JEE Mains · Maths · STD 11 - 6. permutation and combination
Let \(A\) be a matrix of order \(2 \times 2\), whose entries are from the set \(\{0,1,2,3,4,5\}\). If the sum of all the entries of \(A\) is a prime number \(p , 2< p <8\), then the number of such matrices \(A\) is
- A \(-190\)
- B \(190\)
- C \(-190\)
- D \(180\)
Answer & Solution
Correct Answer
(D) \(180\)
Step-by-step Solution
Detailed explanation
Let \(A=\left[\begin{array}{ll} a & b \\ c & d \end{array}\right] ; a , b , c , d \in\{0,1,2,3,4,5\}\) \(a+b+c+d=p, p \in\{3,5,7\}\) Case-\((i)\) \(a+b+c+d=3 ; a, b, c, d \in\{0,1,2,3\}\) No. of ways \(={ }^{3+4-1} C _{4-1}={ }^{6} C _{3}=56\;\;\;.........(1)\) Case-\((ii)\)…
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