$A$ graph of magnetic flux $(\phi)$ versus current $(I)$ is shown for four inductors $A, B, C$ and $D$. Which inductor has the largest value of self-inductance?

If $\frac{ax^2 + bx + c}{(x - 1)(x + 2)(2x + 3)} = \frac{3}{x - 1} + \frac{2}{x + 2} - \frac{5}{2x + 3}$,then:

$A$ rod of length $20 \, cm$ is made of metal $A$. It expands by $0.075 \, cm$ when its temperature is raised from $0^{\circ}C$ to $100^{\circ}C$. Another rod of a different metal $B$ having the same length expands by $0.045 \, cm$ for the same change in temperature. $A$ third rod of the same length is composed of two parts,one of metal $A$ and the other of metal $B$. This rod expands by $0.060 \, cm$ for the same change in temperature. The portion made of metal $A$ has the length ........ $cm$.

In a book of $500$ pages,it is found that there are $250$ typing errors. Assume that Poisson law holds for the number of errors per page. Then,the probability that a random sample of $2$ pages will contain no error,is :

An iron sphere of mass $20 \times 10^{-3} \ kg$ falls through a viscous liquid with terminal velocity $0.5 \ ms^{-1}$. The terminal velocity (in $ms^{-1}$) of another iron sphere of mass $54 \times 10^{-2} \ kg$ is (in $.5$)

Monascus purpureus is a yeast used commercially in the production of :