The total number of ways of selecting six coins out of 20 one-rupee coins, 10 fifty-paisa coins, and 7 twenty-five paisa coins is: (a.) `28` (b.) `56` (c.) `^37 C_6` (d.) none of these

If n objects are arrange in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is a. "^(n-2)C_3 b. "^(n-3)C_2 c. "^(n-3)C_3 d. none of these

The total number of solutions of [x]^2=x+2{x}, where [.] and {.} denote the greatest integer and the fractional part functions, respectively, is equal to: 2 (b) 4 (c) 6 (d) none of these

The number of ways in which we can select four numbers from 1 to 30 so as to exclude every selection of four consecutive numbers is a. 27378 b. 27405 c. 27399 d. none of these

Among 10 persons, A, B, C are to speak at a function. The number of ways in which it can be done if A wants to speak before B and B wants to speak before C is a. 10 !//24 b. 9!//6 c. 10 !//6 d. none of these

Among the 8! [permutations of the digits 1, 2, 3..., 8, consider those arrangements which have the following property. If we take any five consecutive positions the product of the digits in these positions is divisible by 5. The number of such arrangements is equal to a. 7! b. 2.(7!) c. ^7C_4 d. none of these

n is selected from the set {1, 2, 3,.............,100} and the number 2^n+3^n+5^n is formed. Total number of ways of selecting n so that the formed number is divisible by 4 is equal to (A) 50 (B) 49 (C) 48 (D) None of these.

The number of possible outcomes in a throw of n ordinary dice in which at least one of the die shows and odd number is a. 6^n-1 b. 3^n-1 c. 6^n-3^n d. none of these

A bag contains four one-rupee coins, two twenty-five paisa coins, and five ten-paisa coins. In how many ways can an amount, not less than Rs. 1 be taken out from the bag? (Consider coins of the same denominations to be identical.) a. 71 b. 72 c. 73 d. 80

A seven-digit number without repetition and divisible by 9 is to be formed by using seven digits out of 1, 2, 3, 4 5, 6, 7, 8, 9. The number of ways in which this can be done is (a) 9! (b) 2(7!) (c) 4(7!) (d) non of these

In a three-storey building, there are four rooms on the ground floor, two on the first and two on the second floor. If the rooms are to be allotted to six persons, one person occupying one room only, the number of ways in which this can be done so that no floor remains empty is a. "^8P_6-2(6!) b. "^8P_6 c. "^8P_5(6!) d. none of these