Set, Relation and FunctionHard
Question
If the coefficient of x7 in 
equals the coefficient of x-7 in 
, then a and b satisfy the relation
equals the coefficient of x-7 in , then a and b satisfy the relationOptions
A.a - b = 1
B.a + b = 1
C.
= 1
= 1D.ab = 1
Solution
Tr + 1 in the expansion 
= 11Cr(ax2)11-r
11Cr(a)11-r(b)-r(x)22-2r - r
⇒ 22 - 3r = 7 ⇒ r = 5
∴ coefficient of x7 = 11C5(a)6(b)-5 .....(1)
Again Tr + 1 in the expansion
= 11Cr(ax)11-r
= 11C5a11-r (-1)r × (b)r (x)-2r (x)11-r
Now 11 - 3r = - 7 ⇒ 3r = 18 ⇒ r = 6
∴ coefficient of x-7 = 11C 6 a5 × 1 × (b)-6
⇒ 11C5(a)6(b)-5 = 11C6 a5 × (b)-6
⇒ ab = 1
= 11Cr(ax2)11-r 11Cr(a)11-r(b)-r(x)22-2r - r
⇒ 22 - 3r = 7 ⇒ r = 5
∴ coefficient of x7 = 11C5(a)6(b)-5 .....(1)
Again Tr + 1 in the expansion
= 11Cr(ax)11-r= 11C5a11-r (-1)r × (b)r (x)-2r (x)11-r
Now 11 - 3r = - 7 ⇒ 3r = 18 ⇒ r = 6
∴ coefficient of x-7 = 11C 6 a5 × 1 × (b)-6
⇒ 11C5(a)6(b)-5 = 11C6 a5 × (b)-6
⇒ ab = 1
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