The length of the common chord of the circles of radii $15$ and $20$,whose centers are $25$ units of distance apart,is

Which one of the following statements is correct about biodiversity?

If $x^2+\alpha y^2+2 \beta y=a^2$ represents a pair of perpendicular lines,then $\beta$ equals to

$A$ thermodynamic system is taken through the cycle $PQRS P$ process. The net work done by the system is ....... $J$. (Note: Assuming a standard $P-V$ diagram where $P$ is in $kPa$ and $V$ is in $m^3$,with vertices $P(1, 10)$,$Q(3, 10)$,$R(3, 20)$,$S(1, 20)$)

Two pendulums have time periods $T$ and $5T/4$. They start $SHM$ at the same time from the mean position. After how many oscillations of the smaller pendulum will they be again in the same phase?

Let $f: R-\{3\} \rightarrow R-\{1\}$ be defined by $f(x) = \frac{x-2}{x-3}$. Let $g: R \rightarrow R$ be given as $g(x) = 2x-3$. Then, the sum of all the values of $x$ for which $f^{-1}(x) + g^{-1}(x) = \frac{13}{2}$ is equal to