GATE 2012 CS (CS1) – Question 7

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

An entrance arch for a political party’s annual convention has profile $y=2x-0.1x^2$, where y is height in metres. What is its maximum height?

8 metres
10 metres
12 metres
14 metres

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Show answer and explanation

Correct answer: (B) 10 metres

Explanation

Complete the square: $y=10-0.1(x-10)^2$. The squared term is nonnegative, so maximum y is 10 metres at x=10. Alternatively y′=2−0.2x gives the same vertex and y″<0 confirms a maximum. Thus B.

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