State true or false.
If $a = x^{m + n} . y^{1}; b = x^{n + 1} . y^{m}$ and $c = x^{1 + m} . y^{n}$ , then $a^{m - n} . b^{n - 1} . c^{1 - m} = 1$

True

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False

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Solution

The correct option is A True
$\Rightarrow a^{m - n} . b^{n - 1} . c^{1 - m} = 1$

As given $a = x^{m + n} . y^{1}; b = x^{n + 1} . y^{m} a n d c = x^{1 + m} . y^{n}$

Put the value of $a, b, c$ in LHS
$\Rightarrow {(x^{m + n} . y^{1})}^{m - n} . {(x^{n + 1} . y^{m})}^{n - 1} . {(x^{1 + m} . y^{n})}^{1 - m}$

$\Rightarrow x^{m^{2} - n^{2}} . y^{m - n} . x^{n^{2} - 1} . y^{m n - m} . x^{1 - m^{2}} . y^{n - m n}$
$\Rightarrow x^{m^{2} - n^{2} + n^{2} - 1 + 1 - m^{2}} . y^{m - n + m n - m + n - m n}$
$\Rightarrow x^{0} . y^{0}$ $∵ [x^{0} = 1]$
$\Rightarrow 1 \times 1 = 1$
So $L H S = R H S$

The given statement is true.

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Similar questions

Q. If

a = x^{m + n} . y^{l}; b = x^{n + l} . y^{m}

and

c = x^{l + m} . y^{n}

prove that :

a^{m - n} . b^{n - l} . c^{l - m} = 1

Q. If

a = x^{m + n} \cdot y^{1}; b = x^{n + 1} \cdot y^{m} a n d c = x^{1 + m} \cdot y^{n}

,
then prove that

a^{m - n} \cdot b^{n - 1} \cdot c^{1 - m} = 1

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State true or false.

y = \sqrt{\frac{1 - x}{1 + x}} \cdot

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Q. State True or False.

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State true or false.If a=xm+n.y1;b=xn+1.ym and c=x1+m.yn, then am−n.bn−1.c1−m=1

State true or false.
If $a = x^{m + n} . y^{1}; b = x^{n + 1} . y^{m}$ and $c = x^{1 + m} . y^{n}$ , then $a^{m - n} . b^{n - 1} . c^{1 - m} = 1$