The amount of water produced ($\mathrm{in} \mathrm{g}$) in the oxidation of $1$ $\mathrm{mole}$of rhombic sulphur by conc. ${\mathrm{H}\mathrm{N}\mathrm{O}}_3$ to a compound with the highest oxidation state of sulphur is
(Given data: Molar mass of water$=18\mathrm{ }\mathrm{g}\mathrm{ }{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}$ )

A solution of colourless salt \(\mathrm{H}\) on boiling with excess \(\mathrm{NaOH}\) produces a non-flammable gas. The gas evolution ceases after sometime. Upon addition of \(\mathrm{Zn}\) dust to the same solution, the gas evolution restarts. The colourless salt (s) \(\mathrm{H}\) is (are)

According to Bohr's theory \(E_n=\) Total energy, \(K_n=\) Kinetic energy, \(V_n=\) Potential energy, \(r_n=\) Radius of \(n\)th orbit

When \(20 \mathrm{~g}\) of naphthoic acid \(\left(\mathrm{C}_{11} \mathrm{H}_8 \mathrm{O}_2\right)\) is dissolved in \(50 \mathrm{~g}\) of benzene \(\left(K_f=1.72 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\), a freezing point depression of \(2 \mathrm{~K}\) is observed. The van't Hoff factor \((i)\) is

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An aqueous solution of metal ion \(\mathbf{M} 1\) reacts separately with reagents \(\mathbf{Q}\) and \(\mathbf{R}\) in excess to give tetrahedral and square planar complexes, respectively. An aqueous solution of another metal ion M2 always forms tetrahedral complexes with these reagents. Aqueous solution of \(\mathbf{M} 2\) on reaction with reagent \(\mathbf{S}\) gives white precipitate which dissolves in excess of \(\mathbf{S}\). The reactions are summarized in the scheme given below:


Question:
Reagent \(\mathbf{S}\) is

The boiling point of water in a \(0.1\) molal silver nitrate solution (solution \(\mathbf{A}\) ) is \(\mathbf{x}^{\circ} \mathrm{C}\). To this solution \(\mathbf{A}\), an equal volume of \(0.1\) molal aqueous barium chloride solution is added to make a new solution B. The difference in the boiling points of water in the two solutions \(\mathbf{A}\) and \(\mathbf{B}\) is \(\mathbf{y} \times 10^{-2}{ }^{\circ} \mathrm{C}\).
(Assume: Densities of the solutions \(\mathbf{A}\) and \(\mathbf{B}\) are the same as that of water and the soluble salts dissociate completely.
Use: Molal elevation constant (Ebullioscopic Constant), \(K_{b}=0.5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\); Boiling point of pure water as \(100^{\circ} \mathrm{C}\).)
The value of $\mathrm{x}$ is ___.

Which ordering of compounds is according to the decreasing order of the oxidation state of nitrogen?

Let $\overrightarrow{\text{PR}}=3\widehat{i}+\widehat{j}-2\widehat{k}\text{and}\overrightarrow{\text{SQ}}=\widehat{i}-3\widehat{j}-4\widehat{k}$ determine diagonals of a parallelogram PQRS and $\overrightarrow{\text{PT}}=\widehat{i}+2\widehat{j}+3\widehat{k}$ be another vector. Then the volume of the parallelepiped determined by the vectors $\overrightarrow{\mathit{\text{PT}}}\text{,}\overrightarrow{\mathit{\text{PQ}}}\text{and}\overrightarrow{\mathit{\text{PS}}}$  is

Let $X$ be the set of all five digit numbers formed using $1,2,2,2,4,4,0$. For example, $22240$ is in $X$ while $02244$ and $44422$ are not in $X$. Suppose that each element of $X$ has an equal chance of being chosen. Let $p$ be the conditional probability that an element chosen at random is a multiple of $20$ given that it is a multiple of $5$. Then the value of $38 p$ is equal to

A particle of mass $m$ is attached to one end of a massless spring of force constant $k$, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time $t=0$ with an initial velocity $u_0$. When the speed of the particle is $0.5u_0$, it collides elastically with a rigid wall. After this collision :

At 300 K , an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height ( h ) of the solution (density \(=1.00 \mathrm{~g} \mathrm{~cm}^{-3}\) ) where h is equal to 2.00 cm . If the concentration of the dilute solution of the macromolecule is \(2.00 \mathrm{~g} \mathrm{dm}^{-3}\), the molar mass of the macromolecule is calculated to be \(\boldsymbol{X} \times 10^4 \mathrm{~g} \mathrm{~mol}^{-1}\). The value of \(\boldsymbol{X}\) is \(\qquad\) .
Use : Universal gas constant \((\mathrm{R})=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) and acceleration due to gravity \((\mathrm{g})=10 \mathrm{~m} \mathrm{~s}^{-2}\)

Let \(f(\theta)=\sin \left[\tan ^{-1}\left(\frac{\sin \theta}{\sqrt{\cos 2 \theta}}\right)\right]\), where \(-\frac{\pi}{4} < \theta < \frac{\pi}{4}\). Then, the value of \(\frac{d}{d(\tan \theta)}(f(\theta))\) is

The complex showing a spin-only magnetic moment of \(2.82\) B.M. is