PROGRESSIONS-PART-I-(E)-02-Assignment

1. The sequence is (a) H.P. (b) G.P. (c) A.P. (d) None of these 2. term of the series will be (a) (b) (c) (d) 3. If the 9th term of an A.P. be zero, then the ratio of its 29th and 19th term is (a) 1 : 2 (b) 2 : 1 (c) 1 : 3 (d) 3 : 1 4. Which of the following sequence is an arithmetic sequence (a) (b) (c) (d) 5. If the term of an A.P. be q and term be p, then its rth term will be (a) (b) (c) (d) 6. If the 9th term of an A.P. is 35 and 19th is 75, then its 20th term will be (a) 78 (b) 79 (c) 80 (d) 81 7. If are in A.P. then 7th term of the series is (a) (b) – 33 (c) 33 (d) 10 a – 4 8. It are in A.P., then its common difference is (a) (b) (c) (d) None of these 9. The 10th term of the sequence ......is (a) (b) (c) (d) 10. Which term of the sequence (– 8 + 18i), (– 6+15i), (– 4 + 12i), ........is purely imaginary (a) 5th (b) 7th (c) 8th (d) 6th 11. If (m +2)th term of an A.P. is (m+2)2–m2 , then its common difference is (a) 4 (b) – 4 (c) 2 (d) – 2 12. For an A.P., then common difference is (a) 0 (b) 1 (c) – 1 (d) 13 13. If tan then the different values of will be in (a) A.P. (b) G.P. (c) H.P. (d) None of these 14. If the and term of an arithmetic sequence are a, b and c respectively, then the value of [a (q – r)+b(r – p)+ c (p – q)]= (a) 1 (b) – 1 (c) 0 (d) 15. If nth terms of two A.P.'s are 3n + 8 and 7n +15, then the ratio of their 12th terms will be (a) (b) (c) (d) 16. The 6th term of an A.P. is equal to 2, the value of the common difference of the A.P. which makes the product least is given by (a) (b) (c) (d) None of these 17. If times the term of an A.P. is equal to q times the term of an A.P., then term is (a) 0 (b) 1 (c) 2 (d) 3 18. The numbers , and 6 are three consecutive terms of an A.P. If t be real, then the next two terms of A.P. are (a) –2, –10 (b) 14, 6 (c) 14, 22 (d) None of these 19. If the pth term of the series 25, , ,...... is numerically the smallest, then p= (a) 11 (b) 12 (c) 13 (d) 14 20. The second term of an A.P. is (x – y) and the 5th term is (x + y), then its first term is (a) (b) (c) (d) 21. The number of common terms to the two sequences 17, 21, 25, ......417 and 16, 21, 26, ..... 466 is (a) 21 (b) 19 (c) 20 (d) 91 22. In an A.P. first term is 1. If is minimum, then common difference is (a) –5/4 (b) –4/5 (c) 5/4 (d) 4/5 23. Let the sets A={2, 4, 6, 8,......} and B= {3, 6, 9, 12, .....}, and n(A) = 200, n(B) = 250. Then (a) n(A  B) = 67 (b) n(A  B) = 450 (c) n(A  B) = 66 (d) n(A  B) = 384 24. The sum of first n natural numbers is (a) n(n – 1) (b) (c) n(n + 1) (d) 25. The sum of the series to 9 terms is (a) (b) (c) 1 (d) 26. The sum of all natural numbers between 1 and 100 which are multiples of 3 is (a) 1680 (b) 1683 (c) 1681 (d) 168 27. The sum of 1+3+5+7+..... upto n terms is (a) (b) (c) (d) 28. If the sum of the series 2+ 5+ 8+11 ....... is 60100, then the number of terms are (a) 100 (b) 200 (c) 150 (d) 250 29. If the first term of an A.P. be 10, last term is 50 and the sum of all the terms is 300, then the number of terms are (a) 5 (b) 8 (c) 10 (d) 15 30. The sum of the numbers between 100 and 1000 which is divisible by 9 will be (a) 55350 (b) 57228 (c) 97015 (d) 62140 31. If the sum of three numbers of a arithmetic sequence is 15 and the sum of their squares is 83, then the numbers are (a) 4, 5, 6 (b) 3, 5, 7 (c) 1, 5, 9 (d) 2, 5, 8 32. If the sum of three consecutive terms of an A.P. is 51 and the product of last and first term is 273, then the numbers are (a) 21, 17, 13 (b) 20, 16, 12 (c) 22, 18, 14 (d) 24, 20, 16 33. There are 15 terms in an arithmetic progression. Its first term is 5 and their sum is 390. The middle term is (a) 23 (b) 26 (c) 29 (d) 32 34. If where denotes the sum of the first n terms of an A.P. then the common difference is (a) P + Q (b) 2P + 3Q (c) 2Q (d) Q 35. The sum of numbers from 250 to 1000 which are divisible by 3 is (a) 135657 (b) 136557 (c) 161575 (d) 156375 36. Four numbers are in arithmetic progression. The sum of first and last term is 8 and the product of both middle terms is 15. The least number of the series is (a) 4 (b) 3 (c) 2 (d) 1 37. The number of terms of the A.P. 3, 7, 11, 15 ...... to be taken so that the sum is 406 is (a) 5 (b) 10 (c) 12 (d) 14 38. The consecutive odd integers whose sum is 452 – 212 are (a) 43, 45, ....., 75 (b) 43, 45,...... 79 (c) 43, 45, ......, 85 (d) 43, 45, ....., 89 39. If common difference of m A.P.'s are respectively 1, 2,...... m and first term of each series is 1, then sum of their mth terms is (a) (b) (c) (d) None of these 40. The sum of all those numbers of three digits which leave remainder 5 after division by 7 is (a) 551 × 129 (b) 550 × 130 (c) 552 × 128 (d) None of these 41. If and in A.P., then is (a) p2 (b) p3 (c) p4 (d) None of these 42. An A.P. consists of n (odd terms) and its middle term is m. Then the sum of the A.P. is (a) 2 mn (b) (c) mn (d) mn2 43. The minimum number of terms of that add up to a number exceeding 1357 is (a) 15 (b) 37 (c) 35 (d) 17 44. If the ratio of the sum of n terms of two A.P.'s be (7n+1) : (4n+27), then the ratio of their 11th terms will be (a) 2 : 3 (b) 3 : 4 (c) 4 : 3 (d) 5 : 6 45. The interior angles of a polygon are in A.P. If the smallest angle be 120° and the common difference be 5, then the number of sides is (a) 8 (b) 10 (c) 9 (d) 6 46. The sum of integers from 1 to 100 that are divisible by 2 or 5 is (a) 3000 (b) 3050 (c) 4050 (d) None of these 47. If the sum of first n terms of an A.P. be equal to the sum of its first m terms, (m  n), then the sum of its first (m + n) terms will be (a) 0 (b) n (c) m (d) m + n 48. If a1, a2 ,......., an are in A.P. with common difference d, then the sum of the following series is (a) (b) (c) (d) 49. The odd numbers are divided as follows Then the sum of row is (a) (b) (c) (d) 50. If the sum of n terms of an A.P. is then the term will be (a) (b) (c) (d) 51. The nth term of an A.P. is . Choose from the following the sum of its first five terms (a) 14 (b) 35 (c) 80 (d) 40 52. If the sum of two extreme numbers of an A.P. with four terms is 8 and product of remaining two middle term is 15, then greatest number of the series will be (a) 5 (b) 7 (c) 9 (d) 11 53. The ratio of sum of m and n terms of an A.P. is , then the ratio of mth and nth term will be (a) (b) (c) (d) 54. The value of x satisfying will be (a) (b) (c) (d) 55. Sum of first n terms in the following series is given by (a) (b) (c) (d) All of these 56. Let denotes the sum of n terms of an A.P. If then ratio (a) 4 (b) 6 (c) 8 (d) 10 57. If the sum of the first n terms of a series be then its second term is (a) 7 (b) 17 (c) 24 (d) 42 58. All the terms of an A.P. are natural numbers. The sum of its first nine terms lies between 200 and 220. If the second term is 12, then the common difference is (a) 2 (b) 3 (c) 4 (d) None of these 59. If .....up to 100 terms and up to 100 terms of a certain A.P. then its common difference d is (a) (b) (c) (d) None of these 60. In the arithmetic progression whose common difference is non-zero, the sum of first 3n terms is equal to the sum of the next n terms. Then the ratio of the sum of the first 2n terms to the next 2n terms is (a) (b) (c) (d) None of these 61. If the sum of n terms of an A.P. is where A, B are constants, then its common difference will be (a) A – B (b) A + B (c) 2A (d) 2B 62. A number is the reciprocal of the other. If the arithmetic mean of the two numbers be , then the numbers are (a) (b) (c) (d) 63. The arithmetic mean of first n natural number (a) (b) (c) (d) n 64. The four arithmetic means between 3 and 23 are (a) 5, 9, 11, 13 (b) 7, 11, 15, 19 (c) 5, 11, 15, 22 (d) 7, 15, 19, 21 65. The mean of the series a, a + nd, a + 2nd is (a) (b) (c) (d) None of these 66. If n A.M. s are introduced between 3 and 17 such that the ratio of the last mean to the first mean is 3 : 1, then the value of n is (a) 6 (b) 8 (c) 4 (d) None of these 67. The sum of n arithmetic means between a and b, is (a) (b) (c) (d) 68. Given that n A.M.'s are inserted between two sets of numbers a, 2b and 2a, b, where a, b R. Suppose further that mean between these sets of numbers is same, then the ratio a : b equals (a) n – m + 1 : m (b) n – m + 1 : n (c) n : n – m + 1 (d) m : n – m + 1 69. Given two number a and b. Let A denote the single A.M. and S denote the sum of n A.M.'s between a and b, then S/A depends on (a) n, a, b (b) n, b (c) n, a (d) n 70. The A.M. of series is (a) (b) (c) (d) None of these 71. If 11 AM's are inserted between 28 and 10, then three mid terms of the series are (a) (b) (c) (d) 72. If , then the arithmetic mean of and is (a) x (b) y (c) 0 (d) 1 73. If A.M. of the roots of a quadratic equation is and the A.M. of their reciprocals is then the quadratic equation is (a) (b) (c) (d) 74. If a1=0 and a1, a2, a3,.....an are real numbers such that |ai–1+1| for all i, then A.M. of the numbers a1, a2, ......an has the value x where (a) x<1 (b) (c) (d) 75. If A.M. of the numbers and is 13 then the set of possible real values of x is (a) (b) (c) (d) None of these 76. If 2x, x+ 8, 3x + 1 are in A.P., then the value of x will be (a) 3 (b) 7 (c) 5 (d) – 2 77. If log32, log3(2x –5) and log3 are in A.P., then x is equal to (a) (b) (c) (d) None of these 78. If denotes the term of an A.P., then (a) (b) (c) (d) None of these 79. If 1, logy x, logz y, – 15 logxz are in A.P., then (a) (b) (c) (d) (e) All of these 80. If are in A.P., then (a) p, q, r are in A.P. (b) are in A.P. (c) are in A.P. (d) None of these 81. If a, b, c, are in A.P., then is equal to (a) (b) (c) (d) 82. If are in A.P. then are in A.P. if p, q, r are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 83. If the sum of the roots of the equation =0 be equal to the sum of the reciprocals of their squares, then will be in (a) A.P. (b) G.P. (c) H.P. (d) None of these 84. If be consecutive terms of an A.P., then (b – c)2, (c – a)2, (a – b)2 will be in (a) G.P. (b) A.P. (c) H.P. (d) None of these 85. If are in A.P., then (b+ c)–1, and will be in (a) H.P. (b) G.P. (c) A.P. (d) None of these 86. If the sides of a right angled triangle are in A.P., then the sides are proportional to (a) 1, 2, 3 (b) 2, 3, 4 (c) 3, 4, 5 (d) 4, 5, 6 87. If a, b, c are in A.P., then the straight line ax + by + c = 0 will always pass through the point (a) ) (b) (c) (d) 88. If a, b, c are in A.P. then (a) 1 (b) 2 (c) 3 (d) 4 89. If a, b, c, d, e, f are in A.P., then the value of e – c will be (a) 2 (c – a) (b) 2 (f – d) (c) 2 (d – c) (d) d – c 90. If p, q, r are in A.P. and are positive, the roots of the quadratic equation px2+ qx + r = 0 are all real for (a) (b) (c) All p and r (d) No p and r 91. If ....... are in A.P., where for all i, then the value of (a) (b) (c) (d) 92. Given where a, b, c, d are real numbers, then (a) a, b, c, d are in A.P. (b) are in A.P. (c) are in A.P. (d) are in A.P. 93. If a, b, c are in A.P., then (a + 2b – c) (2b+ c – a) (c + a – b) equals (a) (b) abc (c) 2 abc (d) 4 abc 94. If the roots of the equation are in A.P., then their common difference will be (a)  1 (b)  2 (c)  3 (d)  4 95. If 1, are in A.P., then x equals (a) (b) (c) (d) 96. If a, b, c, d, e are in A.P. then the value of a+b+4c – 4d + e in terms of a, if possible is (a) 4a (b) 2a (c) 3 (d) None of these 97. If are in A.P. then is equal to (a) (b) (c) (d) None of these 98. If the non-zero numbers x, y, z are in A.P. and are also in A.P., then (a) (b) (c) (d) 99. If three positive real numbers a, b, c are in A.P. such that abc =4, then the minimum value of b is (a) (b) (c) (d) 100. If and are in A.P., where then lies in the interval (a) (b) (c) (d) None of these 101. If the sides of a triangle are in A.P. and the greatest angle of the triangle is double the smallest angle, the ratio of the sides of the triangle is (a) 3 : 4 : 5 (b) 4 : 5 : 6 (c) 5 : 6 : 7 (d) 7 : 8 : 9 102. If a, b, c of a ABC are in A.P., then (a) (b) (c) (d) 103. If a, b, c are in A.P. then the equation has two roots which are (a) Rational and equal (b) Rational and distinct (c) Irrational conjugates (d) Complex conjugates 104. The least value of 'a' for which are three consecutive terms of an A.P. is (a) 10 (b) 5 (c) 12 (d) None of these 105. are in A.P. and where , then the common difference d is (a) 1 (b) –1 (c) 2 (d) – 2 106. If the sides of a right angled triangle form an A.P. then the sines of the acute angles are (a) (b) (c) , (d) 107. If x, y, z are positive numbers in A.P., then (a) (b) (c) has the minimum value 2 (d) 108. If the and terms of a G.P. be a, b, c respectively, then the relation between a, b, c is (a) (b) (c) (d) 109. 7th term of the sequence is (a) (b) (c) (d) 110. If the 5th term of a G.P. is and 9th term is then the 4th term will be (a) (b) (c) (d) 111. If the 10th term of a geometric progression is 9 and 4th term is 4, then its 7th term is (a) 6 (b) 36 (c) (d) 112. The third term of a G.P. is the square of first term. If the second term is 8, then the 6th term is (a) 120 (b) 124 (c) 128 (d) 132 113. The 6th term of a G.P. is 32 and its 8th term is 128, then the common ratio of the G.P. is (a) – 1 (b) 2 (c) 4 (d) – 4 114. The first and last terms of a G.P. are a and l respectively, r being its common ratio; then the number of term in this G.P. is (a) (b) (c) (d) 115. If first term and common ratio of a G.P. are both The absolute value of nth term will be (a) 2n (b) 4n (c) 1 (d) 4 116. In any G.P. the last term is 512 and common ratio is 2, then its 5th term from last term is (a) 8 (b) 16 (c) 32 (d) 64 117. Given the geometric progression 3, 6, 12, 24, ...... the term 12288 would occur as the (a) 11th term (b) 12th term (c) 13th term (d) 14th term 118. Let be a sequence of integers in GP in which and Then is (a) 12 (b) 14 (c) 16 (d) None of these 119. are the roots of the equation and are the roots of the equation If form an increasing G.P., then = (a) (3, 12) (b) (12, 3) (c) (2, 32) (d) (4, 16) 120. If term a G.P. be m and (p – q)th term be n, then the pth term will be (a) m / n (b) (c) mn (d) 0 121. If the third term of a G.P. is 4 then the product of its first 5 terms is (a) (b) (c) (d) None of these 122. If the first term of a G.P. is unity such that is least, then the common ratio of G.P. is (a) (b) (c) (d) None of these 123. Fifth term of a G.P. is 2, then the product of its 9 terms is (a) 256 (b) 512 (c) 1024 (d) None of these 124. If the nth term of geometric progression is , then the value of n is (a) 11 (b) 10 (c) 9 (d) 4 125. The sum of 100 terms of the series .9+ .09 + .009...... will be (a) (b) (c) (d) 126. If the sum of three terms of G.P. is 19 and product is 216, then the common ratio of the series is (a) (b) (c) 2 (d) 3 127. If the sum of first 6 terms is 9 times to the sum of first 3 terms of the same G.P., then the common ratio of the series will be (a) – 2 (b) 2 (c) 1 (d) 128. If the sum of n terms of a G.P. is 255 and nth term is 128 and common ratio is 2, then first term will be (a) 1 (b) 3 (c) 7 (d) None of these 129. The sum of 3 numbers in geometric progression is 38 and their product is 1728. The middle number is (a) 12 (b) 8 (c) 18 (d) 6 130. The sum of few terms of any ratio series is 728, if common ratio is 3 and last term is 486, then first term of series will be (a) 2 (b) 1 (c) 3 (d) 4 131. The sum of n terms of a G.P. is , then the common ratio is equal to (a) (b) (c) (d) None of these 132. The value of n for which the equation holds is (a) 13 (b) 12 (c) 15 (d) 16 133. The value of the sum where equals (a) i (b) i – 1 (c) – i (d) 0 134. For a sequence given and = Then is (a) (b) (c) 2(1 – 3–20) (d) None of these 135. The sum of is equal to (a) (b) (c) (d) None of these 136. The sum of the first n terms of the series is (a) (b) (c) (d) 137. If the product of three consecutive terms of G.P. is 216 and the sum of product of pair – wise is 156, then the numbers will be (a) 1, 3, 9 (b) 2, 6, 18 (c) 3, 9, 27 (d) 2, 4, 8 138. If is a function satisfying for all such that and Then the value of n is (a) 4 (b) 5 (c) 6 (d) None of these 139. The first term of a G.P. is 7, the last term is 448 and sum of all terms is 889, then the common ratio is (a) 5 (b) 4 (c) 3 (d) 2 140. The sum of a G.P. with common ratio 3 is 364, and last term is 243, then the number of terms is (a) 6 (b) 5 (c) 4 (d) 10 141. A G.P. consists of 2n terms. If the sum of the terms occupying the odd places is , and that of the terms in the even places is then is (a) Independent of a (b) Independent of r (c) Independent of a and r (d) Dependent on r 142. Sum of the series to n terms i (a) (b) (c) (d) 143. If the sum of the n terms of G.P. is S product is P and sum of their inverse is R, then is equal to (a) (b) (c) (d) 144. The minimum value of n such that is (a) 7 (b) 8 (c) 9 (d) None of these 145. If every term of a G.P. with positive terms is the sum of its two previous terms, then the common ratio of the series is (a) 1 (b) (c) (d) 146. If then equals (a) 208.34 (b) 212.12 (c) 212.16 (d) 213.16 147. If are in G.P. with first term 'a' and common ratio 'r' then is equal to (a) (b) (c) (d) 148. The sum of the squares of three distinct real numbers which are in G.P. is If their sum is then (a) (b) (c) (d) 149. If the sum of the series is a finite number, then (a) (b) (c) (d) None of these 150. If , then value of x will be (a) (b) (c) (d) 151. If the sum of an infinite G.P. be 9 and the sum of first two terms be 5, then the common ratio is (a) (b) (c) (d) 152. = (a) (b) (c) (d) None of these 153. The first term of a G.P. whose second term is 2 and sum to infinity is 8, will be (a) 6 (b) 3 (c) 4 (d) 1 154. The sum of infinite terms of a G.P. is x and on squaring the each term of it, the sum will be y, then the common ratio of this series is (a) (b) (c) (d) 155. If then the value of will be (a) (b) (c) (d) 156. The sum can be found of a infinite G.P. whose common ratio is r (a) For all values of r (b) For only positive value of r (c) Only for 0 < r < 1 (d) Only for – 1 < r < 1(r  0) 157. The sum of infinity of a geometric progression is and the first term is The common ratio is (a) (b) (c) (d) 158. The value of ..... is (a) 2 (b) 3 (c) 4 (d) 9 159. 0.14189189189…. can be expressed as a rational number (a) (b) (c) (d) 160. The sum of the series is (a) 6.93378 (b) 6.87342 (c) 6.74384 (d) 6.64474 161. Sum of infinite number of terms in G.P. is 20 and sum of their square is 100. The common ratio of G.P. is (a) 5 (b) 3/5 (c) 8/5 (d) 1/5 162. If in an infinite G.P. first term is equal to the twice of the sum of the remaining terms, then its common ratio is (a) 1 (b) 2 (c) 1/3 (d) – 1/3 163. The sum of infinite terms of the geometric progression is (a) (b) (c) (d) 164. If x > 0, then the sum of the series is (a) (b) (c) (d) 165. The sum of the series is (a) (b) (c) (d) 166. A ball is dropped from a height of 120 m rebounds (4/5)th of the height from which it has fallen. If it continues to fall and rebound in this way. How far will it travel before coming to rest ? (a) 240 m (b) 140 m (c) 1080 m (d)  167. The series has a finite sum if C is greater than (a) – 1/2 (b) – 1 (c) – 2/3 (d) None of these 168. If then the value of r will be (a) (b) (c) (d) 169. The sum to infinity of the following series will be (a) 3 (b) 4 (c) (d) 170. , . Then the value of is (a) (b) (c) (d) 171. The value of where to  is (a) 1 (b) 2 (c) 1/2 (d) 4 172. The sum of an infinite geometric series is 3. A series, which is formed by squares of its terms have the sum also 3. First series will be \ (a) (b) (c) (d) 173. If then is (a) (b) (c) (d) 174. Consider an infinite G.P. with first term a and common ratio r, its sum is 4 and the second term is 3/4 , then (a) (b) (c) (d) 175. Let be a positive integer, then the largest integer m such that divides is (a) 32 (b) 63 (c) 64 (d) 127 176. If |a|<1 and |b|<1, then the sum of the series upto  is (a) (b) (c) (d) 177. If S is the sum to infinity of a G.P., whose first term is a, then the sum of the first n terms is (a) (b) (c) (d) None of these 178. If S denotes the sum to infinity and the sum of n terms of the series such that then the least value of n is (a) 8 (b) 9 (c) 10 (d) 11 179. If exp. {(sin2x+sin4x+sin4x+....+) loge2} satisfies the equation then the value of is (a) (b) (c) 0 (d) None of these 180. If G be the geometric mean of x and y, then (a) (b) (c) (d) 181. If n geometric means be inserted between a and b, then the nth geometric mean will be (a) (b) (c) (d) 182. If be the geometric mean of a and b, then n= (a) 0 (b) 1 (c) 1/2 (d) None of these 183. The G.M. of roots of the equation is (a) 3 (b) 4 (c) 2 (d) 1 184. If five G.M.'s are inserted between 486 and 2/3 then fourth G.M. will be (a) 4 (b) 6 (c) 12 (d) – 6 185. If 4 G.M’s be inserted between 160 and 5 them third G.M. will be (a) 8 (b) 118 (c) 20 (d) 40 186. The product of three geometric means between 4 and will be (a) 4 (b) 2 (c) – 1 (d) 1 187. The geometric mean between –9 and –16 is (a) 12 (b) – 12 (c) – 13 (d) None of these 188. If n geometric means between a and b be ..... and a geometric mean be G, then the true relation is (a) (b) (c) (d) 189. If x and y be two real numbers and n geometric means are inserted between x and y. now x is multiplied by k and y is multiplied and then n G.M’s. are inserted. The ratio of the G.M’s. in the two cases is (a) (b) (c) (d) None of these 190. If a, b, c are in G.P., then (a) (b) (c) (d) None of these 191. If x is added to each of numbers 3, 9, 21 so that the resulting numbers may be in G.P., then the value of x will be (a) 3 (b) (c) 2 (d) 192. If and are in G.P., then x = (a) (b) (c) (d) 193. If are in G.P. then the value of n is (a) 2 (b) 3 (c) 4 (d) Nonexistent 194. If p, q, r are in A.P., then pth, qth and rth terms of any G.P. are in (a) AP (b) G.P. (c) Reciprocals of these terms are in A.P. (d) None of these 195. If a, b, c are in G.P., then (a) are in G.P. (b) are in G.P. (c) are in G.P. (d) None of these 196. Let a and b be roots of and let c and d be the roots of where a, b, c, d form an increasing G.P. Then the ratio of (q + p) : (q – p) is equal to (a) 8 : 7 (b) 11 : 10 (c) 17 : 15 (d) None of these 197. If the roots of the cubic equation are in G.P., then (a) (b) (c) (d) 198. If as well as are in G.P. with the same common ratio, then the points and (a) Lie on a straight line (b) Lie on an ellipse (c) Lie on a circle (d) Are vertices of a triangle 199. Let Then the number of real values of x for which the three unequal numbers are in GP is (a) 1 (b) 2 (c) 0 (d) None of these 200. Sr denotes the sum of the first r terms of a G.P. Then are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 201. If and are in G.P., then x, y, z will be in (a) A.P. (b) G.P. (c) H.P. (d) None of these 202. If x, y, z are in G.P. and , then (a) (b) (c) (d) None of these 203. Three consecutive terms of a progression are 30, 24, 20. The next term of the progression is (a) 18 (b) (c) 16 (d) None of these 204. The 5th term of the H.P., will be (a) (b) (c) (d) 10 205. If 5th term of a H.P. is and 11th term is , then its 16th term will be (a) (b) (c) (d) 206. If the 7th term of a H.P. is and the 12th term is then the 20th term is (a) (b) (c) (d) 207. If 6th term of a H.P. is and its tenth term is then first term of that H.P. is (a) (b) (c) (d) 208. The 9th term of the series 27+ 9 + will be (a) (b) (c) (d) 209. In a H.P., pth term is q and the qth term is p. Then pqth term is (a) 0 (b) 1 (c) pq (d) 210. If a, b, c be respectively the pth, qth and rth terms of a H.P., then equals (a) 1 (b) 0 (c) – 1 (d) None of these 211. If be the harmonic mean between a and b, then the value of n is (a) 1 (b) – 1 (c) 0 (d) 2 212. If the harmonic mean between a and b be H, then (a) 4 (b) 2 (c) 1 (d) a + b 213. If H is the harmonic mean between p and q, then the value of is (a) 2 (b) (c) (d) None of these 214. H. M. between the roots of the equation is (a) (b) (c) (d) 215. The harmonic mean of and is (a) (b) (c) a (d) 216. The sixth H.M. between 3 and is (a) (b) (c) (d) 217. If there are n harmonic means between 1 and and the ratio of 7th and harmonic means is 9 : 5, then the value of n will be (a) 12 (b) 13 (c) 14 (d) 15 218. If m is a root of the given equation and m harmonic means are inserted between a and b, then the difference between last and the first of the means equals (a) b – a (b) ab (b – a) (c) a (b – a) (d) ab(a – b) 219. If then a, b, c are in (a) A.P. (b) G.P. (c) H.P. (d) In G.P. and H.P. both 220. If a, b, c are in H.P., then are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 221. If a, b, c, d are any four consecutive coefficients of any expanded binomial, then are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 222. are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 223. If a, b, c are in H.P., then for all the true statement is (a) (b) (c) (d) None of these 224. Which number should be added to the numbers 13, 15, 19 so that the resulting numbers be the consecutive term of a H.P. (a) 7 (b) 6 (c) – 6 (d) – 7 225. If are in A.P., then will be in (a) A.P. (b) G.P. (c) H.P. (d) None of these 226. If a, b, c, d be in H.P., then (a) (b) (c) (d) 227. If are in H.P., then will be equal to (a) (b) (c) (d) None of these 228. If x, y, z are in H.P., then the value of expression will be (a) (b) (c) (d) 229. If are in H.P., then x, y, z are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 230. If a, b, c, d are in H.P., then (a) a + d > b + c (b) ad > bc (c) Both (a) and (b) (d) None of these 231. If |x| <1, then the sum of the series will be (a) (b) (c) (d) 232. The sum of 0.2+0.004 + 0.00006 + 0.0000008+...... to  is (a) (b) (c) (d) None of these 233. The term of the sequence 1.1, 2.3, 4.5, 8.7,...... will be (a) (b) (c) (d) 234. The sum of infinite terms of the following series .....will be (a) (b) (c) (d) 235. The sum of the series 1+ 3x+ 6x2+10x3+....... will be (a) (b) (c) (d) 236. is equal to (a) 1 (b) 2 (c) (d) 237. The sum of upto n terms is (a) (b) (c) (d) 238. The sum of i – 2 – 3i + 4 + ....... upto 100 terms, where is (a) (b) (c) (d)