1. The speed of a boat in still water is 11 km/hour. It can go 12 km upstream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream.
OR
The difference of squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.
2. A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prizes.
3. Tangents AP and AQ are drawn to circle with centre 0 from an external point A. Prove that ∠ PAQ = 2 ∠OPQ.
4. A right triangle , whose sides other than hypotenuse, are 3 cm and 4 cm is made to revolve about its hypotenuse. Find the volume of the double cone so formed.
OR
A circus tent is in form of a right circular cylinder and a right circular cone above it. The diameter and the height of the cylindrical part are 126 m and 5 m respectively. The total height of the circus tent is 21 m. Find the total surface area of the tent.
5. A bucket made up of a metal sheet is in form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the bucket, if the cost of the metal sheet is Rs. 15 per 100 cm2. (Use π = 22/7)
6. A man on the top of a vertical tower observes a car moving toward the tower. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this car will reach the tower ?
No comments:
Post a Comment