The equation of the circle concentric with the circle $x^2+y^2-6x+12y+15=0$ and having double its area is

If $f(x) = \left| \begin{array}{ccc} x - 3 & 2x^2 - 18 & 3x^3 - 81 \\ x - 5 & 2x^2 - 50 & 4x^3 - 500 \\ 1 & 2 & 3 \end{array} \right|$,then $f(1)f(3) + f(3)f(5) + f(5)f(1) = $

The work functions of metals $A$ and $B$ are in the ratio $1 : 2$. If light of frequencies $f$ and $2f$ are incident on the surfaces $A$ and $B$ respectively,the ratio of the maximum kinetic energy of photoelectrons emitted is ($f$ and $2f$ are both frequencies greater than the threshold frequency of metals $A$ and $B$ respectively).

The effect due to a uniform magnetic field on a freely suspended magnetic needle is as follows:

Velocity and acceleration vectors of a charged particle moving perpendicular to the direction of a magnetic field at a given instant of time are $\overrightarrow{v}=2 \hat{i}+c \hat{j}$ and $\overrightarrow{a}=3 \hat{i}+4 \hat{j}$ respectively. Then the value of $c$ is

Which fungi obtain their nutrition from decaying organic matter?