PRACTICE QUESTIONS CLASSROOM WING

If $\mathrm{x}$ and $\mathrm{y}\in \mathrm{R}$, then $\mathrm{x}\ngtr \mathrm{y}$ can also be written as _____.

Mathch the following

$\begin{array}{|cccc|}\hline & A& & B\\ a& \frac{5}{x+3}>0& p& x>3\\ b& \frac{-5}{x-3}>0& q& x<8\\ c& \frac{5}{x-8}<0& r& x>-8\\ d& \frac{x+8}{-5}<0& s& x?>-3\\ \hline\end{array}$

If $\frac{1}{x-3}>0$,then what is the set of values that $x$ can take? 

In a pilgrim station, on a certain day, if each cottage is occupied by $4$ pilgrims, then $240$ pilgrims will be left, and if each cottage is occupied by $6$ pilgrims, then $40$ cottages will be left unoccupied. Find the number of cottages and the number of pilgrims. Also, find how many pilgrims should be accommodated in each cot- tage so that no cottage will be empty and no pilgrim will be left unaccommodated.

In a test, one mark is awarded for each correct answer and $0.5$ mark is deducted for each incorrect answer. A student attempted all the questions in it. If the mark(s) awarded for each correct answer and the marks deducted for each incorrect answer are interchanged, then he would have got $90$ marks less than what he actually got. Find the number of questions in the test.

For which of the following value(s) of $k$ are the equations $2x+3y= 12$ and$6x + ky= 36$ consistent?

  Solve the inequations $3x + 2y \le 15, 4x-3y\ge 4$ and $x\ge 0$.

Machine $A$ can produce $6$ items per hour and Machine$B$ can produce $11$ items per hour. If Machine $A$ works for $x hr$ and Machine $B$ works for $y hr$ in a day and both the machines produce at the most $200$ items in a day, then frame an inequation to support the above data.