$\mathrm{If} \mathrm{C}\left(20, \mathrm{n} + 2\right) = \mathrm{C}\left(20, \mathrm{n} - 2\right), \mathrm{then} \mathrm{what} \mathrm{is} \mathrm{n} = ?$

• 8

• 10

• 12

• 16

2.

In the expansion of (1 + x)⁴³, if the coefficients of (2r + 1)^th and (r + 2)^th terms are equal, then what is the value of r (r $\ne$ 1) ?

• 5

• 14

• 21

• 22

If the coefficients of am and aⁿ in the expansion of (1+ a)^{m + n} are $\mathrm{\alpha } \mathrm{and} \mathrm{\beta }$, then which one of the following is correct ?

• $\mathrm{\alpha } = 2\mathrm{\beta }$

• $\mathrm{\alpha } = \mathrm{\beta }$

• $2\mathrm{\alpha } = \mathrm{\beta }$

• $\mathrm{\alpha } = \left(\mathrm{m} + \mathrm{n}\right)\mathrm{\beta }$

What is the coefficient of the middle term in the binomial expansion of (2 + 3)⁴ ? 

• 6

• 12

• 108

• 216

Let the coefficient of the middle term of the binomial expansion of (1 + x)²ⁿ be a and those of two middle terms of the binomial expansion of (1 + x)^{2n - 1} be $\mathrm{\beta } \mathrm{and} \mathrm{\gamma }$. Which one of the following relations is correct ?

• $\mathrm{\alpha } > \mathrm{\beta } + \mathrm{\gamma }$

• $\mathrm{\alpha } < \mathrm{\beta } + \mathrm{\gamma }$

• $\mathrm{\alpha } = \mathrm{\beta } + \mathrm{\gamma }$

• $\mathrm{\alpha } = \mathrm{\beta \gamma }$

$$\begin{gathered} \mathrm{The} \mathrm{expansion} \mathrm{of} (\mathrm{x} - \mathrm{y}{)}^{\mathrm{n}}, \mathrm{n} > 5 \mathrm{is} \mathrm{done} \mathrm{in} \mathrm{the} \mathrm{descending} \mathrm{powers} \mathrm{of} \mathrm{r}. \\ \mathrm{If} \mathrm{the} \mathrm{sum} \mathrm{of} \mathrm{the} \mathrm{fifth} \mathrm{and} \mathrm{sixth} \mathrm{term} \mathrm{is} \mathrm{zero}, \mathrm{then} \frac{\mathrm{x}}{\mathrm{y}} = ? \end{gathered}$$

• $\frac{\mathrm{n} - 5}{6}$

• $\frac{\mathrm{n} - 4}{5}$

• $\frac{5}{\mathrm{n} - 4}$

• $\frac{6}{\mathrm{n} - 5}$

In the binary equation (1p101)₂ + (10q1)₂ = (100r 00)₂ where p, q and r are binary digits, what are the possible values of p, q and r respectively ?

• 0, 1, 0

• 1, 1, 0

• 0, 0, 1

• 1, 0, 1

In the expansion of (1 + x)⁵⁰, the sum of the coefficients of odd powers of x is :

• $2^{26}$

• 2⁴⁹

• 2⁵⁰

• 2⁵¹