Which of the following statements are correct? \((A)\) The \(M ^{3+} / M ^{2+}\) reduction potential for iron is greater than manganese \((B)\) The higher oxidation states of first row \(d\) block elements get stabilized by oxide ion. \((C)\) Aqueous solution of \(Cr ^{2+}\) can liberate hydrogen from dilute acid. \((D)\) Magnetic moment of \(V ^{2+}\) is observed between \(4.4-5.2\,BM\) Choose the correct answer from the options given below:

The rate law for the reaction below is given by the expression \(k\left[ A \right]\left[ B \right]\)                                            \(A + B \to\) Product  If the concentration of \(B\) is increased from \(0.1\) to \(0.3\, mole\), keeping the value of \(A\) at \(0.1\, mole\), the rate constant will be

500 J of energy is transferred as heat to 0.5 mol of Argon gas at 298 K and 1.00 atm. The final temperature and the change in internal energy respectively are:
Given : \(\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\)

Value of \(\mathrm{K}_{\mathrm{p}}\) for the equilibrium reaction \(\mathrm{N}_{2} \mathrm{O}_{4(\mathrm{~g})} \rightleftharpoons 2 \mathrm{NO}_{2(9)}\) at \(288 \,\mathrm{~K}\) is \(47.9 .\) The \(\mathrm{K}_{\mathrm{C}}\) for this reaction at same temperature is \(......\) (Nearest integer) \(\left(R=0.083\, L\, \operatorname{bar} \,\mathrm{K}^{-1} \,\mathrm{~mol}^{-1}\right)\)

The correct decreasing order of energy, for the orbitals having, following set of quantum numbers. \((A)\) \(n=3,1=0, m=0\) \((B)\) \(n=4,1=0, m=0\) \((C)\) \(n =3,1=1, m =0\) \((D)\) \(n=3,1=2, m=1\)

Among the statements \((a)-(d)\), the incorrect ones are \((a)\) Octahedral \(Co(III)\) complexes with strong field ligands have very high magnetic moments \((b)\) When \(\Delta_{0}< P\), the \(d-\)electron configuration of \(Co(III)\) in an octahedral complex is \(t_{\text {eg }}^{4} e_{g}^{2}\) \((c)\) Wavelength of light absorbed by \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\) is lower than that of \(\left[\mathrm{CoF}_{6}\right]^{3-}\) \((d)\) If the \(\Delta_{0}\) for an octahedral complex of \(\mathrm{Co}(\mathrm{III})\) is \(18,000 \;\mathrm{cm}^{-1},\) the \(\Delta_{\mathrm{t}}\) for its tetrahedral complex with the same ligand will be \(16,000\;\mathrm{cm}^{-1}\)

Observation of "Rhumann 's purple " is a confirmatory test for the presence of

Complete combustion of \(1.80 \,g\) of an oxygen containing compound \(\left( C _{ x } H _{ y } O _{2}\right)\) gave \(2.64\, g\) of \(CO _{2}\) and \(1.08\, g\) of \(H _{2} O .\) The percentage of oxygen in the organic compound is

\(50\, mL\) of \(0.2\, M\) ammonia solution is treated with \(25\, mL\) of \(0.2\, M\, HCl\). If \(pK_b\) of ammonia solution is \(4.75\), the \(pH\) of the mixture will be

\(\mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{{\rm{sin}}\left( {\pi {{\cos }^2}x} \right)}}{{{x^2}}} = \)

Two sides of a rhombus are along the lines, \(x -y+ 1 = 0\) and \(7x-y-5 =0.\) If its diagonals intersect at \((-1,-2),\) then which one of the following is a vertex of this rhombus?

An electrochemical cell is constructed using half cells in the direction of spontaneous change
\(Fe(OH)_2(s) + 2e^- \rightarrow Fe(s) + 2OH^-(aq) \quad E^\theta = -0.88\) V
and \(AgBr(s) + e^- \rightarrow Ag(s) + Br^-(aq) \quad E^\theta = +0.07\) V
Which of the following option is correct?

Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is ___________.
(Given: \(h=6.63\times10^{-34}\) J.s and \(c=3\times10^{8}m/s\))