1
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let $A=(2,0,-1), B=(1,-2,0), C=(1,2,-1)$ and $D=(0,-1,-2)$ be four points.

If $\theta$ is the acute angle between the plane determined by $A, B, C$ and the plane determined by $A, C, D$, then $\tan \theta=$

A

$\sqrt{\frac{14}{5}}$

B

$\frac{3}{\sqrt{14}}$

C

$\frac{3}{\sqrt{5}}$

D

$\frac{\sqrt{5}}{3}$

2
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $A(0,1,2), B(2,-1,3)$ and $C(1,-3,1)$ are the vertices of a triangle, then the distance between its circumcentre and orthocentre is

A

$\frac{3}{\sqrt{2}}$

B

$\frac{3}{2}$

C

3

D

$\frac{9}{2}$

3
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If the direction cosines of two lines satisfy the equations $l-2 m+n=0, l m+10 m n-2 n l=0$ and $\theta$ is the angle between the lines, then $\cos \theta=$

A

$\frac{\pi}{6}$

B

$\frac{8}{\sqrt{70}}$

C

$\frac{\pi}{3}$

D

$\frac{20}{3 \sqrt{70}}$

4
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin $(0,0,0)$ to a plane, then the equation of that plane is

A

$2 x+y-3 z+6=0$

B

$2 x-y+3 z-14=0$

C

$2 x-y+3 z-13=0$

D

$2 x+y+3 z-10=0$

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