SSC CGL MOST PROBABLE - ALGEBRA QUIZ-1

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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 $\left(x^{2}+y^{2}\right)$.

Question 2:

If $\ x=\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$ and $y=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$ then find the value of $\frac{x^{2}+x y+y^{2}}{x^{2}-x y+y^{2}}$.

Question 3:

If $x^{2 a}=y^{2 b}=z^{2 c} \neq 0$ and $x^{2}=y z$, then the value of $\frac{a b+b c+c a}{b c}$ is?

Question 4:

If $\sqrt{x}+\frac{1}{\sqrt{x}}=11, x>0$, then $x \sqrt{x}(x \sqrt{x}-1298)+11$.

Question 5:

If $x+\frac{1}{x}=17$, then what is the value of $\frac{x^{4}+\frac{1}{x^{2}}}{x^{2}-3 x+1}$?

Question 6:

If $x^{2}-12 x+33=0$, then what is the value of $(x-4)^{4}+\frac{1}{(x-4)^{4}}$

Question 7:

If $(x+a)(x+b)=2$ and $a-b+7=0$ then Find the value of $(x+b)^{3}-(x-a)^{3}=$?

Question 8:

If $p+\frac{1}{p}-5=0$, then $(p-5)^{7}+\frac{1}{p^{7}}$ = 

Question 9:

If $a, b, c$ are non-zero real numbers and $a^{2}+b^{2}+c^{2}$ $+2 a b-2 b c-2 c a=0$, then $\frac{4(a+b+c)+c}{a+b}$ is equal to.

Question 10:

If $ a=2 b=8 c$ and $a+b+c=13$ then the value of $\frac{\sqrt{a^{2}+b^{2}+c^{2}}}{2 c}$ is?
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