The correct order of the wavelength maxima of the absorption band in the ultraviolet-visible region for the given complexes is

The concentration of \(R\) in the reaction \(R \longrightarrow P\) was measured as a function of time and the following data is obtained :
\(\begin{array}{lllll}{[R] \text { (molar) }} & 1.0 & 0.75 & 0.40 & 0.10 \\ t \text { (min) } & 0.0 & 0.05 & 0.12 & 0.18\end{array}\)
The order of the reaction is

In the following carbocation, \(\mathrm{H} / \mathrm{CH}_3\) that is most likely to migrate to the positively charged carbon is

The total number of chiral molecules formed from one molecule of $P$ on complete ozonolysis $\left({\mathrm{O}}_3,\mathrm{Zn}/H_2\mathrm{O}\right)$ is _____

A reversible cyclic process for an ideal gas is shown below. Here, $P,V,\mathrm{a}\mathrm{n}\mathrm{d}T$ are pressure, volume and temperature, respectively. The thermodynamic parameters $q,w,H\mathrm{a}\mathrm{n}\mathrm{d}U$ are heat, work, enthalpy and internal energy, respectively.

The correct option(s) is (are)

A sample \((5.6 \mathrm{~g})\) containing iron is completely dissolved in cold dilute \(\mathrm{HCl}\) to prepare a \(250 \mathrm{~mL}\) of solution. Titration of \(25.0 \mathrm{~mL}\) of this solution requires \(12.5 \mathrm{~mL}\) of \(0.03 \mathrm{M} \mathrm{KMnO}_{4}\) solution to reach the end point. Number of moles of \(\mathrm{Fe}^{2+}\) present in \(250 \mathrm{~mL}\) solution is \(\mathbf{x} \times 10^{-2}\) (consider complete dissolution of \(\mathrm{FeCl}_{2}\) ). The amount of iron present in the sample is \(\mathbf{y} \%\) by weight.
(Assume: \(\mathrm{KMnO}_{4}\) reacts only with \(\mathrm{Fe}^{2+}\) in the solution Use: Molar mass of iron as \(56 \mathrm{~g} \mathrm{~mol}^{-1}\) )
The value of $\mathrm{y}$ is________ .

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Carbon-14 is used to determine the age of organic material. The procedure is based on the formation of \({ }^{14} \mathrm{C}\) by neutron capture in the upper atmosphere.
\(
{ }_7^{14} \mathrm{~N}+{ }_0^1 n \longrightarrow{ }_6^{14} \mathrm{C}+{ }_1 n^1
\)
\({ }^{14} \mathrm{C}\) is absorbed by living organisms during photosynthesis. The \({ }^{14} \mathrm{C}\) content is constant in living organism once the plant or animal dies, the uptake of carbon dioxide by it ceases and the level of \({ }^{14} \mathrm{C}\) in the dead being, falls to the decay which \({ }^{14} \mathrm{C}\) undergoes.
\(
{ }_6^{14} \mathrm{C} \longrightarrow{ }_7^{14} \mathrm{~N}+\beta^{-}
\)
The half life period of \({ }^{14} \mathrm{C}\) is 5770 years. The decay constant \((\lambda)\) can be calculated by using the following formula \(\lambda=\frac{0.693}{t_{1 / 2}}\).
The comparison of the \(\beta^{-}\)activity of the dead matter with that of the carbon still in circulation enables measurement of the period of the isolation of the material from the living cycle. The method however, ceases to be accurate over periods longer than 30,000 years. The proportion of \({ }^{14} \mathrm{C}\) to \({ }^{12} \mathrm{C}\) in living matter is \(1: 10^{12}\).
Question:
A nuclear explosion has taken place leading to increase in concentration of \(C^{14}\) in nearby areas. \(\mathrm{C}^{14}\) concentration is \(C_1\) in nearby areas and \(C_2\) in areas far away. If the age of the fossil is determined to be \(T_1\) and \(T_2\) at the places respectively then

A ball is thrown from the location \(\left(x_0, y_0\right)=(0,0)\) of a horizontal playground with an initial speed \(v_0\) at an angle \(\theta_0\) from the \(+x\)-direction. The ball is to be hit by a stone, which is thrown at the same time from the location \(\left(x_1, y_1\right)=(L, 0)\). The stone is thrown at an angle \(\left(180-\theta_1\right)\) from the \(+x\)-direction with a suitable initial speed. For a fixed \(v_0\), when \(\left(\theta_0, \theta_1\right)=\left(45^{\circ}, 45^{\circ}\right)\), the stone hits the ball after time \(T_1\), and when \(\left(\theta_0, \theta_1\right)=\left(60^{\circ}, 30^{\circ}\right)\), it hits the ball after time \(T_2\). In such a case, \(\left(T_1 / T_2\right)^2\) is _______ .

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

At time \(t=0\), a battery of \(10 \mathrm{~V}\) is connected across points \(A\) and \(B\) in the given circuit. If the capacitors have no charge initially, at what time (in second) does the voltage across them become \(4 \mathrm{~V}\) ?
[Take \(: \ln 5=1.6, \ln 3=1.1]\)

One mole of a monatomic ideal gas is taken through a cycle \(A B C D A\) as shown in the \(p\)-V diagram. Column II gives the characteristics involved in the cycle. Match them with each of the processes given in Column I.

Let $e$ denote the base of the natural logarithm. The value of the real number $a$ for which the right-hand limit $\underset{x\to 0^{+}}{\lim }\frac{{\left(1-x\right)}^{\frac{1}{\chi }}-e^{-1}}{x^a}$ is equal to a non-zero real number, is

The straight line \(2 x-3 y=1\) divides the circular region \(x^2+y^2 \leq 6\) into two parts. If \(S=\left\{\left(2, \frac{3}{4}\right),\left(\frac{5}{2}, \frac{3}{4}\right),\left(\frac{1}{4},-\frac{1}{4}\right),\left(\frac{1}{8}, \frac{1}{4}\right)\right\}\), then the number of point(s) in \(S\) lying inside the smaller part is