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31). If \( \Large \alpha , \beta \) are the roots of equation \( \Large ax^{2}+bx+c=0 \), then \( \Large \frac{ \alpha }{ \alpha \beta +b}+\frac{ \beta }{ \alpha x+b} \) is equal to
A). 2/a
B). 2/b
C). 2/c
D). -2/a
32). If the roots of the equation \( \Large \frac{ \alpha }{x- \alpha }+\frac{ \beta }{x- \beta }=1 \) be equal in magnitude but opposite in sign, then \( \Large \alpha + \beta \) is equal to:
A). 0
B). 1
C). 2
D). none of these
33). If the roots of the equation \( \Large px^{2}+2qx+r=0 \) and \( \Large qx^{2}-2\sqrt{pr}x+q=0 \) be real, then:
A). \( \Large p=q \)
B). \( \Large q^{2}=pr \)
C). \( \Large p^{2}=qr \)
D). \( \Large r^{2}=pq \)
34). If one root of the quadratic equation \( \Large ax^{2}+bx+c=0 \) is equal to nth power of the other root, then the value of \( \Large \left(ac^{n}\right)^{\frac{1}{n+1}} + \left(a^{n}c\right)^{\frac{1}{n+1}} \) is equal to
A). b
B). -b
C). \( \Large b^{1/n+1} \)
D). \( \Large -b^{1/n+1} \)
35). The quadratic in t, such that AM of its roots is A and GM is G is:
A). \( \Large t^{2}-2At+G^{2}=0 \)
B). \( \Large t^{2}-2At-G^{2}=0 \)
C). \( \Large t^{2}+2At+G^{2}=0 \)
D). none of these.


36). If \( \Large n^{2}px+1 \) is a factor of expression \( \Large ax^{3}+bx+c \) then:
A). \( \Large a^{2}+c^{2}=-ab \)
B). \( \Large a^{2}-c^{2}=-ab \)
C). \( \Large a^{2}-c^{2}=ab \)
D). none of these
37). If \( \Large \sqrt{3x^{2}-7x-30} + \sqrt{2x^{2}-7x-5} = x+5 \), then x is equal to:
A). 2
B). 3
C). 6
D). 5
38). The value \( \Large 2+\frac{1}{2+\frac{1}{2+........\infty}} \)
A). \( \Large 1-\sqrt{2} \)
B). \( \Large 1+\sqrt{2} \)
C). \( \Large 1\pm \sqrt{2} \)
D). none of these
39). If the roots of the equation \( \Large qx^{2}+px+q=0 \) are complex, where p, q are real then the roots of the equation \( \Large x^{2}-4qx+p^{2}=0 \) are:
A). real and unequal
B). real and equal
C). imaginary
D). none of these
40). The number or real solution of the equation \( \Large x^{2}-3|x|+2=0 \) is:
A). 2
B). 4
C). 1
D). 3
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