Steam at $100\,^{\circ}C$ is passed into $22\,g$ of water at $20\,^{\circ}C$. The mass of water that will be present when the water acquires a temperature of $90\,^{\circ}C$ (Latent heat of steam is $540\, cal/g$) is ............ $g$.

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}$,where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D = [U(x = \infty) - U_{\text{equilibrium}}]$,what is the value of $D$?

Magnesium wire is heated in the atmosphere of $CO_2$ because

The transformed equation of $3x^2 - 4xy = r^2$ when the coordinate axes are rotated about the origin through an angle of $\operatorname{Tan}^{-1}(2)$ in the positive direction is:

In a meter bridge,a $30 \Omega$ resistance is connected in the left gap and a pair of resistances $P$ and $Q$ in the right gap. Measured from the left,the balance point is $37.5 \text{ cm}$ when $P$ and $Q$ are in series,and $71.4 \text{ cm}$ when they are in parallel. The values of $P$ and $Q$ (in $\Omega$) are:

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 $( g )=10 m s ^{-2}$