by shivamtripathi22 | May 30, 2022 | Uncategorized
(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...
by shivamtripathi22 | May 30, 2022 | Uncategorized
(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...
by shivamtripathi22 | May 28, 2022 | Uncategorized
(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 ...
by shivamtripathi22 | May 28, 2022 | Uncategorized
(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 ...
by shivamtripathi22 | May 28, 2022 | Uncategorized
(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 ...
by shivamtripathi22 | May 28, 2022 | Uncategorized
(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)...
by shivamtripathi22 | May 28, 2022 | Uncategorized
(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...
by shivamtripathi22 | May 28, 2022 | Uncategorized
(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)...
by shivamtripathi22 | May 28, 2022 | Uncategorized
(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...
by shivamtripathi22 | May 6, 2022 | Uncategorized
(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...
