Let $\mathrm{A}=\{(\mathrm{a}, \mathrm{b}, \mathrm{c}): \mathrm{a}, \mathrm{b}, \mathrm{c}$ are non-negative integers and $\mathrm{a}+\mathrm{b}+2 \mathrm{c}=22\}$. The $\mathrm{n}(\mathrm{A})$ is equal to :

JEE Main · 2026 · 04 Apr 2026 · Shift 2 · Permutations and Combinations

Let

A = {(a, b, c) : a, b, c

are non-negative integers and

a + b + 2 c = 22}

.
The

n (A)

is equal to :

Answer: (C)

For each fixed non-negative integer

c

, the equation

a + b = 22 - 2 c

has

(22 - 2 c) + 1 = 23 - 2 c

non-negative integer solutions, and

c

ranges from

0

11

(so that

22 - 2 c \geq 0

). The total is

\sum_{c = 0}^{11} (23 - 2 c) = 23 + 21 + 19 + \dots + 1

, an arithmetic series of

12

odd terms from

1

23

. Its sum is

\frac{12 ( 1 + 23 )}{2} = 144

. Thus

n (A) = 144

JEE Main · 2026 · 04 Apr 2026 · Shift 2 · Single correct option