jee-main 2024 Q62

jee-main · India · session1_27jan_shift2 Indices and Surds Number-Theoretic Reasoning with Indices

Let $\alpha = \frac { ( 4 ! ) ! } { ( 4 ! ) ^ { 3 ! } }$ and $\beta = \frac { ( 5 ! ) ! } { ( 5 ! ) ^ { 4 ! } }$. Then :
(1) $\alpha \in \mathrm { N }$ and $\beta \notin \mathrm { N }$
(2) $\alpha \notin \mathrm { N }$ and $\beta \in \mathrm { N }$
(3) $\alpha \in \mathrm { N }$ and $\beta \in \mathrm { N }$
(4) $\alpha \notin \mathrm { N }$ and $\beta \notin \mathrm { N }$

Let $\alpha = \frac { ( 4 ! ) ! } { ( 4 ! ) ^ { 3 ! } }$ and $\beta = \frac { ( 5 ! ) ! } { ( 5 ! ) ^ { 4 ! } }$. Then :\\
(1) $\alpha \in \mathrm { N }$ and $\beta \notin \mathrm { N }$\\
(2) $\alpha \notin \mathrm { N }$ and $\beta \in \mathrm { N }$\\
(3) $\alpha \in \mathrm { N }$ and $\beta \in \mathrm { N }$\\
(4) $\alpha \notin \mathrm { N }$ and $\beta \notin \mathrm { N }$

Paper Questions

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