If the normal to the curve $y=f(x)$ at the point $(3,4)$ makes an angle $3\pi/4$ with the positive $x$-axis, then $f'(3)$ is

If $\tan \theta + \tan \left(\theta + \frac{\pi}{3}\right) + \tan \left(\theta + \frac{2\pi}{3}\right) = 3$,then which of the following is equal to $1$?

$A$ cell is connected between the points $A$ and $C$ of a circular conductor $\text{ABCD}$ of center $O$ with angle $\angle AOC = 60^{\circ}$. If $B_1$ and $B_2$ are the magnitudes of the magnetic fields at $O$ due to the currents in arc $\text{ABC}$ and arc $\text{ADC}$ respectively,the ratio $\frac{B_1}{B_2}$ is

Which component of a lichen is heterotrophic?

The $V-Q$ graph is shown below. What does the area of $\Delta OAB$ represent in this graph?

What is the time (in $sec$) required for depositing all the silver present in $125 \ mL$ of $1 \ M \ AgNO_3$ solution by passing a current of $241.25 \ A$? $(1 \ F = 96500 \ C)$