The correct statement(s) about O₃ is(are)

Among \(H_2, H e_2^{+}, L i_2, B e_2, B_2, C_2, N_2, O_2^{-}\), and \(F_2\), the number of diamagnetic species is -
(Atomic number : \(H=1, H e=2, L i=3, B e=4, B=5,\) \(C=6, N =7, O=8, F=9\) )

Paragraph:
The hydrogen-like species \(\mathrm{Li}^{2+}\) is in a spherically symmetric state \(S_1\) with one radial node. Upon absorbing light the ion undergoes transition to a state \(S_2\). The state \(S_2\) has one radial node and its energy is equal to the ground state energy of the hydrogen atom.
Question:
The orbtial angular momentum quantum number of the state \(S_2\) is

The IUPAC name of \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{COCl}\) is

Statement I Alkali metals dissolve in liquid ammonia to give blue solutions. Statement II Alkali metals in liquid ammonia give solvated species of the type \(\left(M\left(\mathrm{NH}_3\right)_n\right]^{+}(M=\) alkali metals \()\).

Statement 1 There is a natural asymmetry between converting work to heat and converting heat to work.
Statement 2 No process is possible in which the sole result in the absorption of heat from a reservoir and its complete conversion into work.

Statement I In water, orthoboric acid behaves as a weak monobasic acid.
Statement II In water, orthoboric acid acts as proton donor.

Vessel-1 contains \(\mathbf{w}_2 \mathrm{~g}\) of a non-volatile solute \(\mathbf{X}\) dissolved in \(\mathbf{w}_1 \mathrm{~g}\) of water. Vessel- 2 contains \(\mathbf{w}_2 \mathrm{~g}\) of another non-volatile solute \(\mathbf{Y}\) dissolved in \(\mathbf{w}_1 \mathrm{~g}\) of water. Both the vessels are at the same temperature and pressure. The molar mass of \(\mathbf{X}\) is \(80 \%\) of that of \(\mathbf{Y}\). The van't Hoff factor for \(\mathbf{X}\) is 1.2 times of that of \(\mathbf{Y}\) for their respective concentrations.
The elevation of boiling point for solution in Vessel-1 is ________. \(\%\) of the solution in Vessel-2.

A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $m=0.4kg$ is at rest on this surface. An impulse of $1.0 N s$ is applied to the block at time $t=0$ so that it starts moving along the x-axis with a velocity $v\left(t\right)=v_0{e}^{-\frac{t}{\tau }}$ , where $v_0$ is a constant and $\tau =4$ . The displacement of the block, in meter, at $t=\tau$ is __________. Take $e^{-1}=0.37$

Statement I A block of mass \(m\) starts moving on a rough horizontal surface with a velocity \(v\). It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of \(30^{\circ}\) with the horizontal and the same block is made to go up on the surface with the same initial velocity \(v\). The decrease in the mechanical energy in the second situation is smaller than that in the first situation.
Statement II The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

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 _____

Answer the following by appropriately matching the lists based on the information given in the paragraph.
A musical instrument is made using four different metal strings, $1,\mathrm{ }2,\mathrm{ }3$ and $4$ with mass per unit length $\mathrm{\mu },2\mathrm{\mu },3\mathrm{\mu }$ and $4\mathrm{\mu }$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range ${\mathrm{L}}_0$ and $2{\mathrm{L}}_0.$ It is found that in string- $1\left(\mathrm{\mu }\right)$ at free length ${\mathrm{L}}_0$ and tension ${\mathrm{T}}_0$ the fundamental mode frequency is ${\mathrm{f}}_0.$
List-I gives the above four strings while list-II lists the magnitude of some quantity.

	List I		List II
$\left(\mathrm{a}\right)$	String $-1\left(\mathrm{\mu }\right)$	$\left(\mathrm{p}\right)$	$1$
$\left(\mathrm{b}\right)$	String $-2\left(2\mathrm{\mu }\right)$	$\left(\mathrm{q}\right)$	$\frac{1}{2}$
$\left(\mathrm{c}\right)$	String $-3\left(3\mathrm{\mu }\right)$	$\left(\mathrm{r}\right)$	$\frac{1}{\sqrt{2}}$
$\left(\mathrm{d}\right)$	String $-4\left(4\mathrm{\mu }\right)$	$\left(\mathrm{s}\right)$	$\frac{1}{\sqrt{3}}$
		$\left(\mathrm{t}\right)$	$\frac{3}{16}$
		$\left(\mathrm{u}\right)$	$\frac{1}{16}$

The length of the strings $1,\mathrm{ }2,\mathrm{ }3$ and $4$ are kept fixed at ${\mathrm{L}}_0,\frac{3{\mathrm{L}}_0}{2},\frac{5{\mathrm{L}}_0}{4}$ and $\frac{7{\mathrm{L}}_0}{4},$ respectively. Strings $1,\mathrm{ }2,\mathrm{ }3$ and $4$ are vibrated at their $1^{\mathrm{s}\mathrm{t}},\mathrm{ }{3}^{\mathrm{r}\mathrm{d}},\mathrm{ }{5}^{\mathrm{t}\mathrm{h}}$ and ${14}^{\mathrm{t}\mathrm{h}}$ harmonics, respectively such that all the strings have same frequency. The correct match for the tension in the four strings in the units of ${\mathrm{T}}_0$ will be.

If the value of Avogadro number is $6.023\times {10}^{23}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{–1}$ and the value of Boltzmann constant is $1.380\times {10}^{-23}\mathrm{ }\mathrm{J}{\mathrm{K}}^{-1}$ , then the number of significant digits in the calculated value of the universal gas constant is