If x N and ^ x C _ i , ^ x ^ 2 C _ i and x^ 3 C_ i , (i = 1, 2, 3) are binomial…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
If x \(\in\) N and \({ }^{\mathrm{x}} \mathrm{C}_{\mathrm{i}},{ }^{\mathrm{x}}{ }^{2} \mathrm{C}_{\mathrm{i}}\) and \(x^{3} C_{i},\)(i = 1, 2, 3) are binomial coefficients, then
12\[\left|\begin{array}{ccc} { }^{\mathrm{x}} \mathrm{C}_{1} & { }^{\mathrm{x}} \mathrm{C}_{2} & { }^{\mathrm{x}} \mathrm{C}_{3} \\ \mathrm{x}^{2} \mathrm{C}_{1} & \mathrm{x}^{2} \mathrm{C}_{2} & \mathrm{x}^{2} \mathrm{C}_{3} \\ \mathrm{x}^{3} \mathrm{C}_{1} & \mathrm{x}^{3} \mathrm{C}_{2} & \mathrm{x}^{3} \mathrm{C}_{3} \end{array}\right|\] is divisible by
12\[\left|\begin{array}{ccc} { }^{\mathrm{x}} \mathrm{C}_{1} & { }^{\mathrm{x}} \mathrm{C}_{2} & { }^{\mathrm{x}} \mathrm{C}_{3} \\ \mathrm{x}^{2} \mathrm{C}_{1} & \mathrm{x}^{2} \mathrm{C}_{2} & \mathrm{x}^{2} \mathrm{C}_{3} \\ \mathrm{x}^{3} \mathrm{C}_{1} & \mathrm{x}^{3} \mathrm{C}_{2} & \mathrm{x}^{3} \mathrm{C}_{3} \end{array}\right|\] is divisible by
- x3
- x6
- x9
- x12
Answer
(A) x 3, (B) x 6, (C) x 9
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