Question

If 6th term in the expansion of [1x8/3+x2log10⁡x]8 is 5600, then x is equal to

• A. (A) 5
• B. (B) 4
• C. (C) 8
• D. (D) 10

Answer 1

Answer: (D)

(D) 10

Answer 2

Explanation:
Using binomial theorem, the 6th term of (a+b)8 is 56a3b5Now substituting the given terms, we get,[1x83+x2log10⁡x]General term, ⇒Tr+1=8Cr[1x83]n−r(x2log10⁡x)rFor 6th term, take r=5T6=8C5[1x83]3[x2log10⁡x]55600=8×7×63×2×1×1x8×x10(log10⁡x)5[∵8C3=8×7×63×2×1]102=x2(log10⁡x)5[∵(log10⁡x=1)]x2=102x=10Hence, the correct option is (D).