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GATE 2023 MT – Question 44

Engineering Mathematics · Calculus and vector calculus · 2 marks · Multiple choice

Match plots P–S in Section I (shown) with these functions in Section II:

1. $y=\sin^2x/x$

2. $y=x\sin^2x$

3. $y=\sin x/x$

4. $y=x\sin x$

Diagram for GATE 2023 MT question 44
  1. P – 3, Q – 2, R – 4, S – 1
  2. P – 2, Q – 3, R – 4, S – 1
  3. P – 1, Q – 4, R – 3, S – 2
  4. P – 2, Q – 3, R – 1, S – 4

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Show answer and explanation

Correct answer: (A) P – 3, Q – 2, R – 4, S – 1

Explanation

P is even with decaying envelope and limit 1 at zero: $\sin x/x$ (3). Q has the sign of x and growing envelope: $x\sin^2x$ (2). R is even with growing envelope: $x\sin x$ (4). S is odd with decaying envelope: $\sin^2x/x$ (1). Match: **P–3, Q–2, R–4, S–1; A**.