Home
Class 11
MATHS
The middle term in the expansion of (x//...

The middle term in the expansion of `(x//2+2)^8` is 1120, then `x in R` is equal to a. -2 b. 3 c. `-3` d. `2`

A

`-2`

B

`3`

C

`-3`

D

`2`

Text Solution

Verified by Experts

Middle term is `(n/2+1)` th or `(4+1)^(th)` or `T_(5)`
`rArr T_(5) = .^(8)C_(4) (x/2)^(4) xx 2^(4) = 1120`
or `(8xx7xx6xx5)/(1xx2xx3xx4) x^(4) = 1120`
or `x^(4) = (1120)/(70) = 16`
or `(x^(2) + 4) (x^(2) - 4) = 0`
or `x = +- 2" "(:' x in R)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

Similar Questions

Explore conceptually related problems

The middle term in the expansion of (x + 1/x)^(2n) is

Find the middle term in the expansion of (x + 2)^(6) .

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

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

Find the middle term in the expansion of : (x^2-2/x)^(10)

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

Find the middle term in the expansion of (3x-(x^3)/6)^9

Find the middle term in the expansion of ((2x)/3-3/(2x))^(20)

Find the middle term in the expansion of (1+2x+x^(2))^(10)

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. For the expansion (xsinp+x^(-1)cosp)^(10),(p in R), The greatest v...

    Text Solution

    |

  2. Let (1+x^2)^2(1+x)^n=sum(k=0)^(n+4)ak x^k. If a1, a2 and a3 are in ari...

    Text Solution

    |

  3. The middle term in the expansion of (x//2+2)^8 is 1120, then x in R i...

    Text Solution

    |

  4. If (1+2x+x^2)^n=sum(r=0)^(2n)ar x^r ,then ar is a.(.^nC2)^2 b. .^n ...

    Text Solution

    |

  5. [(^nC0+^n C3+)-1/2(^n C1+^n C2+^n C4+^n C5]^2 + 3/4(^n C1-^n C2+^n C4 ...

    Text Solution

    |

  6. If sum(r=0)^(n)((r+2)/(r+1)).^n Cr=(2^8-1)/6 , then n is (A) 8 (B...

    Text Solution

    |

  7. Let f(x)=a0+a1x+a2x^2+...+an x^n and (f(x))/(1-x)=b0+b1x+b2x^2+...+bn ...

    Text Solution

    |

  8. If (1+x^(2))^(n) = underset(r=0)overset(n)suma(r)x^(r )= (1+x+x^(2)+x^...

    Text Solution

    |

  9. The value of sum(r=1)^(n+1)(sum(k=1)^n "^k C(r-1))( where r ,k ,n in ...

    Text Solution

    |

  10. If (x^2+x+1)/(1-x)=a0+a1x+a2x^2+ ,t h e nsum(r=1)^(50)ar is equal to 1...

    Text Solution

    |

  11. Find dy/dt , if y = (1 - cost)/(1 + cost) is

    Text Solution

    |

  12. The coefficient of x^9 in the expansion of (1+x)(1+ x^2)(1+x^3)....(1...

    Text Solution

    |

  13. The coefficients of three consecutive terms of (1+x)^(n+5) are in the ...

    Text Solution

    |

  14. If (1-x)^(-n)=a0+a1x+a2x^2+...+ar x^r+ ,t h e na0+a1+a2+...+ar is equa...

    Text Solution

    |

  15. The value of sum(r=0)^(20)r(20-r)(.^(20) Cr)^2 is equal to a. 400^(...

    Text Solution

    |

  16. The coefficient of x^(10) in the expansion of (1+x^2-x^3)^8 is 476 b. ...

    Text Solution

    |

  17. If the term independent of x in the (sqrt(x)-k/(x^2))^(10) is 405, the...

    Text Solution

    |

  18. The coefficient of x^2y^3 in the expansion of (1-x+y)^(20) is (20 !)/(...

    Text Solution

    |

  19. The coefficient of x^5 in the expansion of (x^2-x-2)^5 is -83 b. -82 c...

    Text Solution

    |

  20. The coefficient of a^8b^4c^9d^9 in (a b c+a b d+a c d+b c d)^(10) is...

    Text Solution

    |