If $\theta = \frac{\pi}{6}$,then the $10^{\text{th}}$ term of the series $1 + (\cos \theta + i \sin \theta)^1 + (\cos \theta + i \sin \theta)^2 + \dots$ is

Which of the following processes occur during cell division?

The line joining the points $A(2,0)$ and $B(3,1)$ is rotated through an angle of $45^{\circ}$ about $A$ in the anti-clockwise direction. Find the coordinates of $B$ in the new position.

Consider a system of three charges $\frac{q}{3}, \frac{q}{3}$ and $-\frac{2q}{3}$ placed at points $A, B$ and $C$ respectively,as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and $\angle CAB = 60^\circ$.

$\left|\begin{array}{ccc}x+2 & x+3 & x+5 \\ x+4 & x+6 & x+9 \\ x+8 & x+11 & x+15\end{array}\right|$ is equal to

Water is flowing with a velocity of $2\,m/s$ in a horizontal pipe where the cross-sectional area is $2 \times 10^{-2}\, m^2$ at a pressure of $4 \times 10^4\, Pa$. The pressure at a cross-section of area $0.01\, m^2$ in $Pa$ will be: