Practice question on Matrix and determinant for IIT-JEE , NDA and Airforce

Matrix and determinant

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Question no. 1

If A= then what is A + A^-1 equal to?

looks_one 3I

looks_two 5I

looks_3 7I

looks_4 None of these

Option looks_4 None of these

Solution :

Question no. 2

Which one of the following matrices is an elementary matrix?

looks_one

looks_two

looks_3

looks_4

Option looks_3

Solution :
an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation
Only Option 3 is satisfied.

Question no. 3

=

looks_one 1

looks_two 0

looks_3 3

looks_4 a+b+c

Option looks_two 0

Solution :

Question no. 4

If = Ka²b²c² , then K =

looks_one -4

looks_two 2

looks_3 4

looks_4 8

Option looks_two 2

Solution :

Question no. 5

The value of is equal to

looks_one 9a²(a+b)

looks_two 9b²(a+b)

looks_3 a²(a+b)

looks_4 b²(a+b)

Option looks_two 9b²(a+b)

Solution :

Question no. 6

A root of the equation =0 is

looks_one 6

looks_two 3

looks_3 0

looks_4 none of these

Option looks_3 0

Solution :

Question no. 7

=

looks_one 0

looks_two(p-q)(q-r)(r-p)

looks_3 pqr

looks_4 3pqr

Option looks_one 0

Solution :

-(p-q)[-(q-r)(r-p)] + (p-r)[(q-p)(r-q)]
(p-q)(q-r)(r-p) + (p-r)(q-p)(r-q) = 0

Question no. 8

The determinant =0 , if a,b,c are in

looks_one A.P.

looks_two G.P.

looks_3 H.P.

looks_4 none of these

Option looks_two G.P.

Solution :

Question no. 9

The values of the determinant is

looks_one a + b + c

looks_two (a + b + c)²

looks_3 0

looks_4 1 + a + b + c

Option looks_3 0

Solution :

Question no. 10

If a,b,c are unequal, what is the condition that the value of the following determinant is zero ∆=

looks_one 1+abc=0

looks_two a + b+ c + 1= 0

looks_3 (a-b)(b-c)(c-a)=0

looks_4 none of these

Option looks_3 (a-b)(b-c)(c-a)=0

Solution :

Question no. 11

If -9 is a root of the equation =0 then the other two roots are

looks_one 2,7

looks_two -2,7

looks_3 2,-7

looks_4 -2,-7

Option looks_one 2,7

Solution :

Question no. 12

If =k(x+y+z)(x-z)², then k=

looks_one 2xyz

looks_two 1

looks_3 xyz

looks_4 x²y²z²

Option looks_two 1

Solution :

Question no. 13

=

looks_one abc

looks_two 4abc

looks_3 4a²b²c²

looks_4 a²b²c²

Option looks_3 4a²b²c²

Solution :

Question no. 14

=

looks_one abc

looks_two 1/abc

looks_3 0

looks_4 ab+bc+ac

Option looks_3 0

Solution :

Question no. 15

One of the roots of the given equation =0

looks_one -(a+b)

looks_two -(b+c)

looks_3 -a

looks_4 -(a+b+c)

Option looks_4 -(a+b+c)

Solution :

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