The least positive integer $n$ for which $\sqrt{n+1}-\sqrt{n-1} < 0.2$ is

$A$ solution is to be kept between $68\,^{\circ} F$ and $77\,^{\circ} F$. What is the range in temperature in degree Celsius $(C)$ if the Celsius/Fahrenheit $(F)$ conversion formula is given by $F = \frac{9}{5} C + 32$?

In drilling the world's deepest hole,it was found that the temperature $T$ in degrees Celsius,$x \text{ km}$ below the earth's surface,is given by $T = 30 + 25(x - 3)$,where $3 \leq x \leq 15$. At what depth will the temperature be between $155^{\circ}C$ and $205^{\circ}C$?

Let $a$ $(a < 0, a \notin I)$ be a constant and $t$ be a parameter. Then the set of values of $t$ for which the function $f(x) = \left( \frac{|[t]+1|+a}{|[t]+1|+1-a} \right)x$ is a decreasing function of $x$ (where $[.]$ denotes the greatest integer function) is:

The set of values of $x$ which satisfy $5x + 2 < 3x + 8$ and $\frac{x + 2}{x - 1} < 4$ is

Find the sum of all integral values of $a$ such that the equation $||x - 2| - |3 - x|| = 2 - a$ has a solution.