A metallic solid spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 2 cm and 1.5 cm. What is the surface area (in cm²) of the third ball?

 if $$tan(A+B)=\sqrt { 3} \ $$ and $$ tan(A-B)= {1\over \sqrt { 3} \   }; 0^0<(A+B)<90^0;A>B, $$ then the value of A and B are

The breadth ‘b’ of a room is twice its height and half of its length. Find the length of the longest diagonal of the room.

What is the value of the expression?

(tan0° tan1° tan2° tan3° tan4° …… tan89°)

How many grams of water should be mixed in 9 grams of shaving lotion having 50% alcohol content so that the alcohol content in the lotion becomes 30%?

Average weight of 25 students of a class is 50 kg. If the weight of the class teacher is included, the average is increased by 1 kg. The weight of the teacher is 

What is the simplified form the expression (1+x)(1+x²)(1+x⁴)(1+x⁸)(1-x)?

What is the rate of interest per annum for simple interest at which Rs.880 amounts to Rs.913 in $$1{1\over 2}$$years?