QJEEM23Ma46e2: JEE Main 2023 Mathematics - Class 11 JEEM23Ma46e2 Solution: The number of ways of selecting two numbers and and such that 2 …

Question

Verified Solution • 2025–26 Session moderate

The number of ways of selecting two numbers

a

and

b, 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 :

Accepted Answer

$a+b=23\lambda+2$

$\lambda=0,1,2,$ ...., but $\lambda$ cannot be even as $a+b$ is odd

$\lambda=1$ $(a, b)\to12$ pairs

$\lambda=3$ $(a,b)\to35$ pairs

$\lambda=5$ $(a,b)\to42$ pairs

$\lambda=7$ $(a,b)\to19$ pairs

$\lambda=9$ $(a,b)\to0$ pairs

$\vdots$

Total $=12+35+42+19=108$

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