The distance of the point (1, − 2, 4) from the plane passing through the point (1, 2, 2) and perpendicular to the planes x − y + 2z = 3 and 2x − 2y + z + 12 = 0, is :

If  m and M are the minimum and the maximum values of

4 + $${1 \over 2}$$ sin² 2x $$-$$ 2cos⁴ x, x $$ \in $$ R, then M $$-$$ m is equal to :

A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle $$\theta $$ with the horizontal, a point object of mass m is kept. The minimum coefficient of friction $$\mu $$_min between the mass and the inclined surface such that the mass does not move is :

In the following ‘I’ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity :