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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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