# Matrices & Determinants MCQs Part IV

1) The value of the determinant
a) 0
b) -1
c) 1
d) 10

2)
a) a/b is one of the cube roots of unity
b) a is one of the cube roots of unity
c) b is one of the cube roots of unity
d) a/b is one of the cube roots of -1

3) If A, B and C are the angles of a triangle and
then the triangle ABC is

a) isosceles
b) equilateral
c) right angled isosceles
d) none of these

4) If a b c are the sides of a
ABC and A, B,C are respectively the angles opposite to them, then

a) sin A – sin B sin C
b) abc
c) 1
d) 0

5) If m is a positive integer and
Then the value of

a) 0
b)
c)
d)

6)
a) 0
b) 1
c) 2
d) 4 pqr

7) If x, y, z are in A. P., then the value of the determinant
a) 1
b) 0
c) 2a
d) a

8)
a) 0
b) 1
c) 100
d) -100

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

10) If p + q + r = 0 = a + b + c, then the value of the determinant
a) 0
b) pa + qb + rc
c) 1
d) none of these

11) If
are respectively the
terms of a GP, then the value of the
determinant

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

12) If A is an invertible matrix, then
is equal to

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

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

14) The determinant
is divisible by

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

15)
a)
b)
c)
d) none of these

16)

The determinant
is equal to zero, if

 i ii iii iv a, b, c, are in AP a, b, c, are in GP a, b, c are in HP

a) (i) and (ii)
b) (i) and (iii)
c) (iv) only
d) (i) and (iv)

17)
a) 0
b) 1
c)
d) none of these

18) If
are in GP, then the determinant

a) 0
b) 1
c) 2
d) none of these

19) If x, y, a are all distinct and
a) -2
b) -1
c) -3
d) none of these

20)
a) 1
b) 2
c) 3
d) 4

21) If A is square matrix of order n such that its elements are polynomial
in x and its r-rows become identical for
then

a)
b)
c)
d)

22)
then the value of k is

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

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

24) The value of the determinant
a)
b)
c)
d) none of these

25) If A, B, C are the angles of a triangle, then the value of
a) cos A cos B cos C
b) sin A sin B sin C
c) 0
d) none of these

26)
a)
b)
c)
d) none of these

27) If x, y, z are in AP, then the value of the det A is, where
a) 0
b) 1
c) 2
d) none of these

28) If ,
then the value of x satisfying the equation

a) a
b) b
c) c
d) 0

29) If a, b, c are different, then the value of x satisfying
a) a
b) b
c) c
d) 0

30)
a) 3
b) 2
c) 4
d) none of these

31) The value of the determinant
is

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

32) If
is a non-singular matrix and
is a square matrix, then Det
is equal to

a) Det (B)
b) Det (A)
c)
d)

33) The values of
and
for which the system of equations
have no solution are

a)
b)
c)
d)

34) One factor of
a)
b)
c)
d) none of these

35) Let A
a)
b)
c)
d) All the above

36) If a, b,c are non-zero real numbers, then vanishes when
a)
b)
c)
d)

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

38) The system of simultaneous equations x + 2y – z = 1 , (k-1)y – 2z = 2 and
(k+2)z=3 have a unique solution if k equals

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

39) The value determinant
a)
b) 3
c) -3
d) none of these

40) If a, b, c are non-zero real numbers such that
a)
b)
c)
d) all the above

41) If the system of equations x+ay+az=0;bx+y+bz=0 and cx+cy+z=0
where a,b and c are non-zero non unity has a non trivial solution, then the value of

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

42) The determinant
a) a
b)
c)
d)

43) If
is a cube root of unity then a root of the following polynomial
is

a) 1
b)
c)
d) 0

44) If
a)
b)
c)
d)

45)
a) 0
b) 1
c) -1
d) 2

46)
a)
b)
c)
d)

47) The factors of
are

a)
b)
c)
d)

48) If
is a cube root of unity, then

a) 1
b)
c)
d) 0

49)
a)
b)
c)
d)

50) A and B are two non-zero square matrices such that Then,
a) both A and B are singular
b) either of them is singular
c) neither matrix is singular
d) none of these

51) The roots of the equation
a) 1,2
b) -1,2
c) 1,-2
d) -1,-2

52) From the matrix equation
we can conclude
provided

a) A is singular
b) A is non-singular
c) A is symmetric
d) A is square

53) If k is a scalar and A is
square matrix. Then

a)
b)
c)
d)

54)
a) 1
b) 0
c) -1
d) 67

55)
a) 4
b) x + y + z
c) xyz
d) 0

56) A root of the equation
a) a
b) b
c) 0
d) 1

57) Let a, b, c be positive real numbers. The following system of equations
in x, y and z

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

58) If
are the cube roots of unity, then
has the value

a) 0
b)
c)
d) 1

59) In a third order determinant, each element of the first column
consists of sum of two terms, each element of the second column
consists of sum of three terms and each element of the third column
consists of sum of four terms. Then it can be decomposed into
n determinants, where n has the value

a) 1
b) 9
c) 16
d) 24

60) A root of the equation
a) 6
b) 3
c) 0
d) none of these

61)
a) x + y
b) xy
c) x – y
d) 1 + x + y

62)
a) a + b + c = 0
b) -(a + b + c)
c) 0, a + b + c
d) 0,- (a + b + c)

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

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

64)
a)
b)
c)
d)

65) If A is a singular matrix, then A adj A is
a) identity matrix
b) null matrix
c) scalar matrix
d) none of these

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

a) p
b) q
c)
d) 0

67) A square matrix can always be expressed as a
a) sum of symmetric matrix and a skew symmetric matrix
b) sum of diagonal matrix and a symmetric matrix
c) skew matrix
d) skew symmetric matrix

68) For a square matrix A, it is given that
, then A is a

a) orthogonal matrix
b) diagonal matrix
c) symmetric matrix
d) none of these

a) Every scalar matrix is an identity matrix
b) Every identity matrix is a scalar matrix
c) Every diagonal matrix is an identity matrix
d) A square matrix whose each element is 1 is an identity matrix

70) If A and B are square matrices of the same type then
a) A+ B = B+ A
b) A+ B = A – B
c) A – B = B – A
d) AB= BA

71) The value of is
a) 0
b) a + b+ c
c) 4 abc
d) abc

72)
a) a = 1, b = 1
b)
c)
d)

73) If A,B are square matrices of order 3, then
a)
b)
c)
d)

74) A row matrix has only
a) one element
b) one row with one or more columns
c) one column with one or more rows
d) one row and one column

75) A column matrix has only
a) one row and one column
b) one row with one or more columns
c) one column with one or more rows
d) one element

76) If A and B are two matrices such that A+B and AB are both defined,
then

a) A and B can be any matrices
b) A, B are square matrices not necessarily of same order
c) A,B are square matrices of same order
d) Number of columns of A = number of rows of B

77) If A is a square matrix, then adj
is equal to

a)
b)
c) null matrix
d) unit matrix

78) If A=
is a scalar matrix of order nxn such that =k
for all I, then trace of A is equal to

a) nk
b) n+k
c) n/k
d) none of these

79) is
the identity matrix of order n, then rank of
is

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

80) For the equations: x+2y+3z=1,2x+y+3z=2,5x+5y+9z=4
a) there is only one solution
b) there exists infinitely many solution
c) there is no solution
d) none of these

81) From the matrix equation AB = AC we can conclude B=C provided
a) A is singular
b) A is non – singular
c) A is symmetric
d) A is square

82) If
is equal to

a) unit matrix
b) null matrix
c) A
d) -A

83) If
a) AB = BA = 0
b)
c)
d) none of these

84) If then

a)
b) does not exist
c) is a skew symmetric matrix
d) none of these

85) The system of equations 3x + y – z = 0, 5x +2y – 3z= 2, 15x + 6y – 9z
= 5 has

a) a unique solution
b) two distinct solutions
c) no solution
d) infinitely many solutions

86) Matrix Theory was introduced by
a) Newton
b) Cayley-Hamilton
c) Cauchy
d) Euclid

87) If A is singular matrix, then Adj A is
a) Singular
b) Non-singular
c) Symmetric
d) Not defined

88) If A and B are any
matrics, then det (A +B) = 0 implies

a) det A + det B = 0
b) det A = 0 or det B = 0
c) det A = 0 and det B = 0
d) none of these

89) The parameter on which the values of the determinant
does depend upon

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

90) The equation x + 2 y + 3 z = 1,x – y + 4 z = 0, 2x + y + 7 z = 1 have
a) only one solution
b) only two solutions
c) no solution
d) infinitely many solutions

91)
a) 0
b) 1
c) i
d)

92) The number of solutions of
is

a) 0
b) 1
c) 2
d) infinitely many

93) 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

94) 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

95) The matrix is
known as

a) symmetric matrix
b) diagonal matrix
c) upper triangular matrix
d) skew symmetric matrix

96) For a square matrix A, it is given that ,
then A is a

a) orthogonal matrix
b) diagonal matrix
c) symmetric matrix
d) none of these

97) A square matrix can always be expressed as a
a) sum of symmetric matrix and a skew symmetric matrix
b) sum of diagonal matrix and a symmetric matrix
c) skew matrix
d) skew symmetric matrix

98) If A is a square matrix, then is
equal to

a)
b)
c) null matrix
d) unit matrix

99) If A is a non-zero column matrix of order m x 1 and B is a non-zero row
matrix of order 1 x n, then rank of AB is equal to

a) m
b) n
c) 1
d) none of these

100) If A, B and C are the angles of a triangle and
then the triangle must be

a) Equilateral
b) Isosceles
c) Any triangle
d) Right angled