JEE MATHEMATICS MCQ: COMBINATIONS

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There are 10 lamps in a hall. Each one of them can be switched on independently. The number of ways in which the hall can be illuminated, is

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Correct option: C

1023

Option C is correct because each lamp has two states (on or off), and we subtract 1 to exclude the case where all lamps are off, resulting in 2¹⁰ - 1 = 1023.

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A rectangle of dimension

m \times n

(

m

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n

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}}

, then

n

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