The value of \(n\) in the molecular formula \(\mathrm{Be}_n \mathrm{Al}_2 \mathrm{Si}_6 \mathrm{O}_{18}\) is

Among \(\left[ Ni ( CO )_4\right],\left[ NiCl _4\right]^{2-},\left[ Co \left( NH _3\right)_4 Cl _2\right] Cl , Na _3\) \(\left[ CoF _6\right], Na _2 O _2\) and \(CsO _2\), the total number of paramagnetic compounds is

Among the complex ions,
\(\left[\mathrm{Co}\left(\mathrm{NH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{NH}_{2}\right)_{2} \mathrm{Cl}_{2}\right]^{+},\)\(\left[\mathrm{CrCl}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}\right]^{3-},\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}(\mathrm{OH})_{2}\right]^{+}\), \(\left[\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{2}(\mathrm{CN})_{4}\right]^{-},\)\(\left[\mathrm{Co}(\mathrm{NH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{NH}_{2})_{2}\left(\mathrm{NH}_{3}\right) \mathrm{Cl}\right]^{2+}\) and \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}\right]^{2+}\), the number of complex ion(s) that show(s) cis-trans isomerism is

The smallest ketone and its next homologoue are reacted with \(\mathrm{NH}_2 \mathrm{OH}\) to form oxime

The number of aldol reaction(s) that occurs in the given transformation is :

Isomers of hexane, based on their branching, can be divided into three distinct classes as shown in the figure.

The correct order of their boiling point is

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When a metal rod \(M\) is dipped into an aqueous colourless concentrated solution of compound \(\mathrm{N}\), the solution turns light blue. Addition of aqueous \(\mathrm{NaCl}\) to the blue solution gives a white precipitate \(\mathrm{O}\). Addition of aqueous \(\mathrm{NH}_3\) dissolves \(\mathrm{O}\) and gives an intense blue solution.
Question:
The final solution contains

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When a particle is restricted to move along \(x\)-axis between \(x=0\) and \(x=a\), where \(a\) is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends \(x=0\) and \(x=a\). The wavelength of this standing wave is related to the liner momentum \(p\) of the particle according to the de Broglie relation. The energy of the particle of mass \(m\) is related to its linear momentum as \(E=\frac{p^2}{2 m}\). Thus, the energy of the particle can be denoted by a quantum number \(n\) taking values \(1,2,3, \ldots(n=1\), called the ground state) corresponding to the number of loops in the standing wave.
Use the model described above to answer the following three questions for a particle moving in the line \(x=0\) to \(x=a\) [Take \(h=6.6 \times 10^{-34} \mathrm{Js}\) and \(e=1.6 \times 10^{-19} \mathrm{C}\) ]
Question:
The speed of the particle that can take discrete values is proportional to

The correct statement $\left(\mathrm{s}\right)$ related to colloids is(are)

A medium having dielectric constant $K>1$ fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is $d$. The capacitor is connected to a battery of voltage $V$. as shown in Figure (a). Now, both the plates are moved by a distance of $\frac{d}{2}$ from their original positions, as shown in Figure (b).

In the process of going from the configuration depicted in Figure (a) to that in Figure (b), which of the following statement(s) is(are) correct?

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 _______.

An experiment has 10 equally likely outcomes. Let \(A\) and \(B\) be two non-empty events of the experiment. If \(A\) consists of 4 outcomes, the number of outcomes that \(B\) must have so that \(A\) and \(B\) are independent, is

Two spherical planets \(P\) and \(Q\) have the same uniform density \(\rho\), masses \(M_{P}\) and \(M_{Q}\) and surface areas \(A\) and 4A respectively. A spherical planet \(R\) also has uniform density \(\rho\) and its mass is \(\left(M_{P}+M_{Q}\right)\). The escape velocities from the planets \(P, Q\) and \(R\) are \(V_{P}, V_{Q}\) and \(V_{R}\), respectively. Then