1. The real values of a for which $\frac{x^{2}-ax-2}{x^{2}-3x+4}>-1$
for each $x \epsilon R$ , is
a) (– 1, 2)
b) (0, 7)
c) (-7, 1)
d) (2, 7)

Explanation:

2. If $a,b,c \epsilon R$   are distinct, then the condition(s) on a, b, c for which the equation
$\frac{1}{x-a}+\frac{1}{x-b}+\frac{1}{x-c}+\frac{1}{x-b-c+a}=0$
has real roots is
a) $a+b+c\neq 0,a\neq0$
b) $a-b-c\neq 0,a\neq0$
c) 2a = b + c
d) none of these

Explanation:

3. If $f\left(x\right)=ax^{2}+bx+c,f\left(-1\right)< 1,f\left(1\right)>-1$
and $f\left(-3\right)< -4$     then
a) a = 0
b) a < 0
c) a > 0
d) sign of a cannot be determined

Explanation:

4. The set of all values of k for which the equation $x^{2}+2 \left(k-1\right)x+\left(k-5\right)=0$      has at least one non-negative root is
a) $\left[1,\infty\right)$
b) [-1,1]
c) $(-\infty,-5$  ]
d) $\left[5,\infty\right)$

Explanation:

5.If $3\pi/4<\alpha<\pi$   , then the set of values of $\alpha$ for which
$\left(\sin\alpha\right)x^{2}+\left(2\cos\alpha\right)x+\frac{1}{2}\left(\sin\alpha+\cos\alpha\right)$
is square of a linear polynomial is
a) $\left\{\frac{5\pi}{6},\frac{11\pi}{12}\right\}$
b) $\left\{\frac{11\pi}{12}\right\}$
c) $\left\{\frac{5\pi}{6}\right\}$
d) $\phi$

Explanation:

6. If $0\leq\phi\leq3\pi$    , then the set of all values of $\phi$ for which sum of the squares of the roots of the equation
$x^{2}+\left(\sin \phi -1\right)x-\frac{1}{2}\cos^{2}\phi=0$
is greatest is
a) $\left\{\pi,\frac{3\pi}{2},2\pi,3\pi\right\}$
b) $\left\{\pi,3\pi\right\}$
c) $\left\{2\pi,\frac{5\pi}{4}\right\}$
d) $\left\{\frac{3\pi}{2}\right\}$

Explanation:

7. The set of values of b for which $2\log_{1/36}\left(bx+28\right)=-\log_{6}\left(12-4x-x^{2}\right)$
has exactly one solution is
a) $\left(-\infty,-14\right)\cup$   [14/3, $\infty)$
b) [14/9, $\infty)$
c) $(-\infty$ ,-14]  $\cup\left\{4\right\}\cup$  [14/3,$\infty$  ]
d) $\left\{4\right\}$

Explanation:

8. If $2x^{2}+3x+4=0$    and $ax^{2}+bx+c=0$    , where $a,b,c \epsilon N$   have a common root, then the least value of a + b + c is
a) 10
b) 9
c) 8
d) 6

Explanation:

9. Let p, q, r, s be real numbers such that pr = 2(q + s). Consider quadratic equations $x^{2}+px+q=0$    and $x^{2}+rx+s=0$    . Then
a) none of these has real roots
b) both have real roots
c) at least one has real roots
d) at most one has real roots

10. Let $a< 0,a\neq -2$   . The equation $x^{2}+a\mid x\mid+1=0$     has