Calculate the solid angle subtended by the periphery of an area of $1 \, cm^2$ at a point situated symmetrically at a distance of $5 \, cm$ from the area. (in $, sr$)

$A$ far-off planet is estimated to be at a distance $D$ from the Earth. If its diametrically opposite extremes subtend an angle $\theta$ at an observatory situated on the Earth,the approximate diameter of the planet is .............

What is called a basis? What is parallax? Define angular diameter.

Calculate the angle of $(a)$ $1^{\circ}$ (degree),$(b)$ $1^{\prime}$ (minute of arc),and $(c)$ $1^{\prime \prime}$ (second of arc) in radians. Use $360^{\circ} = 2\pi \text{ rad}$,$1^{\circ} = 60^{\prime}$,and $1^{\prime} = 60^{\prime \prime}$.

$A$ man wishes to estimate the distance of a nearby tower from him. He stands at a point $A$ in front of the tower $C$ and spots a very distant object $O$ in line with $AC$. He then walks perpendicular to $AC$ up to $B$,a distance of $100 \; m$,and looks at $O$ and $C$ again. Since $O$ is very distant,the direction $BO$ is practically the same as $AO$; but he finds the line of sight of $C$ shifted from the original line of sight by an angle $\theta = 40^{\circ}$ ($\theta$ is known as 'parallax'). Estimate the distance (in $m$) of the tower $C$ from his original position $A$.

Match List-$I$ (Event) with List-$II$ (Order of the time interval for happening of the event) and select the correct option from the options given below the lists:

List-$I$	List-$II$
$(1)$ Rotation period of earth	$(i)$ $10^5\, s$
$(2)$ Revolution period of earth	$(ii)$ $10^7\, s$
$(3)$ Period of light wave	$(iii)$ $10^{-15}\, s$
$(4)$ Period of sound wave	$(iv)$ $10^{-3}\, s$