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 fathers age is added to the sons 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.

.1.If a1, a2, a3, a14, a4, are the n terms of an A.P. Derive the formula for its nth term.

Q.2.If a1, a2, a3, a4, a4, are the n terms of an A.P. Derive the formula for the sum of its n terms.

Q.3.If nth term of an A.P. is given by an = 5n - 3. Find the sum of its 50 terms.

Q.4.Sum of n terms of a sequence is given by Sn = 2n2 - 2n. If it is an A.P. then find its 20th term.

Q.5.Find the sum of the following series: 10 + 14 + 18 + 22 + 104

Q.6.If the sum of first 13 terms of an A.P. is 91 and sum of its first 30 terms is 465. Find the sum of its 50 terms.

Q. 7.The sum of three numbers which are in A.P. is 9 and sum of their squares is 35. Find the numbers.

Q. 8.Divide 32 into 4 parts such that they are in AP and the ratio of the product of first term and fourth terms = product of second and third terms is equal to 7/15.

Q. 9.If the pth,qth,rth terms of an AP are a,b,c then prove a(q - r) + b(r- p) = c (q - p)

Q.10.If pth term of an A.P be 1/q and the qth term be 1/p, show that the sum of pq terms is

Q.11.The sum of n terms of an A.P. is given by Sn = 5n2 + 3n, find the nth term of A.P.

Q.12.How many terms of the A.P. -6, -11/2, -5, are needed to give the sum -25? Explain the double answer.

Q.13.Find the 30th and 60th terms of the following sequence:

a. 13, 18, 23, 28, 33, .

b. -10, -7, -4, -1 ..

Q.14.Find the sum of the following series:

a. 3+8+13+18+23 .........................248

b. -10, -15, -20, -25, .-105

Q.15.The sum of three numbers which are in A.P. is 9 and sum of their squares is 35. Find the numbers.

Q.16.nth term of a sequence is given by the formula an = 10-3n, find the sum of its 20 terms.

Q.17.The 8th term of an A.P. is 32 and its 12th term is 52. Find the A.P.

Q.18.500 logs are stacked in a way such that 32 logs in the bottom row, 31 in the next row, 30 in the row next to it and so on. In how many rows are the 500 logs placed and how many logs are in the top row?