If the area of a triangle is 1176 cm² and the ratio of base corresponding altitude is 3 : 4, then the altitude of the triangle is :

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

A trader had 16 quintals of wheat. He sold a part of it at 17% profit and the rest at 27% profit, so that he made a total profit of 21%. How much wheat did he sell at 27 % profit? 

O and C are respectively the orthocentre and the circumcentre of an acute angled triangle POR. The points P and O are joined and produced to meet the side QR at S. If ∠POS=60⁰ and ∠QCR = 130°, then ∠RPS = ?

Ram deposited a certain sum of money in a company at 12 % per annum simple interest for 4 years and deposited equal amount in fixed deposit in a bank for 5 years at 15 % per annum simple interest. If the difference in the interest from two sources is ₹ 1350 than the sum deposited in each case is

A boat is moving away from an observation tower. It makes an angle of depression of 60 ° with an observer's eye when at a distance of 50 m from the tower. After 8 sec, the angle of depression becomes 30 °. By assuming that it is running in still water, the approximate speed of the boat is