There are 12 pieces of five, ten and twenty rupee currrencies whose total value is ₹105. When first 2 sorts are interchanged in their numbers its value will be increased by ₹20. Find the number of currencies in each sort.

Two sets have m and k elements. If the total number of subsets of the first set is 112 more than that of the second set, find the values of m and k.

A two digit numbers is such that the product of its digits is 12. When 36 is added to the number the digits interchange their places. Find the number.

Suppose X is the number of tails occurred when three fair coins are tossed once simultaneously. Find the values of the random variable X and number of points in its inverse images.

Suppose X is the number of tails occurred when three fair coins are tossed once simultaneously. Find the values of the random variable X and number of points in its inverse images .

Two forces equal to P and 2P newton act on a particle . If the first be doubled and the second be increased by 20 newton, the direction of the resultant is unaltered . Find the value of P .

In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he "wins" // "loses" .

A six sided die is marked '2' on one face, '3' on two of its faces, and '4' on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find the values of the random variable and number of points in its inverse images.