**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

**Answers**