Let $Q$ be the set of all rational numbers in $[0,1]$ and $f:[0,1] \rightarrow [0,1]$ be defined by $f(x) = \begin{cases} x & \text{for } x \in Q \\ 1-x & \text{for } x \notin Q \end{cases}$. Then,the set $S = \{x \in [0,1] : (f \circ f)(x) = x\}$ is equal to

$A$ hollow pipe of length $0.8 \ m$ is closed at one end. At its open end,a $0.5 \ m$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50 \ N$ and the speed of sound is $320 \ ms^{-1}$,the mass of the string is: (in $g$)

It is now possible to breed plants and animals with desired characters through

$A$ candle of diameter $d$ is floating on a liquid in a cylindrical container of diameter $D$ $(D >> d)$ as shown in the figure. If it is burning at the rate of $2 \ cm/hour$,then the top of the candle will

The complex formed by a pair of synapsed homologous chromosomes is called:

An ideal transformer has $500$ and $5000$ turns in primary and secondary windings respectively. If the primary voltage is connected to a $6\,V$ battery, then the secondary voltage is.......$V$.