$A$ $TV$ transmitter has a range of $50 \ km$. The height of the $TV$ transmitter is . . . . . . (Radius of the earth,$R_e = 6.4 \times 10^6 \ m$). (in $m$)

Charges are placed on the vertices of a square as shown. Let $\overrightarrow{E}$ be the electric field and $V$ be the electric potential at the centre. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively,then:

Find the points on the curve $\frac{x^2}{4} + \frac{y^2}{25} = 1$ at which the tangents are parallel to the $x$-axis.

Two towers $A$ and $B$,each of height $20 \ m$,are situated a distance $200 \ m$ apart. $A$ body is thrown horizontally from the top of tower $A$ with a velocity $20 \ ms^{-1}$ towards tower $B$ and hits the ground at point $P$. Another body is thrown horizontally from the top of tower $B$ with a velocity $30 \ ms^{-1}$ towards tower $A$ and hits the ground at point $Q$. If a car starting from rest from point $P$ reaches point $Q$ in $10 \ s$,the acceleration of the car is . . . . . . . (Acceleration due to gravity $g = 10 \ ms^{-2}$) (in $ms^{-2}$)

The epithelial tissue present on the inner surface of bronchioles and fallopian tubes is

$A$ line is at a constant distance $c$ from the origin and meets the coordinate axes in $A$ and $B$. The locus of the centre of the circle passing through $O, A, B$ is