1. What least number must be subtracted from 7250 to get a perfect square? Also, find the square root of this perfect square

2. What is the least number by which 12348must be divided to obtain a perfect square?

3. Find the cost of erecting a fence around a square field whose area is 9 hectares if fencing costs Rs 3.50 per metre

4. Find the least number of six digits which is a perfect square. Find the square root of this number.

5. Divide

(1) x3 - 1 by x - 1 (2) 7 +15x -13x2 +5x3 by 4 - 3x + x2

6. . x + y + z = 0, prove that x 3+ y3 + z3 = 3xyz. Or, Factorize : (a8 – b8)

7. If ( x2 + 1/X2) = 83 . Find X3- 1/X3

Or, , Factorize (i) 25a² – 4b² + 28bc – 49c² (ii) 5y² – 20y – 8z + 2yz

8. A motor boat covers a certain distance downstream in a river in 5 hours. It covers the same distance upstream in 6 hours. The speed of water is 2 km/hr . Find the speed of the boat in still water.

9. Three prizes are to be distributed in a quiz contest. The value of the second prize is five sixths the value of the first prize and the value of the third prize is four – fifths that of the second prize. If the total value of three prizes is Rs. 150, find the value of each prize.

10. (a) Each side of a triangle is increased by 10 cm. If the ratio of the perimeters of the new triangle and the given triangle is 5 : 4, find the perimeter of the given triangle

(b) . The difference between two positive integers is 36. The quotient, when one integer is divided by the other is 4. Find the two integers.

11. Factorize

(1) x4 – (y + z)4 (2) y2 –7y +12 (3) 6xy – 4y + 6 – 9x (4) a4 – 2a²b² + b4 (5) (x² – 2xy + y²) – z²

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