â€‹sir Q 11 Number of rational terms in the expansion of 2x+3y1348 is - Maths - Binomial Theorem

Question

â€‹sir
Q 11 Number of rational terms in the expansion of 2 x + 3 y 1 3 48
is

Neha Sethi · Accepted Answer

Dear student

In the expansion  of 2x+3y1348 ,the general term is given by :Tr+1=48Cr2xr3y48-r3 , where 0≤r≤48=48Cr 2rxr2y48-r3×348-r3For the terms to be rational, r must be  a multiple of 2 and 48-r must be a multiple of 3
The possible values of r are 6,12,18,24,30,36,42Thus, number of rational terms=7
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​sir Q.11. Number of rational terms in the expansion of 2 x + 3 y 1 3 48 is

sir
Q.11. Number of rational terms in the expansion of ${(2 \sqrt{x} + 3 y^{\frac{1}{3}})}^{48}$ is