The number of ways of arranging `m` positive and `n(lt m+1)` negative signs in a row so that no two are together is a)^m+1p_n` b`^n+1p_m` c)^m+1C_n` d)^n+1c_m`

2m white counters and 2n red counters are arranged in a straight line with (m+n) counters on each side of central mark. The number of ways of arranging the counters, so that the arrangements are symmetrical with respect to the central mark is (A) .^(m+n)C_m (B) .^(2m+2n)C_(2m) (C) 1/2 ((m+n)!)/(m! n!) (D) None of these

The ratio of the sum of m and n terms of an A.P. is m^(2):n^(2) . Show that the ratio of m^(th) and n^(th) term is 2m - 1 : 2n - 1 .

O P Q R is a square and M ,N are the middle points of the sides P Qa n dQ R , respectively. Then the ratio of the area of the square to that of triangle O M N is (a)4:1 (b) 2:1 (c) 8:3 (d) 7:3

The number of ordered pairs (m,n) where m , n in {1,2,3,…,50} , such that 6^(m)+9^(n) is a multiple of 5 is

The number of ways in which we can distribute m n students equally among m sections is given by a. ((m n !))/(n !) b. ((m n)!)/((n !)^m) c. ((m n)!)/(m ! n !) d. (m n)^m

In the expansion of (1+a)^m+n , prove that coefficients of a^m and a^n are equal.

m men and n women are to be seated in a row so that no two women sit together. If (m>n) then show that the number of ways in which they can be seated as (m!(m+1)!)/((m-n+1)!) .

If x and y are positive real numbers and m, n are any positive integers, then Prove that (x^n y^m)/((1+x^(2n))(1+y^(2m))) lt =1/4

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