Home
Class 12
MATHS
Let T(n) denotes the n ^(th) term of a G...

Let `T_(n)` denotes the `n ^(th)` term of a G.P. with common ratio 2 and `(log _(2) (log _(3) ( log _(512) T _(100))))=1.` If three sides of a triangle ABC are the values of `(T _(1) + T _(2)), T_(2) and T_(3)` then area of the triangle is `(sqrt 2160)/(N),` where N is a positive integer. Find the remainder when N is divided by `2 ^(10).`

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos

  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |5 Videos

Similar Questions

Explore conceptually related problems

If t_(n) denotes the n th term of the series 2+3+6+1+18+ …….then t_(50) is

If the angles of a triangle are 30^0a n d45^0 and the included side is (sqrt(3)+1) cm, then area of the triangle is 1/2(sqrt(3)+1)s qdotu n i t s area of the triangle is 1/2(sqrt(3)-1)s qdotu n i t s

Find the domain of f(x)=(log)_(10)(log)_2(log)_(2/pi)(t a n^(-1)x)^(-1)

If (7 + 4 sqrt(3))^(n) + 5 + t , where n and s are positive integers and t is a proper fraction , show that (1 - t) (s + t) = 1

Prove that the area of the triangle whose vertices are (t ,t-2),(t+2,t+2)a n d(t+3,t) is independent of tdot

Find the value of ln(int_(0)^(1) e^(t^(2)+t)(2t^(2)+t+1)dt)

If T_(r)=(1)/(log_(z)4) (where r in N ), then the value of sum_(r=1)^(4) T_(r) is :

If sum _(r =1) ^(n ) T _(r) = (n +1) ( n +2) ( n +3) then find sum _( r =1) ^(n) (1)/(T _(r))

Find the sum of 'n' terms of the series whose n^(th) term is t_(n) = 3n^(2) + 2n .

If t_r denotes the r^(th) term of an G.P. and t_1 t_5 t_10 t_16 t_21 t_25 = 512 , then the value of its 13^(th) term is :

RESONANCE ENGLISH-DPP-QUESTION
  1. If the sum of the first 100 terms of an AP is -1 and the sum of even t...

    Text Solution

    |

  2. If the solution of the equation |(x^4-9) -(x^2 + 3)| = |x^4 - 9| - |x^...

    Text Solution

    |

  3. Let T(n) denotes the n ^(th) term of a G.P. with common ratio 2 and (l...

    Text Solution

    |

  4. Draw the labled graph of following (i) y = |7-2x| , (ii) y = |x-1|-|3...

    Text Solution

    |

  5. Which one of the following inequality holds good:

    Text Solution

    |

  6. If x cos alpha+cos beta-cos(alpha+beta) and y=4 sin.(alpha)/(2)sin.(be...

    Text Solution

    |

  7. Find the sum of the series 1+2(1-x)+3(1-x)(1-2x)+….+n(1-x)(1-2x)(1-3x)...

    Text Solution

    |

  8. If a,b respectively be the number of solutions and sum of solutions of...

    Text Solution

    |

  9. The equation |x + 2| - |x + 1| + |x -1| =K,x in R has two solutions i...

    Text Solution

    |

  10. The "sum" of integral solutions of equations |sin^(2)x+17-x^(2)|=|16-x...

    Text Solution

    |

  11. solution set of the inequality sqrt(7-x) > 2x-3 , is contained by the ...

    Text Solution

    |

  12. a ,b ,c are positive real numbers forming a G.P. If ax^2+2b x+c=0 and ...

    Text Solution

    |

  13. Let y = cosx (cosx - cos 3x). Then y is

    Text Solution

    |

  14. The (m + 1)^(th) term of (x/y+y/x)^(2m + 1 ) is

    Text Solution

    |

  15. The remainder when 2^(2003) is divided by 17 is:

    Text Solution

    |

  16. Solution set of 4 sintheta*costheta-2 costheta-2sqrt3 sin theta+sqrt3 ...

    Text Solution

    |

  17. sin 36^(º)sin 72^(º) sin108^(º) sin 144^(º) =

    Text Solution

    |

  18. In an A.P. the third term is four times the first term, and the sixth ...

    Text Solution

    |

  19. The sum of three numbers in A.P. is 27, and their product is 504, find...

    Text Solution

    |

  20. Determine all pairs (a,b) of real numbers such that 10, a,b,ab are in ...

    Text Solution

    |