JEE Main2012MathematicsBinomial TheoremActual

If n= ^m C₂ , then the value of ^n C₂ is given by

Options

A3 ( ^ m+1 C₄ )
B^ m-1 C₄
C^ m+1 C₄
D2 ( ^ m+2 C₄ )

Correct answer

A. 3 ( ^ m+1 C₄ )

Step-by-step solution

n= ^m C ₂= m(m-1) 2 Since m and (m-1) are two consecutive natural numbers, therefore their product is an even natural number. So m(m-1) 2 is also a natural number. Now m(m-1) 2 = m^2-m 2 aligned & m(m-1) 2 C ₂= ( m^2-m 2 ) ( m^2-m 2 -1 ) 2 & = m(m-1) (m^2-m-2 ) 8 & = m(m-1) [m^2-2 m+m-2 ] 8 & = m(m-1)[m(m-2)+1(m-2)] 8 & = m(m-1)(m-2)(m+1) 8 aligned

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