A plot of the number of neutrons $(\text{N})$ against the number of protons $(\text{P})$ of the stable nuclei exhibits upwards deviation from linearity for atomic number, $\text{Z}>20$. For an unstable nucleus having $\frac{\text{N}}{\text{P}}$ ratio less than $1$, the possible mode(s) of decay is (are):

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The reaction of \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) with freshly prepared \(\mathrm{FeSO}_{4}\) solution produces a dark blue precipitate called Turnbull's blue. Reaction of \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) with the \(\mathrm{FeSO}_{4}\) solution in complete absence of air produces a white precipitate \(\mathbf{X}\), which turns blue in air. Mixing the \(\mathrm{FeSO}_{4}\) solution with \(\mathrm{NaNO}_{3}\), followed by a slow addition of concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4}\) through the side of the test tube produces a brown ring.
Question:
Precipitate \(\mathbf{X}\) is

The nitrogen containing compound produced in the reaction of $\mathrm{H}\mathrm{N}{\mathrm{O}}_3$ with ${\mathrm{P}}_4{\mathrm{O}}_{10}$

The complete hydrolysis of \(\mathrm{ICl}_2 \mathrm{ClF}_3\) and \(\mathrm{BrF}_5\), respectively, gives

The option(s) with only amphoteric oxides is(are)

Among cellulose, polyvinyl chloride, nylon and natural rubber, the polymer in which the intermolecular force of attraction is weakest in

Which of the following liberates ${\mathrm{O}}_2$ upon hydrolysis?

Reaction of iso-propylbenzene with \(\mathrm{O}_2\) followed by the treatment with \(\mathrm{H}_3 \mathrm{O}^{+}\)forms phenol and a by-product \(\mathbf{P}\). Reaction of \(\mathbf{P}\) with 3 equivalents of \(\mathrm{Cl}_2\) gives compound \(\mathbf{Q}\). Treatment of \(\mathbf{Q}\) with \(\mathrm{Ca}(\mathrm{OH})_2\) produces compound \(\mathbf{R}\) and calcium salt \(\mathbf{S}\).
The correct statement(s) regarding \(\mathbf{P}, \mathbf{Q}, \mathbf{R}\) and \(\mathbf{S}\) is(are)

The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?

The positive integer value of \(n>3\) satisfying the equation
\(\frac{1}{\sin \left(\frac{\pi}{n}\right)}=\frac{1}{\sin \left(\frac{2 \pi}{n}\right)}+\frac{1}{\sin \left(\frac{3 \pi}{n}\right)} \text { is }\)

The circuit shown in the figure contains an inductor \(L\), a capacitor \(C_0\), a resistor \(R_0\) and an ideal battery. The circuit also contains two keys \(\mathrm{K}_1\) and \(\mathrm{K}_2\). Initially, both the keys are open and there is no charge on the capacitor. At an instant, key \(K_1\) is closed and immediately after this the current in \(R_0\) is found to be \(I_1\). After a long time, the current attains a steady state value \(I_2\). Thereafter, \(\mathrm{K}_2\) is closed and simultaneously \(\mathrm{K}_1\) is opened and the voltage across \(C_0\) oscillates with amplitude \(V_0\) and angular frequency \(\omega_0\).

Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

A signal which can be green or red with probability \(\frac{4}{5}\) and \(\frac{1}{5}\) respectively, is received by station \(A\) and then transmitted to station B. The probability of each station receiving the signal correctly is \(\frac{3}{4}\). If the signal received at station \(B\) is green, then the probability that the original signal green is

Let \((x, y)\) be any point on the parabola \(y^2=4 x\). Let \(P\) be the point that divides the line segment from \((0,0)\) to \((x, y)\) in the ratio \(1: 3\). Then, the locus of \(P\) is