#### 11th Standard Maths Differentiability & Methods of Differentiation English Medium Free Online Test 1 Mark Questions with Answer key 2020-2021

11th Standard

Reg.No. :
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Maths

Time : 00:10:00 Hrs
Total Marks : 10
10 x 1 = 10
1. If g(x)=(x2+2x+3) f(x) and f(0)=5 and $lim_{x \rightarrow 0}{f(x)-5\over x}=4$,then g'(0) is

(a)

20

(b)

14

(c)

18

(d)

12

2. The derivative of f(x)=x|x| at x =−3 is

(a)

6

(b)

-6

(c)

does not exist

(d)

0

3.  Choose the correct or the most suitable answer from the given four alternatives.
$If\quad y=\sin ^{ -1 }{ x } +\cos ^{ -1 }{ x }$ then$\frac { dy }{ dx }$ is

(a)

1

(b)

$\pi$

(c)

$\frac { \pi }{ 2 }$

(d)

0

4. Choose the correct or the most suitable answer from the given four alternatives.
If $f\left( x \right) =x+1$, then $\frac { d }{ dx } ({ f }_{ 0 }f\left( x \right) )$ is

(a)

1

(b)

0

(c)

2

(d)

x

5. Choose the correct or the most suitable answer from the given four alternatives.
For the curve $\sqrt { x } +\sqrt { y } =1,\quad \frac { dy }{ dx } at\left( \frac { 1 }{ 4 } ,\frac { 1 }{ 4 } \right) is$

(a)

$\frac { 1 }{ 2 }$

(b)

1

(c)

-1

(d)

2

6. 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)

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

7. Choose the correct or the most suitable answer from the given four alternatives.
$If\quad x=a(\theta +\sin { \theta ),y=a(1+\cos { \theta } ) } then\quad \frac { dy }{ dx }$ is

(a)

$\tan { \frac { \theta }{ 2 } }$

(b)

$-\tan { \frac { \theta }{ 2 } }$

(c)

$\cot { \frac { \theta }{ 2 } }$

(d)

$-\cot { \frac { \theta }{ 2 } }$

8. Choose the correct statement

(a)

Derivative of odd functionis odd

(b)

Derivative of even function is even

(c)

Inverse of odd function is even

(d)

Inverse function of sin x is sin-1 x

9. Assertion (A):f (x) =$\begin{cases} \begin{matrix} x+1, & x<2 \end{matrix} \\ \begin{matrix} 2x-1, & x\ge 2 \end{matrix} \end{cases}$ then f'(2) does not exist.
Reason (R) :f(x) is not continuous at 2.

(a)

Both A and it are true and R is the correct explanation of A

(b)

Both A and R are true but R is not the correct explantion of A

(c)

A is true R is false

(d)

A is false R is true

10. Choose the incorrect pair

(a)

330o$\frac{11\pi}{6}$radians

(b)

$\frac{7\pi^c}{3}$ - 200o

(c)

0o - 0c

(d)

2$\pi$c - 360o