Statement 1 Bromobenzene, upon reaction with \(\mathrm{Br}_2 / \mathrm{Fe}\) gives 1, 4-dibromobenzene as the major product.
Statement 2 In bromobenzene, the inductive effect of the bromo group is more dominant than the mesomeric effect in directing the incoming electrophile.

$2 \mathrm{mol}$ of $\mathrm{Hg}\left(\mathrm{g}\right)$ is combusted in a fixed volume bomb calorimeter with excess of ${\mathrm{O}}_2$ at $298 \mathrm{K}$ and $1 \mathrm{atm}$ into $\mathrm{HgO}\left(\mathrm{s}\right)$. During the reaction, temperature increases from $298.0 \mathrm{K}$ to $312.8 \mathrm{K}$. If heat capacity of the bomb calorimeter and enthalpy of formation of $\mathrm{Hg}\left(\mathrm{g}\right)$ are $20.00 \mathrm{kJ} {\mathrm{K}}^{-1}$ and $61.32 \mathrm{kJ} {\mathrm{mol}}^{-1}$ at $298 \mathrm{K}$, respectively, the calculated standard molar enthalpy of formation of $\mathrm{HgO}\left(\mathrm{s}\right)$ at $298 \mathrm{K}$ is $\mathrm{X} {\mathrm{kJmol}}^{-1}$. The value of $\left|\mathrm{X}\right|$ is___[Given: Gas constant $\mathrm{R}=8.3 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$]

Match the electronic configurations in List-I with appropriate metal complex ions in List-II and choose the correct option.[Atomic Number: $\mathrm{Fe} = 26, \mathrm{Mn} = 25, \mathrm{Co} = 27$]

	List I		List II
$\mathrm{P}$	${\mathrm{t}}_{2\mathrm{g}}^6{\mathrm{e}}_{\mathrm{g}}^0$	$1$	${\left[\mathrm{Fe}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{2+}$
$\mathrm{Q}$	${\mathrm{t}}_{2\mathrm{g}}^3{\mathrm{e}}_{\mathrm{g}}^2$	$2$	${\left[\mathrm{Mn}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{2+}$
$\mathrm{R}$	${\mathrm{e}}^2{\mathrm{t}}_2^3$	$3$	${\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}$
$\mathrm{S}$	${\mathrm{t}}_{2\mathrm{g}}^4{\mathrm{e}}_{\mathrm{g}}^2$	$4$	${\left[{\mathrm{FeCl}}_4\right]}^{-}$
		$5$	${\left[{\mathrm{CoCl}}_4\right]}^{2-}$

A sample initially contains only U-238 isotope of uranium. With time, some of the U-238 radioactively decays into \(\mathrm{Pb}-206\) while the rest of it remains undisintegrated.
When the age of the sample is \(\mathbf{P} \times 10^8\) years, the ratio of mass of \(\mathrm{Pb}-206\) to that of \(\mathrm{U}-238\) in the sample is found to be 7 . The value of \(\mathbf{P}\) is ______
[Given: Half-life of U-238 is \(4.5 \times 10^9\) years; \(\log _c 2=0.693\) ]

A mixture of two salts is used to prepare a solution

The correct option (s) for the salt mixture is(are)

The compound (s) having peroxide linkage is(are) :

In the following reactions, P, Q, R and S are the major products.

The correct statement(s) about P, Q, R and S is(are)

Let \(I=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)\) and \(P=\left(\begin{array}{ll}2 & 0 \\ 0 & 3\end{array}\right)\). Let \(Q=\left(\begin{array}{ll}\mathrm{x} & \mathrm{y} \\ \mathrm{z} & 4\end{array}\right)\) for some non-zero real numbers \(x, y\), and \(z\), for which there is \(2 \times 2\) matrix \(R\) with all entries being non-zero real numbers, such that \(Q R=R P\). Then which of the following statements is (are) TRUE?

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

$\text{Δ}z=z\left(\frac{\text{Δ}x}{x}+\frac{\text{Δ}y}{y}\right).$
Question :
The above derivation makes the assumption that $\frac{\text{Δ}r}{x}\ll 1,\frac{\text{Δ}y}{y}\ll 1$. Therefore, the higher powers of these quantities are neglected.

A cylindrical vessel of height \(500 \mathrm{~mm}\) has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it upto height \(H\). Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice and the water level in the vessel becomes steady with height of water column being 200 \(\mathrm{mm}\). Find the fall in height (in \(\mathrm{mm}\) ) of water level due to opening of the orifice.
[Take atmospheric pressure \(=1.0 \times 10^5 \mathrm{Nm}^{-2}\), density of water \(=1000 \mathrm{~kg} \mathrm{~m}^{-3}\) and \(g=10\) \(\mathrm{ms}^{-2}\). Neglect any effect of surface tension.]

The decomposition reaction $2{\mathrm{N}}_2{\mathrm{O}}_5\left(\mathrm{g}\right)\stackrel{ ∆ }{\to }2{\mathrm{N}}_2{\mathrm{O}}_4\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)$ is started in a closed cylinder under the isothermal isochoric condition at an initial pressure of $1 \mathrm{atm}$. After $\mathrm{Y}\times {10}^3\mathrm{ }\mathrm{s}$ , the pressure inside the cylinder is found to be $1.45\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{m}$ . If the rate constant of the reaction is $5\times {10}^{-4}{\mathrm{s}}^{-1}$, assuming ideal gas behaviour, the value of $\mathrm{Y}$ is

During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at $40.0\mathrm{cm}$using a standard resistance of $90\mathrm{}\mathrm{\Omega }$ ,as shown in the figure. The least count of the scale used in the metre bridge is $1\mathrm{mm}$. The unknown resistance is

The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is (are)