In allene \(\left(\mathrm{C}_{3} \mathrm{H}_{4}\right)\), the type(s) of hybridisation of the carbon atoms is (are):

Match the conversions in Column I with the type(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the \(4 \times 4\) matrix given in the ORS.

Consider the kinetic data given in the following table for the reaction $\mathrm{A}+\mathrm{B}+\mathrm{C}\to$ Product.

Ex peri ment No.	\([\text A]\) \((\text{mol}\) \(\text{dm} ^{-3})\)	\([\text B]\) \((\text{mol}\) \(\text{dm} ^{-3})\)	\([\text C]\) \((\text{mol}\) \(\text{dm} ^{-3})\)	Rate of reaction \((\text{mol}\) \(\text{dm} ^{-3}\) \(\text s^{-1})\)
1	0.2	0.1	0.1	\(6.0 \times\) \(10^{-5}\)
2	0.2	0.2	0.1	\(6.0 \times \) \(10^{-5}\)
3	0.2	0.1	0.2	\(1.2 \times \) \(10^{-4}\)
4	0.3	0.1	0.1	\(9.0 \times \) \(10^{-5}\)

The rate of the reaction for $\left[\mathrm{A}\right]=0.15\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{d}{\mathrm{m}}^{-3},\mathrm{ }\left[\mathrm{B}\right]=0.25\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{d}{\mathrm{m}}^{-3}$ and $\left[\mathrm{C}\right]=0.15\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{d}{\mathrm{m}}^{-3}$ is found to be $\mathrm{Y}\times {10}^{-5}\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{d}{\mathrm{m}}^{-3}{\mathrm{s}}^{-1}.$ The value of $\mathrm{Y}$ is __________

(I) 1, 2-dihydroxy benzene
(II) 1, 3-dihydroxy benzene
(III) 1, 4-dihydroxy benzene
(IV) Hydroxy benzene
The increasing order of boiling points of above mentioned alcohols is

The figure below is the plot of potential energy versus internuclear distance $\left(\mathrm{d}\right)$ of ${\mathrm{H}}_2$ molecule in the electronic ground state. What is the value of the net potential energy ${\mathrm{E}}_0$ (as indicated in the figure) in $\mathrm{kJ}{\mathrm{mol}}^{-1},$ for $\mathrm{d}={\mathrm{d}}_0$ at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent? As reference, the potential energy of $\mathrm{H}$ atom is taken as zero when its electron and the nucleus are infinitely far apart.
Use Avogadro constant as $6.023\times {10}^{23}{\mathrm{mol}}^{-1}.$

Mark total potential energy for 2 H-atom (per mole) as answer.

The desired product X can be prepared by reacting the major product of the reactions in LIST-I with one or more appropriate reagents in LIST-II.
(given, order of migratory aptitude: aryl > alkyl hydrogen)

	LIST-I		LIST -II
A)		P)	${\mathrm{I}}_2,\mathrm{NaOH}$
B)		Q)	$\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2\mathrm{OH}\right]$
C)		R)	Fehling solution
D)		S)	$\mathrm{H}\mathrm{C}\mathrm{H}\mathrm{O},\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}$
		T)	$\mathrm{NaOBr}$

Match the extraction processes listed in column I with metals listed in column II.

An infinitely long wire, located on the \(z\)-axis, carries a current \(I\) along the \(+z\)-direction and produces the magnetic field \(\vec{B}\). The magnitude of the line integral \(\int \vec{B} \cdot \overrightarrow{d l}\) along a straight line from the point \((-\sqrt{3} a, a, 0)\) to \((a, a, 0)\) is given by
[ \(\mu_0\) is the magnetic permeability of free space.]

Upon treatment with ammoniacal ${\text{H}}_2\text{S}$, the metal ion that precipitates as a sulphide is

Paragraph :
Treatment of compound \(\mathbf{O}\) with \(\mathrm{KMnO}_{4} / \mathrm{H}^{+}\)gave \(\mathbf{P}\), which on heating with ammonia gave \(\mathbf{Q}\). The compound \(\mathbf{Q}\) on treatment with \(\mathrm{Br}_{2} / \mathrm{NaOH}\) produced \(\mathbf{R}\). On strong heating, \(\mathbf{Q}\) gave \(\mathbf{S}\), which on further treatment with ethyl \(2-\)bromopropanoate in the presence of \(\mathrm{KOH}\) followed by acidification, gave a compound \(\mathbf{T}\).


Question :
The compound \(\mathbf{T}\) is

Half-life of a radio active substance ' \(A\) ' is 4 days. The probability that a nucleus will decay in two half-lives is

A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index \(n\) of the first lens is \(1.5\) and that of the second lens is \(1.2\). Both the curved surface are of the same radius of curvature \(R=14\) \(\mathrm{cm}\). For this bi-convex lens, for an object distance of 40 \(\mathrm{cm}\), the image distance will be

A double slit setup is shown in the figure. One of the slits is in medium $2$ of refractive index $n_2$. The other slit is at the interface of this medium with another medium $1$ of refractive index $n_1\left(\ne n_2\right)$. The line joining the slits is perpendicular to the interface and the distance between the slits is $d$. The slit widths are much smaller than $d$. A monochromatic parallel beam of light is incident on the slits from medium $1$. A detector is placed in medium $2$ at a large distance from the slits, and at an angle $\theta$ from the line joining them, so that $\theta$ equals the angle of refraction of the beam. Consider two approximately parallel rays from the slits received by the detector.
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Which of the following statement(s) is(are) correct?