The exponent of 7 in the coefficient of the greatest term in the expansion of (1+x)200 is
A
0
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B
1
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C
2
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D
3
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Solution
The correct option is D 0 The greatest coefficient will be 200C100 =200!100!.100! Now the exponent of 7 in 200! will be [2007]+[20049] =[28.57]+[4.08] =28+4 =32 The exponent of 7 in 100! will be [1007]+[10049] =[14.28]+[2.04] =14+2 =16 Hence the power of 7 in (100!)2 will be 16+16 =32 Hence the powers of seven in the numerator and denominator will be equal. Hence answer is 0.