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There are two sets of parallel lines, their equations being xcosα+ysinα=p and ycosαxcosα=p;p=1,2,3,....,n and α is a constant angle. If the number of rectangles formed by these two sets of lines is 225 then find the value of n.

Solution
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n(n+1)(2n+1)6=225×6
n(2n2+n+2n+1)=1350 [n2=n(n+1)(2n+1)6]
2n3+3n2+n=1350 [225×6=1350]
By cubic methods,
n8

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