CUET · MATHS · PYQ PAPER 2025
If the integral \(I=\int\left\{\log _e\left(\log _e x\right)^2+\frac{\alpha}{\log _e x}\right\} d x=x \log _e\left(\log _e x\right)^2+C\), where \(C\) is constant of integration. Then the value of \(\alpha\) is :
- A 0
- B -1
- C -2
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
\(\frac{d}{dx}\left[x \log _e\left(\log _e x\right)^2\right] = \log _e\left(\log _e x\right)^2 + x \cdot \frac{d}{dx}\left[\log _e\left(\log _e x\right)^2\right]\)…
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
- From the below-mentioned graph of shaded feasible region of a linear programming problem (LPP) with objective function
\(z=1.50 x+1.00 y\), the maximum value of \(z\) will be;-
CUET 2025 Medium - The probability distribution of a random variable X is given by
If \(a>0\), then \(P(0<X \leq 2)\) is equal toX 0 1 2 P(X) \(1-7 a^2\) \(\frac{1}{2} a+\frac{1}{4}\) \(a^2\) CUET 2025 Hard - In a 100 metre race, \(A\) beats \(B\) by 10 metres and \(C\) by 13 metres. By how many meters will \(B\) beat \(C\) in a 180 metre race?CUET 2023 Easy
- If \(|\vec{a}|=10,|\vec{b}|=2\) and \(\vec{a} \cdot \vec{b}=12\), then value of \(|\vec{a} \times \vec{b}|\) is :CUET 2025 Hard
- If the lines \(\frac{x-5}{7}=\frac{y+2}{-5}=\frac{z}{\lambda}\) and \(\frac{x}{1}=\frac{y}{2 \lambda}=\frac{z}{3}\) are perpendicular to each other, then \(\lambda\) is equal toCUET 2025 Medium
- If \(A=\left[\begin{array}{cc}3 & 2 a \\ 1 & 5\end{array}\right]\) and \(B=\left[\begin{array}{ll}2 & 3 \\ b & 5\end{array}\right]\) are singular matrices, then \(a+b\) is :CUET 2025 Medium
More PYQs from CUET
- \(C_2 H_5 OH \xrightarrow{X} C_2 H_5 Cl \xrightarrow{Y} C_2 H_5 CN\)
\(X\) and \(Y\) used in the above reaction are :CUET 2023 Hard - \(2 A+B \rightarrow A_2 B\)
For the above reaction, the rate law equation is, rate \(=k[A][ B ]^2\) with \(k=2.0 \times 10^{-6} mol^{-2} L^2 s^{-1}\). If the initial concentrations of \(A\) and \(B\) were \(0.1 mol L ^{-1}\) and \(0.2 mol L ^{-1}\), respectively, the rate of reaction after \([A]\) is reduced to 0.06 \(mol L ^{-1}\) will beCUET 2025 Easy - Match List-I with List-II
Choose the correct answer from the options given below:List-I (Function f(x)) List-II (Interval) (A) \(f(x)=x|x|\) (I) Decreases on \((0, \infty)\) (B) \(f(x)=x^2+2 x-5\) (II) Increases on \((3, \infty)\) (C) \(f(x)=x^2-6 x+9\) (III) Decreases on \((-\infty,-1)\) (D) \(f(x)=-x^2\) (IV) Increases on \((-\infty, \infty)\) CUET 2025 Medium - The area of the region bounded by parabola \(x^2=4 y\), straight line \(x=2\) and \(x\)-axis, isCUET 2025 Hard
- At a certain place on earth, the north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points \( 60^{\circ} \) below the horizontal. The horizontal component of the earth's magnetic field is measured to be 0.16 G. The magnitude of the earth's magnetic field at the location is:CUET 2023 Hard
- Which of the following hormones is produced under the condition of stress which stimulates glycogenolysis in the liver of human beings?CUET 2023 Easy