(Q). Consider a polygon of n sides. what is the number of triangles that can be drawn taking vertices of these polygons as vertices of triangles and no side of triangles is common with any side of the polygon?Solution:-Without any restriction number of tiangle formed...
(Q). Consider a polygon of k sides with n points on each side (no point on the vertices)(i) How many straight lines can be drawn from these ‘kn’ points such that each line passes through exactly 2 of the given points.(ii) if ‘T’ is the maximum...
(Q). Consider 37 points in a plane such that no three of them are collinear. A student is told to 1st draw all the possible polyg0ns of same number of sides & then draw all the possible diagonals. What is the maximum number of such diagonals possible? ( if a...
(Q). In how many ways 2 rooks can be placed on a chessboard such that they are not in attacking position?Solution:-We know that rooks can attack only in same row or in same column.The first rook has 64 options to be placed & since the second rook can not be placed...
(Q). Find the number of squares in a chess board of 10×12 Grid instead of 8×8 Grid. Solution:- total number of squares that can be found within an m×n chessboard (m>n) is given by this formula: Here m = 12 & n = 10Hence required number of square is: = 495 ...
(Q). Find the number of rectangles in a chess board of 12×14 grid instead of 8×8 grid. Solution:-2 lines can be selected from 12 parallel lines in ¹²C₂ ways.2 lines can be selected from 14 parallel lines in ¹⁴C₂ ways.Hence number of rectangles = ¹²C₂×¹⁴C₂ ...
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