1
MHT CET 2021 23rd September Evening Shift
+2
-0

If the slopes of the lines given by the equation $$a x^2+2 h x y+b y^2=0$$ are in the ratio $$5: 3$$, then the ratio $$h^2: a b=$$

A
$$15: 16$$
B
$$5: 3$$
C
$$3: 5$$
D
$$16: 15$$
2
MHT CET 2021 23th September Morning Shift
+2
-0

The equation of line, where length of the perpendicular segment from origin to the line is 4 and the inclination of this perpendicular segment with the positive direction of X-axis is 30$$^\circ$$, is

A
$$x+\sqrt{3} y=8$$
B
$$x-\sqrt{3} y=8$$
C
$$\sqrt{3x} -y=8$$
D
$$\sqrt{3x} +y=8$$
3
MHT CET 2021 23th September Morning Shift
+2
-0

If two lines represented by $$a x^2+2 h x y+b y^2=0$$ makes angles $$\alpha$$ and $$\beta$$ with positive direction of $$\mathrm{X}$$-axis, then $$\tan (\alpha+\beta)=$$

A
$$\frac{2 h}{b-a}$$
B
$$\frac{2 h}{a-b}$$
C
$$\frac{h}{a+b}$$
D
$$\frac{2 h}{a+b}$$
4
MHT CET 2021 23th September Morning Shift
+2
-0

The combined equation of a pair of lines passing through the origin and inclined at $$60^{\circ}$$ and $$30=$$ respectively with $$x$$-axis is

A
$$\sqrt{3}\left(x^2+y^2\right)=2 x y$$
B
$$\sqrt{3}\left(x^2+y^2\right)=4 x y$$
C
$$4\left(x^2+y^2\right)=\sqrt{3} x y$$
D
$$2\left(x^2+y^2\right)=\sqrt{3} x y$$
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Medical
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