Home
Class 11
MATHS
Coefficient of x^(18) in (1+x+2x^2+3x^3+...

Coefficient of `x^(18)` in `(1+x+2x^2+3x^3++18 x^(18))^2` equal to `995` b. `1005` c. `1235` d. none of these

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

Coefficient of x^(11) in the expansion of (1+3x+2x^2)^6 is equal to

Find the coefficient of x^(18) in (x^2+2+1/(x^2))^(-5)(1+x^2)^(40)dot

The coefficient of x^(17) in the expansion of (x-1)(x-2)……..(x-18) is

The coefficient of x^(49) in the product (x-1)(x-3)(x-99)i s a. -99^2 b. 1 c. -2500 d. none of these

The coefficient of x^17 in the expansion of(x-1)(x-2)(x-3)….(x-18) is

lim_(xtooo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1)) is equal to (a) 0 (b) oo (c) 1/2 (d) none of these

If f(x)=1-x+x^2-x^3+. . -x^(15)+x^(16)-x^(17) , then the coefficient of x^2 in f(x-1) is a. 826 b. 816 c. 822 d. none of these

Let A = {x_1, x_2, x_3, ,x_7},B={y_1, y_2, y_3} The total number of functions f: A->B that are onto and there are exactly three element x in A such that f(x)=y_2 is equal to a. 490 b. 510 c. 630 d. none of these

The cofficient of x^(17) in the expansion of (x-1)(x-2)(x-3)….(x-18) is -

The coefficient of x^(19) in the polynomial (x-1)(x-2)(x-2^2)(x-2^(19)) is 2^(20)-2^(19) b. 1-2^(20) c. 2^(20) d. none of these

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. For a ,x ,>0 prove tht at most one term of the G.P. sqrt(a-x),sqrt(x),...

    Text Solution

    |

  2. If 1/1^2+1/2^2+1/3^2+.... upto infty=pi^2/6 , then, find 1/1^2+1/3^2+1...

    Text Solution

    |

  3. Coefficient of x^(18) in (1+x+2x^2+3x^3++18 x^(18))^2 equal to 995 b. ...

    Text Solution

    |

  4. Let alpha , beta be the roots of x^2-x+p=0 and gamma,delta be the root...

    Text Solution

    |

  5. If the sum of the first 2n terms of the AP 2,5,8.....is equal to the s...

    Text Solution

    |

  6. Statement 1: If the arithmetic mean of two numbers is 5/2 geometric ...

    Text Solution

    |

  7. Number of positive integral ordered pairs of (x,y), so that 8,x,y are ...

    Text Solution

    |

  8. If three positive real numbers a,b ,c are in A.P such that a b c=4 , t...

    Text Solution

    |

  9. Consider an infinite geometric series with first term a and common rat...

    Text Solution

    |

  10. The maximum sum of the series 20+19 1/3+18 2/3+...... is (A) 310 (B) ...

    Text Solution

    |

  11. The sum of n terms of a progression is (2^n-1). Show that it is a GP a...

    Text Solution

    |

  12. Let a1 , a2 ,... be in harmonic progression with a1 = 5 and a20 = 25. ...

    Text Solution

    |

  13. An infinite G.P. has first term as a and sum 5, then a belongs to a) |...

    Text Solution

    |

  14. Let Ssub(0,pi) denote the set of values of x satisfying the equation 8...

    Text Solution

    |

  15. Find the number of terms of a G.P. whose first term is ¾, common ratio...

    Text Solution

    |

  16. In an A.P. (with usual notations) : (i) given a = 7, a13 = 35, find ...

    Text Solution

    |

  17. Find the geometric progression whose 4th term is 54 and the 7th term i...

    Text Solution

    |

  18. The first term of G.P. is 27 and 8th term is 1/81. Find the sum of its...

    Text Solution

    |

  19. The greatest integer by which 1+sum(r=1)^(30)rxxr ! is divisible is a....

    Text Solution

    |

  20. (lim)(ntooo)sum(r=1)^n r/(1xx3xx5xx7xx9xx.....xx(2r+1)) is equal to 1/...

    Text Solution

    |