A closed pipe and an open pipe have their first overtone equal in frequency. Then, the lengths of these pipe are in the ratio

A conductor $$10 \mathrm{~cm}$$ long is moves with a speed $$1 \mathrm{~m} / \mathrm{s}$$ perpendicular to a field of strength $$1000 \mathrm{~A} / \mathrm{m}$$. The emf induced in the conductor is (Given : $$\mu_0=4 \pi \times 10^{-7} \mathrm{~Wb} / \mathrm{Am}$$ )

Dual nature of light is exhibited by

A carnot engine operates with source at $$227^{\circ} \mathrm{C}$$ and sink at $$27^{\circ} \mathrm{C}$$. If the source supplies $$50 \mathrm{~kJ}$$ of heat energy, the work done by the engine is