Let f(x, y) = xⁿy^m = P. If x is doubled and y is halved, the new value of f is

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PY 17: GATE ME 2014 Official Paper: Shift 4

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Answer 1

Given:

P = xⁿy^m

Now x^’ = 2x, y^’ = y/2

∴ P^’ = (x^’)ⁿ(y^’)^m

P^’ = (2x)ⁿ(y/2)^m

^{\(P' = {\left( {2x} \right)^n}{\left( {\frac{y}{2}} \right)^m} = {2^n}{\left( {\frac{1}{2}} \right)^m}\left( {{x^n}{y^m}} \right) = {2^{n - m}}P\)}

Hence, option 1 is the correct answer.