The correct IUPAC nomenclature for the following compound is

\(0.2 \%(\mathrm{w} / \mathrm{v})\) solution of NaOH is measured to have resistivity \(870.0 \mathrm{~m} \Omega \mathrm{~m}\). The molar conductivity of the solution will be ______ \(\times 10^2 \mathrm{mS} \mathrm{dm}{ }^2 \mathrm{~mol}^{-1}\). (Nearest integer)

Sodium fusion extract of an organic compound \(( Y )\) with \(CHCl _3\) and chlorine water gives violet color to the \(CHCl _3\) layer. 0.15 g of \(( Y )\) gave 0.12 g of the silver halide precipitate in Carius method. Percentage of halogen in the compound \(( Y )\) is _______. (Nearest integer).
(Given : molar mass \(g ~ mol ^{-1} C : 12, H : 1, Cl : 35.5\), \(\operatorname{Br}: 80, I : 127\) )

Which of the following complex has a possibility to exist as meridional isomer?

Which of the following statement(s) is/are correct? \((A)\) The \(pH\) of \(1 \times 10^{-8}\,M\,HCl\) solution is \(8\). \((B)\) The conjugate base \(H _2 PO _4^{-}\)is \(HPO _4{ }^{2-}\). \((C)\) \(K _{ w }\) increases with increase in temperature. \((D)\) When a solution of weak monoprotic acid is titrated against a strong base at half neutralisation point, \(pH =\frac{1}{2} pK _{ a }\) Choose the correct answer from the option given below.

At 298 K, the mole percentage of \(N_{2}(g)\) in air is 80%. Water is in equilibrium with air at a pressure of 10 atm. What is the mole fraction of \(N_{2}(g)\) in water at 298 K ? (\(K_{H}\) for \(N_{2}\) is \(6.5 \times 10^{7}\) mm Hg)

\(\Delta U\) is equal to

Two slits are \(1 \mathrm{~mm}\) apart and the screen is located \(1 \mathrm{~m}\) away from the slits. A light wavelength \(500 \mathrm{~nm}\) is used. The width of each slit to obtain \(10\) maxima of the double slit pattern within the central maximum of the single slit pattern is _______ \(\times 10^{-4} \mathrm{~m}\)

A thermally insulted vessel contains \(150\, g\) of water at \(0\,^oC\). Then the air from the vessel is pumped out a adiabatically. A fraction of water turns into ice and the rest evaporates at \(0\,^oC\) itself. The mass of evaporated water will be closes to ....... \(g\) (Latent heat of vaporization of water \(= 2.10 \times10^6\, Jkg^{-1}\) and Laten heat of Fusion of water \( = 3.36 \times10^5\,Jkg^{-1}\) )

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be..... \(\%\).

The correct statements from the following are : \((A)\) The decreasing order of atomic radii of group \(13\) elements is \(\mathrm{Tl}>\mathrm{In}>\mathrm{Ga}>\mathrm{Al}>\mathrm{B}\). \((B)\) Down the group \(13\) electronegativity decreases from top to bottom. \((C)\) \(\mathrm{Al}\) dissolves in dil. \(\mathrm{HCl}\) and liberate \(\mathrm{H}_2\) but conc. \(\mathrm{HNO}_3\) renders Al passive by forming a protective oxide layer on the surface. \((D)\) All elements of group \(13\) exhibits highly stable +1 oxidation state. \((E)\) Hybridisation of \(\mathrm{Al}\) in \(\left[\mathrm{Al}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}\) ion is \(\mathrm{sp}^3 \mathrm{~d}^2\). Choose the correct answer from the options given below:

Let \(A=\left[\begin{array}{ccc}\cos \theta & 0 & -\sin \theta \\ 0 & 1 & 0 \\ \sin \theta & 0 & \cos \theta\end{array}\right]\). If for some \(\theta \in(0, \pi)\), \(A^2=A^T\), then the sum of the diagonal elements of the matrix \((\mathrm{A}+\mathrm{I})^3+(\mathrm{A}-\mathrm{I})^3-6 \mathrm{~A}\) is equal to _____ .

A molecule \(M\) associates in a given solvent according to the equation \(M\, \rightleftharpoons \,{(M)_n}\) For a certain concentration of \(M,\) the van't Hoff factor was found to be \(0 .9\) and the fraction of associated molecules was \(0.2.\) The value of \(n\) is