India’s No.1 Educational Platform For UPSC,PSC And All Competitive Exam

Download Our App

If x - 11, then the value of x⁵ - 12x⁴ + 12x³ - 12x² + 12x - 1 is?

111
210
312
4-10

Answer:- 1

Explanation:-

Solution:

\begin{aligned} x^{5} - 12 x^{4} + 12 x^{3} - 12 x^{2} + 12 x - 1 \\ = x^{5} - 11 x^{4} - x^{4} + 11 x^{3} + x^{3} - 11 x^{2} - x^{2} + 11 x + x - 1 \\ Put x = 11 \\ = 11^{5} - {11.11}^{4} - 11^{4} + {11.11}^{3} + 11^{3} - {11.11}^{2} - 11^{2} + 11.11 + 11 - 1 \\ = 11 - 1 \\ = 10 \end{aligned}

$\eqalign{ & {x^5} - 12{x^4} + 12{x^3} - 12{x^2} + 12x - 1 \cr & = {x^5} - 11{x^4} - {x^4} + 11{x^3} + {x^3} - 11{x^2} - {x^2} + 11x + x - 1 \cr & {\text{Put }}x = 11 \cr & = {11^5} - {11.11^4} - {11^4} + {11.11^3} + {11^3} - {11.11^2} - {11^2} + 11.11 + 11 - 1 \cr & = 11 - 1 \cr & = 10 \cr}$

Workspace Report

Post your Comments

", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} x^{5} - 12 x^{4} + 12 x^{3} - 12 x^{2} + 12 x - 1 \\ = x^{5} - 11 x^{4} - x^{4} + 11 x^{3} + x^{3} - 11 x^{2} - x^{2} + 11 x + x - 1 \\ Put x = 11 \\ = 11^{5} - {11.11}^{4} - 11^{4} + {11.11}^{3} + 11^{3} - {11.11}^{2} - 11^{2} + 11.11 + 11 - 1 \\ = 11 - 1 \\ = 10 \end{aligned}

$\eqalign{ & {x^5} - 12{x^4} + 12{x^3} - 12{x^2} + 12x - 1 \cr & = {x^5} - 11{x^4} - {x^4} + 11{x^3} + {x^3} - 11{x^2} - {x^2} + 11x + x - 1 \cr & {\text{Put }}x = 11 \cr & = {11^5} - {11.11^4} - {11^4} + {11.11^3} + {11^3} - {11.11^2} - {11^2} + 11.11 + 11 - 1 \cr & = 11 - 1 \cr & = 10 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

Test

Classes

E-Book