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

If $$(a, b, c)$$ are the direction ratios of a line joining the points $$(4,3,-5)$$ and $$(-2,1,-8)$$, then the point $$P(a, 3 b, 2 c)$$ lies on the plane

A
$$x+y+z=0$$
B
$$x+y-2 z=0$$
C
$$x+2 y+3 z=0$$
D
$$x-2 y+3 z=0$$
2
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

The $$x$$-intercept of a plane $$\pi$$ passing through the point $$(1,1,1)$$ is $$\frac{5}{2}$$ and the perpendicular distance from the origin to the plane $$\pi$$ is $$\frac{5}{7}$$. If the $$y$$-intercept of the plane $$\pi$$ is negative and the $$z$$-intercept is positive, then its $$y$$-intercept is

A
$$-5 / 3$$
B
$$-5 / 6$$
C
$$-3 / 2$$
D
$$-5 / 2$$
3
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

If the lines, $$\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{\lambda}$$ and $$\frac{x-2}{3}=\frac{y-3}{2}=\frac{z-2}{3}$$ are coplanar, then $$\sin ^{-1}(\sin \lambda)+\cos ^{-1}(\cos \lambda)$$ is equal to

A
$$8-2 \pi$$
B
$$6-\pi$$
C
$$3 \pi-8$$
D
$$4 \pi-8$$
4
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

The line passing through $$(1,1,-1)$$ and parallel to the vector $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$ meets the line $$\frac{x-3}{-1}=\frac{y+2}{5}=\frac{z-2}{-4}$$ at $$A$$ and the plane $$2 x-y+2 z+7=0$$ at $$B$$. Then $$A B$$ is equal to

A
$$\sqrt{6}$$
B
$$2 \sqrt{6}$$
C
$$3 \sqrt{6}$$
D
$$4 \sqrt{6}$$
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