1
MHT CET 2025 23rd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $x \frac{\mathrm{~d} y}{\mathrm{~d} x}=y(\log y-\log x+1)$, then the solution of the equation is

A
$\log \frac{x}{y}=\mathrm{c} y$, where c is the constant of integration
B
$\log \frac{y}{x}=\mathrm{c} y$, where c is the constant of integration
C
$\log \frac{x}{y}=\mathrm{c} x$, where c is the constant of integration
D
$\log \frac{y}{x}=\mathrm{cx}$, where c is the constant of integration
2
MHT CET 2025 23rd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The order and degree of the differential equation $\sqrt{\frac{\mathrm{d} y}{\mathrm{~d} x}}-4 \frac{\mathrm{~d} y}{\mathrm{~d} x}-7 x=0$ is respectively

A
1,2
B
2,1
C
2,2
D
3,1
3
MHT CET 2025 23rd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The differential equation of all circles touching the Y -axis at the origin and centre on the X -axis is

A
$x^2+y^2+2 x y \frac{\mathrm{~d} y}{\mathrm{~d} x}=0$
B
$x^2-y^2+2 x y \frac{\mathrm{~d} y}{\mathrm{~d} x}=0$
C
$2 x^2+y^2+x y \frac{\mathrm{~d} y}{\mathrm{~d} x}=0$
D
$x^2-2 y^2+2 x y \frac{\mathrm{~d} y}{\mathrm{~d} x}=0$
4
MHT CET 2025 23rd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The area bounded by the curve $x^2=8 y$ and the straight line $x-8 y+2=0$ is

A
$\frac{9}{8}$ sq. units
B
$\frac{15}{16}$ sq. units
C
$\frac{9}{16}$ sq. units
D
$\frac{15}{8}$ sq. units
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