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

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

(a)

6

(b)

-6

(c)

does not exist

(d)

0

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

(a)

1

(b)

\(\pi \)

(c)

\(\frac { \pi }{ 2 } \)

(d)

0

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

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

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

(a)

\(\frac { 4{ x }^{ 3 } }{ 1-{ x }^{ 4 } } \)

(b)

\(-\frac { 4x }{ 1-{ x }^{ 4 } } \)

(c)

\(\frac { 1 }{ 4-{ x }^{ 4 } } \)

(d)

\(\frac { -4{ x }^{ 3 } }{ 1-{ x }^{ 4 } } \)

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

(a)

\(\tan { \frac { \theta }{ 2 } } \)

(b)

\(-\tan { \frac { \theta }{ 2 } } \)

(c)

\(\cot { \frac { \theta }{ 2 } } \)

(d)

\(-\cot { \frac { \theta }{ 2 } } \)

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

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

Choose the incorrect pair?

(a)

330^o - \(\frac{11\pi}{6}\)radians

(b)

\(\frac{7\pi^c}{3}\) - 200^o

(c)

0^o - 0^c

(d)

2\(\pi\)^c - 360^o