The most abundant prokaryotes helpful to humans in making curd from milk and in production of antibiotics are categorised as

Let $A = \{x \in R, x \neq 0, -4 \leq x \leq 4\}$ and $f: A \rightarrow R$ be defined by $f(x) = \frac{|x|}{x}$ for $x \in A$. Then,the range of $f$ is

The mitral valve is supported by which of the following?

$X$ - In deep-sea hydrothermal vents,the average temperature is between $25^{\circ}C$ to $30^{\circ}C$.
$Y$ - Reptiles and amphibians are eurythermal.

$A$ thin converging lens of focal length $f=25 \ cm$ forms the image of an object on a screen placed at a distance of $75 \ cm$ from the lens. The screen is moved closer to the lens by a distance of $25 \ cm$. The distance through which the object has to be shifted,so that its image on the screen is sharp again,is (in $cm$)

If $\sqrt{\frac{y}{x}}+\sqrt{\frac{x}{y}}=2$,then $\frac{d y}{d x}$ is equal to