Braj Education Centre
CBSE, ICSE and JEE-2017
Braj Education Centre
(CULTIVATING ACADEMIC MINDS)
Class
:
XII
Subject
:
Mathematics
Topic
:
Differentiation and Continuity
MM: 60
Time: 2 Hrs
DO ANY 15 QUESTIONS. EACH QUESTION CARRIES 4 MARKS
1.
3
 2x  3 
dy
1 x 9 
A) If y  tan 1  3
  tan 
 , find
dx
 2x  3 
 x 9 
 1
sec _1 
4 3
 x
B) Differentiate
sin 1 x
2.
If y 
3.
If y  sin 1
4.
For
1  x2
what

x

 with respect to
, show that 1  x 2 
d2y
dy
 3x  y  0
2
dx
dx
1 x  1 x
dy
1
, show that

2
dx 2 1  x 2
value
of
k
is
the
following
function
continuous
at x  2,
2 x  1 ; x  2

f  x   k
; x2
 3x  1 ; x  2

5.
If y  eex cos bx, prove that
d 2x
dy
2
 2a
dx
 (a 2  b 2 ) y  0
dy
dy
1  y2

1  x  1  y  a  x  y  Prove that
dx
1  x2
6.
If
7.
Verify Rolle's Theorem for the function f  x   x 2  5x  4 on [1, 4].
8.
x
x
x
sin x
1
x 1
x
1
Given that cos cos cos ... 
, prove that 2 sec2  4 sec2 ...  cos ec 2 x  2
2
4
8
x
2
2 2
4
x
2
2
 2 1 x2  5 1 x2
9. Differentiate: y  cot 
 5 1 x2  2 1 x2

1




Or
Call me 24 x 7 @
22711085; 9818501969
1
email: s_braj@rediffmail.com
Braj Education Centre
CBSE, ICSE and JEE-2017
dy
if x and y are connected parametrically by the equation given below
dx
Find
t
x  a (cos t  log tan ), y  a sin t
2
10. Prove
that
d x 2
a 2 1  x 
2
a

x

sin    a 2  x 2

dx  2
2
 a 
Or
d2y
dy
0
If y  log  x  x 2  1 Pr ove that  x 2  1 2  x


dx
dx
11. Using
Mean Value Theorem,
find a point on the parabola y  ( x  3)2 , where
tangent is parallel to the chord joining (3 , 0) and (5 , 4)
 x5
 x5  a ,x  5

,x 5
12. If f ( x )   a  b
 x5

b ,x 5
 x  5
13. Fins
dy
x2  1
if y  x tan x 
dx
2
14. Differentiate: y  tan
15.
is a continuous function. Find a, and b.

1
 xx

1  x3/ 2






2
d 2x
dy
y  log x  x 2  2  , show that (1+x 2 ) 2  x  2


dx
dy
16. What
are the points of discontinuity of f ( x ) 
x2  x  1
x 2  5x  6
Or
 px 2  1, x  2
For what value of p is f ( x) 
continuous on R
 1x  2
Call me 24 x 7 @
22711085; 9818501969
2
email: s_braj@rediffmail.com