Home
Class 11
MATHS
The fractional part of =(2^(4n))/15 is...

The fractional part of =`(2^(4n))/15` is

A

`15/2`

B

`15/3`

C

`15/4`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS

    PATHFINDER|Exercise QUESTION BANK |266 Videos
  • BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

If the fractional part of the number (2^(403))/(15) is (k)/(15) then k is equal to

The period of function 2^({x}) +sin pi x+3^({x//2})+cos pi x (where {x} denotes the fractional part of x) is

Find the remainder and the fractional part when 5^(99) is divided by 13. Also, prove that the integral part of the number (5^(99))/(13) is odd.

Solve : x^(2) = {x} , where {x} represents the fractional part function.

The fractional part of the sum of all the rational terms in the expansion of (3^(1/4) +4^(1/3))^(12) is ______

Evaluate the following limits (if exists), where {,} denotes the fractional part of x and [,] denotes the greatest integer part lim_(x rarr 4) [(cos alpha)^x-(sin alpha)^x-cos 2alpha]/[(x-4)], a in (0, pi//2)

Evaluate the following limits (if exists), where {,} denotes the fractional part of x and [,] denotes the greatest integer part lim_(x rarr 0) (cos^2(1-cos^2(1-cos^2.......cos^2(x)......)))/(sin[pi((sqrt(x+4) - 2)/x) ]

The domain of the function f(x)=1/(sqrt({sinx}+{sin(pi+x)})) where {dot} denotes the fractional part, is (a) [0,pi] (b) (2n+1)pi/2, n in Z (c) (0,pi) (d) none of these

In the questions, [x]a n d{x} represent the greatest integer function and the fractional part function, respectively. Solve: [x]^2-5[x]+6=0.

In the questions, [x]a n d{x} represent the greatest integer function and the fractional part function, respectively. If y=3[x]+1=4[x-1]-10 , then find the value of [x+2y]dot

PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. The value of 1^2cdotC1+3^2cdotC3+5^2cdotC5+......, is

    Text Solution

    |

  2. Let [x] denotes the greatest integer less then or equal to x. If x=(sq...

    Text Solution

    |

  3. The fractional part of =(2^(4n))/15 is

    Text Solution

    |

  4. If p=(8+3sqrt7)^n and f=p-[p], where [.] denotes the greatest integer ...

    Text Solution

    |

  5. Maximum sum of coefficient in the expansion of (1-xsintheta+x^2)^n is

    Text Solution

    |

  6. If n in N then value of S=sum(r=0)^n(-1)^r((^nCr)/(^(r+2)Cr)) is

    Text Solution

    |

  7. The value of the expression .^47C4 + sum(j = 1)^5.^(52 - j)C3 is equal...

    Text Solution

    |

  8. The sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+.....oo

    Text Solution

    |

  9. Determine the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^n.

    Text Solution

    |

  10. If an=sum(r=0)^n1/(^nCr) , then sum(r=0)^nr/(^nCr) equals

    Text Solution

    |

  11. The number of real negative terms in the binomial expansion of (1+ix)^...

    Text Solution

    |

  12. Let f(n)=10^n+3 . 4^(n+2)+5, n in N. The greatest integer which divide...

    Text Solution

    |

  13. The value of the sum of the series 3cdot^nC0+8cdot^nC1+13cdot^nC2-18cd...

    Text Solution

    |

  14. For natural numbers m, n if (1-y)^m(1+y)^n=1+a1y+a2y^2+.... and a1=a2=...

    Text Solution

    |

  15. The coefficient of the term independent of x in the expansion of [((x+...

    Text Solution

    |

  16. The coefficient of a^3b^4c in the expansion of (1+a-b+c)^9 is equal to

    Text Solution

    |

  17. The remainder when 9^(103) is divided by 25 is equal to

    Text Solution

    |

  18. If (3+x^(2008)+x^(2009))^(2010)=a0+a1x^2+....+anx^n, a0-1/2 a1-1/2 a2+...

    Text Solution

    |

  19. The coefficient of x^ny^n in the expansion of {(1+x)(1+y)(x+y)}^n is

    Text Solution

    |

  20. The remainder when x=5^(5^(5^(......))) (23 times 5) is divided by 24 ...

    Text Solution

    |