Home
Class 11
MATHS
If 1^2+2^2+3^2++2003^2=(2003)(4007)(334)...

If `1^2+2^2+3^2++2003^2=(2003)(4007)(334) `and `(1)(2003)+(2)(2002)+(3)(2001)++(2003)(1)=(2003)(334)(x)`, then `x` is equal to a. `2005` b. `2004` c. `2003` d. `2001`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

If z+(1)/(z)+1=0, "then" z^(2003)+(1)/(z^(2003)) is equal to

(lim)_(x->0)(sin2x)/x is equal to a. 1 b . 1/2 c. 2 d. 0

If x=(7+5sqrt(2))^(1/3)-1/((7+5sqrt(2))^(1/3)) , then the value of x^3+3x-14 is equal to 1 b. 0 c. 2 d. 4

If f(x)=x^3-x^2+100x+2002 ,t h e n f(1000)>f(1001) f(1/(2000))>f(1/(2001)) f(x-1)>f(x-2) f(2x-3)>f(2x)

If 3tan^(-1)(1/(2+sqrt(3)))-tan^(-1)1/x=tan^(-1)1/3, then x is equal to 1 (b) 2 (c) 3 (d) sqrt(2)

Let x=|(x1),(x2),(x3)|,A=|(1,-1, 2),( 2, 0, 1),( 3, 2, 1)|a n d B=[(3),( 2),( 1)]dotIfA X=B , Then X is equal to

If x = (1 ^(2))/(1) =+ (2 ^(2))/( 3) + (3 ^(2))/( 5) +.....+ (1001 ^(2))/( 2001) , y = (1^(2))/(3) + (2 ^(2))/( 5) + (3 ^(2))/(7) + .....+ (1001 ^(2))/(2003), then ([x -y])/(10) is equal to where [.] denotes greatest integer function)

If x=(7+5sqrt(2))^(1/3) -1/((7+5sqrt(2))^(1/3) , then the value of x^3+3x-14 is equal to 1 (b) 0 (c) 2 (d) 4

If (2x^(3)+1)/((x-1)(x+1)(x+2))=A+(B)/(x-1)+(C)/(x+1)+(D)/(x+2) , then find the value of A+B+C+D .

(3x^(2)+x+1)/((x-1)^(4))=(A)/(x-1)+(B)/((x-1)^(2))+(C)/((x-1)^(3))+(D)/((x-1)^(4)) then A+B-C+D=

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If b(n+1)=1/(1-bn)forngeq1a n db1=b3, t h e nsum(r=1)^(2001)b r^ 2001 ...

    Text Solution

    |

  2. Let a1, a2, a3, ,a(100) be an arithmetic progression with a1=3a n dsp...

    Text Solution

    |

  3. If 1^2+2^2+3^2++2003^2=(2003)(4007)(334) and (1)(2003)+(2)(2002)+(3)(2...

    Text Solution

    |

  4. The value of sum(i=1)^nsum(j=1)^isum(k=1)^j1=220 , then the value of ...

    Text Solution

    |

  5. The sum of 0. 2+0.004+0. 00006+0. 0000008+... to oo is a.(200)/(891) ...

    Text Solution

    |

  6. If tn=1/4(n+2)(n+3) for n=1, 2 ,3,.... then 1/t1+1/t2+1/t3+....+1/(t(...

    Text Solution

    |

  7. The coefficient of x^(19) in the polynomial (x-1)(x-2)(x-2^2)(x-2^(19)...

    Text Solution

    |

  8. If 1-1/3+1/5-1/7+1/9-1/(11)+=pi/4 , then value of 1/(1xx3)+1/(5xx7)+1/...

    Text Solution

    |

  9. The positive integer n for which 2xx2^2+3xx2^3+4xx2^4+......+nxx2^n=2...

    Text Solution

    |

  10. If tn denotes the nth term of the series 2+3+6+11+18+...then t(50)...

    Text Solution

    |

  11. The number of positive integral ordered pairs of (a ,b) such that 6,a ...

    Text Solution

    |

  12. Let a ,b >0, let 5a-b ,2a+b ,a+2b be in A.P. and (b+1)^2, a b+1,(a-1)^...

    Text Solution

    |

  13. The difference between the sum of the first k terms of the series ...

    Text Solution

    |

  14. The value of the sum(n=0)^oo(2n+3)/(3^n) is equal to.

    Text Solution

    |

  15. If the roots of 10 x^3-n x^2-54 x-27=0 are in harmonic progression...

    Text Solution

    |

  16. The 5th and 8th terms of a geometric sequence of real numbers are 7! ...

    Text Solution

    |

  17. Let a ,b ,c ,d be four distinct real numbers in A.P. Then the smallest...

    Text Solution

    |

  18. Let a1, a2, a3, ,a(101) are in G.P. with a(101)=25a n dsum(i=1)^(201)...

    Text Solution

    |

  19. Let S=sum(n=1)^(9999)1/((sqrt(n)+sqrt(n+1)) (^4sqrt(n)+^4sqrt(n+1)) , ...

    Text Solution

    |

  20. If the sum of the first 14 terms of an AP is 1050 and its first term i...

    Text Solution

    |