CUET · MATHS · PYQ PAPER 2025
Given differential equation,
\(\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y\)
then which of the following is/are true?
(A) Integrating factor \(=\tan ^{-1} x\)
(B) Integrating factor \(=\tan ^{-1} y\)
(C) Integrating factor \(=e^{\tan ^{-1} y}\)
(D) Degree \(=1\)
Choose the correct answer from the options given below :
- A (B) and (D) only
- B (A) only
- C (C) only
- D (C) and (D) only
Answer & Solution
Correct Answer
(D) (C) and (D) only
Step-by-step Solution
Detailed explanation
\( \left(1+y^2\right) \frac{dx}{dy} = \tan ^{-1} y-x \) \( \frac{dx}{dy} + \frac{1}{1+y^2} x = \frac{\tan ^{-1} y}{1+y^2} \) Integrating Factor \( = e^{\int \frac{1}{1+y^2} dy} = e^{\tan ^{-1} y} \) Degree \( = 1 \)
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 particular solution of the differential equation \(\left[\log \left(\frac{d y}{d x}\right)=3 x+4 y\right.\) satisfying \(y=0\) when \(x=0\) is :CUET 2025 Hard
- Consider the following L.P.P.
Max. \(z=5 x+2 y\), subject to \(-2 x-3 y \leq-6, x-2 y \leq 2,3 x+2 y \leq 12,-3 x+2 y \leq 3\) and \(x, y \geq 0\) thenCUET 2025 Easy - If \(A=\left[\begin{array}{cc}-2 & 3 \\ k & 4\end{array}\right]\) is a singular matrix then value of \(k\) is :CUET 2023 Hard
- If the objective function \(z=p x+q y\) has its maximum value at the points \((2,1)\) and \((0,6)\), then the relationship between \(p\) and \(q\) is :CUET 2025 Medium
- If the relation \(R: A \rightarrow B\), where \(A=\{2,3,4\}\) and \(B=\{3,4,5\}\) is defined by \(R=\{(x, y): x < y, x \in A, y \in B\}\), thenCUET 2023 Easy
- The value of \(x\) for which the slope of the curve \(y=-x^3+3 x^2+x^2+9 x-27\) is maximum, is:CUET 2023 Hard
More PYQs from CUET
- Exposure of chloroform in air in the presence of sunlight releases a gas which is poisonous. Identify the gas.CUET 2023 Hard
- Each resistor shown in figure has a resistance of \( 20 \, \Omega \) and the battery has an emf of 12 V. The current supplied by the battery is
CUET 2025 Easy - \(\int \frac{d x}{\sqrt{5-x}}=\) (where \(C\) is arbitrary constant.)CUET 2023 Easy
- An iron ring of relative permeability \( \mu_r \) is introduced inside a toroidal solenoid having n turns per meter. If the current in the solenoid is I, then the magnetic field in the ring is :CUET 2025 Easy
- For \(x \in R\), if \(f(x)=-(x-1)^2+2\), then
(A) f is an increasing function on \((-\infty, 1)\)
(B) ƒ has no critical points
(C) ƒ has a maximum value at x = 1
(D) ƒ has a minimum value at x = 1
Choose the correct answer from the options given below:CUET 2025 Hard - A current I flows in a circular loop of radius R. The magnetic field at a point on its axis at distance r from the center of the loop isCUET 2025 Medium