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Q.

The value of numerically greatest term in the expansion (5x-2y)7 when x=12,y=13

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a

527,  143526

b

527,  −143526

c

−527,  143526

d

−527,  −143526

answer is B.

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Detailed Solution

(5x−2y)7=(5x)71−2y5x7 Here n=7,X=-2y5x=-25·13·21∵x=12,y=13                                    =−415⇒X=415 Now, (n+1)|X||X|+1=(7+1)×415415+1=8×415195=3219=1.68=1+0.68=I+F∴ Numerically greatest terms are T1 and T2Tr+1=7C r(5x)7−r(−2y)r∴T1=T0+1=7C 0(5x)7(−2y)0                     =1.57.127.1∵x=12,y=13                     =527Also T2=T1+1=7C 1(5x)7−1(−2y)1                           =−7.56.x6.2.y                            =−7.56.126.2.13∵x=12,y=13                            =−143526
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