JEE Mains · Maths · STD 11 - 6. permutation and combination
Let \(A=\left[a_{i j}\right], a_{i j} \in Z \cap[0,4], 1 \leq i, j \leq 2\). The number of matrices \(A\) such that the sum of all entries is a prime number \(p \in(2,13)\) is \(........\).
- A \(203\)
- B \(202\)
- C \(201\)
- D \(204\)
Answer & Solution
Correct Answer
(D) \(204\)
Step-by-step Solution
Detailed explanation
As given \(a+b+c+d=3\) or \(5\) or \(7\) or \(11\) \(\text { if sum }=3\) \(\left(1+x+x^2+\ldots++x^4\right)^4 \rightarrow x^3\) \(\left(1-x^5\right)^4(1-x)^{-4} \rightarrow x^3\) \(\therefore{ }^{4+3-1} C_3={ }^6 C_3=20\) If \(\operatorname{sum}=5\)…
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