Home
Class 12
MATHS
Thr ciefficient of x^(n-2) in the polyno...

Thr ciefficient of `x^(n-2)` in the polynomial `(x-1)(x-2)(x-3)"…."(x-n)`, is

A

`(n(n^(2)+2)(3n+1))/(24)`

B

`(n(n^(2)-1)(3n+2))/(24)`

C

`(n(n^(2)+1)(3n+4))/(24)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos
  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |5 Videos

Similar Questions

Explore conceptually related problems

The coefficient of x^(n-2) in the polynomial (x-1)(x-2)(x-3)...(x-n) is

The coefficient of x^(n) in the polynomial (x+""^(2n+1)C_(0))(X+""^(2n+1)C_(1)) (x+""^(2n+1)C_(2))……(X+""^(2n+1)C_(n)) is

Find the coefficient of x^n in the polynomial (x+^n C_0)(x+3^n C_1)xx(x+5^n C_2)[x+(2n+1)^n C_n]dot

Statement-1: The middle term of (x+(1)/(x))^(2n) can exceed ((2n)^(n))/(n!) for some value of x. Statement-2: The coefficient of x^(n) in the expansion of (1-2x+3x^(2)-4x^(3)+ . . .)^(-n) is (1*3*5 . . .(2n-1))/(n!)*2^(n) . Statement-3: The coefficient of x^(5) in (1+2x+3x^(2)+ . . .)^(-3//2) is 2.1.

The coefficient of x^r[0lt=rlt=(n-1)] in the expansion of (x+3)^(n-1)+(x+3)^(n-2)(x+2)+(x+3)^(n-3)(x+2)^2+.... +(x+2)^(n-1) is a.^n C_r(3^r-2^n) b.^n C_r(3^(n-r)-2^(n-r)) c.^n C_r(3^r+2^(n-r)) d. none of these

Prove that the coefficient of x^n in the expansion of 1/((1-x)(1-2x)(1-3x))i s1/2(3^(n+2)-2^(n+3)+1)dot

Coefficient of x^((n^2+n-14)/2) in, (x-1)(x^2-2)(x^3-3)(x^4- 4).........(x^n-n),(n>=8) is

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

Find the coefficient of x^n in (1+x/(1!)+(x^2)/(2!)+........+(x^n)/(n !))^2 .

If |x|<1, then the coefficient of x^n in expansion of (1+x+x^2+x^3+)^2 is a. n b. n-1 c. n+2 d. n+1

RESONANCE ENGLISH-DPP-QUESTION
  1. The sum of series ^^(20)C0-^^(20)C1+^^(20)C2-^^(20)C3++^^(20)C 10 is 1...

    Text Solution

    |

  2. The term independent of x in the expansion of (x-1/x)^4(x+1/x)^3...

    Text Solution

    |

  3. Thr ciefficient of x^(n-2) in the polynomial (x-1)(x-2)(x-3)"…."(x-n),...

    Text Solution

    |

  4. If alpha, beta are the roots of the equation x^(2)+alphax + beta = 0 s...

    Text Solution

    |

  5. Find the product of the real roots of the equation, x^2+18x +30=2sqrt(...

    Text Solution

    |

  6. Consider the equation: 2^(|x+1|)-2^x=|2^x-1|+1 The least value of x s...

    Text Solution

    |

  7. Consider the equation: 2^(|x+1|)-2^x=|2^x-1|+1 Number of integers les...

    Text Solution

    |

  8. Consider the equation: 2^(|x+1|)-2^x=|2^x-1|+1 Number of composite nu...

    Text Solution

    |

  9. The remainder lfloor1+lfloor2+lfloor3+"……"+lfloor200 is divided by 14 ...

    Text Solution

    |

  10. Solve the equation 2^(|x+1|)-2^(x)=|2^(x)-1|+1

    Text Solution

    |

  11. Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(...

    Text Solution

    |

  12. If n^(th) term of the series 3'1/3,2,1'3/7,1'1/9,"……" is (an+10)/(bn+c...

    Text Solution

    |

  13. If sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2)+1/(3^2))+sqrt(1+1/(3^2)+1/(4...

    Text Solution

    |

  14. In the expansion of (7^((1)/(3)) + 11^((1)/(9)))^(6561) , the number o...

    Text Solution

    |

  15. The coefficient of the middle term in the binomial expansion in powers...

    Text Solution

    |

  16. In the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the binom...

    Text Solution

    |

  17. Prove that difference of squares of two distinct odd natural numbers i...

    Text Solution

    |

  18. If Pa n dQ are sum and product respectively of all real values of x sa...

    Text Solution

    |

  19. The solution set of inequality ((e^(x)-1)(2x-3)(x^(2)+x+2))/((sin x -s...

    Text Solution

    |

  20. The values of x satisfying 2log((1)/(4))(x+5)gt(9)/(4)log((1)/(3sqrt(3...

    Text Solution

    |