Home
Class 12
MATHS
Consider a polygon of sides 'n' which sa...

Consider a polygon of sides 'n' which satisfies the equation `3*.^(n)P_(4)=.^(n-1)P_(5)`.
Q. Number of quadrilaterals thatn can be formed using the vertices of a polygon of sides 'n' if exactly 1 side of the quadrilateral in common with side of the n-gon, is

A

96

B

100

C

150

D

156

Text Solution

Verified by Experts

The correct Answer is:
C
Number of quadrilaterals of which exactly one side is the side of the n-gon
`=nxx.^(n-4)C_(2)=10xx.^(6)C_(2)=150" "[becausen=10]`
Promotional Banner

Similar Questions

Explore conceptually related problems

Consider a plygon of sides 'n' which satisflies the equation 3. .^(n)p_(4) = .^(n-1)p_(5) Rajdhani express travelling from Delhi to Mumbai has n station enroute. Number of ways in which a train can be stopped at 3 stations

Find the number of triangles whose angular points are at the angular points of a given polygon of n sides, but none of whose sides are the sides of the polygon.

The two adjacent sides of a cyclic quadrilateral are 2a n d5 and the angle between them is 60^0dot If the area of the quadrilateral is 4sqrt(3) , find the remaining two sides.

If theta is the internal angle of n sided regular polygon, then sintheta is equal to:

if .^(2n+1)P_(n-1):^(2n-1)P_(n)=7:10 , then .^(n)P_(3) equals

Find the value of n such that ""^(n)P_(5)=42""^(n)P_(3), n gt 4

Find the value of n such that (""^(n)P_(4))/(""^(n-1)P_(4))=(5)/(3), n gt 4

There are 2n points in a plane in which m are collinear. Number of quadrilateral formed by joining these lines

ABCD is a convex quadrilateral and 3, 4, 5, and 6 points are marked on the sides AB, BC, CD, and DA, respectively. The number of triangles with vertices on different sides is

Three forces of magnitudes 2N, 3N and 6N act at corners of a cube along three sides as shown in figure. Find the resultant of these forces in N.