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For each natural number k, let `C_k` denotes the circle radius k centimeters in the counter-clockwise direction.After completing its motion on `C_k`, the particle moves to `C_[k+1]` in the radial direction. The motion of the particle continues in this manner. The particle starts at (1,0).If the particle crosses the the positive direction of the x-axis for first time on the circle `C_n`,then n equal to |
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Answer» Correct Answer - n = 7 It is given that , `C_(1) " has centre " (0, 0)` and radius 1. Similarly, `C_(2)` has centre (0, 0) and radius 2 and `C_(k)` ahs centre (0, 0) and radius k. Now, particle starts it motion from (1, 0) and moves 1 radian on first circle then particle shifts from `C_(1)` to` C_(2)`. After that, particle moves 1 radian on `C_(2)` and then paricle shifts from `C_(2) " to " C_(3)`. Similarly, particle move on n circles. Now, `n ge 2pi` because particle crosses the X-axis for the first time on `C_(n)`, then n is least positive integer. therefore, n = 7. |
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