Home
Class 11
MATHS
The number of real negative terms in the...

The number of real negative terms in the binomial expansion of `(1+i x)^(4n-2),n in N ,x >0` is

A

n

B

n+1

C

n-1

D

2n

Text Solution

Verified by Experts

The correct Answer is:
b
Let `T_(r+1)` be the `(r +1)^(th)` term in the binomial
expanion of `(1 + ix)^(4n -2)` . Then
`T_(r+1) = ""^(4n-2)C_(r)(ix)^(r) = ""^(2n-2)C_(r)x^(r)i^(r)`
Clearly, `T_(r +1) ` is real negative , if ` r=2 ,6,10,14,…`
These values of r from an A.P. with term 2 and common
difference 4. lies between 2 and 4n -2
`therefore 2 le 4k - 2 le 4n - 2 rArr 1 le k le n`
Hence, there are n real negative terms.
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM AND ITS APPLCIATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Assertion Reason Type|13 Videos

  • BINOMIAL THEOREM AND ITS APPLCIATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|103 Videos

  • BINOMIAL THEOREM AND ITS APPLCIATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

  • CARTESIAN CO-ORDINATE SYSTEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|27 Videos

Similar Questions

Explore conceptually related problems

The number of real negavitve terms in the binomial expansion of (1 + ix)^(4n-2) , n in N , n gt 0 , I = sqrt(-1) , is

The coeffiicent of x^(n) in the binomial expansion of ( 1-x)^(-2) is

The middle term in the expansion of (x + 1/x)^(2n) is

The number of terms in the expansion of (x^2+1+1/x^2)^n, n in N , is:

Find the sum of the coefficient of to middle terms in the binomial expansion of (1+x)^(2n-1)

Find the sum of the coefficient of two middle terms in the binomial expansion of (1+x)^(2n-1)

The sum of the coefficients in the binomial expansion of (1/x + 2x)^n is equal to 6561. The constant term in the expansion is

Find the middle term in the expansion of : (1-2x+x^2)^n

If w is a non-real cube root of unity, x is a real number and n in N such that first three terms in the binomial expansion of (w + x)^n are 1,12bar w and 69 w respectively, then

The middle term in the expansion of (1 - (1)/(x))^(n) (1 - x)^(n) is

OBJECTIVE RD SHARMA ENGLISH-BINOMIAL THEOREM AND ITS APPLCIATIONS -Section I - Solved Mcqs
  1. If alpha !=1 is an n^(th) root of unity and n in N such thatfirst thr...

    Text Solution

    |

  2. The coefficient of x^50 in (1+x^2)^25(1+x^25)(1+x^40)(1+ x^45) (1 + x^...

    Text Solution

    |

  3. Let f(n)= sum(k=1)^(n) k^2 ^"(n )Ck)^ 2 then the value of f(5) equals

    Text Solution

    |

  4. If C(0), C(1), C(2), …, C(n) denote the binomial coefficients in th...

    Text Solution

    |

  5. If for n in N ,sum(k=0)^(2n)(-1)^k(^(2n)Ck)^2=A , then find the value...

    Text Solution

    |

  6. sum(r=0)^(n)(-1)^(r)(""^(n)C(r))/(""^(r+3)C(r)) is equal to :

    Text Solution

    |

  7. If C(0), C(1) C(2) ….., denote the binomial coefficients in the exp...

    Text Solution

    |

  8. If C0, C1,C2 ..., Cn, denote the binomial coefficients in the expans...

    Text Solution

    |

  9. For r = 0, 1,"…..",10, let A(r),B(r), and C(r) denote, respectively, t...

    Text Solution

    |

  10. Find the coefficient of x^7 in the expansion of (1 - x -x^2 + x^3)^(6)...

    Text Solution

    |

  11. If the coefficient of x^(3) and x^(4) in the expansion of (1+ax+bx^(2)...

    Text Solution

    |

  12. The sum of coefficient of integral powers of x in the binomial expansi...

    Text Solution

    |

  13. The coefficient of x^9 in the expansion of (1+x)(16 x^2)(1+x^3)(1+x^(1...

    Text Solution

    |

  14. The power of x which has the greatest coefficient inthe expansion of ...

    Text Solution

    |

  15. The term independent of x in the expansion of ((1)/(x^(2)) + (1)/(x) +...

    Text Solution

    |

  16. The sum of rational term(s) in (sqrt3 + 2^(1/3) + 5^(1/4))^8 is equal ...

    Text Solution

    |

  17. If f(x) is periodic with periot 't' such that f(2x + 3) + f(2x+7) = ...

    Text Solution

    |

  18. The number of real negative terms in the binomial expansion of (1+i x)...

    Text Solution

    |

  19. If (3+asqrt2)^100+(3+bsqrt2)^100=7+5sqrt2 number of pairs (a, b) for...

    Text Solution

    |

  20. The value of sum(r=0)^(n) r(n -r) (""^(n)C(r))^(2) is equal to

    Text Solution

    |