SATHEE: Circle 4 Question 13

Circle 4 Question 13

13. For each natural number $k$ . Let $C_{k}$ denotes the circle with radius $k$ centimetres and centre at origin. On the circle $C_{k}$ a particle moves $k$ centimetres 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 continue in this manner. The particle starts at $(1, 0)$ . If the particle crosses the positive direction of the $X$ -axis for the first time on the circle $C_{n}$ , then $n = \dots$

(1997, 2M)

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Answer:

Correct Answer: 13. $n = 7$

Solution:

It is given that, $C_{1}$ has centre $(0, 0)$ and radius 1 .

Similarly, $C_{2}$ has centre $(0, 0)$ and radius 2 and $C_{k}$ has 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 particle shifts from $C_{2}$ to $C_{3}$ . Similarly, particle move on $n$ circles.

Now, $n \geq 2 π$ because particle crosses the $X$ -axis for the first time on $C_{n}$ , then $n$ is least positive integer.

Therefore, $n = 7$ .

Circle 4 Question 13

Answer:

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Circle 4 Question 13

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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