CUET · MATHS · PYQ PAPER 2025

The general solution of the differential equation \(\frac{d y}{d x}=e^{x+y}\) is :

A \(e^x+e^y=C\), where \(C\) is an arbitrary constant
B \(e^x+e^{-y}=C\), where C is an arbitrary constant
C \(e^x-e^{-y}=C\), where C is an arbitrary constant
D \(e^x-e^y=C\), where C is an arbitrary constant

Verified Solution

Answer & Solution

Correct Answer

(B) \(e^x+e^{-y}=C\), where C is an arbitrary constant

Step-by-step Solution

Detailed explanation

\(e^{-y} dy = e^x dx\) \(\int e^{-y} dy = \int e^x dx\) \(-e^{-y} = e^x + C'\) \(e^x + e^{-y} = -C'\) \(e^x + e^{-y} = C\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match List-I with List-II

List-I	List-II
(A) Angle between \(\hat{i}-2 \hat{j}+3 \hat{k}\) and \(2 \hat{i}+\hat{j}\)	(I) \(\cos ^{-1}\left(\frac{2}{\sqrt{18}}\right)\)
(B) Angle between \(\hat{i}+\hat{j}+2 \hat{k}\) and \(2 \hat{i}+2 \hat{j}+4 \hat{k}\)	(II) 0
(C) Angle between \(2 \hat{i}-\hat{j}+\hat{k}\) and \(\hat{i}+\hat{j}+\hat{k}\)	(III) \(90^{\circ}\)
(D) Angle between \(\hat{i}+\hat{j}-\hat{k}\) and \(\hat{i}+\hat{j}+\hat{k}\)	(IV) \(\cos ^{-1}\left(\frac{1}{3}\right)\)

Choose the correct answer from the options given below:

CUET 2023 Easy

Match List-I with List-II
List - I List - II
(A) Point of minima of \(f(x)=|x+1|\) (I) 1
(B) Minimum value of \(f(x)=|x|\) (II) -1
(C) Maximum value of \(f(x)=1-x^2\) (III) 2
(D) Minimum value of \(f(x)=2+\sin ^2 x\) (IV) 0
Choose the correct answer from the options given below :

CUET 2025 Medium

Explore more questions on app

From CUET

Match List I with List II

LIST I	LIST II
A. \(\frac{d y}{d x}=e^{x-y}+x^2 e^{-y}\)	I. Linear Differential Equation of type \(\frac{d y}{d x}+P y=Q\)
B. \(\frac{d y}{d x}-2 y=\cos 3 x\)	II. Homogeneous Differential Equation
C. \(x^2 \frac{d y}{d x}=x^2-2 y^2+x y\)	III. Linear Differential Equation of type \(\frac{d x}{d y}+P x=Q\)
D. \(\left(x+2 y^3\right) \frac{d y}{d x}=y\)	IV. Variable separable

Choose the correct answer from the options given below:

CUET 2023 Easy

Explore more questions on app

LIST I	LIST II
A. Soda Water	I. A solution of gas in gas
B. Sugar Solution	II. A solution of solid in solid
C. German Silver	III. A solution of solid in liquid
D. Air	IV. A solution of gas in liquid

List - I	List - II
(A) Point of minima of \(f(x)=\|x+1\|\)	(I) 1
(B) Minimum value of \(f(x)=\|x\|\)	(II) -1
(C) Maximum value of \(f(x)=1-x^2\)	(III) 2
(D) Minimum value of \(f(x)=2+\sin ^2 x\)	(IV) 0