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)

The reaction of ${\mathrm{HClO}}_3$ with $\mathrm{HCl}$ gives a paramagnetic gas, which upon reaction with ${\mathrm{O}}_3$ produces

All the energy released from the reaction $\mathrm{X}⟶\mathrm{Y},\mathrm{ }{\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{G}}^{\mathrm{o}}=-193\mathrm{ }\mathrm{k}\mathrm{J}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}$ is used for oxidizing ${\mathrm{M}}^{+}$ as ${\mathrm{M}}^{+}⟶{\mathrm{M}}^{3+}+2{\mathrm{e}}^{-}\mathrm{ },\mathrm{ }{\mathrm{E}}^{\mathrm{o}}=\mathrm{ }-0.25\mathrm{ }\mathrm{V}$
Under standard conditions, the number of moles of ${\mathrm{M}}^{+}$ oxidized when one mole of X is converted to Y is
$[\mathrm{F}=96500\mathrm{ }\mathrm{C}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}]$

Correct option(s) for the following sequence of reactions is(are)

Consider a helium $\left(\mathrm{He}\right)$ atom that absorbs a photon of wavelength $330 \mathrm{nm}$. The change in the velocity (in $\mathrm{cm} {\mathrm{s}}^{-1}$) of $\mathrm{He}$ atom after the photon absorption is ______ .
(Assume: Momentum is conserved when photon is absorbed.
Use: Planck constant $=6.6\times {10}^{-34} \mathrm{J} \mathrm{s}$, Avocados number $=6\times {10}^{23}{ \mathrm{mol}}^{-1}$, Molar mass of $\mathrm{He}=4 \mathrm{g}{ \mathrm{mol}}^{-1}$)

In the following monobromination reaction, the number of possible chiral products is

Paragraph: When potassium iodide is added to an aqueous solution of potassium ferricyanide, a reversible reaction is observed in which a complex \(\mathbf{P}\) is formed. In a strong acidic medium, the equilibrium shifts completely towards \(\mathbf{P}\). Addition of zinc chloride to \(\mathbf{P}\) in a slightly acidic medium results in a sparingly soluble complex Q.
Question: The number of zinc ions present in the molecular formula of \(\mathbf{Q}\) is

Let \(L=\lim _{x \rightarrow 0} \frac{a-\sqrt{a^2-x^2}-\frac{x^2}{4}}{x^4}\), \(a>0\). If \(L\) is finite, then

A stationary source is emitting sound at a fixed frequency \(f_0\), which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is \(1.2 \%\) of \(f_0\). What is the difference in the speeds of the cars (in km per hour) to the nearest integer ? The cars are moving at constant speeds much smaller than the speed of sound which is \(330 \mathrm{~ms}^{-1}\).

A single slit diffraction experiment is performed to determine the slit width using the equation, \(\frac{b d}{D}=m \lambda\), where \(b\) is the slit width, \(D\) the shortest distance between the slit and the screen, \(d\) the distance between the \(m^{\text {th }}\) diffraction maximum and the central maximum, and \(\lambda\) is the wavelength. \(D\) and \(d\) are measured with scales of least count of 1 cm and 1 mm, respectively. The values of \(\lambda\) and \(m\) are known precisely to be 600 nm and 3, respectively. The maximum absolute error (in \(\mu \mathrm{m}\)) in the value of \(b\) estimated using the diffraction maximum that occurs for \(m=3\) with \(d=5 \mathrm{~mm}\) and \(D=1 \mathrm{~m}\) is ______.

A solution of $0.1\mathrm{M}$ weak base $\left(\mathrm{B}\right)$ is titrated with $0.1\mathrm{M}$ of a strong acid $\left(\mathrm{HA}\right)$. The variation of $\mathrm{pH}$ of the solution with the volume of $\mathrm{HA}$ added is shown in the figure below. What is the ${\mathrm{pK}}_{\mathrm{b}}$ of the base? The neutralization reaction is given by$\mathrm{B}+\mathrm{HA}\to {\mathrm{BH}}^{+}+{\mathrm{A}}^{-}$.

Let $f:\left[0, 2\right]\to ℝ$ be the function defined by $f\left(x\right)=\left(3-\sin \left(2\pi x\right)\right)\sin \left(\pi x-\frac{\pi }{4}\right)-\sin \left(3\pi x+\frac{\pi }{4}\right)$. If $\alpha , \beta \in \left[0, 2\right]$ are such that $\left\{x\in \left[0, 2\right] :f\left(x\right)\ge 0\right\}=\left[\alpha , \beta \right]$, then the value of $\beta -\alpha$ is _____

The qualitative sketches I, II and III given below show the variation of surface tension with molar concentration of three different aqueous solutions of KCl, $\mathrm{C}{\mathrm{H}}_3\mathrm{O}\mathrm{H}\mathrm{}$ and $\mathrm{C}{\mathrm{H}}_3{\left(\mathrm{C}{\mathrm{H}}_2\right)}_{11}\mathrm{O}\mathrm{S}{\mathrm{O}}_3^{-}\mathrm{}\mathrm{N}{\mathrm{a}}^{+}$ at room temperature. The correct assignment of the sketches is -