The natural number m, for which the coefficient of x in the binomial expansion of

$${\left( {{x^m} + {1 \over {{x^2}}}} \right)^{22}}$$ is 1540, is .............

If the line, 2x - y + 3 = 0 is at a distance
$${1 \over {\sqrt 5 }}$$ and $${2 \over {\sqrt 5 }}$$ from the lines 4x - 2y + $$\alpha $$ = 0
and 6x - 3y + $$\beta $$ = 0, respectively, then the sum of all possible values of $$\alpha $$ and $$\beta $$ is :

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word ’SYLLABUS’ such that two letters are distinct and two letters are alike, is :

An electrical power line, having a total resistance of 2 $$\Omega $$, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately :