GATE 2014 EC (EC4) – Question 4

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

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

$2^{n-m}P$
$2^{m-n}P$
$2(n-m)P$
$2(m-n)P$

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Correct answer: (A) $2^{n-m}P$

Explanation

Substitute the new inputs:f(2x,y/2)=(2x)ⁿ(y/2)ᵐ=2ⁿ2⁻ᵐxⁿyᵐ. Since the original value is P, the new value is **2^(n−m)P,A**. The exponents subtract because the scaling of y is reciprocal.