From the given data, the amount of energy required to break the nucleus of aluminium $$_{13}^{27}$$Al is __________ x $$\times$$ 10^$$-$$3 J.

Mass of neutron = 1.00866 u

Mass of proton = 1.00726 u

Mass of Aluminium nucleus = 27.18846 u

(Assume 1 u corresponds to x J of energy)

(Round off to the nearest integer)

A force of F = (5y + 20)$$\widehat j$$ N acts on a particle. The work done by this force when the particle is moved from y = 0 m to y = 10 m is ___________ J.

A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in 10 s is ____________ $$\pi$$ $$\times$$ 10^$$-$$1 Nm.

In a semiconductor, the number density of intrinsic charge carries at 27$$^\circ$$C is 1.5 $$\times$$ 10¹⁶/m³. If the semiconductor is doped with impurity atom, the hole density increases to 4.5 $$\times$$ 10²²/m³. The electron density in the doped semiconductor is ___________ $$\times$$ 10⁹/m³.