If the sum of the coefficients of all the positive even powers of x in the binomial expansion of (2 x3+(3/x))10 is 510-β ⋅ 39, then β is equal to

Question

If the sum of the coefficients of all the positive even powers of x in the binomial expansion of (2 x3+(3/x))10 is 510-β ⋅ 39, then β is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

T r +1= 10 C r (2 x 3)10- r ((3/ x )) r = 10 C r 210- r 3 r x 30-4 r Put r=0,1,2, ldots .7 and we get β=83

Q. If the sum of the coefficients of all the positive even powers of $x$ in the binomial expansion of $(2 x^{3} + \frac{3}{x})^{10}$ is $5^{10} - β \cdot 3^{9}$ , then $β$ is equal to____

$T_{r + 1} =^{10} C_{r} (2 x^{3})^{10 - r} (\frac{3}{x})^{r}$
$=^{10} C_{r} 2^{10 - r} 3^{r} x^{30 - 4 r}$
Put $r = 0, 1, 2, \dots .7$ and we get $β = 83$

Q. If the sum of the coefficients of all the positive even powers of x in the binomial expansion of (2x3+x3​)10 is 510−β⋅39, then β is equal to____

Tr+1​=10Cr​(2x3)10−r(x3​)r =10Cr​210−r3rx30−4r Put r=0,1,2,….7 and we get β=83

Q. If the sum of the coefficients of all the positive even powers of $x$ in the binomial expansion of $(2 x^{3} + \frac{3}{x})^{10}$ is $5^{10} - β \cdot 3^{9}$ , then $β$ is equal to____

$T_{r + 1} =^{10} C_{r} (2 x^{3})^{10 - r} (\frac{3}{x})^{r}$
$=^{10} C_{r} 2^{10 - r} 3^{r} x^{30 - 4 r}$
Put $r = 0, 1, 2, \dots .7$ and we get $β = 83$