Home
Class 12
MATHS
If the 4th term in the expansion of (a x...

If the 4th term in the expansion of `(a x+1//x)^n` is 5/2, then `a=1/2` b. `n=8` c. `a=2/3` d. `n=6`

A

`a = 1/2`

B

`n = 8`

C

`a = 2/3`

D

`n = 6`

Text Solution

Verified by Experts

The correct Answer is:
A, D
It is given the fourth term in the expansion of `(ax+(1)/(x))^(n)` is `5/2`, therefore,
`.^(n)C_(3) (ax)^(n-3) (1/x)^(3) = 5/2 rArr .^(n)C_(3) a^(n-3)x^(n-6) = 5/2" "(1)`
`rArr n = 6` [`:'` R.H.S. is independent of x]
Putting`n = 6`in (1), we get `.^(6)C_(3) a^(3) = 5/2` or `a^(3) = 1/8` or `a = 1/2`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Matrix|3 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Single)|90 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

  • BINOMIAL THEORM

    CENGAGE|Exercise Question Bank|31 Videos

Similar Questions

Explore conceptually related problems

n th term in the expansion of (x+(1)/(x))^(2n)

If the 4 th term in the expansion of (ax+1/x)^(n) is 5/2, then a=(1)/(2) b.n=8 c.a=(2)/(3) d.n=6

If 4th term in the expansion of (kx+ 1/x)^n is 5/2 then (A) n=8 (B) n=6 (C) k=1/4 (D) k=1/2

Find the (r+1) th term in the expansion of ((x)/(a)-(a)/(x))^(2n)

If the 4 th term in the expansion of (a x + (1)/(x))^(n) is (5)/(2) , for all x in R then the values of a and n are respectively

Find the 7 th term n the expansion of (3x^(2)-(1)/(x^(3)))^(10)

Prove that the middle term in the expansion of (x+ 1/x)^(2n) is (1.3.5…(2n-1)/(n! 2^n

If the 6th,7th, 8th terms in the expansion of (x+y)^(n) be 112,7 and 1/4 find x,y and n.

CENGAGE-BINOMIAL THEOREM-Exercise (Multiple)
  1. The value of x in the expression (x+x^((log)(10)))^5 if third term in ...

    Text Solution

    |

  2. the value of x , for which the 6th term in the expansions of[2^log2sqr...

    Text Solution

    |

  3. If the 4th term in the expansion of (a x+1//x)^n is 5/2, then a=1/2 b....

    Text Solution

    |

  4. In the expansion of (x+a)^n if the sum of odd terms is P and the sum o...

    Text Solution

    |

  5. If (4+sqrt(15))^n=I+f,w h r en is an odd natural number, I is an integ...

    Text Solution

    |

  6. If the coefficients of x^39 and x^40 are equal in the expansion of (p+...

    Text Solution

    |

  7. The sum of the coefficient in the expansion of (1+ax-2x^(2))^(n) is

    Text Solution

    |

  8. Let (1+x^(2))^(2) (1+x)^(n) = sum(k=0)^(n+4) a(k)x^(k).. If a(1), a(2)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. Which of the following is/are true ?

    Text Solution

    |

  15. If sum(r=0)^(n) (n)/(""^(n)C(0))= sum(r=0)^(n) (n^(2)-3n+3)/(2.""^(n)C...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |