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

Find the direction in which a straight line must be drawn through the point $$(1,2)$$ so that its point of intersection with the line $$x+y=4$$ may be at a distance of $$\sqrt{\frac{2}{3}}$$ from this point.

A
$$ 60^{\circ} \text { or } 120^{\circ} $$
B
$$ 50^{\circ} \text { or } 100^{\circ} $$
C
$$ 15^{\circ} \text { or } 75^{\circ} $$
D
$$ 30^{\circ} \text { or } 150^{\circ} $$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The perpendicular distance of a line from the origin is 5 units and its slope is $$-1$$. The equation of the line is

A
$$x+y \pm 5 \sqrt{2}=0$$
B
$$x-y \pm 2 \sqrt{5}=0$$
C
$$x+y \pm 2 \sqrt{5}=0$$
D
$$x-y \pm 5 \sqrt{2}=0$$
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