In an $FM$ system, a $7\, kHz$ signal modulates a $108\, MHz$ carrier such that the frequency deviation is $50\, kHz$. The carrier swing is: (in $ kHz$)

An assembly of identical spring-mass systems is placed on a smooth horizontal surface as shown. At this instant,the springs are relaxed. The left mass is displaced to the left and the right mass is displaced to the right by the same distance and released. The resulting collision is elastic. The time period of the oscillations of the system is

Let $n_e$ be the number density of electrons and $v_d$ be the drift velocity in a semiconductor. When the temperature is increased:

$A$ parallel plate air capacitor is charged to a potential difference of $V$. After disconnecting the battery,the distance between the plates of the capacitor is increased using an insulating handle. As a result,the potential difference between the plates:

An object is placed at a distance of $50 \, cm$ in front of a convex mirror. $A$ plane mirror is inserted covering half of the convex mirror. If the distance between the object and the plane mirror is $30 \, cm$,it is observed that there is no parallax between the images formed by the two mirrors. The radius of curvature of the convex mirror is ..... $cm$.

Two infinite length wires carry currents $8A$ and $6A$ respectively and are placed along the $X$ and $Y$-axes. The magnetic field at a point $P(0, 0, d) \ m$ will be: