BINOMIAL THEOREM-(E)-02-Assignment

1. The approximate value of is (a) 1.6 (b) 1.4 (c) 1.8 (d) 1.2 2. If , then the value of b and n are respectively (a) 4, 2 (b) 2, – 4 (c) 2, 4 (d) – 2, 4 3. If then r is equal to (a) 5 (b) 4 (c) 3 (d) 2 4. If , then correct statement is (a) 2m = n (b) 2m = n(n + 1) (c) 2m = n(n – 1) (d) 2n = m(m – 1) 5. If , then equals (a) nxy (b) nx(x + yn) (c) nx(nx+ y) (d) None of these 6. Let . Then (a) f(x) is a polynomial of the sixth degree in x (b) f(x) has exactly two terms (c) f(x) is not a polynomial in x (d) Coefficient of is 64 7. In the expansion of , the sum of odd terms is P and sum of even terms is Q, then the value of will be (a) (b) (c) (d) 8. is (a) Less than (b) Greater than (c) Less than (d) Greater than 9. The expression has value, lying between (a) 134 and 135 (b) 135 and 136 (c) 136 and 137 (d) None of these 10. The positive integer just greater than is (a) 4 (b) 5 (c) 2 (d) 3 11. (a) 101 (b) (c) (d) 12. The value of is (a) 252 (b) 352 (c) 452 (d) 532 13. The greatest integer less than or equal to is (a) 196 (b) 197 (c) 198 (d) 199 14. The integer next above contains (a) as a factor (b) as a factor (c) as a factor (d) as a factor 15. Let n be an odd natural number greater than 1. Then the number of zeros at the end of the sum is (a) 3 (b) 4 (c) 2 (d) None of these 16. 6th term in expansion of is (a) (b) (c) (d) None of these 17. 16th term in the expansion of is (a) (b) 136 xy (c) (d) 18. In the binomial expansion of , n  5, the sum of the 5¬th and 6th terms is zero. Then is equal to (a) (b) (c) (d) 19. The first 3 terms in the expansion of are 1, 6x and . Then the value of a and n are respectively (a) 2 and 9 (b) 3 and 2 (c) 2/3 and 9 (d) 3/2 and 6 20. If the third term in the expansion of is 1000, then the value of x is (a) 10 (b) 100 (c) 1 (d) None of these 21. If the ratio of the 7th term from the beginning to the seventh term from the end in the expansion of is , then x is (a) 9 (b) 6 (c) 12 (d) None of these 22. The last term in the binomial expansion of is . Then the 5th term from the beginning is (a) (b) (c) (d) None of these 23. In the expansion of is equal to (a) (b) (c) (d) 24. If 6th term in the expansion of is 5600, then x is equal to (a) 8 (b) 9 (c) 10 (d) None of these 25. The value of x in the expression , if the third term in the expansion is 10,00,000 (a) 10 (b) 11 (c) 12 (d) None of these 26. If represent the terms in the expansion of , then (a) (b) (c) (d) 27. The value of x, for which the 6th term in the expansion of is 84, is equal to (a) 4 (b) 3 (c) 2 (d) 1 28. Given that 4th term in the expansion of has the maximum numerical value, the range of value of x for which this will be true is given by (a) (b) (c) (d) None of these 29. If the (r + 1)th term in the expansion of has the same power of a and b, then the value of r is (a) 9 (b) 10 (c) 8 (d) 6 30. If the 6th term in the expansion of the binomial is equal to 21 and it is known that the binomial coefficients of the 2nd, 3rd and 4th terms in the expansion represent respectively the first, third and fifth terms of an A.P. (the symbol log stands for logarithm to the base 10), then x = (a) 0 (b) 1 (c) 2 (d) 3 31. If the fourth term of is equal to 200 and x > 1, then x is equal to (a) (b) 10 (c) (d) 32. To make the term free from x, necessary condition is (a) (b) (c) 3n = r (d) None of these 33. In the expansion of , the term independent of x is (a) (b) (c) (d) 34. The term independent of y in the expansion of is (a) 84 (b) 8.4 (c) 0.84 (d) – 84 35. The term independent of x in the expansion of will be (a) 5 (b) 6 (c) 7 (d) 8 36. In the expansion of , the constant term is (a) – 20 (b) 20 (c) 30 (d) – 30 37. The term independent of x in the expansion of is (a) 1 (b) – 1 (c) – 48 (d) None of these 38. In the expansion of , the term independent of x is (a) (b) (c) (d) 39. In the expansion of , the term independent of x is (a) (b) (c) (d) None of these 40. The term independent of x in is (a) – 7930 (b) – 495 (c) 495 (d) 7920 41. The term independent of x in is (a) (b) (c) (d) None of these 42. The term independent of x in is (a) (b) (c) (d) None of these 43. The ratio of the coefficient of to the term independent of x in is (a) 1 : 32 (b) 32 : 1 (c) 1 : 16 (d) 16 : 1 44. The term independent of x in the expansion of is (a) (b) (c) (d) 45. The term independent of x in the expansion of is (a) (b) (c) (d) 46. The term independent of x in the expansion of is (a) 153090 (b) 150000 (c) 150090 (d) 153180 47. The term independent of x in the expansion of is (a) 4320 (b) 216 (c) – 216 (d) – 4320 48. In the expansion of , the term independent of x is (a) Not existent (b) (c) 2268 (d) – 2268 49. In the expansion of (n  N), the term independent of x is (a) (b) (c) (d) 50. The sum of the coefficients in the binomial expansion of is equal to 6561. The constant term in the expansion is (a) (b) (c) (d) None of these 51. The greatest value of the term independent of x in the expansion of , is (a) (b) (c) (d) None of these 52. If the coefficients of pth, and terms in the expansion of are in A.P., then (a) (b) (c) (d) None of these 53. The coefficient of two consecutive terms in the expansion of will be equal, if (a) n is any integer (b) n is an odd integer (c) n is an even integer (d) None of these 54. In the expansion of , the coefficient of will be (a) (b) (c) (d) 55. If the ratio of the coefficient of third and fourth term in the expansion of is 1 : 2, then the value of n will be (a) 18 (b) 16 (c) 12 (d) – 10 56. In the expansion of , the term containing is (a) (b) (c) (d) None of these 57. If the coefficients of rth term and term are equal in the expansion of , then the value of r will be (a) 7 (b) 8 (c) 9 (d) 10 58. In the expansion of , the coefficient of y will be (a) 20 c (b) 10 c (c) (d) 59. If p and q be positive, then the coefficients of and in the expansion of will be (a) Equal (b) Equal in magnitude but opposite in sign (c) Reciprocal to each other (d) None of these 60. If the coefficients of 5th , 6th and 7th terms in the expansion of be in A.P., then n = (a) 7 only (b) 14 only (c) 7 or 14 (d) None of these 61. Two consecutive terms in the expansion of whose coefficients are equal, are (a) 29th and 30th (b) 30th and 31st (c) 31st and 32nd (d) None of these 62. The coefficient of in the expansion of is (a) – 56 (b) 56 (c) – 14 (d) 14 63. If for positive integers r > 1, n > 2, the coefficient of the (3r)th and (r + 2)th powers of x in the expansion of are equal, then (a) n = 2r (b) n = 3r (c) n = 2r + 1 (d) None of these 64. In the expansion of , the coefficient of is (a) – 1680 (b) 1680 (c) 3360 (d) 6720 65. In the expansion of , the coefficient of is (a) (b) (c) (d) None of these 66. The coefficient of in the expansion of is (a) (b) (c) (d) 67. If coefficient of (2r + 3)th and (r – 1)th terms in the expansion of are equal, then value of r is (a) 5 (b) 6 (c) 4 (d) 3 68. If occurs in the rth term in the expansion of , then r = (a) 7 (b) 8 (c) 9 (d) 10 69. If the coefficients of and in are equal, then n is (a) 56 (b) 55 (c) 45 (d) 15 70. If coefficients of (2r + 1)th term and (r + 2)th term are equal in the expansion of , then the value of r will be (a) 14 (b) 15 (c) 13 (d) 16 71. If the coefficient of 4th term in the expansion of is 56, then n is (a) 12 (b) 10 (c) 8 (d) 6 72. If the coefficients of and in the expansion of are the same, then the value of a is (a) (b) (c) (d) 73. The coefficient of in the expansion of is (a) 14 (b) 21 (c) 28 (d) 35 74. If the coefficient of (2r + 4)th and (r – 2)th terms in the expansion of are equal, then r = (a) 12 (b) 10 (c) 8 (d) 6 75. If occurs in the expansion of , then the coefficient of is (a) (b) (c) (d) None of these 76. If coefficients of 2nd, 3rd and 4th terms in the binomial expansion of are in A.P., then is equal to (a) – 7 (b) 7 (c) 14 (d) – 14 77. The coefficient of in the expansion of is (a) 512 (b) – 512 (c) 521 (d) 251 78. If the coefficient of x in the expansion of is 270, then k = (a) 1 (b) 2 (c) 3 (d) 4 79. In the expansion of the coefficient of pth and terms are respectively p and q. Then p + q = (a) n + 3 (b) n + 1 (c) n + 2 (d) n 80. The coefficient of in the expansion of is (a) – 455 (b) – 105 (c) 105 (d) 455 81. If the coefficients of Tr, Tr +1, Tr +2 terms of are in A.P., then r = (a) 6 (b) 7 (c) 8 (d) 9 82. In the expansion of , coefficients of 2nd, 3rd and 4th terms are in A.P., then n is equal to (a) 7 (b) 9 (c) 11 (d) None of these 83. Coefficient of in the expansion of is (a) (b) (c) – 7 (d) 7 84. The coefficient of in the expansion of is (a) 18 (b) 6 (c) 12 (d) 10 85. If A and B are coefficients of and respectively in the expansion of , then (a) A = B (b) A  B (c) A =  B for some  (d) None of these 86. If the rth term in the expansion of contains , then r is equal to (a) 2 (b) 3 (c) 4 (d) 5 87. The coefficient of in is (a) 0 (b) 120 (c) 420 (d) 540 88. If the coefficient of (r + 1)th term in the expansion of be equal to that of (r + 3)th term, then (a) n – r + 1 = 0 (b) n – r – 1 = 0 (c) n + r + 1 = 0 (d) None of these 89. occurs in the expansion of in (a) (b) (c) (d) None of these 90. In the expansion of , n  N, the coefficient of x and are 8 and 24 respectively. Then (a) a = 2, n = 4 (b) a = 4, n = 2 (c) a = 2, n = 6 (d) a = – 2, n = 4 91. The coefficient of the term independent of x in the expansion of is (a) (b) (c) (d) 92. The coefficient of in the expansion of is (a) (b) (c) (d) None of these 93. The coefficient of in the expansion of is (a) (b) (c) (d) 94. The coefficient of in the following expansion is (a) (b) (c) (d) 95. The sum of the coefficients of even power of x in the expansion of is (a) 256 (b) 128 (c) 512 (d) 64 96. The coefficient of in the expansion of is (a) (b) (c) (d) 97. The coefficient of in the expansion of is (a) (b) (c) (d) 98. If in the expansion of , the coefficient of x and are 3 and – 6 respectively, then m is (a) 6 (b) 9 (c) 12 (d) 24 99. In the expansion of the following expression , the coefficient of is (a) (b) (c) (d) None of these 100. If there is a term containing in , then (a) n – 2r is a positive integral multiple of 3 (b) n – 2r is even (c) n – 2r is odd (d) None of these 101. If the binomial coefficients of 2nd, 3rd and 4th terms in the expansion of are in A.P. and the 6th term is 21, then the value(s) of x is (are) (a) 1, 3 (b) 0, 2 (c) 4 (d) – 1 102. The coefficient of in the expansion of is (a) (b) (c) (d) None of these 103. The coefficient of in the expansion of is (a) (b) (c) (d) None of these 104. The coefficient of in the expansion of is (a) (b) (c) (d) None of these 105. The coefficient of in the expansion of is (a) 4 (b) – 4 (c) 0 (d) None of these 106. The coefficient of in the expansion of (x – 1) (x – 2)…. (x – 18) is (a) 171 (b) – 171 (c) 342 (d) 171/2 107. In the expansion of , the coefficient of is (a) (b) (c) 210 (d) 310 108. The number of non-zero terms in the expansion of is (a) 9 (b) 0 (c) 5 (d) 10 109. The number of terms in the expansion of will be (a) n + 1 (b) n + 3 (c) (d) None of these 110. The total number of terms in the expansion of after simplification is (a) 50 (b) 51 (c) 202 (d) None of these 111. The expression is a polynomial of degree (a) 5 (b) 6 (c) 7 (d) 8 112. The number of terms in the expansion of is (a) 6 (b) 7 (c) 8 (d) None of these 113. If n is a negative integer and |x| < 1 then the number of terms in the expansion of is (a) n + 1 (b) n + 2 (c) (d) Infinite 114. The number of terms in the expansion of is (a) 18 (b) 9 (c) 19 (d) 24 115. The number of terms whose values depend on x in the expansion of is (a) 2n + 1 (b) 2n (c) n (d) None of these 116. The number of real negative terms in the binomial expansion of , is (a) n (b) n + 1 (c) n ¬– 1 (d) 2n 117. In the expansion of , the number of terms is (a) 7 (b) 14 (c) 6 (d) 4 118. The number of distinct terms in the expansion of is (a) n + 1 (b) (c) (d) 119. In how many terms in the expansion of do not have fractional power of the variable (a) 6 (b) 7 (c) 8 (d) 10 120. If the middle term in the expansion of is , then n = (a) 10 (b) 12 (c) 14 (d) None of these 121. The middle term in the expansion of is (a) (b) (c) (d) None of these 122. The middle term in the expansion of will be (a) (b) (c) (d) 123. The coefficient of middle term in the expansion of is (a) (b) (c) (d) None of these 124. The middle term in the expansion of is (a) (b) (c) (d) 125. The middle term in the expansion of is (a) (b) (c) (d) None of these 126. The middle terms in the expansion of is (a) (b) (c) (d) 127. The middle term in the expansion of is (a) (b) (c) (d) None of these 128. If the coefficient of the middle term in the expansion of is p and the coefficients of middle terms in the expansion of are q and r, then (a) p + q = r (b) p + r = q (c) p = q + r (d) p + q + r = 0 129. Middle term in the expansion of is (a) 4th (b) 3rd (c) 10th (d) None of these 130. The coefficient of each middle term in the expansion of , when n is odd, is (a) (b) (c) (d) 131. If the rth term is the middle term in the expansion of then the (r + 3)th term is (a) (b) (c) (d) None of these 132. The coefficient of the middle term in the binomial expansion in powers of x of and of is the same if  equals (a) (b) (c) (d) 133. The sum of the coefficients in the expansion of is 4096. The greatest coefficient in the expansion is (a) 1024 (b) 924 (c) 824 (d) 724 134. The greatest coefficient in the expansion of is (a) (b) (c) (d) 135. If the sum of the coefficients in the expansion of is 1024, then the value of the greatest coefficient in the expansion is (a) 356 (b) 252 (c) 210 (d) 120 136. If n is even, then the greatest coefficient in the expansion of is (a) (b) (c) (d) None of these 137. If x = 1/3, then the greatest term in the expansion of is (a) (b) (c) (d) 138. The numerically greatest term of when x = 3/2 is (a) (b) (c) (d) None of these 139. If the sum of the coefficients in the expansion of is 128, then the greatest coefficient in the expansion of is (a) 35 (b) 20 (c) 10 (d) None of these 140. If the coefficient of the 5th term be the numerically greatest coefficient in the expansion of then the positive integral value of n is (a) 9 (b) 8 (c) 7 (d) 10 141. The greatest term in the expansion of is (a) (b) (c) (d) None of these 142. If n is even positive integer, then the condition that the greatest term in the expansion of may have the greatest coefficient also, is (a) (b) (c) (d) None of these 143. The interval in which x must lie so that the numerically greatest term in the expansion of has the numerically greatest coefficient is (a) (b) (c) (d) 144. is equal to (a) (b) 0 (c) (d) None of these 145. In the expansion of , the sum of the coefficient of odd powers of x is (a) 0 (b) (c) (d) 146. is equal to (a) (b) (c) (d) 147. If denotes the product of all the coefficients in the expansion of , then is equal to (a) (b) (c) (d) 148. (a) n (b) 1/n (c) (d) 149. (a) (b) (c) (d) None of these 150. If n is odd, then (a) 0 (b) 1 (c)  (d) 151. (a) (b) (c) (d) None of these 152. (a) 100 (b) 120 (c) – 120 (d) None of these 153. (a) (b) (c) (d) None of these 154. (a) (b) (c) 0 (d) None of these 155. The sum of where n is an even integer, is (a) (b) (c) (d) None of these 156. In the expansion of the sum of coefficients of odd powers of x is (a) (b) (c) (d) 157. is equal to (a) (b) (c) 0 (d) 158. The value of is (a) 15 (b) – 15 (c) 0 (d) 51 159. If are the binomial coefficients, then equals (a) (b) (c) (d) 160. If m, n, r are positive integers such that r < m, n, then equals (a) (b) (c) (d) None of these 161. The value of is (a) 2 (b) 0 (c) 1/2 (d) 1 162. The value of is (a) (b) (c) (d) 163. The sum of (n + 1) terms of is (a) (b) (c) (d) None of these 164. If sum of all the coefficients in the expansion of is 128, then the coefficient of is (a) 35 (b) 45 (c) 7 (d) None of these 165. The sum of 12 terms of the series is (a) (b) (c) (d) None of these 166. The sum of the coefficients of all the integral powers of x in the expansion of is (a) (b) (c) (d) 167. If , then (a) (b) (c) (d) 168. If , then equals (a) (b) (c) (d) 169. If , then the value of is (a) (b) (c) (d) 170. If is the coefficient of , in the expansion of , then (a) 0 (b) n (c) – n (d) 2n 171. If , then (a) (b) (c) (d) None of these 172. If a and d are two complex numbers, then the sum to (n + 1) terms of the following series is (a) (b) na (c) 0 (d) None of these 173. If , then (a) (b) (c) (d) None of these 174. The sum of the series is (a) (b) (c) (d) None of these 175. If n is a positive integer and , then the value of (a) (b) (c) (d) None of these 176. The sum of the series is (a) (b) (c) (d) 177. If , then the value of is (a) 30 (b) 32 (c) 31 (d) None of these 178. If denote the binomial coefficient in the expansion of , then the value of is (a) (b) (c) (d) 179. If and , then the value of k is (a) (b) (c) (d) None of these 180. , if K  (a) (b) (– , – 2) (c) (2, ) (d) 181. The coefficient of in the polynomial is (a) (b) (c) (d) 182. If n is positive integer then the sum of is equal to (a) 0 (b) (c) (d) None of these 183. The value of is (a) (b) (c) (d) None of these 184. The sum to (n + 1) terms of the following series is (a) 0 (b) 1 (c) – 1 (d) None of these 185. If , then the value of is (a) (b) (c) (d) None of these 186. The value of is (a) (b) (c) (d) 187. Let n be an odd integer. If for every value of , then (a) (b) (c) (d) 188. and for all k  n, then (a) (b) (c) (d) None of these 189. Let n  N. If , and are in A.P. then (a) are in A.P (b) are in H.P (c) n = 7 (d) n = 14 190. If , then equals (a) 10 (b) 20 (c) 210 (d) 420 191. If , then value of and are (a) 0, 6 (b) (c) 1, 6 (d) 0 192. If are in A.P. and , then n is equal to (a) 2 (b) 3 (c) 4 (d) All of these 193. If then is equal to (a) (b) (c) (d) None of these 194. If then (a) (b) (c) (d) None of these 195. The sum of the coefficients in the expansion of will be (a) 0 (b) 1 (c) – 1 (d) 196. The sum of all the coefficients in the binomial expansion of is (a) 1 (b) 2 (c) – 1 (d) 0 197. The sum of the coefficients in is (a) (b) (c) 2 (d) None of these 198. If the sum of the coefficients in the expansion of is equal to the sum of the coefficients in the expansion of , then  = (a) 0 (b) 1 (c) May be any real number (d) No such value exist 199. The sum of coefficients in the expansion of is (a) (b) (c) (d) None of these 200. If the sum of the coefficients in the expansion of is a and if the sum of the coefficients in the expansion of is b, then (a) a = 3b (b) (c) (d) None of these 201. The sum of coefficients in is (a) – 1 (b) 1 (c) 0 (d) 202. The sum of coefficients in the expansion of is (a) 2 (b) (c) (d) 203. If n  N, then the sum of the coefficients in the expansion of the binomial is (a) 1 (b) – 1 (c) 2 (d) 0 204. In the expansion of , the sum of the coefficients of the terms of degree r is (a) (b) (c) (d) 205. The sum of the numerical coefficients in the expansion of is (a) 1 (b) 2 (c) (d) None of these 206. The sum of the coefficients in the expansion of is (a) 7 (b) 8 (c) – 1 (d) 1 207. If , then the value of x in terms of y is (a) (b) (c) (d) 208. The coefficient of x in the expansion of in ascending powers of x, when |x| < 1, is (a) 0 (b) (c) (d) 1 209. If x is positive, the first negative term in the expansion of is (a) 7th term (b) 5th term (c) 8th term (d) 6th term 210. The approximate value of correct to four decimal places is (a) 1.9995 (b) 1.9996 (c) 1.9990 (d) 1.9991 211. Cube root of 217 is (a) 6.01 (b) 6.04 (c) 6.02 (d) None of these 212. If |x| < 1, then in the expansion of , the coefficient of is (a) n (b) n + 1 (c) 1 (d) – 1 213. If |x| < 1, then the value of will be (a) (b) (c) (d) 214. The sum of , will be (a) (b) (c) (d) None of these 215. The first four terms in the expansion of are (a) (b) (c) (d) None of these 216. The coefficient of in the expansion of is (a) (b) (c) (d) None of these 217. If the third term in the binomial expansion of is , then the rational value of m is (a) 2 (b) 1/2 (c) 3 (d) 4 218. can be expanded by binomial theorem, if (a) x < 1 (b) |x| < 1 (c) (d) 219. (r + 1)th term in the expansion of will be (a) (b) (c) (d) None of these 220. If |x| < 1, then the coefficient of in the expansion of will be (a) 1 (b) n (c) n + 1 (d) None of these 221. The general term in the expansion of is (a) (b) (c) (d) None of these 222. The coefficient of in is (a) 6/13 (b) 55/72 (c) 7/19 (d) 2/9 223. The coefficient of in the expansion of is (a) (b) (c) (d) 224. The coefficient of in is (a) 13 (b) 15 (c) 20 (d) 22 225. The value of is (a) (b) (c) (d) 226. The coefficient of in the expansion of is (a) (b) (c) (d) None of these 227. The coefficient of in the expression is (a) (b) (c) (d) 228. The value of is (a) (b) (c) (d) 229. The coefficient of in is (a) (b) (c) (d) 230. The coefficient of x in the expansion of is (a) a + b + c (b) a – b – c (c) – a + b + c (d) a – b + c 231. If x be so small that its 2 and higher power may be neglected, then is equal to (a) 2 + x (b) 2 + 10x (c) 1 – 2x (d) 2 + 11x 232. is equal to (a) (b) (c) (d) 233. The fourth term in the expansion of will be (a) (b) (c) (d) 234. (a) (b) (c) (d) 235. If , then (a, b) = (a) (2, 12) (b) (– 2, 12) (c) (2, – 12) (d) None of these 236. (a) (b) (c) (d) 237. The coefficient of in the expansion of is (a) (b) (c) (d) 238. (a) (b) (c) (d) 239. terms = (a) (b) (c) (d) 240. The sum of the series is equal to (a) (b) (c) (d) 241. If is approximately equal to a + bx for small values of x, then (a, b) = (a) (b) (c) (d) 242. In the expansion of , the coefficient of will be (a) 4n (b) 4n – 3 (c) 4n + 1 (d) None of these 243. The coefficient of in the expansion of will be (a) 8 (b) 32 (c) 50 (d) None of these 244. If , then is equal to (a) (b) (c) (d) None of these 245. If p is nearly equal to q and n > 1, such that , then the value of k is (a) n (b) (c) n + 1 (d) 246. If x is very small compared to 1, then is equal to (a) (b) (c) (d) 247. If x is very small and , then (a) (b) (c) (d) 248. If a, b are approximately equal then the approximate value of is (a) (b) (c) 1 (d) 9/3b 249. If x is nearly equal to 1, then the approximate value of is (a) (b) (c) (d) 250. The coefficient of in the expansion of is (a) (b) (c) 1 (d) None of these 251. If in the expansion of , a, b, c are three consecutive coefficients, then n = (a) (b) (c) (d) None of these 252. If n is a positive integer and three consecutive coefficients in the expansion of are in the ratio 6 : 33 : 110, then n = (a) 4 (b) 6 (c) 12 (d) 16 253. If the three consecutive coefficients in the expansion of are 28, 56 and 70, then the value of n is (a) 6 (b) 4 (c) 8 (d) 10 254. The coefficients of three successive terms in the expansion of are 165, 330 and 462 respectively, then the value of n will be (a) 11 (b) 10 (c) 12 (d) 8 255. The coefficient of in the expansion of is (a) 10 (b) – 20 (c) – 50 (d) – 30 256. The coefficient of in the expansion of is (a) (b) (c) (d) 257. The coefficient of in the expansion of is (a) (b) (c) (d) None of these 258. The number of terms which are free from radical signs in the expansion of is (a) 5 (b) 6 (c) 7 (d) None of these 259. The number of integral terms in the expansion of is (a) 106 (b) 108 (c) 103 (d) 109 260. In the expansion of , the number of terms free from radicals is (a) 730 (b) 715 (c) 725 (d) 750 261. The number of rational terms in the expansion of is (a) 6 (b) 7 (c) 5 (d) 8 262. The number of terms with integral coefficients in the expansion of is (a) 100 (b) 50 (c) 101 (d) None of these 263. The sum of the rational terms in the expansion of is (a) 32 (b) 9 (c) 41 (d) None of these 264. If , where P is an integer and F is a proper fraction then (a) P is an odd integer (b) P is an even integer (c) (d) 265. If [x] denotes the greatest integer less than or equal to x, then (a) Is an even integer (b) Is an odd integer (c) Depends on n (d) None of these 266. Which of the following expansion will have term containing (a) (b) (c) (d) 267. If the second term in the expansion is , then the value of is (a) 4 (b) 3 (c) 12 (d) 6