Which of the following liberates ${\mathrm{O}}_2$ upon hydrolysis?

Both \(\left[\mathrm{Ni}(\mathrm{CO})_4\right]\) and \(\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}\) are diamagnetic. The hybridisations of nickel in these complexes, respectively, are

The qualitative sketches I, II and III given below show the variation of surface tension with molar concentration of three different aqueous solutions of KCl, $\mathrm{C}{\mathrm{H}}_3\mathrm{O}\mathrm{H}\mathrm{}$ and $\mathrm{C}{\mathrm{H}}_3{\left(\mathrm{C}{\mathrm{H}}_2\right)}_{11}\mathrm{O}\mathrm{S}{\mathrm{O}}_3^{-}\mathrm{}\mathrm{N}{\mathrm{a}}^{+}$ at room temperature. The correct assignment of the sketches is -

The treatment of an aqueous solution of 3.74 g of \(\text{Cu} \left(\text{NO} _3\right)_2\) with excess KI results in a brown solution along with the formation of a precipitate. Passing \(\text{H} _2 \text{S}\) through this brown solution gives another precipitate X . The amount of X (in g ) is _____________ [Given: Atomic mass of \(\text{H} =1, \text{N}=14, \text{O} =16, \text{S}=32, \text{K}=39,\) \(\text{Cu} =63, \text{I} =127]\)

\(\mathrm{NiCl}_{2}\left\{\mathrm{P}\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)\right\}_{2}\) exhibits temperature depend-ent magnetic behaviour (paramagnetic/diamagnetic). The coordination geometries of \(\mathrm{Ni}^{2+}\) in the paramagnetic and diamagnetic states are respectively

Which of the following statement(s) (are) correct regarding the root mean square speed $\left({\mathrm{U}}_{\mathrm{r}\mathrm{m}\mathrm{s}}\right)$ and average translational kinetic energy $\left({\mathrm{\epsilon }}_{\mathrm{a}\mathrm{v}}\right)$ of a molecule in a gas at equilibrium?

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A tertiary alcohol \(H\) upon acid catalysed dehydration gives a product \(I\). Ozonolysis of I leads to compounds \(\mathrm{J}\) and \(\mathrm{K}\). Compound \(\mathrm{J}\) upon reaction with
\(\mathrm{KOH}\) gives benzyl alcohol and a compound \(\mathrm{L}\), where \(\mathrm{K}\) on reaction with \(\mathrm{KOH}\) gives only \(M\).

Question:
The structures of compounds \(J, K\) and \(L\), respectively, are

Let complex numbers α and $\frac{1}{\overline{\alpha }}$   lie on circles ${\left(x-x_0\right)}^2+{\left(y-y_0\right)}^2={\text{r}}^2\text{, }$  and  ${\left(x-x_0\right)}^2+{\left(y-y_0\right)}^2={4\text{r}}^2\text{, }$respectively. If $z_0=x_0+i{y}_0$ satisfies the equation $2{\left|z_0\right|}^2=r^2+2\text{,}\text{then}\left|\alpha \right|=$

Complete reaction of acetaldehyde with excess formaldehyde, upon heating with conc. \(\mathrm{NaOH}\) solution, gives \(\mathbf{P}\) and \(\mathbf{Q}\). Compound \(\mathbf{P}\) does not give Tollens' test, whereas \(\mathbf{Q}\) on acidification gives positive Tollens' test. Treatment of \(\mathbf{P}\) with excess cyclohexanone in the presence of catalytic amount of \(p\)-toluenesulfonic acid (PTSA) gives product \(\mathbf{R}\).
Sum of the number of methylene groups \(\left(-\mathrm{CH}_2-\right)\) and oxygen atoms in \(\mathbf{R}\) is ________.

Of the three independent events ${\text{E}}_1$, ${\text{E}}_2$ and ${\text{E}}_3$, the probability that only ${\text{E}}_1$ occurs is $\alpha$, only ${\text{E}}_2$ occurs is $\beta$ and only  ${\text{E}}_3$ occurs is $\gamma$. Let the probability $p$ that none of events ${\text{E}}_1$, ${\text{E}}_2$ or ${\text{E}}_3$ occurs satisfy the equations $\left(\alpha -2\beta \right)p=\alpha \beta$ and $\left(\beta -3\gamma \right)p = 2\beta \gamma$. All the given probabilities are assumed to lie in the interval $\left(\text{0, 1}\right)$.
Then   $\frac{{\text{Probability of occurrence of E}}_1}{{\text{Probability of occurrence of E}}_3}=$ ​

Consider an obtuse angled triangle $ABC$ in which the difference between the largest and the smallest angle is $\frac{\pi }{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius $1$.

(There are two questions based on $\mathrm{PARAGRAPH} " 1 "$, the question given below is one of them)
Let $\alpha$ be the area of the triangle $ABC$. Then the value of $(64\alpha {)}^2$ 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:
What should be the age of fossil for meaningful determination of its age?

For the following reaction $2\mathrm{X}+\mathrm{Y}\stackrel{\mathrm{k}}{\to }\mathrm{P}$ the rate of reaction is $\frac{\mathrm{d}\left[\mathrm{P}\right]}{\mathrm{dt}}=\mathrm{k}\left[\mathrm{X}\right]$. Two moles of $\mathrm{X}$ are mixed with one mole of $\mathrm{Y}$ to make $1.0 \mathrm{L}$ of solution. At $50 \mathrm{s}, 0.5$ mole of $\mathrm{Y}$ is left in the reaction mixture. The correct statement(s) about the reaction is(are) $($Use: $\ln 2=0.693)$