Home
Class 12
MATHS
If the term independent of x in the (sqr...

If the term independent of `x` in the `(sqrt(x)-k/(x^2))^(10)` is 405, then `k` equals `2,-2` b. `3,-3` c. `4,-4` d. `1,-1`

A

`2,-2`

B

`3,-3`

C

`4,-4`

D

`1,-1`

Text Solution

Verified by Experts

The correct Answer is:
B
`T_(r+1) = .^(10)C_(r)(sqrt(x))^(10-r) ((-k)/(x^(2)))^(r) = .^(10)C_(r)x^(5-5r//2)(-k)^(r)`
For this to be important of x,r must be 2, so these
`.^(10)C_(2)k^(2) = 405` or `k = +-3`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.8|10 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

  • BINOMIAL THEORM

    CENGAGE|Exercise Question Bank|31 Videos

Similar Questions

Explore conceptually related problems

If the constant terms in the expansion of (sqrt(x)-k/x^2)^(10) is 405 then |k|=

If the constant term in the binomial expansion of (sqrt(x) - (k)/(x^(2)))^(10) is 405 , then |k| equals :

Find the value of a so that the term independent of x in (sqrt(x)+(a)/(x^(2)))^(10) is 405

If the terms independent of x in the expansion of (3/2 x^2 - (1)/(3x) )^9 is k, then 18 k is equla to

If 4sqrt(3sqrt(x^(2)))=x^(k), then k=

find the term independent of x in the expansion of ((sqrt(x))/(sqrt(3))+(sqrt(3))/(2x^(2)))^(10)

The term independent of x in the expansion of (sqrt(x/3)+2/(2x^2))^10 is (A) 9/4 (B) 3/4 (C) 5/4 (D) 7/4

The term independent of x in the expansion of (x-(1)/(x))^(4)(x+(1)/(x))^(3) is: -3 b.0 c.1 d.3

If (3^(6))/(4^(4)) k is the term, independent of x in the binomial expansion of ((x)/(4)-(12)/(x^(2)))^(12) then k is equal to ____________

CENGAGE-BINOMIAL THEOREM-Exercise (Single)
  1. In the expansion of (x^3-1/(x^2))^n ,n in N , if the sum of the coeff...

    Text Solution

    |

  2. If (1+2x+x^(2))^(n) = sum(r=0)^(2n)a(r)x^(r), then a(r) =

    Text Solution

    |

  3. If the term independent of x in the (sqrt(x)-k/(x^2))^(10) is 405, the...

    Text Solution

    |

  4. The coefficient of x^(53) in the expansion sum(m=0)^(100) ""^(100)C(...

    Text Solution

    |

  5. If the coefficient of x^7 in (ax^2+1/(bx))^11 is equal to the coeffici...

    Text Solution

    |

  6. The coefficient of x^3 in the expansion of (1-x+x^2)^5 is

    Text Solution

    |

  7. The term independent of a in the expansion of (1+sqrt(a)+1/(sqrt(a)-1)...

    Text Solution

    |

  8. The coefficient of x^(10) in the expansion of (1+x^2-x^3)^8 is 476 b. ...

    Text Solution

    |

  9. If the coefficient of x^(n) in (1+x)^(101) (1+x^(3)-x^(6))^(30) is

    Text Solution

    |

  10. The coefficient of x^(28) in the expansion of (1+x^3-x^6)^(30) is 1 b....

    Text Solution

    |

  11. The coefficient of a^8b^4c^9d^9 in (a b c+a b d+a c d d+b c d)^(10) is...

    Text Solution

    |

  12. In the expansion of (1+ x + 7/x)^11find the term not containing x.

    Text Solution

    |

  13. The coefficient of x^(7) in the expansion of (1-x-x^(3)+x^(4))^(8) is ...

    Text Solution

    |

  14. Sum of the coefficients of terms of degree 13 in the expansion of(1+x)...

    Text Solution

    |

  15. The coefficient of x^2y^3 in the expansion of (1-x+y)^(20) is (20 !)/(...

    Text Solution

    |

  16. If coefficient of a^2b^3c^4in(a+b+c)^m(w h e r em in N)i sL(L!=0) , t...

    Text Solution

    |

  17. The coefficient of x^r[0lt=rlt=(n-1)] in lthe expansion of (x+3)^(n-1)...

    Text Solution

    |

  18. If (1+2x+3x^2)^(10)=a0+a1x+a2x^2++a(20)x^(20),t h e na1 equals 10 b. 2...

    Text Solution

    |

  19. If f(x)=1-x^2-x^3++^(15)+x^(16)-x^(17) , then the coefficient of x^2in...

    Text Solution

    |

  20. Let f(x0=a0+a1x+a2x^2++an x^n+ and (f(x))/(1-x)=b0+b1x+b2x^2++bn x^n+ ...

    Text Solution

    |