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
3
 2x + 3 
dy
1 x +9 
−1
1. A) If y tan  3
=
+
tan
, find



dx
 2x + 3 
 x +9 
 1 
sec _1 
x

4 3
x


with respect to
B) Differentiate
sin −1 x
d2y
dy
0
2. If y =
, show that (1 − x ) 2 − 3x − y =
2
dx
dx
1− x
3.
If y = sin −1
4.
For
what
2
dy
−1
1+ x + 1− x
, show that
=
dx 2 1 − x 2
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

d 2x
dx
=
− 2a + ( a 2 + b 2 ) y 0
dy
dy 2
5.
If y
6.
If
7.
Verify Rolle's Theorem for the function f ( x ) = x 2 − 5 x + 4 on [1, 4].
8.
1
x 1
x
1
x
x
x
sin x
Given that cos cos cos ... =
, prove that 2 sec 2 + 4 sec 2 ... =
cos ec 2 x − 2
2
2 2
4
2
4
8
x
x
9.
 2 1 + x2 − 5 1 − x2
Differentiate: y = cot −1 
 5 1 + x2 + 2 1 − x2

eex cos bx, prove that
1 − x 2 + 1 − y 2 = a ( x − y ) Prove that
dy
1 − y2
=
dx
1 − x2




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
d x 2
a 2 −1  x  
2
10. Prove that
a − x + sin    =
dx  2
2
 a 
a2 − x2
Or
d2y
dy
If y = log  x + x 2 + 1  Pr ove that ( x 2 + 1) 2 + x = 0


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 ) =
is a continuous function. Find a, and b.
a + b
 x −5

+b ,x > 5
 x − 5
13. Fins
dy
x2 + 1
=
if y x tan x +
dx
2
14. Differentiate:
15.
 x−x
y = tan −1 
3/ 2
1 + x
(




)
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
continuous on R
For what value of p is f ( x) 
 −1x < 2
Call me 24 x 7 @
22711085; 9818501969
2
email: s_braj@rediffmail.com