Home
Class 11
MATHS
Column I, Column II The coefficien...

Column I, Column II The coefficient of the two consecutive terms in the expansion of `(1+x)^n` will be equal, then `n` can be, p. 9 If `15^n+23^n` is divided, by 19, then `n` can be, q. 10 `^10 C_0^(20)C_(10)-^(10)C_1^(18)C_(10)+^(10)C_2^(16)C_(10)-` is divisible by `2^n ,t h e nn` can be, r. 11 If the coefficients of `T_r , T_(r+1),T_(r+2)` terms of `(1+x)^(14)` are in A.P., then `r` is less than, s. 12

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

Similar Questions

Explore conceptually related problems

If the coefficients of (r-5)t h a n d(2r-1)t h terms in the expansion of (1+x)^(34) are equal, find rdot

If the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the expansion of (1+x)^(14) are in A.P., then r is/are a. 5 b. 11 c. 10 d. 9

If the coefficients of the rth, (r+1)t h ,(r+2)t h terms is the expansion of (1+x)^(14) are in A.P, then the largest value of r is.

If the coefficients of the rth, (r+1)t h ,(r+2)t h terms is the expansion of (1+x)^(14) are in A.P, then the largest value of r is.

Coefficient of n^(-r) in the expansion of log_(10)((n)/(n-1)) is

If the coefficients of x^(9),x^(10),x^(11) in expansion of (1+x)^(n) are in A.P., the prove that n^(2)-41n+398=0 .

If the coefficients of the (n+1)^(t h) term and the (n+3)^(t h) term in the expansion of (1+x)^(20) are equal , then the value of n is a. 10 b. 8 c. 9 d. none of these

The coefficients of (r-1)^(t h),\ r t h\ a n d\ (r+1)^(t h) terms in the expansion of (x+1)^n are in the ratio 1:3:5. Find n\ a n d\ rdot

If the coefficient of r^(th) ,( r +1)^(th) " and " (r +2)^(th) terms in the expansion of (1+x)^n are in A.P then show that n^2 - (4r +1)n + 4r^2 - 2 =0

If the coefficient of the rth, (r+1)th and (r+2)th terms in the expansion of (1+x)^(n) are in A.P., prove that n^(2) - n(4r +1) + 4r^(2) - 2=0 .

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. The number of distinct terms in the expansion of (x+1/x+x^2+1/(x^2))^...

    Text Solution

    |

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

    Text Solution

    |

  3. Column I, Column II The coefficient of the two consecutive terms...

    Text Solution

    |

  4. If the coefficient of x^7in[a x^2-(1/(b x^2))]^(11) equal the coeffici...

    Text Solution

    |

  5. If the coefficients of the (2r+4)t h ,(r-2)t h term in the expansion ...

    Text Solution

    |

  6. If the coefficients of the rth, (r+1)t h ,(r+2)t h terms is the expan...

    Text Solution

    |

  7. If the three consecutive coefficients in the expansion of (1+x)^n are...

    Text Solution

    |

  8. Degree of the polynomial [sqrt(x^2+1)+sqrt(x^2-1)]^8+[2/(sqrt(x^2+1)+...

    Text Solution

    |

  9. Least positive integer just greater than (1+0. 00002)^(50000) is.

    Text Solution

    |

  10. If Un=(sqrt(3)+1)^(2n)+(sqrt(3)-1)^(2n) , then prove that U(n+1)=8Un-4...

    Text Solution

    |

  11. Prove that the coefficient of x^(n) in the expansion of (1)/((1-x)(1-2...

    Text Solution

    |

  12. The value of (30,0)(30,10)-(30,1)(30,11)+(30,2)(30,12)-.............+(...

    Text Solution

    |

  13. Prove that ^n C1(^n C2)(^n C3)^3(^n Cn)^nlt=((2^n)/(n+1))^(n+1C()2),AA...

    Text Solution

    |

  14. Prove that 1/(m !)^n C0+n/((m+1)!)^n C1+(n(n-1))/((m+2)!)^n C2++(n(n-1...

    Text Solution

    |

  15. If n=12 m(m in N), prove that ^n C0-(^n C2)/((2+sqrt(3))^2)+(^n C4)/(...

    Text Solution

    |

  16. In the expansion of (1 + x)^(n) (1 + y)^(n) (1 + z)^(n) , the sum of t...

    Text Solution

    |

  17. Prove that ^100 C0^(100)C2+^(100)C2^(100)C4+^(100)C4^(100)C6++^(100)C(...

    Text Solution

    |

  18. Prove that sum(r=1)^(m-1)(2r^2-r(m-2)+1)/((m-r)^m Cr)=m-1/mdot

    Text Solution

    |

  19. Find the coefficients of x^(50) in the expression (1+x)^(1000)+2x(1+x)...

    Text Solution

    |

  20. If b1, b2 bn are the nth roots of unity, then prove that ^n C1dotb1+^n...

    Text Solution

    |