#### 11th Standard Maths Differential Calculus - Differentiability and Methods of Differentiation English Medium Free Online Test 1 Mark Question 2020-2021

11th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10

Answer all the questions

10 x 1 = 10
1. ${d\over dx}({2\over \pi}sin \ x^o)$is

(a)

${\pi\over 180}cos \ x^o$

(b)

${1\over 90} cos \ x^o$

(c)

${\pi\over 90}cos \ x^o$

(d)

${2\over \pi}cos \ x^o$

2. If y = mx + c and f(0) =$f '(0)=1$,then f(2) is

(a)

1

(b)

2

(c)

3

(d)

-3

3. ${d\over dx}(e^{x+5log \ x})$ is

(a)

exx4(x+5)

(b)

exx(x+5)

(c)

ex$+{5\over x}$

(d)

ex$-{5\over x}$

4. The differential coefficient of log10 x with respect to logx10 is

(a)

1

(b)

-(log10 x)2

(c)

(logx 10)2

(d)

$x^2\over100$

5. If ,then the right hand derivative of f(x) at x = 2 is

(a)

0

(b)

2

(c)

3

(d)

4

6. Choose the correct or the most suitable answer from the given four alternatives.
$Iff\left( x \right) =4{ x }^{ 8 },\quad then$

(a)

$f^{ ' }\left( \frac { 1 }{ 2 } \right) =f^{ ' }\left( \frac { -1 }{ 2 } \right)$

(b)

$f\left( \frac { 1 }{ 2 } \right) =-f^{ ' }\left( \frac { -1 }{ 2 } \right)$

(c)

$f\left( \frac { 1 }{ 2 } \right) =f\left( \frac { -1 }{ 2 } \right)$

(d)

$f\left( \frac { 1 }{ 2 } \right) =f^{ ' }\left( \frac { -1 }{ 2 } \right)$

7.  Choose the correct or the most suitable answer from the given four alternatives.
If $y=\log _{ a }{ x }$ then $\frac { dy }{ dx }$ is

(a)

$\frac { 1 }{ x }$

(b)

$\frac { 1 }{ x\log _{ e }{ a } }$

(c)

$\log { _{ e }^{ a } }$

(d)

$\frac { 1 }{ \log _{ a }{ x } }$

8. Choose the correct or the most suitable answer from the given four alternatives.
The derivative of $\cos ^{ -1 }{ (2{ x }^{ 2 } } -1)$ with respect to $\cos ^{ -1 }{ x }$ is

(a)

2

(b)

$\frac { 1 }{ 2\sqrt { 1-{ x }^{ 2 } } }$

(c)

$\frac { 2 }{ x }$

(d)

$1-{ x }^{ 2 }$

9. Choose the correct or the most suitable answer from the given four alternatives.
$If\quad y=\log { \left( \frac { 1-{ x }^{ 2 } }{ 1+{ x }^{ 2 } } \right) } then\quad \frac { dy }{ dx } \quad is$

(a)

$\frac { 4{ x }^{ 3 } }{ 1-{ x }^{ 4 } }$

(b)

$-\frac { 4x }{ 1-{ x }^{ 4 } }$

(c)

$\frac { 1 }{ 4-{ x }^{ 4 } }$

(d)

$\frac { -4{ x }^{ 3 } }{ 1-{ x }^{ 4 } }$

10. Choose the correct or the most suitable answer from the given four alternatives.
If f(x) is an odd function, then  f'(x) is an ______ function

(a)

even

(b)

odd

(c)

even or odd

(d)

neither even nor odd