AIEEE 2004 (Maths) Mock Test

In a right angle $△ABC,$ $\angle A=90^{\circ }$ and sides $a,b,c$ are respectively, $5\text{cm},4\text{cm}$ and $3\text{cm}.$ If a force $\vec{F}$ has moments $0,9$ and $16$ in $\text{N cm}$ units respectively about vertices $A,B$ and $C,$ then magnitude of $\vec{F}$ is

Three forces $\vec{P},\vec{Q}$ and $\vec{R}$ acting along $IA,IB$ and $IC,$ where $I$ is the incentre of a $△ABC,$ are in equilibrium. Then $\vec{P}:\vec{Q}:\vec{R}$ is

A particle moves towards east from a point $A$ to a point $B$ at the rate of $4\text{km/h}$ and then towards north from $B$ to $C$ at the rate of $5\text{km/h}.$ If $AB=12\text{km}$ and $BC=5\text{km},$ then its average speed for its journey from $A$ to $C$ and resultant average velocity direct from $A$ to $C$ are respectively

A velocity $V=\frac{1}{4}\text{m/s}$ is resolved into two components along $OA$ and $OB$ making angles $30^{\circ }$ and $45^{\circ }$ respectively with the given velocity. Then the component along $OB$ is

If $t_1$ and $t_2$ are the times of flight of two particles having the same initial velocity $u$ and range $R$ on the horizontal, then $t_1^2+t_2^2$ is equal to