The total number of chiral molecules formed from one molecule of $P$ on complete ozonolysis $\left({\mathrm{O}}_3,\mathrm{Zn}/H_2\mathrm{O}\right)$ is _____

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:

The nitrogen oxide(s) that contain(s) N.N bond(s) is (are)

The plot of ${\mathrm{logk}}_{\mathrm{f}}$ versus $\frac{1}{\mathrm{T}}$ for a reversible reaction $\mathrm{A}\left(\mathrm{g}\right)\rightleftharpoons \mathrm{P}\left(\mathrm{g}\right)$ is shown.

Pre-exponential factors for the forward and backward reactions are ${10}^{15} {\mathrm{s}}^{-1}$ and ${10}^{11} {\mathrm{s}}^{-1}$, respectively. If the value of $\mathrm{logK}$ for the reaction at $500 \mathrm{K}$ is $6$, the value of $\left|{\mathrm{logk}}_{\mathrm{b}}\right|$ at $250 \mathrm{K}$ is
$\left[\mathrm{K}=\right.$equilibrium constant of the reaction, ${\mathrm{k}}_{\mathrm{f}}=$rate constant of forward reaction, ${\mathrm{K}}_{\mathrm{b}}=$rate constant of backward reaction]

In the following carbocation, \(\mathrm{H} / \mathrm{CH}_3\) that is most likely to migrate to the positively charged carbon is

Considering the reaction sequence given below, the correct statement(s) is(are)

At \(400 \mathrm{~K}\), the root mean square (rms) speed of a gas \(X\) (molecular weight \(=40\) ) is equal to the most probable speed of gas \(Y\) at \(60 \mathrm{~K}\). The molecular weight of the gas \(Y\) is

An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?

Paragraph :
\(P_{14-16}\) : Paragraph for Questions Nos. 14 to 16 A fixed thermally conducting cylinder has a radius \(R\) and height \(L_0\). The cylinder is open at its bottom and has a small hole at its top. A piston of mass \(M\) is held at a distance \(L\) from the top surface as shown in the figure. The atmospheric pressure is \(p_0\).

Question :
The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is \(\rho\). In equilibrium, the height \(H\) of the water column in the cylinder satisfies

Let $s, t, r$ be non-zero complex numbers and $L$ be the set of solutions $z=x+iy \left(x, y\in \mathrm{ℝ}, i=\sqrt{-1}\right)$ of the equation $sz+t\stackrel{-}{z}+r=0$, where $\stackrel{-}{z}=x-iy$. Then, which of the following statement(s) is (are) TRUE?

The greatest integer less than or equal to ${\int }_1^2{\log }_2\left(x^3+1\right)dx+{\int }_1^{{\log }_{2}9}{\left(2^x-1\right)}^{\frac{1}{3}}dx$ is

Statement 1 For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero.
Statement 2 At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs energy.

Reagent(s) which can be used to bring about the following transformation is(are)