The phase difference between two waves,represented by $y_1 = 10^{-6} \sin \{100t + (x/50) + 0.5\} \ m$ and $y_2 = 10^{-6} \cos \{100t + (x/50)\} \ m$,where $x$ is in meters and $t$ is in seconds,is approximately .... $radians$.

Given that,$a \alpha^2+2 b \alpha+c \neq 0$ and that the system of equations
$\begin{aligned} & (a \alpha+b) x+a y+b z=0 \\ & (b \alpha+c) x+b y+c z=0 \\ & (a \alpha+b) y+(b \alpha+c) z=0\end{aligned}$
has a non-trivial solution,then $a, b$ and $c$ lie in

The magnetic susceptibility of the material of a rod is $499$. Permeability of vacuum is $4 \pi \times 10^{-7} \ H/m$. Absolute permeability of the material of the rod in $H/m$ is:

There is a uniform electric field of strength $10^3 \, V/m$ along the $y$-axis. $A$ body of mass $1 \, g$ and charge $10^{-6} \, C$ is projected into the field from the origin along the positive $x$-axis with a velocity of $10 \, m/s$. Its speed in $m/s$ after $10 \, s$ is (Neglect gravitation).

The relation between the current $i$ (in ampere) in a conductor and the time $t$ (in second) is $i=12t+9t^2$. The charge passing through the conductor between the times $t=2 \ s$ and $t=10 \ s$ is (in $C$)

Electrons with de-Broglie wavelength $\lambda$ fall on the target of an $X$-ray tube. The cut-off wavelength of the emitted $X$-ray is: