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Explanation:

Radius of P1 = r ⇒A(P1) = πr2

Diameter = d = 2r

Side of Q1 = 2r2 = r2 ⇒ A(Q1) = 2r2

Radius of P2 = r22 = r2 ⇒ A(P1) = πr22

Side of Q2 = r2 × 2 = r ⇒ A(Q2) = r... and so on.

i.e., Areas of circles are in G.P. with common ratio = 12

Also, areas of squares are in G.P. with common ratio = 12

SN = Q1 – P2 + Q2 – P3 + Q3 – P4 + …

= (Q1 + Q2 + Q3 + … ) – (P2 + P3 + P4 + … )

= 2r2 1+12+14+... - πr221+12+14+...

1+12+14+...2r2-πr22

= r2 × 11-12 × 4-π2

= (4 - π)r2

SN: A(Q1) = (4 – π)r: 2r2 = (4 – π)/2

Hence, option (a).

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