Which of the following has the shortest \(C-Cl\) bond?

Given below are two statements :
Statement (I): Experimentally determined oxygen-oxygen bond lengths in the \(\mathrm{O}_3\) are found to be same and the bond length is greater than that of a \(\mathrm{O}=\mathrm{O}\) (double bond) but less than that of a single \((O-O)\) bond.
Statement (II) : The strong lone pair-lone pair repulsion between oxygen atoms is solely responsible for the fact that the bond length in ozone is smaller than that of a double bond \((\mathrm{O}=\mathrm{O})\) but more than that of a single bond \((\mathrm{O}-\mathrm{O})\).
In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements :
Statement (I) : Benzyl chloride reacts faster in \(S_N1\) mechanism than ethyl chloride.
Statement (II) : Ethyl carbocation intermediate is less stabilized by hyperconjugation than benzyl carbocation by resonance.
In the light of the above statements, choose the correct answer from the options given below :

Which of the following properties will change when system containing solution 1 will become solution 2?

On heating a mixture of common salt and \(K_{2}Cr_{2}O_{7}\) with concentrated \(H_{2}SO_{4}\), a gas is evolved. Formula of the gas evolved and oxidation state of the central metal atom in the gas respectively are:

In compound \(( Q )\), the percentage of oxygen is __________ %. (Nearest integer)

Which one of the following molecules has maximum dipole moment?

Let \(\lambda \neq 0\) be in \(R\). If \(\alpha\) and \(\beta\) are the roots of the equation, \(x^{2}-x+2 \lambda=0\) and \(\alpha\) and \(\gamma\) are the roots of the equation, \(3 x^{2}-10 x+27 \lambda=0\) then \(\frac{\beta \gamma}{\lambda}\) is equal to

The time dependence of the position of a particle of mass \(m = 2\) is given by \(\vec r\,(t)\, = \,2t\,\hat i\, - 3{t^2}\hat j\) Its angular momentum with respect to the origin at time \(t = 2\) is

The time period of a simple pendulum is given by \(T =2 \pi \sqrt{\frac{\ell}{ g }}\). The measured value of the length of pendulum is \(10\, cm\) known to a \(1\, mm\) accuracy. The time for \(200\) oscillations of the pendulum is found to be \(100\) second using a clock of \(1s\) resolution. The percentage accuracy in the determination of \('g'\) using this pendulum is \('x'\). The value of \('x'\) to the nearest integer is ...........\(\%\)

The value of the integral \(\int \limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{x+\frac{\pi}{4}}{2-\cos 2 x} d x\) is :

\(\operatorname{Lim}_{x \rightarrow 0} \frac{e-(1+2 x)^{\frac{1}{2 x}}}{x}\) is equal to :

An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section \(8.0\times10^{-3}\, m^2\) . Initially the gas is at \(300\, K\) and occupies a volume of \(2.4\times10^{-3}\, m^3\) and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by \(0.1\, m\). The force constant of the spring is \(8000\, N/m\) and the atmospheric pressure is \(1.0\times10^5\, N/m^2\) . The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires of the heater . The heat capacity of the heater coil is also negligible)