CUET · MATHS · PYQ PAPER 2025
Particular solution of the differential equation \(x\left(1+y^2\right) d x-y\left(1+x^2\right) d y=0\), given that \(y=0\) when \(x=1\), is:
- A \(\left(1+x^2\right)=2\left(1+y^2\right)\)
- B \(\left(1+y^2\right)=2\left(1+x^2\right)\)
- C \(\left(1+x^2\right)=4\left(1+y^2\right)\)
- D \(\left(1+y^2\right)=4\left(1+x^2\right)\)
Answer & Solution
Correct Answer
(A) \(\left(1+x^2\right)=2\left(1+y^2\right)\)
Step-by-step Solution
Detailed explanation
\(\frac{x}{1+x^2} d x = \frac{y}{1+y^2} d y\) \(\int \frac{x}{1+x^2} d x = \int \frac{y}{1+y^2} d y\) \(\frac{1}{2} \ln \left(1+x^2\right) = \frac{1}{2} \ln \left(1+y^2\right) + C_1\) \(\ln \left(1+x^2\right) = \ln \left(1+y^2\right) + C\) Given \(y=0\) when \(x=1\):…
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
- Area bounded by the curve \(y=\log x, x\)-axis, \(x=1\) and \(x=2\) in square units is:CUET 2023 Hard
- Which of the following statements are correct?
(A) \(\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1}\left(\frac{x+y}{1-x y}\right), x y<1\)
(B) \(\tan ^{-1} x+\tan ^{-1} y=\pi+\tan ^{-1}\left(\frac{x+y}{1-x y}\right), x y>1\)
(C) \(\sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}, x \in(-1,1)\)
(D) \(\tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}, x \in R\)
(E) \(\cos ^{-1}(-x)=-\cos ^{-1} x, x \in[-1,1]\)
Choose the correct answer from the options given below:CUET 2023 Medium - If X is a normal variate with mean 16 and standard deviation 4, then the value of the standard normal variate Z corresponding to X = 17 is :CUET 2025 Easy
- If \(y=A \sin x+B \cos x\), then which of the following is correct?CUET 2023 Easy
- The value/s of \(\lambda\) for which the given system of equations will have infinitely many solutions \(x+y-6 z=0 ; \lambda x-y+2 z=0 ;-3 x+\lambda y+2 z=0\), is/are:CUET 2023 Easy
- Match List-I with List-II
Choose the correct answer from the options given below:List - I (Differential Equations) List - II (Degree/Order) (A) Degree of the differential equation \(\frac{d^3 y}{d x^3}+2 \log x \cdot y=0\) (I) 3 (B) Order of the differential equation \(\frac{d^4 y}{d x^4}+\left(\frac{d y}{d x}\right)^4+x y=0\) (II) 2 (C) Degree of the differential equation \(\left(\frac{d^4 y}{d x^4}\right)^2+\left(\frac{d y}{d x}\right)^3+x^2 y=0\) (III) 1 (D) Order of the differential equation \(\frac{d^3 y}{d x^3}+y\left(\frac{d y}{d x}\right)^3=0\) (IV) 4 CUET 2025 Hard
More PYQs from CUET
- Mucosa-associated lymphoid tissue (MALT) is located within the lining of -CUET 2025 Easy
- Which reagent will distinguish Benzophenone from acetone ?CUET 2025 Hard
- Which of the following techniques are used for early diagnosis of diseases?
(A). Urine analysis
(B). PCR
(C). ELISA
(D). Recombinant DNA technology (RDT)
Choose the correct answer from the options given below:CUET 2025 Medium - A proton accelerated through potential difference V has de Broglie wavelength \(\lambda\). On doubling the potential, the de Broglie wavelength of the proton :CUET 2024 Medium
- The probability distribution of a random variable X is given below:
x -5 -4 -3 -2 -1 0 1 2 3 4 5 P(X) p 2p 3p 4p 5p 7p 8p 9p 10p 11p 12p CUET 2023 Medium - The father of ecology in India is:CUET 2023 Medium