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CBSE Questions for Class 12 Commerce Maths Continuity And Differentiability Quiz 13 - MCQExams.com
CBSE
Class 12 Commerce Maths
Continuity And Differentiability
Quiz 13
If f is twice differentianle such that f"
(
x
)
=
−
f
(
x
)
,
f
′
(
x
)
=
g
(
x
)
,
h
′
(
x
)
=
(
f
(
x
)
)
2
+
(
g
(
x
)
)
2
and
h
(
0
)
=
2
,
h
(
1
)
=
4
,then equation of
h
(
x
)
represents ?
Report Question
0%
curve of degree
2
0%
curve passing through origin
0%
a straight line with slope
2
0%
a straight line with slope
−
2
The value of
∫
π
/
2
0
sec
2
x
d
x
(
sec
x
+
tan
x
)
n
,
n
>
1
is equal to
Report Question
0%
1
n
2
−
1
0%
1
n
2
+
1
0%
n
n
2
−
1
0%
n
n
2
+
1
Let
f
be the function on
[
0
,
1
]
given by
f
(
x
)
=
x
sin
π
x
f
o
r
x
≠
0
and
f
(
0
)
=
0
. Then
Report Question
0%
Continuous but bounded
0%
Differentiable
0%
Continuous but not bounded
0%
Continuous and bounded
If
f
(
x
)
=
√
x
+
2
√
2
x
−
4
+
√
x
−
2
√
2
x
−
4
, then
f
(
x
)
is differentiable on
Report Question
0%
(
−
∞
,
∞
)
0%
[
2
,
∞
)
−
{
4
}
0%
[
2
,
∞
)
0%
(
0
,
∞
)
If
y
=
sec
−
1
(
√
x
+
1
√
x
−
1
)
+
sin
−
1
(
√
x
−
1
√
x
+
1
)
, then
d
y
d
x
is equal to
Report Question
0%
0
0%
1
√
x
+
1
0%
1
0%
N
o
n
e
o
f
t
h
e
s
e
If
f
(
x
)
is a non constant polynomial function
f
:
R
→
R
such that
7
d
d
x
(
x
f
(
x
)
)
=
3
f
(
x
)
+
4
f
(
x
+
1
)
,
f
(
−
1
)
+
f
(
0
)
=
2
, then number of such function is
Report Question
0%
0
0%
1
0%
2
0%
3
The function
f
(
x
)
=
(
x
2
−
1
)
|
x
2
−
3
x
+
2
|
+
cos
(
|
x
|
)
is not differentiable at
Report Question
0%
−
1
0%
0
0%
1
0%
2
If
y
=
tan
−
1
(
ℓ
n
e
x
2
ℓ
n
x
2
)
+
tan
−
1
3
+
2
ℓ
n
x
1
−
6
ℓ
n
x
then
d
2
y
d
x
2
=
Report Question
0%
2
0%
1
0%
0
0%
−
1
If
f
(
x
)
=
p
|
sin
x
|
+
q
e
|
x
|
+
r
|
x
|
3
and
f
(
x
)
is differentiable at
x
=
0
, then
Report Question
0%
q
+
r
=
0
;
p
is any real number
0%
p
+
q
=
0
;
r
is any real number
0%
q
=
0
,
r
=
0
;
p
is any real number
0%
r
=
0
,
0
\p
=
o
\0
;
q
is any real number
The derivative of
f
(
tan
−
1
x
)
, where
f
(
x
)
=
tan
x
is
Report Question
0%
1
0%
1
1
+
x
2
0%
2
0%
−
1
1
+
x
2
If
x
2
a
2
+
y
2
b
2
=
1
, then
d
2
y
d
x
2
=
Report Question
0%
−
b
4
a
2
y
3
0%
−
b
2
a
y
2
0%
−
−
b
3
a
2
y
3
0%
−
b
3
a
2
y
2
If
f
(
x
)
=
√
x
+
2
√
2
x
−
4
+
√
x
−
2
√
2
x
−
4
, then f(x) is differentiable on
Report Question
0%
(
−
∞
,
∞
)
0%
[
2
,
∞
)
−
{
4
}
0%
[
2
,
∞
)
0%
[
0
,
∞
)
f
(
x
)
=
m
i
n
1
,
c
o
s
x
,
1
−
s
i
n
x
,
−
π
≤
x
≤
π
then
Report Question
0%
f(x) is not differentiable at '0'
0%
f(x) is differentiable at
π
/
2
0%
f(x) has local maximum at '0'
0%
None of these
If y = tan
−
1
√
1
+
x
2
−
1
x
, then
d
y
d
x
=
Report Question
0%
1
1
+
x
2
0%
−
1
1
+
x
2
0%
1
2
(
1
+
x
2
)
0%
2
1
+
x
2
Let
f
be a differentiable function for all
x
. If
f
(
1
)
=
−
2
and
f
′
(
x
)
≥
2
for
x
∈
[
1
,
6
]
then
Report Question
0%
f
(
6
)
<
5
0%
f
(
6
)
=
5
0%
f
(
6
)
≥
8
0%
f
(
6
)
<
8
The number of points at which
g
(
x
)
=
1
1
+
2
f
(
x
)
is not differentiable where
f
(
x
)
=
1
1
+
1
x
is
Report Question
0%
1
0%
2
0%
3
0%
4
If
y
=
c
o
s
−
1
(
x
−
x
−
1
x
+
x
−
1
)
,
then
d
y
d
x
=
Report Question
0%
−
2
1
+
x
2
0%
2
1
+
x
2
0%
1
1
+
x
2
0%
−
1
1
+
x
2
If
C
o
s
−
1
(
x
2
−
y
2
x
2
+
y
2
)
=
a
, then
d
y
d
x
=
Report Question
0%
x
y
0%
−
x
y
0%
y
x
0%
−
y
x
The derivate of
tan
−
1
[
sin
x
1
+
cos
x
]
with respect to
tan
−
1
[
cos
x
1
+
sin
x
]
is
Report Question
0%
2
0%
−
1
0%
0
0%
−
2
If
y
=
cos
−
1
(
x
−
x
−
1
x
+
x
−
1
)
, then
d
y
d
x
is equal to
Report Question
0%
−
2
1
+
x
2
0%
2
1
+
x
2
0%
1
1
+
x
2
0%
−
1
1
+
x
2
if
f
(
x
)
=
a
|
s
i
n
x
|
+
b
e
x
+
c
|
x
3
|
, where
a
,
b
,
c
ϵ
R, is differentiable at
x
=
0
then
Report Question
0%
a
=
0
,
b
a
n
d
c
are real numbers
0%
c
=
0
,
a
=
0
, be is any real numbers
0%
b
=
0
,
c
=
0
a is any real numbers
0%
a
=
0
,
b
=
0
,
c
is any real numbers
If
f
(
x
)
is differentiable function and
f
(
1
)
=
sin
1
,
f
(
2
)
=
sin
4
,
f
(
3
)
=
sin
9
, then the minimum number of distinct solutions of equation
f
′
(
x
)
=
2
x
cos
x
2
in
(
1
,
3
)
is
Report Question
0%
1
0%
2
0%
3
0%
4
Let f be a differentiable function satisfying the condition
f
(
x
y
)
=
f
(
x
)
f
(
y
)
,
for all x, y
(
≠
0
)
ϵ
R
and f(y)
≠
If f'(1)=2, then f'(x) is equal to
Report Question
0%
2 f(x)
0%
f
(
x
)
x
0%
2x f(x)
0%
2
f
(
x
)
x
Let f be a differentiable function satisfying the relation f(xy) = xf(y) - 2xy+yf(x) (where x,y > 0) and f(1) = 3, then
Report Question
0%
f(x) =x
ℓ
n
x
+
3
x
−
x
2
2
0%
f
(
x
)
=
x
ℓ
n
x
0%
x
=
e
−
3
is the abscissa of the point of inflection of f(x)
0%
the equation f(x) = k has two solution if x
∈
(
−
e
−
3
,
0
)
Let
f
:
R
→
R
be a twice differentiable function satisfying
f
′
′
(
x
)
=
5
f
′
(
x
)
+
6
f
≥
0
,
∀
x
≥
0
,
f
(
0
)
=
1
and
f
′
(
0
)
=
0
.
if
f
(
x
)
satisfies
f
(
x
)
≥
a
.
h
(
b
x
)
−
b
⋅
¯
h
(
a
x
)
,
∀
x
≥
0
,
then
a
+
b
is equal to
Report Question
0%
3
0%
1
0%
6
0%
5
S
be the set in which function defined by
f
(
x
)
=
sin
|
x
|
−
|
x
|
+
2
(
x
−
π
)
cos
|
x
|
is differtentiable then no of element in
S
is
Report Question
0%
2
0%
3
0%
4
0%
ϕ
If
y
=
sin
−
1
2
x
1
+
x
2
,
then which of the following is not correct ?
Report Question
0%
d
y
d
x
=
2
1
+
x
2
for
|
x
|
<
1
0%
d
y
d
x
=
−
2
1
+
x
2
for
|
x
|
>
1
0%
d
y
d
x
=
2
for
x
=
−
1
0%
d
y
d
x
does not exist at
|
x
|
=
1
d
d
x
(
sin
−
1
{
√
1
+
x
+
√
1
−
x
2
}
)
=
Report Question
0%
−
1
2
√
1
−
x
2
0%
1
2
√
1
−
x
2
0%
1
√
1
−
x
2
0%
−
1
√
1
−
x
2
If
y
=
cot
−
1
[
√
1
+
sin
x
+
√
1
−
sin
x
√
1
+
sin
x
−
√
1
−
sin
x
]
t
h
e
n
d
y
d
x
i
s
e
q
u
a
l
t
o
Report Question
0%
1
2
0%
2
3
0%
3
0%
2
The number of point at which the function F(x)= max
{
a
−
x
,
a
+
x
,
b
}
−
∞
<
x
<
∞
,
0
<
a
<
b
cannot be differentiable is
Report Question
0%
1
0%
2
0%
3
0%
none of these
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0
Answered
1
Not Answered
29
Not Visited
Correct : 0
Incorrect : 0
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