MCQExams
0:0:1
CBSE
JEE
NTSE
NEET
Practice
Homework
×
JEE Questions for Maths Limits Continuity And Differentiability Quiz 6 - MCQExams.com
JEE
Maths
Limits Continuity And Differentiability
Quiz 6
If
f
(
x
) =
x
|
x
| and g(
x
) = sin
x
Statement I gof is differentiable at
x
= 0 and its derivatives continuous at the point. Statement II gof is twice differentiable at
x
= 0.
Report Question
0%
Statement I is correct . Statement II is correct ; Statement II is correct explanation for statement I
0%
Statement I is correct, Statement II is correct; Statement II is not a correct explanation for Statement I
0%
Statement I is correct, statement II is incorrect
0%
Statement I is incorrect, Statement II is correct
Report Question
0%
p < 0
0%
0 < p < 1
0%
p = 1
0%
p > 1
if
f
(
x
) = ae
|
x
|
+ b|
x
|
2
, a, b ϵ R and
f
(
x
) is differentiable at
x
= 0. Then,
Report Question
0%
a = 0, b ϵ R
0%
a = 1, b = 2
0%
b = 0, a ϵ R
0%
a = 4, b = 5
The set of points, where the function
f
(
x
) =
x
|
x
| is differentiable, is
Report Question
0%
(-∞, ∞)
0%
(-∞,∪ (0, ∞)
0%
(0, ∞)
0%
[0, ∞)
Report Question
0%
not continuous at x = 2
0%
differentiable at x = 2
0%
continuous but not differentiable at x = 2
0%
None of the above
Report Question
0%
n = 1, m = 1
0%
n = 1, m = -1
0%
n = 2, m = 2
0%
n > 2, m = n
Report Question
0%
continuous but not differentiable at x = 0
0%
discontinuous at x = 0
0%
continuous and differentiable at x = 0
0%
not defined at x = 0
Report Question
0%
f(x) is discontinuous at x = a
0%
f(x) is not differentiable at x = a
0%
f(x) is differentiable at x ≥ a
0%
f(x) is continuous at all x < a
Report Question
0%
f(x) is not continuous at x = 1
0%
f(x) is continuous but not differentiable at x = 1
0%
f(x) is both continuous and differentiable at x = 1
0%
None of these
If
f
: R → R is a function defined by
f
(
x
) = min {
x
+ 1, |
x
| + 1}. Then, which of the following is correct ?
Report Question
0%
f(x) ≥ 1 for all x ϵ R
0%
f(x) is not differentiable at x = 1
0%
f(x) is differentiable everywhere
0%
f(x) is not differentiable atx = 0
The set of points, where the function
f
(
x
) = |
x
- 1|e
x
is differentiable, is
Report Question
0%
R
0%
R - {1}
0%
R - {-1}
0%
R - {0}
If
f
(
x
) = |log |
x
||, then
Report Question
0%
f(x) is continuous and differentiable for all x in its domain
0%
f(x) is continuous for all x in its domain but not differentiable at x = ± 1
0%
f(x) is neither continuous nor differentiable at x = ± 1
0%
None of the above
Report Question
0%
0
0%
2
0%
3
0%
4
The set of points, where
f
(
x
) =
x
/(1 + |
x
|) is differentiable, is
Report Question
0%
(-∞,∪ (0, ∞)
0%
(-∞, -∪ (-1, ∞)
0%
(-∞, ∞)
0%
(0, ∞)
Report Question
0%
f(x) is continuous but not differentiable at x= 0
0%
f(x) is differentiable at x = 0
0%
f(x) is not differentiable atx = 0
0%
None of the above
Which one of the following is not correct ?
Report Question
0%
If f(x) is not continuous at x = a, then it is not differentiable at x = a
0%
If f(x) is continuous at x = a, then it is differentiable at x = a
0%
If f(x) and g(x) are differentiable at x = a, then f(x) + g(x) is also differentiable at x = a
0%
If
f
(
x
) = ||
x
|- 1|, then points, where
f
(
x
) is not differentiable, is/(are)
Report Question
0%
0, ± 1
0%
± 1
0%
0
0%
1
Let
f
be differentiable for all
x
, If
f
(= - 2 and
f '
(
x
) ≥ 2 for
x
ϵ [1, 6], then
Report Question
0%
f(= 5
0%
f(< 5
0%
f(< 8
0%
f(≥ 8
If
f
is real valued differentiable function satisfying |
f
(
x
) -
f
(y)| ≤ (
x
- y)
2
,
x
, y ϵ R and
f
(= 0, then
f
(equals
Report Question
0%
1
0%
2
0%
0
0%
-1
Report Question
0%
1
0%
-1
0%
∞
0%
does not exist
Report Question
0%
0 < p ≤ 1
0%
1 ≤ p < ∞
0%
-∞ < p < 0
0%
p = 0
If y = cos
-1
cos [|
x
-
f
(
x
)|], where
Report Question
0%
-1
0%
1
0%
0
0%
cannot be determined
The function
f
(
x
) = max [(1 -
x
), (1 +
x
), 2]
x
ϵ (- ∞, ∞) is
Report Question
0%
continuous at all points
0%
differentiable at all points
0%
differentiable at all points except at x = 1 and x = - 1
0%
None of the above
Report Question
0%
0%
2)
0%
0%
None of these
Report Question
0%
0%
2)
0%
0%
None of these
Report Question
0%
0
0%
1
0%
2
0%
3
If f(x) = (x + 1)
cot x
is continuous at x = 0, then f(equals
Report Question
0%
0
0%
1
0%
‒1
0%
e
The jump of the function at the point of the discontinuity of the function
Report Question
0%
3
0%
2
0%
4
0%
6
If f is a continuous function such that f(= f(= 0, f '(= 2 and y(x) = f(e
x
) e
f(x)
then y'(is
Report Question
0%
0
0%
1
0%
2
0%
none of these
Report Question
0%
0%
b
0%
b2
0%
none of these
Report Question
0%
e–1
0%
e–2
0%
e
0%
e2
The function f(x) = sin|x| is
Report Question
0%
Continuous for all x
0%
Continuous only at certain points
0%
Differentiable at all points
0%
None of the above
If f(x) = |x|, then f(x) is
Report Question
0%
Continuous for all x
0%
Differentiable at x = 0
0%
Neither continuous nor differentiable at x = 0
0%
None of the above
Report Question
0%
f(x) is discontinuous everywhere
0%
f(x) is continuous everywhere
0%
f' (x) exists in (–1, 1)
0%
f' (x) exists in (–2,2)
At the point x = 1, the given function
Report Question
0%
Continuous and differentiable
0%
Continuous and not differentiable
0%
Discontinuous and differentiable
0%
Discontinuous and not differentiable
Let [x] denotes the greatest integer less than or equal to x. If f(x) = [x sin πx], then f(x) is
Report Question
0%
Continuous at x = 0
0%
Continuous in (–1, 0)
0%
Differentiable in (–1, 1)
0%
All of the above
Report Question
0%
Is continuous but not differentiable
0%
Is discontinuous
0%
Is having continuous derivative
0%
Is continuous and differentiable
Report Question
0%
0
0%
1
0%
2
0%
3
Let f be differentiable for all x. If f(= –2 and f \' (x) ≥ 2 for x ϵ [1,6], then
Report Question
0%
f(< 5
0%
f(= 5
0%
f(≥ 8
0%
f(< 8
f(x) = ||x| – 1| is not differentiable at
Report Question
0%
0
0%
±1, 0
0%
1
0%
±1
Let f be continuous on [1,5] and differentiable in (1,5).If f(= –3 and f\'(x) ≥ 9 for all x ∈(1,, then
Report Question
0%
f(≥ 33
0%
f( ≤ 36
0%
f(≥ 9
0%
f(≤ 9
Report Question
0%
0
0%
1
0%
2
0%
3
Let f(x + y) = f(x) + f(y) and f(x) = x
2
g(x) for all x,y ∈ R, where g(x) is continuous function. Then f \' (x) is equal to
Report Question
0%
g' (x)
0%
g(0)
0%
g(+ g'(x)
0%
0
The function f(x) = (x
2
–|x
2
– 3x + 2| + cos (|x|) is not differentiable at
Report Question
0%
–1
0%
0
0%
1
0%
2
Report Question
0%
|x| < 1
0%
x = 1, –1
0%
|x| > 1
0%
None of these
The number of points at which the function f(x) = |x – 0.5| + |x – 1| + tan x does not have a derivative in the interval (0,2), is
Report Question
0%
1
0%
2
0%
3
0%
4
If f(x) is a function such that f\ (x) + f(x) = 0 and g(x) = [f(x)]
2
+ [f\' (x)]
2
and g(= 3, then g(=
Report Question
0%
5
0%
0
0%
3
0%
8
Report Question
0%
0
0%
1
0%
2
0%
–2
In order that the function f(x) = (x + 1)
1/x
is continuous at x = 0, f(must be defined as
Report Question
0%
f(= 0
0%
f(= e
0%
f(= 1/e
0%
f(= 1
Report Question
0%
0%
2)
0%
f(x) is discontinuous at x = 1
0%
None of the above
0:0:1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
0
Answered
0
Not Answered
0
Not Visited
Correct : 0
Incorrect : 0
Report Question
×
What's an issue?
Question is wrong
Answer is wrong
Other Reason
Want to elaborate a bit more? (optional)
Practice Maths Quiz Questions and Answers
<
>
Support mcqexams.com by disabling your adblocker.
×
Please disable the adBlock and continue.
Thank you.
Reload page
