Q. 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: 1. 13, 18, 23, 28, 33,………. 2. -10, -7, -4, -1…………….. Q. 14. Find the sum of the following series: 1. 3+8+13+18+23 .........................248 2. -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? Miscellaneous Questions: Q. 1. Find the roots: (x + 2) / (x - 2) + (x - 2) / (x + 2) = 5/2, x ≠2, x≠ -2 Q. 2. Determine the values of p for which the quadratic equation: 2x2 + px + 8 = 0 has real roots. Q. 3. A shopkeeper buys a number of bananas for Rs. 600. If he had bought 10 dozen more bananas for the same amount, each dozen would have cost him Rs. 2 less. Find the number of bananas bought by him. Q. 4. If the roots of the equation (c2 - ab)x2 – 2(a2 - bc) x + b2-ac = 0 are equal, prove that either a=0 or a3 + b3 + c3=3abc Q. 5. Find three consecutive positive integers whose product is equal to sixteen times their sum. Q. 6. A fraction becomes 6/5 if 1 is added to each of the numerator and the denominator. However, if we subtract 5 from each, the fraction becomes 3/2. find the fraction. Q. 7. For what value of k, the system of equations: 2x - ky + 3 = 0, 4x + 6y - 5 = 0 is consistent? Q. 8. Solve graphically: x + 4y = 10, y + 3x = 8. ===================================================================================================================================== Linear Equations in two Variables 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. ===================================================================================================================================== Some more from Arithmetics: Q. 1.Find the sum of first 25 terms of an ap whose nth term is 1-4n Q. 2. in an AP the sum of it’s first n terms is Nsquare+2n.find its 18th term. Q. 3. if fifth term of an AP is 0 ,show that its 33rd term is four times its 12th term Q. 4. if the Nth term of an AP is (2n+1),find the sum of first n terms of the AP Q. 5. find the sum of first 15 terms of an AP WHOSE Nth term is 9-5n. Q. 6. IF M TIMES THE Mth term is equal to the n times the Nth term. find it’s (m+n)th term. Q. 7. the ratio of the sum of n terms of two AP is (4n+2): (3n+47).find the ratio of the 9th term. Q. 8. if the Pth term of an AP is 1/q and the Qth term is 1/p,then find the sum of its first 20 terms. Q. 9. the 8th term of an AP is 0 .prove that its 38th term is triple it’s 18th term. Q. 10. if the sum of first m terms of an AP is equal to n and the sum of first n terms of an AP is equals to m ,then show that the sum of (m+n) terms is equal to (m+n).