$A$ double slit experiment is immersed in water of refractive index $1.33$. The slit separation is $1 ~mm$ and the distance between the slit and the screen is $1.33 ~m$. The slits are illuminated by light of wavelength $6300 ~Å$. The fringe width is:

The voltage of an $ac$ source varies with time according to the equation $V = 100 \sin(100 \pi t) \cos(100 \pi t)$,where $t$ is in seconds and $V$ is in volts. Then:

If $\frac{\cos x}{\cos (x-2y)} = \lambda$,then $\tan (x-y) \tan y$ is equal to

The reagent used in the preparation of aspirin from salicylic acid is

At $25 \, ^oC$,the equilibrium $SO_2Cl_2(g) \rightleftharpoons SO_2(g) + Cl_2(g)$ is established in a closed vessel. When $Cl_2$ is added to this equilibrium mixture,which of the following statements is true for the system?
$(1)$ The concentrations of $SO_2Cl_2$ and $SO_2$ change.
$(2)$ More $Cl_2$ is produced.
$(3)$ The concentration of $SO_2$ decreases and $SO_2Cl_2$ increases.

Which of the following alkenes does $NOT$ exhibit $cis-trans$ isomerism?