A student performs a titration with different burettes and finds titre values of \(25.2 \mathrm{~mL}, 25.25 \mathrm{~mL}\), and \(25.0 \mathrm{~mL}\).
The number of significant figures in the average titre value is

In the following carbocation, \(\mathrm{H} / \mathrm{CH}_3\) that is most likely to migrate to the positively charged carbon is

The major products obtained from the reactions in List-II are the reactants for the named reactions mentioned in List-I. Match each entry in List-I with the appropriate entry in List-II and choose the correct options.

List - I	List - II
(P) Stephen reaction	(1)
(Q) Sandmeyer reaction	(2)
(R) Hoffmann bromamide degradation reaction	(3)
(S) Cannizzaro reaction	(4)
	(5)

Among the following, the coloured compound is

What is the order of basicity among the following compounds?

Statement 1 Bromobenzene, upon reaction with \(\mathrm{Br}_2 / \mathrm{Fe}\) gives 1, 4-dibromobenzene as the major product.
Statement 2 In bromobenzene, the inductive effect of the bromo group is more dominant than the mesomeric effect in directing the incoming electrophile.

For the first order reaction \(2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g}) \longrightarrow 4 \mathrm{NO}_2(g)+\mathrm{O}_2(g)\)

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When liquid medicine of density \(\rho\) is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop.
We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension \(T\) when the radius of the drop is \(R\). When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.
Question :
If the radius of the opening of the dropper is \(r\), the vertical force due to the surface tension on the drop of radius \(R\) (assuming \(r< < R\) ) is

A block \((B)\) is attached to two unstretched \(S_1\) and \(S_2\) with spring constants \(k\) and \(4 k\), respectively (see figure I). The other ends are attached to identical supports \(M_1\) and \(M_2\) not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block \(B\) is displaced towards wall 1 by a small distance \(x\) (figure II) and released. The block returns and moves a maximum distance \(y\) towards wall 2 . Displacements \(x\) and \(y\) are measured with respect to the equilibrium position of the block \(B\). The ratio \(\frac{y}{-1}\) is

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When a particle of mass \(m\) moves on the \(x\)-axis in a potential of the form \(V(x)=k x^2\), it performs simple harmonic motion.


The corresponding time period is proportional to \(\sqrt{\frac{m}{k}}\), as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of \(x=0\) in a way different from \(k x^2\) and its total energy is such that the particle does not escape to infinity. Consider a particle of mass \(\mathrm{m}\) moving on the \(x\)-axis. Its potential energy is \(V(x)=\alpha x^4(\alpha>0)\) for \(|x|\) near the origin and becomes a constant equal to \(V_0\) for \(|x| \geq X_0\) (see figure).
Question :
The acceleration of this particle for \(|x|>X_0\) is

Extraction for zinc from zinc blende is achieved by

Among the following complexes, the total number of diamagnetic species is_____
\(\left[\mathrm{Mn}\left(\mathrm{NH}_3\right)_6\right]^{3+},\left[\mathrm{MnCl}_6\right]^{3-},\left[\mathrm{FeF}_6\right]^{3-},\left[\mathrm{CoF}_6\right]^{3-},\)\(\left[\mathrm{Fe}\left(\mathrm{NH}_3\right)_6\right]^{3+}\), and \(\left[\mathrm{Co}(\mathrm{en})_3\right]^{3+}\)
[Given, atomic number: \(\mathrm{Mn}=25, \mathrm{Fe}=26, \mathrm{Co}=27\);
\(\text { en } \left.=\mathrm{H}_2 \mathrm{NCH}_2 \mathrm{CH}_2 \mathrm{NH}_2\right]\)

The total number of lone pairs of electrons in melamine is