The ' spin only ' magnetic moment value of \(\mathrm{MO}_4{ }^{2-}\) is _______ BM. (Where \(\mathrm{M}\) is a metal having least metallic radii. among \(\mathrm{Sc}, \mathrm{Ti}, \mathrm{V}, \mathrm{Cr}, \mathrm{Mn}\) and \(\mathrm{Zn}\) ). (Given atomic number: \(\mathrm{Sc}=21, \mathrm{Ti}=22, \mathrm{~V}=23\), \(\mathrm{Cr}=24, \mathrm{Mn}=25\) and \(\mathrm{Zn}=30)\)

The volume \((\text { in } \mathrm{mL})\) of \(0.125\; \mathrm{M}\; \mathrm{AgNO}_{3}\) required to quantitatively precipitate chloride ions in \(0.3\; \mathrm{g}\) of \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}\) is \(^{\mathrm{M}}\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}=267.46 \;\mathrm{g} / \mathrm{mol}\) \(\mathrm{M}_{\mathrm{AgNO}_{3}}=169.87 \;\mathrm{g} / \mathrm{mol}\)

An inorganic Compound \('\mathrm{X}^{\prime}\) on treatment with concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4}\) produces brown fumes and gives dark brown ring with \(\mathrm{FeSO}_{4}\) in presence of concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4} .\) Also Compound \('\mathrm{X}'\) gives precipitate \('Y',\) when its solution in dilute \(\mathrm{HCI}\) is treated with \(\mathrm{H}_{2} \mathrm{~S}\) gas. The precipitate \('Y'\) on treatment with concentrated \(\mathrm{HNO}_{3}\) followed by excess of \(\mathrm{NH}_{4} \mathrm{OH}\) further gives deep blue coloured solution, Compound \('X'\) is :

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:

\(4 \mathrm{~g}\) equimolar mixture of \(\mathrm{NaOH}\) and \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) contains \(\mathrm{x} \mathrm{g}\) of \(\mathrm{NaOH}\) and \(\mathrm{y} \mathrm{g}\) of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\). The value of \(x\) is \(.....g.\) (Nearest integer)

Which of the following is \(NOT\) a correct method of the preparation of benzylamine from cyanobenzene?

At \(298\, K\), the standard reduction potentials are \(1.51\, V\) for \(MnO_4^ - \,|\,M{n^{2 + }}\), \(1.36\, V\) for \(C{l_2}\,|\,C{l^ - }\), \(1.07\, V\) for \(B{r_2}\,|\,B{r^ - }\) and \(0.54\, V\) for \({I_2}\,|\,{I^ - }\). At \(pH\, = 3\) , permanganate is expected to oxidize \(\left( {\frac{{RT}}{F} = 0.059\,V} \right)\)

Given below are two statements: Statement \(I\): IUPAC name of \(\mathrm{HO}-\mathrm{CH}_2-\left(\mathrm{CH}_2\right)_3-\) \(\mathrm{CH}_2-\mathrm{COCH}_3\) is \(7\)-hydroxyheptan-2-one. Statement \(II\): \(2\)-oxoheptan-\(7\)-ol is the correct IUPAC name for above compound In the light of the above statements.
choose the most appropriate answer from the options given below:

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is ______ \(\times 10^{10} \mathrm{~J}\).
(Mass of earth \(=6 \times 10^{24} \mathrm{~kg}\), Radius of earth \(=\) \(6.4 \times 10^6 \mathrm{~m}\), Gravitational constant \(=\)\(\left.6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}\right)\)

The sum of oxidation states of two silver ions in \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]\) complex is .... .

Consider the line \(L\) given by the equation \(\frac{x-3}{2}=\frac{y-1}{1}=\frac{z-2}{1}\). Let \(Q\) be the mirror image of the point \((2,3,-1)\) with respect to \(L\). Let a plane \(P\) be such that it passes through \(Q\), and the line \(L\) is perpendicular to \(P.\) Then which of the following points is on the plane \(P\) ?

What amount of bromine will be required to convert 2 g of phenol into 2,4,6-tribromophenol? (Given molar mass in \(\mathrm{g} \mathrm{mol}^{-1}\) of \(\mathrm{C}, \mathrm{H}, \mathrm{O}, \mathrm{Br}\) are \(12,1,16,80\) respectively )

Consider the integral \(I=\int_{0}^{10} \frac{[x] e^{[x]}}{e^{x-1}} d x,\) where \([ x ]\) denotes the greatest integer less than or equal to \(x\). Then the value of \(I\) is equal to: