SSC CGL MOST PROBABLE - ALGEBRA QUIZ- 18

If $a+b+c=12$ and $a^{2}+b^{2}+c^{2}=134$ then find the value of $b c(b+c)+a c(c+a)+a b(a+b)+3 a b c$

If $\frac{4}{1+\sqrt{2}+\sqrt{3}}=a+b \sqrt{2}-c \sqrt{3}-d \sqrt{6}$, where $a, b, c, d$ are natural numbers, then the value of $a+b+c+d$ is?

If $3^{a}=27^{b}=81^{c}$ and $a b c=144$, then find the value of $36\left(\frac{1}{a}+\frac{1}{2 b}+\frac{1}{5 c}\right)$ is?

If the value of $(a+b-2)^{2}+(b+c-5)^{2}+(c+a-5)^{2}=$ then the value of $\sqrt{(b+c)^{a}+(c+a)^{b}}$ is?

If $b+c=a x, \quad c+a=b y, \quad a+b=c z$, then the value of $\frac{1}{18}\left[\frac{1}{x+1}+\frac{1}{y+1}+\frac{1}{z+1}\right]$ is?

If $27(x+y)^{3}-8(x-y)^{3}=(x+5 y)\left(A x^{2}+B y^{2}+C x y\right)$ then what is the value of $(A-B-C)$?

If $a+b+c=11, a b+b c+c a=3$ and a b c =-135, then what is the value of $a^{3}+b^{3}+c^{3} ?$

On simplification, $\frac{x^{3}-y^{3}}{x\left[(x+y)^{2}-3 x y\right]}$ $\div \frac{y\left[(x-y)^{2}+3 x y\right]}{x^{3}+y^{3}} \times \frac{(x+y)^{2}-(x-y)^{2}}{x^{2}-y^{2}}$ is equal to:

If $a=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ and $b=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$ then $\frac{a^{2}}{b}+\frac{b^{2}}{a}$

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