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61). Given that $$\Large \tan \alpha$$ and $$\Large \tan \beta$$ are the roots of $$\Large x^{2}-px+q=0$$, then the value of $$\Large \sin^{2} \left(\alpha + \beta \right)$$ is equal to:
 A). $$\Large \frac{p^{2}}{p^{2}+ \left(1-q\right)^{2} }$$ B). $$\Large \frac{p^{2}}{p^{2}+q^{2}}$$ C). $$\Large \frac{q^{2}}{p^{2} \left(1-q\right)^{2} }$$ D). $$\Large \frac{p^{2}}{ \left(p+q\right)^{2} }$$
62). The number of values of K for which the system of equations $$\Large \left(K+1\right)x+84=4K$$ and $$\Large Kx+ \left(K+3\right)y=3 K-1$$ has infinitely many solution, is:
 A). 0 B). 1 C). 2 D). infinite
63). The set of all real numbers x for which $$\Large x^{2}-|x+2|+x>0$$ is:
 A). $$\Large \left(-\infty, -2\right) \ \left(2, \infty\right)$$ B). $$\Large \left(-\infty, -\sqrt{2}\right) \ \left(\sqrt{2}, \infty\right)$$ C). $$\Large \left(-\infty, -1\right) \ \left(1, \infty\right)$$ D). $$\Large \left(\sqrt{2}, \infty\right)$$
64). Let a, b, c be positive numbers, the following systems of equations in x, y and z $$\Large \frac{x^{2}}{a^{2}} +\ \frac{y^{2}}{b^{2}}-\frac{z^{2}}{c^{2}}=1; \ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} +\ \frac{z^{2}}{c^{2}}=1 and\ \frac{-x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}}=1$$ has;
 A). no solutions B). unique solution C). infinitely many solution D). finitely many solution.
65). If $$\Large 2 \sin^{2}\frac{ \pi }{8}$$ is a root of equation$$\Large x^{2}+ax+b=0$$, where a and b are rational numbers, then a - b is equal to
 A). $$\Large -\frac{5}{2}$$ B). $$\Large -\frac{3}{2}$$ C). $$\Large -\frac{1}{2}$$ D). $$\Large \frac{1}{2}$$

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