Home
Class 11
MATHS
Let [x] denotes the greatest integer les...

Let [x] denotes the greatest integer less then or equal to x. If `x=(sqrt3+1)^5`, then [x] is equal to

A

75

B

50

C

152

D

151

Text Solution

Verified by Experts

The correct Answer is:
C
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

Let [x] denotes the greatest integer less than or equal to x. If f(x) =[x sin pi x] , then f(x) is

if [x] denotes the greatest integer less than or equal to x then integral int_0^2x^2[x] dx equals

Let [x] denotes the greatest integer less than or equal to x . If the function f(x)="tan"(sqrt([n])x) has period pi/3dot then find the value of ndot

Let [x] denote the greatest integer less than or equal to x, then the value of the integral int_(-1)^(1)(|x|-2[x])dx is equal to-

Let [ x ] denote the greatest integer less than or equal to x, then the value of the integral int_-1^1 (absx - 2[x]) dx is equal to

Let [x] denote the greatest integer less than or equal to x for any real number x. Then lim_(n to oo) ([n sqrt(2)])/(n) is equal to

Let [x] denote the greatest integer less than or equal to x for any real number x. Then underset(n tooo)lim([nsqrt(2)])/(n) is equal to-

If f(x)={:(sin[x]","" ""for "[x]ne0),(0","" ""for "[x]=0):} where [x] denotes the greatest integer less than or equal to x. Then find lim_(xto0)f(x).

let [] denotes the greatest integer less than or equal to x and f(x) = sin x + cos x . Then find the most general solution of f(x) = [f(pi/10)] .

Let f(x)=[tanx[cotx]], x in [(pi)/(12),(pi)/(2)), (where [.] denotes the greatest integer less than or equal to x). The number of points, where f(x) is discontinuous is

PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. .^18C15+2(.^18C16)+^17C16+1=^nC3, then n is equal to

    Text Solution

    |

  2. The value of 1^2cdotC1+3^2cdotC3+5^2cdotC5+......, is

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |