1
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

Starting from the point $$A(-3,4)$$, a moving object touches $$2 x+y-7=0$$ at $$B$$ and reaches the point $$C(0,1)$$. If the object travels along the shortest path, the distance between $$A$$ and $$B$$ is

A
$$\frac{68}{\sqrt{170}}$$
B
$$\frac{9}{\sqrt{5}}$$
C
$$3 \sqrt{2}$$
D
$$\frac{6}{\sqrt{5}}$$
2
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

Suppose a triangle is formed by $$x+y=10$$ and the coordinate axes. Then, the number of points $$(x, y)$$ where $$x$$ and $$y$$ are natural numbers, lying inside the triangle is

A
36
B
55
C
45
D
30
3
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

If the lines represented by $$a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$$ intersect on the $$X$$-axis, which of the following is in general incorrect?

A
$$a b c=2 f g h$$
B
$$g^2=a c$$
C
$$a f^2=c h^2$$
D
$$a f^2+c h^2=2 f g h$$
4
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

For $$\alpha \in\left[0, \frac{\pi}{2}\right]$$, the angle between the lines represented by $$[x \cos \theta-y] [(\cos \theta+\tan \alpha) x-(1-\cos \theta \tan \alpha) y]=0$$ is

A
$$\alpha$$
B
$$\theta$$
C
$$\theta+\alpha$$
D
$$\theta-\alpha$$
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