1. Let $\alpha$ and $\beta$  be the roots of $x^{2}-6x-2=0$    , with $\alpha>\beta$  . If $a_{n}=\alpha^{n}-\beta^{n}$    for $n\geq 1$ , then the value of $\frac{a_{10}-2a_{8}}{2a_{9}}$   is
a) 3
b) 2
c) 1
d) 4

Explanation:

2. A value of b for which the equations
$x^{2}+bx-1=0$
$x^{2}+x+b=0$
have one root in common is
a) $-\sqrt{2}$
b) $i\sqrt{5}$
c) $i\sqrt{3}$
d) $\sqrt{2}$

Explanation:

3. If $x \epsilon R$ , the number of solutions of $\sqrt{2x+1}-\sqrt{2x-1}=1$     is
a) 0
b) 1
c) 4
d) infinite

Explanation:

4. If l, m, n are real, $l+m\neq0$   , then the roots of the equation $\left(l+m\right)x^{2}-3\left(l-m\right)x-2\left(l+m\right)=0$
a) real and unequal
b) complex
c) real and equal
d) purely imaginary

Explanation:

5. If the equation $\sqrt{x+1}-\sqrt{x}=a$    has a solution, then
a) 0 < a < 1
b) a > 1
c) $0 < a \leq 1$
d) $a \leq 1$

Explanation:

6. Let $\alpha$ , $\beta$ be the roots of the equation $x^{2}-ax+b=0$     and $A_{n}=\alpha^{n}+\beta^{n}$    . Then $A_{n+1}-aA_{n}+bA_{n-1}$     is equal to
a) -a
b) b
c) a-b
d) 0

Explanation:

7. If $\alpha,\beta,\gamma$  are such that $\alpha+\beta+\gamma=2,\alpha^{2}+\beta^{2}+\gamma^{2}=6,\alpha^{3}+\beta^{3}+\gamma^{3}=8$
then $\alpha^{4}+\beta^{4}+\gamma^{4}$    is
a) 5
b) 18
c) 12
d) 36

Explanation:

8. In a triangle PQR, $\angle$ R = $\pi$ /4. If tan (P/3) and tan (Q/3) are the roots of the equation ax2 + bx + c = 0, then
a) a + b = c
b) b + c = 0
c) a + c = b
d) b = c

Explanation:

9. The product of the roots of $\sqrt[3]{8+x}+\sqrt[3]{8-x}=1$     is
a) -21
b) -189
c) -9
d) -5

10. If all the roots of $x^{3}+px+q=0$    p, q $\epsilon$ R , $q\neq 0$  are real, then