13. A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A, with uniform speed. At that point, angle of depression of the boat with the man's eye is 30 (Ignore man's height). After sailing for 20 seconds, towards the base of the tower (which is the level of water), the boat has reached a point B, where the angel of depression is 45. Then the time taken (in second) by the boat from B to reach the base of the tower is: (b) 10 (3+1) (c) 10 (d) 103 The total number of positive integral solutions (x, y, z) such that xyz = 24 is : (a) 10 (3-1) 14. (a) 30 15. (b) 24 (c) 36 (d) 45 Let a be the angle between the lines whose direction cosines satisfy the equations | +m-n= 0 and 12+ m - n = 0. Then the value of sina + cosa is: 1 5 (a) (b) 8 16. The value of the integral 3 (c) 8 (d) 34 sinesine (sin 0+sin 0+sin0)2 sin* 0+3sin0+6 1-cos 20 -de (where c is a constant of integration) (a) [9- [9-2sin60-3sin 0-6 sin 0 +C (b) 18 1 [11-18 cos0+9cos * 0-2 cos 0]+c 18 1 3 (c) [11-18sin0+9sin 02 sin' 2 sin 0] + c (d) [9-cos 0-3cos* -cos 0-3 cos 0-6 cos -6cos 8+c 18 18