Let $a_1, a_2, \dots, a_{10}$ be in $A.P.$ and $h_1, h_2, \dots, h_{10}$ be in $H.P.$ If $a_1 = h_1 = 2$ and $a_{10} = h_{10} = 3$,then $a_4 h_7$ is

Which of the following sequences is an arithmetic sequence?

If $a, b, c$ are positive integers,then $(a + b)(b + c)(c + a)$ is

$A$ person is to count $4500$ currency notes. Let $a_n$ denote the number of notes he counts in the $n^{th}$ minute. If $a_1 = a_2 = \ldots = a_{10} = 150$ and $a_{10}, a_{11}, \ldots$ are in an $A.P.$ with common difference $-2$,then the time taken by him to count all notes is ............... minutes.

$\left[\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\frac{1}{3 \times 4}+\cdots+\frac{1}{99 \times 100}\right]$ is equal to

For $x \in R$,let $[x]$ denote the greatest integer $\le x$. Find the sum of the series $\left[ -\frac{1}{3} \right] + \left[ -\frac{1}{3} - \frac{1}{100} \right] + \left[ -\frac{1}{3} - \frac{2}{100} \right] + \dots + \left[ -\frac{1}{3} - \frac{99}{100} \right]$.