The ratio of 4^(th) term and 5^(th) term in the expansion of (x+(sinx)/(x))^(6) is (16)/(3pi^(2)), then x is equal to (1) (pi)/(2) (2) -(pi)/(2) (3) (pi)/(3) (4) Both (1) & (2)

The ratio of 4^(th) term and 5^(th) term in the expansion of (x+(sinx)

1.	The ratio of 4^(th) term and 5^(th) term in the expansion of (x+(sinx)/(x))^(6) is (16)/(3pi^(2)), then x is equal to (1) (pi)/(2) (2) -(pi)/(2) (3) (pi)/(3) (4) Both (1) & (2)
Answer» Solution :Answer (1) `T_(4)=.^(6)C_(3)x^(3)((sinx)/(x))^(3)` `T_(5)=.^(6)C_(4)x^(4)((sinx)/(x))^(2)` Now, `(T_(4))/(T_(5))=(16)/(3PI^(2))` `implies(.^(6)C_(3)SIN^(3)x)/(.^(6)C_(4)x^(2)*sin^(2)x)=(16)/(3pi^(2))` `implies(20sinx)/(15x^(2))=(16)/(3pi^(2))` `implies(sinx)/(x^(2))=(16xx15)/(20xx3pi^(2))=(4)/(pi^(2))` `impliesx=(pi)/(2)`

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The ratio of 4^(th) term and 5^(th) term in the expansion of (x+(sinx)/(x))^(6) is (16)/(3pi^(2)), then x is equal to (1) (pi)/(2) (2) -(pi)/(2) (3) (pi)/(3) (4) Both (1) & (2)

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