AIEEE 2006 Mock Test

A particle has two velocities of equal magnitude $u$ inclined to each other at an angle $\theta$. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then $\theta$ is:

At a telephone enquiry system, the number of phone calls regarding relevant enquiry follows a Poisson distribution with an average of $5$ phone calls during $10\text{-minute}$ time intervals. The probability that there is at most one phone call during a $10\text{-minute}$ time period is:

A body falling from rest under gravity passes a certain point $P$. It was at a distance of $400\text{m}$ from $P$, $4\text{s}$ prior to passing through $P$. If $g=10{\text{m/s}}^2$, then the height above the point $P$ from where the body began to fall is:

${\int }_0^{\pi }xf(\sin x)dx$ is equal to:

A straight line through the point $A(3,4)$ is such that its intercept between the axes is bisected at $A$. Its equation is: