Question
The equation xy = 0 in three dimensional space is represented by:
- A plane
- Two plane are right angles
- A pair of parallel planes
- A pair of st. line
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($1$) Let $p_i$ be the probability that a randomly chosen point has $i$ many friends, $i=0,1,2,3,4$. Let $X$ be a random variable such that for $i=0,1,2,3,4$, the probability $P(X=i)=p_i$. Then the value of $7 E(X)$ is
($2$) Two distinct points are chosen randomly out of the points $A_1, A_2, \ldots, A_{4 g}$. Let $p$ be the probability that they are friends. Then the value of $7 p$ is
$g(\alpha)=\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{\sin ^{\alpha} x}{\cos ^{\alpha} x+\sin ^{\alpha} x} d x$