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.
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.
4. If the amount of Rs. 400/- for 2 years is 441 then find the annual rate of compound interest.
5. If x, 12, y, 27 are in continued proportion then find the values of x and y.
6. If each side of a cube increases 50% by length, then what is the parcentage increase in total
surface area of the cube?
7. Solve: (2x+1)+(3/2x+1) = 4 (x ≠ 1/2)
8. The total interest of a principal in n yrs. at the rate of simple interest of r % per annum is 25
the principal will be
(a) Rs. 2p
(b) Rs. 4p
(c) Rs. 2p
(d) Rs. 4p
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.
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.
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.
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.
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.
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.
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.