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51). If x is real the expression $$\Large \frac{x+2}{2x^{2}+3x+6}$$ takes all values in the interval:
 A). $$\Large \left(\frac{1}{13}, \frac{1}{3}\right)$$ B). $$\Large \left(- \frac{1}{13}, \frac{1}{3}\right)$$ C). $$\Large \left(- \frac{1}{3}, \frac{1}{13}\right)$$ D). none of these.
52). If x is real, then the maximum and minimum values of the expression $$\Large \frac{x^{2} -3x+4}{x^{2}+3x+4}$$ will be:

 A). 2,1 B). $$\Large 5, \frac{1}{5}$$ C). $$\Large 7, \frac{1}{7}$$ D). none of these.
53). The number of real solutions of the equation $$\Large |x^{2}+4x+3|+2x+5=0$$ are:
 A). 1 B). 2 C). 3 D). 4
54). If the roots of the given equation:
$$\Large \left(\cos p-1\right)x^{2}+ \left(\cos p\right)x+\sin p = 0$$ are real, then:

 A). $$\Large P \epsilon \left(- \pi ,0\right)$$ B). $$\Large P \epsilon \left(- \frac{ \pi }{2}, \frac{ \pi }{2} \right)$$ C). $$\Large P \epsilon \left(0, \pi \right)$$ D). $$\Large P \epsilon \left(0, 2 \pi \right)$$
55). The solution of the quadratic equation $$\Large \left(3|x|-3\right)^{2}=|x|+7$$ which belongs to the domain of definition of function $$\Large \gamma = \sqrt{x \left(x-3\right) }$$ are given by:
 A). $$\Large \pm \frac{1}{9}, \pm 2$$ B). $$\Large -\frac{1}{9}, 2$$ C). $$\Large \frac{1}{9}, -2$$ D). $$\Large -\frac{1}{9}, -2$$

56). The number of solution of $$\Large \frac{log 5 + log \left(x^{2}+1\right) }{log \left(x-2\right) }=2$$
 A). 2 B). 3 C). 1 D). none of these
57). If the expression $$\Large \left(mx-1+\frac{1}{x}\right)$$ is always nonnegative, then the minimum value of m must be:
 A). $$\Large -\frac{1}{2}$$ B). 0 C). $$\Large \frac{1}{4}$$ D). $$\Large \frac{1}{2}$$
58). The value of x in the given equation $$\Large 4^{x}-3^{x-\frac{1}{2}}=3^{x+\frac{1}{2}}-2^{2x-1}$$ is:
 A). $$\Large \frac{4}{3}$$ B). $$\Large \frac{3}{2}$$ C). $$\Large \frac{2}{1}$$ D). $$\Large \frac{5}{3}$$
59). The harmonic mean of the roots of equation $$\Large \left(5+\sqrt{2}x^{2}-14+\sqrt{5}\right)x+8+2\sqrt{5}=0$$ is:
 A). 2 B). 4 C). 6 D). 8
60). For what value of $$\Large \lambda$$ the sum of the squares of the roots of $$\Large x^{2}+ \left(2+\lambda\right)n-\frac{1}{2} \left(1+\lambda\right)=0$$ is minimum?
 A). $$\Large \frac{3}{2}$$ B). 1 C). $$\Large \frac{1}{2}$$ D). $$\Large \frac{11}{4}$$
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