Which of the following statements are correct, if the threshold frequency of caesium is \(5.16 \times 10^{14} \mathrm{~Hz}\) ?
A. When Cs is placed inside a vacuum chamber with an ammeter connected to it and yellow light is focused on Cs the ammeter shows the presence of current.
B. When the brightness of the yellow light is dimmed, the value of the current in the ammeter is reduced.
C. When a red light is used instead to the yellow light, the current produced is higher with respect to the yellow light.
D. When a blue light is used, the ammeter shows the formation of current.
E. When a white light is used, the ammeter shows formation of current.
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Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason \(R\) Assertion \(A\) : Zero orbital overlap is an out of phase overlap. Reason \(R\) : It results due to different orientation/ direction of approach of orbitals. In the light of the above statements. Choose the correct answer from the options given below.

For the reaction, \( N_{2}O_{4}\rightleftharpoons 2NO_{2}, \) graph is plotted as shown below. Identify correct statements.
A. Standard free energy change for the reaction is -5.40 kJ mol⁻¹.
B. As \( \Delta G^{\ominus} \) in graph is positive, \( N_{2}O_{4} \) will not dissociate into \( NO_{2} \) at all.
C. Reverse reaction will go to completion.
D. When 1 mole of \( N_{2}O_{4} \) changes into equilibrium mixture, value of \( \Delta G^{\ominus}=-0.84 \, kJ \, mol^{-1} \).
E. When 2 mole of \( NO_{2} \) changes into equilibrium mixture, \( \Delta G^{\ominus} \) for equilibrium mixture is -6.24 kJ mol⁻¹.

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Which among the following purification methods is based on the principle of "Solubility" in two different solvents?

At \( 27^{\circ}C \) in presence of a catalyst, activation energy of a reaction is lowered by 10 kJ \( mol^{-1} \). The logarithm ratio of \( \frac{k(catalysed)}{k(uncatalysed)} \) is ....
(Consider that the frequency factor for both the reactions is same)

The Gibbs energy for the decomposition of \(Al_2O_3\) at \(500\,^oC\) is as follows \(\frac{2}{3}A{l_2}{O_3} \to \frac{4}{3}Al + {O_2},{\Delta _r}G =  + 940\,kJ\,mo{l^{ - 1}}\) The potential difference needed for the electrolytic reduction of aluminium oxide ............... \(\mathrm{V}\)

Which of the following statements is not true about partition chromatography ?

The half-life of \(Au ^{198}\) is \(2.7\, days.\) The activity of \(1.50\, mg\) of \(Au ^{198}\) if its atomic weight is \(198\, g mol ^{-1}\) is .......\(Ci\) \(\left( N _{ A }=6 \times 10^{23}\, / mol \right)\)

If the probability that a randomly chosen \(6\)-digit number formed by using digits \(1\) and \(8\) only is a multiple of \(21\) is \(p\), then \(96\;p\) is equal to

Let \(S_n\) denote the sum of the first \(n\) terms of an arithmetic progression. If \(\mathrm{S}_{10}=390\) and the ratio of the tenth and the fifth terms is \(15: 7\), then \(S_{15}-S_5\) is equal to :

A small circular loop of conducting wire has radius \(a\) and carries current \(I\). It is placed in a uniform magnetic field \(\mathrm{B}\) perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period \(T\). If the mass of the loop is \(m\) then 

The correct \(IUPAC\) name of the following compound is .... .

Two blocks of masses \(m\) and \(M,(M \gt m)\), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then
(\(\mu=\) coefficient of friction between the two blocks)

(A) The time period of small oscillation of the two blocks is \(\mathrm{T}=2 \pi \sqrt{\frac{(\mathrm{~m}+\mathrm{M})}{\mathrm{k}}}\)
(B) The acceleration of the blocks is \(\mathrm{a}=\frac{\mathrm{kx}}{\mathrm{M}+\mathrm{m}}\) (\(\mathrm{x}=\) displacement of the blocks from the mean position)
(C) The magnitude of the frictional force on the upper block is \(\frac{m \mu|x|}{M+m}\)
(D) The maximum amplitude of the upper block, if it does not slip, is \(\frac{\mu(M+m) g}{k}\)
(E) Maximum frictional force can be \(\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}\).
Choose the correct answer from the options given below: