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Let $E = [\frac{1}{3} + \frac{1}{50}] + [\frac{1}{3} + \frac{2}{50}] + [\frac{1}{3} + \frac{3}{50}] + \dots +$ up to 50 terms, then the exponent of 2 in E! is

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Correct option is C

Let, E=13+x50 where x = 1,2, ... ,50 For, 1≤x≤33,13<13+x50<1∴ 13+x50=0, for 1≤x≤33For 34≤x≤50, 1<13+x50<43⇒13+x50=1 , For 34≤x≤50Thus, E=17 and p=2∵24<17<25∴a=4Exponent of 2 in (17)!=172+174+178+1716 =8+4+2+1=15

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Let E=13+150+13+250+13+350+…+ up to 50 terms, then the exponent of 2 in E! is

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Let $E = [\frac{1}{3} + \frac{1}{50}] + [\frac{1}{3} + \frac{2}{50}] + [\frac{1}{3} + \frac{3}{50}] + \dots +$ up to 50 terms, then the exponent of 2 in E! is