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Exercise, , 1, The sum of the series ! + : ‘ ‘ +...0f 9 terms is, (b) - 2, , (a) = 9/6, (ot (d) - a2, gp — tht tt __ 27 the value of n is, He Oe dle 4 10 terms, (a) 35 (b) 36 (c) 37 (d) 40, , 8. If the sum of the series 2, 5, 8, 11, ... is 60100, then, n is equal to, (a) 100 (b) 200, (c) 150 (d) 250, 4. Lot S, donotes the sum of first n terms of an AP, if, 4'S,, =38,, then tho ratio S,,/S, is equal to, (a) 4 (b) 6, () 8 (d) 10, 5. If sum of n terms of an AP is 3n’ + 5n and T,, = 164,, then m is equal to, , (a) 26 (b) 27, (c) 28 (d) None of these, 6, The sum of the first ‘n’ terms of the series, 292428), is, 2 4 8 #16, (a) 2" -n-1 (b) 1-27", (ce) n+2°-"% -1 (d) 2" -1, , 7. An AP consists of n (odd terms) and its middle term, is m. Then, the sum of the AP is, , (a) 2mn ) dm, (c) mn (a) mn?, , 8. If xsitatd+a+ to o(lal<1) and, Yalt+b+b? +b’ + to o(fal<1), _ then, 1+ ab +a’b* + a'b® +--< is equal to, ) —2 ) ee, , z+y-1 xty+t, @ = (a) None of these, x-yt+l, , 9. In a GP, if the (m+ n)th term be p and (m~-n)th, term be q, then its mth term is, , (2) (eq) (b) pia), (©) Ja7p) () Jp+q, , d. The sum of n terms of an AP is an (n -1). The sum, of the squares of these terms is equal to, 2, , (a) an? (n-1)? ) &ain~He@n=1), , 2 2, 72 nin-yen-) — ) Xnnsnensy, , 11. Ifa,b,¢ are in AP, pagel are in HP and ap. baer _, , P © is equal to, », in GP, then : + P, , a c, @ £-¢ Oo*s, pg 2-4, (©) q +) q b, The tree | harmonic _ i080 a 6 an, ©) a7" O53" 11" 7, , (d) None of these, , B83, is, w|3~, , 13. If S be the sum to infinity of a GP, whose first torr,, is a, then the sum of first n terms is, , ws(1-2) ws(1-(1-2)], (c) {i - () - J] (d) None of these, , ¥ 1, My If a,b,c are in GP, then 7 + E is equal to, 1s, , (b) 4b? -c?, , (a) 1/(¢? - b*), (0) 1b? -c*), , () Vc? - a?), 15. If the non-zero numbers a,b,c are in AP ang, tan~'a, tan™'b,tan”'c are also in AP, then, (epa=bec (0) 6? = 2ac, (c) a? = be (4) c? = ab, 16. The harmonic mean of two numbers is 4, their AM, e is A and GM is G satisfy the relation 2A + G? =27,, The two numbers are, , ) 6,3 (b) 5,4 4, (©) §-25 (d) - 31, , 17. The geometric and harmonic means of two numbers, (x, and x, are 18 and 19-5 respectively. The value, of |x, -x, | is equalto, (a) 5 (b) 10 (c) 15 (d) 20, 18. The value of x + y +z is 15, if a,x, y,z,b are in AP, while the value of +44 is > if a,x, y,2,b a, , y, in HP. Then, a and b are, , (a) 1,9 (b) 3,7, (c) 7,3 (d) None of these, 19. If a,b,c be in AP and a’,b?,c? are in HP, then, (a) aebec (0) a® = b? =c?/2, (c) a,b,c are in GP (d) - a/2, b,c are in GP

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sequernn- sr Series, , go. Hf the harmon,, , numbers is to their GM's. 2 tiene, , in the ratio 13, the "2 Patiitive, (a) 4,9 + the numbers are, (c) 6,5, , (b) 7,5, i (a) Ni, 21. Two AM's A, and Aces One Of these, , HM's H, and #1. GM's. G, and ., , , , numbers, then Hy Tie ed ives, fe =, (2) Ag'+ A," 2 §8 equal to mw, 6,6, ©) Go'4g-1, ry A\+a_?, rt Az (9) oo", , att ty pner, , 22. If “Hap? |8 the arithmetic temp, and 5, then n is equal to aia, @-1 (b) -2 +o, , (4, 23, If first three terms of sequence .1, , +a,b,4, geometric series and 16 ‘~ in, harmonic series, then ¢|, (a) ae-tbat, , the last, , he values of a terms are, , and b will be, dant yt, 12, , (c) Both (a) and (b) are true (qd) one Stinese, 24. The sum oe 24 8 <, 5, , Bp *' Upto nterms is, ty 2 -+5 25 4, 1% 16x51 ) B-Sts, 2-Re8 2, 7 st (d) None of these, 25. The harmonic mean of —2_ ang —@, 7 T—ab ™4 Tg is equal to, a, Fra “ire Oe @— 5, , 26. If (m+ 1)th,(17+1)th and (r+ th t, lerms of, are in GP and m,n,r are in HP then the ratio whe, , first term of the AP to its comm ference, terms of n is equal to sa a, , (a) n/2 (b) -n/2 (c) n/3 (d) -n/3, , Directions (Q. Nos. 27-29) Given two series, S$,=1+2+4+8+-. to 100 terms, and S,=1+4+7+10+--- to 100 terms, 27. Find last term of series S,. ae, 2% 2" a ay, , 28, Find the number of common terms in both of the, series, , (a) 4 (o) 5 (6 @7, 29. Find the sum of all the terms of series S,., , (a) 14450 (b) 14590, , (c) 14950 (d) 19450, , 49, , Directions (Q. Nos 30-32) Read the following, information carefully and onswer the question that foltow, Consider a sequence whose sum to a terms is given by, quadratic function, S, =3a? +50., 30. The nature of the given series is, (a) AP (b) GP (c) HP (d) AGP, 31. For the given sequence the number 5456 is the, {a} (153)th term (b) (932)th term, , (c) (707)th term (a) (909)th term, 32. Sum of the squares of the first 3 terms of the given, series is, {a) 1100 (0) 660 () 799 (a) 1000, , Directions (Q. Nos 33-38) The following question are, Assertion-Reason type question. Each of these questions, contains two statements Statement | (Assertion) and Statement, Il (Reason) Each of these question also has four alternative, choices, only one of which is the correct answer., , 33. Statement 1 4, 8, 16 are in GP, then 12, 16, 24 are, , in HP., , Statement I If middle term is added in three, , consecutive terms of a GP, resultant will be in HP., , (a) Statement | is true, Statement Il ts true; Statement Il is, a correct explanation for Staternent |, , (b) Statement | is true, Statement I is true; Statemrént It is, not a correct explanation for Statement |, , (©) Statement | is true, Statement I is talse, , (d) Staternent | is false, Statement Il is true, , 34. Statement I If sum of n terms of a series is, 5n? +3n+1, then the series is an AP, , Statement II Sum of n terms of an AP is always of, , the form an* +bn, , (a) Statement | is true, Statement Il is true; Statement Il is, a correct explanation for Statement |, , (b) Statement | is true. Statement Il is true; Statement li is, not a correct explanation for Statement |, , (c) Statement | is true, Statement il is false, , {d) Statement | is false, Statement Ii is true, , 35. Statement I If a,b,c are 3 positive numbers in GP,, 3abe, , at+b+c = /, then ( 3 as) {abe}, , Statement II (Arithmetic mean) (Harmonic mean)=, , (Geometric mean)*, , (a) Statement | is true, Statement II is true; Statement Il is, @ correct explanation for Statement |, , (bo) Statement | is true, Statement Il is true; Statement Hl is, Not a correct explanation for Statement |, , (c) Statement | is true, Statement Il is false, , (d) Statement | is faise, Statement Il is true, , , , AL

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50, , he first five terms and tho sy,, , 42. The sum of U re same. Which op. th,, , , , , , Statement 1 Th: 2 of first n terms of the series riz terme of an AP \, hive el following is the correct statement? {NDA Boag, 465? eam bot 2 fa) The test terms mest De peerine _ %, iterence must e pve, (o) The common ¢, Statement I Sum of first # natural numbers (c) Ether the test term of the common CPerere,, nine) negative but not both, , 2 {d) Both the first term and the COMMON Gere,, (a) Statement 1 is tue, Statement It is true, Statement I is negative ., , seventh term of the sequence, , a Correct exptanaton tor Statement 1 ga What ti hes, hat is, 0, 3, 8, 15, 24, -- 7 ENDA 2015,, , (®) Statement | is truo, Statement M1 ts true, Statement Mt is, , not a conect explanation for Statement | I,, (©) Statement 115 tue, Statement It is false (a) 63 tb) 48 7/8 ea”, (@) Statement | is tatse, Statement It is tue 44, If the numbers 7 -3,4n-2, 5n+1 are in ap, , Is is the value of n? INDA 2129,, , 37, Statement 11, 2. 4. 8... is aG, P: 4, H, 16, 32,, aGP, then 1+ 4.24 8.4 + 16,8 + 32,,.. is also a GP @t, , Statement MH Let general term of a GP with 45, What is the sum of first eight terms of the ny, 1 1, , (0) 2 () 3 (4, , , , common ratio r be f,,, and general term of another 1 7, GP with common ratio r be (’;,,. then the series so ae rae INDA 291247, whose general term "4, = 454 +44) is also a GP a ST 4, with common ratio r () 535 ©) 334, (a) Statement | ts true. Statement I is true; Statement I is, , & correct explanation for Statement | () = (0) None oF Bese, (©) Statement | is true, Statement Il is true; Statement Il is, , Rot a correct explanation for statement | 46. The angles of a triangle are in AP and the, (c) Statoment | is true, Statement Il is false angle is 30°. What is the greatest angle (in radianp, (d) Statement | is false, Statement Il is true * - * INDA 201271),, , 38. Statement I Let a be the first term, d be the @ 5 3 a5 Or, , eonee difference, S,, denotes the sum of n terms, and a, denotes the nth term of the AP then D ions (Q. Nos. 47-48) The sum of frst », , Se=Timen) forsome mee terms and 20 terms of an AP are 120 and 440, respective,, 2am+1 47. What is its first term? INDA 2012¢;, Statement 1 Thon, d =20 2 = ae wa 4 ae, (a) Statement | is true, Statement Il is true; Statement Il is 48. What is the common difference?, @ correct explanation for Statement | f@1 (0) 2 (3 4, (>) Statement | i . Statement Statement, Sasa etna eoaehaton ior Stowe is 49. What is the geometric mean of the sequence, (c) Statement | is true, Statement It is false 1, 2, 4, By ow 2° peg ENDA 20180, (0) Statement | is false, Statement Ii is true (a)2” (0) 2°, (2iee)-4 (2°, 39. If the mth and the nth term of a HP are n m, respectively, then the math term is, , (a) 0 () 1 ENDA 201201, a2 @: ~ fan () (n+ N2 ()a(n+ NR n+, 2 51. The mean of 10 observations is 5. If 2 is added », 40. If the positive integers a, b, c and d are in AP then each observation and then multiplied by 3, he, the numbers abc, abd, acd and bed are in what will be the new mean? ENDA 2012100), INDA 2013.0D] 5 7, ates wae f@ (b) (c) 15 , @ 21, (¢) GP (@) None of these 52. What does the series 1+3?+3+L.., 41. What is 0. 9+ 0.09+ 0.009+--- equal to? 3, represent? {NDA 201210), , [NDA 2018(ID] AP, (a) 1 () 101 (0) 1.001 @y 1.1 (a) (©) GP, (He (d) None ot these

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sequences ANd Series, , 59. What is the nth term of, , 1% 09, oy Me sequen, , W204 4, (8) Nano of then, , (en, , fa4n-d INDA sore), , 4. Ip. and rare iy AP, an |, of the following is cee “GR then which one, @ Pager W) pegar (©) pe INDA 201211), Wor, , , , , , 65. WA, Ve, 1/10 are () peqer, v "Hi HE then watts the value of, @ (b) 6 INDA 2012, , , , 7, , 66. If the sequence (5,) is oo, On 4 Reomen, , S51, © S)Sq. thon what is the ae a pr, , as ae INDA gory), , (4) Cannot be determined, , 57. What is the sum of the series 11,1, , =r 4s, , , , tea, , ai was ine ca, , 58. battled and (n+ 1)! are in GP then the value of, i e, , INDA, , (a) 3 (b) 4 6 () ale, , 59. What is the 10th common term series, 246410++-and 146441 aor eee 1), , (a) 180 (b) 186 (c) 196 (d) 206 =, , 60. If a. bo &. d. e, fare in AP. then (e = equal, which one of the following? : ina sia;, , (a) 2 =a) (b)2d-c) (C)2r-d) (dd -c), , 61. If the 10the term of a GP is 9 and, then what is its 7th term? suet cae, , fa) 6 (b) 14 (c) 27/14 (@) S65, 62, Which one of the following statements is correct?, INDA 2011(D), , (a) sin® 30°, sin? 45°, sin? 60° are in GP, (b) cos* 30°, cos® 45°, cos® 60° are in GP, (c) cot® 30°, cot® 45°, cot? 60° are in AP, (d) tan® 30°, tan® 45°, tan* 60° are in GP, , , , 63. metre +4, then a.b.e are in, Seas cee (NDA 2011], (a) AP (b) GP, (c) HP (d) None of these, 64. Which term of the series id seo. IS - 126?, [NDA 201100), (a) 9th (bo) 10th =) Mth =) 12th, , 1. 4, 65. What is the sum of V3 +e +—pe te?, V3" 3 wpa 2011001, , @ = (d) v3, , 51, , 66. In a GP of positive terme, any term Is equal to, one-third of the sum of next two torms. What is the, common ratio af the GP? INDA 201100), , Jidet i919, we m5, a) wm (a) 413, , 67. If the AM and GM between two numbers are in the, ratio m:n, then what is the ratio between the two, , numbers? INDA 201001), a) Mt ee to ™2, , m- jm o mn, , at =P i? 4? - tn, Oer © eae, , 68, ‘Tho sum of an infinite geometric progression is 6. If, the sum of the first two terms is 9/2, then what is, , the first term? [NDA 2010(11)}, (a) 1 (bo) 8/72, (c) Sor 2 (d) 903, , 69. A square is drawn by joining mid-points of the sides, of a square. Another square is drawn inside the, second square in the same way and the process is, continued indefinitely. If, the side of the first square, is 16 cm, then what is the sum of the areas of all, , the squares? INDA 2010011), (a) 256 sqm (b) 512 5q em, (c) 1024 sq.cm (8) 512/38q cm, , 70. Tho arithmetic mean of two numbers exceeds their, geometric mean by 2 and the geometric mean, exceeds their harmonic mean by 1.6, What are the, , two numbers? INDA 2010(11), (a) 16,4 (b) 81,9, (©) 256. 16 (d) 625, 25, , 71. The 59th term of an AP is 449 and the 449th term, is 59, Which term is equal to 0 (zero)?, , {NDA 2010(1), (a) 501st term (6) 502nd term, {c) 508th term {d) 509th tern, , 72. What is the sum of all natural numbers between, 200 and 400 which are divisible by 7?, , INDA 2010(), , (a) 6729, , (c) 8729, , 73. Let a,b,c be in an AP., , Consider the following statements, ae in an AP, b oh’ eat he 2, , 1 L 1, " Tose Verda Tarde, {a) Only!, (tb) Only ti, , (c) Both | and ti, (d) Neither | nor I, , (b) 8712, (d) 9276, , (NDA 2010(D}

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52, , 74, Mf p times the pth term of an AP is q times the qth, , term, then what is the tert val to?, Coe sos "NDA 201000), , @ore 0) pg fe) 1 mo, , 75. The gvometric mean of three numbers was, computed as 6, It was subsequently found that, in, this computation, a number 8 was read as, , 12. What is the correct geometric mean?, INDA 2010(D1, to) ¥8, , (a) 4, (c) 2916 {d) None of these, 76. If the AM and HM of two numbers are 27 and 12, respectively, then what is their GM equal to?, t, , NDA 2010(1)), (a) 12 (b) 18 (c) 24 () 27, , THM (14 D4 Stet ple (Tt 34 See +Q), , w(14345 e408), , where each set of parentheses contains the sum of, consecutive odd integers as shown, what is the, smallest possible value of (p +q + 1) where p>6?, , {NDA 2000(ID), (a) 12 () 21 (c) 45 (@) 54, 78. If x?, y*,2? are in AP, then y + 2,2+%,x+ y are in, {NDA 2009 (11D), (a) AP (b) HP, (c) GP (d) None of these, , 79. In an AP. the mth term 1/n and nth term is 1/m., , What is its (mn)th term? [NDA 2009(11)), (a) (mn) (b) min, (c) nim (1, , 80. If a.2a+2,3a+3 are in GP, then what is the fourth, , term of the GP? INDA 2009 (11), (@) - 135 (b) 13.5, () -27 (oh) 27, , Sears, , 1 1, 81. Which torm of the sequence 20,104.10 .178,, , tive term’? INDA 2009,, bt ee, {e) 20h {d) No uch term exints, , Natural numbers are divided into groups as 1), (2.3), (4, 5,0), (7, 8 9. 10) and so on. What jy ©, sum of the numbers in the 11th group?, , INDA 2009 (41), (a) 605 (bo) 615 () 671 (dy 693, , 83. If the sum of the first two terms and the sum of y,, first four terms of @ Progression wig,, positive common ratio are 6 and 60 respect, then what is the oth term? ENDA 20004);, (a) 88 (o) 243 (c) 486 (3) 1488, , 84, If x>1 and log, x log, X-log, 16 are in GR. they, , what is x equal to? INDA 20001),, (a) 9 (b) 8, (c) 4 (a) 2, , 85. In a geometric with first term a, tn a goometric Pahet is the arithmetic mean of fex, five terms? NDA 2009¢), (a) a+ 2r (0) a?, a? -wr-9 (@) ay? - M50 ~1), , 86, The harmonic mean of two numbers is 21.6. If one, of the numbers is 27, then what is the other, , number? UNDA 20091), (a) 16.2 (b) 17.3, () 18 (d) 20, , 87. If the number of terms of an AP is (2n +1), thes, what is the ratio of the sum of the odd terms to the, , sum of even terms? INDA 2009 (1),, © el: wit! ot!, eal On i ir