Continuity and Differentiability Test

Result

Continuity and Differentiability Test - 7

Score
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Rank
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Weekly Quiz Competition

Question 1
1 / -0.25

A

B

C
-1

D

Solution
Question 2
1 / -0.25

The function, f (x) = (x –a) sin for x ≠ a and f (a) = 0 is

A
Not continuous at x = a

B
Derivable at x = a

C
Continuous but not derivable at x = a

D
None of these

Solution
Question 3
1 / -0.25

If x sin (a + y) = sin y, then is equal to

A

B

C

D

Solution

x sin(a+y) = sin y
⇒
Question 4
1 / -0.25

A
e²

B
e^1/2

C
e

D
none of these

Solution
Question 5
1 / -0.25

A
a

B
1/2a

C
1/a

D
none of these

Solution
Question 6
1 / -0.25

If [x] stands for the integral part of x, then

A

B

C

D
none of these

Solution

If c is an integer , then Does not exist.
Question 7
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Let f (x) = [x], then f (x) is

A
continuous nowhere

B
differentiable for all x ∈(R −I).

C
differentiable for all x ∈R

D
continuous for all x ∈R

Solution

f(x) = [x] is derivable at all x except at integral points i.e. on R –I .
Question 8
1 / -0.25

A
is positive

B
is negative

C
vanishes

D
does not exist.

Solution
Question 9
1 / -0.25

A
x³ e^2x

B
x² e^2x (2+3x)

C
x² e^2x (2x+3)

D
none of these

Solution
Question 10
1 / -0.25

A

B

C

D
none of these

Solution
Question 11
1 / -0.25

A
1

B
–1

C
0

D
none of these

Solution
Question 12
1 / -0.25

The function f (x) = [x] is

A
derivable for all x

B
discontinuous only for integral x

C
continuous for all x

D
a constant function

Solution

The function f (x) = [x] isdiscontinuous only for all integral values of x.
Question 13
1 / -0.25

Let f be a function satisfying f(x + y) = f(x) + f(y) for all x, y ∈R, then f ‘(x) =

A
0 for all x ∈R

B
f (0) for all x ∈R

C
f ‘(0) for all x ∈R

D
none of these

Solution
Question 14
1 / -0.25

A
1+y²

B
1 −y²

C
y² +1

D
none of these

Solution
Question 15
1 / -0.25

If x = at² , y = 2at, then is equal to

A

B
0

C

D
none of these

Solution