Differentiation...

The letters of word 'ZENITH' are written in all positive ways. If all these words are written in the order of a dictionary, then the rank of the word 'ZENITH' is

$$ f(x)=x^{2}+x g^{\prime}(1)+g^{\prime \prime}(2) $$ and $$ g(x)=f(1) x^{2}+x f^{\prime}(x)+f^{\prime \prime}(x) $$
The value of $$ f(3) $$ is

The next number in the pattern 62, 37, 12 ____ is

the area of a triangle with vertices $$ (-3, 0),(3,0) $$ and $$ (0, k) $$ is $$ 9 $$ sq units. then the value of $$ k $$ will be 

Derivative of $${\log{x}}^{\displaystyle\cos{x}}$$ with respect to $$x$$ is

lf $${f}'({x})={g}({x})$$ and $${g}'({x})=-{f}({x})$$ for all $$x$$ and $${f}(2)=4= {g}(2)$$, then $${f}^{2}(24)+{g}^{2}(24)$$ is

Assertion(A): Let $${ f }({ x })$$ be twice differentiable function such that $$f^{ '' }(x)=-{ f }({ x })$$ and $$f^{ ' }(x)={ g }({ x })$$. lf $${ h }({ x })=[{ f }({ x })]^{ 2 }+[{ g }({ x })]^{ 2 }$$ and $${ h }(1)=8$$, then $${ h }(2)=8$$

$$f(x)=|x-1|+|x-3|$$ then $$f^{'}(2)=$$

Assertion (A): lf $$f(x)=\cos^{2}x+\cos^{2}\left(x+\dfrac{\pi}3\right)- \cos x \cos \left(x+\dfrac{\pi}3\right)$$ then $$f'(x)=0$$

Given that $$f (x)$$
is a differentiable function of $$ x$$ and that $$f(x)$$ . $$f (y)$$ =  $$f (x) $$+ $$f (y)$$ + $$f (xy) -2$$ and that
$$f (2) =5$$.

Then $$f (3)$$ is equal to?