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Trigonometry ex 8.1 | important questions of boards | chapter 8 maths

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class 10 exercise 8.4 question 4 part 1and2

There are 3 parts A,B and C in a question paper of Math's, which includes 6,7 and 8 questions respectivelty. From these parts 3,4 and 5 questions respectively are to be solved. In how many ways can a student select the questions from these parts?

Consider a chessboard of size 8 units xx8 units (i.e., each small square on the board has a side length of 1 unit). Let S be the set of all the 81 vertices of all the squares on the board. What is number of line segments whose vertices are in S_(1) and whose length is a positive integer? (The segments need not be parallel to the sides of the board).