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JEE MATHEMATICS MCQ: COMBINATIONS

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Application +4 | -1

The number of ways of selecting two numbers a and

b, \quad a \in\{2,4,6, \ldots .100\}

and

b \in(1,3,5, \ldots, 99)

such that 2 is the remainder when

a+b

is divided by 23 is

View answer and explanation

Correct option: A

108

Option A (108) is correct because by considering the possible values of

\lambda

in the equation

a+b = 23\lambda + 2

, and counting the number of pairs (a, b) that satisfy the conditions, the total number of ways is 108.

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n