Home
Class 12
MATHS
The sum of all rational terms in the exp...

The sum of all rational terms in the expansion of
` (3^(1//4) + 4^(1//3))^(12)` is

A

91

B

251

C

273

D

283

Text Solution

Verified by Experts

The correct Answer is:
d
In the expansion of `(3^(1//4)+ 2^(2//3))^(12) ` , the general term is
`T_(r+1) = ""^(12)C_(r) (3^(1//4))^(12-r) (2^(2//3))^(r) = ""^(12)C_(r)3^(3-(r)/(4)) 2^((2r)/(3))`
Now , ` 0 lt r le 12 `
` therefore r = -0, 12 `
Rotional terms are ` T_(0+1) "and " T_(12 + 1)`
Now , ` T_(1) = ""^(12)C_(0) 3^(3) 2^(0) = 27`
`rArr T_(13) = ""^(12)C_(12) 3^(0) *2^(8) = 256`
` therefore ` Required sum `= T_(1) + T_(13) = 27 + 256 = 283` .
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the general term in the expansion of (5x-3)^(12)

The number of terms in the expansion of [(2x+y^(3))^(4)]^(7) is 8 .

The constant term in the expansion of (2x^(2)-1/x)^(12) is ……..

The constant term in the expansion of (1/2x^(1/3)+x^(-1/5))^(8) is ……….. term .

Find the 4^th term in the expansion of (x-2y)^12 .

The sum of coefficients of the two middle terms in the expansion of (1+x)^(2n-1) is equal to (2n-1)C_(n)

The constant term in the expansion of (x-1/(3x^(2)))^(9) is the ……… term .

The numbers of terms in the expansion [(x+4y)^(4)]^(5) is .........

The sum of the coefficient in the expansion (1+x-3x^(2))^(4331) is ………

Show that the coefficient of the middle term in the expansion of (1+x)^(2n) is equal to the sum of the coefficients of two middle terms in the expansion of (1 + x)^(2n-1)