Home
Class 12
MATHS
Find coeff. of x^(25) in the expansion ...

Find coeff. of `x^(25)` in the expansion of `sum_(k=0)^(50)(-1)^(k)""^(50)C_(k)(2x-3)^(50-k)(2-x)^(k)`.

Text Solution

Verified by Experts

The correct Answer is:
`-""^(50)C_(25)5^(25)3^(25)`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise EXERCISE - 1.3 (Level - 1) |42 Videos

  • AREAS

    AAKASH SERIES|Exercise Exercise-3.2|21 Videos

  • CIRCLE

    AAKASH SERIES|Exercise EXERCISE -1.4|38 Videos

Similar Questions

Explore conceptually related problems

Show that the coefficient of x^(k) (0 le k le n) in the expansion of 1+(1+x)+(1+x)^(2)+…+(1+x)^(n) is ""^(n+1)C_(K+1) .

If C_k is the coefficient of x^k in the expansion of (1 + x)^2005 and if a,d are real numbers then sum_(k = 0)^(2005) (a + kd).C_k =

Prove that : If the k^("th") term is the middle term in the expansion of (x^(2)-(1)/(2x))^(20) , find T_(k) and T_(k+3) .

Find the value of k, if (ii) (k)/(x^(2)-4) = (1)/(x-2)-(1)/(x+2)

Given that 0 lt x lt (pi)/(4), (pi)/(4) lt y lt (pi)/(2) and sum_(k = 0)^(infty) (-1)^(k) tan^(2k) x = p, sum_(k = 0)^(infty)(-1)^(k) cot^(2k) y = q then sum_(k = 0)^(infty) tan^(2k) x cot^(2k) y is

If n in N, sum_(k=1)^(n)cos^(-1)(x_(k))=npi then the value of sum_(k=1)^(n)sin^(-1)(x_(k))=

Evaluate sum_(k=1)^11(2+3^k)

AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - 1.4 (Level-2)
  1. Find the coefficient of term independent of x in the expansion of ((x+...

    Text Solution

    |

  2. Find coeff. of x^(25) in the expansion of sum(k=0)^(50)(-1)^(k)""^(5...

    Text Solution

    |

  3. Find the coefficient of x^6 in the expansion of (1+ x^2 - x^3)^8

    Text Solution

    |

  4. Find the coefficient of x^(10) in the expansion of (1+x^(2)-x^(3))^(8)

    Text Solution

    |

  5. Find the coefficent of x^(6) in (1+3x+9x^(2))^(10)

    Text Solution

    |

  6. If the 6th term in the expansion of ((1)/(x^(8//3))+x^2 log10 x)^8 is ...

    Text Solution

    |

  7. Find the range of values of the term independent of x in (x sin^(-1)p+...

    Text Solution

    |

  8. The remainder when 5^(99) is divided by 13 is

    Text Solution

    |

  9. Find the remainder when 3^(37) is divided with 80 ?

    Text Solution

    |

  10. Find the remainder when 2^(60) is divided with 7.

    Text Solution

    |

  11. Find the number of distinct terms in the expansion (x + 2y + 3z + ...

    Text Solution

    |

  12. Find the number of distinct terms in the following expansions. (x^(2...

    Text Solution

    |

  13. Find the number of distinct terms in the following expansions. (p+q)...

    Text Solution

    |

  14. Find the number of distinct terms in the expansion (x+ y + z)^10+ ...

    Text Solution

    |

  15. Prove that, C(0) *""^(2n)C(n)-C(1)*""^((2n-2))C(n)+C(2) *""^((2n-4))C(...

    Text Solution

    |

  16. If (1+x)^(n)=sum(r=0)^(n)""^(n)C(r )x^(r ) and if sum(r=0)^(n) (1)/(""...

    Text Solution

    |

  17. Prove that C(0)-(1)/(3)*C(1)+(1)/(5)*C(2) - …+(-1)^(n)*(1)/(2n+1)C(n) ...

    Text Solution

    |

  18. If a, b, c, d be 3^(rd), 4^(th), 5^(th) and 6^(th) terms of the expans...

    Text Solution

    |

  19. Show that sum(r=0)^(n) (-1)^(r ). ""^(n)C(r ) {(1)/(2^(r )) +(3^(r ))/...

    Text Solution

    |

  20. If sum(r = 0)^(2n) a(r ) (x-2)^(r ) = sum(r = 0)^(2n) b(r ) (x-3)^(r )...

    Text Solution

    |