1
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1

Assuming $$1 \,\mu \mathrm{g}$$ of trace radioactive element X with a half life of 30 years is absorbed by a growing tree. The amount of X remaining in the tree after 100 years is ______ $$\times\, 10^{-1} \mu \mathrm{g}$$.

[Given : ln 10 = 2.303; log 2 = 0.30]

2
JEE Main 2022 (Online) 29th July Morning Shift
Numerical
+4
-1

The reaction between X and Y is first order with respect to X and zero order with respect to Y.

Experiment $${{[X]} \over {mol\,{L^{ - 1}}}}$$ $${{[Y]} \over {mol\,{L^{ - 1}}}}$$ $${{Initial\,rate} \over {mol\,{L^{ - 1}}\,{{\min }^{ - 1}}}}$$
I 0.1 0.1 $$2 \times {10^{ - 3}}$$
I L 0.2 $$4 \times {10^{ - 3}}$$
III 0.4 0.4 $$M \times {10^{ - 3}}$$
IV 0.1 0.2 $$2 \times {10^{ - 3}}$$

Examine the data of table and calculate ratio of numerical values of M and L. (Nearest Integer)

3
JEE Main 2022 (Online) 28th July Evening Shift
Numerical
+4
-1

For a reaction, given below is the graph of $$\ln k$$ vs $${1 \over T}$$. The activation energy for the reaction is equal to ____________ $$\mathrm{cal} \,\mathrm{mol}^{-1}$$. (nearest integer)

(Given : $$\mathrm{R}=2 \,\mathrm{cal} \,\mathrm{K}^{-1} \,\mathrm{~mol}^{-1}$$ )

4
JEE Main 2022 (Online) 28th July Morning Shift
Numerical
+4
-1

For the given first order reaction

$$\mathrm{A} \rightarrow \mathrm{B}$$

the half life of the reaction is $$0.3010 \mathrm{~min}$$. The ratio of the initial concentration of reactant to the concentration of reactant at time $$2.0 \mathrm{~min}$$ will be equal to ___________. (Nearest integer)

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