Two perfect numbers are ............ and ............

Two perfect gases at absolute temperature T_(1) and T_(2) are mixed. There is no loss of energy. The masses of the molecules are m_(1) and m_(2) . The number of molecules in the gases are n_(1) and n_(2) . The temperature of the mixture is

Find the smallest perfect square number divisible by 24 , 30 and 60 .

Define a perfect number. Write two perfect numbers.

STATEMENT-1 : The dual statement of "xis a perfect square or xis a prime number" is "x is a perfect square and a prime number and STATEMENT-2 : If x is a prime number, then it isnot a perfect square.

using the method of successive subtraction examine whether or not the following numbers are perfect cube (i) 130 (ii) 345 (iii) 792 (iv) 1331 Find the smallest number that must be subtracted from those of the numbers in above question which are not perfect cubes, to make them perfect cubes. What are the corresponding cube roots?

Find the smallest perfect square number, which is divisible by 8 and 12 .

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number(iii) a number divisible by 5.

A box contains 90 discs which are numbered from 1 to 90. If one discs is drawn at random from the box, find the probability that it bears (i) a two digit number (ii) a perfect square number (iii) a number divisible by 5.

Two perfect gases (1) and (2) are at temperatures T_(1) and T_(2) . If the number of molecules of the two gases are n_(1) and n_(2) and the masses of the molecules m_(1) and m_(2) , find the resulting temperature when the two gases are mixed. Assume that there is no loss of energy on mixing the two gases.

Cards marked with numbers 1, 2, 3, 4, ..... 20 are well shuffled and a card is drawn at random. What is the probability that the number on the card is : a perfect square ?