To an evacuated vessel with movable piston under external pressure of \(1 \mathrm{~atm}\), \(0.1\) mole of He and \(1.0\) mole of an unknown compound (vapour pressure \(0.68 mathrm{~atm}\) at \(0^{\circ} \mathrm{C}\) ) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at \(0^{\circ} \mathrm{C}\) is close to

List-I contains various reaction sequences and List-II contains different phenolic compounds.
Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

When 100 mL of 1.0 M HCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a temperature increase of ${5.7}^{\mathrm{o}}\mathrm{C}$ was measured for the beaker and its contents (Expt.1). Because the enthalpy of neutralization of a strong acid with a strong base is a constant $(-57.0\mathrm{ }\mathrm{k}\mathrm{J}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1})$ , this experiment could be used to measure the calorimeter constant. In a second experiment (Expt. 2), 100 mL of 2.0 M acetic acid $({\mathrm{K}}_{\mathrm{a}}=2.0\times {10}^{-5})$ was mixed with 100 mL of 1.0 M NaOH (under identical conditions to Expt. 1) where a temperature rise of ${5.6}^{\mathrm{o}}\mathrm{C}$ was measured. (Consider heat capacity of all solutions as $4.2\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{g}}^{-1}\mathrm{ }{\mathrm{K}}^{-1}$ and density of all solutions as $1.0\mathrm{ }\mathrm{g}\mathrm{ }\mathrm{m}{\mathrm{L}}^{-1}$ )
The pH of the solution after Expt. 2 is

Match the compounds in LIST-$\mathrm{I}$ with the observations in LIST-$\mathrm{II}$, and choose the correct option.

	LIST-$\mathrm{I}$		LIST-$\mathrm{II}$
$\left(\mathrm{I}\right)$	Aniline	$\left(\mathrm{P}\right)$	Sodium fusion extract of the compound on boiling with ${\mathrm{FeSO}}_4$, followed by acidification with conc. ${\mathrm{H}}_2{\mathrm{SO}}_4$, gives Prussian blue color.
$\left(\mathrm{II}\right)$	$\mathrm{o}-$Cresol	$\left(\mathrm{Q}\right)$	Sodium fusion extract of the compound on treatment with sodium nitroprusside gives blood red color.
$\left(\mathrm{III}\right)$	Cysteine	$\left(\mathrm{R}\right)$	Addition of the compound to a saturated solution of ${\mathrm{NaHCO}}_3$ results in effervescence.
$\left(\mathrm{IV}\right)$	Caprolactam	$\left(\mathrm{S}\right)$	The compound reacts with bromine water to give a white precipitate.
		$\left(\mathrm{T}\right)$	Treating the compound with neutral ${\mathrm{FeCl}}_3$ solution produces violet color.

For a double strand DNA, one strand is given below:

The amount of energy required to split the double strand DNA into two single strands is _______ kcal \(\mathrm{mol}^{-1}.\)
[Given: Average energy per \(\mathrm{H}\)-bond for A-T base pair \(=1.0 \mathrm{kcal} \mathrm{mol}^{-1}, \mathrm{G}-\mathrm{C}\) base pair \(=1.5 \mathrm{kcal}\) \(\mathrm{mol}^{-1}\), and A-U base pair \(=1.25 \mathrm{kcal} \mathrm{mol}^{-1}.\) Ignore electrostatic repulsion between the phosphate groups.]

In the nuclear transmutation ${}_4^9\text{Be}+\text{X}⟶{}_4^8\text{Be}+\text{Y}$, identify $\left(\mathrm{X}, \mathrm{Y}\right)$.

The option(s) in which at least three molecules follow Octet Rule is(are)

A black body of temperature \(T\) is inside chamber of temperature \(T_0\). Now, the closed chamber is slightly opened to sun such that temperature of black body \((T)\) and chamber \(\left(T_0\right)\) remains constant.

Among the species given below, the total number of diamagnetic species is _____________.
\(H\) atom, \(N O_2\) monomer, \(O_2^{-}\)(superoxide), dimeric sulphur in vapour phase,
\(Mn_3 O_4, \left(NH_4\right)_2\left[FeCl_4\right], \left(NH_4\right)_2\left[NiCl_4\right],\) \(K_2 MnO_4, K_2 CrO_4\)

Area of the region $\{\left(x,y\right)\in R^2: y\ge \sqrt{\left|x+3\right|},$ $5y\le x+9\le 15\}$ is equal to

Paragraph:

Let \(O\) be the origin, and \(\overrightarrow{O X}, \overrightarrow{O Y}, \overrightarrow{O Z}\) be three unit vectors in the directions of the sides \(\overrightarrow{Q R}, \overrightarrow{R P}\), \(\overrightarrow{P Q}\), respectively, of a triangle \(P Q R\).


Question:

\(|\overrightarrow{O X} \times \overrightarrow{O Y}|=\)

One mole of a monatomic ideal gas undergoes the cyclic process \(\mathrm{J} \rightarrow \mathrm{K} \rightarrow \mathrm{L} \rightarrow \mathrm{M} \rightarrow \mathrm{J}\), as shown in the P-T diagram.

Match the quantities mentioned in List-I with their values in List-II and choose the correct option.
[\(\mathcal{R}\) is the gas constant.]

List-I	List-II
(P) Work done in the complete cyclic process	(1) \(R T_0-4 R T_0 \ln 2\)
(Q) Change in the internal energy of the gas in the process JK	(2) \(0\)
(R) Heat given to the gas in the process KL	(3) \(3 K T_0\)
(S) Change in the internal energy of the gas in the process MJ	(4) \(-2 R T_0 \ln 2\)
	\((5)-3 R T_0 \ln 2\)

A ball is projected from the ground at an angle of ${45}^o$ with the horizontal surface. It reaches a maximum height of $120\mathrm{ m}$ and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of ${30}^o$ with the horizontal surface. The maximum height it reaches after the bounce (in meters) is _____________.