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Q.

The greatest integer less than or equal to (2+1)6 is 

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a

197 

b

198

c

196

d

199

answer is A.

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Detailed Solution

Let (2+1)6=I+F , where IN and 0<F<1

Clearly, I is the greatest integer less than or equal to (2+1)6 

Let G = (2+1)6 .Then , 

I+F+G=(2+1)6+(21)6

I+F+G=2 6C0(2)6+6C2(2)62+

I+F+G=An even integer . 

F+G=1 

Again , I+F+G 

=2 6C0(2)6+6C2(2)62+6C4(2)64+6C6(2)66

I+1=2(8+15×4+15×2+1)           [F+G=1]

I=197

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The greatest integer less than or equal to (2+1)6 is