Data Entry - Physics

Observe the statements given below :
Assertion $(A)$ : $f(x)=x e^{-x}$ has the maximum at $x=1$
Reason $(R)$ : $f^{\prime}(1)=0$ and $f^{\prime \prime}(1) < 0$
Which of the following is correct?

If $\frac{x-4}{x^2-5x+6}$ can be expanded in the ascending powers of $x$,then the coefficient of $x^3$ is

Which of the following ions forms a hydroxide that is readily soluble in water?

If $lx^2+3xy-2y^2-5x+5y+k=0$ represents a pair of perpendicular lines,then

$A$ complex compound of $Co^{3+}$ with molecular formula $CoCl_{x} \cdot yNH_3$ gives a total of $3$ ions when dissolved in water. How many $Cl^{-}$ ions satisfy both primary and secondary valencies in this complex?