A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the removed cards is k, then `k-20` is equal to

A pack contains n cards m=numbered form 1 to n . Two consecutive numbered cards are removed from the pack and the sum of the numbers of the remaining cards is 1224. .If thesmaller of the numberse on the removed cards is k , then k-20 =

The sum of the cubes of 1st n natural numbers is

Two consecutive numbers from 1,2,3,.....,n are removed, then arithmetic mean of the remaining numbers is 105/4, then n/10 must be equal to

The houses of a row are numbered consecutively 45 cm from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. And find this value of x. [Hint: S_(x-1) = S_(49) -S_(x)]

Three cards are drawn at random from a pack of 52 playing cards find the probability distribution of the number of aces

Six cards are drawn one by one from a set of unlimited number of cards, each card is marked with numbers -1, 0 or 1 . Number of different ways in which they can be drawn if the sum of the numbers shown by them vanishes is

From a set of 100 cards numbered 1 to 100, one card is drawn at random. The probability that the number obtained on the card is dividible by 6 is-

From a collection of 20 consecutive natural numbers, four are selected such that they are not consecutive. The number of such selections is

What is the number of ways of choosing 4 cards from a pack of 52 playing cards ? In how many of these are face cards,