A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is 30 cm and the refractive index of the lens material is 1.5, then the focal length of the lens (in cm) is ______.

A body A, of mass m = 0.1 kg has an initial velocity of 3$$\widehat i$$ ms^-1 . It collides elastically with another body, B of the same mass which has an initial velocity of 5$$\widehat j$$ ms^-1. After collision, A moves with a velocity $$\overrightarrow v = 4\left( {\widehat i + \widehat j} \right)$$. The energy of B after collision is written as $${x \over {10}}$$. The value of x is ___________.

Effective capacitance of parallel combination of two capacitors C₁ and C₂ is 10 μF. When these capacitors are individually connected to a voltage source of 1V, the energy stored in the capacitor C₂ is 4 times that of C₁. If these capacitors are connected in series, their effective capacitance will be :