1
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The distance from a point $(1,1,1)$ to a variable plane $\pi$ is 12 units and the points of intersections of the plane $\pi$ and $X, Y, Z$ - axes are $A, B, C$ respectively, If the point of intersection of the planes through the points $A, B, C$ and parallel to the coordinate planes is $P$, then the equation of the locus of $P$ is
A
$\left(\frac{1}{x y}+\frac{1}{y z}+\frac{1}{z x}\right)=143\left(\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}\right)$
B
$\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=144$
C
$\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}-1\right)^2=144\left(\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}\right)$
D
$\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}-1\right)^2=144\left(\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}\right)^2$
2
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The shortest distance between the skew lines $\mathbf{r}=(-\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})+t(3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})$ and $\mathbf{r}=(7 \hat{\mathbf{i}}+4 \hat{\mathbf{k}})+s(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})$ is
A
15
B
0
C
9
D
16
3
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $A(1,2,0), B(2,0,1), C(-3,0,2)$ are the vertices of $\triangle A B C$, then the length of the internal bisector of $\angle B A C$ is
A
$3 \sqrt{6}$
B
$\frac{2 \sqrt{14}}{3}$
C
$6 \sqrt{14}$
D
$\frac{2 \sqrt{6}}{3}$
4
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The perpendicular distance from the point $(-1,1,0)$ to the line joining the points $(0,2,4)$ and $(3,0,1)$ is
A
10
B
$\frac{2 \sqrt{5}}{5}$
C
$\frac{5}{\sqrt{2}}$
D
8
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