One of the products formed from the reaction of permanganate ion with iodide ion in neutral aqueous medium is

The correct functional group \(X\) and the reagent/reaction conditions \(Y\) in the following schemes are \(\mathrm{X}-\left(\mathrm{CH}_2\right)_4-X\)

The standard enthalpies of formation of $C{O}_2\left(g\right)$ ${\text{, H}}_2\text{O}\left(\mathit{\text{l}}\right)$ and glucose (s) at $25^{\text{o}}C$ are $-\text{400 kJ}/\text{mol}$, $-\text{300 kJ}/\text{mol}$ and $-\text{1300 kJ}/\text{mol}$, respectively. The standard enthalpy combustion per gram of glucose at $25^{\text{o}}C$ is $\left(\Delta H_f^0=-1300kJmo{l}^{-}for\text{glucose}\right)$

Which of the given statement(s) about \(\mathbf{N}, \mathbf{O}, \mathbf{P}\) and \(\mathbf{Q}\) with respect to \(\mathbf{M}\) is (are) correct?

A tin chloride $\mathrm{Q}$ undergoes the following reactions (not balanced)
$\mathrm{Q}+\mathrm{C}{\mathrm{l}}^{-}\to \mathrm{X}$
$\mathrm{Q}+\mathrm{M}{\mathrm{e}}_3\mathrm{N}\to \mathrm{Y}$
$\mathrm{Q}+\mathrm{C}\mathrm{u}\mathrm{C}{\mathrm{l}}_2\to \mathrm{Z}+\mathrm{C}\mathrm{u}\mathrm{C}\mathrm{l}$
$\mathrm{X}$ is a monoanion having pyramidal geometry. Both $\mathrm{Y}$ and $\mathrm{Z}$ are neutral compounds. Choose the correct option(s).

Ozonolysis of ${\mathrm{ClO}}_2$ produces an oxide of chlorine. The average oxidation state of chlorine in this oxide is ______ .

Considering the following reaction sequence,

the correct option(s) is(are)

A thin uniform annular disc (see figure) of mass \(M\) has outer radius \(4 R\) and inner radius \(3 R\). The work required to take a unit mass from point \(P\) on its axis to infinity is

In the given circuit, a charge of \(+80 \mu C\) is given to the upper plate of the \(4 \mu F\) capacitor. Then in the steady state, the charge on the upper plate of the \(3 \mu F\) capacitor is

\(5.6 \mathrm{~L}\) of helium gas at STP is adiabatically compressed to \(0.7 \mathrm{~L}\). Taking the initial temperature to be \(T_1\), the work done in the process is

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A point charge \(Q\) is moving in a circular orbit of radius \(R\) in the \(x-y\) plane with an angular velocity \(\omega .\) This can be considered as equivalent to a loop carrying a steady current \(\frac{Q \omega}{2 \pi}\). A uniform magnetic field along the positive \(z\)-axis is now switched on, which increases at a constant rate from 0 to \(B\) in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant \(\gamma\).

Question:

The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is

Two particles, 1 and 2 , each of mass \(m\), are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their center of mass at \(x_0\), are oscillating with amplitude \(a\) and angular frequency \(\omega\). Thus, their positions at time \(t\) are given by \(x_1(t)=\left(x_0+d\right)+a \sin \omega t\) and \(x_2(t)=\left(x_0-d\right)-a \sin \omega t\), respectively, where \(d>2 a\). Particle 3 of mass \(m\) moves towards this system with speed \(u_0=a \omega / 2\), and undergoes instantaneous elastic collision with particle 2 , at time \(t_0\). Finally, particles 1 and 2 acquire a center of mass speed \(v_{\mathrm{cm}}\) and oscillate with amplitude \(b\) and the same angular frequency \(\omega\).

If the collision occurs at time \(t_0=\pi /(2 \omega)\), then the value of \(4 b^2 / a^2\) will be ________ .

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The amount of energy required to break a bond is same as the amount of energy released when the same bond is formed. In gaseous state, the energy required for homolytic cleavage of a bond is called Bond Dissociation Energy (BDE) or Bond Strength. BDE is affected by \(s\)-character of the bond and the stability of the radicals formed. Shorter bonds are typically stronger bonds. BDEs for some bonds are given below:












Question:
Correct match of the \(\mathbf{C}-\mathbf{H}\) bonds (shown in bold) in Column \(\mathbf{J}\) with their BDE in Column \(\mathbf{K}\) is