Consider a rectangle ABCD having 5, 6, 7, 9 p | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the number of points on sides $AB, BC, CD, DA$ be $n_1=5, n_2=6, n_3=7, n_4=9$ respectively.$\alpha$ is the number of triangles formed by choo

Vedclass · Accepted Answer

$717$

Vedclass · Answer

(D) Let the number of points on sides $AB, BC, CD, DA$ be $n_1=5, n_2=6, n_3=7, n_4=9$ respectively.$\alpha$ is the number of triangles formed by choosing $3$ points from different sides.To form a triangle,we select $3$ sides out of $4$ and then $1$ point from each selected side.$\alpha = (n_1 n_2 n_3) + (n_1 n_2 n_4) + (n_1 n_3 n_4) + (n_2 n_3 n_4)$$\alpha = (5 \cdot 6 \cdot 7) + (5 \cdot 6 \cdot 9) + (5 \cdot 7 \cdot 9) + (6 \cdot 7 \cdot 9)$$\alpha = 210 + 270 + 315 + 378 = 1173$$\beta$ is the number of quadrilaterals formed by choosing $4$ points from different sides.To form a quadrilateral,we select $1$ point from each of the $4$ sides.$\beta = n_1 \cdot n_2 \cdot n_3 \cdot n_4$$\beta = 5 \cdot 6 \cdot 7 \cdot 9 = 1890$Therefore,$(\beta-\alpha) = 1890 - 1173 = 717$.

Similar Questions

There are $10$ points in a plane,of which no three points are collinear except $4$. Then,the number of distinct triangles that can be formed by joining any three points of these ten points,such that at least one of the vertices of every triangle formed is from the given $4$ collinear points is

Suppose that $20$ pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars,then the total number of beams is

$A$ simple graph contains $24$ edges. The degree of each vertex is $3$. The number of vertices is:

Let $l_1$ and $l_2$ be two lines intersecting at $P$. If $A_1, B_1, C_1$ are points on $l_1$,and $A_2, B_2, C_2, D_2, E_2$ are points on $l_2$,and if none of these points coincides with $P$,then the number of triangles formed by these eight points is:

$A$ polygon has $44$ diagonals. Then the number of sides of the polygon is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module