1
MHT CET 2021 22th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

Solution of the differential equation $$\mathrm{y'=\frac{(x^2+y^2)}{xy}}$$, where y(1) = $$-$$2 is given by

A
$$y^2=4 x^2 \log x^2+x^2$$
B
$$y^2=x^2 \log x-x^2$$
C
$$y^2=x \log x^2+4 x^2$$
D
$$\mathrm{y}^2=\mathrm{x}^2 \log \mathrm{x}^2+4 \mathrm{x}^2$$
2
MHT CET 2021 22th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The differential equation of all family of lines $$y=m x+\frac{4}{m}$$ obtained by eliminating the arbitrary constant $$\mathrm{m}$$ is

A
$$y\left(\frac{d y}{d x}\right)=4$$
B
$$x\left(\frac{d y}{d x}\right)^2+y\left(\frac{d y}{d x}\right)+4=0$$
C
$$x\left(\frac{d y}{d x}\right)+4=0$$
D
$$x\left(\frac{d y}{d x}\right)^2-y\left(\frac{d y}{d x}\right)+4=0$$
3
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\text{I} : y^{\prime}=\frac{y+x}{x} ; \quad \text { II }: y^{\prime}=\frac{x^2+y}{x^3} ; \quad \text { III }: y^{\prime}=\frac{2 x y}{y^2-x^2}$$

S1 : Differential equations given by I and II are homogeneous differential equations.

S2 : Differential equations given by II and III are homogeneous differential equations.

S3 : Differential equations given by I and III are homogeneous differential equations.

A
only S1 is valid
B
both S1 and S2 are valid
C
only S3 is valid
D
only S2 is valid.
4
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The differential equation of the family of circles touching $$y$$-axis at the origin is

A
$$x^2-y^2-2 x y \frac{d y}{d x}=0$$
B
$$x^2-y^2+2 x y \frac{d y}{d x}=0$$
C
$$x^2+y^2-2 x y \frac{d y}{d x}=0$$
D
$$x^2+y^2+2 x y \frac{d y}{d x}=0$$
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