G L Mittal and TARUN MITTAL Solutions for Chapter: Vectors, Exercise 3: FOR DIFFERENT COMPETITIVE EXAMINATIONS

If a unit vector is represented by $0.5\hat{\mathrm{i}}+0.8\hat{\mathrm{j}}+c\hat{\mathrm{k}}$ then the value of $c$ is:

In the arrangement shown in the figure below, the ends $P$ and $Q$ of the unstretchable string, move downward with a uniform speed $u$. Pulleys $A$ and $B$ are fixed. The mass $M$ moves upward with a speed:

A particle is moving towards east with a velocity of $5 \mathrm{m} {\mathrm{s}}^{-1}$. In $10$ seconds the velocity changes to $5 \mathrm{m} {\mathrm{s}}^{-1}$ towards north. Average acceleration in this time is:

Select the correct alternative. The coordinates of a particle moving in a plane are given by $x=a \cos pt$ and $y=b \sin pt$, where $a, b$ and $p$ are positive constants of appropriate dimensions. Then:

The coordinates of a particle at time $t$ are $x=2t+4t^2$, where $x$ and $y$ are in metre and $t$ is in second. The acceleration of the particle at $t=5 s$ is :

A person aiming to reach just opposite point on bank of stream swims at speed of $0.5 \mathrm{m}/\mathrm{s}$ at angle $120°$ with direction of flow of water. The speed of water in stream is _____.

A river is flowing from west to east at speed of $5 \mathrm{m}/\mathrm{minute}$. A man who can swim at rate of $10 \mathrm{m}/\mathrm{minute}$ in still water is standing on south bank of river. He wants to swim across river in the shortest time. He should swim in a direction:

A boat which has speed of $5 \mathrm{km}/\mathrm{h}$ in still water crosses a river of width $1 \mathrm{km}$ along the shortest possible in $15$ minutes. The velocity of river water in $\mathrm{km}/\mathrm{h}$ is