Mean and variance of six observations are 6 and 12 respectively. If each observation is multiplied by 3, then new variance of the resulting observations is

Words of length 10 are formed by using the letters A, B, C, D, E, F, G, H, I, J. Let $x$ be number of such words where no letter is repeated and $y$ be number of such words where exactly two letters are repeated twice and no other letter is repeated, then the value of $\frac{y}{x}$ is

$\triangle \mathrm{OAB}$ is formed by the lines $x^2-4 x y+y^2=0$ and the line $A B$. The equation of line $A B$ is $2 x+3 y-1=0$. Then the equation of the median of the triangle drawn from the origin is

A particle performing S.H.M. with maximum velocity ' $V$ '. If the amplitude double and periodic time is made, $\left(\frac{1}{3}\right)^{\text {rd }}$ then the maximum velocity is