Home
Class 12
MATHS
The largest term in the expansion of ((...

The largest term in the expansion of `((b)/(2) + (b)/(2))^(100) ` is

A

`b^(100)`

B

`((b)/(2))^(100)`

C

`""^(100)C_(50)((b)/(2))^(100)`

D

`""^(100)C_(50)b^(100)`

Text Solution

Verified by Experts

The correct Answer is:
c
Here, n = 100 , so the total number of terms is 101.
` therefore ` Largest term = Middle term = 51th term
`= ""^(100)C_(50) ((b)/(2))^(50) ((b)/(2))^(50) = ""^(100)C_(50)((b)/(2))^(100)` .
Promotional Banner

Topper's Solved these Questions

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|21 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise For Session 4|14 Videos

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|23 Videos

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|16 Videos

Similar Questions

Explore conceptually related problems

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

Find the middle term (terms) in the expansion of ((x)/(a) - (a)/(x))^(10)

The number of irrational terms in the expansion of (root(8)(5)+ root(6)(2))^(100) is

The term independent of x in the expansion of ((3)/(2) x^(2) - (1)/(3x) )^(9) is :

Find the 4th term in the expansion of (x-2y)^12 .

Write the general term in the expansion of (x^2 - y)^6

Find the term independent of x in the expansion of ((3)/(2) x^(2) - (1)/(3x) )^(9) .

Find the number of terms in the expansion of (root(2)(9) + root(2)(8) )^(500) which are integers .

Find the middle term in the expansion of : (a/x+\ b x)^(12)

ARIHANT MATHS-BIONOMIAL THEOREM-Exercise (Single Option Correct Type Questions)
  1. If the number of terms in (x + 2+ (1)/(x))^(n) (n in I ^(+) " is " 40...

    Text Solution

    |

  2. The vaule of sum(r=0)^(n-1) (""^(C(r))/(""^(n)C(r) + ""^(n)C(r +1)))...

    Text Solution

    |

  3. The largest term in the expansion of ((b)/(2) + (b)/(2))^(100) is

    Text Solution

    |

  4. Solve the following quadratic equation 4x^2 -1 = 0

    Text Solution

    |

  5. The coefficient of x^m in (1+x)^m +(1+m)^(m+1) +...+(1+x)^n ,m≤n is

    Text Solution

    |

  6. The number of values of 'r' satisfying the equation ""^(39)C(3r-1)-...

    Text Solution

    |

  7. The sum S = ""^(20)C(2) + 2*""^(20)C(3) + 3 *""^(20)C(4) + ...+ 19 * "...

    Text Solution

    |

  8. The remainder, if 1+2+2^2++2^(1999) is divided by 5 is.

    Text Solution

    |

  9. The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a).(...

    Text Solution

    |

  10. The last two digits of the number 19^(9^(4))is

    Text Solution

    |

  11. If the second term of the expansion [a^(1/(13))+a/(sqrt(a^(-1)))]^n is...

    Text Solution

    |

  12. If 6^(83) + 8^(83) is divided by 49 , the raminder is

    Text Solution

    |

  13. The sum of all rational terms in the expansion of (3^(1//4) + 4^(1...

    Text Solution

    |

  14. Sum of last three digits of the number N=7^(100)-3^(100) is.

    Text Solution

    |

  15. If 5^(99) is divided by 13, the remainder is

    Text Solution

    |

  16. Find the value of {3^(2003)//28}, w h e r e{dot} denotes the fractiona...

    Text Solution

    |

  17. The value of sum(r=0)^(20)r(20-r)(^(20)Cr)^2 is equal to 400^(39)C(20)...

    Text Solution

    |

  18. Find the roots of the following quadratic equation x^2 + x - 1 = 0

    Text Solution

    |

  19. The total number of terms which are dependent on the value of x in the...

    Text Solution

    |

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

    Text Solution

    |