CDS ALGEBRA QUIZ 34

Question 1:

If $x^{4}+x^{2} y^{2}+y^{4}=133$ and $x^{2}+x y+y^{2}=7$, then find the value of $\left(x^{2}+y^{2}\right)$.

19

17

15

13

Question 2:

If $x-11=3 \sqrt{11}$, then $\sqrt{x-1}-\frac{1}{\sqrt{x-1}} = ?$

$2\sqrt{3}$

$3\sqrt{2}$

$2\sqrt{2}$

$3\sqrt{3}$

Question 3:

If $(2 x+3 y+4)(2 x+3 y-5)$ is equal to $\left(a x^{2}+\right.$ by $\left.^{2}+2 \mathrm{~h} x \mathrm{y}+2 \mathrm{~g} x+2 \mathrm{fy}+\mathrm{c}\right)$, then what is the value of $\left\{\frac{(g+f-c)}{a b h}\right\}$ ?

$\frac{35}{432}$

$\frac{19}{108}$

$\frac{19}{216}$

$\frac{37}{216}$

Question 4:

If $x=\frac{2 \sqrt{24}}{\sqrt{3}+\sqrt{2}}$, then the value of $\frac{x+\sqrt{8}}{x-\sqrt{8}}+\frac{x+\sqrt{12}}{x-\sqrt{12}}$ is

1

2

3

$-2$

Question 5:

If $1+4 r^{2}+16 r^{4}=256$ and $1+2 r+4 r^{2}=32$, then find the value of $\frac{1}{r} + \frac{1}{r^{2}}$.

$\frac{7}{36}$

$\frac{5}{36}$

$\frac{7}{6}$

$\frac{5}{6}$

Question 6:

If $x+\frac{1}{x}=1$ then the value of $\frac{x^{2}+4 x+1}{x^{2}+5 x+1}$

$\frac{1}{3}$

$\frac{7}{5}$

$\frac{5}{6}$

2

Question 7:

If $2 x-\frac{1}{2 x}=6$, then find $x^{2}+\frac{1}{16 x^{2}}=$ ?

$\frac{15}{2}$

$\frac{21}{2}$

$\frac{23}{2}$

$\frac{19}{2}$

Question 8:

if $(a-1)^{2}+(b+2)^{2}+(c-1)^{2}=0$ then find $2 a$ $-3 b+7 c$.

12

15

0

27

Question 9:

If $a+\frac{1}{a}+2=0$, then the value of $(a+2)^{2}+\frac{1}{(a+2)^{3}}$ is

2

6

4

3

Question 10:

If $x^{4}+x^{2} y^{2}+y^{4}=28$ and $x^{2}+x y+y^{2}=7$, then the value of $\left(\frac{1}{x^{2}}+\frac{1}{y^{2}}\right)$.

$\frac{23}{9}$

$\frac{27}{8}$

$\frac{22}{9}$

$\frac{8}{27}$