A man appears in an examination in which there are four papers with a maximum of m marks for each paper.show that the number of ways of getting 2m marks on the whole is `(1/3)(m+2)(2m^2+4m+3)`

Show that m_4 ge m_2^2 .

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)!) .

There are n seats round a table marked 1,2,3,…..n the number of ways in which m(len) persons can take seats is

The ratio of the sums 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) .

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

To obtain grade A is an examination a student must score an average of 90 marks or more in five papers each of 100 marks. If his marks in first four papers are 82,92,94 and 88, then find the minumum marks he should score in fifth paper if he wants to get grade A in the examination.

If a body weighs m_1 gm-wt in air of density d and m_2 g-wt in a liquid of density D show that the density of the material of the body = ((m_1D)/(m_1-m_2)-(m_2d)/(m_1-m_2))gm//cm^2 .

There are m A.P. Whose common differences are 1,2,3,.. M respectively, the first term of each being unity. Show that the sum of their nth terms is (m)/(2)(mn -m+n+1) .

Find the values of 'm' for which the equation x^4-(m-3)x^2+m =0 has Four real roots

If A.M. and G.M. between two numbers is in the ratio m : n then prove that the numbers are in the ratio (m+sqrt(m^2-n^2)):(m-sqrt(m^2-n^2))dot