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GATE 2022 BM – Question 18

Signals and Systems · Signals and Sampling · 1 mark · Multiple choice

Find the time separation in seconds between corresponding peaks of v₁(t)=2cos(6t+60°) and v₂(t)=−3sin(6t).

  1. $300\pi/360$
  2. $10\pi/360$
  3. $50\pi/360$
  4. $200\pi/360$

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Correct answer: (C) $50\pi/360$

Explanation

Convert −sin(6t) to cos(6t+90°). The two cosine phases differ by thirty degrees, or π/6 radians, at common angular frequency six rad/s. Hence the nearest peak separation is Δt=(π/6)/6=π/36=10π/360 s. This calculation gives B, whereas the published key is C=50π/360; C corresponds to the complementary phase selection of one hundred fifty degrees. The official grading is retained and this discrepancy is identified.

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