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GATE 2020 ME (ME1) – Question 9

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

Select the graph that schematically represents BOTH $y=x^m$ and $y=x^{1/m}$ properly in $0\le x\le1$, for integral m > 1. The choices are arranged A, B in the top row and C, D in the bottom row.

Diagram for GATE 2020 ME (ME1) question 9
  1. Graph A
  2. Graph B
  3. Graph C
  4. Graph D

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Show answer and explanation

Correct answer: (A) Graph A

Explanation

For 0<x<1, increasing the exponent decreases the value, so $x^m<x<x^{1/m}$. The power m curve is convex and the reciprocal-power curve is concave. Both pass through (0,0),(1,1) and are reflections across y=x. Only **A** has the correct labels and shapes.