JEE Main 2017 · 8 Apr · Shift 1 · Mathematics Q77

MathematicsSingle correct+4 / -1Question 77 of 90

The curve satisfying the differential equation, $y\,dx-(x+3y^2)\,dy=0$ and passing through the point (1, 1), also passes through the point :

\left(\dfrac14,-\dfrac12\right)

\left(-\dfrac13,\dfrac13\right)

\left(\dfrac13,-\dfrac13\right)

\left(\dfrac14,\dfrac12\right)

Answer and worked solution

Official answer: B

$\dfrac{y\,dx-x\,dy}{y^2}=3\,dy$ gives $\dfrac xy=3y+c$ . Through (1, 1), $c=-2$ , so $x=3y^2-2y$ . At $y=\frac13$ : $x=\frac13-\frac23=-\frac13$ .

JEE Main 2017 · 8 Apr · Shift 1, Mathematics question 77