Avogadro's law is valid for

The correct stability order of the following carbocations is
\(\underset{\text{I}}{\mathrm{H}_2 \stackrel{\oplus}{\mathrm{C}}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_3}\)
\(\underset{\text{II}}{\stackrel{\oplus}{\mathrm{C}} \mathrm{H}_2-\mathrm{CH}=\mathrm{CH}-\mathrm{BMe}_2}\)
\(\underset{\text{III}}{\mathrm{H}_2 \stackrel{\oplus}{\mathrm{C}}-\mathrm{CH}=\mathrm{CH}-\mathrm{NMe}_2}\)
\(\underset{\text{Iv}}{\mathrm{H}_2 \stackrel{\oplus}{\mathrm{C}}-\mathrm{CH}=\mathrm{CH}-\mathrm{OMe}}\)

The value of \(\Delta H\) for cooling 2 mole of an ideal monoatomic gas from \(225^{\circ} \mathrm{C}\) to \(125^{\circ} \mathrm{C}\) at constant pressure will be [given \(\left.C_{p}=\frac{5}{2} R\right]\)

In \(\mathrm{SOCl}_{2}\), the \(\mathrm{Cl} - \mathrm{S}-\mathrm{Cl}\) and \(\mathrm{Cl}-\mathrm{S}-\mathrm{O}\)
bond angles are

In the IUPAC system, \(PhCH_{2}CH_{2}\mathrm{CO}_{2} \mathrm{H}\) is named as

Addition of excess potassium iodide solution to a solution of mereuric chloride gives the halide complex

Which of the following compounds does not exhibit optical isomerism?
en = ethylenediamine).

The number of lone pairs of electrons on the central atoms of \(\mathrm{H}_{2} \mathrm{O}, \mathrm{SnCl}_{2}, \mathrm{PCl}_{3}\) an \(\mathrm{XeF}_{2}\)
respectively, are

The locus of points \((x, y)\) in the plane satisfying \(\sin ^2 x+\sin ^2 y=1\) consists of

A glass slab consists of thin uniform layers of progressively decreasing refractive indices RI (see figure) such that the RI of any layer is \(\mu-m \Delta \mu\). Here, \(\mu\) and \(\Delta \mu\) denote the \(\mathrm{RI}\) of 0 th layer and the difference in RI between any two consecutive layers, respectively. The integer \(m=0,1,2,3, \ldots\) denotes the numbers of the successive layers. A ray of light from the oth layer enters the 1st layer at an angle of incidence of \(30^{\circ}\). After undergoing the mth refraction, the ray emerges parallel to the interface. If \(\mu=1.5\) and \(\Delta \mu=0.015,\) the value of \(m\) is

\(20 \mathrm{mL~} 0 .1\) (N) acetic acid is mixed with \(10 \mathrm{mL}\) \(0.1(\mathrm{N})\) solution of NaOH. The pH of the resulting solution is \(\left(p K_{a}\right.\) of acetic acid is \(\left.4.74\right)\)

\(\int \frac{\cos 2 x}{\cos x} d x=\)

If \(f(x)=x\left(\frac{1}{x-1}+\frac{1}{x}+\frac{1}{x+1}\right), x>1\). Then