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

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.

Prove that the parallelogram circumscribing a circle is a rhombus.

The following table gives production yield per hectare (in quintals) of wheat of 100 farms of a village :

Change the distribution to 'a more than' type distribution and draw its ogive.

OR

The median of the following data is 525. Find the values of x and y, if total

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 6 m. At a point on the plane, the angle of elevation of the bottom and top of the flag-staff are 30° and 45° respectively. Find the height of the tower. (Take √3 = 1.73)