Verified Solution • 2025–26 Session moderate

QJEEM20Ma6f15: JEE Main 2020 Mathematics - Class 11 JEEM20Ma6f15 Solution: If {p} denotes the fractional part of the number p, then , is…

If {p} denotes the fractional part of the number p, then
{32008}\left\{ {{{{3^{200}}} \over 8}} \right\} , is equal to :

Multiple Choice Options

  • A 58{5 \over 8}
  • B 78{7 \over 8}
  • C 18{1 \over 8}
  • D 38{3 \over 8}

Step-by-Step Verified Solution

{32008}\left\{ {{{{3^{200}}} \over 8}} \right\}

= {(32)1008}\left\{ {{{{{\left( {{3^2}} \right)}^{100}}} \over 8}} \right\}

= {(1+8)1008}\left\{ {{{{{\left( {1 + 8} \right)}^{100}}} \over 8}} \right\}

= {1+100C1.8+100C2.82+....+100C100.81008}\left\{ {{{1 + {}^{100}{C_1}.8 + {}^{100}{C_2}{{.8}^2} + .... + {}^{100}{C_{100}}{{.8}^{100}}} \over 8}} \right\}

= {1+8K8}\left\{ {{{1 + 8K} \over 8}} \right\}

= {18+K}\left\{ {{1 \over 8} + K} \right\} where K ∈\in Integer

∴\therefore Fractional part = 18{{1 \over 8}}

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