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JEE Advanced 2024 Paper 2 Online
Numerical
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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 $\mathrm{U}-238$ is $4.5 \times 10^9$ years; $\log _e 2=0.693$ ]

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2
JEE Advanced 2024 Paper 1 Online
Numerical
+4
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Consider the following reaction,

$$ 2 \mathrm{H}_2(\mathrm{~g})+2 \mathrm{NO}(\mathrm{g}) \rightarrow \mathrm{N}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g}) $$

which follows the mechanism given below :

$$ \begin{array}{ll} 2 \mathrm{NO}(\mathrm{g}) \stackrel{k_1}{\underset{k_{-1}}{\rightleftharpoons}} \mathrm{N}_2 \mathrm{O}_2(\mathrm{~g}) & \text { (fast equlibrium) } \\\\ \mathrm{N}_2 \mathrm{O}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g}) \xrightarrow{k_2} \mathrm{~N}_2 \mathrm{O}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g}) & \text { (slow reaction) } \\\\ \mathrm{N}_2 \mathrm{O}(\mathrm{g})+\mathrm{H}_2(\mathrm{~g}) \xrightarrow{k_3} \mathrm{~N}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g}) & \text { (fast reaction) } \end{array} $$

The order of the reaction is __________.

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3
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0
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$$_{92}^{238}U$$ is known to undergo radioactive decay to form $$_{82}^{206}Pb$$ by emitting alpha and beta particles. A rock initially contained 68 $$ \times $$ 10$$-$$6 g of $$_{92}^{238}U$$. If the number of alpha particles that it would emit during its radioactive decay of $$_{92}^{238}U$$ to $$_{82}^{206}Pb$$ in three half-lives is Z $$ \times $$ 1018, then what is the value of Z?
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4
JEE Advanced 2019 Paper 2 Offline
Numerical
+3
-0
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The decomposition reaction

$$2{N_2}{O_5}(g)\buildrel \Delta \over \longrightarrow 2{N_2}{O_4}(g) + {O_2}(g)$$

is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm. After Y $$ \times $$ 103 s, the pressure inside the cylinder is found to be 1.45 atm. If the rate constant of the reaction is 5 $$ \times $$ 10-4s-1, assuming ideal gas behaviour, the value of Y is ...............
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