Home
Class 11
MATHS
Let R =(5 sqrt5+11)^(2n+1) and and f=R-[...

Let `R =(5 sqrt5+11)^(2n+1)` and and f=R-[R], where [ ] denotes the greatest integer function, prove that `Rf=4^(2n+1)`.

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    MODERN PUBLICATION|Exercise EXERCISE|221 Videos
  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|291 Videos

Similar Questions

Explore conceptually related problems

f(x)=1/sqrt([x]^(2)-[x]-6) , where [*] denotes the greatest integer function.

If f(x) =[ sin ^(-1)(sin 2x )] (where, [] denotes the greatest integer function ), then

int_(-1)^(2)[([x])/(1+x^(2))]dx , where [.] denotes the greatest integer function, is equal to

If f(x)=(sin([x]pi))/(x^2+x+1) , where [dot] denotes the greatest integer function, then

f(x)= cosec^(-1)[1+sin^(2)x] , where [*] denotes the greatest integer function. then range of f(x) is

Find the domain and range of f(x)=log[ cos|x|+1/2] ,where [.] denotes the greatest integer function.

Let f(x)=sqrt([sin 2x] -[cos 2x]) (where I I denotes the greatest integer function) then the range of f(x) will be

Range of f(x)=[1/(log(x^(2)+e))]+1/sqrt(1+x^(2)), where [*] denotes greatest integer function, is

The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greatest integer function, is discontinuous

The value of lim_(xtoa)[sqrt(2-x)] , where a in[0,1/2] and [.] denotes the greatest integer function is:

MODERN PUBLICATION-BINOMIAL THEOREM-EXERCISE
  1. The letters of the word COCHIN are permuted and all the permutations a...

    Text Solution

    |

  2. The sum of series .^(20)C0-^(20)C1+^(20)C2-^(20)C3+....+^(20)C 10 is

    Text Solution

    |

  3. In the binomial expansion of (a -b)^n, nge5, the sum of the 5th and 6t...

    Text Solution

    |

  4. How many different words can be formed by jumbling the letters of the ...

    Text Solution

    |

  5. The number of 7-digit integers, with sum of the digits equal to 10 and...

    Text Solution

    |

  6. The remainder left out when 8^(2n) - (62)^(2n +1) is divided by 9 , i...

    Text Solution

    |

  7. From 6 different novels and 5 different dictionaries, 4 novels and 1 d...

    Text Solution

    |

  8. There are two urns. Urn A has 4 distinct red balls and urn B has 5 dis...

    Text Solution

    |

  9. There are 10 points in a plane, out of these 6 are collinear. If N is ...

    Text Solution

    |

  10. For r = 0 ,1,2,…, 10 , letA(r), B(r) "and " C(r) denote respectively ,...

    Text Solution

    |

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

    Text Solution

    |

  12. Find the number of ways in which five identical balls can be distribut...

    Text Solution

    |

  13. A committee of 12 is to be formed from nine women and eight men. In ho...

    Text Solution

    |

  14. A committee of 12 is to be formed from nine women and eight men. In ho...

    Text Solution

    |

  15. A question paper consists of two sections having respectively 3 and 4 ...

    Text Solution

    |

  16. Let R =(5 sqrt5+11)^(2n+1) and and f=R-[R], where [ ] denotes the grea...

    Text Solution

    |

  17. Give that : C1+2C2 x+3C3 x^2+.....+2n. C(2n). x^(2n-1)=2n(1+x)^(2n-1)...

    Text Solution

    |

  18. Prove that underset(r=1)overset(k)sum(-3)^(r-1) .^(3n)C(2r-1) = 0 , wh...

    Text Solution

    |

  19. If a(0),a(1),a(2) ,…, a(2n) are the coefficients in the expansion ...

    Text Solution

    |

  20. Find the value of x for which the sixth term of : (sqrt(2^(log(10-3^x)...

    Text Solution

    |