The expression $1+x \log _e a+\frac{x^2}{2 !}(\log _e a)^2+\frac{x^3}{3 !}(\log _e a)^3+\ldots$ for $a>0, x \in R$ is equal to:

$A$ cybrid is a hybrid carrying

At $25 \ ^\circ C,$ the solubility product of $Mg(OH)_2$ is $1.0 \times 10^{-11}.$ At which $pH$ will $Mg^{2+}$ ions start precipitating in the form of $Mg(OH)_2$ from a solution of $0.001 \ M \ Mg^{2+}$ ions?

For a reversible reaction $A \rightleftharpoons B$,which one of the following statements is wrong from the given energy profile diagram?

If $\left[\begin{array}{rrr}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]$ is a singular matrix,then $x$ is equal to

$A$ hollow metal sphere of radius $5\, cm$ is charged so that the potential on its surface is $10\, V$. The potential at the centre of the sphere is.....$V$