Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength $$\lambda$$. The value of principal quantum number '$$n$$' of the excited state will be : ($$\mathrm{R}:$$ Rydberg constant)

A particle is moving in a straight line such that its velocity is increasing at 5 ms^$$-$$1 per meter. The acceleration of the particle is _____________ ms^$$-$$2 at a point where its velocity is 20 ms^$$-$$1.

Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be $$\sqrt x$$ m. The value of x is ____________.

A block of ice of mass 120 g at temperature 0$$^\circ$$C is put in 300 g of water at 25$$^\circ$$C. The x g of ice melts as the temperature of the water reaches 0$$^\circ$$C. The value of x is _____________.

[Use specific heat capacity of water = 4200 Jkg^$$-$$1K^$$-$$1, Latent heat of ice = 3.5 $$\times$$ 10⁵ Jkg^$$-$$1]