$A$ disc has mass $M$ and radius $R$. How much tangential force should be applied to the rim of the disc,so as to rotate with angular velocity $\omega$ in time $t$?

The chemicals and the reaction conditions required for the preparation of ethane are:

Two sources of sound placed close to each other are emitting progressive waves given by $y_1 = 4 \sin(600\pi t)$ and $y_2 = 5 \sin(608\pi t)$. An observer located near these two sources of sound will hear:

If $f: R \rightarrow C$ is defined by $f(x)=e^{2 i x}$ for $x \in R$, then $f$ is (where $C$ denotes the set of all complex numbers)

Seven balls are drawn simultaneously from a bag containing $5$ white and $6$ green balls. The probability of drawing $3$ white and $4$ green balls is:

The magnetic needle of a vibration magnetometer makes $12$ oscillations per minute in the horizontal component of the earth's magnetic field. When an external short bar magnet is placed at some distance along the axis of the needle in the same line,it makes $15$ oscillations per minute. If the poles of the bar magnet are interchanged,the number of oscillations it makes per minute is