If `n` integers taken at random are multiplied together , then the probability that the last digit of the product is 1, 3, 7, or 9 is a. `2^n//5^n` b. `4^n-2^n//5^n` c. `4^n//5^n` d. none of these

A 2n digit number starts with 2 and all its digits are prime, then the probability that the sum of all 2 consecutive digits of the number is prime is a. 4xx2^(3n) b. 4xx2^(-3n) c. 2^(3n) d. none of these

If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form 7^m+7^n is divisible by 5, equals

2n boys are randomly divided into two subgroups containint n boys each. The probability that the two tallest boys are in different groups is a. n//(2n-1) b. (n-1)//(2n-1) c. (n-1)//4n^2 d. none of these

n whole are randomly chosen and multiplied Column I, Column II The probability that the last digit is 1,3,7, or 9 is, p. (8^n-4^n)/(10^n) The probability that the last digit is 2,4,6, or 8 is, q. (5^n-4^n)/(10^n) The probability that the last digit is 5 is, r. (4^n)/(10^n) The probability that the last digit is zero is, s. (10^n-8^n-5^n+4^n)/(10^n)

If n be a positive integer and P(n):4^(5n)-5^(4n) When n=3 then the last digit of the expression will be -

P(n):11^(n+2)+1^(2n+1) where n is a positive integer If n=3 , then the last digit of expression is -

In a sequence of (4n+1) terms, the first (2n+1) terms are n A.P. whose common difference is 2, and the last (2n+1) terms are in G.P. whose common ratio is 0.5 if the middle terms of the A.P. and LG.P. are equal ,then the middle terms of the sequence is (n .2 n+1)/(2^(2n)-1) b. (n .2 n+1)/(2^n-1) c. n .2^n d. none of these

In the expansion of (x^3-1/(x^2))^n ,n in N , if the sum of the coefficients of x^5a n dx^(10) is zero , then n is a. 25 b. 20 c. 15 d. none of these

In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be a. 4n b. 4n-3 c. 4n+1 d. none of these

The total number of ways in which 2n persons can be divided into n couples is a. (2n !)/(n ! n !) b. (2n !)/((2!)^3) c. (2n !)/(n !(2!)^n) d. none of these