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IPMAT Indore 2025 · Question 33 of 90 · Quantitative Ability (MCQ)

IPMAT Indore 2025 — Question 33

The remainder when $1 1^{1011} + 101 1^{11}$ is divided by 9 is

A8
B7
C0
D9

Reveal answer

Correct answer

A.8

Reveal solution

$11 \equiv 2 (mod 9)$ , so $1 1^{1011} \equiv 2^{1011} (mod 9)$ . $2^{6} \equiv 1$ , and $1011 = 6 \cdot 168 + 3$ , so $2^{1011} \equiv 8$ . $1011 \equiv 3 (mod 9)$ , so $101 1^{11} \equiv 3^{11}$ . $3^{2} = 9 \equiv 0$ , so $3^{11} \equiv 0$ . Sum: $8 + 0 = 8$ .

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