Among the following oxides of 3d elements, the number of mixed oxides are _______
\(Ti_{2}O_{3}, V_{2}O_{4}, Cr_{2}O_{3}, Mn_{3}O_{4}, Fe_{3}O_{4}, Fe_{2}O_{3}, Co_{3}O_{4}\)

Decomposition of A is a first order reaction at T(K) and is given by \(A(g) \rightarrow B(g) + C(g)\). In a closed 1 L vessel, 1 bar A(g) is allowed to decompose at T(K). After 100 minutes, the total pressure was 1.5 bar. What is the rate constant (in \(min^{-1}\)) of the reaction? (\(log 2 = 0.3\))

If \(80\, \mathrm{~g}\) of copper sulphate \(\mathrm{CuSO}_{4} \cdot{ } {5 \mathrm{H}_{2} \mathrm{O}}\) is dissolved in deionised water to make \(5 \,\mathrm{~L}\) of solution. The concentration of the copper sulphate solution is \(\mathrm{x} \times 10^{-3}\, \mathrm{~mol}\, \mathrm{~L}^{-1} .\) The value of \(\mathrm{x}\) is .... . [Atomic masses \(\mathrm{Cu}: 63.54\, \mathrm{u}, \mathrm{S}: 32\, \mathrm{u}, \mathrm{O}: 16 \,\mathrm{u}, \mathrm{H}: 1\, \mathrm{u}]\)

The number of optical isomers in following compound is _______.

An organic compound undergoes first order decomposition. If the time taken for the \(60 \,\%\) decomposition is \(540\,s\), then the time required for \(90\,\%\) decomposition will be is \(..........s\). (Nearest integer). Given : \(\ln 10=2.3 ; \log 2=0.3\)

\(100\, \mathrm{~mL}\) of \(\mathrm{Na}_{3} \mathrm{PO}_{4}\) solution contains \(3.45\, \mathrm{~g}\) of sodium. The molarity of the solution is \(.....\times 10^{-2}\) \(\operatorname{mol} \,\mathrm{L}^{-1} \cdot(\) Nearest integer \()\) [Atomic Masses - \(\mathrm{Na}: 23.0\, \mathrm{u}, \mathrm{O}: 16.0\, \mathrm{u}, \mathrm{P}: 31.0 \,\mathrm{u}]\)

\(0.8\, \mathrm{~g}\) of an organic compound was analysed by Kjeldahl's method for the estimation of nitrogen. If the percentage of nitrogen in the compound was found to be \(42\, \%\), then \(....\,\mathrm{mL}\) of \(1\, \mathrm{M}\) \(\mathrm{H}_{2} \mathrm{SO}_{4}\) would have been neutralized by the ammonia evolved during the analysis.

If one were to apply Bohr model to a particle of mass \('m'\) and charge \('q'\) moving in a plane under the influence of a magnetic field \('B',\) the energy of the charged particle in the \(n^{th}\) level will be

A solution containing \(10 \mathrm{~g}\) of an electrolyte \(\mathrm{AB}_2\) in \(100 \mathrm{~g}\) of water boils at \(100.52^{\circ} \mathrm{C}\). The degree of ionization of the electrolyte \((\alpha)\) is _______ \(\times 10^{-1}\). (nearest integer) [Given : Molar mass of \(\mathrm{AB}_2=200 \mathrm{~g} \mathrm{~mol}^{-1} \cdot \mathrm{K}_{\mathrm{b}}\) (molal boiling point elevation const. of water) \(=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\), boiling point of water \(=100^{\circ} \mathrm{C}\); \(\mathrm{AB}_2\) ionises as \(\left.\mathrm{AB}_2 \rightarrow \mathrm{A}^{2+}+2 \mathrm{~B}^{-}\right]\)

If \(\in\), \( E \) and \( t \) represent the free space permittivity, electric field and time respectively, then the unit of \( \frac{eE}{t} \) will be :

Match List\(-I\) with List\(-II\).

List\(-I\)	List\(-II\)
\(A\) \(16\,g \text { of } CH _{4( g )}\)	\(I\) Weighs \(28\,g\)
\(B\) \(1\,g \text { of } H _{2( g )}\)	\(II\) \(60.2 \times 10^{23}\) electrons
\(C\) \(1\,mole \text { of } N _{2( g )}\)	\(III\) Weighs \(32\,g\)
\(D\) \(0.5\,mol\) of \(SO _{2( g )}\)	\(IV\) Occupies \(11.4\,L\) volume at STP

Choose the correct answer from the options given below:

Let \(\vec{a} = \sqrt{7}\hat{i} + \hat{j} - \hat{k}\) and \(\vec{b} = \hat{j} + 2\hat{k}\). If \(\vec{r}\) is a vector such that \(\vec{r} \times \vec{a} + \vec{a} \times \vec{b} = \vec{0}\) and \(\vec{r} \cdot \vec{a} = 0\), then \(|3\vec{r}|^2\) is equal to:

The height \({ }^{\prime} h ^{\prime}\) at which the weight of a body will be the same as that at the same depth \('h'\) from the surface of the earth is (Radius of the earth is \(R\) and effect of the rotation of the earth is neglected):