1. If $\alpha$ and $\beta$ $\left(\alpha<\beta\right)$   are the roots of the equation $x^{2}+bx+c$    , where c < 0 < b, then
a) $\alpha < 0<\beta<\mid\alpha\mid$
b) $\beta>\mid\alpha\mid$
c) $\mid\alpha\mid +\mid\beta\mid<2$
d) none of these

Explanation:

2. If x is real, and y = $\frac{x^{2}+2x+c}{x^{2}+4x+3}$     takes all real values then
a) 0 < c < 2
b) $0\leq c\leq 1$
c) – 1 < c < 1
d) $-3\leq c\leq 1$

Explanation:

3. The smallest integer x for which the inequality $\frac{x-5 }{x^{2}+5x-14}>0$    is satisfied is given by
a) -6
b) -5
c) -4
d) -3

Explanation:

4. If $\mid a\pm b \mid>c$   and $a \neq0$  , then the quadratic equation $a^{2}x^{2}+\left(b^{2}+a^{2}-c^{2}\right)x+b^{2}=0$
a) has two real roots
b) both positive roots
c) cannot have real roots
d) none of these

Explanation:

5. If abc < 0, then the equation $ax^{2}+2\left(b+c-a\right)x+bc=0$      , has
a) real roots
b) one positive and one negative root
c) both positive roots
d) both a and b

Explanation:

6. The equation $1+\sqrt{1-\sqrt{x^{4}-x^{2}}}=x,x \epsilon R$
has
a) only positive solutions
b) exactly one solution
c) at least two solutions
d) both a and b

Explanation:

7. The equation $x+\sqrt{x}+\sqrt{x+2}+\sqrt{x^{2}+2x}=3$
has
a) no solution
b) at least one solution
c) only positive solutions
d) both b and c

Explanation:

8.Let a, b, c be the sides of an obtuse angled triangle with $\angle C >\pi/2$   . The equation $a^{2}x^{2}+\left(b^{2}+a^{2}-c^{2}\right)x+b^{2}=0$
has
a) two positive roots
b) one positive and one negative root
c) two real roots
d) two imaginary roots

Explanation: It has two imaginary roots

9. The equation $\sqrt{x-1}+\sqrt{x+3}+2\sqrt{\left(x-1\right)\left(x+3\right)}=4-2x$
has
a) exactly one integral solution
b) all its solutions in [1, 2]
c) sum of all the solutions is 1
d) All of the above

10. The equation $x^{3}+1=2 \left(2x-1\right)^{1/3}$     has