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GATE 2023 MT – Question 9

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

The coefficient of $x^4$ in $(x-1)^3(x-2)^3$ is ______.

  1. 33
  2. −3
  3. 30
  4. 21

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Show answer and explanation

Correct answer: (A) 33

Explanation

Write the polynomial as $(x^2-3x+2)^3$. An $x^4$ term comes either from two $x^2$ factors and one constant, giving $3(2)=6$, or one $x^2$ and two $-3x$ factors, giving $3(9)=27$. Total coefficient is **33, A**.