(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 ...
(Q). Find the number of rectangles in a chess board of 11×11 grid instead of 8×8 grid.Solution:-Chess board has 11 + 1 = 12 set of parallel lines & another set of 11 + 1 = 12 set of parallel lines.Hence number of rectangle = ¹²C₂ × ¹²C₂ ...
(Q). Let Kₙ denotes the number of triangles which can b formedusing the vertices of a regular polygon of ‘n’ sides. Which one of the following could be the value of Pₙ₊₁ – Pₙ₋₁? (a) 194 (b) 195 (c)196 (d)...
(Q). Consider ‘n’ points in a plane, if number of heptagon is equal to number of octagons then find the number of triangles that can be drawn from these n points. Solution:- number of heptagon = number of octagon ⟹ ⁿC₇ = ⁿC₈ Hence n = 7 + 8 = 15 ∴ number...
(Q). Find the number of non-congruent rectangles on a chess board.Solution:-Here we need non-congruent rectangles means every rectangle should have unique pair of length and breadth i.e. no two rectangles should have same length and breadth.Hence dimension (a, b)...
(Q). Consider three set of parallel lines in a plane containing ‘x’, ‘y’, ‘z’ parallel lines respectively. What is the highest number of parallelograms that can be formed with these set of parallel lines?Solution:-Consider pair of...
(Q). The sides AB, BC, CA of a triangle ABC have 4, 5 and 6 interior points respectively on them. Find the number of triangles that can be constructed using given interior points as vertices? Solution:- Total number of points = 4 + 5 + 6 = 15 if none of them are...
(Q). Consider n points in a plane no three of which are collinear and the ratio of number of hexagon & octagon that can be formed from these n points is 7:69 then find the value of...
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