Q. 1. For what value of k, the quadratic equation 16x2 – 9kx + 1 = 0 has real and equal roots.
Q. 2. For what values of ‘p’ and ‘q’, the following system of linear equations will have infinite number of solutions?
2x – (p – 4)y = 2q + 1 4x – (p – 1)y = 5q – 1.
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. Solve the following system of equations: 3 ( 2u + v) = 7 u v 3 ( u + 3 v) = 11 u v
Q. 5. The sum of a two-digit number and the number obtained by reversing the order of digits is 132. If 12 is added to the number, the new number becomes 5 times the sum of the digits. Find the number.
Q. 6. Solve graphically: x + y = 4, 3x - 2y = -3
Shade the region bounded by the lines and x- axis. Write the vertices of and find its area.
Q. 7. A certain number of students planned a picnic. The budget for food was Rs 3600. But 15 of these students failed to go and thus the cost of food for each student increased by Rs 8. How many students attended the picnic?
Q. 8. An express train takes 4 hours less for a journey of 1200 km if its speed is increased by 15 km/hr from its usual speed. Find its usual speed.
Q. 9. Solve for x and y (by cross multiplication method): 5mx + 6ny = 28 3mx + 4ny = 18.
Q. 10. Solve the equation by quadratic formula: 5x2 – 16x + 3 = 0.
Q. 11. A man can row 40 km upstream and 24 km downstream in 7 hours. He can also row 32 km upstream and 36 km downstream in 7 hours. Find his speed of rowing in still water and the speed of the stream.