1
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

The area of the triangle whose vertices are $$(-2, a)(2,-6)$$ and $$(5,4)$$ is 35 sq units then the value of '$$\mathrm{a}$$' is

A
4
B
$$\frac{53}{3}$$
C
$$-\frac{23}{3}$$
D
$$\frac{128}{3}$$
2
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

The line joining two points $$A(2,0) B(3,1)$$ is rotated about $$A$$ in anticlockwise direction through an angle of $$15^{\circ}$$. If $$B$$ goes to $$C$$ in the new position, then the coordinates of $$C$$ is

A
$$ \left(2+\frac{1}{\sqrt{3}}, \sqrt{\frac{3}{2}}\right) $$
B
$$ \left(2, \sqrt{\frac{3}{2}}\right) $$
C
$$ \left(2+\frac{1}{\sqrt{3}}, 1\right) $$
D
$$ \left(2+\frac{1}{\sqrt{2}}, \sqrt{\frac{3}{2}}\right) $$
3
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

The points on the $$x$$-axis whose perpendicular distance from the line $$\frac{x}{3}+\frac{y}{4}=1$$ is 4 units are

A
$$(8,0)$$ and $$(-2,0)$$
B
$$(-8,0)$$ and $$(-2,0)$$
C
$$(8,0)$$ and $$(2,0)$$
D
$$(-8,0)$$ and $$(2,0)$$
4
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

Let $$\mathrm{ABC}$$ be a triangle with equations of its sides $$\mathrm{AB}, \mathrm{BC}$$. $$\mathrm{CA}$$ respectively are $$x-2=0, y-5=0$$ and $$5 x+2 y-10=0$$. Then the orthocentre of triangle lies on the line

A
$$ 3 x+y=1 $$
B
$$ x-2 y=1 $$
C
$$ 4 x+y=13 $$
D
$$ x-y=0 $$
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