Q. 2. If (x - 3) (x + 5) is the HCF of the polynomials
p(x) = (x2 - 5x +6) (3x2 + 8x + a) and
q(x) = (x2 + x - 20) (2x2 - x + b).
Find the values of a and b.
Q. 7. Two circles intersect each other at A and B. From a point C on AB produced, two tangents CP and CQ are drawn to the two circles touching them at P and Q. Prove that CP = CQ.
Q. 8. Find the sum of all the natural numbers between 200 and 300 which are divisible by 4.
Q. 10. A household article is available for Rs. 1,500 cash or Rs. 360 cash down payment followed by three equal monthly instalments. If the rate of interest charged under the instalment plan is 16% per annum, find the amount of instalment
Q. 11. Draw the graphs of the equations
2x - y + 6 = 0 and 4x + 5y - 16 = 0
Also determine the co-ordinates of the vertices of the triangle formed by these lines and the x-axis.
Q. 15. The Arithmetic Mean of the following frequency distribution is 25. Determine the value of p.
| Classes | 0 -10 |
10 - 20 |
20 - 30 |
30 - 40 |
40 - 50 |
| Frequency | 5 |
18 |
15 |
p |
6 |
Q. 19. A box contains 19 balls bearing numbers 1, 2, 3… 19. A ball is drawn at random from the box. Find the probability that the number on the ball is
Q. 21. Prove that in a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite to the first side is a right angle.
Using the above, prove the following:
In 
such that AD2 = BD.DC. Prove that 
is right angled at A.
