Home
Class 12
MATHS
In the expansion of (x^3-1/(x^2))^n ,n i...

In the expansion of `(x^3-1/(x^2))^n ,n in N` , if the sum of the coefficients of `x^5a n dx^(10)` , then `n` is a. 25 b. 20 c. 15 d. none of these

A

`25`

B

`20`

C

`15`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `((1)/(x^(2))-x^(3))^(n)`
`T_(r+1)=(n!)/(r!(n-r)!)(-1)^(n-r)x^(5r-2n)`
If `5r-2n=5`, then `5r=2n+5`
`r=(2n)/(5)+1`
If `5r-2n=10`, then `5r=2n+10`
`r=(2n)/(5)+2`
Let `n=5k`
According to question
`(5k!)/((2k+1)!(3k-1)!)-(5k!)/((2k+2)!(3k-2)!)=0`
`(1)/(3k-1)-(1)/(2k+2)=0`
`k=3`, `n=15`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Multiple Correct Answer|4 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Comprehension|11 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise JEE Previous Year|16 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

  • BINOMIAL THEORM

    CENGAGE|Exercise Question Bank|31 Videos

Similar Questions

Explore conceptually related problems

In the expansion of (x^(3)-(1)/(x^(2)))^(n),n in N if sum of the coefficients of x^(5) and x^(10) is 0 then n is

If in the expansion of (x^3-1/x^2)^n the sum of the coefficients of x^5 and x^10 is 0 , then the coefficient of :the third term

In the expansion of (3^(-(x)/(4))+3^((sx)/(4)))^(n),n in N if sum of the binomial coefficients is 64 then n is:

If the sum of the coefficients in the expansion of (1-3x+10x^(2))^(n) isa and if the sum of the coefficients in the expansion of (1+x^(2))^(n) isb, then a=3b b.a=b^(3) c.b=a^(3) d.none of these

What is the sum of the coefficients in the expansion of (1+x)^(n) ?

If n in N , then the sum of the coefficients in the expansion of the binomial (5 x - 4y)^(n) , is

CENGAGE-BINOMIAL THEOREM-Single correct Answer
  1. If the constant term in the binomial expansion of (x^2-1/x)^n ,n in N...

    Text Solution

    |

  2. If p^(4)+q^(3)=2(p gt 0, q gt 0), then the maximum value of term indep...

    Text Solution

    |

  3. In the expansion of (x^3-1/(x^2))^n ,n in N , if the sum of the coeff...

    Text Solution

    |

  4. Find the coefficient of t^8 in the expansion of (1+2t^2-t^3)^9.

    Text Solution

    |

  5. The term independent of 'x' in the expansion of (9x-(1)/(3sqrt(x)))^(1...

    Text Solution

    |

  6. In the expansion of ((x)/(costheta)+(1)/(xsintheta))^(16), if l(1) is ...

    Text Solution

    |

  7. If A(i,j) be the coefficient of a^i b^j c^(2010-i-j) in the expansion ...

    Text Solution

    |

  8. The coefficient of x^(301 ub the expansion of (1+x)^(500)+x(1+x)^(499)...

    Text Solution

    |

  9. The coefficient of x^70 in the product (x-1)(x^2-2)(x^3-3)....(x^12-12...

    Text Solution

    |

  10. Given (1-x^(3))^(n)=sum(k=0)^(n)a(k)x^(k)(1-x)^(3n-2k) then the value ...

    Text Solution

    |

  11. Find the sum of the roots (real or complex) of the equation x^2001 + (...

    Text Solution

    |

  12. If the 4^(th) term of {sqrt(x^((1)/(1+log(10)x)))+root(12)(x)}^(6) is ...

    Text Solution

    |

  13. The number of distinct terms in the expansion of (x+y^(2))^(13)+(x^(2)...

    Text Solution

    |

  14. The value of sum(r=1)^n(sum(p=0)^(r-1) ^nCr ^rCp 2^p) is equal to

    Text Solution

    |

  15. If in the expansion of (x^(3)-(2)/(sqrt(x)))^(n) a term like x^(2) exi...

    Text Solution

    |

  16. In (3 3+1/(3 3))^n if the ratio of 7th term from the beginning to the ...

    Text Solution

    |

  17. The number of distinct terms in the expansion of is (x^(3)+(1)/(x^(3))...

    Text Solution

    |

  18. If r^[th] and (r+1)^[th] term in the expansion of (p+q)^n are equal, ...

    Text Solution

    |

  19. If (3+asqrt2)^100+(3+bsqrt2)^100=7+5sqrt2 number of pairs (a, b) for...

    Text Solution

    |

  20. The middle term in the expansion of (1-3x+3x^2-x^3)^(2n) is

    Text Solution

    |