If $$\theta$$ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then cos $$\theta$$ = _______

Six students P, Q, R, S, T and U, with distinct heights, compare their heights and make the following observations:

Observation I : S is taller than R.

Observation II : Q is the shortest of all.

Observation III : U is taller than only one student.

IV : T is taller than S but is not the tallest.

The number of students that are taller than R is the same as the number of students shorter than ________.

The number of student in three classes is in the ratio 3 : 13 : 6. If 18 students are added to each class, the ratio changes to 15 : 35 : 21.

The total number of students in all the three classes in the beginning was :

The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in year 3 was Rs. 1, which was half the cost/unit in year 2. The cost/unit in year 3 was one-third of the cost/unit in year 1. Taxes were paid on the selling price at 10%, 13% and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year.

The ratio of the selling price in Year 2 to the selling price in Year 3 is _______