A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then :

The solution of the differential equation

$$x{{dy} \over {dx}} + 2y$$ = x² (x $$ \ne $$ 0) with y(1) = 1, is :

A plane passing through the points (0, –1, 0) and (0, 0, 1) and making an angle $${\pi \over 4}$$ with the plane y – z + 5 = 0, also passes through the point

Let the sum of the first n terms of a non-constant A.P., a₁, a₂, a₃, ..... be $$50n + {{n(n - 7)} \over 2}A$$, where A is a constant. If d is the common difference of this A.P., then the ordered pair (d, a₅₀) is equal to