1
JEE Main 2024 (Online) 31st January Evening Shift
+4
-1

Let $$A(a, b), B(3,4)$$ and $$C(-6,-8)$$ respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point $$P(2 a+3,7 b+5)$$ from the line $$2 x+3 y-4=0$$ measured parallel to the line $$x-2 y-1=0$$ is

A
$$\frac{17 \sqrt{5}}{6}$$
B
$$\frac{15 \sqrt{5}}{7}$$
C
$$\frac{17 \sqrt{5}}{7}$$
D
$$\frac{\sqrt{5}}{17}$$
2
JEE Main 2024 (Online) 31st January Morning Shift
+4
-1

Let $$\alpha, \beta, \gamma, \delta \in \mathbb{Z}$$ and let $$A(\alpha, \beta), B(1,0), C(\gamma, \delta)$$ and $$D(1,2)$$ be the vertices of a parallelogram $$\mathrm{ABCD}$$. If $$A B=\sqrt{10}$$ and the points $$\mathrm{A}$$ and $$\mathrm{C}$$ lie on the line $$3 y=2 x+1$$, then $$2(\alpha+\beta+\gamma+\delta)$$ is equal to

A
8
B
5
C
12
D
10
3
JEE Main 2024 (Online) 30th January Evening Shift
+4
-1

If $$x^2-y^2+2 h x y+2 g x+2 f y+c=0$$ is the locus of a point, which moves such that it is always equidistant from the lines $$x+2 y+7=0$$ and $$2 x-y+8=0$$, then the value of $$g+c+h-f$$ equals

A
8
B
14
C
29
D
6
4
JEE Main 2024 (Online) 30th January Morning Shift
+4
-1

A line passing through the point $$\mathrm{A}(9,0)$$ makes an angle of $$30^{\circ}$$ with the positive direction of $$x$$-axis. If this line is rotated about A through an angle of $$15^{\circ}$$ in the clockwise direction, then its equation in the new position is :

A
$$\frac{y}{\sqrt{3}+2}+x=9$$
B
$$\frac{x}{\sqrt{3}+2}+y=9$$
C
$$\frac{x}{\sqrt{3}-2}+y=9$$
D
$$\frac{y}{\sqrt{3}-2}+x=9$$
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