Among P, Q, R and S, the aromatic compound(s) is/are

The species having bond order different from that in \(\mathrm{CO}\) is

The species which by definition has zero standard molar enthalpy of formation at \(298 \mathrm{~K}\) is

The compound(s) which generate(s) $N_2$ gas upon thermal decomposition below ${300}^{o}C$ is (are)

The pair(s) of complexes wherein both exhibit tetrahedral geometry is(are)
(Note: $\mathrm{py}=$ pyridine Given: Atomic numbers of $\mathrm{Fe}, \mathrm{Co}, \mathrm{Ni}$ and $\mathrm{Cu}$ are $26, 27, 28$ and $29$, respectively)

An organic compound \(\mathbf{P}\) having molecular formula \(\mathrm{C}_6 \mathrm{H}_6 \mathrm{O}_3\) gives ferric chloride test and does not have intramolecular hydrogen bond. The compound \(\mathbf{P}\) reacts with 3 equivalents of \(\mathrm{NH}_2 \mathrm{OH}\) to produce oxime \(\mathbf{Q}\). Treatment of \(\mathbf{P}\) with excess methyl iodide in the presence of \(\mathrm{KOH}\) produces compound \(\mathbf{R}\) as the major product. Reaction of \(\mathbf{R}\) with excess iso-butylmagnesium bromide followed by treatment with \(\mathrm{H}_3 \mathrm{O}^{+}\)gives compound \(\mathrm{S}\) as the major product.
The total number of methyl \(\left(-\mathrm{CH}_3\right)\) group(s) in compound \(\mathbf{S}\) is ________. (consider maximum value if there are two values)

Consider an electrochemical cell: $\text{A}\left(\text{s}\right)\left|{\text{ A}}^{\text{n+}}\left(\text{aq, 2 M}\right)\right|\left|{\text{ B}}^{\text{2n+}}\left(\text{aq, 1 M}\right)\right|\text{ B}\left(\text{s}\right)$. The value of ${\text{ΔH}}^{\text{o}}$ for the cell reaction is twice that of ${\text{ΔG}}^{\text{o}}$ at $\text{300 K}\text{.}$ If the emf of the cell is zero, the magnitude of $\mathrm{\Delta }{\text{S}}^o$ $\left(\text{in} {\text{J}}^{-1}{\text{K}}^{-1} {\text{mol}}^{-1}\right)$ of the cell reaction per mole of $\text{B}$ formed at $\text{300}\text{K}$ is ____
(Given: R $\text{=}\text{8}\text{.3}{\text{JK}}^{-\text{1}}{\text{mol}}^{-1}.$ $\text{H,}\text{S}$ and $\text{G}$ are enthalpy, entropy and Gibbs energy, respectively.)

For the following electrochemical cell at $\text{289 K,}$
\(\operatorname{Pt}( s ) \mid H _2(g, 1\) bar \() \mid H ^{+}( aq , 1 M ) \| M ^{4+}(\) aq. \(), M ^{2+}(\) aq. \() \mid \operatorname{Pt}( s )\)
${\mathrm{E}}_{\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}}=0.092\mathrm{ }\mathrm{V}$ when $\frac{\left[{\mathrm{M}}^{2+}\left(\mathrm{a}\mathrm{q}.\right)\right]}{\left[{\mathrm{M}}^{4+}\left(\mathrm{a}\mathrm{q}.\right)\right]}={10}^{\mathrm{x}}$
Given: ${\mathrm{E}}_{{\mathrm{M}}^{4+}/{\mathrm{M}}^{2+}}^0=0.151\mathrm{ }\mathrm{V}\mathrm{ };2.303\frac{\mathrm{R}\mathrm{T}}{\mathrm{F}}=0.059$
The value of $\text{x}$ is -

If \(r, s, t\) are prime numbers and \(p, q\) are the positive integers such that LCM of \(p, q\) is \(r^2 s^4 t^2\), then the number of ordered pairs \((p, q)\) is

Let ${\mathrm{E}}_1\left(\mathrm{r}\right),\mathrm{ }{\mathrm{E}}_2\left(\mathrm{r}\right)$ and ${\mathrm{E}}_3\left(\mathrm{r}\right)$ be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density $\mathrm{\lambda }$ , and an infinite plane with uniform surface charge density $\mathrm{\sigma }$ . If ${\mathrm{E}}_1\left({\mathrm{r}}_0\right)={\mathrm{E}}_2\left({\mathrm{r}}_0\right)={\mathrm{E}}_3\left({\mathrm{r}}_0\right)$ at a given distance ${\mathrm{r}}_0$ , then

Statement \(1 \mathrm{In}\) a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.
and Statement 2 Resistance of a metal increase with increase in temperature.

A glass tube of uniform internal radius \((r)\) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius \(r\). End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve,

Paragraph : If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation $z =\frac{x}{y}$. If the errors in $x, y \mathrm{a}\mathrm{n}\mathrm{d} z \mathrm{a}\mathrm{r}\mathrm{e} ∆x, ∆y \mathrm{a}\mathrm{n}\mathrm{d} ∆z$ , respectively, then

$z\pm ∆z=\frac{x\pm ∆x}{y\pm ∆y}=\frac{x}{y}\left(1\pm \frac{∆x}{x}\right){\left(1\pm \frac{∆y}{y}\right)}^{-1}$

The series expansion for ${\left(1\pm \frac{∆y}{y}\right)}^{-1}$, to first power in $∆y/y, \mathrm{i}\mathrm{s} 1\mp \left(∆y/y\right)$. The relative errors in independent variables are always added. So the error in $z$ will be

$\text{Δ}z=z\left(\frac{\text{Δ}x}{x}+\frac{\text{Δ}y}{y}\right).$
The above derivation makes the assumption that \(\Delta r / x \ll 1, \Delta y / y < 1\). Therefore, the higher powers of these quantities are neglected.
Question : Consider the ratio \(r=\frac{(1-a)}{(1+a)}\) to be determined by measuring a dimensionless quantity a If the error in the measurement of a is \(\Delta a(\frac{\Delta a}{a}<<1)\), then what is the error \(\Delta r\) in determining \(r\) ?