Which of the following halides react(s) with \(\mathrm{AgNO}_{3}(\mathrm{aq})\) to give a precipitate that dissolves in \(\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}(\mathrm{aq})\) ?

In the scheme given below, the total number of intramolecular aldol condensation products formed from ' \(Y\) ' is

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Thermal decomposition of gaseous \(\mathrm{X}_{2}\) to gaseous \(\mathrm{X}\) at \(298 \mathrm{~K}\) takes place according to the following equation:

\(\mathrm{X}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{X}(\mathrm{g})\)

The standard reaction Gibbs energy, \(\Delta_{r} G^{\circ}\), of this reaction is positive. At the start of the reaction, there is one mole of \(\mathrm{X}_{2}\) and no \(\mathrm{X}\). As the reaction proceeds, the number of moles of \(\mathrm{X}\) formed is given by \(\beta\). Thus, \(\beta_{\text {equilibrium }}\) is the number of moles of \(\mathrm{X}\) formed at equilibrium. The reaction is carried out at a constant total pressure of \(2\) bar. Consider the gases to behave ideally. (Given : \(R=0.083 \mathrm{~L}\) bar \(\mathrm{K}^{-1} \mathrm{~mol}^{-1}\) )

Question:
The INCORRECT statement among the following, for this reaction, is

If the freezing point of a 0.01 molal aqueous solution of a cobalt (III) chloride-ammonia complex (which behaves as a strong electrolyte) is $-{0.0558}^{\mathrm{o}}\mathrm{C}$ , the number of chloride(s) in the coordination sphere of the complex is
$[{\mathrm{K}}_{\mathrm{f}}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}=1.86\mathrm{ }\mathrm{K}\mathrm{ }\mathrm{k}\mathrm{g}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}]$

The coordination number of \(\mathrm{Al}\) in the crystalline state of \(\mathrm{AlCl}_3\) is

In an atom, the total number of electrons having quantum numbers $\mathrm{n}=4,\mathrm{ }\left|{\mathrm{m}}_{\mathcal{l}}\right|=1$ and ${\mathrm{m}}_{\mathrm{s}}=–1/2$ is

A gas described by van der Waals' equation

A particle of mass $m$ moves in circular orbits with potential energy $U\left(r\right)=Fr$, where $F$ is a positive constant and $r$ is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle's orbit is denoted by $R$ and its speed and energy are denoted by $v$ and $E$ respectively, then for the $n^{\mathrm{th}}$ orbit (here $h$ is the Planck's constant)

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Two plane harmonic sound waves are expressed by the equations.
\(\begin{aligned}
& y_1(x, t)=A \cos (0.5 \pi x-100 \pi t) \\
& y_2(x, t)=A \cos (0.46 \pi x-92 \pi t)
\end{aligned}\)
(All parameters are in MKS)
Question :
How many times does an observer hear maximum intensity in one second?

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 $1.0\mathrm{ }\mathrm{g}\mathrm{ }\mathrm{m}{\mathrm{L}}^{-1}$ )
Enthalpy of dissociation $\left(\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{k}\mathrm{J}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}\right)$ of acetic acid obtained from the Expt. 2 is

A line L : $y=\mathit{\text{m}}x+3$ meets $y-\mathrm{a}\mathrm{x}\mathrm{\text{is}}$ at E(0,3) and the arc of the parabola $y^2=16x\text{,}0\le y\le 6$ at the point $F\left(x_0,y_0\right)$.The tangent to the parabola at $F\left(x_0,y_0\right)$ intersects the y-axis at $G\left(0,y_1\right)$.The slope m of the line L is chosen such that the area of the triangle EFG has a local maximum.
Match List I with List II and select the correct answer using the code given below the lists :
 

	List I		List II
A.	m =	P.	$\frac{1}{2}$
B.	Maximum area of ΔEFG is	Q.	4
C.	y0​ =	R.	2
D.	y1 =	S.	1

Let $X$ be the set consisting of the first $2018$ terms of the arithmetic progression $\mathrm{1,6},11,\dots ,$ and $Y$ be the set consisting of the first $2018$ terms of the arithmetic progression $\mathrm{9,16,23},\dots$ . Then, the number of elements in the set $X\cup Y$ is___.

The work functions of silver and sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for silver to that of sodium is