m balls are distributed among a boys and b girls. Prove that the probability that odd numbers of balls are distributed to boys is `((b+a)^m - (b+a)^m)/ (2 (a+b)^m)`.

If the papers of 4 students randomly distributed for checking among 7 teacher, then the probability that all the 4 papers are checked by exactly 2 teachers is n/m where n, m are natural number and HCF(n,m)=1 . Then number of positive divisiors of (n+m) is

Suppose m boys and m girls take their seats randomly around a circle. The probability of their sitting is (.^(2m-1)C_m)^(-1), when

5 girls and 10 boys sit at random in a row having 15 chairs numbered as 1 to 15. Find the probability that end seats are occupied by the girls and between any two girls odd numbers of boys sit.

A probability distribution of random variable X is as follows. b= ….., E(X) =…..

A box B_(1) contains 1 white ball, 3 red balls, and 2 black balls. An- other box B_(2) contains 2 white balls, 3 red balls and 4 black balls. A third box B_(3) contains 3 white balls, 4 red balls, and 5 black balls. If 2 balls are drawn (without replecement) from a randomly selected box and one of the balls is white and the other ball is red the probability that these 2 balls are drawn from box B_(2) is

A ball A moving with a velocity 5 m/s collides elastically with another identical ball at rest such that the velocity of A makes an angle of 30^(@) with the line joining the centres of the balls. Then consider following statements : (A) Balls A an B move at right angles after collision (B) kinetic energy is conserved (C) speed of A after collision is (5/2) m/s (D) speed of B after collision is ( 5sqrt(3)//2 ) m/s Select correct alternative :-

A box B_1 contains 1 white ball, 3 red balls and 2 black balls. Another box B_2 contains 2 white balls, 3 red balls and 4 black balls. A third box B_3 contains 3 white balls, 4 red balls and 5 black balls. If 1 ball is drawn from each of the boxes B_1 , B_2 and B_3 , then the probability that all 3 drawn balls are of the same colour , is

A rectangular plate of mass M and dimension axxb is held in horizontal position by striking n small balls (each of mass m) per unit area per second. The balls are striking in the shaded half region of the plate. The collision of the balls with the plate is elastic. What is v? (Given n=100, M =3 kg, m=0.01 kg, b = 2m, a =1m, g = 10m/s^2).

If A.M. and G.M. of two positive numbers a and b are 10 and 8, respectively, find the numbers.

If a set A has m elements and a set B has n elements then the number of relation from a to B is ...........