CUET · MATHS · PYQ PAPER 2023
Match List - I with List - II.
| LIST - I | LIST - II |
| (A) \(x^x\) has a stationary point at \(x\) equal to | (I) \(e\) |
| (B) For \(x>0\), minimum value of \(x^x\) | (II) \(1 / e\) |
| (C) The greatest value of \(\left(\frac{1}{x}\right)^x\) | (III) \(e^{1 / e}\) |
| (D) The stationary point of \(\frac{\log x}{x}\) for \(x\), where \(x>0\), is | (IV) \(e^{-1 / e}\) |
- A (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
- B (A)-(II), (B)-(IV), (C)-(III), (D)-(I)
- C (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
- D (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
Answer & Solution
Correct Answer
(B) (A)-(II), (B)-(IV), (C)-(III), (D)-(I)
Step-by-step Solution
Detailed explanation
(A) \(x^x\) has a stationary point at \(x\) equal to \(y = x^x \implies \frac{dy}{dx} = x^x (\log x + 1)\) \(\frac{dy}{dx} = 0 \implies \log x + 1 = 0 \implies \log x = -1\) \(x = e^{-1} = 1/e\) (B) For \(x>0\), minimum value of \(x^x\) Stationary point at \(x = 1/e\) Minimum…
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