1, 1000, 11011, 1000000, 1111101, ?

Options

A. 1100101
B. 11011000
C. 10000000
D. None of these

Answer

B

Explanation

The given sequence of number is in Binary system and follows the pattern
Cubes ofnatural numbers ie. `1^(3), 2^(3), 3^(3), 4^(3), 5^(3)," and "ul(6)^(ul(3))` Converting this binary system into Decimal system,
We get `1 implies 1xx2^(@)implies1=1^(3)`
`1000implies1xx2^(3)+0+2^(2)+0xx2^(1)+0xx2^(@)`
`implies8+0+0+0=8=2^(3)`
`implies1xx2^(4)+1xx2^(3)+0xx2^(2)+1xx2^(1)+1xx2`
`16+8+2+1=3^(3)`
`1000000 implies1 xx 2^(6) + 0 xx 2^(5) + 0 xx 2^(4) + 0 xx 2^(3)+ 0xx2^(2)+0xx2^(1)+0xx2^(@)`
`implies64+0+0+0+0+0+0=64=4^(3)`.
`1111101 implies 1 xx 2^(6) + 1 xx 2^(5) + 1 xx 2^(2) + 1 xx 2^(3) + 1 xx 2^(2) + 0 xx 2^(1) + 1 xx 2^(@)`
`implies 64 + 32 + 16 + 8 + 4 + 0 + 1 = 125 = 53`.
`ul(11011000)implies 1 xx 2^(7) + 1 xx 2^(6) + 0 xx 2^(5) + 1 xx 2^(4) + 1 xx 2^(3) + 0 xx 2^(2)+ 0 xx 2^(1) + 0 xx 2^(0)`
`implies 128 + 64 + 0 + 16 + 8 + 0 + 0 + 0`
`= ul(216)=ul(6)^(ul(3))`.
Therefore, Missing number `=6^(3)=216 =11011000.`