Home
Class 12
MATHS
If (1 + x + x^(2) + x^(3))^(n) = sum(r=0...

If `(1 + x + x^(2) + x^(3))^(n) = sum_(r=0)^(3n) a_(r) x^(r) "and" sum_(r=0)^(3n) a_(r) = k ` and if
` sum_(r=0)^(3n) r a_(r) = (lambda n k)/(2) ` , the value of ` lambda ` is

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Let (1 + x + x^(2))^(n) = sum_(r=0)^(2n) a_(r) x^(r) . If sum_(r=0)^(2n)(1)/(a_(r))= alpha , then sum_(r=0)^(2n) (r)/(a_(r)) =

If (1+2x+x^(2))^(n) = sum_(r=0)^(2n)a_(r)x^(r) , then a_(r) =

If (1+x+x^2+x^3)^n=sum_(r=0)^(3n)b_r x^r and sum_(r=0)^(3n)b_r=k ,"t h e n"sum_(r=0)^(3n)r b_r is

If (1+x^(2))^(n) =sum_(r=0)^(n) a_(r)x^(r )= (1+x+x^(2)+x^(3))^(100) . If a = sum_(r=0)^(300)a_(r) , then sum_(r=0)^(300) ra_(r) is

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of sum_(r=0)^(n)a_(r) is

sum_(r=1)^(n) r^(2)-sum_(r=1)^(n) sum_(r=1)^(n) is equal to

If ninN,ngt4 and (1-x^(3))^(n)=sum_(r=0)^(n)a_(r)x^(r)(1-x)^(3n-2r) , then sum_(r=0)^(n)a_(r)=lambda^(n) , find lambda .

If a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)) , find the value of sum_(r=0)^(n) (r)/(""^(n)C_(r))

If a_n=sum_(r=0)^n1/(nC_r), then sum_(r=0)^n r/(nC_r) equals

Find the sum sum_(r=0)^n^(n+r)C_r .

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. If chocolates of a particular brand are all identical then the number ...

    Text Solution

    |

  2. The maximum value of function f(x)=x^3-12 x^2+36 x+17 in the interval ...

    Text Solution

    |

  3. If (1 + x + x^(2) + x^(3))^(n) = sum(r=0)^(3n) a(r) x^(r) "and" sum(r...

    Text Solution

    |

  4. One angle of an isosceles triangle is 120^0 and the radius of its incr...

    Text Solution

    |

  5. Number of ways in which 7 people can occupy 6 seats, 3 seats on eac...

    Text Solution

    |

  6. If by dropping a stone in a quiet lake a wave moves in circle at a ...

    Text Solution

    |

  7. Consider 8 vertices of a regular octagon and its centre. If T denotes ...

    Text Solution

    |

  8. The number of ways in which four different toys and five indistinguish...

    Text Solution

    |

  9. Statement 1: f(x)=cos x is continous at x=0a n dg(x)=[tanx],"w h e r e...

    Text Solution

    |

  10. We wish to select 6 persons from 8, but if the person A is chosen, the...

    Text Solution

    |

  11. The family of straight lines 3(a+1)x-4(a-1)y+3(a+1)=0 for different va...

    Text Solution

    |

  12. Let f(x)=x+3log(x-2)andg(x)=x+5log(x-1), then the set of x satisfying ...

    Text Solution

    |

  13. Find the number of diagonals of a 16-sided polygon.

    Text Solution

    |

  14. Number of different points on the curve y^2=x(x+1)^2 where the tangent...

    Text Solution

    |

  15. Statement 1: Let E=[1/3+1/(50)]+[1/3+2/(50)]+ upto 50 terms, then E is...

    Text Solution

    |

  16. We are required to form different words with the help of the letters o...

    Text Solution

    |

  17. If all the letters of the word "SUCCESS" are written down at random in...

    Text Solution

    |

  18. about to only mathematics

    Text Solution

    |

  19. The total number of words that can be made by writing the letters of t...

    Text Solution

    |

  20. Consider the statement p: 'New Delhi is a city'. Which of the followin...

    Text Solution

    |