CUET UG 2025 — General Test Quantitative Reasoning

To find the remainder when $(44)^2$(44)2 is divided by 9, find what remainder 44 gives when divided by 9.

Dividing 44 by 9:

$$9 \times 4 = 36$$9×4=36

$$44 - 36 = 8$$44−36=8

So 44 leaves remainder 8 when divided by 9.

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When finding remainders, 44 can be replaced with 8 (its remainder) to get the same final answer.

Square this remainder:

$$8^2 = 64$$82=64

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Find the remainder when 64 is divided by 9.

Dividing 64 by 9:

$$9 \times 7 = 63$$9×7=63

$$64 - 63 = 1$$64−63=1

So 64 leaves remainder 1 when divided by 9.

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The remainder of a square equals the square of the remainder.

Remainder of $(44)^2 \div 9$(44)2÷9 = Remainder of $(8)^2 \div 9$(8)2÷9 = Remainder of $64 \div 9 = 1$64÷9=1

Therefore, the remainder is 1.