IoMA Entrance
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ISI Entrance
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CMI Entrance
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ISI & CMI Entrance Solutions, Problems & Discussions
B.Stat and B.Math Entrance of Indian Statistical Institute, and B.Sc. Math Entrance of Chennai Mathematical Institute are two of the most challenging tests at the end of high school in India.
The problems include Math Olympiad standard number theory, combinatorics and algebra (apart from regular high school topics). These problems are usually much more difficult (and non-standard) than usual engineering entrances.
Problem Garden
Mathematics is not a Spectator Sport. Try these problems selected from I.S.I. & C.M.I. Entrance. Avoid looking up solutions. Some of our discussion pages have sequential hints. Use them instead of a full solution.
Test of Mathematics at 10+2 level subjective solutions and problems
- Prime as a sum of Geometric Series (Tomato Subjective 11)
- Sum of the Digits 7 (Tomato Subjective 15)
- Odd Coefficients (Tomato Subjective 17)
- Sum of odd powers of n consecutive numbers (Tomato Subjective 31)
- Divisible by
power of 3 (Tomato Subjective 32) - Symmetrical Minima. (Tomato Subjective 33)
- Divisibility by 16 (Tomato Subjective 35)
- Invariance Principle (Tomato Subjective 36)
- The prime 13 (Tomato Subjective 37)
- When 30 divides a prime (Tomato Subjective 38)
- Polynomial with Integer Coefficients (Tomato Subjective 42)
- Integer Roots (Tomato Subjective 43)
- Number of Onto Functions (TOMATO Subjective 46)
- The Gifts Distribution (TOMATO Subjective 48)
- Arrangement of Similar Items (TOMATO Subjective 49)
- Dictionary Ranking (TOMATO Subjective 50)
- Partition of a set of functions (Tomato Subjective 55)
- Number of Four Digit Integers (Tomato Subjective 56)
- Number of six letter words (Tomato subjective 57)
- Balls of different color (Tomato subjective 58)
- Number of squares (Tomato subjective 59)
- Equivalence Class (I.S.I. Tomato subjective 60)
- Symmetric Polynomial (Tomato subjective 61)
System of Equations (Tomato subjective 62)- Pair of Straight Lines (Tomato subjective 63)
- Functional Equation (Tomato subjective 64)
- Minimum Value of Quadratic (Tomato subjective 65)
Range of a Polynomial (Tomato subjective 66)- Four real roots (Tomato subjective 67)
- Coefficients of Polynomial (Tomato subjective 69)
- Equal Roots (Tomato subjective 70)
- Real solutions (Tomato subjective 71)
- Polynomial Problem (Tomato subjective 72)
- Coefficients of a quadratic (Tomato subjective 73)
- Sum of squares of digits (Tomato subjective 74)
- Continuity and roots of a polynomial (Tomato subjective 75)
- Range of a rational polynomial (Tomato subjective – 76)
- Rational Function Inequality (Tomato Subjective 77)
- Absolute Value Inequality (I.S.I. Tomato subjective 78)
- Trigonometric Inequality (Tomato subjective 79)
- Inequality problem (TOMATO 80
- Cyclic and Symmetric Simultaneous Equations (TOMATO Subjective 81)
- Inequality on four positive real numbers (TOMATO 82)
- Two numbers adding up to 1 (TOMATO 83)
- Comparing Equations (TOMATO Subjective 84)
- Complex Roots of a Real Polynomial (TOMATO Subjective 87)
- Complex Numbers with a Property (TOMATO Subjective 88)
- Graphing inequality (Tomato subjective 90)
- Perpendiculars from Center (Tomato Subjective 107)
- Ratio of diagonals of cyclic quadrilateral (TOMATO 110)
- Vertices of a Triangle (Tomato Subjective 113)
- Asteroid (Tomato Subjective 114)
- Trigonometric Relation (Tomato Subjective 115)
- Angles in a triangle (Tomato Subjective 116)
- Graphing integer value function (Tomato Subjective 117)
- Graph sketching (Tomato Subjective 124)
- Function on natural numbers (Tomato subjective 125)
- Graphs of absolute value functions (Tomato Subjective 126)
- Graphing relations (Tomato Subjective 127)
- Graphing min value function (Tomato Subjective 128
- Finding a Function’s Upper Bound (TOMATO Subjective 144)
- Maximum of nth roots of n (TOMATO 150)
- The Lim 1/(n+r) Problem (TOMATO Subjective 155 with some modifications)
- Limit of a product (TOMATO 157)
- The Grazing Field (Tomato Subjective 166)
- Infinite Circles (TOMATO Subjective 170)
- Tomato Subjective 175(Integer Roots)
- Value of a Polynomial at x = n+1 (TOMATO 176)
- The Famous Doors Problem (TOMATO subjective 177)
- Diagonal Moves (TOMATO 181)
- The Numbered Chessboard (TOMATO Subjective 188)
Test of Mathematics at 10+2 level Objective solutions and problems
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