# If the middle term of (1x+xsinx)10 is equal to 778, then value of x is ______. - Mathematics

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If the middle term of (1/x + x sin x)^10 is equal to 7 7/8, then value of x is ______.

#### Options

• 2npi + pi/6

• npi + pi/6

• npi + (-1)^n  pi/6

• npi + (-1)^n  pi/3

#### Solution

If the middle term of (1/x + x sin x)^10 is equal to 7 7/8, then value of x is npi + (-1)^n  pi/6.

Explanation:

Given expression is (1/x + x sin x)^10

Number of terms = 10 + 1 = 11 odd

∴ Middle term = (11 + 1)/2 th term = 6th term

T6 = T5+1

= ""^10"C"_5 (1/x)^(10 - 5)  (x sin x)^5

∴ ""^10"C"_5 (1/x)^5 * x^5 * sin^5x = 7 7/8

⇒ ""^10"C"_5 * sin^5x = 63/8

⇒ (10*9*8*7*6)/(5*4*3*2*1) * sin^5x = 63/8

⇒ 252 * sin^5x = 63/8

⇒ sin^5x = 63/(8 xx 252)

⇒ sin^5x = 1/32

⇒ sin^5x = (1/2)^5

⇒ sin x = 1/2

⇒ sin x = sin  pi/6

∴ x = "n"pi + (-1)^"n" * pi/6

Concept: General and Middle Terms
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#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 8 Binomial Theorem
Exercise | Q 24 | Page 145

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