1. Solve the following system of equations:
(2)
Or
Solve the following system of linear equations: ax + by = 2ab, bx + ay = a2 + b2
2. The HCF and LCM of two polynomials p(x) and q(x) are (x + 3) and x3 + 4x2 + x – 6 respectively. If p(x) = x2 +5x + 6, find q(x). (2)
3. Solve the following system of equations graphically: 3x + y – 12 = 0 , x – 3y + 6 = 0 Also find the coordinates of the points where the lines meet the x – axis.(3)
4. Find the value of p and q for which the following system of linear equations has infinite number of solutions. 2x + 3y = 7 and (p + q )x + (2p – q)y = 3 ( p + q + 1).(2)
5. The sum of the digits of a 2-digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18. Find the number. (3)
6. There are some lotus flowers in a lake. If one butterfly sits on each flower , one butterfly is left behind. If two butterflies sit on each flower, one flower is left behind. What is the number of flowers? What is the number of butterflies? (3)
7. A 90% acid solution is mixed with a 97% acid solution to obtain 21 liters of a 95% acid solution. Find the quantity of each of the solutions to get the resultant mixture.(3)
8. Simplify the following rational expression: (3)
9. 
(3)
10. Solve 4x + 6/y = 15 and 6x – 8/y = 14 and hence find p if y = px – 2. (3)
11. For what value of k will the equations x + 2y + 7 =0, 2x + ky + 14 =0 represent coincident lines? (2)
12. For what value of k , will the system of equations x + 2y = 5 , 3x + ky = -15 has no solution? (2)
13. 8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days. Find the time taken by one man alone and that by one boy alone to finish the work.
14. For any rational expressions R and S prove that R3 + S3 = (R + S) (R2 + S2 – RS)
