Permutations an...

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

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 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

If $$\dfrac { ^{ n }{ P }_{ r-1 } }{ a } =\dfrac { ^{ n }{ P }_{ r } }{ b } =\dfrac { ^{ n }{ P }_{ r+1 } }{ c } $$, then which of the following holds good:

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

The number of permutations of the letters of the word $$HONOLULU$$ taken $$4$$ at a time is

Function f(x)=$$\left| {x - 2} \right| - 2\left| {x - 4} \right|\,is$$ discontinous at:

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

Number of arrangements of the letter $$HOLLYWOOD$$ in which all $$Os$$ are separated.

How many committee of five persons with a chairperson can be selected from $$12$$ persons.