Rajdhani Express going from Bombay to Delhi stops at five intermediate stations, 10 passengers enter the train during the journey with 10 different ticket of two class. The number of different sets of tickets they may have is a. `^15 C_(10)` b. `^20 C_(10)` c. `^30 C_(10)` d. none of these

The total number of five-digit numbers of different digits in which the digit in the middle is the largest is a. sum_(n=4)^9^n P_4 b. 33(3!) c. 30(3!) d. none of these

A fair die is thrown 20 times. The probability that on the 10th throw, the fourth six appears is a. "^20 C_(10)xx5^6//6^(20) b. 120xx5^7//6^(10) c. 84xx5^6//6^(10) d. none of these

The sum of 20 terms of a series of which every even term is 2 times the term before it, every odd term is 3 times the term before it, the a. (2/7)(6^(10)-1) b. (3/7)(6^(10)-1) c. (3/5)(6^(10)-1) d. none of these

The term independent of a in the expansion of (1+sqrta+ 1/(sqrta-1))^-30 is (a) 30C_20 (b) 0 (c) 30C_10 (d) non of these

The box contains tickets numbered from 1 to 20. Three tickets are drawn from the box with replacement. The probability that the largest number on the tickets is 7 is (A) 2/19 (B) 7/20 (C) 1-(7/200)^3 (D) none of these

The coefficient of x^4 in (x//2-3//x^2)^10 is (405)/(256) b. (504)/(259) c. (450)/(263) d. none of these

There are 10 stations on a circular path. A train has to stop at 3 stations such that no two stations are adjacent. The number of such selections must be: (A) 50 (B) 84 (C) 126 (D) 70

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)

The coefficient of a^8b^4c^9d^9 in (a b c+a b d+a c d+b c d)^(10) is 10 ! b. (10 !)/(8!4!9!9!) c. 2520 d. none of these

A natural number is chosen at random from the first 100 natural numbers. The probability that x+(100)/x > 50 is 1//10 b. 11//50 c. 11//20 d. none of these