PGDBA 2023 Question Paper | Quant

PGDBA Previous Year Paper | PGDBA Quant Questions | Question 3

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Question 3 : Let \(P(x)\), and \(Q(x)\) be two distinct polynomials with degree at most 2 . Let \(a_0, \ldots, a_{n-1}\) be distinct elements of \(R\). Consider the following set \[ X=\left\{i \in\{0,1, \ldots,(n-1)\}: P\left(a_i\right) \neq Q\left(a_i\right)\right\} . \] Which of the following is always correct?

  1. The number of distinct elements in the set \(X\) is at least \((n-2)\)
  2. The number of distinct elements in the set \(X\) is less than \((n-2)\)
  3. The number of distinct elements in the set \(X\) is greater than \((n-2)\)
  4. The number of distinct elements in the set \(X\) is equal to \((n-2)\)

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The answer is 'The number of distinct elements in the set \(X\) is at least \((n-2)\)'

Choice A is the correct answer.

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