The offspring produced from the cross between two pure parents are more vigorous and high-yielding. What is this phenomenon called?

The angle of a prism is $A.$ One of its refracting surfaces is silvered. Light rays falling at an angle of incidence $2A$ on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index $\mu$ of the prism is

$\frac{\sin 5 \theta}{\sin \theta}$ is equal to

If the function $f: R \rightarrow R$ defined by $f(x) = \begin{cases} \frac{\sin(a+1)x + \sin x}{x}, & x < 0 \\ b, & x = 0 \\ \frac{\sqrt{x+x^2} - \sqrt{x}}{x^{3/2}}, & x > 0 \end{cases}$ is continuous on $R$,then $a+b =$

Arrange the carbanions,$(CH_3)_3\bar{C}$,$\bar{C}Cl_3$,$(CH_3)_2\bar{C}H$,$C_6H_5\bar{C}H_2$ in order of their decreasing stability.

One mole of an ideal gas $(\gamma = 1.4)$ is adiabatically compressed so that its temperature rises from $27\,^oC$ to $35\,^oC$. The change in the internal energy of the gas is .... $J$. (Given $R = 8.3\,J/mol\cdot K$)