Home
Class 12
MATHS
In the expansion of (a+b)^(n), if two co...

In the expansion of `(a+b)^(n)`, if two consecutive terms are equal, then which of the following is/are always integer ?
(a)`((n+1)b)/(a+b)` (b)`((n+1)a)/(a+b)` (c)`(na)/(a-b)` (d)`(na)/(a+b)`

A

`((n+1)b)/(a+b)`

B

`((n+1)a)/(a+b)`

C

`(na)/(a-b)`

D

`(na)/(a+b)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
We have `(a+b)^(n)`
`(T_(r+1))/(T_(r)) = (n-r+1)/(r ) . b/a = 1`
`:. (n+1)b-r = ar`
`:. r = -((n+1)b)/(a+b)` is integer
Also, considering `(b+a)^(n)`.
`(T_(r+1))/(T_(r)) = (n-r+1)/(r ) . a/b = 1`
`:. R = ((n+1)a)/(a+b)` is integer
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Linked Comphrension|20 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Matrix|4 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Single Correct Answer|152 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise For problems 3 and 4|2 Videos

Similar Questions

Explore conceptually related problems

If Aa n dB are symmetric and commute, then which of the following is/are symmetric? A^(-1)B b. A B^(-1) c. A^(-1)B^(-1) d. none of these

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

If a, b and c are three consecutive coefficients terms in the expansion of (1+x)^n , then find n.

Find a, b and n in the expansion of (a+b)^n if the first three terms of the expansion are 729, 7290 and 30375, respectively.

If (T_(2))/(T_(3)) is the expansion of (a+b)^(n)and(T_(3))/(T_(4)) is the expansion of (a+b)^(n+3) are equal , then n is equal to -

The number of terms in the expansion of (a+b+c)^n where ninN is

If alpha and beta are the rootsof he equations x^2-a x+b=0a n dA_n=alpha^n+beta^n , then which of the following is true? a) A_(n+1)=a A_n+b A_(n-1) b) A_(n+1)=b A_(n-1)+a A_n c) A_(n+1)=a A_n-b A_(n-1) d) A_(n+1)=b A_(n-1)-a A_n

If (a^(n)+b^n)/ (a^(n-1) +b^(n-1)) is the A.M. between a and b, then find the value of n.

If (a^n+b^n)/(a^(n-1)+b^(n-1)) is the A.M. between a and b, then find the value of n.

CENGAGE PUBLICATION-BINOMIAL THEOREM-Multiple Correct Answer Type
  1. 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

    |

  2. For natural numbers m ,n ,if(1-y)^m(1+y)^n=1+a1y+a2y^2+... , and a1=a2...

    Text Solution

    |

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

    Text Solution

    |

  4. In the expansion of (3-sqrt(17/4+3sqrt2))^15 the 11th term is a

    Text Solution

    |

  5. For the expansion (x sin p + x^(-1)cos p)^(10), (p in R),

    Text Solution

    |

  6. For which of the following values of x ,5t h term is the numerically g...

    Text Solution

    |

  7. Which of the following is/are true ?

    Text Solution

    |

  8. If sn= sum(r=0)^n 1/(^"nCr) and tn=sum(r=0)^n r/("^nCr) then tn/sn is ...

    Text Solution

    |

  9. The value of .^(n)C(1)+.^(n+1)C(2)+.^(n+2)C(3)+"….."+.^(n+m-1)C(m) is ...

    Text Solution

    |

  10. The number of terms in the expansion of (x^2+1+1/x^2)^n, n in N , is:

    Text Solution

    |

  11. In the expansion of (7^(1//3)+11^(1//9))^(6561) ,

    Text Solution

    |

  12. If (1+x)^(n) = C(0) + C(1)x + C(2)x^(2) + "….." + C(n)x^(n), then fin...

    Text Solution

    |

  13. In the expansion of (a+b)^(n), if two consecutive terms are equal, the...

    Text Solution

    |

  14. If for z as real or complex, (1+z^2+z^4)^8=C0+C1z^2+C2z^4+...+C(16)z^(...

    Text Solution

    |

  15. If f(m) = sum(i=0)^m ({:(30),(30-i):})({:(20),(m-i):}) where ({:(p),(...

    Text Solution

    |

  16. If (1+x)^n=C0+C1x+C2 x^2+...+Cn x^n , n in N ,then C0-C1+C2-.....+(-1...

    Text Solution

    |

  17. If sum(r=0)^(n) (pr+2).""^(n)C(r)=(25)(64) where n, p in N, then (a) p...

    Text Solution

    |

  18. If (x+1/x+1)^(6)=a(0)+(a(1)x+(b(1))/(x))+(a(2)x^(2)+(b(2))/(x^(2)))+"....

    Text Solution

    |

  19. Find the value of .^(20)C(0) xx .^(13)C(10) - .^(20)C(1) xx .^(12)C(...

    Text Solution

    |

  20. The sum 2 xx ""^(40)C(2) + 6 xx ""^(40)C(3) + 12 xx ""^(40)C(4) + 20 x...

    Text Solution

    |