If $$ a={{\sqrt{3}+\sqrt{2}}\over {\sqrt{3}-\sqrt{2}}}$$ and $$ b={{\sqrt{3}-\sqrt{2}}\over {\sqrt{3}+\sqrt{2}}}$$, then find the value  of $$ {a^2\over b}+{b^2\over a}=?$$

The length of diagonal of a square is $${15\sqrt { 2}}$$cm. Its area is

The simple interest and the true discount on a certain sum for a given period and at a given rate are 25 and 20 respectively. The sum is 

The rate of wheat increased by 25%. How many percent may the use of wheat be reduced so that the expenditure on that item remains the same?

If the height and the radius of the base of a cone are both doubled, the volume of the cone becomes _______ of its previous volume.

In an exam, 3 marks are scored on the correct solution, but 2 marks are deducted on the wrong solution. If a student scores 75 questions and gets 75 marks, the correct answer is the number of questions.

In ΔPQR, PQ=QR and O is an interior point of ΔPQR such that ∠OPR=∠ORP.

Consider the following statements:

(i) ΔPOR is an isosceles triangle.

(ii) O is the centroid of ΔPQR.

(iii) ΔPQO is congruent to ΔRQO.

Which of the above statements are correct?

The third proportional of two numbers 9 and  24 is