The locus of the centroid of the triangle with vertices at $(a \cos \theta, a \sin \theta)$,$(b \sin \theta, -b \cos \theta)$ and $(1, 0)$ is (where $\theta$ is a parameter).

If $x$ is real,then the maximum and minimum values of the expression $\frac{x^2-3x+4}{x^2+3x+4}$ are

The minimum force required to start pushing a body up a rough (having coefficient of friction $\mu$) inclined plane is $F_1$, while the minimum force needed to prevent it from sliding down is $F_2$. If the inclined plane makes an angle $\theta$ with the horizontal such that $\tan \theta = 2\mu$, then the ratio $F_1 / F_2$ is

If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane is

The electron affinity values of elements $A, B, C$ and $D$ are respectively $-135, -60, -200$ and $-348 \ kJ \ mol^{-1}$. The outer electronic configuration of element $B$ is

$A$ metal $M$ which is not affected by strong acids like conc. $HNO_3$,conc. $H_2SO_4$ and conc. solutions of alkalies like $NaOH$,$KOH$ forms $MCl_3$ which finds use for toning in photography. The metal $M$ is