The coefficient of 1y2 in (y+c3y2)10 is 3360. If the value of y=2, then
A
c=3√2
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B
greatest term will be 2880
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C
5th term will be coefficient of y−2
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D
3rd term will have greatest numerical value
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Solution
The correct option is D3rd term will have greatest numerical value The general term of the given expansion is Tr+1=10Cry10−r(c3y2)r⇒Tr+1=10Cry10−3rc3r
Now for y−2 term 10−3r=−2⇒r=4
Hence 5th term will have y−2
Now the coefficient will be 3360=10C4c12⇒210c12=210×16⇒c3=2
Now for numerically greatest term ∣∣∣Tr+1Tr∣∣∣≥1⇒∣∣∣11−rr⋅c3y3∣∣∣≥1⇒∣∣∣11−r4r∣∣∣≥1⇒r≤115
Hence for r=2 the term will be greatest
The greatest term will be T2+1=10C2y10−6c6=2880