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21). If one roots of the equation is reciprocal of the other, then which one of the following is correct?
 A). a = b B). b = c C). ac = 1 D). a = c
22). Number of solutions of the equation $$\Large \sqrt{x^{2}-x+1}+\frac{1}{\sqrt{x^{2}-x+1}}=2-x^{2}$$ is
 A). 0 B). 1 C). 2 D). 4
23). If $$\Large x = \sqrt{\frac{\sqrt{5}+1}{\sqrt{5}-1}}$$, then $$\Large x^{2}-x-1$$ is equal to
 A). 0 B). 1 C). 2 D). 5
24). If one of the roots of the equation $$\Large x^{2}-bx+c=0$$ is the square of the other, then which of the following option is correct?
 A). $$\Large b^{2} = 3bc+c^{2}+c$$ B). $$\Large c^{3} = 3bc+b^{2}+b$$ C). $$\Large 3bc = c^{3}+b^{2}+b$$ D). $$\Large 3bc = c^{3}+b^{3}+b^{2}$$
25). Two students A and B solve an equation of the form $$\Large x^{2}+px+q=0$$. A starts with a wrong value of p and obtains the roots as 2 and 6. B starts with a wrong value of q and gets the roots as 2 and -9. What are the correct roots of the equation?
 A). 3 and -4 B). -3 and -4 C). -3 and 4 D). 3 and 4

26). If the roots of equations $$\Large ax^{2}+bx+c=0$$ be $$\Large \ \alpha \ and\ \beta$$ then the roots of equations $$\Large cx^{2}+bx+a=0$$ are:
 A). $$\Large - \alpha ,\ - \beta$$ B). $$\Large \alpha ,\ \frac{1}{ \beta }$$ C). $$\Large \frac{1}{ \alpha },\ \frac{1}{ \beta }$$ D). none of these
27). Both the roots of the given equation. $$\Large \left(x-a\right) \left(x-b\right)+ \left(x-b\right) \left(x-c\right)+ \left(x-c\right) \left(x-a\right)=0$$ are always
 A). positive B). negative C). real D). imaginary
28). If the difference of roots of the equation $$\Large x^{2}-bx+c=0$$ be 1, then;
 A). $$\Large b^{2}-4c-1=0$$ B). $$\Large b^{2}-4c=0$$ C). $$\Large b^{2}-4c+1=0$$ D). $$\Large b^{2}+4c-1=0$$
29). If $$\Large 2+i\sqrt{3}$$ is a root of the equation $$\Large x^{2}+px+q=0$$ where p and q are real, then $$\Large p, q$$ is equal to:
 A). (-4, 7) B). (4,-7) C). (4, 7) D). (-4, -7)
30). If $$\Large x=\sqrt{1+\sqrt{1+\sqrt{1}+.....}}$$, the x is equal to
 A). $$\Large \frac{1+\sqrt{5}}{2}$$ B). $$\Large \frac{1-\sqrt{5}}{2}$$ C). $$\Large \frac{1\pm \sqrt{5}}{2}$$ D). none of these .
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