Question

If the sum of the co-efficients of all the positive even powers of x in the binomial expansion of $(2x^3+\frac{3}{x})^{10}$ is 510 – β·39, the β is equal to ____.

Answer 1

The correct answer is: 83.

$T_{r+1}=10C_r(2x^3)^{10-r}(\frac{3}{x})^r$

$=C_r^{10}2^{10-r}3^rx^{30-4r}$

So, r ≠ 8, 9, 10

Sum of required Coeff.

$(2.1^3+\frac{3}{1})^{10}(c^{10}_82^23^8+c^{10}_92^13^9+c^{10}_{10}2^03^{10})$

$β=\frac{4}{3}.^{10}c_8+20+3=83$