Home
Class 12
MATHS
The sum of [1/2]+[1/2+1/(2000)]+[1/2+2/(...

The sum of `[1/2]+[1/2+1/(2000)]+[1/2+2/(2000)]+[1/2+3/(2000)]++[1/2+(1999)/(2000)]` where [.] denote the greatest integer function, is equal to: 1000 (b) 999 (c) 1001 (d) none of these

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    RESONANCE DPP|Exercise All Questions|4 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    RESONANCE DPP|Exercise All Questions|62 Videos

Similar Questions

Explore conceptually related problems

[(1)/(2)]+[(1)/(2)+(1)/(1000)]+*[(1)/(2)+(2946)/(1000)] where [.] denote greatest integer function ?

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

int[cot x]dx ,where [.] denotes the greatest integer function,is equal to (1)pi/2 (2) 1(3) (4)

int_(-1)^(2)[([x])/(1+x^(2))]dx, where [.] denotes the greater integer function,is equal to -2(b)-1zero (d) none of these

The value of int_(0)^(2)[x^(2)-x+1]dx (where,[*] denotes the greatest integer function) is equal to

The value of int_(-2)^(1)[x[1+cos((pi x)/(2))]+1]dx where [.] denotes the greatest integer function,is 1 (b) 1/2 (c) 2 (d) none of these

The value of int_(0)^(2)[x^(2)-x+1] dx (where , [.] denotes the greatest integer function ) is equal to

The value of int_(-1)^(3){|x-2|+[x]} dx , where [.] denotes the greatest integer function, is equal to

he value of 1=int_(0)^(3)([x]+[x+(1)/(3)]+[x+(2)/(3)])dx where [.] denotes the greatest integer function is equal to

RESONANCE DPP-BOARD PAPER SOLUTIONS-All Questions
  1. The number N=(1+2(log)3 2)/((1+(log)3 2)^2)+log6 2 2 when simplified r...

    Text Solution

    |

  2. The complete solution set of the inequation, -2<[x+2]lt=5w h e r e[dot...

    Text Solution

    |

  3. The sum of [1/2]+[1/2+1/(2000)]+[1/2+2/(2000)]+[1/2+3/(2000)]++[1/2+(1...

    Text Solution

    |

  4. Number of roots of equation 3^(|x|)-|2-|x||=1 is a. 0 b. 2 c. 4 d. 7

    Text Solution

    |

  5. Number of solution satisfying, sqrt(5-(log)2x)=3-(log)2x are: 1 (b) 2 ...

    Text Solution

    |

  6. If x=(log)k b=(log)b c=1/2(log)c d , then (log)k d is equal to 6x (b)...

    Text Solution

    |

  7. The number of solution of the equation, log (-2x)=2"log"(x+1) is a. ze...

    Text Solution

    |

  8. Number of integral solutions of the equation (log)(x-3)((log)(2"x"^2-2...

    Text Solution

    |

  9. Find the equation of whose roots is greater by unity than the roots...

    Text Solution

    |

  10. For theta in(0,pi/2) , the maximum value of sin(theta+pi/6)+cos(theta+...

    Text Solution

    |

  11. the quadratic equation x^2-9x+3=0 has roots alpha and beta. If x^2-bx-...

    Text Solution

    |

  12. If product of the roots of the equation 3x^2-4x+(loga^2-log(-a)+3)=0 i...

    Text Solution

    |

  13. If every pair from among the equations x^2+px+qr=0,x^2+qx+rp=0 and x...

    Text Solution

    |

  14. The roots alphaa n dbeta of the quadratic equation a x^2+b x+c=0 are r...

    Text Solution

    |

  15. x^2-2x+2=0"( 2)"x^2-3x+3=0x^2-3x+4=0"( 4)"x^2-5x+5=0 A quadratic equat...

    Text Solution

    |

  16. If the equation sin^4x-(k+2)sin^2x=(k+3) has a solution then ' k ' mus...

    Text Solution

    |

  17. Simplify: 5^(1/((log)7log))+1/(sqrt(-(log)(10)(0. 1)))3

    Text Solution

    |

  18. A polynomial P(x) of third degree vanish when x=1 & x=-2 . This polyno...

    Text Solution

    |

  19. A polynomial P(x) of third degree vanish when x=1 & x=-2 . This polyno...

    Text Solution

    |

  20. Let cos(alpha+beta)=4/5 and let sin(alpha-beta)=5/(13),w h e r e0lt=al...

    Text Solution

    |