As shown in the figure, two infinitely long, identical wires are bent by 90^o and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP = OQ = 4cm, and the magnitude of the magnetic field at O is 10^–4 T, and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at O will be ($$\mu $$₀ = 4$$\pi $$ $$ \times $$ 10^–7 NA^–2) :

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60^o with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is :

An ideal gas occupies a volume of 2m³ at a pressure of 3 $$ \times $$ 10⁶ Pa. The energy of the gas is :

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K₁ and the of the outer cylinder is K₂. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is :