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JEE Questions for Maths Limits Continuity And Differentiability Quiz 3 - MCQExams.com
JEE
Maths
Limits Continuity And Differentiability
Quiz 3
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0%
0
0%
3/5
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2
0%
5/3
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0%
π/10
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3π/10
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3π/2
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3π/5
Discuss the continuity of the function
f
(
x
) = sin 2
x
- 1 at the point
x
= 0 and
x
= π
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Continuous x = 0 and x = π
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Discontinuous at x= 0 but continuous at x= π
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continuous at x = 0 but discontinuous at x = π
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Discontinuous at x = 0, π
The value of
f
at
x
= 0 , so that function
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0
0%
log 4 4
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4
0%
e4
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a + b
0%
a - b
0%
a
0%
b
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-6
0%
0
0%
1
0%
-1
If
f
(
x
) =
x
(√
x
- √(
x
+ 1)) , then
f
(
x
) is continuous in
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[0, ∞)
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(0, ∞)
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(-∞, ∞)
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(3,∞)
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-1
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1
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0
0%
2
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1/3
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2/3
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3/2
0%
3
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1
0%
-1
0%
2
0%
-2
0%
3
If a function
f
: R → R, where R is the set of real numbers satisfying the equation
f
(
x
+ y) =
f
(
x
) +
f
(y), ∀< i>x, y. If
f
(
x
) is continuous at
x
= 0, then
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f(x) is discontinuous, for all x ϵ R
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f(x) is continuous, for all x ϵ R
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f(x) is continuous for x ϵ {1,2,3,4}
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None of the above
The function
f
(
x
) is defined by
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0
0%
1/4
0%
- (1/2)
0%
None of these
Let [] denotes the greatest integer function and
f
(
x
) = [tan
2
x
]. Then,
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f(x) is continuous at x = 0
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f(x) is not differentiable at x = 0
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f(x) = 1
The points of discontinuity of tan
x
are
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nπ, n ϵ I
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2nπ, n ϵ I
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(2n+1)π/2, n ϵ I
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None of these
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1
0%
-1
0%
0
0%
2
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a2
0%
2a2
0%
3a2
0%
4a2
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0
0%
1/2
0%
1/4
0%
- (1/2)
0%
None of these
The function
f
(
x
) =
x
- |
x
-
x
2
| is
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continuous at x = 1
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discontinuous at x = 1
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not defined at x = 1
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None of these
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f(x) is continuous at x = 0
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f(|x|) is continuous at x = 0
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f(x) is discontinuous at x = 0
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None of these
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1
0%
0
0%
1/2
0%
-1
If the function
f
: R → R given by
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4
0%
3
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2
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1
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1
0%
0
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1/2
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-1
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m = 1, n = 0
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m = nπ/2 + 1
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n = m π/2
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m = n = π/2
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a = 0, b = 0
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a = 1, b = 1
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a = -1, b = 1
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a = 1, b = -1
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continuous
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discontinuous
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differentiable
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non - Zero
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1
0%
1/2
0%
-1/2
0%
-1
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1
0%
-2
0%
2
0%
1/2
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0%
2)
0%
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f(x) continuous at x = 0
If
f
: R → R is defined by
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(1/2, 1/2)
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(0, -1)
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(0, 2)
0%
(1, 0)
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3
0%
-3
0%
e3
0%
e-3
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1/2 loge 2
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loge 4
0%
loge 8
0%
loge 2
If
f
: R → R is defined by
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R
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R - {-2}
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R - {-1}
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R - {-1, -2}
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x = 1 only
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x = 1 and x = -1
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x= 1 and x = -1 and x = -3
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x = , x = - 1, x = -3 and other values of x
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discontinuous at origin because |x| is discontinuous
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continous at origin
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discontinuous at origin because both |x|and |x|/ x are discontinuous there
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discontinuous at the origin because |x|/x is discontinuous there
The function represented by the following graph is
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continuous but not differentiable at x = 1
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differentiable but not continuous at x = 1
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continuous and differentiable at x = 1
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neither continuous nor differentiable at x = 1
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continuous for all values of x
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discontinuous at x = π/2
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not differentiate for some values of x
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discontinuous at x = - 2
If
f
(
x
+ y) =
f
(
x
)
f
(y) and
f
(
x
) = 1 + sin (3
x
) g(
x
), where g(
x
) is continuous , then
f
'(
x
) is equal to
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f(x) g(0)
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3g(0)
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f(x) cos 3x
0%
3f(x) g(0)
0%
None of these
If
f
(
x
) is a differentiable function and
f
'(
4
) = 5. Then,
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0%
0
0%
5
0%
20
0%
-20
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f(x) is continuous at x= 1
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f(x) is not continuous at x = 1
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f(x) is differentiable at x = 1
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f(x) is not differentiable at x = 1
The function
f
(
x
) = |
x
- 1| is
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continuous everywhere
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continuous everywhere, except at x = 1
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differentiable everywhere
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differentiable nowhere
f
(
x
) =
x
sin (1/
x
)
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is continuous but not differentiable at x = 0
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is discontinuous but differentiable at x = 0
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is differentiable at x = 0
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cannot be determined
f
(
x
) = |
x
- 3|is...at
x
= 3
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continuous and not differentiable
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continuous and not differentiable
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discontinuous and not differentiable
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continuous and differentiable
Function
f
(
x
) = |
x
- 1|+ |
x
- 2|,
x
ϵ R is
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differentiable everywhere in R
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except x = 1 and x = 2 differentiable everywhere in R
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not continuous at x = 1 and x = 2
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increasing in R
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continuous and differentiable at x = 3
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continuous at x = 3 but not differentiable at x = 3
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continuous and differentiable everywhere
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continuous at x = 1 but not differentiable at x = 1
If
f
(
x
) = |log
e
|, then
f
'(
x
) equals
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1/|x|, x ≠ 0
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1/x for |x| > 1 and -1/x for |x| < 1
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-1/x for |x|> 1 and 1/x for |x| < 1
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1/x for x > 0 and - (1/x) for x = 0
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c = 0 and a = 2b
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a = b and c ϵ R
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a = b and c = 0
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a = b and c ≠ 0
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-1/9
0%
-2/9
0%
-13
0%
1/3
0%
None of these
The function
f
(
x
) = e
-|
x
|
is
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continuous everywhere but not differentiable at x = 0
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continuous and differentiable everywhere
0%
not continuous at x = 0
0%
None of the above
The
f
(
x
) is differentiable at
x
= 1 and
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0%
8
0%
5
0%
4
0%
3
At
x
= 0, the function
f
(
x
) = e
-|
x
|
is
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0%
continuous but not differentiable
0%
discontinuous and differentiable
0%
discontinuous and not differentiable
0%
continous and differentiable
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