1
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
2
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
$$a f^2+c h^2=2 f g h$$
3
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
$$\theta-\alpha$$
4
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

When the axes are rotated through an angle 45$$^\circ$$, the new coordinates of a point P are (1, $$-$$1). The coordinates of P in the original system are

A
($$\sqrt2$$, $$\sqrt2$$)
B
($$\sqrt2$$, 0)
C
(0, $$\sqrt2$$)
D
($$-\sqrt2$$, 0)
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