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 \(y=\sqrt { \sin { x+y } } \quad then\quad \frac { dy }{ dx }\) is _________

(a)

\(\frac { \sin { x } }{ 2y-1 } \)

(b)

\(\frac { \sin { x } }{ 1-2y } \)

(c)

\(\frac { \cos { x } }{ 1-2y } \)

(d)

\(\frac { \cos { x } }{ 2y-1 } \)

Choose the correct or the most suitable answer from the given four alternatives.
If f(x) is an even functions, thenf^'(x) is an ______function

(a)

even

(b)

odd

(c)

even and odd

(d)

even or odd

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)

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

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