Statement I Molecules that are not superimposable on their mirror images are chiral.
Statement II All chiral molecules have chiral centres.

The species which by definition has zero standard molar enthalpy of formation at \(298 \mathrm{~K}\) is

For the identification of $\mathrm{\beta }$ -naphthol using dye test, it is necessary to use

Thermal decomposition of ${\mathrm{AgNO}}_3$ produces two paramagnetic gases. The total number of electrons present in the antibonding molecular orbitals of the gas that has the higher number of unpaired electrons is _____ .

Molar volume \(\left(V_m\right)\) of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with \(V_m\) as the variable. The ratio (in \(\mathrm{mol} \mathrm{dm}^{-3}\) ) of the coefficient of \(V_m^2\) to the coefficient of \(V_m\) for a gas having van der Waals constants \(a=6.0 \mathrm{dm}^6 \mathrm{~atm} \mathrm{~mol}^{-2}\) and \(b=0.060 \mathrm{dm}^3 \mathrm{~mol}^{-1}\) at 300 K and 300 atm is _____ .
Use: Universal gas constant \((R)=0.082 \mathrm{dm}^3 \mathrm{~atm} \mathrm{~mol}{ }^{-1} \mathrm{~K}^{-1}\)

If the reaction sequence given below is carried out with $15$ moles of acetylene, the amount of the product $\mathrm{D}$ formed (in $\mathrm{g}$) is The yields of $\mathrm{A},\mathrm{B},\mathrm{C}$ and $\mathrm{D}$ are given in parentheses. [Given: Atomic mass of $\mathrm{H}=1,\mathrm{C}=12,\mathrm{O}=16,\mathrm{Cl}=35$]

In \(1 \mathrm{~L}\) saturated solution of \(\mathrm{AgCl}\left[K_{\mathrm{sp}} \mathrm{AgCl}=1.6 \times 10^{-10}\right], 0.1\) mole of \(\mathrm{CuCl}\left[K_{\mathrm{sp}}(\mathrm{CuCl})=1.0 \times 10^{-6}\right]\) is added. The resultant concentration of \(\mathrm{Ag}^{+}\)in the solution is \(1.6 \times 10^{-x}\). The value of \(x\) is

Paragraph:
Let \(a\), b and \(c\) be three real numbers satisfying \(\left[\begin{array}{lll}a & b & c\end{array}\right]\left[\begin{array}{lll}1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7\end{array}\right]=\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]\)
Question:
Let \(\omega\) be a solution of \(x^3-1=0\) with \(\operatorname{Im}(\omega)>0\). If \(a=2\), with \(b\) and \(c\) satisfying Eq. (E), then the value of \(\frac{3}{\omega^a}+\frac{1}{\omega^b}+\frac{3}{\omega^c}\)

Paragraph :
Redox reaction play a pivotal role in chemistry and biology. The values of standard redox potential \(\left(E^{\circ}\right)\) of two half-cell reactions decide which way the reaction is expected to proceed. A simple example is a Daniel cell in which zinc goes into solution and copper gets deposited. Given below are a set of half-cell reactions (acidic medium) along with their \(E^{\circ}(V\) with respect to normal hydrogen electrode) values. Using this data obtain the correct explanations to Questions 14-19.
\(\mathrm{I}_2+2 e^{-} \longrightarrow 2 \mathrm{I}^{-} E^{\circ}=0.54 \)
\( \mathrm{Cl}_2+2 e^{-} \longrightarrow 2 \mathrm{Cl}^{-} E^{\circ}=1.36 \)
\( \mathrm{Mn}^{3+}+e^{-} \longrightarrow \mathrm{Mn}^{2+} E^{\circ}=1.50 \)
\( \mathrm{Fe}^{3+}+e^{-} \longrightarrow \mathrm{Fe}^{2+} E^{\circ}=0.77 \)
\( \mathrm{O}_2+4 \mathrm{H}^{+}+4 e^{-} \longrightarrow 2 \mathrm{H}_2 \mathrm{O} E^{\circ}=1.23\)
Question :
Sodium fusion extract, obtained from aniline, on treatment with iron (II) sulphate and \(\mathrm{H}_2 \mathrm{SO}_4\) in presence of air gives a prussian blue precipitate. The blue colour is due to the formation of

An infinitely long uniform line charge distribution of charge per unit length $\mathrm{\lambda }$ lies parallel to the $\mathrm{y}$ -axis in the $\mathrm{y}$ - $\mathrm{z}$ plane at $\mathrm{z}=\frac{\sqrt{3}}{2}\mathrm{\alpha }$ (see figure). If the magnitude of the flux of the electric field through the rectangular surface $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ lying in the $\mathrm{x}$ - $\mathrm{y}$ plane with its centre at the origin is $\frac{\mathrm{\lambda }\mathrm{L}}{\mathrm{n}{\mathrm{\epsilon }}_0}$ ( ${\mathrm{\epsilon }}_0=$ permittivity of free space), then the value of $\mathrm{n}$ is

Two solid cylinders \(P\) and \(Q\) of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder \(P\) has most of its mass concentrated near its surface, while \(Q\) has most of its mass concentrated near the axis. Which statement(s) is(are) correct?

Paragraph:
In a mixture of \(\mathrm{H}-\mathrm{H}^{+}\)gas \(\left(\mathrm{He}^{+}\right.\)is singly ionised \(\mathrm{He}\) atom), \(\mathrm{H}\) atoms and \(\mathrm{He}^{+}\)ions are excited to their respective first excited states. Subsequently, \(\mathrm{H}\) atoms transfer their total excitation energy to \(\mathrm{He}^{+}\)ions (by collisions). Assume that the Bohr model of atom is exactly valid.
Question:
The ratio of the kinetic energy of the \(n=2\) electron for the \(\mathrm{H}\) atom to that of \(\mathrm{He}^{+}\) ion is

Paragraph:
\(RCONH _2\) is converted into \(RNH _2\) by means of Hofmann bromamide degradation.

In this reaction, \(R \mathrm{CONHBr}\) is formed from which this reaction has derived its name. Electron donating group at phenyl activates the reaction. Hofmann degradation reaction is an intramolecular reaction.
Question:
Which is the rate determining step in Hofmann bromamide degradation?