Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202523 Jan 2025Morning ShiftMathematicsBinomial TheoremActual

The sum of all rational terms in the expansion of (1+2^ 1 / 3 +3^ 1 / 2 )^6 is equal to

Correct answer

0

Step-by-step solution

The general term of multinomial expansion is 6! ! ! ! (1)^ (2^ 1 3 )^ (3^ 1 2 )^ For terms to be rational 3 and 2 array c|c|c|c & & & Term 0 & 0 & 6 & 1 0 & 2 & 4 & 15.3=45 0 & 4 & 2 & 15.3^2=135 0 & 6 & 0 & 1.3^3=27 3 & 0 & 3 & 20.2=40 3 & 2 & 1 & 60.2 .3=360 6 & 0 & 0 & 1.4=4 array Sum of rational terms =1+45+135+27+40+360+4=612

Practice Binomial Theorem on Quantrex Academy →

More from Binomial Theorem

If 26 ( 2^3 3 12 2 + 2^5 5 12 4 + 2^7 7 12 6 + + 2¹³ 13 12 12 ) = 3¹³ - , then is equal to: 2026If (1 - x^3)¹⁰ = _ r=0 ¹⁰ a_r x^r (1-x)^ 30-2r , then 9a₉ a₁₀ is equal to __________. 2026If the coefficients of the middle terms in the binomial expansions of (1 + x)²⁶ and (1 - x)²⁸ , 0 , are equal, then the value of is: 2026The coefficient of x^2 in the expansion of (2x^2 + 1 x )¹⁰ , x 0 , is : 2026If the sum of the coefficients of x^7 and x¹⁴ in the expansion of ( 1 x^3 - x^4 )^n , x 0 , is zero, then the value of n is __________. 2026In the expansion of (9x- 1 3 x )¹⁸ , x>0 , if the term independent of x is (221)k , then k is equal to: 2026Let the smallest value of k N , for which the coefficient of x^3 in (1+x)^3 + (1+x)^4 + (1+x)^5 + + (1+x)⁹⁹ + (1+kx)¹⁰⁰ , x 0 , is (43n + 101 4 ) (¹⁰⁰C₃ ) for some n N , be p . The 2026If for 3 r 30 , 30 30-r + 3 30 31-r + 3 30 32-r + 30 33-r = m r , then m equals: 2026 Full Binomial Theorem list All JEE Main PYQs