$A$ two-digit number is four times the sum of its digits and three times the product of its digits. The number is:

The polynomial equation of degree $5$ whose roots are the roots of the equation $x^5-3x^4-x^3+11x^2-12x+4=0$ each increased by $2$,is

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4-4x^3+3x^2+2x-2=0$ such that $\alpha$ and $\beta$ are integers and $\gamma, \delta$ are irrational numbers,then $\alpha+2\beta+\gamma^2+\delta^2=$

If ${x^2} + 2x + 2xy + my - 3$ has two rational factors,then the value of $m$ will be

Which of the following conditions implies that the roots of the equation $\frac{1}{4}x^2 + bx + c = 0$ are integers?

The solution set of $8x \equiv 6 \pmod{14}$,$x \in \mathbb{Z}$,is