"3 $\\times$ 722 + 2 $\\times$ 1022 $-$ 44 when divided by 18 leaves the remainder __________."

"3(1 + 6) 22 + 2 . (1 + 9) 22 $-$ 44 = (3 + 2 $-$ 44) = 18 . I = $-$ 39 + 18 . I = (54 $-$ 39) + 18(I $-$ 3) = 15 + 18I 1 $\\Rightarrow$ Remainder = 15"

Medium INTEGER +4 / -1 PYQ · JEE Mains 2021

3 $\times$ 7²² + 2 $\times$ 10²² $-$ 44 when divided by 18 leaves the remainder __________.

Answer (integer) 15

Solution

3(1 + 6)22 + 2 . (1 + 9)22 $-$ 44 = (3 + 2 $-$ 44) = 18 . I = $-$ 39 + 18 . I = (54 $-$ 39) + 18(I $-$ 3) = 15 + 18I1 $\Rightarrow$ Remainder = 15

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Subject: Mathematics · Chapter: Binomial Theorem · Topic: Binomial Expansion

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3 $\times$ 722 + 2 $\times$ 1022 $-$ 44 when divided by 18 leaves the remainder __________.

Solution

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3 $\times$ 7²² + 2 $\times$ 10²² $-$ 44 when divided by 18 leaves the remainder __________.