Home
Class 12
MATHS
In the expansion of (7^(1/3)+11^(1/9))^(...

In the expansion of `(7^(1/3)+11^(1/9))^(6561)`, the number of terms free from radicals is:

A

`730`

B

`725`

C

`729`

D

`750`

Text Solution

Verified by Experts

The correct Answer is:
A
`T_(r+1) =^(6561) C_(r),(7)^((6561-r)/(3))(11)^((r)/(9))`
`rArr r` is multiple of `9`
`:. r = 0,9,18"…….",6561`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE|Exercise PART : 1MATHEMATICS SEC - 1|1 Videos

  • TEST PAPERS

    RESONANCE|Exercise PART : 1MATHEMATICS|9 Videos

  • TEST PAPER

    RESONANCE|Exercise CHEMISTRY|37 Videos

  • TEST SERIES

    RESONANCE|Exercise MATHEMATICS|131 Videos

Similar Questions

Explore conceptually related problems

If the expansion of (y^(1//2)+x^(1//3))^(54) , the number of terms free from radical sign (number of rational terms) are independent where |x| and |y| have no common factor except 1 annd x,y ne Q, is (1) 9 (2) 8 (3) 10 (4) 11.

In the expansion of (y^(1//5)+x^(1//10))^55 , the number of terms free of radical sign are

The number of terms in the expansion of (1+x^(1/5))^55 which are free from radicals is _____.

In the expansion of (5^(1/2)+7^(1/8))^(1024), the number of integral terms is 128 b.129c.130

In the expansion of (7^(1/3)+11^(1/9))^(6561) (a)there are exactly 730 rational term (bthere are exactly 5831 irrational term (bthe term which involves greatest binomial coefficients is irrational (d)the term which involves greatest binomial coefficients is rational

If the number of terms free from radicals in the expansion of (7^((1)/(3))+11^((1)/(9)))^(6561) is k, then the value of (k)/(100) is equal to

In the expansion of (a^(1/3)+b^(1/9))^6561 , where 'a' and 'b' are distinct prime numbers, then the number of irrational terms are

In the expansion of (1+x+(7)/(x))^(11) find the term not containing x.

RESONANCE-TEST PAPERS-MATHEMATICS
  1. In the expansion of (7^(1/3)+11^(1/9))^(6561), the number of terms fre...

    Text Solution

    |

  2. The least positive integral value of 'k' for which there exists at lea...

    Text Solution

    |

  3. The locus of the midpoint of a chord of the circle x^2+y^2=4 which sub...

    Text Solution

    |

  4. If f(x)=x+tanx and g(x) is inverse of f(x) then g^(')(x) is equal to

    Text Solution

    |

  5. Tangents PA and PB are drawn to parabola y^(2)=4x from any arbitrary p...

    Text Solution

    |

  6. If lim(nrarroo) (n.2^(n))/(n(3x-4)^(n)+n.2^(n+1)+2^(n))=1/2 where "n" ...

    Text Solution

    |

  7. Eccentricity of ellipse 2(x-y+1)^(2)+3(x+y+2)^(2)=5 is

    Text Solution

    |

  8. If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y. Then which ...

    Text Solution

    |

  9. If f:RrarrR is a continuous function satisfying f(0)=1 and f(2x)-f(x)=...

    Text Solution

    |

  10. tan^(-1)(sinx)=sin^(-1)(tanx) holds true for

    Text Solution

    |

  11. is The function f(x)=(x^2-1)|x^2-3x+2|+cos(|x|) is differentiable not ...

    Text Solution

    |

  12. Consider parabola P(1)-=y=x^(2) and P(2)-=y^(2)=-8x and the line L-=lx...

    Text Solution

    |

  13. If the normals at (x(i),y(i)) i=1,2,3,4 to the rectangular hyperbola x...

    Text Solution

    |

  14. Let f(x)=x^(3)-x^(2)+x+1 and g(x)={("max "f(t) 0letlex 0lexle1),(3-x 1...

    Text Solution

    |

  15. The value(s) of x satisfying tan^(-1)(x+3)-tan^(-1)(x-3)=sin^(-1)(3/5)...

    Text Solution

    |

  16. For an ellipse having major and minor axis along x and y axes respecti...

    Text Solution

    |

  17. If f:[0,1]rarrR is defined as f(x)={(x^(3)(1-x)"sin"1/(x^(2)) 0ltxle1)...

    Text Solution

    |

  18. If f(x)=root (3)(8x^(3)+mx^(2))-nx such that lim(xrarroo)f(x)=1 then

    Text Solution

    |

  19. For the curve y=4x^3-2x^5,find all the points at which the tangent pa...

    Text Solution

    |

  20. Minimum value of (sin^(-1)x)^(2)+(cos^(-1)x)^(2) is greater than

    Text Solution

    |

  21. If y+a=m(1)(x+3a),y+a=m(2)(x+3a) are two tangents to the parabola y^(2...

    Text Solution

    |