Home
Class 12
MATHS
The sum of the co-efficients of all odd ...

The sum of the co-efficients of all odd degree terms in the expansion of `(x+sqrt(x^3-1))^5+(x-(sqrt(x^3-1))^5, (x gt 1)`

A

2

B

-1

C

0

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
`(x+sqrt(x^(3)-1))^(5) + (x-sqrt(x^(3)-1))^(5)`
`= 2[.^(5)C_(0)x^(5)+.^(5)C_(2)x^(3)(sqrt(x^(3)-1))^(2) + .^(5)C_(4)x(sqrt(x^(3)-1))^(4)]`
`=2[x^(5)+10x^(3)(x^(3)-1)+5x(x^(3)-1)^(2)]`
`= 2[x^(5)+10x^(6)-10x^(3)+5x^(7)-10x^(4)+5x]`
`:.` Sum of the coeffcient of odd degree terms
`= 2(1-0+5+5) = 2`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|4 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Comprehension|11 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Numerical|25 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|7 Videos

Similar Questions

Explore conceptually related problems

The sum of the coefficients of all even degree terms in x in the expansion of (x+sqrt(x^(3)-1))^(6)+(x-sqrt(x^(3)-1))^(6) , (xlt1) is equal to 4k. The value of k is ________

Find the number of terms in the expansion of (x+sqrt(x^2-1))^6+(x-sqrt(x^2-1))^6

The sum of the co-efficients of all the even powers of x in the expansion of (2x^2 - 3x + 1)^11 is -

Find the sum of the coefficients of all the integral powers of x in the expansion of (1+2sqrt(x))^(40)dot

Find the general term in the expansion of (1- (5x)/(3))^(-3)

The co-efficient of x in the expansion of (1-2x^3+3x^5)(1+1/x)^8 is:

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

The sum of the rational terms in the expansion of (2^(1//5) + sqrt(3))^(20) , is

Find the term independent of x in the expansion of (sqrt(x/3)+((sqrt3)/(2x^2)))^10

Find the term independent of x in the expansion of ( sqrt(x / 7) - (sqrt5)/(x^2) )^10