The equilibrium \(\mathrm{Cr}_2 \mathrm{O}_7^{2-} \rightleftharpoons 2 \mathrm{CrO}_4^{2-}\) is shifted to the right in _______.

The cell potential for the given cell at \(298 \,K\) \(Pt\) \(\mid H _{2}\) \((g,1 \,bar)\) \(\left| H ^{+}( aq ) \| Cu ^{2+}( aq )\right| Cu ( s )\) is \(0.31\, V\). The \(pH\) of the acidic solution is found to be \(3 ,\) whereas the concentration of \(Cu ^{2+}\) is \(10^{- x } \,M\). The value of \(x\) is \(.....\) (Given: \(E _{ Cu ^{2+} / Cu }^{\ominus}=0.34 \,V\) and \(\frac{2.303 RT }{ F }=0.06\, V\) )

A compound '\(A\)' on reaction with ' \(X\) ' and ' \(Y\) produces the same major product but different by product '\(a\)' and '\(b\)'. Oxidation of '\(a\)' gives a substance produced by ants. '\(X\) ' and ' \(Y\) ' respectively are :

The correct order of first \((\Delta_i H_1)\) and second \((\Delta_i H_2)\) ionisation enthalpy values of Cr and Mn are :
A. \(\Delta_i H_1 :\) Cr \(>\) Mn
B. \(\Delta_i H_2 :\) Cr \(>\) Mn
C. \(\Delta_i H_1 :\) Mn \(>\) Cr
D. \(\Delta_i H_2 :\) Mn \(>\) Cr
Choose the correct answer from the options given below :

The molecular geometry of \(S\,F _{6}\) is octahedral. What is the geometry of \(S\,F _{4}\) (including lone pair(s) of electrons, if any)?

The reaction rate for the reaction \(\left[\mathrm{PtCl}_{4}\right]^{2-}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}_{3}\right]^{-}+\mathrm{Cl}^{-}\) was measured as a function of concentrations of different species. It was observed that \(\frac{-\mathrm{d}\left[\left[\mathrm{PtCl}_{4}\right]^{2-}\right]}{\mathrm{dt}}=4.8 \times 10^{-5}\left[\left[\mathrm{PtCl}_{4}\right]^{2-}\right]-2.4 \times10^{-3}\)
\(\left[\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}_{3}\right]^{-}\right]\left[\mathrm{Cl}^{-}\right]\) where square brackets are used to denote molar concentrations. The equilibrium constant \(\mathrm{K}_{\mathrm{c}}=....\). (Nearest integer)

During the qualitative analysis of salt with cation \(y ^{2+}\), addition of a reagent \(( X )\) to alkaline solution of the salt gives a bright red precipitate. The reagent \(( X )\) and the cation \(\left( y ^{2+}\right)\) present respectively are .... .

If the shortest distance of the parabola \(y^2=4 x\) from document security settings le \(x^2+y^2-4 x-16 y+64=0\) is \(\mathrm{d}\), then \(\mathrm{d}^2\) is equal to :

Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure.
If the mass of each disc is 600 gm and applied torque between two discs is \(43 \times 10^{5}\) dyne cm, the angular acceleration of the discs about the given axis \(AB\) is ___________\(rad/s^{2}\).

In a scries \(LR\) circuit, power of \(400\, W\) is dissipated from a source of \(250\, V , 50\, Hz\). The power factor of the circuit is \(0.8 .\) In order to bring the power factor to unity, a capacitor of value \(C\) is added in series to the \(L\) and \(R\). Taking the value of \(C\) as \(\left(\frac{ n }{3 \pi}\right) \mu F ,\) then value of \(n\) is\(......\)

Moment of inertia of a body about a given axis is \(1.5\, kg\, m^2\) Initially the body is at rest. In order to produce a rotational kinetic energy of \(1200\, J\), the angular acceleration of \(20\, rad/s^2\) must be applied about the axis of rotation for a duration of ......... \(\sec\).

Given below are two statements: one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\). Assertion \((A)\) : Haloalkanes react with \(\mathrm{KCN}\) to form alkyl cyanides as a main product while with \(\mathrm{AgCN}\) form isocyanide as the main product. Reason \((R)\) : \(\mathrm{KCN}\) and \(\mathrm{AgCN}\) both are highly ionic compounds. In the light of the above statement, choose the most appropriate answer from the options given below:

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) :


Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities \(v_{\mathrm{A}}=5 \mathrm{~m} / \mathrm{s}, v_{\mathrm{B}}=2 \mathrm{~m} / \mathrm{s}, v_{\mathrm{C}}=4 \mathrm{~m} / \mathrm{s}\). If we wait sufficiently long for elastic collision to happen, then \(v_{\mathrm{A}}=4 \mathrm{~m} / \mathrm{s}, v_{\mathrm{B}}=2 \mathrm{~m} / \mathrm{s}\), \(v_{\mathrm{C}}=5 \mathrm{~m} / \mathrm{s}\) will be the final velocities.

Reason (R): In an elastic collision between identical masses, two objects exchange their velocities.
In the light of the above statements, choose the correct answer from the options given below :