Four resistances of 15$$\Omega $$, 12$$\Omega $$, 4$$\Omega $$ and 10$$\Omega $$ respectively in cyclic order to form Wheatstone's network. The resistance that is to be connected in parallel with the resistance of 10$$\Omega $$ to balance the network is _____$$\Omega $$.

A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length $$\ell $$. The other end is fixed. The system is given an angular speed $$\omega $$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is :

A leak proof cylinder of length 1m, made of a metal which has very low coefficient of expansion is floating vertically in water at 0°C such that its height above the water surface is 20 cm. When the temperature of water is increased to 4°C, the height of the cylinder above the water surface becomes 21 cm. The density of water at T = 4°C, relative to the density at T = 0°C is close to :

Boolean relation at the output stage-Y for the following circuit is :