1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The length of the internal bisector of angle $A$ in $\triangle A B C$ with vertices $A(4,7,8), B(2,3,4)$ and $C(2,5,7)$ is
A
$\frac{1}{3} \sqrt{29}$
B
$\frac{2}{3} \sqrt{29}$
C
$\frac{2}{3} \sqrt{34}$
D
$\frac{4}{3} \sqrt{34}$
2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the direction cosines of lines are given by $l+m+n=0$ and $m n-2 l m-2 n l=0$, then the acute angle between those lines is
A
$2 \pi / 5$
B
$\pi / 3$
C
$\pi / 4$
D
$\pi / 60$
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the angle $\theta$ between the line $\frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}$ and the plane $2 x-y+\sqrt{\lambda} z+4=0$ is such that $\sin \theta=\frac{1}{3^{\prime}}$ then the value of $\lambda=$
A
$\frac{3}{5}$
B
$\frac{5}{4}$
C
$\frac{5}{3}$
D
$\frac{4}{3}$
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let $f(x)=\left\{\begin{array}{cl}1+\frac{2 x}{a}, & 0 \leq x \leq 1 \\ a x, & 1 < x \leq 2\end{array}\right.$.If $\lim _{x \rightarrow 1} f(x)$ exists, then the sum of the cubes of the possible values of $a$ is

A
1
B
5
C
9
D
7
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