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CBSE Questions for Class 12 Commerce Maths Continuity And Differentiability Quiz 14 - MCQExams.com
CBSE
Class 12 Commerce Maths
Continuity And Differentiability
Quiz 14
If
f
(
x
)
is a differentiable function in the interval
(
0
,
∞
)
such that
f
(
1
)
=
1
and
lim
t
→
x
t
2
f
(
x
)
−
x
2
f
(
t
)
t
−
x
=
1
, for each
x
>
0
, then
f
(
3
2
)
is equal to:
Report Question
0%
25
9
0%
13
6
0%
23
18
0%
31
18
Let
f
(
x
)
=
x
|
x
|
,
g
(
x
)
=
s
i
n
x
and
h
(
x
)
=
(
g
o
f
)
(
x
)
.
Then
Report Question
0%
h
′
(
x
)
is differentiable at x=0
0%
h
′
(
x
)
is continuous at x=0 but is not differentiable at x=0
0%
h
′
(
x
)
is differentiable at x=0 but
h
′
(
x
)
differentiable is not continuous at x=0
0%
h
′
(
x
)
is not differentiable at x=0
If
f
(
x
)
=
0
for
x
<
0
and
f
(
x
)
is differentiable at
x
=
0
, then for
x
≥
0
,
f
(
x
)
may be
Report Question
0%
x
2
0%
x
0%
−
x
0%
−
x
3
/
2
The value of
f
(
4
)
is
Report Question
0%
160
0%
240
0%
200
0%
N
o
n
e
o
f
t
h
e
s
e
If
y
=
sin
−
1
x
+
sin
−
1
√
1
−
x
2
, then
d
x
d
x
Report Question
0%
0
0%
1
0%
−
2
x
0%
y
x
y
=
x
20
,
find
d
2
y
d
x
2
Report Question
0%
381
x
18
0%
380
x
18
0%
389
x
18
0%
370
x
18
If
x
=
θ
−
1
θ
,
y
=
θ
+
1
θ
then
d
y
d
x
=
Report Question
0%
x
y
y
2
+
2
0%
y/x
0%
-x/y
0%
-y/x
Explanation
x
=
θ
−
1
θ
d
x
d
θ
=
1
−
(
−
1
θ
2
)
∴
d
x
d
θ
=
1
+
1
θ
2
y
=
θ
+
1
θ
d
y
d
θ
=
1
+
(
−
1
θ
2
)
∴
d
y
d
θ
=
1
−
1
θ
2
∴
d
y
d
x
=
d
y
d
θ
d
x
d
θ
=
1
−
1
θ
2
1
+
1
θ
2
We have
x
=
θ
−
1
θ
and
y
=
θ
+
1
θ
⇒
x
y
=
θ
2
−
1
θ
2
and
y
2
=
(
θ
+
1
θ
)
2
⇒
y
2
=
θ
2
+
1
θ
2
−
2
θ
1
θ
⇒
y
2
=
θ
2
+
1
θ
2
−
2
⇒
y
2
+
2
=
θ
2
+
1
θ
2
∴
d
y
d
x
=
1
−
1
θ
2
1
+
1
θ
2
=
x
y
y
2
+
2
If
y
=
cos
−
1
(
x
−
x
−
1
x
+
x
−
1
)
t
h
e
n
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
d
x
{
s
i
n
−
1
(
5
x
+
12
√
1
−
x
2
13
)
}
=
Report Question
0%
1
√
1
−
x
2
0%
−
1
√
1
+
x
2
0%
2
√
1
−
x
2
0%
0
Let fbe twice differentiable function such that
g
1
(
x
)
=
−
f
(
x
)
a
n
d
f
1
(
x
)
=
g
(
x
)
,
h
(
x
)
=
(
f
(
x
)
)
2
+
(
g
(
x
)
)
2
.
I
f
h
(
5
)
=
11
,
t
h
e
n
h
(
10
)
i
s
Report Question
0%
22
0%
11
0%
0
0%
8
If
y
=
tan
−
1
[
x
+
√
1
+
x
2
]
then
d
y
d
x
=
Report Question
0%
1
1
+
x
2
0%
1
2
(
1
+
x
2
)
0%
2
1
+
x
2
0%
None of these
d
[
sec
−
1
(
sin
x
+
x
2
)
]
d
x
=
Report Question
0%
sin
2
x
+
x
2
sin
x
+
x
2
(
)
√
(
sin
x
+
x
2
)
2
−
1
0%
cos
x
+
2
x
sin
x
+
x
2
(
)
√
(
sin
x
+
x
2
)
2
−
1
0%
2
x
sin
x
√
sin
x
−
1
0%
None of these
f
(
x
)
=
log
1
−
2
x
(
1
+
2
x
)
for
x
≠
0
=
k
for
x
=
0
is continuous at
x
=
0
, find
k
.
Report Question
0%
1
0%
−
1
0%
0
0%
1
2
T
h
e
f
u
n
c
t
i
o
n
g
(
x
)
=
|
x
+
b
x
<
0
cos
x
x
≥
0
c
a
n
b
e
m
a
d
e
d
i
f
f
e
r
e
n
t
i
a
b
l
e
a
t
x
=
0
Report Question
0%
i
f
b
i
s
e
q
u
a
l
t
o
z
e
r
o
0%
i
f
b
i
s
n
o
t
e
q
u
a
l
t
o
z
e
r
o
0%
i
f
b
i
s
n
o
t
e
q
u
a
l
t
o
z
e
r
o
0%
f
o
r
n
o
v
a
l
u
e
o
f
b
If
y
=
t
a
n
−
1
(
1
−
c
o
s
2
x
1
+
c
o
s
2
)
,
, then
d
y
x
y
=
Report Question
0%
s
i
n
x
1
+
c
o
s
4
x
0%
s
i
n
x
1
+
c
o
s
2
x
0%
s
i
n
2
x
1
+
c
o
s
4
x
0%
s
i
n
2
x
1
+
c
o
s
2
x
Solve
d
tan
−
1
d
x
(
5
x
+
1
3
−
x
−
6
x
2
)
=
Report Question
0%
0
0%
1
0%
1
1
+
(
3
x
+
2
)
2
+
1
1
+
(
2
x
−
1
)
2
0%
3
1
+
(
3
x
+
2
)
2
+
2
1
+
(
2
x
−
1
)
2
If
cos
−
1
x
+
cos
−
1
y
=
π
2
then
d
y
d
x
Report Question
0%
x
y
0%
−
2
x
y
0%
−
x
y
0%
−
y
x
Let
f
be a function defined by
2
f
(
sin
x
)
+
f
(
cos
x
)
=
x
∀
x
∈
R
, then set of points where
f
is not differentiable is
Report Question
0%
set of all natural numbers
0%
set of all irrational number
0%
{
0
,
1
,
−
1
}
0%
{
1
,
−
1
}
If
f
(
x
)
=
√
1
−
√
1
−
x
2
, then
f
(
x
)
is
Report Question
0%
continuous on
[
−
1
,
1
]
0%
differentiable on
(
−
1
,
0
)
∪
(
0
,
1
)
0%
both (a) and (b)
0%
None of the above
y
=
c
o
s
−
1
(
9
−
x
2
)
(
9
+
x
2
)
then
Y
′
(
−
1
)
is equal to:
Report Question
0%
3
5
0%
3
5
0%
2
7
0%
3
8
The number of values of
x
at which
f
(
x
)
=
|
x
−
3
2
|
+
|
x
−
2
|
+
(
x
−
1
)
|
x
−
1
|
is not differentiable
Report Question
0%
2
0%
3
0%
4
0%
1
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 solution of equation
f
′
(
x
)
=
2
x
cos
x
2
in
(
1
,
3
)
is
Report Question
0%
1
0%
2
0%
3
0%
4
Solve :
d
d
x
[
tan
−
1
√
1
+
x
2
−
cot
−
1
(
−
√
1
+
x
2
)
]
=
?
Report Question
0%
π
0%
1
0%
0
0%
2
x
√
1
+
x
2
The derivative of
cos
−
1
x
w.r.t.
√
1
−
x
2
is
Report Question
0%
1
√
1
−
x
2
0%
√
1
−
x
2
0%
1
2
x
0%
1
x
let f be the differeniable at x=0 and f'(0)=1 then
l
i
m
b
→
0
f
(
h
)
−
f
(
−
2
h
)
h
Report Question
0%
3
0%
2
0%
1
0%
-1
If
f
is twice differentiable such that
f
′
′
(
x
)
=
−
f
(
x
)
and
f
′
(
x
)
=
g
(
x
)
.
If
h
(
x
)
is a twice differentiable function that
h
′
(
x
)
=
(
f
(
x
)
)
2
+
(
g
(
x
)
)
2
.
If
h
(
0
)
=
2
,
h
(
1
)
=
4
,
then the equation
y
=
h
(
x
)
represents :
Report Question
0%
a curve of degree
2
0%
a curve passing through the origin
0%
a straight line with slope
2
0%
a straight line with
y
intercept equal to
2
f
(
x
)
=
{
x
(
a
e
1
|
x
|
+
3
e
−
1
x
(
a
+
2
)
e
1
|
x
|
−
e
−
1
x
)
,
x
≠
0
0
,
x
=
0
is differentiable at
x
=
0
then
[
a
]
=
.
.
.
.
.
.
(
[
]
denotes greatest integer function)
Report Question
0%
0
0%
−
1
0%
−
2
0%
N
o
n
e
o
f
t
h
e
s
e
If
y
=
cot
−
1
(
sin
x
1
+
cos
x
)
then
d
y
d
x
is
Report Question
0%
−
1
2
0%
1
2
0%
0
0%
1
Number of points in
[
0
,
π
]
, where
f
(
x
)
=
[
x
tan
x
sin
x
+
cos
x
]
is non-differentiable is/are (where
[
.
]
denotes the greatest integer function)
Report Question
0%
0
0%
4
0%
9
0%
N
o
n
e
o
f
t
h
e
s
e
Let F(x) =
(
f
(
x
)
)
2
+
(
f
(
x
)
)
2
,
F
(
0
)
−
6
where f(x) is a differential function such that
|
f
(
x
)
|
≤
1
∀
x
∉
[
−
1
,
1
]
then choose the correct statement (s)
Report Question
0%
There is atleast one point in each of the intervals (-1, 0) and (0, 1) where
|
f
′
(
x
)
|
≤
2
0%
there is atleast one point in a each of the interval (-1, 0) and (0, 1) where f(x)
≤
S
0%
there is no point of local maximum of F(x) in (-1, 1)
0%
For some
c
∈
(
−
1
,
1
)
,
F
′
(
c
)
≥
6
,
F
"
(
c
)
≤
0
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Incorrect : 0
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