NEET 2015 Code A - Mock Test

A remote-sensing satellite of earth revolves in a circular orbit at a height of $0.25\times 10^6\text{m}$ above the surface of earth. If earth’s radius is $6.38\times 10^6\text{m}$ and $g=9.8{\text{ms}}^{-2}$, then the orbital speed of the satellite is:

The position vector of a particle $\vec{R}$ as a function of time is given by:
$$\vec{R}=4\sin (2\pi t)\hat{i}+4\cos (2\pi t)\hat{j}$$
Where $R$ is in meters, $t$ is in seconds and $\hat{i}$ and $\hat{j}$ denote unit vectors along $x$ - and $y$ -directions, respectively. Which one of the following statements is wrong for the motion of particle?

A string is stretched between fixed points separated by $75.0\text{cm}$. It is observed to have resonant frequencies of $420\text{Hz}$ and $315\text{Hz}$. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is:

Point masses $m_1$ and $m_2$ are placed at the opposite ends of a rigid rod of length $L$, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point $P$ on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity ${\omega }_0$ is minimum, is given by:

At the first minimum adjacent to the central maximum of a single-slit diffraction pattern, the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the midpoint of the slit is: