1. The number of irrational roots of the equation $\frac{4x}{x^{2}+x+3}+\frac{5x}{x^{2}+5x+3}=-\frac{3}{2}$
is
a) 0
b) 1
c) 2
d) 3

Explanation:

2. If $\alpha,\beta,\gamma,\delta$  are the roots of $\left(x^{2}+x+4\right)^{2}+3x\left(x^{2}+x+4\right)+2x^{2}=0$           then $\mid\alpha\mid+\mid\beta\mid+\mid\gamma\mid+\mid\delta\mid$      is equal
a) 6
b) 8
c) 12
d) 25

Explanation:

3. x = 1 is a root of $\left(x^{2}-x+1\right)^{4}-6x^{2}\left(x^{2}-x+1\right)^{2}+5x^{4}=0$
of multiplicity
a) 2
b) 3
c) 4
d) 6

Explanation:

4. The number of irrational roots of the equation $\left(x^{2}-3x+1\right)\left(x^{2}+3x+2\right)\left(x^{2}-9x+20\right)=-30$
is
a) 0
b) 2
c) 4
d) 6

Explanation:

5.The number of roots of the equation $\sqrt{3x^{2}+6x+7}+\sqrt{5x^{2}+10x+14}=4-2x-x^{2}$
is
a) 4
b) 3
c) 2
d) 1

Explanation:

6. The number of real values of x which satisfy the equation $\mid\frac{x^{2}-6\sqrt{x}+7}{x^{2}+6\sqrt{x}+7}\mid=1$
a) 0
b) 1
c) 2
d) infinite

Explanation:

7. The number of real values of x which satisfy the equation $\mid\frac{x}{x-1}\mid+\mid x\mid =\frac{x^{2}}{\mid x-1\mid}$
a) 1
b) 2
c) 5
d) infinite

Explanation:

8. Sum of all the real values of x which satisfy the equation $\frac{\sqrt{2-x}}{\sqrt{2+x}}=\frac{2-x}{2+x}$
a) 0
b) 2
c) 7.5
d) 11.5

Explanation:

9. The set of real values of a for which the equation $\frac{2a^{2}+x^{2}}{a^{3}-x^{3}}-\frac{2x}{ax+a^{2}+x^{2}}+\frac{1}{x-a}=0$
has a unique solution is
a) $\left(-\infty,1\right)$
b) $\left(-1,\infty\right)$
c) $\left(-1,1\right)$
d) $R-\left\{0\right\}$

10. The set of real values of a for which sum of the roots of the equation$\frac{1}{x}+\frac{1}{a}-\frac{1}{a^{2}}=\frac{1}{x+a-a^{2}}$
is less than $a^{3}/4$  is
a) $\left(0,2\right)\cup\left(2,\infty\right)$
b) $\left(3,\infty\right)$
c) $\left(-1,0\right)\cup\left(3,\infty\right)$
d) $\left(2,\infty\right)$