Home
Class 12
MATHS
Let [x] denote the greatest integer part...

Let `[x]` denote the greatest integer part of a real number x, if `M sum_(n=1)^(40)[(n^(2))/(2)]` then M equals

A

5700

B

5720

C

5740

D

11060

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos
  • EQUATIONS

    RESONANCE|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |7 Videos

Similar Questions

Explore conceptually related problems

Let [N] denote the greatest integer part of a real number x.If M=sum_(n=1)^(40)[(n^(2))/(2)] then M equals

Let [x] denote the greatest integer less than or equal to x . Then, int_(1)^(-1)[x]dx=?

If [x] be the greatest integer less than or equal to x then sum_(n=8)^(100) [ ((-1)^n n)/(2)] is equal to :

where f (n) = [(1)/(3) + (3n)/(100)] n, where [ n] denotes the greatest integer less than or equal to n. Then sum_(n=1)^(56)int (n) is equal to :

Let [x] denote the greatest integer less than or equal to x for any real number x. then lim_(xrarroo)([nsqrt2])/(n) is equal to

For eR let [x] denote the greatest integer <=x. Largest natural number n for which E=[(pi)/(2)]+[(1)/(100)+(pi)/(2)]+[(2)/(100)+(pi)/(2)]+[(n)/(100)+(pi)/(2)]<43

Let [x] denotes the greatest integer less than or equal to x and f(x)= [tan^(2)x] .Then

RESONANCE-DPP-QUESTION
  1. Let alpha,beta,gamma and delta are four positive real numbers such tha...

    Text Solution

    |

  2. If the sum of the series S=1+5/11+12/((11)^2)+22/((11)^3)+35/((11)^4)+...

    Text Solution

    |

  3. Let [x] denote the greatest integer part of a real number x, if M sum(...

    Text Solution

    |

  4. Then sum sum(r=1)^(50) r.(2^(r)+2^(50-r)) equals

    Text Solution

    |

  5. lf abcd=1 where a,b,c,d are positive reals then the minimum value of ...

    Text Solution

    |

  6. Solve for x:log(2)(sin""(x)/(2))lt-1

    Text Solution

    |

  7. Suppose that P(x) is a quadratic polynomial such that P(0)=cos^3 40^@,...

    Text Solution

    |

  8. Let y=ax^2+ bx + c be a quadratic expression having its vertex at (3,-...

    Text Solution

    |

  9. Let y=ax^(2)+bx+c be a quadratic expression have its vertex at (3-2) a...

    Text Solution

    |

  10. Through the centriod of an equilateral triangle a line parallel to the...

    Text Solution

    |

  11. Let 'X' denotes the value of the product.(1+a+a^2+a^3+.........oo)(1+b...

    Text Solution

    |

  12. 50th term of the sequence 3+12+25+42+ is 5145 b. 5148 c. 5142 d. 5195

    Text Solution

    |

  13. Consider two quadratic expression f(x)=ax^(2)+bx+c and g(x)=ax^(2)+px+...

    Text Solution

    |

  14. Let alpha, beta be the roots of x^(2)-x+p=0and gamma,delta"be the root...

    Text Solution

    |

  15. Let f(theta) = 1/2 + 2/3 cosec^(2)theta + 3/8 sec^(2) theta. The least...

    Text Solution

    |

  16. If f(x)=(1-s in2x+cos2x)/(2cos2x) , then the value of f(16^0)dotf(29^0...

    Text Solution

    |

  17. If P = (tan(3^(n+1)theta) - tan theta) and Q = sum(r=0)^(n) (sin(3^(r)...

    Text Solution

    |

  18. Let a sequence whose n^(th) term is {a(n)} be defined as a(1) = 1/2 ...

    Text Solution

    |

  19. Which of the following are the solutons of equations 2sin 11x + cos 3x...

    Text Solution

    |

  20. If cos3theta + sin3theta+(2sin2theta-3)(sintheta-costheta) lt 0, then ...

    Text Solution

    |