For a- b- R defined by a-b-a-a-b- where a-b 0- If a-b-5- then the value of b-a is

Finding the value of 𝑏*𝑎:Given, a*b=a/(a+b) amp; a*b=5Therefore, [ a/a+b = 5; 4a ...

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Byju's Answer

Standard XII

Mathematics

Arithmetic Progression

For a, b∈ R d...

Question

For $a, b \in R$ defined by $a * b = \frac{a}{(a + b)}$ , where $a + b \neq 0$ . If $a * b = 5$ , then the value of $b * a$ is

$5$

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$- 5$

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Solution

The correct option is B
$- 4$

Finding the value of $b * a$ :
Given, $a * b = \frac{a}{(a + b)}$ & $a * b = 5$
Therefore,
$\begin{array}{rcl} \frac{a}{a + b} & = & 5 \\ 4 a & = & - 5 b \\ b & = & \frac{- 4 a}{5} . . . (i) \end{array}$
Now,
$b * a = \frac{b}{a + b}$ put the value of $b$
$\begin{array}{rcl} b * a & = & \frac{\frac{4 a}{5}}{a \frac{- 4 a}{5}} \\ = & \frac{- 4 a}{a} \\ = & - 4 \end{array}$
Hence, correct option is $(B)$

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Similar questions

Q. Check the commutativity and associativity of each of the following binary operations:
(i) '*'. on Z defined by a * b = a + b + ab for all a, b ∈ Z
(ii) '*'. on N defined by a * b = 2^ab for all a, b ∈ N
(iii) '*'. on Q defined by a * b = a − b for all a, b ∈ Q
(iv) '⊙' on Q defined by a ⊙ b = a² + b² for all a, b ∈ Q
(v) 'o' on Q defined by

a o b = \frac{a b}{2}

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(vi) '*' on Q defined by a * b = ab² for all a, b ∈ Q
(vii) '*' on Q defined by a * b = a + ab for all a, b ∈ Q
(viii) '*' on R defined by a * b = a + b − 7 for all a, b ∈ R
(ix) '*' on Q defined by a * b = (a − b)² for all a, b ∈ Q
(x) '*' on Q defined by a * b = ab + 1 for all a, b ∈ Q
(xi) '*' on N, defined by a * b = a^b for all a, b ∈ N
(xii) '*' on Z defined by a * b = a − b for all a, b ∈ Z
(xiii) '*' on Q defined by

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(xiv) '*' on Z defined by a * b = a + b − ab for all a, b ∈ Z
(xv) '*' on N defined by a * b = gcd(a, b) for all a, b ∈ N

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For a,b∈R defined by a*b=a(a+b), where a+b≠0. If a*b=5, then the value of b*a is

The correct option is B -4Finding the value of b*a:Given, a*b=a(a+b)& a*b=5Therefore, aa+b=54a=-5bb=-4a5...(i)Now, b*a=ba+bput the value of b b*a=4a5a-4a5=-4aa=-4Hence, correct option is (B)

For $a, b \in R$ defined by $a * b = \frac{a}{(a + b)}$ , where $a + b \neq 0$ . If $a * b = 5$ , then the value of $b * a$ is