c) -a – b – c
d) -1

23) If
a) 0
b) abc
c) -abc
d) none of these

24) If are
real numbers then

a) -1
b)
c)
d) 0

25) If a, b and c are non-zero real numbers, then
a) abc
b)
c) bc + ca + ab
d) 0

26) If each element of a
matrix is multiplied by 3, then the determinant of the newly formed matrix
is

a) 3 det A
b) 9 det A
c) 27 det A
d)

27) Let
denote the element of the ith row and jth column in a
determinant
and let
for every
and j. Then the determinant has all the principal diagonal elements as

a) 1
b) -1
c) 0
d) none of these

28) The value of the determinant
a) 1
b) -1
c) 0
d) none of these

29) The value of the determinant
a) 1
b) 0
c) 2
d) 3

30) If x,y,z are in A.P., then the value of the det
a) 0
b) 1
c) 2
d) none of these

31) If
are the roots of the equation
then value of the

a) p
b) q
c)
d) 0

32) If a,b,c are in A.P., then the value of
a) 3
b) -3
c) 0
d) none of these

33) If a > 0, b > 0, c > 0 are respectively, the pth, qth,
rth terms of a G.P., then the value of the determinant

a) 1
b) 0
c) -1
d) none of these

34) If a, b, c are in G.P ., then the value of the determinant
a) 1
b) 0
c) -1
d) none of these

35) Given then
the value of

a) 0
b)
c) 1
d) 2

36) Let A be an invertible matrix. Which of the following is not true?
a)
b)
c)
d) none of these

37) Let Then,

a)
b)
c)
d)

38) The determinant
a)
b)
c)
d)

39) If the system of equations
and
has a non-trivial solution, then the value of
is

a) -1
b) 0
c) 1
d) none of these

40) The value of a for which the system equation

has a non- zero solution is

a) 1
b) 0
c) -1
d) none of these

41) If
then the value of
is

a) 1
b) 2
c) 4
d) 3

42) If in
then
is

a) 0
b) -D
c) D
d)

43) Inverse of
is

a)
b)
c)
d) none of these

44) A and B are square matrices of order
is equal to

a)
b)
c)
d)

45) If
Then
is equal to

a) 0
b) 1
c) 100
d) -100

46) The value of
is

a) 0
b) a + b+ c
c) 4 abc
d) abc

47) If A and B are square matrices of order 3 such that
then

a) -9
b) -81
c) -27
d) 81

48) For any
matrix A, if A (adj. A)

a) 0
b) 10
c) 20
d) 100

49) If
the value of x which satisfies the equation
is

a) x = a
b) x = b
c) x = c
d) x=0

50) If
is cube root of unity , then

a)
b)
c)
d)

51) If every element of a third order determinant of value is multiplied by 5 then the value of the new determinant is
a)
b)
c)
d)

52) If=,
then x=

a) 6
b) 7
c) 8
d) none of these

53) If=0,
then one of the values of x is

a) a+b+c
b) -(a+b+c)
c)
d)

54) Cofactor of 4 in the determinant
is equal to

a) 2
b) -2
c) -5
d) none of these

55) If x+y+z=,
then the value of
is equal to

a) 0
b) 2sinB tanA cosC
c) 1
d) none of these

56) The value of determinant
a) -2
b)
c) 2
d) none of these

57) If one root of the equation
is x=-9, then the other root are

a) 2,6
b) 3,6
c) 2,7
d) 3,7

58) If
is a cube root of unity, then a root of the equation
is

a) x=1
b)
c)
d) x = 0

59) If the value of a third order determinant is 11, then the value of the
square of the determinant formed by the cofactors will be

a) 11
b) 121
c) 1331
d) 14641

60) LetThe

lies in the interval

a) [3,4]
b) [2,4]
c) [1,4]
d) none of these

61) is
equal to

a) m(m+1)
b) 0
c) 1
d) m(m-1).

62) If a,b,c are different and
then

a) a+b+c=0
b) abc=1
c) a+b+c=1
d) ab+bc+ca=0.

63) If
are given determinants, then

a)
b)
c)
d)

64) For the system of equations
if
then the system has

a) more than two solutions
b) one trivial and one non-trivial solution
c) No solution
d) only trivial solution(0,0,0).

65) If the system of linear equationshave
a non-zero solution, then a, b,c are in

a) A P
b) G P
c) H P
d) none of these

66) The value of
for which the system of equations 2x-y+3=0; x+y+7=0;
3x+2y-2=0 is consistent is given by

a) – 3
b) – 9
c) -45/13
d) 45/13

67) If are
respectively the cofactors of the elements
of the determinant

a)
b)
c)
d) none of these

68) If
then the real value of x is

a) 2
b) 3
c) 4
d) 6

69) The parameter, on which the value of the determinant
does not depend upon, is

a) a
b) p
c) d
d) x

70) The determinant
if

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

71) Let
where p is a constant. Then
at x=0 is

a) p
b)
c)
d) Independent of p.

72) If x is a positive integer, then
is equal to

a)
b)
c)
d)

73) If
then

a) –1/3
b) 1/4
c) 1/2
d) none of these

74) If
then

a) a is one of the cube roots of unity
b) b is one of the cube roots of unity
c) (a/b)is one of the cube roots of unity
d) none of these

75)
a) 0
b) a
c) 3
d) 2a

76)
a) p + q + r
b) 0
c) p – q – r
d) – p + q + r

77) If
then

a) x = 3, y = 1
b) x = 1, y = 3
c) x = 0, y = 3
d) x = 0, y = 0

78) The determinant for all if
a) x, y, z are in AP
b) x, y, z are in GP
c) x, y, z are in HP
d) xy, yz, zx are in AP

79) The determinant
then

a) d=0
b) a + d = 0
c) d = 0 or a + d = 0
d) none of these

80) The value of the determinant,
where a, b, c are the pth, qth and rth terms of a HP, is

a) ap + bq + cr
b) (a+b+c)(p+q+r)
c) 0
d) none of these

81) The sum of two non-integral roots of
is

a) 5
b) -5
c) -18
d) none of these

82) If x, y, z are integers in AP, lying between 1 and 9, and x51, y41 and z31 are
three-digit numbers, then the value of
is

a) x + y + z
b) x – y + z
c) 0
d) none of these

83) The value of
is equal to

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

84) Eliminating a, b, c from
we get

a)
b)
c)
d) none of these

85) The system of equations
has

a)
b)
c)
d)

86)
a) abc > 1
b) abc > -8
c) abc < -8
d) abc > -2

87)
a) Zero
b) positive
c) negative
d)

88)
a)
b)
c)
d) none of these

89) Given that xyz = -1, the value of the determinant
is

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

90)
a)
b)
c) 1
d) none of these

91) The value of the determinant
is

a)
b)
c)
d) none of these

92)
a)
b)
c)
d) none of these

93) Let
then the value of

a) 0
b) a + b + c
c) ab + bc + ca
d) none of these

94)
is
a polynomial of degree

a) 2
b) 3
c) 4
d) none of these

95)
then
equals

a)
b)
c)
d) none of these

96) If
then k equals

a) 1
b) -1
c)
d)

97) If
is an imaginary cube root of unity, then the value of

a) 0
b)
c)
d)

98)
a)
b)
c)
d) none of these

99)
a)
b)
c)
d)

100) The largest value of a third order determinant whose elements are 0 or 1,
is

a) 1
b) 0
c) 2
d) 3