Two waves $Y_{1} = 0.25 \sin(316 t)$ and $Y_{2} = 0.25 \sin(310 t)$ are propagating along the same direction. The number of beats produced per second is:

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:

$A$ metal wire $PQ$ slides on parallel metallic rails having separation $0.25 \ m,$ each having negligible resistance. There is a $2 \ \Omega$ resistor and $10 \ V$ battery as shown in the figure. There is a uniform magnetic field directed into the plane of the paper of magnitude $0.5 \ T.$ $A$ force of $0.5 \ N$ to the left is required to keep the wire $PQ$ moving with constant speed to the right. With what speed is the wire $PQ$ moving? (Neglect self-inductance of the loop).

If $y = mx + c$ is a tangent to the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$,then the value of $c$ is

Identify the plant and structure marked $A$ and $B:-$

$A$ thin magnetic iron rod of length $30 \ cm$ is suspended in a uniform magnetic field. Its time period of oscillation is $4 \ s$. It is broken into three equal parts. The time period in seconds of oscillation of one part when suspended in the same magnetic field is