Permutations And Combinations

Question
CBSEENMA11015490

If x, y, z are in A.P. and tan−1 x, tan−1 y and tan−1 z are also in A.P., then

  • x= y= z

  • 2x =3y = 6z

  • 6x = 3y= 2z

  • 6x = 4y = 3z

Solution

A.

x= y= z

If x, y, z are in A.P.
2y = x + z and
tan−1 x, tan−1 y, tan−1 z are in A.P.
2 tan−1 y = tan−1 x + tan−1
z ⇒ x = y = z.

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