A gas balloon is going up with a constant velocity of $10 \mathrm{~m} / \mathrm{s}$. When this balloon reached a height of 75 m , a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is $\_\_\_\_$ m. (Take $g=10 \mathrm{~m} / \mathrm{s}^2$ )

The velocity $(v)$ versus time $(t)$ plot of a particle is shown in the figure, for a time interval of 40 s . The total distance travelled by the particle and the average velocity during this period are, respectively

$\_\_\_\_$.

Two cars $A$ and $B$ are moving in the same direction along a straight line with speeds $100 \mathrm{~km} / \mathrm{h}$ and $80 \mathrm{~km} / \mathrm{h}$, respectively such that car $A$ is moving ahead of car $B$. A person in car $B$ throws a stone with a speed $v$ so that it hits the car $A$ with a speed of $5 \mathrm{~m} / \mathrm{s}$. The value of $v$ is $\_\_\_\_$ $\mathrm{km} / \mathrm{h}$.

A particle starts moving from time $t=0$ and its coordinate is given as $x(t) = 4t^3 - 3t$

A. The particle returns to its original position (origin) 0.866 units later

B. The particle is 1 unit away from origin at its turning point

C. Acceleration of the particle is non-negative

D. The particle is 0.5 units away from origin at its turning point

E. Particle never turns back as acceleration is non-negative

Choose the correct answer from the options given below :