Evaluate:

Two schools P and Q want to award their selected students on the values of Discipline, Politeness and Punctuality. The school P wants to award ₹ x each, ₹ y each and ₹ z each for the three respective values to its 3, 2 and 1 students with a total award money of ₹ 1,000.School Q wants to spend ₹ 1,500 to award its 4, 1, and 3 students on the respective values (by giving the same award money for the three values as before). If the total amount of awards for one prize on each value is
₹ 600, using matrices find the award money for each value. Apart from the above three values, suggest one more value for awards.

Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is

Find the area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x² + y² = 32.

Find the distance between the point (7, 2, 4) and the plane determine by the points A(2, 5, –3),B(–2, –3, 5) and C(5, 3, - 3).

OR

Find the distance of the point (-1, - 5, - 10) from the point of intersection of the lineand the plane