Direction TestMTP Dec 2023 Series IIQuestion 2322 of 165
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Pankaj is facing west. He turns 45∘\displaystyle 45^{\circ} in the clockwise direction and then again another turns with 180∘\displaystyle 180^{\circ} in the same direction i.e. clockwise direction, after that he turns 270∘\displaystyle 270^{\circ} in the anticlockwise direction. Which direction is he facing now?

Options

ANorth-West
BWest
CSouth-West
DSouth
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Correct Answer

✅ Option c — South-West

All Options:

  • ANorth-West
  • BWest
  • CSouth-West
  • DSouth

Detailed Solution & Explanation

Let the initial direction West be represented as 180∘\displaystyle 180^\circ.
- Turns 45∘\displaystyle 45^\circ clockwise   ⟹  +45∘\displaystyle \implies +45^\circ.
- Turns 180∘\displaystyle 180^\circ clockwise   ⟹  +180∘\displaystyle \implies +180^\circ.
- Turns 270∘\displaystyle 270^\circ anticlockwise   ⟹  −270∘\displaystyle \implies -270^\circ.
His net angular displacement from West is:
Net Rotation=+45∘+180∘−270∘=−45∘\text{Net Rotation} = +45^\circ + 180^\circ - 270^\circ = -45^\circ
A rotation of −45∘\displaystyle -45^\circ (clockwise is positive, so this is 45∘\displaystyle 45^\circ counterclockwise) from West (180∘\displaystyle 180^\circ) points to South-West (135∘\displaystyle 135^\circ).
Hence, **Option C** is the correct answer.

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