JEE Main 2024 Mathematics question
The number of elements in the set S = {(x, y, z) : x, y, z ∈ ℤ, x + 2y + 3z = 42, x, y, z ≥ 0} equal .
Answer: 169
Solution
For each z = 0, …, 14 the number of (x, y) is ⌊(42 − 3z)/2⌋ + 1; the total is 169.
The number of elements in the set S = {(x, y, z) : x, y, z ∈ ℤ, x + 2y + 3z = 42, x, y, z ≥ 0} equal .
For each z = 0, …, 14 the number of (x, y) is ⌊(42 − 3z)/2⌋ + 1; the total is 169.