If $x^2+\alpha y^2+2 \beta y=a^2$ represents a pair of perpendicular lines,then $\beta$ equals to

$A$ car weighs $1800\,kg$. The distance between its front and back axles is $1.8\,m$. Its centre of gravity is $1.05\,m$ behind the front axle. Force exerted by the level ground on each front wheel is ........ $N$.

Who among the following is known as the 'Father of Taxonomy'?

An ideal gas is subjected to a cyclic process involving four thermodynamic states. The amounts of heat $(Q)$ and work $(W)$ involved in each of these states are:
$\begin{aligned} & Q_1=6000 \text{ J}, \quad Q_2=-5500 \text{ J}, \quad Q_3=-3000 \text{ J}, \quad Q_4=3500 \text{ J} \\ & W_1=2500 \text{ J}, \quad W_2=-1000 \text{ J}, \quad W_3=-1200 \text{ J}, \quad W_4=x \text{ J} \end{aligned}$
The ratio of the net work done by the gas to the total heat absorbed by the gas is $\eta$. The values of $x$ and $\eta$ respectively are:

Two long parallel wires are at a distance $2d$ apart. They carry steady equal currents flowing out of the plane of the paper,as shown. The variation of the magnetic field $B$ along the line $XX'$ is given by

Which of the following is a hormone-releasing $IUD$?