Which of the following elements is used in thermometry at high temperatures?

$A$ circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

The solution of $x \frac{dy}{dx} = y + x e^{y/x}$ with $y(1) = 0$ is

$A$ police car with a siren of frequency $8 \, kHz$ is moving with uniform velocity $36 \, km/hr$ towards a tall building which reflects the sound waves. The speed of sound in air is $320 \, m/s$. The frequency of the siren heard by the car driver is .... $kHz$.

In the figure,the potentiometer wire $AB$ of length $L$ and resistance $9r$ is joined to the cell $D$ of $emf$ $\varepsilon$ and internal resistance $r$. The cell $C$'s $emf$ is $\varepsilon / 2$ and its internal resistance is $2r$. The galvanometer $G$ will show no deflection when the length $AJ$ is

If we completely remove the decomposers from an ecosystem,its functioning will be adversely affected because