In the Compton scattering process,the incident $X$-radiation is scattered at an angle of $60^{\circ}$. The wavelength of the scattered radiation is $0.22 \ \mathring{A}$. The wavelength of the incident $X$-radiation in $\mathring{A}$ units is:

$A$ body of mass $m$ is moving in a circle of radius $r$ with a constant speed $v$. The force on the body is $\frac{mv^2}{r}$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle?

At $300 K$ , an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height $(h)$ of the solution $($density $=1.00 g cm ^{-3} )$ where h is equal to $2.00 cm$ . If the concentration of the dilute solution of the macromolecule is $2.00 g dm ^{-3}$, the molar mass of the macromolecule is calculated to be $X \times 10^4 g mol ^{-1}$. The value of $X$ is $...$ .
Use : Universal gas constant $(R)=8.3 J K ^{-1} mol^{-1}$ and acceleration due to gravity $( g )=10 m s ^{-2}$

$A$ thin uniform,circular ring is rolling down an inclined plane of inclination $30^\circ$ without slipping. Its linear acceleration along the inclined plane will be

If $\log 2=a, \log 3=b, \log 7=c$ and $6^x=7^{x+4}$,then $x$ is equal to:

Consider the following reaction: $A \longrightarrow \text{Products}$. This reaction is completed in $100 \ min$. The rate constant of this reaction at $t_1 = 10 \ min$ is $10^{-2} \ min^{-1}$. What is the rate constant (in $min^{-1}$) at $t_2 = 20 \ min$?