Mathematics Times – July 2019

32

DETERMINANTS [ONLINE QUESTIONS]

1. The number of values of k for which the system of
   linear equations, ( 2) 10k x y k  
   kx k y k ( 3)   1 has no solution, is: [2018]
   (a) 1 (b) 2 (c) 3 (d) 4


2. If

2

cos 1

( ) 2sin 2

tan 1

x x

f x x x x

x x

 , then lim '( )

x

f x

 x

[2018]

(a) does not exist

(b) exists and is equal to-2

(c) exists and is equal to 0

(d) exists and is equal to 2

3. If  

0 cos sin

0,2 : sin 0 cos 0 ,

cos sin 0

x x

S x x x

x x



  

   

 

 

 

then tan 3

x S

x





  

   is equal to [2017]

(a) 4 2 3 (b)  2 3

(c)  2 3(d)  4 2 3

4. Let A be any 3 3 invertible matrix. Then which
   one of the following is not always true? [2017]
   (a) adjA A A. ^1

(b) adj adj A A A.

(c)      

2 1

adj adjA A. adjA





(d)      

1

adj adj A A. adj A





5. The number of real values of

has infinitely many solutions, is : [2017]

(a) 0 (b) 1 (c) 2 (d) 3

6. If

 for which the

system of linear equations

2 4x y z   0

4 x y z   2 0

x y z  2 2 0

4 1

,

3 1

A

 

 

 

then the determinant of the

matrix A^2016  2 A A^2015 ^2014  is : [2016]

(a) -175 (b) 2014 (c) 2016 (d) -25

7. The number of distinct real roots of the equation,

is : [2016]

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

8. Let A be a

DETERMINANTS [ONLINE QUESTIONS]

1.

[2018]

2.

[2018]

3.

[2017]

4.

[2017] Statement-I^ :^

cosx sin x sin x

sin x cosx sin x 0

sin x sin x cos x

 in the interval ,

4 4

  

 

  

3 3 matrix such that A A I^2   5 7 0.

(^1)  
(^15).
7
A  I A
Statement-II : The polynomial^3 2 3^2
5.
[2017]
6.
[2016]
7.
[2016]
8.
Statement-I :
Statement-II : A A A I  
can be reduced to 5 4 .A I 
Then :

.

.

.