The strength of an aqueous \(NaOH\) solution is most accurately determined by titrating  (Note : consider that an appropriate indicator is used)

Consider the following half cell reaction
\(\mathrm{Cr}_2 \mathrm{O}_7^{2-}(\mathrm{aq})+6 \mathrm{e}^{-}+14 \mathrm{H}^{+}(\mathrm{aq})\) \(\rightarrow 2 \mathrm{Cr}^{3+}(\mathrm{aq})+7 \mathrm{H}_2 \mathrm{O}(\mathrm{l})\)
The reaction was conducted with the ratio of \(\frac{\left[\mathrm{Cr}^{3+}\right]^2}{\left[\mathrm{Cr}_2 \mathrm{O}_7^{2-}\right]}=10^{-6}\). The pH value at which the EMF of the half cell will become zero is ________. (nearest integer value)
[Given : standard half cell reduction potential
\(\left.\mathrm{E}_{\mathrm{Cr}_2 \mathrm{O}_7^{2-}, \mathrm{H}^{+} / \mathrm{Cr}^{3+}}^{\mathrm{o}}=1.33 \mathrm{~V}, \frac{2.303 \mathrm{RT}}{\mathrm{~F}}=0.059 \mathrm{~V}\right]\)

In the depression of freezing point experiment
A. Vapour pressure of the solution is less than that of pure solvent
B. Vapour pressure of the solution is more than that of pure solvent
C. Only solute molecules solidify at the freezing point
D. Only solvent molecules solidify at the freezing point

\(10\, mL\) of \(1\,mM\) surfactant solution forms a monolayer covering \(0.24\, cm^2\) on a polar substrate. If the polar head is approximated as cube, what is its edge length ?

The reagent \((s)\) required for the following conversion are

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

List-\(I\) (Species)	List-\(II\) (Electronic distribution)
\((A)\) \(\mathrm{Cr}^{+2}\)	\((I)\) \(3 \mathrm{~d}^8\)
\((B)\) \(\mathrm{Mn}^{+}\)	\((II)\) \(3 \mathrm{~d}^3 4 \mathrm{~s}^1\)
\((C)\) \(\mathrm{Ni}^{+2}\)	\((III)\) \(3\mathrm{~d}^4\)
\((D)\) \(\mathrm{V}^{+}\)	\((IV)\) \(3 \mathrm{~d}^5 4 \mathrm{~s}^1\)

Choose the correct answer from the options given below:

\(1 \times 10^{-5}\,M \textrm {AgNO } _ { 3 }\) is added to \(1\,L\) of saturated solution of \(AgBr\). The conductivity of this solution at \(298\,K\) is \(.........\times 10^{-8}\,S\,m ^{-1}\) \(\left[\right.\) Given : \(K _{ sp }( AgBr )=4.9 \times 10^{-13}\) at \(298 K\) \(\lambda_{ Ag ^{+}}^0=6 \times 10^{-3} Sm ^2\,mol ^{-1}\) \(\lambda_{ Br ^{-}}^0=8 \times 10^{-3} Sm ^2\,mol ^{-1}\) \(\left.\lambda_{ NO _3^{-}}^0=7 \times 10^{-3} Sm ^2\,mol ^{-1}\right]\)

A fringe width of \(\,6 mm\) was produced for two slits separated by \(1\, mm\) apart. The screen is placed \(10\, m\) away. The wavelength of light used is \('x'\, nm.\) The value of \('x'\) to the nearest integer is

The electric field of an electromagnetic wave travelling through a medium is given by \(\overline{E}(x,t) = 25\ sin(2.0 \times 10^{15}t - 10^{7}x)\hat{n}\) then the refractive index of the medium is ___________.
(All given measurement are in SI units)

A particle having the same charge as of electron moves in a circular path of radius \(0.5
\,cm\) under the influence of a magnetic field of \(0.5\,T.\) If an electric field of \(100\,V/m\) makes it to move in a straight path, then the mass of the particle is (given charge of electron \(= 1.6 \times 10^{-19}\, C\) )

The correct sequence of decreasing number of \(\pi -\) bonds in the structures of \(H_2SO_3, H_2SO_4\) and \(H_2S_2O_7\) is

If the angle between the line \(2(x + 1)\,= y\, = z + 4\)  and the plane \(2x -\sqrt \lambda  \,z+4\,=0\) is \(\frac{\pi}{6}\), then the value of \(\lambda \), is

Let the plane \(2 x+3 y+z+20=0\) be rotated through a right angle about its line of intersection with the plane \(x-3 y+5 z=8\). If the mirror image of the point \(\left(2,-\frac{1}{2}, 2\right)\) in the rotated plane is \(B ( a , b , c )\), then