If the quotient and remainder obtained when the expression $3 x^5-6 x^4+2 x^3+4 x^2-5 x+8$ is divided by the expression $x^2-2 x+3$ are $a x^3+b x^2+c x+d$ and $p x+q$ respectively, then $a b+c d=$

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $12 x^4-56 x^3+89 x^2-56 x+12=0$ such that $\alpha \beta=\gamma \delta=1$ and $\frac{\alpha+\beta}{\gamma+\delta}>1$, then $\frac{\alpha+\beta}{\gamma+\delta}=$

If all the letters of the word ACADEMICIAN are permuted in all possible ways, then the number of permutations in which no two $A^{\prime} s$ are together and all the consonants are together is

The number of all possible three letter words that can be formed by choosing three letters from the letters of the word FEBRUARY so that a vowel always occupies the middle place is