Comprehension Let \( M=\left\{(x, y) R \times R: x^{2}+y^{2} \leq r^{2}\right\} \), where \( r0 ...

Channel:
PW Solutions
Subscribers:
443,000
Published on ● Video Link: https://www.youtube.com/watch?v=cs2dncKfs5o


Duration: 12:15
4 views
0

Comprehension Let \( M=\left\{(x, y) R \times R: x^{2}+y^{2} \leq r^{2}\right\} \),
where \( r0 \). Consider the geometric progression
\( a_{n}=\frac{1}{2^{n-1}}, n=1,2,3, \ldots \). Let \( S_{0}=0 \) and for \( n \geq 1 \), let \( S_{n} \) denote the
sum of the first \( n \) terms of this progression. For \( n \geq 1 \), let \( C_{n} \) denote the circle with center \( \left(S_{n-1}, 0\right) \) and radius \( a_{n} \) and \( D_{n} \) denote the circle with center \( \left(S_{n-1}, S_{n-1}\right) \) and radius \( a_{n} \).
- Consider \( M \) with \( r=\frac{1025}{513} \). Let \( \mathrm{k} \) be the number of all those circles \( C_{n} \) that are inside \( M \). Let 1 be the maximum possible number of circles among these \( k \) circles such that no two - circles intersect. Then
- (a) \( k+21=22 \)
(b) \( 2 k+1=26 \)
- (c) \( 2 k+31=34 \)
(d) \( 3 k+21=40 \)
šŸ“²PW App Link - https://bit.ly/YTAI_PWAP
šŸŒPW Website - https://www.pw.live



Other Videos By PW Solutions


2023-07-08For a given parabola \( y^{2}=4 a x \) two variable chords \( P Q \) and \( R S \) at right angl...
2023-07-08Through the vertex \( O \) of parabola \( y^{2}=4 x \), chords \( O P \) and \( O Q \) are drawn...
2023-07-08Three normals to \( y^{2}=4 x \) pass through the point \( (15,12) \). Show that one of the norm...
2023-07-08The tangent and normal at the point \( P\left(a t^{2}, 2 a t\right) \) to the parabola \( y^{2}=...
2023-07-08Comprehension Let \( M=\left\{(x, y) R \times R: x^{2}+\right. \) \( \left.y^{2} \leq r^{2}\righ...
2023-07-08A circle of radius 2 units passes through the vertex and the focus of the parabola \( y^{2}=2 x ...
2023-07-08Let \( P_{1} \) be a parabola with vertex \( (3,2) \) and focus \( (4,4) \) and \( P_{2} \) be i...
2023-07-08Let \( S=\left\{(x \cdot y): x^{2}+y^{2}-6 x-8 y+21 \leq 0\right\} \) \begin{tabular}{|l|l|l|l|}...
2023-07-08The points on the axis of the parabola \( x^{2}+2 x+4 y+13= \) 0 from the where three distinct n...
2023-07-08Let \( K \) denotes the square of the diameter of the circle whose diameter is the common chord ...
2023-07-08Comprehension Let \( M=\left\{(x, y) R \times R: x^{2}+y^{2} \leq r^{2}\right\} \), where \( r0 ...
2023-07-08Consider three circles: \[ \begin{array}{l} C_{1}: x^{2}+y^{2}=r^{2} \\ C_{2}:(x-1)^{2}+(y-1)^{2...
2023-07-08If at \( x=1, y=2 x \) is tangent to the parabola \( y=a x^{2}+b x+c \), then respective values ...
2023-07-08Comprehension \( P \) is variable point on the line \( L=0 \). Tangents are drawn to the circle ...
2023-07-08Find the intervals of the values of a for which the line \( y+x=0 \) bisects two chords drawn fr...
2023-07-08Let \( A \equiv(0,0), B \equiv(4,0) \) and on segment \( A B \) is given a point \( M \). On the...
2023-07-08In the given figure, the circle \( x^{2}+y^{2}=25 \) intersects \( x \)-axis at points \( A \) a...
2023-07-08Let \( A B C \) be a triangle whose vertices are \( A(-5,5) \) and \( B(7,-1) \). If vertex \( C...
2023-07-08Comprehension The line \( y=a x+b \) intersects the curve \( c: x^{2}+y^{2}+6 x+10 y+1=0 \) at t...
2023-07-08Tangents are drawn to the circle \( x^{2}+y^{2}=50 \) from a point \( P \) lying on the \( x \...
2023-07-08A line cuts the \( X \)-axis at \( A(7,0) \) and the \( Y \)-axis at \( B(0,-5) \). A variable l...