$\mathrm{\alpha }, \mathrm{\beta }, \mathrm{\gamma }$ are the roots of the equation x³ - 10x² + 7x + 8=0. Match the following and choose the correct answer.

$$\begin{gathered} A. \mathrm{\alpha } + \mathrm{\beta } + \mathrm{\gamma } \left(1\right) - \frac{43}{7} \\ \mathrm{B}. {\mathrm{\alpha }}^2 + {\mathrm{\beta }}^2 + {\mathrm{\gamma }}^2 \left(2\right) - \frac{7}{8} \\ \mathrm{C}. \frac{1}{\mathrm{\alpha }} + \frac{1}{\mathrm{\beta }} + \frac{1}{\mathrm{\gamma }} \left(3\right) 86 \\ \mathrm{D}. \frac{\mathrm{\alpha }}{\mathrm{\beta \gamma }} + \frac{\mathrm{\beta }}{\mathrm{\gamma \alpha }} + \frac{\mathrm{\gamma }}{\mathrm{\alpha \beta }} \left(4\right) 0 \\ \left(10\right) \end{gathered}$$

Match the following elements of $\left[\begin{array}{ccc}1& - 1& 0\\ 0& 4& 2\\ 3& - 4& 6\end{array}\right]$ with their co-factors and choose the correct answer

$$\begin{gathered} \mathrm{Element} \mathrm{Co}-\mathrm{factor} \\ \mathrm{A} - 1 \left(1\right) - 2 \\ \mathrm{B} 1 \left(2\right) 32 \\ \mathrm{C} 3 \left(3\right) 4 \\ \mathrm{D} 6 \left(4\right) 6 \\ \left(5\right) - 6 \end{gathered}$$

Match the points on the curve 2y² = x + 1 with the slopes of normals at those points and choose the correct answer.

      Point           Slope of the normal

A    (7, 2)         1 - 4$\sqrt{2}$

B    (0, $\frac{1}{\sqrt{2}}$)     2  - 8

C    (1, - 1)       3, 4

D    (3, $\sqrt{2}$)      4, 0

$$\begin{gathered} \mathrm{If} \mathrm{f} : \mathrm{N} \to \mathrm{Z} \mathrm{is} \mathrm{defined} \mathrm{by} \\ \mathrm{f}\left(\mathrm{n}\right) =\left\{ 2 \mathrm{if} \mathrm{n} = 3\mathrm{k}, \mathrm{k} \in \mathrm{Z} \\ 10 \mathrm{if} \mathrm{n} = 3\mathrm{k} + 1, \mathrm{k} \in \mathrm{Z} \\ 0 \mathrm{if} \mathrm{n} = 3\mathrm{k} + 2, \mathrm{k} \in \mathrm{Z}\right\} \\ \mathrm{Then}, \left\{\mathrm{n} \in \mathrm{N} : \mathrm{f}\left(\mathrm{n}\right) > 2\right\} \mathrm{is} \mathrm{equal} \mathrm{to} \end{gathered}$$

• {3, 6, 4}

• {1, 4, 7}

• {4, 7}

• {7}

The value of $\sqrt{42 + \sqrt{42 + \sqrt{42 + ...}}}$ is equal to

• 7

• - 6

• 5

• 4

$\mathrm{If} {\log }_{27}\left({\log }_3\left(\mathrm{x}\right)\right) = \frac{1}{3}, \mathrm{then} \mathrm{the} \mathrm{value} \mathrm{of} \mathrm{x} \mathrm{is}$

• 3

• 6

• 9

• 27

S₁, S₃, ...... ,S₁₀ are the speakers in a conference. If S₁ addresses only after S₂,then the number of ways the speakers address iS

• 10!

• 9!

• $10! \times 8!$

• $\frac{10!}{2}$

8.

The number of positive odd divisors of 216 is

• 4

• 6

• 8

• 12

The binomial coefficients which are in decreasing order are

• ${}^{15}{\mathrm{C}}_{5,}{ }^{15}{\mathrm{C}}_{6,}{ }^{15}{\mathrm{C}}_{7,}$

• ${}^{15}{\mathrm{C}}_{10} ,{ }^{15}{\mathrm{C}}_9 ,{ }^{15}{\mathrm{C}}_8$

• ${}^{15}{\mathrm{C}}_6 ,{ }^{15}{\mathrm{C}}_7 ,{ }^{15}{\mathrm{C}}_8$

• ${}^{15}{\mathrm{C}}_7 ,{ }^{15}{\mathrm{C}}_6 ,{ }^{15}{\mathrm{C}}_5$

$$\begin{gathered} \mathrm{If} \frac{\mathrm{x} - 4}{{\mathrm{x}}^2 -5\mathrm{x} + 6} \mathrm{can} \mathrm{be} \mathrm{expanded} \mathrm{in} \mathrm{the} \mathrm{ascending} \mathrm{power} \mathrm{of} \mathrm{x}, \\ \mathrm{then} \mathrm{the} \mathrm{coefficient} \mathrm{of} {\mathrm{x}}^3 \mathrm{is} \end{gathered}$$

• $- \frac{73}{648}$

• $\frac{73}{648}$

• $\frac{71}{648}$

• $- \frac{71}{648}$