Mathematics Times – July 2019

16.Let

(a)

1

3 (b)

1

3

 (c)^1

13

 (d)^1

13

f x x x g x  ,  sinx and

h x gof x   . Then [2014]

(a)

17.Let for

h x  is not differentiable at x0.

(b) h x  is differentiable at x0, but h x'  is

not continuous at x 0

(c) h x'  is continuous at x 0 but it is not

differentiable at x 0

(d) h x'  is differentiable at x 0

i1,2,3,P xi  be a polynomial of degree 2

in x, P xi'  and P xi''  be the first and second

order derivative of P xi  respectively. Let,

 

     

     

     

1 1 2

2 2 2

3 3 3

' ''

' ''

' ''

P x P x P x

A x P x P x P x

P x P x P x

 

 

 

 

and      .

T

B x A x A x   Then determinant of

B x : [2014]
(a) is a Polynomial of degree 6 in x.
(b) is a Polynomial of degree 3 in x.
(c) is a Polynomial of degree 2 in x.
(d) does not depend on x.
18.If the Rolle’s theorem holds for the function

f x x ax bx  2 3 ^2  in the interval 1,1 for

the point

(^1) ,
2
c then the value of 2 a b is:
[2014]
(a) 1 (b)  1 (c) 2 (d)
19.Consider the function
 2
f x x        1 , 1x x 3 where x is the
greatest integer function.
Statement 1: f is not continuous at x0,1,2
and 3.
Statement 2:  
; 1 0
1 ; 0 1
1 ; 1 2
2 ; 2 3.
x x
x x
f x
x x
x x
   
  

  
   
(a) Statement 1 is true; statement 2 is false
(b) Statement 1 is true; statement 2 is true ;
Statement 2 is not the correct explanation for
statement 1
(c) Statement 1 is true; statement 2 is true ;
statement 2 is the correct explanation for
statement 1
(d) Statement 1 is false; statement 2 is true
20.Let f be a composite function of x defined by
  2  
(^1) , (^1).
2 1
f u u x
u u x
 
   Then the
number of points x where f is discontinuous is :
[2013]
(a) 4 (b) 3 (c) 2 (d) 1
21.Let f x     1 x 2 , and g x  1 ;x then
the set of all points where fog is discontinuous is :
[2013]
(a) {0,2} (b) {0,1,2}
(c) {0} (d) An empty set
22.If the curves
2 2
1
4
x y

  and y^3  16 x intersect
at right angles, then the value of  is : [2013]
(a) 2 (b)
23.For
4
3 (c)
1
2 (d)
3
4
0, 0, ,
2
a t
 
  
 
let
sin^1 t
x a

 and
cos^1
y a t.

 Then
2
1
dy
dx
 
   equals :^ [2013]
(a)
DETERMINANTS [ONLINE QUESTIONS]

1. a 2. b 3. c 4. b 5. b
   6. d 7. c 8. d 9. a 10. d
   11. a 12. c 13. a 14. d 15. c
   16. a 17. b 18. d 19. b 20. b
   21. b 22. c 23. d

[OFFLINE QUESTIONS]

1. d 2. a 3. b 4. c 5. d
   6. b 7. a 8. c 9. c 10. b

2

2

x

y (b)

2

2

y

x

(c)

2 2

2

x y

y



(d)

16. 
    

[2014]

17. 
    

[2014]

18. 
    

[2014]

19. 
    

Statement 1:

Statement 2:

20.

[2013]

21.

[2013]

22.

[2013]

23.

[2013]

2 2

2

x y

x



DETERMINANTS [ONLINE QUESTIONS]

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[OFFLINE QUESTIONS]

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