JIPMAT (QA) PYQs

If $x^3 + y^3 = 468$ and $x + y = 12$, then value of $x^4 + y^4$ will be

Which of the following is the value of $m$ for which the polynomial $x^4 + 10x^3 + 25x^2 + 15x + m$ is exactly divisible by $x+7$?

$\frac{(4.53-3.07)^2}{(3.07-2.15)(2.15-4.53)} + \frac{(3.07-2.15)^2}{(2.15-4.53)(4.53-3.07)} + \frac{(2.15-4.53)^2}{(4.53-3.07)(3.07-2.15)}$ is simplified to