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

The ozone layer forms naturally by

In the following compound, the number of sp-bybridised carbons are

The following equilibrium constants are given
\(\begin{array}{l}
\mathrm{N}_{2}+3 \mathrm{H}_{2} \rightleftharpoons 2 \mathrm{NH}_{3} ; K_{1} \\
\mathrm{N}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO} ; K_{2}
\end{array}\)
\(\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O} ; K_{3}\)
The equilibrium constant for the oxidation of 2 mole of \(\mathrm{NH}_{3}\) to give NO is

Hybridization of \(\mathrm{C}_2\) and \(\mathrm{C}_3\) of \(\mathrm{H}_3 \mathrm{C}-\mathrm{CH}=\mathrm{C}=\mathrm{CH}-\mathrm{CH}_3\) are

The correct relationship between molecules I and II is

Which of the following compounds shows evidence of the strongest hydrogen bonding?

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

Let \(g(x)=\int_{x}^{2 x} \frac{f(t)}{t} d t\) where \(x>0\) and \(f\) be continuous function and \(f(2 x)=f(x)\), then

Given an A.P. and a G.P. with positive terms, with the first and second terms of the progressions being equal. If \(a_n\) and \(b_n\) be the \(n^{\text {th }}\) term of A.P. and G.P. respectively then

In a region, the intensity of an electric field is given by \(\mathbf{E}=2 \mathbf{i}+3 \mathbf{j}+\mathbf{k}\) in \(\mathrm{NC}^{-1}\). The electric flux through a surface \(\mathbf{S}=10 \mathbf{i} \mathrm{m}^{2}\) in the region is

If \(\mathrm{P}(\mathrm{x})=a \mathrm{x}^{2}+\mathrm{bx}+\mathrm{c}\) and \(\mathrm{Q}(\mathrm{x})=-\mathrm{ax}^{2}+\mathrm{dx}+\mathrm{c}\), where \(\mathrm{ac} \neq 0 \quad[\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}\) are all real], then \(\mathrm{P}(\mathrm{x}) \cdot \mathrm{Q}(\mathrm{x})=0\) has

Let \(x_{n}=\left(1-\frac{1}{3}\right)^{2}\left(1-\frac{1}{6}\right)^{2}\left(1-\frac{1}{10}\right)^{2} \ldots\) \(\left(1-\frac{1}{\frac{n(n+1)}{2}}\right)^{2}, n \geq 2\) Then, the value of \(\lim _{n \rightarrow \infty} x_{n}\) is