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  1. If   x =
    3
    , then the value of 27x3 – 54x2 + 36x – 11 is
    2
    1. 11
      3
      8
    2. 11
      5
      8
    3. 12
      3
      8
    4. 12
      5
      8
Correct Option: D

x =
3
(Given)
2

∴  27x3 – 54x2 + 36x – 11
= (3x)3 – 3 × (3x)2 × 2 + 3 × 3x
(2)2 – (2)3 – 3
= (3x – 2)3 – 3
[∵  (a – b)3 = a3 – 3a2 b + 3ab2 – b3]
=
3 × 3
− 2 3 − 3
2

=
9
− 2 3 − 3
2

=
9 − 4
3 − 3
2

=
5
3 − 3
2

=
125
− 3
8

=
125 − 24
8

=
101
8

12
5
8



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