$A$ huge circular arc of length $4.4 \; ly$ subtends an angle of $4''$ (arcseconds) at the centre of the circle. How long would it take for a body to complete $4$ revolutions if its speed is $8 \; AU/s$?
Given: $1 \; ly = 9.46 \times 10^{15} \; m$,$1 \; AU = 1.5 \times 10^{11} \; m$.

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	$(iv)$ $10^{-3}\, s$

In an experiment, a set of readings are obtained: $1.24 \ mm, 1.25 \ mm, 1.23 \ mm, 1.21 \ mm$. The expected least count of the instrument used in recording these readings is . . . . . . $mm$.

Precise measurements of physical quantities are a need of science. For example,to ascertain the speed of an aircraft,one must have an accurate method to find its positions at closely separated instants of time. This was the actual motivation behind the discovery of radar in World War $II$. Think of different examples in modern science where precise measurements of length,time,mass,etc.,are needed. Also,wherever you can,give a quantitative idea of the precision needed.

$A$ cuboidal block has dimensions $(1.5 \times 1.5 \times 1.0) \ cm$. What is the total surface area of the cuboid (in $cm^2$)?

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 $, sr$)