The reactivity of compound Z with different halogens under appropriate conditions is given below:

The observed pattern of electrophilic substitution can be explained by

For the reaction, \(\mathbf{X}(s) \rightleftharpoons \mathbf{Y}(s)+\mathbf{Z}(g)\), the plot of \(\ln \frac{p_{\mathbf{Z}}}{p^{\theta}}\) versus \(\frac{10^{4}}{T}\) is given below (in solid line), where \(p_{\mathbf{Z}}\) is the pressure (in bar) of the gas \(\mathbf{Z}\) at temperature \(T\) and \(p^{\theta}=1\) bar.

(Given, \(\frac{\mathrm{d}(\ln K)}{\mathrm{d}\left(\frac{1}{T}\right)}=-\frac{\Delta H^{\theta}}{R}\), where the equilibrium constant, \(K=\frac{p_{z}}{p^{\theta}}\) and the gas constant, \(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) )
The value of standard enthalpy, $∆{\mathrm{H}}^{\mathrm{o}}$ (in $\mathrm{kJ} {\mathrm{mol}}^{-1}$) for the given reaction is ___.

The pair(s) of reagents that yield paramagnetic species is/are

With respect to the compounds$\mathrm{I}-\mathrm{V}$choose the correct statement(s).

Match the conversions in Column I with the type(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the \(4 \times 4\) matrix given in the ORS.

Consider the following four compounds I, II, III, and IV.

Choose the correct statement(s).

According to Bohr's theory \(E_n=\) Total energy, \(K_n=\) Kinetic energy, \(V_n=\) Potential energy, \(r_n=\) Radius of \(n\)th orbit

Let \(\mathbb{R}\) denote the set of all real numbers. Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) and \(g: \mathbb{R} \rightarrow(0,4)\) be functions defined by \(f(x)=\log _e\left(x^2+2 x+4\right)\), and \(g(x)=\frac{4}{1+e^{-2 x}}\)
Define the composite function \(f \circ g^{-1}\) by \(\left(f \circ g^{-1}\right)(x)=\left(g^{-1}(x)\right)\), where \(g^{-1}\) is the inverse of the function \(g\).
Then the value of the derivative of the composite function \(f \circ g^{-1}\) at \(x=2\) is ________ .

Let \(\theta, \varphi \in[0,2 \pi]\) be such that \(2 \cos \theta(1-\sin \varphi)\) \(=\sin ^{2} \theta ~\times\) \(\left(\tan \frac{\theta}{2}+\cot \frac{\theta}{2}\right) \cos \varphi-1, \tan\) \((2 \pi-\theta)>0\) and \(-1 < \sin \theta < -\frac{\sqrt{3}}{2}\), then \(\varphi\) cannot satisfy

For non-negative integers $n,$ let
$f\left(n\right)=\frac{\sum _{k=0}^n\sin \left(\frac{k+1}{n+2}\pi \right)\sin \left(\frac{k+2}{n+2}\pi \right)}{\sum _{k=0}^n{\sin }^2\left(\frac{k+1}{n+2}\pi \right)}$
Assuming ${\cos }^{-1}x$ takes values in $\left[0, \pi \right],$ which of the following options is/are correct?

The circular scale of a screw gauge has 50 divisions and pitch of \(0.5 \mathrm{~mm}\). Find the diameter of sphere. Main scale reading is 2 .

The correct order of acid strength of the following carboxylic acids is -

The stoichiometric reaction of $516 \mathrm{g}$ of dimethyldichlorosilane with water results in a tetrameric cyclic product $\mathbf{X}$ in $75\%$ yield. The weight (in $\mathrm{g}$) of $\mathbf{X}$ obtained is ____________
\(\left[\right.\)Use, molar mass\(.\left(\text{gmol} ^{-1}\right):\text H =1,\text C =12,\)\(\text O =16, \text{Si} =28, \text{Cl} =35.5]\)