NDA 2026 — Mathematics PYQ
NDA | Mathematics | 2026If n=mC2, then what is nC2 equal to?
यदि n=mC2 है, तो nC2 किसके बराबर है ?
Choose the correct answer:
- A.
m+1C4
- B.
2×m+1C4
3×m+1C4
Explanation
To solve this, we use the definition of the binomial coefficient: nCr=r!n(n−1)…(n−r+1). Specifically, nC2=2n(n−1).
Given Relation:
We are given n=mC2=2m(m−1).
Evaluating nC2:
nC2=2n(n−1)
Substitute n=2m(m−1):
nC2=2(2m(m−1))(2m(m−1)−1)
nC2=2(2m(m−1))(2m2−m−2)
Factorizing the Expression:
Factor the quadratic m2−m−2 as (m−2)(m+1):
nC2=2(2m(m−1))(2(m−2)(m+1))
nC2=8m(m−1)(m−2)(m+1)
Comparing with Options:
We know that m+1C4=4!(m+1)m(m−1)(m−2).
Since 4!=24:
m+1C4=24(m+1)m(m−1)(m−2)
Comparing this to our result:
nC2=8m(m−1)(m−2)(m+1)=3×24(m+1)m(m−1)(m−2)
nC2=3×m+1C4
Correct Option: (c) 3×m+1C4
Explanation
To solve this, we use the definition of the binomial coefficient: nCr=r!n(n−1)…(n−r+1). Specifically, nC2=2n(n−1).
Given Relation:
We are given n=mC2=2m(m−1).
Evaluating nC2:
nC2=2n(n−1)
Substitute n=2m(m−1):
nC2=2(2m(m−1))(2m(m−1)−1)
nC2=2(2m(m−1))(2m2−m−2)
Factorizing the Expression:
Factor the quadratic m2−m−2 as (m−2)(m+1):
nC2=2(2m(m−1))(2(m−2)(m+1))
nC2=8m(m−1)(m−2)(m+1)
Comparing with Options:
We know that m+1C4=4!(m+1)m(m−1)(m−2).
Since 4!=24:
m+1C4=24(m+1)m(m−1)(m−2)
Comparing this to our result:
nC2=8m(m−1)(m−2)(m+1)=3×24(m+1)m(m−1)(m−2)
nC2=3×m+1C4
Correct Option: (c) 3×m+1C4