A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. Find the original speed of the train.

Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial f(x)=a x²+bx + c, a ≠ 0, c ≠ 0

OR

Divide the polynomial f(x)=3 x²-x³-3 x+5 by the polynomial g(x)=x-1-x² and verify the division algorithm.

Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are given by 2 y-x=8,5 y-x=14 and y-2 x=1

OR

If 4 is a zero of the cubic polynomial x³-3 x²-10 x+24, find its other two zeroes.

Prove that the parallelogram circumscribing a circle is a rhombus.

Prove that : 2(sin⁶ θ +cos⁶ θ )-3(sin⁴ θ + cos⁴ θ) + 1= 0.