For a suitably chosen real constant $a$,let a function $f: R-\{-a\} \rightarrow R$ be defined by $f(x) = \frac{a-x}{a+x}$. Further,suppose that for any real number $x \neq -a$ and $f(x) \neq -a$,$(f \circ f)(x) = x$. Then $f(-\frac{1}{2})$ is equal to

$540\, g$ of ice at $0\,^{\circ}C$ is mixed with $540\, g$ of water at $80\,^{\circ}C$. The final temperature of the mixture is:

The locus of the poles of focal chords of the parabola $y^2 = 4ax$ is

$A$ particle at the end of a spring executes simple harmonic motion with a period $t_1$,while the corresponding period for another spring is $t_2$. If the period of oscillation with the two springs in series is $T$,then

$A$ weak base $MOH$ of $0.1 \ N$ concentration shows a $pH$ value of $9$. What is the percentage degree of ionisation of the base? $......\%$

Two identical blocks $A$ and $B$,each of mass $m$,are placed on a smooth horizontal surface and are connected by a light spring of length $L$ and force constant $k$. $A$ third identical block $C$ of mass $m$ moves along the line joining $A$ and $B$ with velocity $v$ and collides with block $A$. The maximum compression in the spring is: