1. If $x>0$ and $y>0$, then $\sqrt{ 64 \sqrt{ 16 x^{ 8} y^{ 6}}}$ =

    $\displaystyle 32\,x^2\,y^{{{3}\over{2}}}$

    $\displaystyle 2\,x^4\,y^3$

    $\displaystyle 16\,x^2\,y^{{{3}\over{2}}}$

    $\displaystyle 16\,x^2\,y^{{{3}\over{2}}}$

    $\displaystyle 16\,x^4\,y^4$

  2. $\displaystyle \frac{1}{ -5 + \sqrt{2}}$ =

    $\displaystyle \frac{ -5 - \sqrt{2}} { 23} $

    $\displaystyle \frac{ -5 + \sqrt{2}} { 27} $

    $\displaystyle \frac{ -5 - \sqrt{2}} { 27} $

    $\displaystyle \frac{ -5 + \sqrt{2}} { 23} $

    $5 + \sqrt{2} $

  3. The graph of $\displaystyle y=-3\,x^2-3\,x+12$ is symmetric with respect to the line

    $\displaystyle y=-{{1}\over{2}}$

    $\displaystyle x=-{{1}\over{2}}$

    $\displaystyle y={{1}\over{2}}$

    $\displaystyle x={{1}\over{2}}$

    x = −1

  4. $\displaystyle {{x+4}\over{x^2-16}} \times {{8\,x-32}\over{4\,x+16}} $ = ?

    $\displaystyle {{8}\over{x+4}}$

    $\displaystyle {{2}\over{x-4}}$

    $\displaystyle {{4}\over{x-4}}$

    $\displaystyle {{2}\over{x^2-16}}$

    $\displaystyle {{2}\over{x+4}}$

  5. The graph of the system of equations \begin{displaymath}\begin{cases} x-2\,y=3 \\ [1ex] 6\,y+3\,x=9 \end{cases}\end{displaymath} consists of

    one line

    two lines intersecting where x = 3

    two distinct parallel lines

    two lines intersecting where x = 3

    two lines intersecting where y = 3

  6. The inequality $\displaystyle x^2-12\,x<13$ is equivalent to

    −1 < x < 13

    −12 < x < 1

    x <  − 1 or x > 13

    −13 < x < 1

    −1 < x < 12

  7. An equation of the line passing through ( 1 , 4 ) having slope $\displaystyle {{3}\over{4}}$ is

    3x − 4y = −19

    3x − 4y = −13

    3x − 4y = 13

    4y + 3x = 13

    4y + 3x = −13


Department of Mathematics
Last modified: 2025-10-18