JEE Mains · Maths · STD 11 - 6. permutation and combination
The total number of positive integral solutions \(( x , y , z )\) such that \(xyz =24\) is
- A \(36\)
- B \(24\)
- C \(45\)
- D \(30\)
Answer & Solution
Correct Answer
(D) \(30\)
Step-by-step Solution
Detailed explanation
\(xyz =2^{3} \times 3^{1}\) Let \(x=2^{\alpha_{1}} \times 3^{\beta_{1}}\) \(y =2^{\alpha_{2}} \times 3^{\beta_{2}}\) \(z =2^{\alpha_{3}} \times 3^{\beta_{2}}\) Now \(\alpha_{1}+\alpha_{2}+\alpha_{3}=3\). No. of non-negative intergal \(sol ={ }^{5} C _{2}=10\)…
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