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I.S.I. Entrance Problems

New: I.S.I. B.Stat and B.Math Entrance 2017

In this page we have gathered links to some posts which discuss problems relevant to I.S.I. Entrance (B.Stat, B.Math), C.M.I. Entrance (B.Sc. Math) Advanced Placement (United States) and STEP (Cambridge University).

If you are looking for I.S.I. M.Math Papers and discussion check this page.

(TOMATO = Test of Mathematics at 10+2 Level)

I.S.I. B.Stat Subjective Papers I.S.I B.Math Subjective Papers I.S.I. B.Stat Objective Papers I.S.I. B.Math Objective Papers
TOMATO Objectives TOMATO Subjectives C.M.I. B.Sc. Math Entrance Papers STEP Papers

I.S.I. B.Stat Subjective Papers

From 2012 I.S.I. B.Stat and B.Math entrance papers merged. This is bad news for problem solvers. We have 40 problems less every year from this power house of mathematics. Nevertheless we have listed the merged papers under B.Stat.

2005 2006 2007 2008 2009
2010 2011 2012 2013 2014
2015 2016 2017 2018 2019

I.S.I. B.Math Subjective Papers

From 2012 I.S.I. B.Stat and B.Math entrance papers merged. This is bad news for problem solvers. We have 40 problems less every year from this power house of mathematics. Nevertheless we have listed the merged papers under B.Stat.

2005 2006 2007 2008 2009
2010 2011

I.S.I. B.Stat and B.Math Objective Papers

B.Stat – B.Math B.Stat B.Math
2014  2005

C.M.I. B.Sc. Math Papers

These are official papers and solutions (they are available in C.M.I. website). Most recent one may not be yet officially published. It is based on the feed back of exam takers.

2010 2011 2012
Solution
2013
Solution
2014

Test of Mathematics Subjective Problems

  1. Prime as a sum of Geometric Series (Tomato Subjective 11)
  2. Sum of the Digits 7 (Tomato Subjective 15)
  3. Odd Coefficients (Tomato Subjective 17)
  4. Sum of odd powers of n consecutive numbers (Tomato Subjective 31)
  5. Divisible by power of 3 (Tomato Subjective 32)
  6. Symmetrical Minima. (TOMATO Subjective 33)
  7. Divisibility by 16 (Tomato Subjective 35)
  8. Invariance Principle (Tomato Subjective 36)
  9. The prime 13 (Tomato Subjective 37)
  10. When 30 divides a prime (Tomato Subjective 38)
  11. Polynomial with Integer Coefficients (Tomato Subjective 42)
  12. Integer Roots (Tomato Subjective 43)
  13. Number of Onto Functions (TOMATO Subjective 46)
  14. The Gifts Distribution (TOMATO Subjective 48)
  15. Arrangement of Similar Items (TOMATO Subjective 49)
  16. Dictionary Ranking (TOMATO Subjective 50)
  17. Partition of a set of functions (Tomato Subjective 55)
  18. Number of Four Digit Integers (Tomato Subjective 56)
  19. Number of six letter words (Tomato subjective 57)
  20. Balls of different color (Tomato subjective 58)
  21. Number of squares (Tomato subjective 59)
  22. Equivalence Class (I.S.I. Tomato subjective 60)
  23. Symmetric Polynomial (Tomato subjective 61)
  24. System of Equations (Tomato subjective 62)
  25. Pair of Straight Lines (Tomato subjective 63)
  26. Functional Equation (Tomato subjective 64)
  27. Minimum Value of Quadratic (Tomato subjective 65)
  28. Range of a Polynomial (Tomato subjective 66)
  29. Four real roots (Tomato subjective 67)
  30. Coefficients of Polynomial (Tomato subjective 69)
  31. Equal Roots (Tomato subjective 70)
  32. Real solutions (Tomato subjective 71)
  33. Polynomial Problem (Tomato subjective 72)
  34. Coefficients of a quadratic (Tomato subjective 73)
  35. Sum of squares of digits (Tomato subjective 74)
  36. Continuity and roots of a polynomial (Tomato subjective 75)
  37. Range of a rational polynomial (Tomato subjective – 76)
  38. Rational Function Inequality (Tomato Subjective 77)
  39. Absolute Value Inequality (I.S.I. Tomato subjective 78)
  40. Trigonometric Inequality (Tomato subjective 79)
  41. Inequality problem (TOMATO 80
  42. Cyclic and Symmetric Simultaneous Equations (TOMATO Subjective 81)
  43. Inequality on four positive real numbers (TOMATO 82)
  44. Two numbers adding up to 1 (TOMATO 83)
  45. Comparing Equations (TOMATO Subjective 84)
  46. Complex Roots of a Real Polynomial (TOMATO Subjective 87)
  47. Complex Numbers with a Property (TOMATO Subjective 88)
  48. Graphing inequality (Tomato subjective 90)
  49. Perpendiculars from Center (Tomato Subjective 107)
  50. Ratio of diagonals of cyclic quadrilateral (TOMATO 110)
  51. Vertices of a Triangle (Tomato Subjective 113)
  52. Asteroid (Tomato Subjective 114)
  53. Trigonometric Relation (Tomato Subjective 115)
  54. Angles in a triangle (Tomato Subjective 116)
  55. Graphing integer value function (Tomato Subjective 117)
  56. Graph sketching (Tomato Subjective 124)
  57. Function on natural numbers (Tomato subjective 125)
  58. Graphs of absolute value functions (Tomato Subjective 126)
  59. Graphing relations (Tomato Subjective 127)
  60. Graphing min value function (Tomato Subjective 128
  61. Finding a Function’s Upper Bound (TOMATO Subjective 144)
  62. Maximum of nth roots of n (TOMATO 150)
  63. The Lim 1/(n+r) Problem (TOMATO Subjective 155 with some modifications)
  64. Limit of a product (TOMATO 157)
  65. The Grazing Field (Tomato Subjective 166)
  66. Infinite Circles (TOMATO Subjective 170)
  67. Tomato Subjective 175(Integer Roots)
  68. Value of a Polynomial at x = n+1 (TOMATO 176)
  69. The Famous Doors Problem (TOMATO subjective 177)
  70. Diagonal Moves (TOMATO 181)
  71. The Numbered Chessboard (TOMATO Subjective 188)

TOMATO Objectives

Indian Statistical Institute (East West Press) publishes a problem collection every year. It is christened as ‘Test of Mathematics at Ten plus Two Level’. High School problem solvers fondly call this book as TOMATO. It has many beautiful non standard problems (about 1300 MCQ and 300 long answer type problems). Our students solve these problems as a part of the course work. We are collecting some discussions on these problems. Click on the problem number to go the discussion. Not all discussions are available.

Objective Problems

Problems 1-50

1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50

Problems 51 – 100

51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100

Problems 101 – 150

101 102 103 104 105 106 107 108 109 110
111 112 113 114 115 116 117 118 119 120
121 122 123 124 125 126 127 128 129 130
131 132 133 134 135 136 137 138 139 140
141 142 143 144 145 146 147 148 149 150

Problems 151 – 200

151 152 153 154 155 156 157 158 159 160
161 162 163 164 165 166 167 168 169 170
171 172 173 174 175 176 177 178 179 180
181 182 183 184 185 186 187 188 189 190
191 192 193 194 195 196 197 198 199 200

Problems 201 – 250

201 202 203 204 205 206 207 208 209 210
211 212 213 214 215 216 217 218 219 220
221 222 223 224 225 226 227 228 229 230
231 232 233 234 235 236 237 238 239 240
241 242 243 244 245 246 247 248 249 250

Problems 251 – 300

251 252 253 254 255 256 257 258 259 260
211 212 213 214 215 216 217 218 219 220
221 222 223 224 225 226 227 228 229 230
231 232 233 234 235 236 237 238 239 240
241 242 243 244 245 246 247 248 249 250

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