Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference d. If the fourth term of GP is 3 r², then r² $$-$$ d is equal to :

Which of the following is not correct for relation R on the set of real numbers ?

The integral $$\int {{1 \over {\root 4 \of {{{(x - 1)}^3}{{(x + 2)}^5}} }}} \,dx$$ is equal to : (where C is a constant of integration)

If p and q are the lengths of the perpendiculars from the origin on the lines,

x cosec $$\alpha$$ $$-$$ y sec $$\alpha$$ = k cot 2$$\alpha$$ and

x sin$$\alpha$$ + y cos$$\alpha$$ = k sin2$$\alpha$$

respectively, then k² is equal to :