# 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 (x**

_{1},y

_{1});(x

_{2},y

_{2});(x

_{3},y

_{3}), 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
admit
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)**

**Answers**