Differentiation...

If $$f(x)=\dfrac{a^x}{x^a}$$ then $$f'(a)=$$?

If the letters of the word "VARUN" are written in all possible ways and then are arranged as in a dictionary, then the rank of the word VARUN is?

If the vertices of a triangle are $$(1,2),(4,-6)$$ and $$(3,5)$$, then its area is

The unit's place digit in $$(1446)^{4n + 3}$$ is

Number of rectangles in the grid shown which are not squares is?

Number of ways in which $$7$$ green bottles and $$8$$ blue bottles can be arranged in a row if exactly $$1$$ pair of green bottles is side by side is (Assume all bottles to be a like except for the colour).

The last three digits in $$10!$$ are ?

The number of zeroes, at the end of $$50!$$, is

Garlands are formed using 6 red roses and 6 yellow roses of different sizes. The number of arrangements in garland which have red roses and yellow roses come alternately is

The three digits in 10! are: