1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the probability distribution of a random variable $X$ is as follows, then $k$ is equal to

$$ \begin{array}{c|l|l|l|l} \hline X=x & 1 & 2 & 3 & 4 \\ \hline P(X=x) & 2 k & 4 k & 3 k & k \\ \hline \end{array} $$

A
$\frac{1}{10}$
B
$\frac{2}{10}$
C
$\frac{3}{10}$
D
$\frac{4}{10}$
2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
In a binomial distribution $B(n, p)$ the sum and product of the mean and the variance are 5 and 6 respectively, then $6(n+p-q)$ is equal to
A
50
B
53
C
52
D
51
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The locus of the mid-point of the portion of the line $x \cos \alpha+y \sin \alpha=p$ intercepted by the coordinate axes, where $p$ is a constant, is
A
$\frac{1}{x^2}+\frac{1}{y^2}=\frac{3}{p^2}$
B
$\frac{1}{x^2}+\frac{1}{y^2}=\frac{4}{p^2}$
C
$x^2+y^2=2 p^2$
D
$\frac{2}{x^2}+\frac{2}{y^2}=\frac{1}{p^2}$
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The origin is shifted to the point $(2,3)$ by translation of axes and then the coordinate axes are rotated about the origin through an angle $\theta$ in the counter - clockwise sense. Due to this if the equation $3 x^2+2 x y+3 y^2-18 x-22 y+50=0$ is transformed to $4 x^2+2 y^2-1=0$, then the angle $\theta$ is euqal to
A
$\frac{\pi}{4}$
B
$\frac{\pi}{3}$
C
$\frac{\pi}{6}$
D
$\frac{\pi}{2}$
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