Among PbS, CuS, HgS, MnS, $\mathrm{A}{\mathrm{g}}_2\mathrm{S}$ , NiS, CoS, $\mathrm{B}{\mathrm{i}}_2{\mathrm{S}}_3$ and $\mathrm{S}\mathrm{n}{\mathrm{S}}_2$ , the total number of black coloured sulphides is

Assuming that Hund's rule is violated, the bond order and magnetic nature of the diatomic molecule \(\mathrm{B}_2\) is

Consider the following molecules : ${\mathrm{Br}}_3{\mathrm{O}}_8, {\mathrm{F}}_2\mathrm{O},{\mathrm{H}}_2 {\mathrm{S}}_4{\mathrm{O}}_6,{\mathrm{H}}_2 {\mathrm{S}}_5{\mathrm{O}}_6$, and ${\mathrm{C}}_3{\mathrm{O}}_2$. Count the number of atoms existing in their zero oxidation state in each molecule. Their sum is

For a first order reaction, \(A \rightarrow P\), the temperature \((T)\) dependent rate constant \((k)\) was found to follow the equation, \(\log k=-(2000) / T+6.0\)
The pre-exponential factor \(A\) and the activation energy \(\left(E_a\right)\), respectively, are

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Upon heating \(\mathrm{KClO}_{3}\) in the presence of catalytic amount of \(\mathrm{MnO}_{2}\), a gas \(\mathbf{W}\) is formed. Excess amount of \(\mathbf{W}\) reacts with white phosphorus to give \(\mathbf{X}\). The reaction of \(\mathbf{X}\) with pure \(\mathrm{HNO}_{3}\) gives \(\mathbf{Y}\) and \(\mathbf{Z}\).
Question:
\(\mathbf{W}\) and \(\mathbf{X}\) are, respectively

Which of the following liberates ${\mathrm{O}}_2$ upon hydrolysis?

\(\mathrm{Ag}^{+}+\mathrm{NH}_3 \rightleftharpoons\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)\right]^{+} ; k_1=3.5 \times 10^{-3}\) \(\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)\right]^{+}+\mathrm{NH}_3 \rightleftharpoons\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+} ; k_2\) \(=1.7 \times 10^{-3}\) then the formation constant of \(\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}\)is

An aqueous solution of X is added slowly to an aqueous solution of Y as shown in List I. The variation in conductivity of these reactions is given in List II. Match List I with List II and select the correct using answer the code given below the lists :

List - I	List - II
a. \(\underset{\quad\quad~~ X }{( C _2 H _5)_3 N}+\underset{ Y }{CH _3 COOH}\)	p. Conductivity decreases and then increases
b. \(\underset{\quad\quad~~ X }{KI (0.1 M )}+\underset{ Y }{AgNO _3(0.01 M )}\)	q. Conductivity decreases and then does not change much
c. \(\underset{\text X }{CH _3 COOH}+\underset{\text Y }{KOH}\)	r. Conductivity increases and then does not change much
d. \(\underset{\text X }{NaOH}+\underset{\text Y }{HI}\)	s. Conductivity does not change much and then increases

Let $f:\left(0,1\right)\to \mathrm{ℝ}$ be the function defined as $f\left(x\right)=\left[4x\right]{\left(x-\frac{1}{4}\right)}^2\left(x-\frac{1}{2}\right)$, where $\left[x\right]$ denotes the greatest integer less than or equal to $x$. Then which of the following is(are) true?

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\(\mathbf{X}\) and \(\mathbf{Y}\) are two volatile liquids with molar weights of \(10 \mathrm{~g} \mathrm{~mol}^{-1}\) and \(40 \mathrm{~g} \mathrm{~mol}^{-1}\) respectively. Two cotton plugs, one soaked in \(\mathbf{X}\) and the other soaked in \(\mathbf{Y}\), are simultaneously placed at the ends of a tube of length \(L=24 \mathrm{~cm}\), as shown in the figure. The tube is filled with an inert gas at \(1\) atmosphere pressure and a temperature of \(300 \mathrm{~K}\). Vapours of \(\mathbf{X}\) and \(\mathbf{Y}\) react to form a product which is first observed at a distance \(\mathbf{d} \mathrm{~cm}\) from the plug soaked in \(\mathbf{X}\). Take \(\mathbf{X}\) and \(\mathbf{Y}\) to have equal molecular diameters and assume ideal behaviour for the inert gas and the two vapours.



Question:

The value of \(\mathbf{d}\) in \(\mathbf{c m}\) (shown in the figure), as estimated from Graham's law, is

A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter 11.54 mm on the top of the block. The refractive index of the liquid is

A uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $\sigma$ . The angle of contact between water and the wall of the capillary tube is $\theta$ . Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

Two parallel chords of a circle of radius 2 are at a distance \(\sqrt{3}+1\) apart. If the chords subtend at the centre, angles of \(\frac{\pi}{k}\) and \(\frac{2 \pi}{k}\), where \(k>0\), then the value of \([k]\) is
[Note : \([k]\) denotes the largest integer less than or equal to \(k\) ]