Intercalary meristem results in

$A$ cylindrical conductor of radius $R$ carries a current $i$. The value of the magnetic field at a point which is $R/4$ distance inside from the surface is $10 \ T$. Find the value of the magnetic field at a point which is $4R$ distance outside from the surface.

The solution of $\frac{dy}{dx} + 1 = e^{x+y}$ is

The equation of a straight line passing through the point $(1,2)$ and inclined at $45^{\circ}$ to the line $y=2x+1$ is

The perimeter of a $\triangle ABC$ is $6$ times the arithmetic mean of the sine of its angles. If its side $BC$ is of unit length,then $\angle A=$

$A$ ray of light refracts from medium $1$ into a thin layer of medium $2$,crosses the layer,and is incident at the critical angle on the interface between medium $2$ and $3$ as shown in the figure. If the angle of incidence of the ray is $\theta$,the value of $\theta$ is