If the plane $3x - 2y - z - 18 = 0$ meets the coordinate axes at $A$, $B$, and $C$, then the centroid of $\triangle ABC$ is:

If $4x^2 - 5xy + y^2 = 0$ represents a pair of lines with slopes $m_1$ and $m_2$,then the value of $|m_1 - m_2|$ equals

$A$ conducting wire frame is placed in a magnetic field which is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced current in wires $AB$ and $CD$ are

Anoxygenic photosynthesis is characteristic of

$A$ parallel plate capacitor with air between the plates has a capacitance of $9 \, pF$. The separation between its plates is $d$. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1 = 3$ and thickness $d/3$,while the other one has dielectric constant $K_2 = 6$ and thickness $2d/3$. The new capacitance of the capacitor is .... $pF$.

If the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ $(a \neq b)$ have a common root,then $a+b$ is equal to