Let $n \geq 1$ be a positive integer. Suppose, between two distinct positive real numbers $k$ and $l, n$ arithmetic means $a_1, a_2, \cdots, a_n$ and $n$ harmonic means $h_1, h_2, \cdots, h_n$ are inserted. For $i=1,2, \cdots, n$ and $j=1,2, \cdots, n$, let $p(i, j)=a_i h_j$ then

• Correct answer
  A

  $p(i, j)=k l$ for some $i$ and $j$.
• Correct answer
  B

  if $n$ is even, there are an even number of ordered pairs $(i, j)$, such that $p(i, j)=k l$.
• C

  if $n$ is odd, there are an even number of ordered pairs $(i, j)$, such that $p(i, j)=k l$.
• Correct answer
  D

  whenever $n$ is odd there is an $i$ such that $p(i, i)=k l$.

Hence, the correct answer is options: 'A', 'B', 'D'.