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 PapersI.S.I B.Math Subjective PapersI.S.I. B.Stat Objective PapersI.S.I. B.Math Objective Papers
TOMATO ObjectivesTOMATO SubjectivesC.M.I. B.Sc. Math Entrance PapersSTEP 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.

20052006200720082009
20102011201220132014
20152016201720182019

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.

20052006200720082009
20102011

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

B.Stat – B.MathB.StatB.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.

201020112012
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

12345678910
11121314151617181920
21222324252627282930
31323334353637383940
41424344454647484950

Problems 51 – 100

51525354555657585960
61626364656667686970
71727374757677787980
81828384858687888990
919293949596979899100

Problems 101 – 150

101102103104105106107108109110
111112113114115116117118119120
121122123124125126127128129130
131132133134135136137138139140
141142143144145146147148149150

Problems 151 – 200

151152153154155156157158159160
161162163164165166167168169170
171172173174175176177178179180
181182183184185186187188189190
191192193194195196197198199200

Problems 201 – 250

201202203204205206207208209210
211212213214215216217218219220
221222223224225226227228229230
231232233234235236237238239240
241242243244245246247248249250

Problems 251 – 300

251252253254255256257258259260
211212213214215216217218219220
221222223224225226227228229230
231232233234235236237238239240
241242243244245246247248249250