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UPSC CDS 2 2018 Math Paper

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Question : 19 of 100

Marks: +1, -0

If a =

xy^{p-1}

yz^{q-1}

zx^{r-1}

a^{q-r}b^{r-p}c^{p-q}

abc
xyz
0
None of the above

Solution:

a^{9-t}=x^{9-t}\cdot y^{\\;\text{pq-pr-q+t}\\;}

b^{t-p}=y^{r-p}\cdot z^{qr-r-pq+p}

C^{p-q}=Z^{p-q}\cdot x^{pr-p-qr+q}

a^{q-r}\cdot b^{r-p}\cdot c^{p-q}

=(X^{q-r}\cdot y^{pq-pr-q+r})\times(y^{r-p}\cdot z^{qr-t-pq+p})x

z^{p-q}\cdot X^{pr-p-qr+q}

=X^{q-r+pr-p-qr+q}y^{pq-pr-q+r+r-p}z^{qr-r-pq+p+p-q}

=X^{2q-t+pr-p-qr}y^{pq-pr-q+2r-p}z^{qr-t-pq+2p-q}

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