r=1∑15r2(15Cr)⇒15r=1∑15r14Cr−115r=1∑15(r−1+1)14Cr−115⋅14r=1∑1513Cr−2+15r=1∑1514Cr−115⋅14⋅213+15⋅21431⋅213(70+10)31⋅213⋅8031⋅51⋅217 m=17n=1k=1 option (1)
If 1^2 · ( ^15 C_1 )+2^2 · ( ^15 C_2 )+3^2 · ( ^15 C_3 )+… +15^2 · ( ^15 C_15 )=2^m · 3^n · 5^k, where m, n, k ∈ N, then m+ n+ k is equal to :
JEE Main 2025 — Mathematics Algebra
2025mcqmedium
If 12⋅(15C1)+22⋅(15C2)+32⋅(15C3)+… +152⋅(15C15)=2m⋅3n⋅5k, where m,n,k∈N, then m+n+k is equal to :
Official previous-year question
Held on 4 Apr 2025 · Verified 6 Jul 2026.
Options
- A
19
- B
21
- C
18
- D
20
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