Two coherent monochromatic point sources $${S_1}$$ and $${S_2}$$ of wavelength $$\lambda = 600\,nm$$ are placed symmetrically on either side of the center of the circle as shown. The sources are separated by a distance $$d=1.8$$ $$mm.$$ This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is $$\Delta \theta .$$ Which of the following options is/are correct?

The instantaneous voltages at three terminals marked $$X,Y$$ and $$Z$$ are given by

$${V_x} = {V_0}\,\sin \,\omega t,$$

$${V_Y} = {V_0}\,\sin $$ $$\left( {\omega t + {{2\pi } \over 3}} \right)$$

and $$Vz = {V_0}\sin \left( {\omega t + {{4\pi } \over 3}} \right)$$

An ideal voltmeter is configured to read $$rms$$ value of the potential difference between its terminals. It is connected between points $$X$$ and $$Y$$ and then between $$Y$$ and $$Z.$$ The reading(s) of the voltmeter will be

A uniform magnetic field $$B$$ exist in the region between $$x=0$$ and $$x = {{3R} \over 2}$$ (region $$2$$ in the figure) pointing normally into the plane of the paper. A particle with charge $$+Q$$ and momentum $$p$$ directed along $$x$$-axis enters region $$2$$ from region $$1$$$ at point $${P_1}\left( y \right) = - R).$$ Which of the following option(s) is/are correct?

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $$\delta T = 0.01$$ seconds and he measures the depth of the well to be $$L=20$$ meters. Take the acceleration due to gravity $$g = 10m{s^{ - 2}}$$ and the velocity of sound is $$300$$ $$m{s^{ - 1}}$$. Then the fractional error in the measurement, $$\delta L/L,$$ is closest to