Home
Class 12
MATHS
If the middle term in the binomial expan...

If the middle term in the binomial expansion of `(1/x+xsinx)^(10)` is equal to `(63)/8,` find the value of `xdot`

Text Solution

Verified by Experts

The correct Answer is:
`x = npi + (-1)^(n)'(pi)/(6), n in Z`
Here middle term is `T_(6)`.
`:. T_(6) = .^(10)C_(5) (1)/(x^(5)).x^(5) sin^(5)x = (63)/(8)`
or `sin^(5)x = (1)/(2^(5))`
or `sinx = 1/2`
`rArr x = npi + (-1)^(n) '(pi)/(6), n in Z`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Concept Application Exercise 8.2|10 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Concept Application Exercise 8.3|7 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Example|10 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|7 Videos

Similar Questions

Explore conceptually related problems

If the middle term in the binomial expansion of ((1)/(x) + x sin x )^(10) is ( 63)/( 8) , then the value of 6sin^(2) x +sin x -2 is

If the middle term in the expansion of ((1)/(x)+x sinx)^(10) is equal to 7(7)/(8) , then the principal value of x is:

Find the middle term in the expansion of (2x^2-1/x)^7

Find the middle term in the expansion of (2x^2-1/x)^7

If the middle term in the expansion of (1/x+xsinx)^(10) is equal to 7 7/8 , then the value of x is (i) 2npi+(pi)/6 (ii) npi+(pi)/6 (iii) npi+(-1)^(n)(pi)/6 (iv) npi+(-1)^(n)(pi)/3

Find the middle term in the expansion of : (1-2x+x^2)^n

Find the middle term in the expansion of (x- 1/(2x))^12

Find the middle term in the expansion of (x/y-y/x)^7

Find the 10th term in the binomial expansion of (2x^2+1/x)^(12)dot

Find the 10th term in the binomial expansion of (2x^2+1/x)^(12)dot

CENGAGE ENGLISH-BINOMIAL THEOREM-Concept Application Exercise 8.1
  1. The first three terms in the expansion of (1+a x)^n(n!=0) are 1,6xa n ...

    Text Solution

    |

  2. If the coefficient of 4th term in the expansion of (a+b)^n is 56, then...

    Text Solution

    |

  3. The two successive terms in the expansion of (1+x)^24 whose coefficie...

    Text Solution

    |

  4. If the number of terms in the expansion of (x+y+z)^n are 36, then find...

    Text Solution

    |

  5. Find the value of 1/(81^n)-((10)/(81^n))^(2n)C1+((10^2)/(81^n))^(2n)C2...

    Text Solution

    |

  6. sum(r=0)^n(-1)^r^n Cr[1/(2^r)+3/(2^(2r))+7/(2^(3r))+(15)/(2^(4r))+ u p...

    Text Solution

    |

  7. Find n in the binomial (2^(1/3)+1/(3^(1/3)))^n , if the ration 7th ter...

    Text Solution

    |

  8. If the coefficients of (r-5)^(t h) and (2r-1)^(t h) terms in the expan...

    Text Solution

    |

  9. Find the number of irrational terms in the expansion of (5^(1//6)+2^(1...

    Text Solution

    |

  10. Represent cos 6 theta in terms of cos theta.

    Text Solution

    |

  11. Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(...

    Text Solution

    |

  12. Find the value of (sqrt(2)+1)^6-(sqrt(2)-1)^6dot

    Text Solution

    |

  13. Find the degree of the polynomial 1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^7-...

    Text Solution

    |

  14. Let R=(5sqrt(5)+11)^(2n+1)a n df=R-[R]w h e r e[] denotes the greatest...

    Text Solution

    |

  15. If the middle term in the binomial expansion of (1/x+xsinx)^(10) is eq...

    Text Solution

    |

  16. Find the middle term in the expansion of (x^2+1/(x^2)+2)^ndot

    Text Solution

    |

  17. If the number of terms in the expansion (1+2x-3y+4z)^(n) is 286, then...

    Text Solution

    |