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NDA 2022

Exam: NDA
Year: 2022
Subject: Mathematics
Chapter: Binary Numbers

NDA 2022 · Mathematics · Binary Numbers

If x^3+y^3=(100010111)_2 and x+y=(11111)_2 , then what is (x-y)^2+x...

If

x^3+y^3=(100010111)_2

and

x+y=(11111)_2

, then what is

(x-y)^2+x y

equal to?

Options

A $(1101)_2$
B $(1001)_2$
C $(1011)_2$
D $(1111)_2$

Correct answer

B. $(1001)_2$

Step-by-step solution

\begin{aligned} & x^3+y^3=2^8+2^4+2^2+2^1+2^0 \\ & =256+16+4+2+1=279 \\ & x+y=2^4+2^3+2^2+2^1+2^0 \\ & =16+8+4+2+1=31\end{aligned}

Now,

(x-y)^2+x y=\frac{(x+y)\left[x^2-x y+y^2\right]}{x+y}=\frac{x^3-y^3}{x+y}=\frac{279}{31}=9\therefore <table class="qx-match-list qx-match-table" border="1" cellpadding="6" cellspacing="0"><tr><td>2</td><td>9</td><td></td></tr><tr><td>2</td><td>4</td><td>1</td></tr><tr><td>2</td><td>2</td><td>0</td></tr><tr><td></td><td>1</td><td>0</td></tr></table>

\therefore 9=[1001]_2

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