Q. 4. If (x - 3) (x + 5) is the HCF of the polynomials p(x) = (x2 + 3x - 12) (2x2 + 5x + a) and q(x) = (x2 + 3x - 10) (3x2 - 10x + b).
Find the value of a and b.
Q. 8. A household article is available for Rs. 2,500 cash or Rs. 520 cash down payment followed by four equal monthly instalments. If the rate of interest charged under the instalment plan is 25% per annum, find the amount of instalment.
Q. 9. In a right 
, the perpendicular BD on hypotenuse AC is drawn.
Prove that AC.CD = BC2
Q. 10. Find the sum of all the natural numbers between 100 and 500 which are divisible by 8.
Q. 11. Draw the graphs of the equations
3x + 2y + 6 = 0 3x + 8y — 12 = 0
Also determine the co-ordinates of the vertices of the triangle formed by these lines and the x-axis.
Q. 14. The Arithmetic Mean of the following frequency distribution is 50. Determine the value of p.
| Classes | 0 -20 |
20 - 40 |
40 - 60 |
60 -80 |
80 - 100 |
| Frequency | 16 |
p |
30 |
32 |
14 |
Q. 16. A bag contains 4 white balls, 6 red balls, 7 black balls and 3 blue balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is:
Q. 21. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
Using the above result, do the following:
The area of two similar triangles ABC and PQR are 25cm2 and 49cm respectively, If QR = 9.8 cm, find BC.
