The total number of lone pairs of electrons in melamine is 

A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of $400\mathrm{ }\mathrm{pm}$ . If the density of the substance in the crystal is $8 \mathrm{g}\mathrm{ }{\mathrm{cm}}^{-3},\mathrm{ }$ then the number of atoms present in $256 \mathrm{g}$ of the crystal $\mathrm{is}\mathrm{ }\mathrm{N}\mathrm{ }\times \mathrm{ }{10}^{24}$ . The value of $\mathrm{N}$is

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p-amino-N, N-dimethylaniline is added to a strongly acidic solution of \(X\). The resulting solution is treated with a few drops of aqueous solution of \(Y\) to yield blue colouration due to the formation of methylene blue. Treatment of the aqueous solution of \(Y\) with the reagent potassium hexacyanoferrate(II) leads to the formation of an intense blue precipitate. The precipitate dissolves an excess addition of the reagent. Similarly, treatment of the solution of \(Y\) with the solution of potassium hexacyanoferrate(III) leads to a brown colouration due to the formation of \(Z\).
Question:
The compound \(Y\), is

The heating of \(\mathrm{NH}_4 \mathrm{NO}_2\) at \(60-70^{\circ} \mathrm{C}\) and \(\mathrm{NH}_4 \mathrm{NO}_3\) at \(200-250^{\circ} \mathrm{C}\) is associated with the formation of nitrogen containing compounds \(\mathbf{X}\) and \(\mathbf{Y}\), respectively. \(\mathbf{X}\) and \(\mathbf{Y}\), respectively, are

The compound (s) that exhibit (s) geometrical isomerism is (are)

The total number of lone pairs of electrons in ${\mathrm{N}}_2{\mathrm{O}}_3$ is

The option(s) with correct sequence of reagents for the conversion of \(\mathbf{P}\) to \(\mathbf{Q}\) is(are) :

An infinitely long thin wire, having a uniform charge density per unit length of \(5 \mathrm{nC} / \mathrm{m}\), is passing through a spherical shell of radius \(1 \mathrm{~m}\), as shown in the figure. A \(10 \mathrm{nC}\) charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points \(\mathrm{P}\) and \(\mathrm{R}\), in Volt, is _______ .
[Given: In SI units \(\frac{1}{4 \pi \epsilon_0}=9 \times 10^9, \ln 2=0.7\). Ignore the area pierced by the wire.]

Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25^o C. For this process, the correct statement is 

Let \(y^{\prime}(x)+y(x) g^{\prime}(x)=g(x) g^{\prime}(x) y(0)=0, x \in R\), where \(f^{\prime}(x)\) denotes \(\frac{d f(x)}{d x}\) and \(g(x)\) is a given non-constant differentiable function on \(R\) with \(g(0)=g(2)=0\). Then, the value of \(y\) (2) is...

A nuclear power plant supplying electrical power to a village uses a radioactive material of half life $\mathrm{T}$ years as the fuel. The amount of fuel at the beginning is such that the total power requirement of the village is 12.5% of the electrical power available from the plant at that time. If the plant is able to meet the total power needs of the village for a maximum period of $\mathrm{n}\mathrm{T}$ years, then the value of $\mathrm{n}$ is

One end of a taut string of length 3m along the x axis is fixed at x = 0. The speed of the waves in the string is $100\mathrm{ }\mathrm{m}{\mathrm{s}}^{-1}$ . The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is (are)

Circle(s) touching $x$-axis at a distance $3$ from the origin and having an intercept of length $2\sqrt{7}$ on $y$-axis is (are)