Question 1

1.Solve the following system of linear equations:

6(ax + by) = 3a + 2b, 6(bx – ay) = 3b – 2a

Question 2

2.Using quadratic formula, solve the following quadratic equation for  x: p²x² + (p² – q²)x – q² = 0

Question 3

3.If (x – 3) (x + 2) is the GCD of the polynomials

P(x) = (x² – 2x – 3) (2x² + ax – 2) and Q(x) = (x² + x – 2) (3x² + bx – 3) find the value of a and b.

Question 4

4.If

 Express [P ´ Q ¸ R] as a rational expression in the lowest form.

Question 5

5.The 8^th term of an arithmetic progression (A.P.) is 37 and its 12^th term is  57. Find the A.P.

Question 6

6.Find the sum of the first 25 terms of an A.P. whose nth term is given by t_n = 7 – 5n.

Question 7

7.An electric fan is available for Rs. 600 cash or for Rs. 250 cash down payment followed by 3 monthly installments of Rs. 125 each. Find the rate of interest charged under the installment plan. 

Question 8

8.A loan of Rs. 4,200 is to be returned in two equal annual installments.  If the rate of interest is 10% per annum, compounded annually, calculate the amount of each installment.

Question 9

9.In figure 1, ABCD is a trapezium in which AB ||DC. The diagonals AC and BD intersect at O. Prove  that

Fig.1

Question 10

10.In figure 2, AB is a diameter of a circle, with centre O. If ÐABC = 70°, ÐCAD = 30° and ÐBAE = 60°. Find ÐBAC, ÐACD and ÐABE.

 Fig.2