With reference to aqua regia, choose the correct option(s).

In a galvanic cell, the salt bridge

The number of resonance structures for N is

The maximum number of isomers (including stereoisomers) that are possible on monochlorination of the following compounds, is

The pair(s) of diamagnetic ions is(are)

Paragraph:
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:
Ammonia is always added in this reaction. Which of the following must be incorrect?

The standard state Gibb's free energies of formation of  $\mathrm{C}$ (graphite) and $\mathrm{C}$ (diamond) at $\mathrm{T}=298\mathrm{ }\mathrm{K}$ are
${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{G}}^{\mathrm{o}}\left[\mathrm{C} (\mathrm{graphite}\right]=0\mathrm{ }\mathrm{kJ}\mathrm{ }{\mathrm{mol}}^{-1}$
${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{G}}^{\mathrm{o}}\left[\mathrm{C} \left(\mathrm{diamond}\right)\right]=2.9\mathrm{ }\mathrm{kJ}\mathrm{ }{\mathrm{mol}}^{-1}$
The standard state means that the pressure should be 1 bar, and substance should be pure at a given temperature. The conversion of graphite [$\mathrm{C}$ (graphite)] to diamond [$\mathrm{C}$ (diamond)] reduces its volume by $2\times {10}^{-6}\mathrm{ }{\mathrm{m}}^3 {\mathrm{mol}}^{-1}$ . If $\mathrm{C}$ (graphite) is converted to $\mathrm{C}$ (diamond) isothermally at $\mathrm{T}=298 \mathrm{K}$, the pressure at which $\mathrm{C}$ (graphite) is in equilibrium with $\mathrm{C}$ (diamond), is
[Useful information:
\(1 J=1 kg m ^2 s^{-2}, 1 Pa=1 kg m ^{-1} s^{-2} ;\) \(1 bar =10^5 Pa]\)

Let $a$ and $b$ be positive real numbers. Suppose $\overrightarrow{PQ}=a\hat{i}+b\hat{j}$ and $\overrightarrow{PS}=a\hat{i}-b\hat{j}$ are adjacent sides of a parallelogram $PQRS.$ Let $\overrightarrow{u}$ and $\overrightarrow{v}$ be the projection vectors of $\overrightarrow{w}=\hat{i}+\hat{j}$ along $\overrightarrow{PQ}$ and $\overrightarrow{PS}$, respectively. If $\left|\overrightarrow{u}\right|+\left|\overrightarrow{v}\right|=\left|\overrightarrow{w}\right|$ and if the area of the parallelogram $PQRS$ is $8,$ then which of the following statements is/are TRUE?

Consider the region \(R=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x \geq 0\right.\) and \(\left.y^{2} \leq 4-x\right\}\). Let \(\mathcal{F}\) be the family of all circles that are contained in \(R\) and have centers on the \(x\)-axis. Let \(C\) be the circle that has largest radius among the circles in \(\mathcal{F}\). Let \((\alpha, \beta)\) be a point where the circle \(C\) meets the curve \(y^{2}=4-x\).
The value of $\alpha$ is _____.

Let \(S_n=\sum_{k=0}^n \frac{n}{n^2+k n+k^2}\) and \(T_n=\sum_{k=0}^{n-1} \frac{n}{n^2+k n+k^2}\), for \(n=1,2,3, \ldots\), then

The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is (are)

Suppose $a, b$ denote the distinct real roots of the quadratic polynomial $x^2+20x-2020$ and suppose $c, d$ denote the distinct complex roots of the quadratic polynomial $x^2-20x+2020$. Then the value of $ac\left(a-c\right)+ad\left(a-d\right)+bc\left(b-c\right)+bd\left(b-d\right)$

A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated ($P$) by the metal. The sensor has a scale that displays ${\log }_2\left(\frac{P}{P_0}\right)$, where $P_0$ is a constant. When the metal surface is at a temperature of $487 °\mathrm{C}$, the sensor shows a value $1$. Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to $2767 °\mathrm{C}$?