| 1. (2) | 2. (2) |
| 9. (3) | 10. (1) |
| 17. (1) | 18. (2) |
| 25. (36) | 26. (25) |
| 33. (2) | 34. (2) |
| 41. (1) | 42. (2) |
| 49. (3) | 50. (1) |
| $57 . ( 8 )$ | 58. (2) |
| 65. (1) | 66. (4) |
| 73. (2) | 74. (3) |
| 81. (9) | 82. (1) |
| 89. (39) | 90. (19) |
Q90. Let $\mathrm { a } , \mathrm { b }$ and c denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked $1,2,3,4$. If the probability that $a x ^ { 2 } + b x + c = 0$ has all real roots is $\frac { m } { n } , \operatorname { gcd } ( \mathrm {~m} , \mathrm { n } ) = 1$, then $\mathrm { m } + \mathrm { n }$ is equal to $\_\_\_\_$
\section*{ANSWER KEYS}
\begin{center}
\begin{tabular}{|l|l|}
\hline
1. (2) & 2. (2) \\
\hline
9. (3) & 10. (1) \\
\hline
17. (1) & 18. (2) \\
\hline
25. (36) & 26. (25) \\
\hline
33. (2) & 34. (2) \\
\hline
41. (1) & 42. (2) \\
\hline
49. (3) & 50. (1) \\
\hline
$57 . ( 8 )$ & 58. (2) \\
\hline
65. (1) & 66. (4) \\
\hline
73. (2) & 74. (3) \\
\hline
81. (9) & 82. (1) \\
\hline
89. (39) & 90. (19) \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}
\setcounter{enumi}{2}
\item (4)
\item (2)
\item (3)
\item (160)
\item (1)
\item (1)
\item (164)
\item (3)
\item (1)
\item (1)
\item (9)
\item (4)
\item (2)
\item (3)
\item (10)
\item (4)
\item (2)
\item (4)
\item (4)
\item (3)
\item (3)
\item (32)
\item (2)
\item (2)
\item (3)
\item (200)
\item (1)
\item (4)
\item (2)
\item (3)
\item (2)
\item (2)
\item (25)
\item (4)
\item (2)
\item (100)
\item (15)
\item (1)
\item (2)
\item (82)
\item (2)
\item (1)
\item (4)
\item (14)
\item (2)
\item (3)
\item (1)
\item (3)
\item (20)
\item (17)
\item (4)
\item (3)
\item (4)
\item (3)
\item (4)
\item (4)
\item (4)
\item (3)
\item (2)
\item (3)
\item (3)
\item (1)
\item (1)
\item (2)
\item (1010)
\item (81)
\end{enumerate}