A $$100 \mathrm{~mL}$$ solution of $$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{MgBr}$$ on treatment with methanol produces $$2.24 \mathrm{~mL}$$ of a gas at STP. The weight of gas produced is _____________ mg. [nearest integer]

The minimum value of the sum of the squares of the roots of $$x^{2}+(3-a) x+1=2 a$$ is:

If $$z=x+i y$$ satisfies $$|z|-2=0$$ and $$|z-i|-|z+5 i|=0$$, then :

$$ \text { Let } A=\left[\begin{array}{l} 1 \\ 1 \\ 1 \end{array}\right] \text { and } B=\left[\begin{array}{ccc} 9^{2} & -10^{2} & 11^{2} \\ 12^{2} & 13^{2} & -14^{2} \\ -15^{2} & 16^{2} & 17^{2} \end{array}\right] \text {, then the value of } A^{\prime} B A \text { is: } $$