JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of matrices of order \(3 \times 3\), whose entries are either \(0\) or \(1\) and the sum of all the entries is a prime number, is\(....\)
- A \(282\)
- B \(283\)
- C \(284\)
- D \(281\)
Answer & Solution
Correct Answer
(A) \(282\)
Step-by-step Solution
Detailed explanation
\(A =\left[\begin{array}{lll} a _{11} & a _{12} & a _{13} \\ a _{21} & a _{22} & a _{23} \\ a _{31} & a _{32} & a _{33}\end{array}\right] a _{ ij } \in\{0,1\}\) \(\sum a_{i j}=2,3,5,7\) Total matrix \(={ }^{9} C _{2}+{ }^{9} C _{3}+{ }^{9} C _{5}+{ }^{9} C _{7}\) \(=282\)
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