1
JEE Main 2023 (Online) 6th April Morning Shift
+4
-1

The straight lines $$\mathrm{l_{1}}$$ and $$\mathrm{l_{2}}$$ pass through the origin and trisect the line segment of the line L: $$9 x+5 y=45$$ between the axes. If $$\mathrm{m}_{1}$$ and $$\mathrm{m}_{2}$$ are the slopes of the lines $$\mathrm{l_{1}}$$ and $$\mathrm{l_{2}}$$, then the point of intersection of the line $$\mathrm{y=\left(m_{1}+m_{2}\right)}x$$ with L lies on :

A
$$6 x-y=15$$
B
$$6 x+y=10$$
C
$$\mathrm{y}-x=5$$
D
$$y-2 x=5$$
2
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1

The combined equation of the two lines $$ax+by+c=0$$ and $$a'x+b'y+c'=0$$ can be written as

$$(ax+by+c)(a'x+b'y+c')=0$$.

The equation of the angle bisectors of the lines represented by the equation $$2x^2+xy-3y^2=0$$ is :

A
$$3{x^2} + xy - 2{y^2} = 0$$
B
$${x^2} - {y^2} - 10xy = 0$$
C
$${x^2} - {y^2} + 10xy = 0$$
D
$$3{x^2} + 5xy + 2{y^2} = 0$$
3
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1

If the orthocentre of the triangle, whose vertices are (1, 2), (2, 3) and (3, 1) is $$(\alpha,\beta)$$, then the quadratic equation whose roots are $$\alpha+4\beta$$ and $$4\alpha+\beta$$, is :

A
$$x^2-20x+99=0$$
B
$$x^2-22x+120=0$$
C
$$x^2-19x+90=0$$
D
$$x^2-18x+80=0$$
4
JEE Main 2023 (Online) 29th January Morning Shift
+4
-1

Let $$B$$ and $$C$$ be the two points on the line $$y+x=0$$ such that $$B$$ and $$C$$ are symmetric with respect to the origin. Suppose $$A$$ is a point on $$y-2 x=2$$ such that $$\triangle A B C$$ is an equilateral triangle. Then, the area of the $$\triangle A B C$$ is :

A
$$\frac{10}{\sqrt{3}}$$
B
$$2 \sqrt{3}$$
C
$$3 \sqrt{3}$$
D
$$\frac{8}{\sqrt{3}}$$
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