If local maximum of $f(x)=\frac{a x+b}{(x-1)(x-4)}$ exists at $(2,-1)$, then $a+b=$

If $1+2 i$ is a root of the equation $x^4-3 x^3+8 x^2-7 x+5=0$, then sum of the squares of the other roots is

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+\frac{a}{2} x+b=0$ and $(\alpha-\beta)(\alpha-\gamma),(\beta-\alpha)(\beta-\gamma),(\gamma-\alpha),(\gamma-\beta)$ are the roots of the equation

$(y+a)^3+K(y+a)^2+L=0$, then $\frac{L}{K}=$

All the letters of the word MOTHER are arranged in all possible ways and the resulting words (may or may not have meaning) are arranged as in the dictionary. The number of words that appear after the word MOTHER is