JEE Main 2026 Apr 4 Shift 2, Mathematics Q17: Combinations

JEE Main2026Apr 4, Shift 2Mathematics

Let $A = {(a, b, c) : a, b, c are non-negative integers and a + b + 2 c = 22}$ .

The $n (A)$ is equal to:

Solution

For each fixed $c$ , the equation $a + b = 22 - 2 c$ has $22 - 2 c + 1$ non-negative integer solutions (since $a$ runs from $0$ to $22 - 2 c$ ).

$c$ ranges from $0$ to $11$ (so that $22 - 2 c \geq 0$ ). The counts are:

$c = 0$ : 23, $c = 1$ : 21, $c = 2$ : 19, ..., $c = 11$ : 1.

Sum of the arithmetic series $1 + 3 + 5 + \dots + 23$ (12 odd terms):

$\sum = 1 2^{2} = 144$ .

Concept behind this question

Concept-wise practice with instant solutions on Fundamenthol.