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

To receive grade $A$ in a course,one must obtain an average of $90$ marks or more in five examinations (each of $100$ marks). If Sunita's marks in the first four examinations are $87, 92, 94,$ and $95,$ find the minimum marks that Sunita must obtain in the fifth examination to get grade $A$ in the course.

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

$A$ company manufactures cassettes. Its cost and revenue functions are $C(x) = 26000 + 30x$ and $R(x) = 43x$,respectively,where $x$ is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realize some profit?

Find all pairs of consecutive odd positive integers,both of which are smaller than $18$,such that their sum is more than $20$.