State true or false.

A polyhedron can have 10 faces, 20 edges and 15 vertices.

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True

False

answer is B.

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Detailed Solution

It is given a polyhedron can have 10 faces, 20 edges and 15 vertices.
Euler’s formula is F+V-E=2
where F is face, V is vertices and E is edges.
Use Euler’s formula and put the values,

⇒ F + V − E ⇒ 10 + 15 − 20 ⇒ 25 − 20 ⇒ 5

From the calculation we get, it is not equal to 2.
A polyhedron having 10 faces, 20 edges and 15 vertices is not possible as Euler’s formula is not satisfied.
Therefore, the given statement is false.
Hence option (2) is correct.

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