The reaction of ozone with oxygen atoms in the presence of chlorine atoms can occur by a two step process shown below \({O_3}(g)\, + \,C{l^ * }(g)\, \to \,{O_2}(g) + Cl{O^ * }(g)\) ..... \((i)\)               \([{K_i} = 5.2 \times {10^9}\,\,L\,mo{l^{ - 1}}\,{s^{ - 1}}]\) \(Cl{O^ * }(g) + {O^ * }(g)\, \to \,{O_2}(g) + \,C{l^ * }(g)\) ..... \((ii)\)                \([{K_{ii}} = 2.6 \times {10^{10}}\,\,L\,mo{l^{ - 1}}\,{s^{ - 1}}]\) The closest rate constant for the overall reaction  \({O_3}(g){\mkern 1mu}  + {\mkern 1mu} {O^*}(g){\mkern 1mu}  \to {\mkern 1mu} 2{O_2}(g)\) is  ........... \(L\,\,mo{l^{ - 1}}\,{s^{ - 1}}\)

The lanthanoid that does NOT show \(+4\) oxidation state is

The wavelength of spectral line obtained in the spectrum of \(LI^{2+}\) ion, when the transition takes place between two levels whose sum is 4 and difference is 2, is

Arrange the following labelled hydrogens in decreasing order of acidity

Choose the correct tests with respective observations.
(A) \(\mathrm{CuSO}_4\) (acidified with acetic acid) \(+ \mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right] \rightarrow\) Chocolate brown precipitate.
(B) \(\mathrm{FeCl}_3+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right] \rightarrow\) Prussian blue precipitate.
(C) \(\mathrm{ZnCl}_2+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]\), neutralised with \(\mathrm{NH}_4 \mathrm{OH}\) \(\rightarrow\) White or bluish white precipitate.
(D) \(\mathrm{MgCl}_2+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right] \rightarrow\) Blue precipitate.
(E) \(\mathrm{BaCl}_2+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]\), neutralised with NaOH \(\rightarrow\) White precipitate.
Choose the correct answer from the options given below :

Molality of \(0.8 \ \mathrm{M} \mathrm{H}_2 \mathrm{SO}_4\) solution (density \(1.06 \mathrm{~g} \mathrm{~cm}^{-3}\) ) is _______ \(\times 10^{-3} m\).

A sample of a hydrate of barium chloride weighing \(61\,g\) was heated until all the water of hydration is removed. The dried sample weight is \(52\,g.\) The formula of the hydrated salt is : ( atomic mass, \(Ba = 137\,amu,\,\,Cl = 35.5\,amu\) )

The product of all possible values of \(\alpha\), for which \(\displaystyle\lim_{x \to 0}\left(\dfrac{1 - \cos(\alpha x)\cos((\alpha+1)x)\cos((\alpha+2)x)}{\sin^2((\alpha+1)x)}\right) = 2\), is:

A wire of density \(9 \times 10^{-3} \,kg\, cm ^{-3}\) is stretched between two clamps \(1\, m\) apart. The resulting strain in the wire is \(4.9 \times 10^{-4}\). The lowest frequency of the transverse vibrations in the wire is......\(HZ\) (Young's modulus of wire \(Y =9 \times 10^{10}\, Nm ^{-2}\) ), (to the nearest integer),

In an ac generator, a rectangular coil of \(100\) turns each having area \(14 \times 10^{-2}\,m ^2\) is rotated at \(360\,rev / min\) about an axis perpendicular to a uniform magnetic field of magnitude \(3.0 T\). The maximum value of the emf produced will be \(............V\). \(\left(\right.\) Take \(\left.\pi=\frac{22}{7}\right)\)

Observe the following equilibrium in a 1 L flask.
\(A(g) \rightleftharpoons B(g)\)
At T(K), the equilibrium concentrations of A and B are 0.5 M and 0.375 M respectively. 0.1 moles of A is added into the flask and heated to T(K) to establish the equilibrium again. The new equilibrium concentrations (in M) of A and B are respectively.

If the eccentricity of the standard hyperbola passing, through the point \((4, 6)\) is \(2\), then the equation of the tangent to the hyperbola at \((4, 6)\) is

A plane electromagnetic wave having a frequency \(n = 23.9\, GHz\) propagates along the positive \(z-\) direction in free space. The peak value of the electric field is \(60\, V/m\). Which among the following is the acceptable magnetic field component in the electromagnetic wave?