Home
Class 12
MATHS
If A and B are coefficients of x^r and x...

If A and B are coefficients of `x^r` and `x^(n-r)` respectively in the expansion of `(1 + x)^n`, then

A

`alpha=beta`

B

`alpha+beta=n`

C

`alpha=kbeta` for some constant k

D

`alpha+beta=2^(n)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL INDUCTION AND BINOMIAL THEOREM

    MCGROW HILL PUBLICATION|Exercise EXERCISE (LEVEL 2 Single Correct Answer Type Questions)|10 Videos
  • MATHEMATICAL INDUCTION AND BINOMIAL THEOREM

    MCGROW HILL PUBLICATION|Exercise EXERCISE (Numerical Answer Type Questions)|20 Videos
  • MATHEMATICAL INDUCTION AND BINOMIAL THEOREM

    MCGROW HILL PUBLICATION|Exercise EXERCISE (Concept-based Single Correct Answer Type Questions)|10 Videos
  • LIMITS AND CONTINUITY

    MCGROW HILL PUBLICATION|Exercise Previous Years B-Architecture Entrance Examination Paper|12 Videos
  • MATHEMATICAL REASONING

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B. ARCHITECTURE ENTRANCE EXAMINATION PAPERS|11 Videos

Similar Questions

Explore conceptually related problems

If a and b denote respectively the coefficients of x^(m) and x^(n) in the expansion of (1+x)^(m+n) then write the relation between a and b

in If the coefficient of x^(r) and x^(r+1) are equal in the expansion of (1+x)^(2n+1), then find the value of r.

If A and B are the coefficients of x^(n) in the expansion (1+x)^(2n) and (1+x)^(2n-1) respectively,then

The coefficient of x^(n) y^(n) in the expansion of [(1 + x)(1+y) (x +y)]^(n) , is

Consider the expansion of (1 + x)^(2n+1) If the coefficients of x^(r) and x^(r+1) are equal in the expansion, then r is equal to

how that the coefficient of (r+1) th in the expansion of (1+x)^(n+1) is equal to the sum of the coefficients of the r th and (r+1) th term in the expansion of (1+x)^(n)

MCGROW HILL PUBLICATION-MATHEMATICAL INDUCTION AND BINOMIAL THEOREM-EXERCISE (LEVEL 1 Single Correct Answer Type Questions)
  1. Coefficient of the term independent of x in the expansion of (1+x)^(2n...

    Text Solution

    |

  2. Find the coefficient of x^4 in the expansion of (x//2-3//x^2)^(10)dot

    Text Solution

    |

  3. If A and B are coefficients of x^r and x^(n-r) respectively in the e...

    Text Solution

    |

  4. If the coefficients of (2r + 4)th and (r - 2)th terms in the expansion...

    Text Solution

    |

  5. The total number of terms in the expansion of (x + a)^(200) + (x - a)^...

    Text Solution

    |

  6. Sum of all the digits of the coefficient of x^(5) in the expansion of ...

    Text Solution

    |

  7. Given positive integers r >1,n >2 and that the coefficient of (3r d)t ...

    Text Solution

    |

  8. If (1 +px)^(n) = 1 + 24x + 264x^(2) + .. . then

    Text Solution

    |

  9. find the sum of the series sum(r=0)^n(-1)^r *"^nCr[1/(2^r)+(3^r)/(2^(...

    Text Solution

    |

  10. The value of .^(n)C(0).^(n)C(n).^(n)C(1).^(n)C(n-1)+...+.^(n)C(n)....

    Text Solution

    |

  11. Express: ((x+sqrt(x^2+1)^6+ (x-sqrt(x^2+1))^6 as a polynomial in x

    Text Solution

    |

  12. The number of distinct terms in the expansion of (1+ 3x + 3x^(2) + x^(...

    Text Solution

    |

  13. If x > 0, then the number of positive real terms in the expansion of (...

    Text Solution

    |

  14. The total number of terms which depand on the value of x in the ex...

    Text Solution

    |

  15. If the third term in the expansion of (1/x+"""x"(log)(10 x))^5 is 1000...

    Text Solution

    |

  16. Let R =(sqrt2+1)^(2n+1),ninN and f= R- [R], where [] denote the greate...

    Text Solution

    |

  17. The coefficient of x^(60) in (1+x)^(51)(1-x+x^(2))^(50) is

    Text Solution

    |

  18. Which is larger : (99^(50)+100^(50)) or (101)^(50).

    Text Solution

    |

  19. (1+x-2x^2)^6=sum(r=0)^12 ar x^r then a2+a4+..... +a12=

    Text Solution

    |

  20. The sum of the coefficients in the expansion of (1 +x-3x^(2))^(4321) i...

    Text Solution

    |