The refractive index of a glass convex lens is $1.5$. The radius of curvature of each of the two surfaces of the lens is $20 ~cm$. The ratio of the power of the lens when immersed in a liquid of refractive index $1.25$ to that when placed in air is:

$A$ minimum value of $\int_0^x t e^{t^2} d t$ is

When a metallic surface is illuminated with radiation of wavelength $\lambda$,the stopping potential is $V$. If the same surface is illuminated with radiation of wavelength $2\lambda$,the stopping potential is $\frac{V}{4}$. The threshold wavelength for the metallic surface is:

$A$ student records $\Delta Q, \Delta U$ and $\Delta W$ for a thermodynamic cycle $A \to B \to C \to A$. Certain entries are missing. Find the correct entry from the following options.

Process	$AB$	$BC$	$CA$
$\Delta W$	$40 \ J$	$ $	$30 \ J$
$\Delta U$	$ $	$50 \ J$	$ $
$\Delta Q$	$150 \ J$	$10 \ J$	$ $

In an unbiased $p-n$ junction,holes diffuse from the $p-$ region to $n-$ region because

$Na^+$,$Mg^{2+}$,$Al^{3+}$,and $Si^{4+}$ are isoelectronic. What is the order of their ionic radii?