Home
Class 12
MATHS
The coefficient of x^(1274) in the expan...

The coefficient of `x^(1274)` in the expansion of `(x+1)(x-2)^(2)(x+3)^(3)(x-4)^(4)…(x+49)^(49)(x-50)^(50)` is

A

`1275`

B

`-1275`

C

`-sum_(i=1)^(50)i^(2)`

D

`-sum_(i=1)^(50)i^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `(x+1)(x-2)^(2)(x+3)^(3)(x-4)^(4)...(x+49)^(49)(x-50)^(50)`
Degree of the expression is `1+2+3+…+50=1275`
Coefficient of `x^(1274)` is `(1-2-2+3+3+3-4-4-4-4…)`
`=1^(2)-2^(2)+3^(2)-4^(2)+…+49^(2)-50^(2)`
`=-(1+2+3+..+50)`
`=-1275`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise Comprehension|7 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|4 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

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

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

The coefficient of x^(-10) in the expansion of (x^2-1/x^3)^10 is

The coefficient of x^7 in the expansion of (1-x-x^2+x^3)^6 is

The coefficient of x^4 in the expansion of (1+x+x^2+x^3)^11 is

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

The coefficient of x^5 in the expansion of (x^2-x-2)^5 is

The coefficient of x^5 in the expansion of (1+x^2)(1+x)^4 is

Find the coefficients of x^(-2) in the expansion of (3x-(7)/(x))^(8)

The coefficient of x^(-4) in the expansion of ((3)/(2)-(3)/(x^(2)))^(10) is-