Wavelength of high energy transition of H-atoms is 91.2 nm. Calculate the corresponding wavelength of He atoms.

Calculate the molarity of water if it's density is 1000 kg/m³

If $$f$$ is an even function then prove that
$$\int\limits_0^{\pi /2} {f\left( {\cos 2x} \right)\cos x\,dx = \sqrt 2 } \int\limits_0^{\pi /4} {f\left( {\sin 2x} \right)\cos x\,dx.} $$

(i) Find the equation of the plane passing through the points $$(2, 1, 0), (5, 0, 1)$$ and $$(4, 1, 1).$$
(ii) If $$P$$ is the point $$(2, 1, 6)$$ then find the point $$Q$$ such that $$PQ$$ is perpendicular to the plane in (i) and the mid point of $$PQ$$ lies on it.