$A$ man of $50\, kg$ mass is standing in a gravity-free space at a height of $10\, m$ above the floor. He throws a stone of $0.5\, kg$ mass downwards with a speed of $2\, m/s$. When the stone reaches the floor,the distance of the man above the floor will be ........ $m.$

$A$ young infant may be feeding entirely on mother's milk,which is white in color,but the stools which the infant passes out are quite yellowish. What is this yellow color due to?

The minimum number of times a fair coin needs to be tossed,so that the probability of getting at least two heads is at least $0.96$ is

If $PM$ is the perpendicular from $P(2, 3)$ onto the line $x+y=3$,then the coordinates of $M$ are

$A$ whistle revolves in a circle with an angular speed of $20\, rad/s$ using a string of length $50\, cm$. If the frequency of sound from the whistle is $385\, Hz$,then what is the minimum frequency heard by an observer,who is far away from the centre in the same plane? (Speed of sound is $340\, m/s$)

$A$ circle passes through the point $(3, 4)$ and cuts the circle $x^2 + y^2 = a^2$ orthogonally. The locus of its centre is a straight line. If the distance of this straight line from the origin is $25$,then $a^2$ is equal to