The range of the projectile projected at an angle of 15$$^\circ$$ with horizontal is 50 m. If the projectile is projected with same velocity at an angle of 45$$^\circ$$ with horizontal, then its range will be

A particle executes S.H.M. of amplitude A along x-axis. At t = 0, the position of the particle is $$x=\frac{A}{2}$$ and it moves along positive x-axis. The displacement of particle in time t is $$x = A\sin (wt + \delta )$$, then the value of $$\delta$$ will be

The de Broglie wavelength of a molecule in a gas at room temperature (300 K) is $$\lambda_1$$. If the temperature of the gas is increased to 600 K, then the de Broglie wavelength of the same gas molecule becomes

The equivalent resistance of the circuit shown below between points a and b is :