Advertisement Remove all ads

# 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

Advertisement Remove all ads

#### 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?
Advertisement Remove all ads

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Q 9 | Page 25
Advertisement Remove all ads

#### Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?