Competishun Header
Competishun
Contact Us
Back

Report Issue

JEE Main 2026
02 - 04 2026 S2
Question
Let $x=x(y)$ be the solution of the differential equation $2 y^2 \frac{\mathrm{~d} x}{\mathrm{~d} y}-2 x y+x^2=0, y>1, x(\mathrm{e})=\mathrm{e}$. Then $x\left(\mathrm{e}^2\right)$ is equal to :
Select the correct option:
A
$\frac{3}{2} \mathrm{e}^2$
B
$\frac{2}{3} \mathrm{e}^2$
C
$e^2$
D
$2 \mathrm{e}^2$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Question Tags
JEE Main
Mathematics
Easy
Start Preparing for JEE with Competishun
YouTube
Books
App
Tests
Filters 0
JEE Main
JEE Advance
Easy
Medium
Hard
Showing 18 questions
QJEE MAIN_2026
The rain drop of mass 1 g , starts with zero velocity from a height of 1 km . It...
JEE MainPhysicsMedium
View Solution→
QJEE MAIN_2026
The potential energy of a particle changes with distance x from a fixed origin as $V=\frac{A \sqrt{x}}{x+B}$, where A and...
JEE MainPhysicsMedium
View Solution→
QJEE MAIN_2026
The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length I and diameter $d$. The...
JEE MainPhysicsMedium
View Solution→
Q JEE Main 20262026
The number of points in the interval [2,4], at which the function $f(x)=\left[x^2-x-\frac{1}{2}\right]$, where [-] denotes the greatest integer function,...
JEE MainMathematicsEasy
View Solution→
Q JEE Main 20262026
If the area of the region bounded by $16 x^2-9 y^2=144$ and $8 x-3 y=24$ is A , then $...
JEE MainMathematicsEasy
View Solution→
QJEE Main 20262026
Let A be the point $(3,0)$ and circles with variable diameter AB touch the circle $x^2+y^2=36$ internally. Let the curve...
JEE MainMathematicsEasy
View Solution→
QJEE Main 20262026
Consider the matrices $\mathrm{A}=\left[\begin{array}{ll}2 & -2 \\ 4 & -2\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{ll}3 & 9 \\ 1 & 3\end{array}\right]$. If matrices...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN_2026
A circular loop of radius 20 cm and resistance $2 \Omega$ is placed in a time varying magnetic field $...
JEE MainPhysicsEasy
View Solution→
QJee Main 20262026
The number of points, at which the function $f(x)=\max \left\{6 x, 2+3 x^2\right\}+|x-1| \cos \left|x^2-\frac{1}{4}\right|, x \in(-\pi, \pi)$, is not...
JEE MainMathematicsMedium
View Solution→
QJEE Main 20262026
Let $\mathrm{A}=\{2,3,4,5,6\}$. Let R be a relation on the set $\mathrm{A} \times \mathrm{A}$ given by $(x, y) \mathrm{R}(z, w)$ if...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN_2026
When an external resistance of $5 \Omega$ is connected across terminals of a cell, a current of 0.25 A flows...
JEE MainPhysicsEasy
View Solution→
QJee Main 20262026
Let $\overrightarrow{a_k}=\left(\tan \theta_k\right) \hat{i}+\hat{j}$ and $\overrightarrow{b_k}=\hat{i}-\left(\cot \theta_k\right) \hat{j}$, where $\theta_k=\frac{2^{k-1} \pi}{2^n+1}$, for some $n \in \mathbb{N}, n>5$. Then the value...
JEE MainMathematicsHard
View Solution→
QJEE MAIN_2026
A series LCR circuit with R $=20 \Omega, \mathrm{~L}=1.6 \mathrm{H}$ and $\mathrm{C}=40 \mu \mathrm{~F}$ is connected to a variable frequency...
JEE MainPhysicsEasy
View Solution→
Q JEE Main 20262026
Let $x=x(y)$ be the solution of the differential equation $2 y^2 \frac{\mathrm{~d} x}{\mathrm{~d} y}-2 x y+x^2=0, y>1, x(\mathrm{e})=\mathrm{e}$. Then $x\left(\mathrm{e}^2\right)$...
JEE MainMathematicsEasy
View Solution→
QJee Main 20262026
If $\mathrm{A}=\frac{\sin 3^{\circ}}{\cos 9^{\circ}}+\frac{\sin 9^{\circ}}{\cos 27^{\circ}}+\frac{\sin 27^{\circ}}{\cos 81^{\circ}}$ and $\mathrm{B}=\tan 81^{\circ}-\tan 3^{\circ}$, then $\frac{\mathrm{B}}{\mathrm{A}}$ is equal to $\_\_\_\_$ .
JEE MainMathematicsMedium
View Solution→
QJEE MAIN_2026
The heat extracted out of x gram of water initially at $50^{\circ} \mathrm{C}$ to cool it down to $0^{\circ} \mathrm{C}$...
JEE MainPhysicsEasy
View Solution→
Q JEE Main 20262026
Let $f(x)=\int\left(\frac{x^2+2 x-15}{x^2}\right) \mathrm{d} x$. If $f(4)=14 \log _e(3)$ and $f(7)=\log _e\left(2^\alpha-3^\beta\right), \alpha, \beta \in \mathbf{N}$, then $\alpha+\beta$ is equal...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN_2026
A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of...
JEE MainPhysicsEasy
View Solution→
Check this project | Best Developer Portfolio