JEE Main · MathematicsEasy

$If^{n} C_{2} = 10, what is the value of n ?$

A. $4$
B. $6$
C. $5$
D. $7$

Show correct answer & step-by-step solution

Correct answer: C — $5$

Solution

The formula for^{n} C_{2} is \frac{n ( n - 1 )}{2} . Setting \frac{n ( n - 1 )}{2} = 10 leads to n^{2} - n - 20 = 0, which factors to (n - 5) (n + 4) = 0, giving n = 5 .

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