Home
Class 12
MATHS
Find the fifth term in the expansion of ...

Find the fifth term in the expansion of `(6x-a^3/x)^10`

Text Solution

Verified by Experts

5th term i.e. (4+1)th term in the expansion of
`(6x-a^3/x)^10` is `"^10C_4 (6x)^(10-4) (-a^3/x)^4`
= `(10!)//4!6! (6x)^6 a^12/x^4` = `(10.9.8.7)/(4.3.2.1) 6^6x^2a^12`
= `210xx6^6x^2a^12`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    MBD PUBLICATION|Exercise QUESTION BANK|87 Videos

  • INTEGRATION

    MBD PUBLICATION|Exercise QUESTION BANK|418 Videos

Similar Questions

Explore conceptually related problems

Find the 6th term in the expansion of (x^2+a^4/y^2)^10 .

Find the middle term in the expansion of the (x+1/x)^9

Find the middle term in the expansion of the (x^(3/2)-y^(3/2))^8

Find the number of terms in the expansion of (1+x)^n(1-x)^n .

Find the middle term in the expansion of the (a/b+b/a)^6 .

Answer the following: If 6th term in the expansion of (x+*)^n is equal to "^nC_5x^(n-10) find *.

Find the 3rd term in expansion of (2x^3-1/x^6)^4 using rules of Pascal Triangle.

Determine the middle term in the expansion of (1/3a+1/3b)^8 .

Find the coefficient of x^4 in the expansion of (1+3x+10x^2)(x+1/x)^10

Find the coefficient of 1/y^10 in the expansion of (y^3+a^7/y^5)^10

MBD PUBLICATION-Elements of Mathematics-QUESTION BANK
  1. Find the middle term in the expansion of the (x^(3/2)-y^(3/2))^8

    Text Solution

    |

  2. Find the 6th term in the expansion of (x^2+a^4/y^2)^10.

    Text Solution

    |

  3. Find the fifth term in the expansion of (6x-a^3/x)^10

    Text Solution

    |

  4. Find the coefficient of 1/y^10 in the expansion of (y^3+a^7/y^5)^10

    Text Solution

    |

  5. In the expansion of (y^3+a^7/y^5)^10, Does there exist a term indepen...

    Text Solution

    |

  6. Find the coefficient of x^4 in the expansion of (1+3x+10x^2)(x+1/x)^10

    Text Solution

    |

  7. Find the term independent of x in the above expansion. (1+3x+10x^2)(x+...

    Text Solution

    |

  8. Show that the coefficient of a^m and a^n in expansion of (1+a)^(m+n) a...

    Text Solution

    |

  9. An expression of the form (a+b+c+d+ .... ) consisting of sum of many d...

    Text Solution

    |

  10. State and prove a multinomial Theorem.

    Text Solution

    |

  11. Prove that "^(2n)C0 + ^(2n)C2 + .... + ^(2n)C(2n) = 2^(2n-1)

    Text Solution

    |

  12. Prove that "^(2n)C1 + ^(2n)C3 + .... + ^(2n)C(2n-1) = 2^(2n-1)

    Text Solution

    |

  13. Find the sum of C1 + 2C2 + 3C3 + .... + nCn

    Text Solution

    |

  14. Find the sum of C0 + 2C1 + 3C2 + .... + (n+1)Cn

    Text Solution

    |

  15. Compute ((1+k)(1+k/2) ..... (1+k/n))/((1+n)(1+n/2) ..... (1+n/k))

    Text Solution

    |

  16. Show that C0 C1 + C1 C2 + C2 C3 + .... + C(n-1) Cn = (2n!)/((n-1)!(n...

    Text Solution

    |

  17. C0 C1 + C1 C2 + .... + C(n-1) Cn = (2^n.n.1.3.5... (2n-1))/(n+1)

    Text Solution

    |

  18. Show that 3C0-8C1 + 13C2 - 18C3 + ..... + (n+1)^(th) term = 0

    Text Solution

    |

  19. Show that C0 n^2 + C1 (2-n)^2 + C2 (4-n)^2 + .... + Cn (2n-n)^2 = n.2^...

    Text Solution

    |

  20. Show that C0 + 3C1 + 5C2 + .... +(2n+1) Cn = (n+1)(2^n)

    Text Solution

    |