What is the final product $(B)$ of this sequence?

$A$ function $y = f(x)$ satisfies $(x + 1) f'(x) - 2(x^2 + x) f(x) = \frac{e^{x^2}}{x + 1}$ for all $x > -1$. If $f(0) = 5$,then $f(x)$ is:

$A$ mixture of plane polarised and unpolarised light falls normally on a polarizing sheet. On rotating the polarizing sheet about the direction of the incident beam,the transmitted intensity varies by a factor of $4$. Find the ratio of the intensities $I_P$ and $I_0$,respectively of the polarized and unpolarized components in the incident beam.

The enthalpy of combustion of benzene from the following data will be
$(i) \ 6C_{(s)} + 3H_{2(g)} \to C_6H_{6(l)}; \Delta H = + 45.9 \ kJ$
$(ii) \ H_{2(g)} + \frac{1}{2}O_{2(g)} \to H_2O_{(l)}; \Delta H = - 285.9 \ kJ$
$(iii) \ C_{(s)} + O_{2(g)} \to CO_{2(g)}; \Delta H = - 393.5 \ kJ$
........$kJ$

Two equally charged metal spheres $A$ and $B$ repel each other with a force of $4 \times 10^{-5} ~N$. Another identical uncharged sphere $C$ is touched to $A$ and then placed at the midpoint of the line joining the spheres $A$ and $B$. The net electric force on the sphere $C$ is

$A$ light ray of wavelength $\lambda$ is passing through a pinhole of diameter $D$ and the effect is observed on a screen placed at a distance $L$ from the pinhole. The approximations of geometrical optics are applicable,if