Question

If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =

Options

• 2

•  3

• 4

• none of these

Answer 1

3

\[a^2 - a = 2 + 4\]  [∵

\[{}^n C_x =^n C_y \Rightarrow n = x + y\ \text{or} x = y\]]

\[\Rightarrow a^2 - a - 6 = 0\]
\[ \Rightarrow a^2 - 3a + 2a - 6 = 0\]
\[ \Rightarrow a \left( a - 3 \right) + 2 \left( a - 3 \right) = 0\]
\[ \Rightarrow \left( a + 2 \right) \left( a - 3 \right) = 0\]

\[\Rightarrow a = - 2 \text{or} a = 3\]\

But, 

\[a = - 2\] is not possible.

∴\[a = 3\]