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High School Mathematics - II
2. Solve :-
3. Using long division, show that (x+3) is a factor of
What are the other factors?
4. Find the quotient and the remainder, if any, when
is divided by (a-3).
5. Factorize the following:-
(a) x² + 17x + 60
(b) x² -5x - 36.
(c) x² + 9y² -6xy - 25a²
(d) 2x + 6y - 3(x+3y)²
6. Find the Greatest Common Divisor of
7. A bag contains coins of denomination $5 and $2. The total value of thse coins is $1272. If the number of $2 coins is 15% of the $5 coins, find the number of coins of each denomination.
8. The sum of digits of a two digit number is 15 and if 9 is added to the number, the digits are interchanged. Find the number.
9. In how many years will $5000 amount to $6655 at 10% per annum interest compounded annually?
10. If the volumes of two cones are in the ratio 1:4 and their diameters are in the ratio 4:5, find the ratio of their heights.
11. If the height and perimeter of the base of a right circular cone are respectively 15 m and 44 m, then what is the volume?
12. The ratios of heights of two cones of equal volumes is 16:9. What is the ratio of their base areas?
13. If the numerical value of the curved surface area of a right circular cylinder is equal to the numerical value of its volume, the numerical value of the radius of the base of cyliner is ________.
14. The lateral surface of a cyliner is developed into a square whose diagonal is √5 cms. What is the area of the base of the cylinder in square cms?
15. If the diameter of the base of a closed right circular cylinder be equal to its height h, then what is its surface area?
16. A cow is tied to a pole with an 8 m long rope. What is the area of the land on which it can graze?
17. If a square is inscribed in a circle, what is the ratio of the areas of the circle and the square?
18. Find the dimensions of a rectangular room if its diagonal is 17 meters and its perimeter is 46 meters.
19. A right circular cylinder and a sphere have the same volume and same radius. The ratio of the areas of their curved surfaces is ____________.
20. If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then what is the surface area of each ball in square centimeters?
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