16:I[8216,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"BackButton"] 17:I[1553,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"QuestionViewer"] 15:T48c,{"@context":"https://schema.org","@type":"Quiz","name":"Iat Iiser 2026 Binomial Theorem PYQ with Solution","url":"https://pyq-test-series-platform-alsjdcxu2-sameers-projects-41c5a71e.vercel.app/iat-iiser/questions/2026/mathematics/binomial-theorem/jt-mr96hxhj","educationalLevel":"Entrance exam preparation","about":"Iat Iiser / Mathematics / Binomial Theorem","hasPart":{"@type":"Question","name":"Iat Iiser 2026 Binomial Theorem PYQ with Solution","text":"Let n = 20^{26}. What is the remainder when 49^n + 41^n + 10n is divided by 100?","eduQuestionType":"mcq","acceptedAnswer":{"@type":"Answer","text":"D"},"comment":{"@type":"Comment","text":"We need the remainder of 49^n + 41^n + 10n when divided by 100, where n = 20^{26} First, notice that n = 20^{26} is an even number and is also divisible by 5. Now check each part modulo 100. For 49^n: 49^2 = 2401 So, 49^2 \\equiv 1 \\pmod{100} Since n = 20^{26} is even, we can write n as a multiple of 2. So, 49^n \\equiv 1 \\pmod{100} Now for 41^n: Let us see the pattern of powers of 41 modulo 100. 41^1 \\equiv 41 \\pmod{100} 41^2 = 1681 \\equiv 81 \\pmod{100} 41^3 \\equiv 81 \\times 41 = 3321 \\equiv 21..."}}}18:T54a,

We need the remainder of

$$49^n + 41^n + 10n$$

when divided by $100$, where

$$n = 20^{26}$$

First, notice that $n = 20^{26}$ is an even number and is also divisible by $5$.

Now check each part modulo $100$.

For $49^n$:

$$49^2 = 2401$$

So,

$$49^2 \equiv 1 \pmod{100}$$

Since $n = 20^{26}$ is even, we can

Binomial Theorem

Continue this paper

Similar Binomial Theorem PYQs

More practice from this question