Mathematics Times – July 2019

(a) Both the statements are true

(b) Both the statements are false

(c) Statement-I is true, but Statement-II is false.

(d) Statement I is false, but Statement-II is true.

9. If

2

2

2

1 2

2 3 1 3 3 3 12,

2 3 2 1 2 1

x x x x

x x x x ax

x x x x

  

    

   

then ‘a’

is equal to [2015]
(a) 24 (b) -12 (c) -24 (d) 12
10.The least value of the product xyz for which the

determinant

1 1

1 1

1 1

x

y

z

is non-negative, is : [2015]

(a) -1 (b) 2 2 (c) 16 2 (d) -8

11.If A is a 3 3 matrix such that 5.adj 5,A then

A is equal to : [2015]

(a)

12.If  

1

5

 (b)

1

25

 (c)  1 (d)  5

1 cos 1

sin 1 cos

1 sin 1

f



  



  



and A and B

are respectively the maximum and the minimum

values of f, then (A,B) is equal to : [2014]

(a)

13.If B is a

3, 1 (b) 4,2 2 

(c) 2 2,2 2   (d) 2 2, 1 

3 3 matrix such that B^2 0, then

 

det. 1 B^50  50 B

  is equal to:^ [2014]

(a) 1 (b) 2 (c) 3 (d) 50

14.If

 

 ^2   

2 1 3 2

1

2

(^11)
1 1 3 4
2 2
r
r r r
n n a
n n
n n n
 
  

  
[2014]
(a) Depends only on a
(b) Depends only on n
(c) Depends both on a and n
(d) Is independent of both a and n

15. If

then the value of

1

1

n

r

r







2 2 2

2 2 2

2 2 2

a b c

(a ) (b ) (c )

(a ) (b ) (c )

     

     

a b c^222

k a b c , 0

1 1 1

   then k is equal to :-[2014]

(a) 4 abc (b)   4 2 (c) 4 ^2 (d)  4 abc

16.Let A be a 3 3 matrix such that

1 2 3 0 0 1

0 2 3 1 0 0

0 1 1 0 1 0

A

   

   

   

    

Then A^1 is : [2014]

(a)

3 1 2

3 0 2

1 0 1

 

 

 

 

(b)

3 2 1

3 2 0

1 1 0

 

 

 

 

(c)

0 1 3

0 2 3

1 1 1

 

 

 

 

(d)

1 2 3

0 1 1

0 2 3

 

 

 

 

17. If a,b,c are non-zero real numbers and if the system
    of equations [2014]
    a x y z^1    ,
    b y z x^1    ,
    c z x y^1    ,
    has a non-trivial solution, then ab bc ca 
    equals:
    (a) a b c  (b) abc (c) 2 (d) 3

18.Let  

11 12

11 22

21 22

: ij 0,1,2 ,

a a

S a a a

a a

  

    

  

Then the number of non-singular matrices in the

set S is : [2013]

(a) 27 (b) 24 (c) 10 (d) 20

19.Let A, other than I or -I be a 2 2 real matrix such

that A I^2  , I being the unit matrix. Let Tr A  be

the sum of diagonal elements of A. [2013]

9. 
   

[2015]

10. 
    

[2015]

11. 
    

[2015]

12. 
    

[2014]

13. 
    

[2014]

14. 
    

[2014]

15.

[2014]

16.

[2014]

17.

[2014]

18.

[2013]

19.

[2013]