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

n whole numbers are randomly chosen and multiplied. Now, match the following lists. {:(" List I"," List II"),("a. The probability that the last digit is 1, 3, 7, or 9 is","p. "(8^(n)-4^(n))/(10^(n))),("b. The probability that the last digit is 2, 4, 6, 8 is ","q. "(5^(n) - 4^(n))/(10^(n))),("c. The probability that the last digit is 5 is","r. " (4^(n))/(10^(n))),("d. The probability that the last digit is zero is","s. "(10^(n) - 8^(n) - 5^(n) + 4^(n))/(10^(n))):}

2n boys are randomly divided into two subgroups containint n boys each. The probability that eh two tallest boys are in different groups is n//(2n-1) b. (n-1)//(2n-1) c. (n-1)//4n^2 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

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

If m parallel lines in a plane are intersected by a family of n parallel lines, the number of parallelograms that can be formed is a. 1/4m n(m-1)(n-1) b. 1/4m n(m-1)(n-1) c. 1/4m^2n^2 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

In a n- sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is (2^n C_2)/(^(^(n C_(2-n)))C_2) b. (^(n(n-1))C_2)/(^(^(n C_(2-n)))C_2) c. (^n C_4)/(^(^(n C_(2-n)))C_2) d. none of these

If ^n C_3+^n C_4>^(n+1)C_3 , then a. n >6 b. n >7 c. n<6 d. none of these

The numbers 1, 2, 3, ..., n are arrange in a random order. The probability that the digits 1, 2, 3, .., k( k < n) appear as neighbours in that order is (a) 1 n ! (b) k ! / n! (c) (n-k)! / n! (d) (n-k+1)! / n!