KI in acetone, undergoes S_N2 reaction with each of P, Q, R and S. The rates of the reaction vary as

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Tollen's reagent is used for the detection of aldehyde when a solution of \(\mathrm{AgNO}_3\) is added to glucose with \(\mathrm{NH}_4 \mathrm{OH}\) then gluconic acid is formed
\(\mathrm{Ag}^{+}+e^{-} \rightarrow \mathrm{Ag} E_{\text {red }}^{\circ}=0.8 \mathrm{~V} \)
\( \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow \text { Gluconic acid }\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_7\right)\) \(+~2 \mathrm{H}^{+}+2 e^{-} ; -E_{\mathrm{red}}^{\circ}=-0.05 \mathrm{~V} \)
\( \mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}+e^{-} \rightarrow \mathrm{Ag}(s)+2 \mathrm{NH}_3 ; E_{\mathrm{red}}^{\circ}\) \(=0.337 \mathrm{~V}\)
[Use \(2.303 \times \frac{R T}{F}=0.0592\) and \(\frac{F}{R T}=38.92\) at \(298 \mathrm{~K}\)]
Question:
\(2 \mathrm{Ag}^{+}+\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow 2 \mathrm{Ag}(\mathrm{s})\) \(+~\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_4+2 \mathrm{H}^{+}\). Find \(\ln \mathrm{K}\) of this reaction.

List-I contains various reaction sequences and List-II contains the possible products. Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

Correct option(s) for the following sequence of reactions is(are)

The smallest ketone and its next homologoue are reacted with \(\mathrm{NH}_2 \mathrm{OH}\) to form oxime

For the process ${\mathrm{H}}_2\mathrm{O}\mathrm{ }\left(\mathcal{l}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)\mathrm{ }$ at $\mathrm{T}={100}^{\mathrm{o}}\mathrm{C}\mathrm{ }$ and 1 atmosphere pressure, the correct choice is

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\(\mathbf{X}\) and \(\mathbf{Y}\) are two volatile liquids with molar weights of \(10 \mathrm{~g} \mathrm{~mol}^{-1}\) and \(40 \mathrm{~g} \mathrm{~mol}^{-1}\) respectively. Two cotton plugs, one soaked in \(\mathbf{X}\) and the other soaked in \(\mathbf{Y}\), are simultaneously placed at the ends of a tube of length \(L=24 \mathrm{~cm}\), as shown in the figure. The tube is filled with an inert gas at \(1\) atmosphere pressure and a temperature of \(300 \mathrm{~K}\). Vapours of \(\mathbf{X}\) and \(\mathbf{Y}\) react to form a product which is first observed at a distance \(\mathbf{d} \mathrm{~cm}\) from the plug soaked in \(\mathbf{X}\). Take \(\mathbf{X}\) and \(\mathbf{Y}\) to have equal molecular diameters and assume ideal behaviour for the inert gas and the two vapours.



Question:

The experimental value of \(\mathbf{d}\) is found to be smaller than the estimate obtained using Graham's law. This is due to

Let \(f\) be a non-negative function defined on the interval \([0,1]\). If \(\int_0^x \sqrt{1-\left\{f^{\prime}(t)\right\}^2} d t=\int_0^x f(t) d t, \quad 0 \leq x \leq 1\)
\[
\text { and } f(0)=0 \text {, then }
\]

The species having pyramidal shape is

The value of \(n\) in the molecular formula \(\mathrm{Be}_n \mathrm{Al}_2 \mathrm{Si}_6 \mathrm{O}_{18}\) is

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Consider the function \(f:(-\infty, \infty) \rightarrow(-\infty, \infty)\) defined by \(f(x)=\frac{x^2-a x+1}{x^2+a x+1} ; 0 < a < 2\)Question:
Which of the following is true?

Let $f:[1.\infty )\to \mathrm{ℝ}$ be a differentiable function such that $f\left(1\right)=\frac{1}{3}$ and $3{\int }_1^{x}f\left(t\right)dt=xf\left(x\right)-\frac{x^3}{3},x\in [1,\infty )$. Let $e$ denote the base of the natural logarithm. Then the value of $f\left(e\right)$ is

Let $f\left(x\right)=\sin \left(\pi \cos x\right)$ and $g\left(x\right)=\cos \left(2\pi \sin x\right)$ be two functions defined for $x>0.$ Define the following sets whose elements are written in the increasing order:
$X=\left\{x:f\left(x\right)=0\right\}, Y=\left\{x:f^{\text{'}}\left(x\right)=0\right\}$
$Z=\left\{x:g\left(x\right)=0\right\}, W=\left\{x:g^{\text{'}}\left(x\right)=0\right\}$
List- $\mathrm{I}$ contains the sets $X, Y, Z$ and $W.$ List- $\mathrm{I}\mathrm{I}$ contains some information regarding these sets.
 

	List-  I		List-  II
$\left(I\right)$	$X$	$\left(P\right)$	$\supseteq \left\{\frac{\pi }{2},\frac{3\pi }{2}, 4\pi , 7\pi \right\}$
$\left(II\right)$	$Y$	$\left(Q\right)$	an arithmetic progression
$\left(III\right)$	$Z$	$\left(R\right)$	NOT an arithmetic progression
$\left(IV\right)$	$W$	$\left(S\right)$	$\supseteq \left\{\frac{\pi }{6},\frac{7\pi }{6},\frac{13\pi }{6}\right\}$
		$\left(T\right)$	$\supseteq \left\{\frac{\pi }{3},\frac{2\pi }{3}, \pi \right\}$
		$\left(U\right)$	$\supseteq \left\{\frac{\pi }{6},\frac{3\pi }{4}\right\}$

Which of the following is the only correct combination?