Verified Solution • 2025–26 Session moderate

QJEEM23Ma982b: JEE Main 2023 Mathematics - Class 12 JEEM23Ma982b Solution: Let N denote the sum of the numbers obtained when two dice are…

Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that {2^N} < N! is mn{m \over n} , where m and n are coprime, then 4m−3n4m-3n is equal to :

Multiple Choice Options

  • A 12
  • B 6
  • C 8
  • D 10

Step-by-Step Verified Solution

NN denote the sum of the numbers obtained when two dice are rolled.

Such that 2^N < N !

 i.e., 4≤N≤12 i.e., N∈{4,5,6,…12}\text { i.e., } 4 \leq N \leq 12 \text { i.e., } N \in\{4,5,6, \ldots 12\}

Now, P(N=2)+P(N=3)=136+236=336=112P(N=2)+P(N=3)=\frac{1}{36}+\frac{2}{36}=\frac{3}{36}=\frac{1}{12}

So, required probability =1−112=1112=mn=1-\frac{1}{12}=\frac{11}{12}=\frac{m}{n}

4m−3n=4×11−3×12=44−36=84 m-3 n=4 \times 11-3 \times 12=44-36=8

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