For the transistor circuit shown below,if $\beta = 100$ and the voltage drop between the emitter and base is $0.7\ V$,then the value of $V_{CE}$ will be.....$V$.

If the potential at the centre of a uniformly charged ring is $V_0$,then the electric field at its centre will be (assume radius $= R$):

For any $y \in R$,let $\cot ^{-1}(y) \in (0, \pi)$ and $\tan ^{-1}(y) \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$. Then the sum of all the solutions of the equation $\tan ^{-1}\left(\frac{6 y}{9-y^2}\right)+\cot ^{-1}\left(\frac{9-y^2}{6 y}\right)=\frac{2 \pi}{3}$ for $0 < |y| < 3$,is equal to

When the pollen tube enters the ovule through the integuments,the process is known as?

$A$ spherically symmetric gravitational system of particles has a mass density $\rho = \begin{cases} \rho_0 & \text{for } r \leq R \\ 0 & \text{for } r > R \end{cases}$ where $\rho_0$ is a constant. $A$ test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed $V$ as a function of distance $r$ $(0 < r < \infty)$ from the centre of the system is represented by:

Let $\overline{a}, \overline{b}$ and $\overline{c}$ be three vectors having magnitudes $1, 1$ and $2$ respectively. If $\overline{a} \times(\overline{a} \times \overline{c})+\overline{b}=\overline{0}$,then the acute angle between $\overline{a}$ and $\overline{c}$ is