1. Write the condition for the roots to become equal in the equation ax2bx + c = 0, (a, b, c are

real, a ≠ 0).**Ans:** **b² – 4ac = 0**

2. The radius of a circle is 10 cm and the length of a chord is 12 cm. Then, calculate the distance

between the chord and centre of the circle.**Ans:**

3. If the ratio of the volumes of two cubes is 1 : 8, then find the ratio of the total surface areas

of the two cubes.**Ans:**

4. If the amount of Rs. 400/- for 2 years is 441 then find the annual rate of compound interest.**Ans:**

5. If x, 12, y, 27 are in continued proportion then find the values of x and y.**Ans:**

6. If each side of a cube increases 50% by length, then what is the parcentage increase in total

surface area of the cube?**Ans:**

7. Solve: (2x+1)+(3/2x+1) = 4 (x ≠ 1/2)**Ans:**

8. The total interest of a principal in n yrs. at the rate of simple interest of r % per annum is 25

pnr ,

the principal will be

(a) Rs. 2p

(b) Rs. 4p

(c) Rs. 2p

(d) Rs. 4p**Ans:**

9. If the height of two right circular cylinders are in the ratio 3 : 4 and perimeters are in the ratio

1 : 2, then find the ratio of their volumes.**Ans:**

10. AB and AC are two chords of a circle which are perpendicular to each other. If AB = 4 cm. and

AC = 3 cm., then find the length of the radius of the circle.**Ans:**

11. If simple interest and compound interest of a certain sum of money for two years are Rs. 8400 and

Rs. 8652, then find the sum of money and the rate of interest.**Ans:**

12. If the ratio of two roots of the quadratic equation ax²+bx+c=0 [a ≠ 0] 1 : r, then show that (r+1)²/r = b²/ac.**Ans:**

13. Prove that if any straight line passing through the centre of a circle bisects any chord, which is not

a diameter, then the straight line will be perpendicular on that chord.**Ans:**

14. AB is a radius of a circle with centre O. C is a point on the circle. If ∠OBC = 60º then find the

value of ∠OCA.**Ans:**

15. Height of a right circular cylinder is twice of its radius. If the height would be 6 times of its radius,

then the volume of the cylinder would be greater by 539 cubic dcm., find the height of the cylinder.**Ans:**