Q. 22

# Mark the correct alternative in the following:

The number of diagonals that can be drawn by joining the vertices of an octagon is

A. 20

B. 28

C. 8

D. 16

Answer :

An octagon has 8 vertices.

The number of diagonals of a polygon is given by . (Where n = number of vertices)

Number of diagonals of an octagon =

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Prove that the product of 2n consecutive negative integers is divisible by (2n)!

RD Sharma - MathematicsThere are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.[Hint: Required number = 210 – 1].

Mathematics - ExemplarIf ^{n+1}C_{r+1} : ^{n}C_{r} = 11 : 6 and ^{n}C_{r} : ^{n–1}C_{r–1} = 6 : 3, find n and r.

If ^{n}C_{r–1} = 36, ^{n}C_{r} = 84 and ^{n}C_{r+1} = 126, find r.

Fill in the Blanks

If ^{n}P_{r} = 840, ^{n}C_{r} = 35, then r = ______.

The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is

Mathematics - Exemplar