DETERMINANT-(E)-02-ASSIGNMENT

1. If a, b and c are non -zero real numbers, then is equal to (a) (b) (c) (d) None of these 2. If is a cube root of unity and , then is equal to (a) (b) (c) 1 (d) 3. The determinant is not equal to (a) (b) (c) (d) 4. If is the cube root of unity, then = (a) 1 (b) 0 (c) (d) 5. If , then the solution of the equation is (a) 0 (b) (c) 0, (d) 0, 6. (a) (b) (c) (d) 7. = (a) (b) (c) (d) 0 8. = (a) (b) (c) (d) 9. If , then the value of k is (a) –1 (b) 0 (c) 1 (d) None of these 10. The value of the determinant is (a) (b) (c) (d) None of these 11. (a) 1 (b) 0 (c) x (d) xy 12. (a) (b) (c) (d) None of these 13. The value of the determinant is (a) –75 (b) 25 (c) 0 (d) –25 14. The value of the determinant is (a) (b) (c) 0 (d) 15. (a) 1 (b) 0 (c) (d) 16. is equal to (a) (b) (c) (d) 17. = (a) (b) 0 (c) (d) None of these 18. (a) 0 (b) (c) 3 abc (d) 19. (a) (b) (c) 0 (d) 20. (a) (b) (c) (d) None of these 21. (a) (b) (c) (d) 22. If is a cube root of unity, then (a) (b) (c) (d) 23. (a) 0 (b) (c) (d) None of these 24. The value of the determinant is (a) –2 (b) 0 (c) 81 (d) None of these 25. The value of the determinant is (a) 20 (b) 10 (c) 0 (d) 250 26. The value of the determinant is (a) –7 (b) 0 (c) 15 (d) 27 27. (a) 0 (b) 187 (c) 354 (d) 54 28. (a) (b) (c) (d) 29. The value of the determinant is (a) – 440 (b) 0 (c) 328 (d) 488 30. is equal to (a) 150 (b) –110 (c) 0 (d) None of these 31. (a) (b) (c) (d) 32. For non-zero a, b, c if , then the value of (a) (b) (c) (d) None of these 33. The value of the determinant is equal to (a) 0 (b) e (c) (d) 34. If , then equals (a) O (b) D (c) –D (d) None of these 35. The value of the determinant is (a) 0 (b) l (c) m (d) lm 36. If is a complex cube root of unity, then the value of the determinant is (a) 0 (b) (c) 2 (d) 4 37. If , the value of is (a) (b) (c) (d) 38. If are pth, qth and rth terms of an A.P., then is equal to (a) 1 (b) –1 (c) 0 (d) 39. (a) 1 (b) 0 (c) 3 (d) 40. The value of the determinant is (a) 2 (b) –2 (c) 0 (d) 5 41. If , then the value of A is (a) 0 (b) 1 (c) 2 (d) 3 42. The value of is (a) 88 (b) – 8 (c) – 40 (d) 56 43. The value of is (a) 1 (b) – 1 (c) 0 (d) None of these 44. (a) 20 (b) 10 (c) 0 (d) 5 45. The value of is (a) –100 (b) 0 (c) 100 (d) 1000 46. The value of is (a) 4 (b) 6 (c) 8 (d) 10 47. The value of the determinant is (a) (b) (c) (d) None of these 48. The value of the determinant is (a) 0 (b) (c) (d) 49. equals to (a) (b) (c) 0 (d) None of these 50. equals (a) (b) (c) 0 (d) 51. The value of the determinant is (a) 0 (b) 10 (c) 46 (d) 50 52. The value of the determinant is (a) 0 (b) xyz (c) 2 xyz (d) 4 xyz 53. If a, b, c are all different and = 0, then correct statement is (a) (b) (c) (d) None of these 54. If and , then the value of is (a) 1 (b) 0 (c) 2 (d) 55. The value of is (a) 652 (b) 576 (c) 0 (d) None of these 56. If is a cube root of unity, then one root of the equation is (a) 1 (b) (c) (d) 0 57. If then equals (a) –4 (b) 4 (c) 2 (d) None of these 58. If and then (a) (b) abc = 1 (c) (d) 59. is equal to (a) (b) (c) (d) 60. = (where x, y, z being positive) (a) (b) (c) (d) 0 61. If then k = (a) 1 (b) 2 (c) 3 (d) 4 62. Let , then lies in the interval (a) [2, 3] (b) [3, 4] (c) [1, 4] (d) (2, 4) 63. If and , then the value of is (a) 0 (b) 1 (c) –1 (d) 2 64. The value of the determinant is (a) 0 (b) (c) (d) 65. If a, b, c are negative distinct real numbers, then the determinant is (a) (b) (c) (d) 66. If A, B, C are the angles of a triangle, then the value of is (a) (b) (c) 0 (d) None of these 67. (a) (b) (c) (d) 68. (a) 1 (b) 0 (c) –1 (d) 67 69. (a) 4 (b) (c) (d) 0 70. The value of the determinant is equal to (a) –4 (b) 0 (c) 1 (d) 4 71. (a) 0 (b) (c) (d) 72. If a, b, c are in A.P., then the value of is (a) (b) (c) (d) 0 73. The value of the determinant given below is (a) 20 (b) 10 (c) 0 (d) 5 74. is not depend (a) On x (b) On n (c) Both on x and n (d) None of these 75. The value of is (a) 8 (b) –8 (c) 400 (d) 1 76. The value of is equal to (a) (b) (c) (d) 77. The value of (a) 2 (b) 4 (c) 0 (d) 1 78. Let Then the value of the determinant is (a) (b) (c) (d) 79. If , then the value of the determinant is (a) (b) (c) (d) None of these 80. (a) (b) (c) (d) 3 81. (a) 0 (b) abc (c) 1/abc (d) None of these 82. (a) 0 (b) 2abc (c) (d) None of these 83. The determinant is equal to zero if a, b, c are in (a) G.P. (b) A.P. (c) H.P. (d) None of these 84. If , then k = (a) 1 (b) 2 (c) –1 (d) –2 85. The value of the determinant is (a) 2(10! 11!) (b) 2(10! 13!) (c) 2(10! 11! 12!) (d) 2(11! 12! 13!) 86. The value of is (a) (b) (c) (d) 87. is equal to (a) (b) (c) 0 (d) 88. If , then (a) (b) (c) (d) 89. The determinant , then (a) (b) (c) or (d) None of these 90. The value of the determinant is (a) 0 (b) (c) (d) None of these 91. If , then the value of A is (a) 12 (b) 24 (c) –12 (d) –24 92. (a) (b) (c) (d) 0 93. (a) abc (b) 2abc (c) 3abc (d) 4abc 94. If a, b, c are unequal what is the condition that the value of the following determinant is zero (a) (b) (c) (d) None of these 95. If , then is equal to (a) 0 (b) abc (c) –abc (d) None of these 96. The value of the determinant is equal to (a) 1 (b) 0 (c) 2 (d) 3 97. If then the value of is (a) 1 (b) 2 (c) 4 (d) 3 98. The parameter, on which the value of the determinant does not depend upon is (a) a (b) p (c) d (d) x 99. The value of the determinant is (a) (b) (c) (d) 100. If and than is equal to (a) (b) (c) (d) None of these 101. The value of is (a) (b) (c) (d) None of these 102. If a, b, c are all different and , then the value of is (a) (b) 0 (c) (d) 103. is divisor of (a) (b) (c) (d) 104. If , then a, b, c are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 105. If , then the value of k is (a) –1 (b) 1 (c) 2 (d) –2 106. If and discriminant of is negative, then is (a) Positive (b) (c) Negative (d) 0 107. The determinant , if a, b, c are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 108. The value of the determinant is (a) (b) (c) 1 (d) 0 109. In a , if , then (a) (b) (c) 1 (d) 110. If and , then (a) 3 (b) 2 (c) 1 (d) 0 111. If , then (a) for all (b) A is an odd function of (c) for (d) A is independent of 112. l, m, n are the pth, qth and rth term of a G.P., all positive, then equals (a) –1 (b) 2 (c) 1 (d) 0 113. If a, b, c are respectively the terms of an A.P., then (a) 1 (b) –1 (c) 0 (d) pqr 114. The value of the determinant , where a, b, c are the terms of a H.P. is (a) (b) (c) 0 (d) None of these 115. The value of is equal to (a) (b) 0 (c) (d) None of these 116. If are non-real numbers satisfying then the value of is equal to (a) 0 (b) (c) (d) None of these 117. The value of the determinant is (a) 0 (b) – (6 !) (c) 80 (d) None of these 118. has the value (a) 0 (b) 1 (c) (d) None of these 119. The value of is (a) 1 (b) –1 (c) 0 (d) –xyz 120. If and is non real cube root of unity then the value of is equal to (a) 1 (b) i (c) (d) 0 121. The value of , where , is (a) 1 if m is a multiple of 4 (b) 0 for all real m (c) –i if m is a multiple of 3 (d) None of these 122. If the determinant is expanded in powers of then the constant term in the expansion is (a) 1 (b) 2 (c) –1 (d) None of these 123. Let where the symbols have their usual meanings. The f(n) is divisible by (a) (b) (c) (d) None of these 124. is equal to (a) (b) (c) (d) None of these 125. (a) 2 (b) –2 (c) (d) None of these 126. The roots of the equation are (a) –1, –2 (b) –1, 2 (c) 1, –2 (d) 1, 2 127. The roots of the equation are (a) 0, –3 (b) 0, 0, –3 (c) 0, 0, 0, –3 (d) None of these 128. If –9 is a root of the equation , then the other two roots are (a) 2, 7 (b) –2, 7 (c) 2, –7 (d) –2, –7 129. If , then one root of is (a) (b) (c) (d) 130. If , then x equals (a) 2 (b) 3 (c) 4 (d) None of these 131. The number of roots of the equation is (a) 1 (b) 2 (c) 3 (d) 4 132. The roots of the equation are (a) 1, 1 (b) 1, a (c) 1, b (d) a, b 133. If , then the values of x are (a) 1, 2 (b) –1, 2 (c) –1, –2 (d) 1, –2 134. If , then (a) 8/3 (b) 2/3 (c) 1/3 (d) None of these 135. The factors of are (a) and (b) and (c) and (d) and 136. The roots of the equation are (a) 1, 2 (b) –1, 2 (c) 1, –2 (d) –1, –2 137. A root of the equation is (a) 6 (b) 3 (c) 0 (d) None of these 138. One of the root of the given equation is (a) (b) (c) (d) 139. If , then (a) a is one of the cube root of unity (b) b is one of the cube root of unity (c) is one of the cube root of unity (d) is one of the cube root of –1 140. If satisfy , then abc = (a) (b) 0 (c) (d) 141. At what value of x, will (a) (b) (c) (d) None of these 142. is an equation of x, where are the complex cube roots of unity, what is the value of x (a) 0 (b) 1 (c) –1 (d) 2 143. If 5 is one root of the equation , then other two roots of the equation are (a) –2 and 7 (b) –2 and –7 (c) 2 and 7 (d) 2 and –7 144. Solutions of the equation are (a) (b) (c) (d) 145. If , then is equal to (a) abc (b) 0 (c) 1 (d) None of these 146. If , then x is (a) 0, –6 (b) 0, 6 (c) 6 (d) –6 147. The values of x in the following determinant equation (a) (b) (c) (d) 148. If , then x = (a) 0 (b) 2 (c) 3 (d) 1 149. If and then is equal to (a) i (b) –i (c) 1 (d) 0 150. If , then x is (a) 0 (b) a (c) 3 (d) 2a 151. The sum of two non-integral roots of is (a) 5 (b) –5 (c) – 18 (d) None of these 152. The solution set of the equation is (a) (1, 2) (b) (1, –2) (c) (1, –3) (d) (0, 1) 153. If a, b, c are in A.P., then the value of is (a) (b) (c) (d) 0 154. The value of x obtained from the equation will be (a) 0 and (b) 0 and (c) 1 and (d) 0 and 155. If and , then one of the value of x is (a) (b) (c) (d) None of these 156. If , then for (a) (b) All real x (c) (d) None of these 157. If , such that then (a) (b) x has no real value (c) (d) None of these 158. Let be an identity in x, where a, b, c, d, are independent of x. Then the value of is (a) 3 (b) 2 (c) 4 (d) None of these 159. Using the factor theorem it is found that and are three factors of determinant . The other factor in the value of the determinant is (a) 4 (b) 2 (c) (d) None of these 160. The roots of are independent of (a) (b) a, b (c) (d) None of these 161. If , then (a) 15 (b) 45 (c) 405 (d) None of these 162. If and , then (a) (b) (c) (d) 163. If , , , then which relation is correct (a) (b) (c) (d) None of these 164. If , then is equal to (a) (b) (c) (d) 165. If the entries in a determinant are either 0 or 1, then the greatest value of this determinant is (a) 1 (b) 2 (c) 3 (d) 9 166. If the elements of the first row of the product of and are respectively A and B then the elements of the second row of the product are (a) A, B (b) B, A (c) –B, A (d) –B, –A 167. If for every element of any determinant of odd order , then the value of determinant is (a) 0 (b) 1 (c) –1 (d) 168. The sum of the products of the elements of any row of a determinant A with the corresponding cofactors of the same row is always equal to (a) (b) (c) 1 (d) 0 169. If and , then (a) (b) (c) (d) None of these 170. If , then is equal to (a) (b) (c) (d) 171. If every element of a third order determinant of value is multiplied by 5, then the value of new determinant is (a) (b) (c) (d) 172. If , then p is given by (a) (b) (n + 1) (c) Either A or B (d) Both A and B 173. If , then equals (a) (b) (c) (d) None of these 174. If , then (a) (b) (c) (d) 175. If and , then B is given by (a) (b) (c) (d) 176. Let and , then can be expressed as the sum of how many determinants (a) 9 (b) 3 (c) 27 (d) 2 177. If , then (a) (b) (c) (d) None of these 178. In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has the value (a) 1 (b) 9 (c) 16 (d) 24 179. If and , then (a) (b) (c) (d) None of these 180. Consider the following statements with reference to determinants (I) The value of determinant is unchanged if the rows and columns are interchanged (II) If any two rows or columns of a determinant are interchanged, the sign of the determinant is changed. (III) If any two rows or columns are identical, the value of determinant is zero (a) I and III are correct (b) II and III are correct (c) Only I is correct (d) I, II and III are correct 181. Let denote the element of the ith row and jth column in a determinant ( ) and let for every i and j . Then the determinant has all the principal diagonal elements as (a) 1 (b) –1 (c) 0 (d) None of these 182. If , then the value of is (a) 5 (b) 25 (c) 125 (d) 0 183. Two non-zero distinct numbers a, b are used as elements to make determinants of the third order. The number of determinants whose value is zero for all a, b is (a) 24 (b) 32 (c) (d) None of these 184. If in the determinant etc. be the co-factors of etc., then which of the following relations is incorrect (a) (b) (c) (d) 185. If are respectively the co-factors of the elements of the determinant , then (a) (b) (c) (d) None of these 186. The cofactors of 1,–2, –3 and 4 in are (a) 4, 3, 2, 1 (b) –4, 3, 2, –1 (c) 4, –3, –2, 1 (d) –4, –3, –2, –1 187. The cofactor of 2 in is (a) 1 (b) –5 (c) 8 (d) –8 188. If cofactor of 2x in the determinant is zero, then x equals to (a) 0 (b) 2 (c) 1 (d) –1 189. The cofactor of element 0 in determinant is (a) –1 (b) 0 (c) 2 (d) –2 190. The cofactor of element 0 in determinant is (a) 2 (b) 5 (c) –5 (d) 9 191. The minors of the element of the first row in the determinant are (a) 2, 7, 11 (b) 7, 11, 2 (c) 11, 2, 7 (d) 7, 2, 11 192. The value of the determinant of 3rd order is 9 then the value of where is a determinant formed by cofactors of the element of is (a) 9 (b) 81 (c) 729 (d) 6561 193. If and , then is equal to (a) ac (b) bd (c) (d) None of these 194. equals (a) (b) (c) (d) 195. The value of is (a) (b) (c) (d) 196. If and , then n equals (a) 4 (b) 6 (c) 7 (d) 8 197. (a) 7 (b) 10 (c) 13 (d) 17 198. If square of determinant of the third order then is equal to (a) (b) (c) (d) None of these 199. If , then the value of (a) 1 (b) –1 (c) 0 (d) None of these 200. Let , then the value of is (a) 0 (b) (c) (d) None of these 201. Let m be a positive integer and then the value of is given by (a) 0 (b) (c) (d) 202. If , then (a) 0 (b) 25 (c) 625 (d) None of these 203. If , then is equal to (a) 0 (b) 1 (c) (d) None of these 204. If , then the value of is independent of (a) x (b) y (c) z (d) n 205. If , then is equal to (a) (b) (c) 0 (d) None of these 206. Let f, g, h and k be differentiable in (a, b). If F is defined as , then is given by (a) (b) (c) (d) 207. If , then equals (a) (b) (c) (d) None of these 208. If , then is equal to (a) 0 (b) –1 (c) 1 (d) 2 209. Let ,then equals (a) 0 (b) 1 (c) –2 (d) None of these 210. If , then (a) (b) (c) (d) None of these 211. If , then maximum value of is (a) 0 (b) 2 (c) 4 (d) 6 212. If , then is equal to (a) (b) (c) (d) None of these 213. If and are three polynomials of degree 2, then is polynomial of degree (a) 2 (b) 3 (c) 4 (d) 0 214. Let , where p is a constant, then at is (a) p (b) (c) (d) Independent of p 215. If , then at x = 0 is (a) 0 (b) p (c) (d) Independent of p 216. If , then (a) 4 (b) 2 (c) 3 (d) 0 217. If , has non-zero solution, then (a) –1 (b) 0 (c) 1 (d) –3 218. The number of solutions of the equations is (a) 0 (b) 1 (c) 2 (d) Infinite 219. The following system of equations , has a solution other than for equal to (a) 1 (b) 2 (c) 3 (d) 5 220. The number of solutions of equations is (a) 0 (b) 1 (c) 2 (d) Infinite 221. If the system of following equations be consistent, then k = (a) –2, (b) –1, (c) –6, (d) 6, 222. If the equation have non-zero solutions, then (a) (b) (c) (d) 223. If the system of equations , , has infinite number of solutions, then (a) 7 (b) –7 (c) 5 (d) –5 224. The system of equations is (a) Consistent (unique solution) (b) Inconsistent (c) Consistent (infinite solutions) (d) None of these 225. The system of equations , , , will have a non-zero solution if real values of are given by (a) 0 (b) 1 (c) 3 (d) 226. The equations have (a) Only one solution (b) Only two solutions (c) No solution (d) Infinitely many solutions 227. The number of solutions of is (a) 0 (b) 1 (c) 2 (d) Infinitely many 228. The existence of unique solution of the system depends on (a) b only (b) a only (c) a and b (d) Neither a nor b 229. The value of k for which the set of equations , and has a non-trivial solution is (a) 15 (b) 16 (c) 31/2 (d) 33/2 230. then x, y, z are respectively (a) 3, 2, 1 (b) 1, 2, 3 (c) 2, 1, 3 (d) None of these 231. Consider the system of equations , , if , then the system has (a) More than two solutions (b) One trivial and one non-trivial solutions (c) No solution (d) Only trivial solution (0, 0, 0) 232. If , , , then x = (a) (b) (c) (d) None of these 233. The system of equations , and has (a) A unique solution (b) No solution (c) An infinite number of solutions (d) Zero solution as the only solution 234. If then find the value of x (a) (b) (c) (d) None of these 235. Equations will have (a) Only one solution (b) Many finite solutions (c) No solution (d) None of these 236. If the system of equations and has a non zero solution, then the possible value of k are (a) –1, 2 (b) 1, 2 (c) 0, 1 (d) –1, 1 237. The system of equations , and has (a) No solution (b) Exactly one solution (c) Infinite solutions (d) None of these 238. The existence of the unique solution of the system depends on (a) only (b) only (c) and both (d) Neither nor 239. The number of solutions of the following equations , , is (a) Zero (b) One (c) Two (d) Infinite 240. The number of values of k for which the system of equations has infinitely many solutions, is (a) 0 (b) 1 (c) 2 (d) Infinite 241. For what value of , the system of equations is inconsistent (a) (b) (c) (d) 242. The values of the x, y, z in order, of the system of equations are (a) 2, 1, 5 (b) 1, 1, 1 (c) 1, –2, –1 (d) 1, 2, –1 243. The number of solutions of the system of equations is (a) 3 (b) 2 (c) 1 (d) 0 244. The system of equations has no solution for (a) (b) (c) (d) None of these 245. The system of equations has non-trivial solution if a, b, c are in (a) AP (b) GP (c) HP (d) None of these 246. The system of equations [has infinite number of nontrivial solutions for] (a) (b) (c) (d) No real value of 247. The system of equations is solvable if is (a) 6 (b) 8 (c) –8 (d) –6 248. The system of the equations has (a) Infinitely many solutions (b) No solution (c) Unique solution (d) None of these 249. If the equations and are the consistent having non-trivial solution, then (a) (b) (c) (d) None of these 250. The value of a for which the system of equations , and has a non-zero solution is (a) –1 (b) 0 (c) 1 (d) None of these 251. The values of which make the system of linear equations , , to have the solution are (a) 3 or 4 (b) or (c) 1 or 2 (d) , where K is an arbitrary constant 252. If the equations and have a solution other than and , then a, b and c are connected by the relation (a) (b) (c) (d) None of these 253. If and where x, y, z are not all zero, then (a) 0 (b) 1 (c) –1 (d) 2 254. Let a, b, c be positive real numbers. the following system of equations in x, y, and z , , has (a) No solution (b) Unique solution (c) Infinitely many solutions (d) Finitely many solutions 255. The system of the linear equations has a unique solution if (a) (b) (c) (d) 256. If and the system of equations , , has a non-trivial solution then both the roots of the quadratic equation are (a) Real (b) Of opposite sign (c) Positive (d) Complex 257. If , , , , , then the values of x and y are respectively (a) and (b) and (c) log and (d) and 258. If the equations , , , where , , admit of nontrivial solutions then is (a) 2 (b) 1 (c) (d) None of these 259. If the system of equations , and has a solution then the system of equations , has (a) Only one solution (b) No solution (c) Infinite number of solutions (d) None of these 260. The value of is (a) (b) (c) (d) None of these 261. The value of is (a) 0 (b) (c) (d) None of these 262. The value of the determinant is (a) (b) (c) 0 (d) 263. The value of an even order skew symmetric determinant is (a) 0 (b) Perfect square (c) (d) None of these 264. The value of an odd order skew symmetric determinant is (a) Perfect square (b) Negative (c) (d) 0 265. In a skew-symmetric matrix, the diagonal elements are all (a) Different from each other (b) Zero (c) One (d) None of these 266. The value of is (a) Purely real (b) Purely imaginary (c) Non real complex (d) None of these 267. If , then the two triangles whose vertices are , , and , , , are (a) Congruent (b) Similar (c) Equal in area (d) None of these 268. If A, B and C are the angles of a triangle and , then the triangle must be (a) Equilateral (b) Isosceles (c) Any triangle (d) Right angled. 269. If , then (a) –200 (b) 100 (c) 112 (d) –108 270. If a, b, c are the sides of a and A, B, C are respectively the angles opposite to them, then is equal to (a) (b) abc (c) 1 (d) 0 271. If , then is independent of (a) x (b) y (c) z (d) 272. If , then is equal to (a) ax (b) (c) (d) None of these 273. If f(x) is a polynomial satisfying and , then the value of is (a) 126 (b) 626 (c) –124 (d) 624 274. If , then is equal to (a) (b) (c) (d) 275. If , then is independent of (a) x, y, z (b) y only (c) z only (d) only 276. If , then the value of the determinant is (a) 0 (b) (c) 1 (d) None of these 277. If [a] denotes the greatest integer less than or equal to a and , then is equal to (a) [x] (b) [y] (c) [z] (d) None of these