CAT Exam Numerical Ability Geometry

If perimeter of a triangle with integer sides is equal to 15. How many such triangles are possible?

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CAT Other Question

coefficient of x in the expansion of (1+x)(1+2x)(1+3x)(1+4x).......(1+100x) is ? A page is torn from a book. The sum of the remaining digits is 10000. What is the sum of the two page-numbers on the torn page of this book?