The logic gate equivalent to the circuit shown in the figure is

The circumcentre of the triangle formed by the lines $xy + 2x + 2y + 4 = 0$ and $x + y + 2 = 0$ is:

Five very long,straight wires are bound together to form a small cable. Currents carried by the wires are $I_1 = 20\ A, I_2 = -6\ A, I_3 = 12\ A, I_4 = -7\ A, I_5 = 18\ A$. The magnetic induction at a distance of $10\ cm$ from the cable is

The structure of $X$ is

$A$ smooth sphere $A$ is moving on a frictionless horizontal plane with an angular velocity $\omega$ and a linear velocity $v$ of its center of mass. It undergoes an elastic head-on collision with an identical sphere $B$ which is at rest. If there is no friction anywhere,then after the collision,their angular speeds are $\omega_A$ and $\omega_B$ respectively. Then:

Two bar magnets $A$ and $B$ are placed one over the other and are allowed to vibrate in a vibration magnetometer. They make $20$ oscillations per minute when the similar poles of $A$ and $B$ are on the same side,while they make $15$ oscillations per minute when their opposite poles lie on the same side. If $M_A$ and $M_B$ are the magnetic moments of $A$ and $B$ and if $M_A > M_B$,the ratio of $M_A$ and $M_B$ is