1
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$A(1,2,1), B(2,3,2), C(3,1,3)$ and $D(2,1,3)$ are the vertices of a tetrahedron. If $\theta$ is the angle between the faces $A B C$ and $A B D$, then $\cos \theta=$
A
$\frac{5}{\sqrt{14}}$
B
$\frac{15}{8 \sqrt{7}}$
C
$\frac{3}{\sqrt{14}}$
D
$\frac{5}{2 \sqrt{7}}$
2
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
Consider the tetrahedron with the vertices $A(3,2,4)$, $B\left(x_1, y_1, 0\right), C\left(x_2, y_2, 0\right)$ and $D\left(x_3, y_3, 0\right)$.If the $\triangle B C D$ is formed by the lines $y=x, x+y=6$ and $y=1$, then the centroid of the tetrahedron is
A
$\left(\frac{9}{4}, \frac{7}{4}, 1\right)$
B
$\left(\frac{11}{4}, \frac{5}{4}, 1\right)$
C
$\left(3, \frac{7}{4}, 1\right)$
D
$(3,2,1)$
3
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $P(2, \beta, \alpha)$ lies on the plane $x+2 y-z-2=0$ and $Q(\alpha,-1, \beta)$ lies on the plane $2 x-y+3 z+6=0$, then the direction cosines of the $P Q$ are
A
$\left(-\frac{4}{\sqrt{17}}, 0, \frac{1}{\sqrt{17}}\right)$
B
$\left(+\frac{4}{\sqrt{17}}, 0, \frac{1}{\sqrt{17}}\right)$
C
$\left(\frac{1}{\sqrt{17}}, 0, \frac{4}{\sqrt{17}}\right)$
D
$\left(-\frac{1}{\sqrt{17}}, 0, \frac{4}{\sqrt{17}}\right)$
4
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
Let $\pi$ be the plane that passes through the point $(-2,1,-1)$ and parallel to the plane $2 x-y+2 z=0$. Then the foot of perpendicular drawn from the point $(1,2,1)$ to the plane $\pi$ is
A
$(-3,-1,1)$
B
$(-1,1,-3)$
C
$(-3,3,-1)$
D
$(-1,3,-1)$
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