From an observation tower ‘h’ meter above the level of river, the angle of depression of a point on the near shore is A^° and that of a point directly on the far shore is B^°. Find the width of the river.

In ΔABC θ is an acute angle and tanθ is equal to three times of cotθ. Find the value of $$ {sin^{2}θ+cosec^{2}θ-{1\over 2}cot^{2}θ}$$.

A right pyramid stands on a rectangular base whose sides are 24 cm and 18 cm and on the shorter side, the slant height is 17 cm. Find the volume of the pyramid.

Find the square root of  $$ {k+l+m+n+2\sqrt{ml+mk}+2\sqrt{mn}+2\sqrt{kn+ln}}$$

If x₁ and x₂ are the roots of the equations bx²-ax + log₂m^y=0 such that x₁²=a²+x₂² then evaluate the roots in terms of a and b.

Solve for x if $$ {x^{a^{3}}}.x^{b^{3}}.x^{3ab(a+b)}=(2^{5})^{25},a+b=5 $$

If $$ {y\over x-z}={y+x\over z}={x\over y}$$ the find x:y:z is?

If a, b and c are in GP and a^1/x=b^1/y=c^1/z. The value of 2y is?