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Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1 - KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD–32 PRACTICE PAPER 05 (2023-24) CHAPTER 05 ARITHMETIC PROGRESSION SUBJECT: MATHEMATICS MAX. MARKS : 40 CLASS : X DURATION : 11⁄2 hrs General Instructions: (i). All questions are compulsory. (ii). This question paper contains 20 questions divided into five Sections A, B, C, D and E. (iii). Section A comprises of 10 MCQs of 1 mark each. Section B comprises of 4 questions of 2 marks each. Section C comprises of 3 questions of 3 marks each. Section D comprises of 1 question of 5 marks each and Section E comprises of 2 Case Study Based Questions of 4 marks each. (iv). There is no overall choice. (v). Use of Calculators is not permitted SECTION – A Questions 1 to 10 carry 1 mark each. 1. In an AP, if a = 3.5, d = 0, n = 101, then an will be (a) 0 (b) 3.5 (c) 103.5 (d) 104.5 2. If p – 1, p + 3, 3p – 1 are in AP, then p is equal to ________. (a) 3 (b) 4 (c) 2 (d) none of these 3. In an AP, if d = –2, n = 5 and an = 0, the value of a is (a) 10 (b) 5 (c) –8 (d) 8 4. If the common difference of an AP is 3, then a20 – a15 is (a) 5 (b) 3 (c) 15 (d) 20 5. The next term of the AP 18, 50, 98,..... is (a) 146 (b) 128 (c) 162 (d) 200 6. The common difference of the AP 1 1 1 2 , , ,.... p p p p p   .... is (a) p (b) – p (c) –1 (d) 1 7. An AP consists of 31 terms. If its 16th term is m, then sum of all the terms of this AP is (a) 16 m (b) 47 m (c) 31 m (d) 52 m 8. If the sum of first n terms of an AP is An + Bn 2 where A and B are constants, the common difference of AP will be (a) A + B (b) A – B (c) 2A (d) 2B In the following questions 9 and 10, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as: (a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c)Assertion (A) is true but reason (R) is false. (d)Assertion (A) is false but reason (R) is true. 9. Assertion (A): The sum of series with the nth term an = (9 – 5n) is 220 when no. of terms n = 6 Reason (R): Sum of first n terms in an A.P. is given by the formula: [2 ( 1) ] 2 n n S a n d   
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 2 - 10. Assertion (A): The value of n, if a = 10, d = 5, an = 95 is 20 Reason (R): The formula of general term an is an = a + (n - 1)d. SECTION – B Questions 11 to 14 carry 2 marks each. 11. Determine k so that 4k + 8, 2k 2 + 3k + 6 and 3k 2 + 4k + 4 are three consecutive terms of an AP. 12. In an AP, the 24th term is twice the 10th term. Prove that the 36th term is twice the 16th term. 13. Find 10th term from end of the AP 4, 9, 14, .... , 254. 14. If the sum of first n terms of an AP is given by Sn = 3n 2 + 2n, find the nth term of the AP. SECTION – C Questions 15 to 17 carry 3 marks each. 15. Find the value of the middle term of the following AP: –6, –2, 2, ..., 58. 16. Which term of the progression 19, 1 2 18 ,17 ,... 5 5 ... is the first negative term. 17. If the pth, qth, rth terms of an AP be x, y, z respectively, show that x(q – r) + y(r – p) + z(p – q) = 0. SECTION – D Questions 18 carry 5 marks. 18. If S1, S2, S3 are the sum of n terms of three APs, the first term of each being unity and the respective common difference being 1, 2, 3; prove that S1 + S3 = 2S2. SECTION – E (Case Study Based Questions) Questions 19 to 20 carry 4 marks each. 19. Aditya is a fitness freak and great athlete. He always wants to make his nation proud by winning medals and prizes in the athletic activities. An upcoming activity for athletes was going to be organised by Railways. Aditya wants to participate in 200 m race. He can currently run that distance in 51 seconds. But he wants to increase his speed, so to do it in 31 seconds. With each day of practice, it takes him 2 seconds less.
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 3 - (i) He wants to makes his best time as 31 sec. In how many days will be able to achieve his target? (2) (ii) What will be the difference between the time taken on 5th day and 7th day. (2) OR (ii) Which term of the arithmetic progression 3, 15, 27, 39 .... will be 120 more than its 21st term? (2) 20. In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year. Based on the above information answer the following questions. (i) Find the production in the 1st year. (1) (ii) Find the production in the 12th year. (1) (iii) Find the total production in first 10 years. (2) OR (iii) In how many years will the total production reach 31200 cars? (2)