If (m + 1) = √n + 3, the value of   $${1\over 2}\left({m^3-6m^2+12m-8\over \sqrt { n}}-n \right)  \ $$ is

If the areas of two isosceles triangles are in the ratio of X² : Y², then the ratio of their corresponding heights is:

$$\left({1\over cosecθ}-{1\over sinθ} \right)+{1\over {cosecθ-cotθ}} -{1\over secθ+tanθ} =?$$

What sum of money must be given as simple interest for six months at 4% per annum in order to earn 150 interest?

The acid and water in two vessels A and B are in the ratio 4:3 and 2:3. In what ratio should the liquid in both the vessels be mixed to obtain a new mixture in vessel C containing half acid and half water?

If the total surface area of a sphere of radius r cm is equal to the total surface area of a cube of side s cm, which of the following is true?

If   $$x+{1\over x}=2 $$ then the value of    $$x^{12}-{1\over x^{12}} $$ is

$$ if \ {1\over x}+x=4,$$ then find $${1\over x^2}+x^2$$