1
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
Let $P(\alpha, 4,7)$ and $Q(\beta, \beta, 8)$ be two points. If $Y Z$-plane divides the join of the points $P$ and $Q$ in the ratio $2: 3$ and $Z X$-plane divides the join of $P$ and $Q$ in the ratio $4: 5$, then length of line segment $P Q$ is
A
$\sqrt{107}$
B
$\sqrt{27}$
C
$\sqrt{83}$
D
$\sqrt{97}$
2
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the distance between the planes $2 x+y+z+1=0$ and $2 x+y+z+\alpha=0$ is 3 units, then product of all possible values of $\alpha$ is
A
-43
B
43
C
53
D
-53
3
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If P divides the line segment joining the points $$A(1,2,-1)$$ and $$B(-1,0,1)$$ externally in the ratio 1 : 2 and $$Q=(1,3,-1)$$, then $$PQ=$$

A
$$\sqrt{10}$$
B
3
C
1
D
$$\sqrt{13}$$
4
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the direction cosines of a line are $$\left(\frac{a}{\sqrt{83}}, \frac{5}{\sqrt{83}}, \frac{c}{\sqrt{83}}\right)$$ and $$c-a=4$$, then $$ca=$$

A
24
B
21
C
18
D
33
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