Slope of a line passing through P(2, 3) and intersecting the line, x + y = 7 at a distance of 4 units from P, is :

If the fourth term in the binomial expansion of $${\left( {{2 \over x} + {x^{{{\log }_8}x}}} \right)^6}$$ (x > 0) is 20 × 8⁷, then a value of x is :

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 :