The greatest integer less than or equal to (√2+1)6 is?
A
196
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B
197
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C
198
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D
199
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Solution
The correct option is B 197 Let (√2+1)6=I+F, Where I is an integer and 0< F<1. f=√2−1=1√2+1⇒0<√2−1<1⇒0<f<1
Also I+F+f=(√2+1)6+(√2−1)6
= 2[6C0.23+6C2.22+6C4.2+6C6] =2(8+60+30+1)=198
Hence, F+f=198−I is an integer. But 0<F+f<2. ∴F+f=1, and thus, I=197