Quadratic Equation-PART-I-(E)-02-Assignment

1. A real root of the equation is (a) 1 (b) 2 (c) 3 (d) 4 2. The roots of the equation are (a) 4, 5 (b) 2, – 3 (c) 2, 3 (d) 3, 5 3. The solution set of the equation is (a) (b) (c) (d) None of these 4. The solution of the equation is given by (a) (b) (c) (d) 5. If then x is (a) 3 (b) 2 (c) (d) 6. The solution of is (a) (b) (c) (d) None of these 7. If then x equals (a) 1 (b) 0 (c) 2 (d) 3 8. The real roots of the equation are (a) (b) (c) (d) None of these 9. If then the values of x are (a) (b) (c) (d) 10. (a) (b) (c) (d) 11. If then x = (a) (b) (c) (d) None of these 12. If then x = (a) (b) (c)  (d) 13. The roots of the given equation are (a) (b) (c) (d) 14. The solution of the equation will be (a) 2, –1 (b) (c) (d) None of these 15. One root of the following given equation is (a) 1 (b) 3 (c) 5 (d) 7 16. The roots of the equation are (a) 1, 1, 1, 1 (b) 2, 2, 2, 2 (c) 3, 1, 3, 1 (d) 1, 2, 1, 2 17. One root of the equation is (a) –1 (b) 2 (c) 1 (d) 0 18. If then the solution pair is (a) (1, 2) (b) (2, 3) (c) (2, 4) (d) (1, 3) 19. In the equation the value of x will be (a) (b) – 2 (c) – 3 (d) 1 20. The roots of the equation are (a) 1 and 2 (b) 2 and 3 (c) 3 and 4 (d) 4 and 5 21. The root of the equation is (a) 3 (b) 19 (c) 3, 19 (d) 3, –19 22. The solution of the equation is (a) 1 (b) – 1 (c) 5/4 (d) None of these 23. If then (a) x is an irrational number (b) (c) (d) None of these 24. The real values of x which satisfy the equation are (a) (b) (c) (d) 25. If one root of the equation is 1 then, its other roots is (a) (b) (c) (d) None of these 26. The imaginary roots of the equation are (a) (b) (c) (d) None of these 27. GM of the roots of the equation is (a) 6 (b) 3 (c) – 3 (d) 28. The solution set of the equation is (a) (b) (c) (d) 29. is (a) 49 (b) 50 (c) 51 (d) None of these 30. The value of is (a) –1 (b) 1 (c) 2 (d) 3 31. If then value of is (a) –1,1 (b) 1 (c) –1 (d) 0 32. For what value of a the curve touches the x- axis (a) 0 (b) (c) (d) None of these 33. Let , be the roots of the quadratic equation If is a point on the parabola then the roots of the quadratic equation are (a) 4, – 2 (b) – 4, – 2 (c) 4, 2 (d) – 4, 2 34. If expression satisfies the equation find the value of (a) (b) (c) (d) None of these 35. The roots of equation are (a) 3, – 3 (b) 5, – 5 (c) (d) 36. If then x = (a) {3, 4} (b) {3, – 3} (c) {3, 4, – 3, – 4} (d) {– 3, – 3} 37. The some of all real roots of the equation is (a) 2 (b) 4 (c) 1 (d) None of these 38. A two digit number is four times the sum and three times the product of its digits. The number is (a) 42 (b) 24 (c) 12 (d) 21 39. The number of real solutions of the equation are (a) 1 (b) 2 (c) 3 (d) 4 40. The number of the real values of x for which the equality holds good is (a) 4 (b) 3 (c) 2 (d) 1 41. The number of real solutions of the equation is (a) 0 (b) 1 (c) 2 (d) Infinitely many 42. The number of the real solutions of the equation is (a) 1 (b) 2 (c) 0 (d) 4 43. The number of solutions of is (a) 50 (b) 52 (c) 53 (d) None of these 44. The equation has (a) No solution (b) One solution (c) Two solutions (d) More than two solution 45. The number of real roots of is (a) 1 (b) 2 (c) 3 (d) 4 46. The number of roots of the quadratic equation is (a) Infinite (b) 1 (c) 2 (d) 0 47. The number of values of x in the interval satisfying the equation is (a) 0 (b) 5 (c) 6 (d) 10 48. The maximum number of real roots of the equation is (a) 2 (b) 3 (c) n (d) 2n 49. The equation has (a) No real root (b) One real root (c) Two equal roots (d) Infinitely many roots 50. The number of real roots of equation is (a) 2 (b) 1 (c) 0 (d) 3 51. The number of roots of the equation are (a) 3 (b) 2 (c) 1 (d) None of these 52. Number of real roots of the equation is (a) 0 (b) 1 (c) 2 (d) 3 53. The minimum value of is (a) 3 (b) 7 (c) 5 (d) 9 54. Rationalised denominator of is (a) (b) (c) (d) 55. If then (a) 4 (b) 6 (c) 3 (d) 2 56. If and then (a) 2 (b) 65/8 (c) 37/6 (d) None of these 57. The equation can be written as (a) (b) (c) (d) 58. If and 2, 3 are roots of the equation then the value of m and n are (a) – 5, – 30 (b) – 5, 30 (c) 5, 30 (d) None of these 59. The number of real solutions of the equation is (a) 1 (b) 2 (c) 0 (d) None of these 60. The sum of the real roots of the equation is (a) 4 (b) 0 (c) – 1 (d) None of these 61. The number of values of a for which is an identity in x is (a) 0 (b) 2 (c) 1 (d) 3 62. The number of values of the pair (a, b) for which is an identity in x is (a) 0 (b) 1 (c) 2 (d) Infinite 63. If then the number of values of x is (a) 2 (b) 4 (c) 1 (d) None of these 64. The number of real solutions of the equation is (a) Two (b) One (c) Zero (d) None of these 65. The number of real solutions of is (a) One (b) Two (c) Three (d) None of these 66. If , then solution of the equation is (a) 1, 5/3 (b) 5/3 (c) 1/3 (d) None of these 67. The real roots of are (a) 0, 2 (b)  1 (c)  2 (d) 1, 2 68. The number of real solutions of the equation is (a) One (b) Two (c) Four (d) Infinite 69. The number of negative integral solutions of is (a) 0 (b) 1 (c) 2 (d) 4 70. The equation has (a) Only one real root x = 0 (b) At least two real roots (c) Exactly two real roots (d) Infinitely many real roots 71. The number of real roots of the equation are (a) 1 (b) 2 (c) Infinite (d) None of these 72. If a, b, c are positive real numbers, then the number of real roots of the equation is (a) 2 (b) 4 (c) 0 (d) None of these 73. The number of real solutions of equation are (a) 4 (b) 1 (c) 2 (d) 3 74. The equation has (a) At least one real solution (b) Exactly three real solutions (c) Exactly one irrational solution (d) All the above 75. The number of solutions of , where [x] is the greatest integer is , is (a) 2 (b) 4 (c) 1 (d) Infinite 76. Let f(x) be a function defined by , , where [x] is the greatest integer less than or equal to x. then the number of solutions of (a) 0 (b) Infinite (c) 1 (d) 2 77. If m be the number of integral solutions of equation and n be the number of real solutions of equation , then m = (a) n (b) 2n (c) n/2 (d) 3n 78. The set of values of c for which is of the form (,  real) is given by (a) {0} (b) {4} (c) {0, 4} (d) Null set 79. If for r = 1, 2, 3, ….., k and m be the number of real solutions of equation and n be the number of real solution of equation , then (a) (b) (c) (d) 80. Let be a polynomial such that n is even. Then the number of real roots of is (a) 0 (b) n (c) 1 (d) None of these 81. The number of all possible triplets such that for all x is (a) Zero (b) One (c) Three (d) Infinite 82. The solutions of the equation , where [x] = the greatest integer less than or equal to x, are (a) (b) (c) (d) 83. The number of real solutions of is (a) 0 (b) 1 (c) 2 (d) 4 84. The equation has (a) One real solution (b) No real solution (c) Infinitely many real solutions (d) None of these 85. If then the number of values of the pair (x, y) such that and , is (a) 1 (b) 2 (c) 0 (d) None of these 86. The number of real solutions of the equation is (a) 1 (b) 2 (c) 0 (d) None of these 87. The product of all the solutions of the equation is (a) 2 (b) – 4 (c) 0 (d) None of these 88. If and , where [x] is the greatest integer less than or equal to x, the number of possible values of x is (a) 34 (b) 32 (c) 33 (d) None of these 89. The solution set of , where (x) is the least integer greater than or equal to x, is (a) (2, 4) (b) (– 5, – 4]  (2, 3] (c) [– 4, – 3)  (3, 4] (d) None of these 90. If , where [x] = the greatest integer less than or equal to x, then x must be such that (a) (b) (c) (d) None of these 91. The solution set of is (a) (b) (c) {–1, 1} (d) or 92. If has real solutions, , then the set of possible values of the parameter a is (a) [–1, 1] (b) [–1, 0) (c) (0, 1] (d) (0, +) 93. The roots of the quadratic equation , are (a) Irrational (b) Rational (c) Imaginary (d) None of these 94. The roots of the equation are (a) Real and equal (b) Rational and equal (c) Irrational and equal (d) Irrational and unequal 95. If l, m, n are real and l  m, then the roots of the equation are (a) Complex (b) Real and distinct (c) Real and equal (d) None of these 96. If a and b are the odd integers, then the roots of the equation , , will be (a) Rational (b) Irrational (c) Non-real (d) Equal 97. If , then the roots of the equation are (a) Complex (b) Real and unequal (c) Real and equal (d) One real and one imaginary 98. Let a, b and c be real numbers such that and . Then the quadratic equation has (a) Real roots (b) Complex roots (c) Purely imaginary roots (d) Only one root 99. If , then the roots of the equation are (a) Real and distinct (b) Real and equal (c) Imaginary (d) None of these 100. If , then at least one of the equations and has (a) Real roots (b) Purely imaginary roots (c) Imaginary roots (d) None of these 101. In the equation , if G and H are real and , then the roots are (a) All real and equal (b) All real and distinct (c) One real and two imaginary (d) All real and two equal 102. The equation , has (a) All the roots real (b) One real and two imaginary roots (c) Three real roots namely (d) None of these 103. For the equation , the roots are (a) One and only one real number (b) Real with sum one (c) Real with sum zero (d) Real with product zero 104. If , then both the roots of the equation (a) Are real and negative (b) Have negative real parts (c) Are rational numbers (d) None of these 105. Let one root of , where a, b, c are integers be , then the other root is (a) (b) 3 (c) (d) None of these 106. If is a root of the equation , then the other roots are (a) 1 and (b) –1 and (c) 0 and 1 (d) –1 and 107. If a, b, c are nonzero, unequal rational numbers then the roots of the equation are (a) Rational (b) Imaginary (c) Irrational (d) None of these 108. The equation , , has (a) Real and unequal roots for all  (b) Real roots for only (c) Real roots for only (d) Real and unequal roots for only 109. If , roots of the equation are (a) One positive and one negative (b) Both negative (c) Both positive (d) Both nonreal complex 110. If the roots of the equation be real, then the roots of the equation will be (a) Rational (b) Irrational (c) Real (d) Imaginary 111. If the roots of the equation are real, then (a) (b) (c) (d) 112. If the roots of the given equation are real, then (a) (b) (c) (d) 113. The greatest value of a non-negative real number  for which both the equations and have real roots is (a) 9 (b) 12 (c) 15 (d) 16 114. If p, q, r are positive and are in A.P., then roots of the equation are real if (a) (b) (c) For all values of p, r (d) For no value of p, r 115. Let p, . The number of equations of the form having real roots is (a) 15 (b) 9 (c) 7 (d) 8 116. The least integer k which makes the roots of the equation imaginary is (a) 4 (b) 5 (c) 6 (d) 7 117. If , and the roots ,  of the equation are non-real complex numbers, then (a) (b) (c) (d) None of these 118. If roots of the equation are equal,, then a, b, c are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 119. If the equation has equal roots, then l, m and n satisfy (a) (b) (c) (d) 120. The condition for the roots of the equation to be equal is (a) (b) (c) (d) None of these 121. If the roots of the equation are equal, then (a) (b) (c) (d) 122. If one root of is 4 and roots of the equation are equal, then q is equal to (a) 49/4 (b) 4/49 (c) 4 (d) None of these 123. If the roots of the equation are same, then the value of m will be (a) 3 (b) 0 (c) 2 (d) –1 124. If the roots of the equation are equal then m is equal to (a) 3, – 5 (b) – 3, 5 (c) 3, 5 (d) – 3, – 5 125. For what value of k will the equation have equal roots (a) 5 (b) 9 (c) Both the above (d) 0 126. The value of k for which the quadratic equation has real and equal roots are (a) –11, – 3 (b) 5, 7 (c) 5, –7 (d) None of these 127. If the roots of are equal, then absolute value of p is (a) 144 (b) 12 (c) – 12 (d)  12 128. The value of k for which has equal and real roots are (a) – 9 and – 7 (b) 9 and 7 (c) – 9 and 7 (d) 9 and – 7 129. The roots of are equal, then the value of p is (a) (b) (c) (d) 130. If the equation has coincident roots, then (a) (b) (c) (d) 131. If two roots of the equation are same, then the roots will be (a) 2, 2, 3 (b) 1, 1, – 2 (c) – 2, 3, 3 (d) – 2, – 2, 1 132. The equation can have real solutions for x if a belongs to the interval (a) (–, 4] (b) (–, – 4] (c) (4, ) (d) [– 4, 4] 133. The set of values of m for which both roots of the equation are real and negative consists of all m such that (a) (b) (c) (d) or 134. Both the roots of the given equation are always (a) Positive (b) Negative (c) Real (d) Imaginary 135. If and where , then , has at least (a) Four real roots (b) Two real roots (c) Four imaginary roots (d) None of these 136. The conditions that the equation has both the roots positive is that (a) a, b and c are of the same sign (b) a and b are of the same sign (c) b and c have the same sign opposite to that of a (d) a and c have the same sign opposite to that of b 137. If [x] denotes the integral part of x and , then the integral value of  for which the equation has integral roots is (a) 1 (b) 2 (c) 4 (d) None of these 138. If the roots of the equation are real and of the form and , then the value of is (a) (b) (c) (d) None of these 139. Equation (a, b, c, m, n  R) has necessarily (a) All the roots real (b) All the roots imaginary (c) Two real and two imaginary roots (d) Two rational and two irrational roots 140. If cos , sin , sin  are in G.P. then roots of are always (a) Equal (b) Real (c) Imaginary (d) Greater than 1 141. If f(x) is a continuous function and attains only rational values and , then roots of equation are (a) Imaginary (b) Rational (c) Irrational (d) Real and equal 142. The roots of , where and coefficients are real, are non-real complex and . Then (a) (b) (c) (d) None of these 143. The equation has roots rational for (a) All rational values of a except (b) All real values of a except (c) Rational values of (d) None of these 144. The quadratic equation (a) Cannot have a real root if (b) Can have a rational root if  is a perfect square (c) Cannot have an integral root if where (d) None of these 145. If the roots of the equation are  and  and roots of the equation are , then the roots of the equation will be (a) Both negative (b) Both positive (c) Both real (d) One negative and one positive 146. If equation has equal roots, a, b, c > 0, n  N, then (a) (b) (c) (d) 147. If is a polynomial in x for two values of p and q of k, then roots of equation cannot be (a) Real (b) Imaginary (c) Rational (d) Irrational 148. If for x > 0, , and equation has imaginary roots, then number of real roots of equation is (a) 0 (b) 2 (c) 4 (d) None of these 149. Let p, q  {1, 2, 3, 4}. The number of equations of the form having real and unequal roots is (a) 15 (b) 9 (c) 7 (d) 8 150. If and are the roots of the equations and respectively and system of equations and has a non-zero solution. Then (a) (b) (c) (d) None of these 151. If a, b, c, d are four consecutive terms of an increasing AP then the roots of the equation are (a) Real and distinct (b) Nonreal complex (c) Real and equal (d) Integers 152. If a, b, c are three distinct positive real numbers then the number of real roots of is (a) 4 (b) 2 (c) 0 (d) None of these 153. If a  R, b  R then the equation has (a) One positive root and one negative root (b) Both roots positive (c) Both roots negative (d) Non-real roots 154. The number of integral values of a for which has both roots positive and has both roots negative is (a) 0 (b) 1 (c) 2 (d) Infinite 155. The quadratic equations and have (a) No common root for all a  R (b) Exactly one common root for all a  R (c) Two common roots for some a  R (d) None of these 156. If for every real number x then the minimum value of f (a) Does not exist because f is unbounded (b) Is not attained even though f is bounded (c) Is equal to 1 (d) Is equal to –1 157. If x, y, z are real and distinct then is always (a) Non-negative (b) Nonpositive (c) Zero (d) None of these 158. If a  R, b  R then the factors of the expression are (a) Real and different (b) Real and identical (c) Complex (d) None of these 159. If a, b, c are in H.P. then the expression (a) Has real and distinct factors (b) Is a perfect square (c) Has no real factor (d) None of these 160. If a, b, c are in G.P., where a, c are positive, then the equation has (a) Real roots (b) Imaginary roots (c) Ratio of roots = 1 : w where w is a nonreal cube root of unity (d) Ratio of roots = b : ac 161. The polynomial , has (a) Four real zeros (b) At least two real zeros (c) At most two real zeros (d) No real zeros 162. If ,  are roots of the equation , then the value of is (a) (b) (c) (d) 163. If ,  are roots of the equation , then is equal to (a) 2n (b) (c) (d) 164. If  and  are the roots of the equation (a  0; a, b, c being different), then (a) Zero (b) Positive (c) Negative (d) None of these 165. If ,  are the roots of the equation , then the value of is (a) (b) (c) (d) 4 166. If ,  are the roots of the equation , then the value of is equal to (a) 0 (b) 1 (c) q (d) 2q 167. If ,  are the roots of the equation , then (a) c (b) c – 1 (c) 1 – c (d) None of these 168. If , ,  are the roots of the equation , then (a) 2 (b) 3 (c) 4 (d) 5 169. If roots of are ,  then (a) 6/7 (b) 7/6 (c) 7/10 (d) 8/9 170. If ,  are the roots of , then is equal to (a) 16 (b) 32 (c) 64 (d) None of these 171. If the roots of the equation are , , then the value of will be (a) (b) 0 (c) (d) None of these 172. If ,  be the roots of the equation , then the value of is equal to (a) 1 (b) 64 (c) 8 (d) None of these 173. If  and  are roots of , then is equal to (a) (b) (c) (d) 174. If ,  are the roots of the equation , then is equal to (a) (b) (c) 32 (d) 175. If , ,  are roots of equation , then (a) (b) (c) (d) 176. If ,  are roots of , then the value of is (a) 9 (b) 18 (c) – 9 (d) –18 177. If A.M. of the roots of a quadratic equation is 8/5 and A.M. of their reciprocals is 8/7, then the equation is (a) (b) (c) (d) 178. The quadratic in t, such that A.M. of its roots is A and G.M. is G, is (a) (b) (c) (d) None of these 179. In a triangle ABC, the value of A is given by , then the equation whose roots are sin A and tan A will be (a) (b) (c) (d) 180. If is the quadratic whose roots are and where a and b are the roots of , then (a) (b) (c) (d) None of these 181. The roots of the equation are p and q, then the equation whose roots are and will be (a) (b) (c) (d) 182. The equation whose roots are and is (a) (b) (c) (d) 183. If ,  are the roots of the equation then the equation whose roots are and is (a) (b) (c) (d) 184. If ,  are the roots of , then the equation with the roots is (a) (b) (c) (d) 185. If ,  are the roots of the equation , then the equation whose roots are and , is (a) (b) (c) (d) None of these 186. If ,  are the roots of , then the equation whose roots are is (a) (b) (c) (d) None of these 187. If ,  are the roots of , then the equation whose roots are is (a) (b) (c) (d) 188. If ,  are the roots of the equation , then the equation with roots 1/, 1/ will be (a) (b) (c) (d) 189. Let be the roots of , then the equation whose roots are is (a) (b) (c) (d) 190. If ,  are roots of the equation then the equation with roots will be (a) (b) (c) (d) 191. The equation whose roots are reciprocal of the roots of the equation is (a) (b) (c) (d) None of these 192. The sum of the roots of a equation is 2 and sum of their cubes is 98, then the equation is (a) (b) (c) (d) 193. Sum of roots is –1 and sum of their reciprocals is , then equation is (a) (b) (c) (d) 194. If ,  are the roots of the quadratic equation , then the equation whose roots are b and c is (a) (b) (c) (d) 195. If ,  are roots of , then the equation with roots and is (a) (b) (c) (d) 196. Given that tan and tan are the roots of , then the value of (a) (b) (c) (d) 197. If is a root of the equation , then (p, q) is equal to (a) (7, – 4) (b) (– 4, 7) (c) (4, 7) (d) (7, 4) 198. In the equation , the coefficient of x was taken as 17 in place of 13 and its roots were found to be –2 and –15. The correct roots of the original equation are (a) –10, – 3 (b) 10, 3 (c) –10, 3 (d) 10, – 3 199. Two students while solving a quadratic equation in x, one copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of correctly as – 6 and 1 respectively. The correct roots are (a) 3, – 2 (b) – 3, 2 (c) – 6, –1 (d) 6, –1 200. If 8, 2 are the roots of and 3, 3 are the roots of , then the roots of are (a) 8, –1 (b) –9, 2 (c) – 8, – 2 (d) 9, 1 201. The equation formed by decreasing each root of by 1 is , then (a) (b) (c) (d) 202. If p and q are non-zero constants, the equation has roots u and v, then the equation has roots (a) u and (b) and v (c) and (d) None of these 203. If the sum of the roots of the equation is equal to the sum of their squares, then (a) (b) (c) (d) None of these 204. If the sum of the roots of the equation is three times their difference, then which one of the following is true (a) (b) (c) (d) 205. If the sum of the roots of the quadratic equation is equal to the sum of the squares of their reciprocals, then (a) 2 (b) – 2 (c) 1 (d) – 1 206. If the sum of the two roots of the equation is zero, then the roots are (a) 1, 2, – 2 (b) (c) (d) 207. If the roots of the equation are l and 2l, then (a) (b) (c) (d) 208. If ,  are the roots of the equation and , then the value of p are (a)  3 (b)  6 (c)  8 (d)  9 209. If , ,  are the roots of , then (a) – 1 (b) 3 (c) 2 (d) 1 210. If ,  be the roots of and are the roots of , then (a) (b) (c) (d) 211. The quadratic equation with real coefficients whose one root is will be (a) (b) (c) (d) 212. The quadratic equation with one root as the square root of is (a) (b) (c) (d) 213. The quadratic equation whose one root is will be (a) (b) (c) (d) None of these 214. The quadratic equation with one root is (a) (b) (c) (d) 215. The quadratic equation whose roots are three times the roots of the equation is (a) (b) (c) (d) 216. If ,  are the roots of then are the roots of the equation (a) (b) (c) (d) 217. If a root of the equation be reciprocal of a root of the equation , then (a) (b) (c) (d) None of these 218. One root of is reciprocal of other root if (a) (b) (c) (d) 219. If the roots of the equation be reciprocals of each other, then k is equal to (a) 0 (b) 5 (c) 1/6 (d) 6 220. If one root of the equation is reciprocal of the other, then the correct relationship is (a) (b) (c) (d) 221. If the roots of the quadratic equation are reciprocal to each other, then (a) (b) (c) (d) 222. The roots of the quadratic equation will be reciprocal to each other if (a) (b) (c) (d) 223. If the absolute difference between two roots of the equation is , then p equals (a) – 3, 4 (b) 4 (c) – 3 (d) None of these 224. If the roots of equation differ by 1, then (a) (b) (c) (d) None of these 225. The numerical difference of the roots of is (a) 5 (b) (c) (d) 226. If the difference of the roots of be 2, then the value of p is (a)  2 (b)  4 (c)  6 (d)  8