Radius of the first excited state of Helium ion is given as : \(\mathrm{a}_0 \rightarrow\) radius of first stationary state of hydrogen atom.

\(10.0 \,\mathrm{~mL}\) of \(0.05\, \mathrm{M}\, \mathrm{KMnO}_{4}\) solution was consumed in a titration with \(10.0\, \mathrm{~mL}\) of given oxalic acid dihydrate solution. The strength of given oxalic acid solution is \(.....\,\times 10^{-2} \,\mathrm{~g} / \mathrm{L}\) (Round off to the nearest integer)

When concentrated \(HCl\) is added to an aqueous solution of \(CoCl_2\), its colour changes from reddish pink to deep blue . Which complex ion gives blue colour in this reaction?

For the given reaction

The mass of silver (Molar mass of \(\mathrm{Ag}: 108\  \mathrm{gmol}^{-1}\) ) displaced by a quantity of electricity which displaces \(5600 \mathrm{~mL}\) of \(\mathrm{O}_2\) at \(S.T.P.\) will be_____________\( g.\)

The mismatched combinations are \(A.\) Chlorophyll - Co \(B.\) Water hardness - EDTA \(C.\) Photography \(-\left[ Ag ( CN )_2\right]^{-}\) \(D.\) Wilkinson catalyst - \(\left[\left(P h_3 P\right)_3 R h C l\right]\) \(E.\) Chelating ligand - D - Penicillamine Choose the correct answer from the options given below:

Consider the following two half-cell reactions along with the standard reduction potential given:
\(CO_2 + 6H^+ + 6e^- \rightarrow CH_3 OH + H_2 O \quad E°_{red} = 0.02\) V
\(\dfrac{1}{2} O_2 + 2H^+ + 2e^- \rightarrow H_2 O \quad E°_{red} = 1.23\) V
A fuel cell was set up using the above two reactions such that the cell operates under the standard condition of \(1\) bar pressure and \(298\) K temperature. The fuel cell works with \(80\%\) efficiency. If the work derived from the cell using \(1\) mol of \(CH_3 OH\) is used to compress an ideal gas isothermally against a constant pressure of \(1\) kPa, then the change in the volume of the gas, \(\Delta V = \) _____ m\(^3\). (nearest integer)
Given: \(F = 96500\) C mol\(^{-1}\)

If \({ }^{1} \mathrm{P}_{1}+2 \cdot{ }^{2} \mathrm{P}_{2}+3 \cdot{ }^{3} \mathrm{P}_{3}+\ldots+15 \cdot{ }^{15} \mathrm{P}_{15}={ }^{\mathrm{q}} \mathrm{P}_{\mathrm{r}}-\mathrm{s}, 0 \leq \mathrm{s} \leq 1\) then \({ }^{\mathrm{q}+\mathrm{s}} \mathrm{C}_{\mathrm{r}-\mathrm{s}}\) is equal to .... .

A block of mass \(m\) slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given \({m}=8 \,{kg}, {M}=16\, {kg}\) Assume all the surfaces shown in the figure to be frictionless.

For some \(\theta\in(0,\frac{\pi}{2}),\) let the eccentricity and the length of the latus rectum of the hyperbola \(x^{2}-y^{2}sec^{2}\theta=8\) be \(e_{1}\) and \(l_{1}\), respectively, and let the eccentricity and the length of the latus rectum of the ellipse \(x^{2}sec^{2}\theta+y^{2}=6\) be \(e_{2}\) and \(l_{2},\) respectively. If \(e_{1}^{2}=e_{2}^{2}(sec^{2}\theta+1)\), then \((\frac{l_{1}l_{2}}{e_{1}e_{2}})tan^{2}\theta\) is equal to ___ .

When an object is kept at a distance of \(30\, cm\) from a concave mirror, the image is formed at a distance of \(10\, cm\) from the mirror. If the object is moved with a speed of \(9\, cms ^{-1}\), the speed (in \(cms ^{-1}\) ) with which image moves at that instant is\(....m/s\)

A \(10\,m\) long horizontal wire extends from North East to South West. It is falling with a speed of \(5.0\,ms^{-1},\) at right angles to the horizontal component of the earth’s magnetic field, of \(0.3\times 10^{-4}\,Wb/m^2\). The value of the induced \(emf\) in wire is 

The ground state energy of hydrogen atom is \(-13.6\, eV\). The energy of second excited state of \(He^+\) ion in \(eV\) is