CBSE Test Paper (Calculus : Continuity and Differentiability) (Class - XII Mathematics ) Class 12 Notes | EduRev

Class 12 : CBSE Test Paper (Calculus : Continuity and Differentiability) (Class - XII Mathematics ) Class 12 Notes | EduRev

 Page 1


CBSE TEST PAPER-02 
CLASS - XII MATHEMATICS (Calculus : Continuity and Differentiability) 
Topic:- Differentiation 
1. Find all points of discontinuity if [4] 
| | 3,  if      x -3
( ) 2 ,     if      -3 < x < 3
6x+2,    if      x 3
x
f x x
+ =
?
?
= - ?
?
=
?
 
2. Differentiate
3 2 5
cos .sin ( )
I
B
y x x = [4] 
3. Find
dy
dx
 if  
3 2 2 3
81 x x y xy y + + + = [4] 
4. Differentiate xy = e
(x-y)
[4] 
5. Find
dy
dx
 if (cos sin 0)  and  (sin 0 cos ) x a y a ? ? ? ? = + = - [4] 
6. If y = 3 cos (log x) + 4 sin (log x). Show that x
2
y
2
 + xy
1
 + y = 0 [4] 
7. Verify Rolle’s Theorem for the function  f(x) = x
2
 + 2x – 8, x?[-4, 2] [4] 
8. Find
dy
dx
1
sin
tan
1 cos
x
y
x
- ? ?
=
? ?
+
? ?
[4] 
9. If x = a (cos t + t sin t) and  y = a (sin t – t cos t), find
2
2
d y
dx
[4] 
10. If
f(x)      g(x)      h(x) 
l            m          n 
a            b          c 
y = Prove that 
f'(x)    g'(x)    h'(x)
l           m        n   
a           b         c 
dy
dx
= [4] 
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