For the reaction sequence given below, the correct statement(s) is(are)

(In the options, \(X\) is any atom other than carbon and hydrogen, and it is different in \(\mathbf{P}, \mathbf{Q}\) and \(\mathbf{R}\) )

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In hexagonal system of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between them. A space-filling model of this structure, called hexagonal close-packed (HCP), is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of the three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with a third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be ' \(r\) '.
Question:
The empty space in this \(\mathrm{HCP}\) unit cell is

The shape of \(\mathrm{XeO}_{2} \mathrm{~F}_{2}\) molecule is

Among the following, the number of elements showing only one non-zero oxidation state is O, Cl, F, N, P, Sn, Tl, \(\mathrm{Na}, \mathrm{Ti}\)

In dilute aqueous ${\mathrm{H}}_2\mathrm{S}{\mathrm{O}}_4$ , the complex diaquodioxalatoferrate (II) is oxidized by ${\mathrm{M}\mathrm{n}\mathrm{O}}_4^{-}$ . For this reaction, the ratio of the rate of change of $\left[{\mathrm{H}}^{+}\right]$ to the rate of change of $\left[{\mathrm{M}\mathrm{n}\mathrm{O}}_4^{-}\right]$ is

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the $n^{\mathrm{t}\mathrm{h}}$ orbit of the atom and List-II contains options showing how they depend on $n$ .
 

List - I	List - II
(I) Radius of the $n^{\mathrm{t}\mathrm{h}}$ orbit	$\left(\mathrm{P}\right)$ $\propto n^{-2}$
(II) Angular momentum of the electron in the $n^{th}$ orbit	$\left(\mathrm{Q}\right)$ $\propto n^{-1}$
(III) Kinetic energy of the electron in the $n^{\mathrm{t}\mathrm{h}}$ orbit	$\left(\mathrm{R}\right)$ $\propto n^0$
(IV) Potential energy of the electron in the $n^{\mathrm{t}\mathrm{h}}$ orbit	$\left(\mathrm{S}\right)$ $\propto n^1$
	$\left(\mathrm{T}\right)$ $\propto n^2$
	$\left(\mathrm{U}\right)$ $\propto n^{1/2}$

Which of the following options has the correct combination considering List-I and List-II?

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

In a particular system of units, a physical quantity can be expressed in terms of the electric charge $e$, electron mass $m_e$. Planck's constant $h$, and Coulomb's constant $k=\frac{1}{4\pi {\epsilon }_0}$, where ${\epsilon }_0$ is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is $\left[B\right]={\left[e\right]}^{\alpha }{\left[m_e\right]}^{\beta }{\left[h\right]}^{\gamma }{\left[k\right]}^{\delta }$. The value of $\alpha +\beta +\gamma +\delta$ is _______.

A flat plate is moving normal to its plane through a gas under the action of a constant force F. The gas is kept at a very low pressure. The speed of the plate v I much less than the average speed u of the gas molecules. Which of the following options is true?

The least value of $\alpha \in R$ for which, $4\alpha x^2+\frac{1}{x} \ge 1,$ for all $x>0,$ is 

A parallel beam of light is incident from air at an angle $\alpha$ on the side PQ of a right angled triangular prism of refractive index $n=\sqrt{2}$ . Light undergoes total internal reflection in the prism at the face PR when $\alpha$ has a minimum value of ${45}^o.$ The angle $\theta$ of the prism is:

A circuit with an electrical load having impedance \(Z\) is connected with an AC source as shown in the diagram. The source voltage varies in time as \(V(t)=300 \sin (400 t) \mathrm{V}\), where \(t\) is time in s. List-I shows various options for the load. The possible currents \(i(t)\) in the circuit as a function of time are given in List-II.

Choose the option that describes the correct match between the entries in List-I to those in List-II.

	List-I		List-II
\((P)\)		\((1)\)
\((Q)\)		\((2)\)
\((R)\)		\((3)\)
\((S)\)		\((4)\)
		\((5)\)

Consider a system of three connected strings, \(S_1, S_2\) and \(S_3\) with uniform linear mass densities \(\mu \mathrm{kg} / \mathrm{m}\), \(4 \mu \mathrm{~kg} / \mathrm{m}\) and \(16 \mu \mathrm{~kg} / \mathrm{m}\), respectively, as shown in the figure. \(S_1\) and \(S_2\) are connected at the point \(P\), whereas \(S_2\) and \(S_3\) are connected at the point \(Q\), and the other end of \(S_3\) is connected to a wall. A wave generator O is connected to the free end of \(S_1\). The wave from the generator is represented by \(y=y_0\) \(\cos (\omega t-k x) \mathrm{cm}\), where \(y_0, \omega\) and \(k\) are constants of appropriate dimensions. Which of the following statements is/are correct: