Chapter_pending — JEE Main PYQs

A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are

A particle just clears a wall of height $b$ at distance $a$ and strikes the ground at a distance $c$ from the point of projection. The angle of projection is

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

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

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

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

A particle is projected from a point O with velocity $u$ at an angle of $60^{\circ }$ with the horizontal. When it is moving in a direction at right angles to its direction at O, its velocity then is given by

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

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 $4\mathrm{km}/\mathrm{h}$ and then towards north from $B$ to $C$ at the rate of $5\mathrm{km}/\mathrm{h}$. If $AB=12\mathrm{km}$ and $BC=5\mathrm{km}$, then its average spee …

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 ${\mathrm{t}}_1^2+{\mathrm{t}}_2^2$ is equal to