AIEEE 2005 Maths Question Paper Mock Test

Let $A$ and $B$ be two events such that $P(\bar{A}\cup \bar{B})=1/6$, $P(A\cap B)=1/4$ and $P(\bar{A})=1/4$, where $\bar{A}$ stands for complement of event $A$. Then events $A$ and $B$ are:

A lizard, at an initial distance of $21\text{ cm}$ behind an insect, moves from rest with an acceleration of $2{\text{ cm/s}}^2$ and pursues the insect which is crawling uniformly along a straight line at a speed of $20\text{ cm/s}$. Then the lizard will catch the insect after:

Two points $A$ and $B$ move from rest along a straight line with constant acceleration $f$ and $f^{\prime }$ respectively. If $A$ takes $m\text{ sec.}$ more than $B$ and describes $n$ units more than $B$ in acquiring the same speed then:

$A$ and $B$ are two like parallel forces. A couple of moment $H$ lies in the plane of $A$ and $B$ and is combined with them. The resultant of $A$ and $B$ after combining is displaced through a distance:

The resultant $R$ of two forces acting on a particle is at right angles to one of them and its magnitude is one third of the other force. The ratio of larger force to smaller one is: