The system of equations $$x+y+z=6,$$ $$x+4y+6z=20,$$ $$x + 4y + \lambda z = \mu $$ has no solution for values of $$\lambda $$ and $$\mu $$ given by

Consider a closed surface $$'S'$$ surrounding a volume $$V.$$ If $$\overrightarrow r $$ is the position vector of a point inside $$S$$ with $$\overrightarrow n $$ the unit normal on $$'S',$$ the value of the integral is

A fair dice is tossed two times. The probability that the $$2$$^nd toss results in a value that is higher than the first toss is

The solution of differential equation $${{dy} \over {dx}} = ky,y\left( 0 \right) = C$$ is