Show that $$2\sin x + \tan x \ge 3x$$ where $$0 \le x < {\pi \over 2}$$.

A point $$P$$ is given on the circumference of a circle of radius $$r$$. Chord $$QR$$ is parallel to the tangent at $$P$$. Determine the maximum possible area of the triangle $$PQR$$.

Let $$f:R \to R$$ and $$\,\,g:R \to R$$ be continuous functions. Then the value of the integral
$$\int\limits_{ - \pi /2}^{\pi /2} {\left[ {f\left( x \right) + f\left( { - x} \right)} \right]\left[ {g\left( x \right) - g\left( { - x} \right)} \right]dx} $$ is

Column - I gives the three physical quantities. Select the appropriate units for the choices given in Column - II. Some of the physical quantities may have more than one choice correct:

Column I	Column II
Capacitance	(i) ohm-second
Inductance	(ii) coulomb2 - joule-1
Magnetic Induction	(iii) coulomb (volt)-1
	(iv) newton (amp-meter)-1
	(v) volt-second (ampere)-1