CUET · MATHS · PYQ PAPER 2023
The maximum value of \(\left( \frac{1}{x} \right)^x\) is :
- A \(e\)
- B \(e^e\)
- C \(\frac{1}{e}\)
- D \(\left( \frac{1}{e} \right)^{\frac{1}{e}}\)
Answer & Solution
Correct Answer
(D) \(\left( \frac{1}{e} \right)^{\frac{1}{e}}\)
Step-by-step Solution
Detailed explanation
Let \(f(x) = \left( \frac{1}{x} \right)^x = x^{-x}\). Take \(\ln f(x)\): \(\ln f(x) = -x \ln x\). Differentiate: \(\frac{f'(x)}{f(x)} = -(\ln x + 1)\). Set \(f'(x) = 0 \implies -(\ln x + 1) = 0\). \(\ln x = -1 \implies x = e^{-1} = \frac{1}{e}\). Maximum value:…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from MATHS
- The area enclosed between \(y^2=4 x, x=1, x=4\) in first quadrant is :CUET 2023 Medium
- If the area bounded by the curve \(y^2 = 16x\) and the line \(y = mx\) is \(\frac{2}{3}\) sq. units, then the value of m is:CUET 2023 Hard
- If \(x, y, z\) are non-zero numbers, then the inverse of matrix \(\mathrm{A}=\left[\begin{array}{lll}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{array}\right]\) isCUET 2025 Hard
- Three pipes A, B & C fill a tank in 3 hours working simultaneously. The pipe C is twice as faster as B and B is twice as fast as A . The time taken by pipe A alone to fill the tank is :CUET 2025 Medium
- The value of a washing machine purchased two years ago depreciates at the annual rate of 10%. If its present value is ₹ 50,000, then its value after two years will be :CUET 2023 Easy
- If \(x=a t^2, y=2 a t\); then \(\frac{d^2 y}{d x^2}\) is equal toCUET 2025 Hard
More PYQs from CUET
- The area (in sq., units) of the region bounded by the parabola \(y^2=4 x\) and the line \(x=1\) is:CUET 2025 Easy
- Two parallel conductors each carrying a current of 10 mA in opposite directions are placed at a distance 10 cm apart. The force per unit length between two conductors isCUET 2025 Easy
- The female reproductive system consists of :
(A) Ovaries
(B) External genitalia
(C) Cervix and vagina
(D) Oviducts and uterus
Choose the most appropriate answer from the options given below:CUET 2025 Hard - Any feasible solution which optimizes the objective function is called:CUET 2023 Hard
- In an electrical circuit, the three resistors of 3 \( \Omega \), 6 \( \Omega \) and 9 \( \Omega \) are connected in series. The voltage drop across 3 \( \Omega \) is 5 V. The voltage drop across the combination isCUET 2025 Medium
- Match List-I with List-II
List-I (Potential difference across the terminal of a battery) List-II (Situations) (A) V = E (I) Cell is being charged (B) V = 0 (II) The internal resistance of a cell is zero (C) V = E - ir (III) cell is short-circuited (D) V = E + ir (IV) current is being drawn from a cell
Choose the correct answer from the options given below :CUET 2025 Easy