Home
Class 12
MATHS
The term independent of a in the expansi...

The term independent of `a` in the expansion of `(1+sqrt(a)+1/(sqrt(a)-1))^(-30)i s` `^30 C_(20)` b. `0` c. `^30 C_(10)` d. none of these

A

`.^(30)C_(20)`

B

`0`

C

`.^(30)C_(10)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(1+sqrt(a) + (1)/(sqrt(a)-1))^(-30)`
`= (a/(sqrt(a)-1))^(-30)`
`= ((sqrt(a)-1)/(a))^(30)`
`= (1)/(a^(30)) (1-sqrt(a))^(30)`
`=(1)/(a^(30)){.^(30)C_(0)-.^(30)C_(1)sqrt(a) + "...."+.^(30)C_(30)(sqrt(a))^(30)}`
There is no term independent of a.
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|10 Videos

  • CIRCLE

    CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

Similar Questions

Explore conceptually related problems

The term independent of a in the expansion of (1+sqrta+ 1/(sqrta-1))^-30 is (a) 30C_20 (b) 0 (c) 30C_10 (d) non of these

Find the greatest term in the expansion of sqrt(3)(1+1/(sqrt(3)))^(20)dot

The coefficient of x^(28) in the expansion of (1+x^3-x^6)^(30) is 1 b. 0 c. 30 C_6 d. ^30 C_3

Rajdhani Express going from Bombay to Delhi stops at five intermediate stations, 10 passengers enter the train during the journey with 10 different ticket of two class. The number of different sets of tickets they may have is a. ^15 C_(10) b. ^20 C_(10) c. ^30 C_(10) d. none of these

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

The coefficient x^5 in the expansion of (1+x)^(21)+(1+x)^(22)++(1+x)^(30) is a. "^51 C_5 b. "^9C_5 c. "^31 C_6 -"^(21)C_6 d. "^30 C_5 + "^(20)C_5

The sum of rational term in (sqrt(2)+^3sqrt(3)+^6sqrt(5))^(10) is equal to 12632 b. 1260 c. 126 d. none of these

The value of lim_(x->0)(sqrt(1/2(1-cos2x)))/x i s (a)1 (b) -1 (c) 0 (d) none of these

The value of sin^(-1)("cot"(sin^(-1)((2-sqrt(3))/4+cos^(-1)(sqrt(12))/4+sec^(-1)sqrt(2))))i s (a) 0 (b) pi/2 (c) pi/3 (d) none of these

If the last tem in the binomial expansion of (2^(1/3)-1/(sqrt(2)))^n i s(1/(3^(5/3)))^(log_3 8) , then 5th term from the beginning is 210 b. 420 c. 105 d. none of these

CENGAGE-BINOMIAL THEOREM-Exercise (Single)
  1. If the coefficient of x^(7) in [ax^(2) + (1/(bx))]^(11) equals the coe...

    Text Solution

    |

  2. Find a positive value of m for which the coefficient of x^2 in the exp...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. The coefficient of x^n in (1+x)^(101)(1-x+x^2)^(100) is nonzero, then ...

    Text Solution

    |

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

    Text Solution

    |

  7. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Statement 1: The coefficient of x^n is (1+x+(x^2)/(2!)+(x^3)/(3!)++(x^...

    Text Solution

    |

  18. In the expansion of (3^(-x//4)+3^(5x//4))^(n) the sum of binomial coef...

    Text Solution

    |

  19. The sum of the coefficients of even power of x in the expansion of (1+...

    Text Solution

    |

  20. Maximum sum of coefficient in the expansion of (1-xsintheta+x^2)^n is ...

    Text Solution

    |