Home
Class 12
MATHS
u(n) = |{:(1,,k,,k),(2n,,k^(2)+k+1,,k^(2...

`u_(n) = |{:(1,,k,,k),(2n,,k^(2)+k+1,,k^(2)+k),(2n-1,,k^(2),,k^(2)+k+1):}|`and
`sum_(n=1)^(k) u_(n)=72` then k=

A

8

B

9

C

6

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have

[Applying `C_(2)toC_(2)-C_(1)`]
`k(k^(2)+k+1)-K(3)=k(k+1)=71`
`k=8`
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 4

    CAREER POINT|Exercise MATHS|30 Videos

  • MOCK TEST 6

    CAREER POINT|Exercise Part (C) (MATHS)|30 Videos

Similar Questions

Explore conceptually related problems

if D_(k) = |{:( 1,,n,,n),(2k,,n^(2)+n+1 ,,n^(2)+n),(2k-1,,n^(2),,n^(2)+n+1):}|" and " Sigma_(k=1)^(n) D_(k)=56 then n equals

if U_n = |[1 , k , k] , [2n , k^2+k+1 , k^2+k] , [2n-1 , k^2 , k^2+k+1]| and sum_(k=1->n)U_n=72 then value of k is:

If Delta_(k) = |(k,1,5),(k^(2),2n +1,2n +1),(k^(3),3n^(2),3n +1)|, " then " sum_(k=1)^(n) Delta_(k) is equal to

If U_(n) = |[1,K,K],[2n,K^(2)+K+1,K],[2n+1,K^(2)+K+1,K]| and sum_(n=1)^(K)U_(n)=-90 then absolute value of K is equal to

sum_(k =1)^(n) k(1 + 1/n)^(k -1) =

Find the sum_(k=1)^(oo) sum_(n=1)^(oo)k/(2^(n+k)) .

sum_(k=1)^(2n+1)(-1)^(k-1)k^(2)=

If Delta_k=|(1,n,n), (2k, n^2+n+1, n^2+n), (2k-1, n^2, n^2+n+1)| and sum_(k=1)^n Delta_k = 56, then n is equal to (i)4 (ii)6 (iii)8 (iv)none

Let U_(n)=sum_(k=1)^(n)(n)/(n^(2)+k^(2)),S_(n)=sum_(k=0)^(n-1)(n)/(n^(2)+k^(2)) then

CAREER POINT-MOCK TEST 5-Part (C) (MATHS)
  1. Total number of integral values of 'a' so that x^(2)-(a+1)x+a-1=0 has ...

    Text Solution

    |

  2. If a,b,c,d are such unequal real numbers that (a^(2)+b^(2)+c^(2))p^(2)...

    Text Solution

    |

  3. If (x) donotes the greates integer lex, then the value of int(4)^(10)...

    Text Solution

    |

  4. The area of the portion of the circle x^(2)+y^(2)=1 which lies inside ...

    Text Solution

    |

  5. Solution of the differential equation x dy -y dx = 0 represents-

    Text Solution

    |

  6. k=lim(xtooo)[(sum(k=1)^(1000)(x+k)^(m))/(x^(m)+10^(1000))] (mgt101) is...

    Text Solution

    |

  7. if roots of ax^(2)+bx+c=0 where epsiR^(+), are two positive consecutiv...

    Text Solution

    |

  8. If cos^(-1)(cosx)=sqrt(1sin2x)AAxepsi(0,2pi), then no. of solution =

    Text Solution

    |

  9. For a what value (s) of a, will the two points (1,a,1) and (-3,0,a) li...

    Text Solution

    |

  10. The number of integer values of x for which the inequality "log "(10) ...

    Text Solution

    |

  11. If three vectors (sec^(2)A) hati+hatj+hatk, hati+(sec^(2)B)hatj+hatk,...

    Text Solution

    |

  12. Maximum value of the expression (10x^(12))/(x^(24)+2x^(12)+3x^(16)+...

    Text Solution

    |

  13. if f be a differentiable function such that f(x) =x^(2)int(0)^(x)e^(-t...

    Text Solution

    |

  14. For what values of a, m and b, Lagrange's mean value theerorem is appl...

    Text Solution

    |

  15. The value of x for which f(x)=(sin.({x})/({x})+cos.({x})/({x})) is max...

    Text Solution

    |

  16. If l^r(x) means logloglog.......x being repeated r times, then int [ (...

    Text Solution

    |

  17. Consider the non-empty set consisting of children in a family and a r...

    Text Solution

    |

  18. u(n) = |{:(1,,k,,k),(2n,,k^(2)+k+1,,k^(2)+k),(2n-1,,k^(2),,k^(2)+k+1):...

    Text Solution

    |

  19. Let (p) x be a polynomial of degree 4 having extemum at x= 1,2 and lim...

    Text Solution

    |

  20. The mean of 50 observation is 36. if two observation 30 and 42 are to ...

    Text Solution

    |