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in Permutations and combinations by (46.6k points)

In a plane, there are two families of lines y = x + r, y = – x + r, where r ∈ {0, 1, 2, 3, 4). The number of squares of diagonals of length 2 formed by the lines is

(A)  9 

(B)  16 

(C)  25 

(D)  None of these

1 Answer

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Best answer

Correct option  (B)  16

There are two sets of five parallel lines at equal distances. Clearly, lines like l1 , l3 , m1 , m3 form a square whose length of the diagonal is 2.

So, the number of required squares = 3 x 3

[Since, choices are (I1 , I3), (I2 , I4) (I3 , I5) for one set, etc.]

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