Continuity and Differentiability Test

Result

Continuity and Differentiability Test - 4

Score
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Rank
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TIME Taken - -

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Question 1
1 / -0.25

A
1/48

B

C
1/24

D
none of these

Solution
Question 2
1 / -0.25

then is equal to

A
1

B
1/2

C
0

D
none of these
Question 3
1 / -0.25

A
–f ‘(a)

B
f ‘(a)

C
does not exist

D
none of these.

Solution
Question 4
1 / -0.25

If f(x) be any function which assumes only positive values and f ’(x) exists then f ’(x) is equal to

A

B

C

D
none of these

Solution
Question 5
1 / -0.25

If y = a sin mx + b cos m x, then is equal to

A
m² y

B
my₁

C
−m² y

D
none of these

Solution

y = a sin mx+b cos mx ⇒y₁ = am cos mx −bm sin mx
⇒y₂ = −am² sin mx −bm² cosmx ⇒y₂ = −m² (a sin mx+b cos mx)
Question 6
1 / -0.25

A
1/2

B
1/3

C
3/2

D
none of these

Solution
Question 7
1 / -0.25

A

B
1

C
0

D

Solution
Question 8
1 / -0.25

If y = tan⁻¹ x and z = cot⁻¹ x then is equal to

A
π/2

B
-1

C
1

D
none of these

Solution
Question 9
1 / -0.25

A

B
cosec x

C

D
none of these

Solution
Question 10
1 / -0.25

A

B

C

D
none of these

Solution
Question 11
1 / -0.25

A
3/4

B

C
4/3

D
none of these

Solution
Question 12
1 / -0.25

If both f and g are defined in a nhd of 0 ; f(0) = 0 = g(0) and f ‘(0) = 8 = g ’(0), then equal to

A
0

B
16

C
1

D
none of these

Solution

(by using L ’Hospital Rule)
Question 13
1 / -0.25

A
−1

B
−1

C
−1 ⩽x <1

D
−1 ⩽x ⩽1

Solution
Question 14
1 / -0.25

The differential coefficient of log (| log x |) w.r.t. log x is

A

B

C

D
none of these

Solution
Question 15
1 / -0.25

If f is derivable at x = a , then is equal to

A
f(a)−a f ′(a)

B
f ‘(a)

C
a f ‘9a) –f (a)

D
none of these

Solution