The work functions of \(\mathrm{Ag}, \mathrm{Mg}, \mathrm{K}\) and \(\mathrm{Na}\) respectively in \(\mathrm{eV}\) are \(4.3,3.7,2.25,2.30\). When an electromagnetic radiation of wavelength of \(300 \mathrm{~nm}\) is allowed to fall on these metal surface, the number of metals from which the electrons are ejected is
\[
\left(\mathbf{e V}=1.6022 \times 10^{-19} \mathrm{~J}\right)
\]

Identify the product \(\mathrm{Y}\) in the given reaction

Gold crystallises in fcc lattice. The edge length of the unit cell is \(4 Å\). The closest distance between gold atoms is ' \(x\) ' \(Å\) and density of gold is ' \(y\) ' \(\mathrm{g} \mathrm{cm}^{-3}\). What are \(x\) and \(y\) respectively?
\(\left(\right.\) Molar mass of gold \(\left.=197 \mathrm{~g} \mathrm{~mol}^{-1} ; \mathrm{N}=6 \times 10^{23} \mathrm{~mol}^{-1}\right)\)

Identify the reactions in which dichromate acts as an oxidising reagent.
I. \(\mathrm{Cr}_2 \mathrm{O}_7^{2-}+6 \mathrm{Fe}^{2+}+14 \mathrm{H}^{+} \longrightarrow 2 \mathrm{Cr}^{3+}+6 \mathrm{Fe}^{3+}+7 \mathrm{H}_2 \mathrm{O}\)
II. \(\mathrm{Cr}_2 \mathrm{O}_7^{2-}+2 \mathrm{OH}^{-} \longrightarrow 2 \mathrm{CrO}_4^{2-}+\mathrm{H}_2 \mathrm{O}\)
III. \(\mathrm{Cr}_2 \mathrm{O}_7^{2-}+6 \mathrm{I}^{-}+14 \mathrm{H}^{+} \longrightarrow 2 \mathrm{Cr}^{3+}+3 \mathrm{I}_2+7 \mathrm{H}_2 \mathrm{O}\)
IV. \(\mathrm{Na}_2 \mathrm{Cr}_2 \mathrm{O}_7+2 \mathrm{KCl} \longrightarrow \mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7+2 \mathrm{NaCl}\)

What is \(Z\) in the following sequence of reaction? 2-methyl-2-bromopropane
\(\underset{\text { Dry ether }}{\stackrel{\mathrm{Mg}}{\longrightarrow}} X \stackrel{\mathrm{H}_2 \mathrm{O}}{\longrightarrow} Z\)

Among the following organic halides in the increasing order of their dehydrohalogenation reactions in the presence of alcoholic \(\mathrm{KOH}\)
\(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br}\)
(A)
\(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{Br}\)
(B)
\(\mathrm{CH}_3 \mathrm{CH}(\mathrm{Br}) \mathrm{CH}_3\)
(C)
\(\left(\mathrm{CH}_3\right)_3 \mathrm{CBr}\)
(D)

Which of the following is not explained by hyperconjugation?

The sum of all the coefficients in the binomial expansion of \((1+2 x)^n\) is 6561. Let \(R=(I+2 x)^n=I+F\), where \(I \in N\) and \(0 < F < \mathrm{l}\).
If \(x=\frac{1}{\sqrt{2}}\), then \(1-\frac{F}{1+(\sqrt{2}-1)^4}=\)

The property of light which cannot be explained by Huygen's construction of wavefront is

If \(\tan \left(\frac{x}{2}\right)=\frac{m}{n}\), then the value of \(m\) \(\sin (x)+n \cos (x)\) is equal to

The \(V-I\) graph for a conductor at temperature \(T_1\) and \(T_2\) are as shown in the figure. \(T_2-T_1\) is proportional to

\(\operatorname{cosec} 48^{\circ}+\operatorname{cosec} 96^{\circ}+\operatorname{cosec} 192^{\circ}+\operatorname{cosec} 384^{\circ}=\)

The enthalpy of formation \(\left(\Delta \mathrm{H}_f\right)\) of methanol, formaldehyde and water are \(-239,-116\) and \(-286 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively. The enthalpy change for the oxidation of methanol to formaldehyde and water in \(\mathrm{kJ}\) is