If Tr denotes the rth term in the expansion of x-1-y23 then

The correct option is C T_12 = xy T_13 T_12 = ^23 C_11x^12 ( 1/y)^11 = ^23C_11x^12/y^11 , T_13=^23C_12 x^11 ( 1/y)^12 = ^23C_11x^11/y^12 , T_ ...

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Byju's Answer

Standard XII

Mathematics

General Term of Binomial Expansion

If Tr denot...

Question

If $T_{r}$ denotes the rth term in the expansion of ${(x + \frac{1}{y})}^{23}$ then

T_{12} = T_{13}

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x^{2} T_{13} = T_{12}

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T_{12} = x y T_{13}

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T_{12} + T_{12} = 25

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Solution

The correct option is C $T_{12} = x y T_{13}$
$T_{12} =^{23} C_{11} x^{12} {(\frac{1}{y})}^{11} =^{23} C_{11} \frac{x^{12}}{y^{11}}$ ,
$T_{13} =^{23} C_{12} x^{11} {(\frac{1}{y})}^{12} =^{23} C_{11} \frac{x^{11}}{y^{12}}$ ,
$T_{12} = x y (^{23} C_{11} \frac{x^{11}}{y^{12}}) = x y T_{13}$

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If Tr denotes the rth term in the expansion of (x+1y)23 then

The correct option is C T12=xyT13T12=23C11x12(1y)11=23C11x12y11,T13=23C12x11(1y)12=23C11x11y12,T12=xy(23C11x11y12)=xyT13

If $T_{r}$ denotes the rth term in the expansion of ${(x + \frac{1}{y})}^{23}$ then

The correct option is C $T_{12} = x y T_{13}$
$T_{12} =^{23} C_{11} x^{12} {(\frac{1}{y})}^{11} =^{23} C_{11} \frac{x^{12}}{y^{11}}$ ,
$T_{13} =^{23} C_{12} x^{11} {(\frac{1}{y})}^{12} =^{23} C_{11} \frac{x^{11}}{y^{12}}$ ,
$T_{12} = x y (^{23} C_{11} \frac{x^{11}}{y^{12}}) = x y T_{13}$