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If ( a 2 − a ) C 2 = ( a 2 − a ) C 4 , Then a = (A) 2 (B) 3 (C) 4 (D) None of These - Mathematics

MCQ

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

Options

  • 2

  •  3

  • 4

  • none of these

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Solution

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.
∴\[a = 3\]
  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Q 9 | Page 25
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