Question

For each natural number k, let Ck denote the circle with radius centimeters and centre at the origin O, on the circle Ck a particle moves k centimeters in the counter-clockwise direction. After completing its motion on Ck, the particle moves to Ck + 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 positive direction of x-axis for the first time on the circle Cn then n =

Solution

Correct option is

7

 

The motion of the particle on the first four circles is shown with bold line in the figure. Note that on every circle the particle travels just one radian. The particle crosses the positive direction of x-axis first time onCn where n is least positive integer such that     

               

                   

 
                                                                   

 

 

SIMILAR QUESTIONS

Q1

Two points P and Q are taken on the line joining the points A (0, 0) and B (3a, 0) such that AP = PQ = QB. Circles are drawn onAPPQ, and QB as diameters. The locus of the point S, the sum of the squares of the lengths of the tangents from which to the three circles is equal to b2, is

Q2

If OA and OB are two equal chords of the circle x2 + y2 – 2x + 4y = 0 perpendicular to each other and passing through the origin O, the slopes of OA and OB are the roots of the equation 

Q3

An equation of the chord of the circle x2 + y2 = a2 passing through the point (2, 3) farthest from the centre is

Q4

The lengths of the intercepts made by any circle on the coordinates axes are equal if the centre lies on the line (s) represented by

Q5

A circle touches both the coordinates axes and the line  the coordinates of the centre of the circle can be

Q6

If the tangent at the point P on the circle x2 + y2 + 6x + 6y = 2 meets the straight line 5x – 2y + 6 = 0 at a point Q on the y-axis, then the length ofPQ is

Q7

If a > 2b > 0 then the positive value of m for which  is a common tangent to x2 + y2 = b2 and (x – a)2y2 = b2 is   

 

Q8

Let PQ  and RS be tangents at the extremities of a diameter PR of a circle of radius r. Such that PS and RQ intersect at a point X on the circumference of the circle, then diameter of the circle equals. 

Q9

A triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then QPR is equal to

Q10

If the area of the quadrilateral formed by the tangent from the origin to the circle x2 + y2 + 6x – 10y + c = 0 and the pair of radii at the points of contact of these tangents to the circle is 8 square units, then c is a root of the equation