Let f(x) be a polynomial of degree 6 in x, in which the coefficient of x⁶ is unity and it has extrema at x = $$-$$1 and x = 1. If $$\mathop {\lim }\limits_{x \to 0} {{f(x)} \over {{x^3}}} = 1$$, then $$5.f(2)$$ is equal to _________.

A proton, a deuteron and an $$\alpha$$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is _________ and their speed is _______, in the ratio.

A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force F₁. Now a spherical cavity of radius $$\left( {{R \over 2}} \right)$$ is made in the sphere (as shown in figure) and the force becomes F₂. The value of F₁ : F₂ is

An $$\alpha$$ particle and a proton are accelerated from rest by a potential difference of 200V. After this, their de Broglie wavelengths are $$\lambda$$_$$\alpha$$ and $$\lambda$$_p respectively. The ratio $${{{{\lambda _p}} \over {{\lambda _\alpha }}}}$$ is :