Differentiation...

The number of ways in which we can select 5 letters of the word INTERNATIONAL is equal to

$$\frac{d^n}{dx^n}[log(ax+b)]$$ is equal to:

The area of the triangle whose vertices are (3,8), (-4,2) and (5,-1) is 

Statement I: The function f(x) in the figure is differentiable at x = a
Statement II: The function f(x) continuous at x = a

The total number of non-negative integer n satisfying the
equation $$ {n^2} = p + q\,and\,{n^3} = {p^2} + {q^2}$$, where p and q are
integers, is

Given $$y=\dfrac {3}{x}, \dfrac {dy}{dx}=$$

If $$ f(x) = \bigg[ \frac {a+x}{1+x} \bigg]^{a+1+2x} $$ then $$ {a^{a+1}} \bigg [ 2 \ log \ a + {\frac {1-a ^2}{a}} \bigg]$$ is

Pam likes the numbers 1689 and 6891. Knowing this, which pair of numbers will she like among the ones below?

If $$(1+3+5+....+p)+(1+3+5+....+q)=(1+3+5+.....+r),$$ where each set of parentheses contains the sum of consecutive odd integers as shown, the smallest possible value of $$p+q+r$$, (where $$P>6$$ ) is :

The total number of different combinations of one
or more letters which can be made from the letter of the word MISSISSIPPI is,