A wire of density 9 $$ \times $$ 10^–3 kg cm^–3 is stretched between two clamps 1 m apart. The resulting strain in the wire is 4.9 $$ \times $$ 10^–4. The lowest frequency of the transverse vibrations in the wire is : (Young’s modulus of wire Y = 9 $$ \times $$ 10¹⁰ Nm^–2), (to the nearest integer), _________

A light ray enters a solid glass sphere of refractive index $$\mu $$ = $$\sqrt 3 $$ at an angle of incidence 60^o. The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is ________.

A particle of mass m is moving along the x-axis with initial velocity $$u\widehat i$$. It collides elastically with a particle of mass 10 m at rest and then moves with half its initial kinetic energy (see figure). If $$\sin {\theta _1} = \sqrt n \sin {\theta _2}$$ then value of n is ________.

A square shaped hole of side l = $${a \over 2}$$ is carved out at a distance d = $${a \over 2}$$ from the centre ‘O’ of a uniform circular disk of radius a. If the distance of the centre of mass of the remaining portion form O is $$ - {a \over X}$$ , value of X (to the nearest integer) is :