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 :

The amount of calcium oxide produced on heating 150 kg limestone ( \(75 \%\) pure) is ______ kg. (Nearest integer)
Given : Molar mass (in \(\mathrm{g} \mathrm{mol}^{-1}\)) of Ca-40, O-16, C-12

The correct decreasing order for acidic strength is

The disproportionation of \(MnO _{4}^{2-}\) in acidic medium resulted in the formation of two manganese compounds \(A\) and \(B\). If the oxidation state of \(Mn\) in \(B\) is smaller than that of \(A\), then the spin-only magnetic moment \((\mu)\) value of \(B\) in \(BM\) is \(.........\) (Nearest integer)

The formal charges on the atoms marked as (1) to (4) in the Lewis representation of \(HNO_{3}\) molecule respectively are

\(2-\) hexene \(\xrightarrow[(ii)H_2O]{(i) O_3}\) Products The two products formed in above reaction are -

If the radius of the \(3^{\text {rd }}\) Bohr's orbit of hydrogen atom is \(r_{3}\) and the radius of \(4^{\text {th }}\) Bohr's orbit is \(r_{4}\). Then ....

Two particles \({A}\) and \({B}\) having charges \(20\, \mu {C}\) and \(-5\, \mu {C}\) respectively are held fixed with a separation of \(5\, {cm}\). At what position a third charged particle should be placed so that it does not experience a net electric force?

A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to \(\operatorname{arc} \mathrm{AB}\) to ' O ' is ' E ' is magnitude. What would be the magnitude of electric field at ' O ' due to arc ABC ?

Given below are two statements: one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\) : Assertion \((A)\) : \(\mathrm{S}_{\mathrm{N}} 2\) reaction of \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathrm{Br}\) occurs more readily than the \(\mathrm{S}_{\mathrm{N}} 2\) reaction of \(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br}\). Reason \((R)\) : The partially bonded unhybridized p-orbital that develops in the trigonal bipyramidal transition state is stabilized by conjugation with the phenyl ring. In the light of the above statements, choose the most appropriate answer from the options given below:

Let \(y(x)\) be the solution of the differential equation \(\left( {xlogx} \right)\frac{{dy}}{{dx}} + y = 2xlogx,\left( {x \ge 1} \right)\) . Then \(y(e) \) is equal to :      \([y(1)=0]\)

The electric current in a circular coil of four turns produces a magnetic induction \(32\,T\) at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be \(..........\,T\)

A screw gauge with a pitch of \(0.5 \ mm\) and a circular scale with \(50\) divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that wen the two jaws of the screw gauge are brought in contact, the \(45^{th} \)division coincides with the main scale line and the zero of the main scale is barely visible. What is the thickness of the sheet (in \(mm\)) if the main scale reading is \(0.5\ mm\) and the \(25^{th}\) division coincides with the main scale line