A variable name in certain computer language must be either an alphabet or an alphabet followed by a decimal digit. The total number of different variable names that can exist in that language is equal to a. `280` b. `390` c. `286` d. `296`

Fifteen identical balls have to be put in five different boxes. Each box can contain any number of balls. The total number of ways of putting the balls into the boxes so that each box contains at least two balls is equal to a. .^9C_5 b. .^10 C_5 c. .^6C_5 d. .^10 C_6

Total numbers formed less than 3xx10^8 and can be formed using the digits 1, 2, 3 is equal to a. 1/2(3^9+4xx368) b. 1/2(3^9-3) c. 1/2(7xx3^8-3) d. 1/2(3^9-3+3^8)

A person predicts the outcome of 20 cricket matches of his home team. Each match can result in either a win, loss, or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct is equal to a. ^20 C_(10)xx2^(10) b. ^20 C_(10)xx3^(20) c. ^20 C_(10)xx3^(10) d. ^20 C_(10)xx2^(20)

Assertion: The number of different number plates which can be made if the number plte contain three letters of the English alphabet followied by athree digit number is (26)^3xx(900) (if represents are allowed) Reason: The number of permutationis of n different things taken r at time when repetitios are allowed is n^r . (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Two players P_1a n dP_2 play a series of 2n games. Each game can result in either a win or a loss for P_1dot the total number of ways in which P_1 can win the series of these games is equal to a. 1/2(2^(2n)-^ "^(2n)C_n) b. 1/2(2^(2n)-2xx^"^(2n)C_n) c. 1/2(2^n-^"^(2n)C_n) d. 1/2(2^n-2xx^"^(2n)C_n)

For each of the following numbers, write the place value of each digit, express in expanded form and give the number name: a. 15874 b. 50679 c. 67032 d. 43201 e. 75430 f. 26070