Home
Class 12
MATHS
If x is positive, the first negative ter...

If `x` is positive, the first negative term in the expansion of `(1+x)^(27//5)i s(|x|<1)` `5t ht e r m` b. `8t ht e r m` c. `6t ht e r m` d. `7t ht e r m`

A

`5^(th)` term

B

`8^(th)` term

C

`6^(th)` term

D

`7^(th)` term

Text Solution

Verified by Experts

The correct Answer is:
B
`T_(r+1)` in `(1+x)^(n)` is
`(n(n-1)(n-2)"……"(n-r+1))/(r!) x^(r)`
For first negative term,
`n -r + 1 lt 0`
or `27/5 - r +1 lt 0` or `r gt 32/5`
Thus, first negative term occurs when `r = 7`,
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Multiple Correct Answer Type|27 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Linked Comphrension|20 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Concept Application Exercise 8.8|10 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|7 Videos

Similar Questions

Explore conceptually related problems

If 0 lt x lt 1 , the first negative term in the expansion of (1+x)^(27//5) is

Write down the first three terms in the expansion of (3 + x)^(-3//2)

Write down the first three terms in the expansion of (4 - 5x)^(-1//2)

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

If (r+1)t h term is the first negative term in the expansion of (1+x)^(7//2), then find the value of rdot

Find the 5th term in the expansion of (1+x^2)^12

Write down the first three terms in the expansion of (8 - 7x)^10

Find the constant term in the expansion of (x-1//x)^6dot

Find the 10th term in the expansion of 5^x

Constant term in the expansion of ( x- (1)/(x)) ^(10) is

CENGAGE ENGLISH-BINOMIAL THEOREM-Single Correct Answer
  1. The coefficient of x^5in(1+2x+3x^2+)^(-3//2)i s(|x|<1) 21 b. 25 c. 26...

    Text Solution

    |

  2. If |x|<1, then the coefficient of x^n in expansion of (1+x+x^2+x^3+)^2...

    Text Solution

    |

  3. If x is positive, the first negative term in the expansion of (1+x)^(2...

    Text Solution

    |

  4. If x is so small that x^3 and higher powers of x may be neglectd, then...

    Text Solution

    |

  5. If the expansion in power of x of the function (1)/(( 1 - ax)(1 - b...

    Text Solution

    |

  6. If (x^(2)+x+1)/(1-x) = a(0) + a(1)x+a(2)x^(2)+"….", then sum(r=1)^(50...

    Text Solution

    |

  7. If (1-x)^(-n)=a0+a1x+a2x^2++ar x^r+ ,t h e na0+a1+a2++ar is equal to (...

    Text Solution

    |

  8. The coefficient of x^(103) in (1+x+x^(2) +x^(3)+x^(4))^(199)(x-1)^(201...

    Text Solution

    |

  9. The term independent of x in the product (4 + x + 7x^2)(x-3/x)^11 is (...

    Text Solution

    |

  10. The 13^(th) term in the expanion of (x^(2)+2//x)^(n) is independent of...

    Text Solution

    |

  11. Coefficient of x^(2009) in (1+x+x^(2)+x^(3)+x^(4))^(1001) (1-x)^(1002)...

    Text Solution

    |

  12. If the constant term in the binomial expansion of (x^2-1/x)^n ,n in N...

    Text Solution

    |

  13. If p^(4)+q^(3)=2(p gt 0, q gt 0), then the maximum value of term indep...

    Text Solution

    |

  14. In the expansion of (x^3-1/(x^2))^n ,n in N , if the sum of the coeff...

    Text Solution

    |

  15. Find the coefficient of t^8 in the expansion of (1+2t^2-t^3)^9.

    Text Solution

    |

  16. The term idependent of 'x' in the expansion of (9x-(1)/(3sqrt(x)))^(18...

    Text Solution

    |

  17. In the expansion of ((x)/(costheta)+(1)/(xsintheta))^(16), if l(1) is ...

    Text Solution

    |

  18. If A(i,j) be the coefficient of a^i b^j c^(2010-i-j) in the expansion ...

    Text Solution

    |

  19. The coefficient of x^(301 ub the expansion of (1+x)^(500)+x(1+x)^(499)...

    Text Solution

    |

  20. The coefficient of x^70 in the product (x-1)(x^2-2)(x^3-3)....(x^12-12...

    Text Solution

    |