1. What is the sum of 2 + 4 + 6 + 8 + 10 + .........200?
2. What is the sum of 11² + 12² + 13² + 14² + ........... 20²?
3. Prove by mathematical induction that 1³ + 2³ + 3³ + ..... n³ is.
4. The surface areas of two spheres are in the ratio 49:81. Find the ratio of their radii.
5. The radius and the height of a right circular cone are in the ratio 5:12. It its volume is 314 cu.cm, find the radius and slant height. (For convenience, pi may be taken as 3.14).
6.A solid metal cylinder of radius 28 cm and height 42 cm is melted and recast into spheres of diameter 7 cm. How many spheres can be made?
7. In a university of 60 students, 40 play basketball, 25 play tennis and 10 play golf. 15 play both basketball and tennis and 5 play both basket ball and golf. 3 play both tennis and golf. None of the players play all the three games. How many students play none of these games?
8. An amount deposited at compound interest compounded annually for 2 years amounts to $2662/- at 10% per annum. How much lesser would have been the interest at the same rate of interest for the same period at simple interest?
6x+2y-5z = 13
3x+3y-2z = 13
7x+5y-3z = 26
1/x - 2/y + 4 = 0
1/y - 1/z + 1 = 0
2/z + 3/x = 14
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