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JEE MATHEMATICS MCQ: COMBINATIONS

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The number of diagonals in a polygon of

m

sides is

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Correct option: C

\frac{1}{{2!}}m\left( {m - 3} \right)

Option C is correct because the number of diagonals in a polygon with m sides is given by mC2 - m, which simplifies to m(m-3)/2.

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A rectangle of dimension

m \times n

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being odd) is divided into square of unit length by drawing horizontal and vertical lines. The number of rectangles having side of odd unit length is The number of ways selecting three numbers from 1 to 30, so as to exclude every selection of three consecutive number is: Team A consists of 7 boys and n girls and Team B has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams, when a boy plays against a boy and a girl plays against a girl, then n is equal to The number of ways choosing a committee of 4 woman and 5 men from 10 women and 9 men, if Mr.

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{\;^{n + 2}}{C_8}:{\;^{n - 2}}{P_4} = \frac{{57}}{{16}}

n