Home
Class 12
MATHS
Cofficient of x^(4) in the expansion of ...

Cofficient of `x^(4)` in the expansion of `(1-3x+x^(2))/(e^(x))` is

A

`(5)/(24)`

B

`(4)/(25)`

C

`(24)/(25)`

D

`(25)/(24)`

Text Solution

AI Generated Solution

To find the coefficient of \( x^4 \) in the expansion of \( \frac{1 - 3x + x^2}{e^x} \), we can follow these steps: ### Step 1: Rewrite the expression We start with the expression: \[ \frac{1 - 3x + x^2}{e^x} \] This can be rewritten as: ...
Promotional Banner

Topper's Solved these Questions

  • EXPONENTIAL AND LOGARITHMIC SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|26 Videos

  • EXPONENTIAL AND LOGARITHMIC SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|5 Videos

  • ELLIPSE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • HEIGHTS AND DISTANCES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|45 Videos

Similar Questions

Explore conceptually related problems

The coefficient of x^(r) in the expansion of (1-ax-x^(2))/(e^(x)) is

Find the coefficient of x^(5) in the expansion of ((2 + 3x + 4x^(2)))/(e^(x))

The coefficient of x^4 in the expansion of ((1 -3x)^2)/((1 - 2x)) is

The coeffiecinet of x^k in the expansion of (1-2x -x^2)/(e^(-x)) is

The coefficient of x^(4) in the expansion of (1+x+x^(2)+x^(3))^(11) is where ({:(n),(r):}) = nC_(r)

The coefficient of x^(4) in the expansion of (1+x+x^(2))^(6) is

The coefficient of x^(8) in the expansion of (1+x+x^(2)+x^(3))^(4) is

Cofficient of x^(12) in the expansion of (1+x^(2))^50(x+1/x)^(-10)

Coefficient of x^(10) in the expansion of (2+3x)e^(-x) is

The coeffiecient of x^n in the expansion of (e^(7x) +e^x)/(e^(3x)) is

OBJECTIVE RD SHARMA ENGLISH-EXPONENTIAL AND LOGARITHMIC SERIES-Chapter Test
  1. Cofficient of x^(4) in the expansion of (1-3x+x^(2))/(e^(x)) is

    Text Solution

    |

  2. The series expansion of log{(1+x)^(1+x)(1-x)^(1-x)} is

    Text Solution

    |

  3. 2log x-log(x+1)-log(x-1) is equals to

    Text Solution

    |

  4. The coefficient of x^(n) in the expansion of log(e)(1+3x+2x^2) is

    Text Solution

    |

  5. If x ne 0 then the sum of the series 1+(x)/(2!)+(2x^(2))/(3!)+(3x^(3...

    Text Solution

    |

  6. If log(1-x+x^(2))=a(1)x+a(2)x^(2)+a(3)x^(3)+…and n is not a mutiple of...

    Text Solution

    |

  7. If log(1-x+x^(2))=a(1)x+a(2)x^(2)+a(3)x^(3)+… then a(3)+a(6)+a(9)+.....

    Text Solution

    |

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

    Text Solution

    |

  9. The coeffiecent of n^(-r) in the expansion of log(10)((n)/(n-1)) is

    Text Solution

    |

  10. The sum of the series (x-1)/(x+1)+1/2(x^(2)-1)/(x+1)^(2)+1/3(x^(3)-1...

    Text Solution

    |

  11. The sum of series 2[ 7^(-1)+3^(-1).7^(-3)+5^(-1).7^(-5)+...] is

    Text Solution

    |

  12. The coefficient of x^(6) in the expansion of log{(1+x)^(1+x)(1-x)^(...

    Text Solution

    |

  13. The sum of the series 1/2x^2+2/3x^3+3/4x^4+4/5x^5+... is :

    Text Solution

    |

  14. If x,y,z are three consecutive positive integers and X-Z + 2 = 0, then...

    Text Solution

    |

  15. The sum of the series ((1)^(2).2)/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+(...

    Text Solution

    |

  16. The value of 1-log(e)2+(log(e)2)^(2)/(2!)-(log(e)2)^(3)/(3!)+.. is

    Text Solution

    |

  17. 1+(loge n)^2 /(2!) + (loge n )^4 / (4!)+...=

    Text Solution

    |

  18. (2)/(3!)+(4)/(5!)+(6)/(7!)+..is equal to

    Text Solution

    |

  19. Sum of n terms of the series 1/(1.2.3.4.)+1/(2.3.4.5) +1/(3.4.5.6)+.....

    Text Solution

    |

  20. The value of 1+(log(e)x)+(log(e)x)^(2)/(2!)+(log(e)x)^(3)/(3!)+…inft...

    Text Solution

    |

  21. If |x|lt1 then the coefficient of x^(3) in the expansion of log(1+x+x^...

    Text Solution

    |