Based on VSEPR theory, the number of 90 degree \(\mathrm{F}-\mathrm{Br}-\mathrm{F}\) angles in \(\mathrm{BrF}_5\) is

Match the thermodynamic processes given under Column I with the expressions given under Column II.

	Column I		Column II
A.	Freezing of water at 273 K and 1 atm	P.	$\mathrm{q}=0$
B.	Expansion of 1 mol of an ideal gas into a vacuum under isolated conditions	Q.	$\mathrm{w}=0$
C.	Mixing of equal volumes of two ideal gases at constant temperature and pressure in an isolated container	R.	$\mathrm{\Delta }{\mathrm{S}}_{\mathrm{s}\mathrm{y}\mathrm{s}}<0$
D.	Reversible heating of ${\mathrm{H}}_2\left(\mathrm{g}\right)$ at 1 atm from 300 K to 600 K, followed by reversible cooling to 300 K at 1 atm	S.	$\mathrm{\Delta }\mathrm{U}=0$
		T.	$\mathrm{\Delta }\mathrm{G}=0$

For a dilute solution containing \(2.5 \mathrm{~g}\) of a non-volatile non-electrolyte solute in \(100 \mathrm{~g}\) of water, the elevation in boiling point at 1 atm pressure is \(2^{\circ} \mathrm{C}\). Assuming concentration of solute is much lower than the concentration of solvent, the vapour pressure ( \(\mathrm{mm}\) of \(\mathrm{Hg}\) ) of the solution is (take \(K_{b}=0.76 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\) )

Which of the given statement(s) about \(\mathbf{N}, \mathbf{O}, \mathbf{P}\) and \(\mathbf{Q}\) with respect to \(\mathbf{M}\) is (are) correct?

The density (in \(\mathrm{g} \mathrm{cm}^{-3}\) ) of the metal which forms a cubic close packed (ccp) lattice with an axial distance (edge length) equal to 400 pm is \(\qquad\) .
Use: Atomic mass of metal \(=105.6 \mathrm{amu}\) and Avogadro's constant \(=6 \times 10^{23} \mathrm{~mol}^{-1}\)

The mole fraction of a solute in a solution is $0.1$. At $298 \mathrm{K}$, the molarity of this solution is the same as its molality. The density of this solution at $298 \mathrm{K}$ is $2.0\mathrm{ }\mathrm{g}\mathrm{ }\mathrm{c}{\mathrm{m}}^{–3}$. The ratio of the molecular weights of the solute and solvent, $\left(\frac{\mathrm{M}{\mathrm{W}}_{\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{e}}}{\mathrm{M}{\mathrm{W}}_{\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}}}\right)$, is:

Consider an ionic solid $\mathrm{MX}$, with $\mathrm{NaCl}$ structure. Construct a new structure $\left(\mathrm{Z}\right)$, whose unit cell is constructed from the unit cell of $\mathrm{MX}$, following the sequential instructions given below. Neglect the charge balance.
$\left(\mathrm{i}\right)$ Remove all the anions $\left(\mathrm{X}\right)$, except the central one.
$\left(\mathrm{ii}\right)$ Replace all the face centered cations $\left(\mathrm{M}\right)$, by anions $\left(\mathrm{X}\right)$.
$\left(\mathrm{iii}\right)$ Remove all the corner cations $\left(\mathrm{M}\right)$.
$\left(\mathrm{iv}\right)$ Replace the central anion $\left(\mathrm{X}\right)$, with cation $\left(\mathrm{M}\right)$.
The value of $\left(\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}}{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}}\right)$ in $\mathrm{Z}$ is _____.

In a bimolecular reaction, the steric factor $\mathrm{P}$ was experimentally determined to be $4.5$. The correct option(s) among the following is(are)

A cylindrical furnace has height $\left(H\right)$ and diameter $\left(D\right)$ both $1 \mathrm{m}$. It is maintained at temperature $360 \mathrm{K}$. The air gets heated inside the furnace at constant pressure $P_a$ and its temperature becomes $T=360 \mathrm{K}$. The hot air with density $\rho$ rises up a vertical chimney of diameter $d=0.1 \mathrm{m}$ and height $h=9 \mathrm{m}$ above the furnace and exits the chimney (see the figure). As a result, atmospheric air of density ${\rho }_a=1.2 \mathrm{kg} {\mathrm{m}}^{-3}$, pressure $P_a$ and temperature $T_a=300 \mathrm{K}$ enters the furnace. Assume air as an ideal gas, neglect the variations in $\rho$ and $T$ inside the chimney and the furnace. Also ignore the viscous effects.
[Given: The acceleration due to gravity $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ and $\pi =3.14$]

Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is _____ $\mathrm{gm} {\mathrm{s}}^{-1}$.

Paragraph :
A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are \(20 \mathrm{~mm}\) and \(1 \mathrm{~mm}\), respectively. The upper end of the container is open to the atmosphere.

Question :
If the density of air is \(\rho_{a}\) and that of the liquid \(\rho_{\ell}\), then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to

A source (S) of sound has frequency \(240 \mathrm{~Hz}\). When the observer \((\mathrm{O})\) and the source move towards each other at a speed \(v\) with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the sound to be \(288 \mathrm{~Hz}\). However, when the observer and the source move away from each other at the same speed \(v\) with respect to the ground (as shown in Case 2 in the figure), the observer measures the frequency of sound to be \(n \mathrm{~Hz}\). The value of \(n\) is ______

Let ${\theta }_1,{\theta }_2,\dots ,{\theta }_{10}$ be positive valued angles (in radian) such that ${\theta }_1+{\theta }_2+\cdots +{\theta }_{10}=2\pi$. Define the complex numbers $z_1=e^{i{\theta }_1},z_k=z_{k-1}{e}^{i{\theta }_k}$ for $k=2,3,\dots ,10$, where $i=\sqrt{-1}$. Consider the statements $P$ and $Q$ given below:
\(P:\left|z_2-z_1\right|+\left|z_3-z_2\right|+\cdots+\left|z_{10}-z_9\right|\) \(+\left|z_1-z_{10}\right| \leq 2 \pi \)
\( Q:\left|z_2^2-z_1^2\right|+\left|z_3^2-z_2^2\right|+\cdots+\left|z_{10}^2-z_9^2\right|\) \(+\left|z_1^2-z_{10}^2\right| \leq 4 \pi\)

Three identical capacitors $C_1,C_2\mathrm{a}\mathrm{n}\mathrm{d}{C}_3$ have a capacitance of $1.0\mu F$ each and they are uncharged initially. They are connected in a circuit as shown in the figure and $C_1$ is then filled completely with a dielectric material of relative permittivity ${ϵ}_r$ . The cell electromotive force (emf) $V_0=8V$ . First the switch $S_1$ is closed while the switch $S_2$ is kept open. When the capacitor $C_3$ is fully charged, $S_1$ is opened and $S_2$ is closed simultaneously. When all the capacitors reach equilibrium, the charge on $C_3$ is found to be $5\mu C$ . The value of ${ϵ}_r$ =____________.