Q. 1. For what value of k, the system of equations: 2x - ky + 3 = 0, 4x + 6y - 5 = 0 is consistent?
Q. 2. For what value of k, the quadratic equation 16x2 – 9kx + 1 = 0 has real and equal roots.
Q. 3. If twice the father’s age is added to the son’s age, the sum is 77. Five years ago, the father was 15 times the age of his son, then. Find their present ages.
Q. 4. Determine the values of p for which the quadratic equation: 2x2 + px + 8 = 0 has real roots.
Q. 5. The sum of n terms of an A.P. is given by Sn = 5n2 + 3n, find the nth term of A.P.
Q. 6. How many terms of the A.P. -6, -11/2, -5, …………are needed to give the sum -25? Explain the double answer.
Q. 7. Find the 30th and 60th terms of the following sequence:
Q. 8. Find the sum of the following series:
Q. 9. From a point on the ground, 40 m away from the foot of a tower, angle of elevation of the top of the tower is 300. The angle of elevation of the top of a water tank kept on top of the tower is 450. Find :
Q. 10. Determine graphically whether the given pair of equations is consistent or not.
3x – 5y = 1;
2x – y = –3
If consistent, find the solution of the above equations.
Q.11. Solve the following equations by cross – multiplication method:
x – y = 3 ;
2x – 3y = 8
