The reduction potential of a hydrogen half-cell will be negative if:

$A$ radioactive material decays by simultaneous emission of two particles with respective half-lives $1620 \, years$ and $810 \, years$. The time, in years, after which one-fourth of the material remains is

$A$ compound $X$ upon reaction with $H_{2}O$ produces a colorless gas $Y$ with a rotten fish smell. Gas $Y$ is absorbed in a solution of $CuSO_{4}$ to give $Cu_{3}P_{2}$ as one of the products. Predict the compound $X$.

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-6x^2+11x-6=0$ and if $a=\alpha^2+\beta^2+\gamma^2$,$b=\alpha\beta+\beta\gamma+\gamma\alpha$ and $c=(\alpha+\beta)(\beta+\gamma)(\gamma+\alpha)$,then the correct inequality among the following is

The incorrect stability order of $+3$ and $+1$ states of $13^{th}$ group elements (boron family) is

If $y=y(x)$ is the solution of the differential equation $x\frac{dy}{dx} + 2y = x^2$ satisfying $y(1)=1$,then $y\left(\frac{1}{2}\right)$ is equal to