The area (in square units) of the triangle formed by $x+y+1=0$ and the pair of straight lines $x^2-3xy+2y^2=0$ is

$\sec h^{-1}\left(\frac{1}{2}\right)-\operatorname{cosec} h^{-1}\left(\frac{3}{4}\right)$ is equal to

Particles of masses $m, 2m, 3m, \dots, nm$ grams are placed on the same line at distances $l, 2l, 3l, \dots, nl$ cm from a fixed point. The distance of the centre of mass of the particles from the fixed point in centimetres is:

Two bodies have their moments of inertia $I$ and $2I$ respectively about their axes of rotation. If their kinetic energies of rotation are equal,their angular momenta will be in the ratio:

$A$ ray of light of intensity $I$ is incident on a parallel glass slab at point $A$ as shown in the diagram. It undergoes partial reflection and refraction. At each reflection, $25\%$ of incident energy is reflected. The rays $AB$ and $A'B'$ undergo interference. The ratio of $I_{max}$ and $I_{min}$ is (in $: 1$)

Three plates of common surface area $A$ are connected as shown. The effective capacitance between points $A$ and $B$ will be