# Matrices & Determinants MCQs Part I

1) The number of lines that
are parallel to 2x+6y+7=0 and have an intercept of length 10 between the coordinate
axes is

a) 1
b) 2
c) 4
d) infinitely many

2) If
is the identity matrix of order n, then

a) does not exist
b)
c) =0
d)

3) If A is any square matrix, then A (Adj A) is equal to
a) I
b)
c) 0
d)

4) If A and B be two invertible matrices of order 3, then
is equal to

a)
b)
c)
d)

5) If the equations ax + by + cz = 0, bx + cy + az = 0, and cx + ay
+ bz = 0 have a non-zero solution, then which one of the following is true

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

6) If
a) x = 2, y = 5
b) x = 4, y = 2
c) x = 2, y = 4
d) x = 4, y = 5

7) If then
the correct statement is

a) A = -B
b) A+B = A – B
c) AC = BC
d) CA = CB

8) For
matrices A, B and I, if A+B = I and 2 A – 2 B = I, then A equals

a)
b)
c)
d)

9) If
and
then AB equals

a) [-8 3]
b)
c)
d)

10) If
a) A
b) 2 A
c) 3 A
d) 4 A

11) If
a)
b)
c)
d)

12) If
a)
b)
c)
d)

13) The value of x for which the matrix productequals
an identity matrix is

a)
b)
c)
d)

14) If
is to be square root of the two rowed unit matrix, then
should satisfy the relation

a)
b)
c)
d)

15) The value of the determinant
a) 0
b) e
c)
d)

16) If
a) O
b) D
c) -D
d) none of these

17) If
matrix and
is the co-factor of the element
in Det (A), then the expression

a) 0
b) -1
c) 1
d) Det (A)

18) The value of the determinant
a) 0
b)
c) m
d) lm

19) The value of
for which the following system of equations does not have a solution x +
y + z = 6, ,
3x + 2y – 4z = -8

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

20) The value of the determinant
a) 0
b) x + y + z
c) 1 + x + y + z
d) (x – y) (y – z) (z – x )

21) If
is a complex cube root of unity, then the value of the determinant

a) 0
b)
c) 2
d) 4

22) The value of the determinant
a) 0
b) abc + pqr + xyz
c) (a – x ) ( y – z ) ( r – p )
d) none of these

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

24) The value of the determinant
a) 0
b) log (xyz)
c) log (6 xyz)
d) 6 log (xyz)

25) If
denotes the greatest integer less than or equal to the real number under consideration,
and ,
then the value of determinant

a)
b)
c)
d) none of these

26) An
equilateral triangle has each side equal to a. If the coordinates of its vertices
are (x1,y1);(x2,y2);(x3,y3), then the square of the determinant

equals

a)
b)
c)
d) none of these

27) If
then the two triangles whose vertices are and
,
are

a) congruent
b) similar
c) equal in area
d) none of these

28) If
are non-real numbers satisfying
then the value of
is equal to

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

29) The value of
is equal to zero when
m is

a) 6
b) 4
c) 5
d) none of these

30) If x> 0 and >
0 and 1,
z > 0 and1
then the value of
is

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

31) The value of is
a) 0
b)
c)
d) none of these

32) The value of the determinant
is

a) 0
b) -(6!)
c) 80
d) none of these

33)
has the value

a) 0
b) 1
c) sin A sin B cos C
d) none of these

34) The value of
is

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

35) If
= i, and
is a non-real cube root of unity then the value of
is equal to

a) 1
b) i
c)
d) 0

36) If
then f(100)
is equal to

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

37) The value of ,
where ,
is

a) 1 if m is a multiple of 4
b) 0 for all real m
c)
d) none of these

38) If such that then
a) x = 5
b) x has no real value
c) x=0
d) none of these

39) Let be an identity in , where p,q,r,s,t, are independent of . Then the value of t is
a) 4
b) 0
c) 1
d) none of these

40) Let be an identity in x, where are independent of x. Then the value of is
a) 3
b) 2
c) 4
d) none of these

41) Using the factor theorem it is found that b+c, c+a and a+b are three factors
of the determinant .
The other factor in the value of the determinant is

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

42) If the determinant
is expanded in powers of sinx, then the constant term in the expansion is

a) 1
b) 2
c) -1
d) none of these

43) If then is equal to
a)
b)
c) 0
d)

44) The system of equations
has non-trivial solutions. If a, b, c are in

a) AP
b) GP
c) HP
d) none of these

45) If the equations
and
where
of non-trivial solutions then
is

a) 2
b) 1
c)
d) none of these

46) The system of equations
is solvable if
is

a) 6
b) 8
c) -8
d) -6

47)
is divisible by

a)
b)
c)
d) all the above

48) The equation
has

a) one pair of equal real roots
b) modulus of each root 1
c) three pairs of equal roots
d) all of above

49) Let
and a,b,c be nonzero real numbers. Then the determinant

is divisible by

a) abcx
b)
c)
d) all the above

50) The arbitrary constant on which the value of the determinant
does not depend is

a)
b) p
c) d
d) a

51) Let
and
where a,b,c,d are in AP, then the common difference of the AP is

a) 1
b) 2
c) -1
d) none of these

52) If
then

a) Re (z) = 4
b) Im (z) = 0
c) lm(z) = -4
d) Im(z) = -1

53) If
then x is

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

54) A value of c for which the system of equations
is solvable (consistent) is

a) 1
b) 2
c) 5
d) none of these

55) If A is an invertible matrix, then det
a) det(A)
b)
c) 1
d) none of these

56) If A is a skew-symmetric matrix and n is a positive integer, then is
a) a symmetric matrix
b) skew-symmetric matrix
c) a diagonal matrix
d) none of these

57) If A =then
a) AB=0, BA=0
b)
c)
d)

58) If A=,
then =

a) A
b) -A
c) 2A
d) -2A

59) If A=and
B=, then

a) AB=BA
b)
c) AB=2BA
d) None of these.

60) If A=,
then =

a)
b)
c)
d)

61) If A=,
then

a)
b)
c) 0
d) I

62) If A=,
then

a) A
b) I
c) 0
d) 5I

63) Let A=
and B=
and X be a matrix. such that A=BX, Then X=

a)
b)
c)
d) None of these

64) If A=
a) x=0, y=5
b) x +y = 5
c) x = y
d) None of these

65) If A=then A is
a) Diagonal matrix
b) Scalar Matrix
c) Unit Matrix
d) None of these

66) If A is symmetric as well as skew symmetric matrix, then A is
a) Diagonal
b) Null
c) Triangular
d) None of these

67) Let A=Then
A is

a) Nilpotent
b) Idempotent
c) Scalar
d) None of these

68) If A=
and B=,
then

a) AB, BA exist and are equal
b) AB, BA exist and are not equal
c) AB exist and BA does not exist
d) AB does not exist and BA exists.

69) If the matrix AB is zero, then
a) A =0 or B =0
b) A =0 and B =0
c) It is not necessary that either A=0 or B=0
d) All these statements are wrong

70)
a) A
b)
c) 3A
d)

71)
a)
b)
c)
d)

72) If A=
a) A
b)
c)
d)

73) If
a)
b)
c)
d) none of these

74) The matrix is
a singular matrix if  is

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

75) If
then

a)
b)
c)
d) none of these

76) If
then
exists (i.e.A is invertible) if

a)
b)
c)
d) none of these

77) The reciprocal matrix of
is

a)
b)
c)
d) none of these

78) If
a) 5
b) 0
c) 1
d) none of these

79) The rank of the matrix
is

a) 3
b) 2
c) 1
d) none of these

80) The rank of the matrix
is 3 if

a)
b)
c)
d) none of these

81) The rank of the matrix
is

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

82) The system of equations x + y + z = 2, 2x – y + 3z = 5, x – 2y – z + 1 = 0 written in matrix form is
a)
b)
c)
d) none of these

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

84) 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

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

86) Given
then the value of

a) 0
b)
c) 1
d) 2

87) If the matrix
a)
b)
c) non-existent
d) none of these

88) The equations:
a) unique solution
b) no solution
c) infinitely many solutions
d) None of these.

89) For the equations: x+2y+3z=1,2x+y+3z=2, 5x+5y+9z=4,
a) There is only one solution
b) There exist infinitely many solutions
c) There is no solution
d) None of these

90) The system of linear equation:
a) No solution
b) A unique solution
c) An infinitely many solutions
d) None of these

91) is a (i)rectangular matrix (ii)singular matrix (iii)square matrix (iv)nonsingular matrix
a) i and ii
b) ii and iii
c) iii and iv
d) none of these

92) If
then

a) A + B exists
b) AB exists
c) BA exists
d) none of these

93) If p + q + r = a +b +c = 0. Then the
a) 0
b) ap + bq + cr
c) 1
d) none of these.

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

95) Let
Then,

a)
b)
c)
d)

96) Let
Then

a)
b)
c)
d)

97) For each real number x such that -1 < x < 1, let A (z) be the matrix
and

a) A (z) = A (x) + A (y)
b)
c)
d)

98)
a)
b)
c)
d)

99) If
form a G.P and
for all then

a)
b)
c) zero
d)

100) The determinant
a)
b)
c)
d)