If $\alpha$ and $\beta$ are the irrational roots of the equation $3 p^2 x^3+p x^2+q x+3=0$ when $p=1$ and $q=-7$, then $|\alpha-\beta|=$

The roots of a cubic equation $f(x)=0$ are diminished by $\frac{-3}{2}$ so, as to remove the term containing $x^2$ and the transformed equation is $8 x^3-54 x-78=0$. Then, the equation $f(x)=0$ is

If ${ }^m P_r-{ }^{(m-1)} p_r=a \cdot{ }^{(m-1)} P_s$, then $a-s=$

The total number of ways of selecting 4 letters from all the letters of the word TSEAMCET is