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

The greatest possible number of points of intersection of $8$ distinct straight lines and $4$ distinct circles is

How many triangles can be formed using $5$ points on a line and $3$ points on a parallel line?

$110$ triangles can be formed by joining $10$ points as vertices,in which $n$ points are collinear. Then the value of $n$ is:

There are $n$ straight lines in a plane,no two of which are parallel and no three pass through the same point. Their points of intersection are joined. Then the number of fresh lines thus obtained is

In a tournament with five teams,each team plays against every other team exactly once. Each game is won by one of the playing teams and the winning team scores one point,while the losing team scores zero. Which of the following is $NOT$ necessarily true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module