(Q). In how many ways 2 + and 2 – signs are filled into 4×4 cell where each cell can contain maximum one character such that each row & column can not contain same sign...
(Q). Let Tₙ be the number of all possible triangles formed by joining vertices of an n – sided regular polygon. if Tₙ₊₁ – Tₙ = 10, then what will be the value of n? Solution:- As per the given conditionⁿ⁺¹C₃ – ⁿC₃ = 10we know that ⁿCᵣ + ⁿCᵣ ₋ ₁ = ⁿ...
(Q). A rectangle with sides 2n-1 and 2m-1 is divided into squares of unit length by drawing parallel lines as shown in the diagram, then the number of rectangles possible with odd side length is?Solution:-...
we have following cases in this question:-case (i): if one point is selected from each side then number of triangle is = 3×4×5 = 60case (ii): if one point is selected from one side and 2 points from another side then number of ways is= ³C₂×(4 + 5) + ⁴C₂×(5+3)...
(Q). 150 circles are drawn on a plane. What is the maximum number of regions made by this system of 150 circles?Solution:-we know the formula that if number of circle is n then number of regions is n(n-1) + 2Hence when number of circles is 150 thn maximum regions is=...
1. In how many ways 15 students can be seated on 20 seats in a row ? 2. In how many ways 5 distinct volume of chemistry and 7 distinct volume of Botany book can be arranged on a bookshelf such that no two chemistry books are together ? 3. In how many ways 15 students...
(Q). Consider ‘n’ straight lines in a plane such that no two of which are parallel and no three of which pass through the same point. How many new straight lines can be drawn from the point of intersection of these straight lines?Solution:-Since each line...
(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...
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