Find the ratio of `.^20C_r and .^(25)C_r` when each of them has the greatest possible value.

Find the ratio of ^20 C_ra n d^(25)C_r when each of them has the greatest possible value.

Find the value of :^50C_4+sum_(r=1)^6 .^(56-r)C_3.

If a,b,c in R - {0} and a^(2) = bc and a + b +c = abc then the least possible value of a^(2) is

If .^(n)P_(r)=720 and .^(n)C_(r)=120 then find the value of r.

The maximum value of .^(n)C_(r) is obtained when r is equal to

In the circuit shown in figure E_1, E_2=20V, R_1=R_2=10kOmega and C=1muF . Find the current through R_1,R_2 and C when (a) S has been kept connected to A for a long time. (b) The switch is suddenly shifted to B .

Find the rate of change of the area of a circle with respect to its radius r when(a) r = 3 c m (b) r = 4 c m

If .^(15)C_(r): .^(15)C_(R-1) = 11:5 , then find the value of 'r'.

A body has maximum range R_1 when projected up the plane. The same body when projected down the inclined plane, it has maximum range R_2 . Find the maximum horizontal range. Assume equal speed of projection in each case and the body is projected onto the inclined plane in the line of the greatest slope.

If ^15 C_(3r):^(15)C_(r+1)=11 :3 , find the value of rdot