In a $P-N$ junction diode,if the $P$ region is more heavily doped than the $N$ region,then the depletion layer is:

Which of the following bonds is the most polar?

The formation of the oxide ion $O^{2-}_{(g)}$ requires first an exothermic and then an endothermic step as shown below:
$O_{(g)} + e^- \rightarrow O^{-}_{(g)}$; $\Delta H_{eg} = -142 \ kJ \ mol^{-1}$
$O^{-}_{(g)} + e^- \rightarrow O^{2-}_{(g)}$; $\Delta H_{eg} = +844 \ kJ \ mol^{-1}$
This is because:

Factors affecting the Hardy-Weinberg principle are:
$(I)$ Gene flow
$(II)$ Genetic drift
$(III)$ Mutation
$(IV)$ Genetic recombination
$(V)$ Natural selection
The correct combination is:

Let $\alpha, \beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation $x^2-qx+r=0$. Then the value of $r$ is

For $x \in \mathbb{R}$,the range of $3 \cos (4x - 5) + 4$ lies in the interval