Using the binomial expansion (1+x)n=C0n+C1nx+C2nx2.......+Cnnxn
We get,
α=64(1+8)n−8n−1=C2n+C3n8+C4n82+…Similarly β=C2n+C3n5+C4n52+….
So α−β=C3n(8−5)+C4n(82−52)+…+Cnn(8n−2−5n−2)
So, option (C) is the answer.
JEE Main 2022 — Mathematics Algebra
Let n≥5 be an integer. If 9n−8n−1=64α and 6n−5n−1=25β, then α−β is equal to:
Held on 29 Jun 2022 · Verified 6 Jul 2026.
1+C2n(8−5)+C3n(82−52)+…+Cnn(8n−1−5n−2)
1+C3n(8−5)+C4n(82−52)+…+Cnn(8n−2−5n−2)
C3n(8−5)+C4n(82−52)+…+Cnn(8n−2−5n−2)
C4n(8−5)+C5n(82−52)+…+Cnn(8n−3−5n−3)
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