$A$ transverse harmonic wave on a string is described by $y = 3 \sin(36t + 0.018x + \frac{\pi}{4})$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. The least distance between two successive crests in the wave is .... $m$. (in $.5$)

An inductor coil stores $U$ energy when $i$ current is passed through it and dissipates energy at the rate of $P$. The time constant of the circuit,when this coil is connected across a battery of zero internal resistance is

The solution of $\frac{dy}{dx} + 1 = e^{x+y}$ is

Enzymes are sensitive to

Three bodies,a ring,a solid cylinder,and a solid sphere,roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. Which of the bodies reaches the ground with maximum velocity?

The angle of elevation of an object on a hill is observed from a certain point in the horizontal plane through its base to be $30^{\circ}$. After walking $120 \ m$ towards it on level ground,the angle of elevation is found to be $60^{\circ}$. The height of the object (in metres) is: