CUET · MATHS · PYQ PAPER 2025
\(\frac{d^2}{d x^2}\left(\operatorname{det}\left[\begin{array}{cc}x^3 & x \\ 2 & e^x\end{array}\right]\right)\) equals
- A \(\left(x e^x\left(x^2-6 x+6\right)\right.\)
- B \(\left(x^2 e^x\left(x^2+6 x+6\right)\right.\)
- C \(\left(x e^x\left(x^2+6 x+6\right)\right.\)
- D \(\left(e^x\left(x^2-6 x+6\right)\right.\)
Answer & Solution
Correct Answer
(C) \(\left(x e^x\left(x^2+6 x+6\right)\right.\)
Step-by-step Solution
Detailed explanation
\( \operatorname{det}\left[\begin{array}{cc}x^3 & x \\ 2 & e^x\end{array}\right] = x^3 e^x - 2x \) \( \frac{d}{dx}(x^3 e^x - 2x) = 3x^2 e^x + x^3 e^x - 2 \) \( \frac{d^2}{dx^2}(x^3 e^x - 2x) = \frac{d}{dx}(3x^2 e^x + x^3 e^x - 2) \)…
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 mean of numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is:CUET 2023 Easy
- Objective function \(z=200 x+500 y\), subject to the constraints
\(x+2 y \geq 10, \quad 3 x+4 y \leq 24, \quad x \geq 0, \quad y \geq 0\),
the minimum value of \(z\) is :CUET 2023 Medium - The number of arbitrary constants in the general solution of a differential equation of order 4 and degree 1 isCUET 2025 Medium
- There are two values of a for which the determinant, \(\Delta = \begin{vmatrix} 1 & -2 & 5 \\ 0 & a & -1 \\ 0 & 4 & 2a \end{vmatrix} = 86\), then the sum of these values of a is:CUET 2023 Easy
- The solution of a LPP with basic feasible solutions (0,0), (10,0), (0,20), (10, 15) and objective function Max Z = 2x + 3y is:CUET 2023 Medium
- If A is an invertible symmetric matrix, then \(A^{-1}\) isCUET 2025 Hard
More PYQs from CUET
- Mr. 'X' wishes to purchase a house for ₹ \(49,65,000\) with a down payment of ₹ \(15,00,000\) and balance amount in EMI for 25 years. If bank charges \(6 \%\) per annum compounded monthly. Then the EMI is: [Given that \((1.005)^{300}=4.4650\) ]CUET 2025 Hard
- Consider the following L.P.P minimize \(z=x-7 y+190\) subject to \(x+y \leq 8, x+y \geq 4, x \leq 5, y \leq 5\) and \(x, y \geq 0\). Then which of the following is/are true?
(A) It's feasible region is unbounded
(B) It's feasible region is bounded
(C) It's feasible region has 5 corner polnts
(D) It's feasible region has 6 corner polnts
Choose the correct answer from the options given below :CUET 2025 Medium - If \(\vec{a}, \vec{b}\), and \(\vec{c}\) are unit vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\), then value of \(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}\) is :CUET 2023 Hard
- The maximum value of \(y=x^3-3 x\) is :CUET 2023 Hard
- Which of the following is an example of a minimum boiling azeotrope?CUET 2023 Hard
- For a parallel plate capacitor having plate area \( 1.13 \times 10^3 \, m^2 \) and separation between plates 0.5 cm, the capacitance isCUET 2025 Easy