Let f(x) be a cubic polynomial with f(1) = $$-$$10, f($$-$$1) = 6, and has a local minima at x = 1, and f'(x) has a local minima at x = $$-$$1. Then f(3) is equal to ____________.

Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 $$\times$$ 10³ kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y = 2.0 $$\times$$ 10¹¹ Pa, g = 9.8 m/s²]

A current of 1.5 A is flowing through a triangle, of side 9 cm each. The magnetic field at the centroid of the triangle is :

(Assume that the current is flowing in the clockwise direction.)

A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of light rod. The distance between the centres of the two spheres is 5 m. What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint?