SSC CGL Tier-2 20-February-2018 Maths

Which of the following statement(s) is/are TRUE?
I. $$\surd11 + \surd7 < \surd10 + \surd8$$.
II. $$\surd17 + \surd11 > \surd15 + \surd13$$

Which of the following statement(s) is/are TRUE?

I. $$\sqrt{12}>\sqrt[3]{16}>\sqrt[4]{24} $$

II. $$\sqrt[3]{25}>\sqrt[4]{32}>\sqrt[6]{48}$$

III. $$\sqrt[4]{9}>\sqrt[3]{15}>\sqrt[6]{24}$$

If $$x + y + z = 22$$ and $$xy + yz + zx = 35$$, then what is the value of $$(x - y)^2 + (y - z)^2 + (z - x)^2$$?

If $$\frac{(x + y)}{z} = 2$$, then what is the value of $$\left[\frac{y}{(y - z)}\right] + \left[\frac{x}{(x - z)}\right]$$?

If $$\alpha$$ and $$\beta$$ are the roots of equation $$x^2 - 2x + 4 = 0$$, then what is the equation whose roots are $$\frac{\alpha^3}{\beta^2}$$ and $$\frac{\beta^3}{\alpha^2}$$?

If one root of the equation $$Ax^2 +Bx + C = 0$$ is two and a half times the others, then which of the following is TRUE?

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

If $$a^4 + 1 = \left[\frac{a^2}{b^2}\right] (4b^2 - b^4 - 1)$$, then what is the value of $$a^4 + b^4$$?

If $$3\sqrt{\frac{1-a}{a}} + 9 =19 - 3\sqrt{\frac{a}{1-a}}$$, then what is the value of $$a$$?

If $$a + b =10$$ and $$\sqrt{\frac{a}{b}} - 13 = -\sqrt{\frac{b}{a}} -11$$, then what is the value of $$3ab + 4a^2 + 5b^2$$