List of top Atmospheric Science Questions on Differential Equations asked in CUET (PG)

Match List I with List - II

List - I (Set Laws)List - II (Form)
A. Idempotent lawIII. \(A \cup A = A\)
B. Commutative lawI. \(A \cup B = B \cup A\)
C. Associative lawII. \(A \cap (B \cap C) = (A \cap B) \cap C\)
D. De-Morgan lawIV. \((A \cap B)' = A' \cup B'\)
The Laplace transform of function $f(t)=t^{3}$ is:

Match LIST-I with LIST-II 
LIST-I (Differential Equation) 
(A) \(\frac{dy}{dx} = 2x(y-x^2+1)\) 
(B) \(x\frac{dy}{dx} + 2(x^2+1)y=6\) 
(C) \((x^2+1)\frac{dy}{dx} + 2xy = x \sin x\) 
(D) \(x^3\frac{dy}{dx} + 2xy = 2x^2e^{x^2}\) 
LIST-II (Integrating Factor) 
(I) \(x^2\) 
(II) \(e^{-x^2}\) 
(III) \(x^2e^x\) 
(IV) \(1+x^2\) 
Choose the correct answer from the options given below:

The differential equation \( (1+3x^2y^2+\beta x^2y^4)dx + (2x^3y+2x^3y^3)dy = 0 \) will be exact differential equation if (assuming typos in original question are corrected as shown):