If X = {8ⁿ − 7n − 1 ; n ∈ ℕ} and Y = {49n − 49 ; n ∈ ℕ}, then:

Correct option is A

Given:

X = {8ⁿ − 7n − 1 : n ∈ ℕ}
Y = {49n − 49 : n ∈ ℕ}

Check first few terms:
For X:
n = 1 → 0
n = 2 → 49
n = 3 → 490
X = {0, 49, 490, …}

For Y:
n = 1 → 0
n = 2 → 49
n = 3 → 98
n = 4 → 147
n = 5 → 196
n = 6 → 245
n = 7 → 294
n = 8 → 343
n = 9 → 392
n = 10 → 441
n = 11 → 490
Y = {0, 49, 98, 147, 196, 245, 294, 343, 392, 441, 490, …}

Clearly, every element of X (0, 49, 490, …) appears in Y (for n = 1, 2, 11, … respectively),
but Y has additional elements not in X.

Conclusion:
X ⊂ Y

Correct answer: (a) X ⊂ Y