Problem

Problem

| Column I | | Column II | |-----|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----|---------------------------------| | (A) | If log⁡1/x{2(x−2)(x+1)(x−5)}≥1\log_{1/x} \left\{ \frac{2(x-2)}{(x+1)(x-5)} \right\} \ge 1 , then xx can belong to | (p) | (0,13]\left( 0, \frac{1}{3} \right] | | (B) | If log⁡3x−log⁡32x≤32log⁡(1/2)24\log_3 x - \log_3^2 x \le \frac{3}{2} \log_{(1/2)\sqrt{2}} 4 , then xx can belong to | (q) | [1,2][1, 2] | | (C) | If log⁡1/2(4−x)≥log⁡1/22−log⁡1/2(x−1)\log_{1/2}(4-x) \ge \log_{1/2} 2 - \log_{1/2}(x-1) , then xx belongs to | (r) | [3,4][3, 4] | | (D) | Let α\alpha and β\beta are the roots of the quadratic equation (λ2−3λ+4)x2−4(2λ−1)x+16=0(\lambda^2 - 3\lambda + 4)x^2 - 4(2\lambda - 1)x + 16 = 0 , if α\alpha and β\beta satisfy the condition β>1>α\beta > 1 > \alpha , then pp can lie in | (s) | (3,8)(3, 8) |

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