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JAMB Mathematics 2011 Paper

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Question : 20

Total: 46

A binary operation

\oplus

om real numbers is defined by x

\oplus

y = xy + x + y for two real numbers x and y. Find the value of 3

\oplus

\frac{2}{3}

.

- $\frac{1}{2}$
$\frac{1}{3}$
-1
2

Solution:

Concept:

Use the given rule:

x \oplus y = xy + x + y

. Substitute the given values of

x

and

y

and simplify.

Explanation:

Here,

x = 3

and

y = -\frac{2}{3}

.

Substitute into the operation:

3 \oplus \left(-\frac{2}{3}\right) = 3\left(-\frac{2}{3}\right) + 3 + \left(-\frac{2}{3}\right)

First, compute

3\left(-\frac{2}{3}\right) = -2

.

Then simplify the rest:

-2 + 3 - \frac{2}{3} = 1 - \frac{2}{3}

Convert

1

to a fraction with denominator

3

:

1 - \frac{2}{3} = \frac{3}{3} - \frac{2}{3} = \frac{1}{3}

Answer:

The value is

\frac{1}{3}

, so the correct option is B.

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