Home
Class 12
MATHS
Find the coefficients of x^(50) in the e...

Find the coefficients of `x^(50)` in the expression `(1+x)^(1000)+2x(1+x)^(999)+3x^2(1+x)^(998)++1001 x^(1000)` .

A

`""^(1001)C_(50)`

B

`""^(1000)C_(50)`

C

`""^(1002)C_(50)`

D

`""^(1002)C_(51)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICS TIPS

    FIITJEE|Exercise ASSIGNMENT -OBJECTIVE|84 Videos

  • MATHEMATICS TIPS

    FIITJEE|Exercise ASSERTION - REASONING|8 Videos

  • MATHEMATICS TIPS

    FIITJEE|Exercise NUMERICAL DECIMAL BASED QUESTIONS|21 Videos

  • MATHEMATICS

    FIITJEE|Exercise NUMERICAL DECIMAL BASED QUESTIONS|15 Videos

  • MATRICES

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

Find the coefficients of x^(50) in the expression (1+x)^(1000)+2x(1+x)^(999)+3x^(2)(1+x)^(998)+...+1001x^(1000)

Find the coefficients of x^4 in the expansion of (1+x+x^2)^3

Find the coefficient of x^(50) in the expansion of (1+x)^(101)xx(1-x+x^(2))^(100)

Find the coefficient of x^(n) in the expansion of (1)/((1-x)(1-2x)(1-3x))

Find the coefficient of x in the expansion of (1 - 3x + 7x^(2)) (1 - x)^(16) .

Find the coefficient of x^(13) in the expansion of (1-x)^(5)xx(1+x+x^(2)+x^(2))^(4)

Find the coefficient of : x in the expansion of (1-3x+7x^(2))(1-x)^(16)

Find the coefficient of x^3 in the expansion of 1+(1+x)+(1+x)^2+(1+x)^3+...+(1+x)^n

FIITJEE-MATHEMATICS TIPS-ASSIGNMENT (SECTION (I) : MCQ (SINGLE CORRECT)
  1. The coefficient of x^(53) in the expansion sum(m=0)^(100)^(100)Cm(x-3)...

    Text Solution

    |

  2. If x^(2)+ax+b=0 and x^(2)+bx+a=0,(a ne b) have a common root, then a+b...

    Text Solution

    |

  3. Find the coefficients of x^(50) in the expression (1+x)^(1000)+2x(1+x)...

    Text Solution

    |

  4. Let R=(5sqrt(5)+11)^(2n+1)a n df=R-[R]w h e r e[] denotes the greatest...

    Text Solution

    |

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

    Text Solution

    |

  6. If (1+x)^(n) = C(0)+C(1)x + C(2) x^(2) +...+C(n)x^(n) then C(0)""^...

    Text Solution

    |

  7. (1)/(n!) +(1)/(2!(n-2)!) +(1)/(4!(n-4)!) +... is equal to

    Text Solution

    |

  8. If x + y = 1, then sum(r-0)^n r nCr x^r y^(n-r) equals

    Text Solution

    |

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

    Text Solution

    |

  10. The total number of ways of selecting two numbers from the set {1,,...

    Text Solution

    |

  11. Total numbers of regions in which 'n' coplanar lines can divide the pl...

    Text Solution

    |

  12. The total number of ways of selecting 10 balls out of an unlimited num...

    Text Solution

    |

  13. n different toys have to be distributed among n children. Find the num...

    Text Solution

    |

  14. If b^(2) lt 2ac, the equation ax^(3)+bx^(2)+cx+d=0 has (where a, b, c,...

    Text Solution

    |

  15. There are n numbered seats around a round table. Total number of ways ...

    Text Solution

    |

  16. Total number of ways in which 4 boys and 4 girls can be seated around ...

    Text Solution

    |

  17. If letters of the word 'KUBER' are written in all possible orders and ...

    Text Solution

    |

  18. The total number of ways in with three distinct numbers in A.P. can...

    Text Solution

    |

  19. Two players P1a n dP2 play a series of 2n games. Each game can resu...

    Text Solution

    |

  20. Total number of ways in which the letters of the word 'MISSISSIPPI' ca...

    Text Solution

    |