JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Permutations and Combinations

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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)210
(B)180
(C)170✓ Correct
(D)190

Answer: (C)

Solution

Joining a pillar to every non-adjacent pillar is the same as drawing all the diagonals of a

20

-gon. The total number of segments between

20

points is

(2 20) = 190

, and removing the

20

sides, which join adjacent pillars, leaves

190 - 20 = 170

beams.

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Single correct option

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