JEE 2023 Mathematics PYQ — Let be the smallest number such that the expansion of has a term … | Mathem Solvex | Mathem Solvex
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JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023
Let \alpha > 0 be the smallest number such that the expansion of (x2/3+x32)30 has a term βx−α,β∈N. Then α is equal to:
Choose the correct answer:
A.
2
(Correct Answer)
B.
3
C.
4
D.
5
Correct Answer:
2
Explanation
Solution:
General term Tr+1 likhte hain:
Tr+1=30Cr(x2/3)30−r(x32)r=30Cr⋅2r⋅x20−32r−3r
Power of x=20−311r=−α.
Smallest \alpha > 0 ke liye humein r ki aisi value leni hogi jo 20−311r ko negative banaye aur jahan r ek integer ho aur r ko 3 ka multiple hona chahiye (kyunki x ki power integer honi chahiye β∈N ke liye).
Yadi r=6: power =20−22=−2⟹α=2.
Explanation
Solution:
General term Tr+1 likhte hain:
Tr+1=30Cr(x2/3)30−r(x32)r=30Cr⋅2r⋅x20−32r−3r
Power of x=20−311r=−α.
Smallest \alpha > 0 ke liye humein r ki aisi value leni hogi jo 20−311r ko negative banaye aur jahan r ek integer ho aur r ko 3 ka multiple hona chahiye (kyunki x ki power integer honi chahiye β∈N ke liye).
