SSC MTS MATHS QUIZ

If $(x+6 y)=8$, and $x y=2$, where $x>0$, what is the value of $x^3+216 y^3$ ?

If $x-y+z=0$, then find the value of $\frac{y^2}{2 x z}-\frac{x^2}{2 y z}-\frac{z^2}{2 x y}$.

Find the value of the following expression:

$\frac{\left(a^{2}-4 b^{2}\right)^{3}+64\left(b^{2}-4 c^ {2}\right)^{3}+\left(16 c^{2}-a^{2}\right)^{3}}{(a-2 b)^{3}+(2 b- 4 c)^{3}+(4 c-a)^{3}}$

What is the value of

$\sqrt{-\sqrt{3}+\sqrt{3+8 \sqrt{7+4 \sqrt{3}}}}$ ?

If $a^{2}+b^{2}=25, x^{2}+y^{2}=17$ and $a x+b y=8$, then what is the value of $(ay -b x )$?

If $a+b=3$ and $a^2+b^2=89$, then What is the value of $\frac{1}{a}+\frac{1}{b}$ ?

If $a+b+c=5, a^2+b^2+c^2=35$, and $a^3+b^3+c^3=197$, then the value of $a b c+1$ is:

If $x^4+\frac{1}{x^4}=47$, what is the value of $\left(x^7+\frac{1}{x^7}\right)$ ?

If the roots of the equation $(q-r) x^2+(r-p) x+(p-q)=0$ are equal, then which of the following is true ?