JEE Main 2023 (Online) 31st January Evening Shift | Permutations and Combinations Question 41 | Mathematics

Let $\mathrm{A}=\left[\mathrm{a}_{i j}\right], \mathrm{a}_{i j} \in \mathbb{Z} \cap[0,4], 1 \leq i, j \leq 2$.

The number of matrices A such that the sum of all entries is a prime number $\mathrm{p} \in(2,13)$ is __________.

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JEE Main 2023 (Online) 31st January Evening Shift

Numerical

-1

If ${ }^{2 n+1} \mathrm{P}_{n-1}:{ }^{2 n-1} \mathrm{P}_{n}=11: 21$,

then $n^{2}+n+15$ is equal to :

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JEE Main 2023 (Online) 31st January Morning Shift

Numerical

-1

Let 5 digit numbers be constructed using the digits $$0,2,3,4,7,9$$ with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is __________.

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