Let, f(x) = 2x³ + ax² + 11x + a + 3

Now, we have

2x – 1 = 0

x = 1/2

As per the question,

f(x) is exactly divisible by 2x – 1 which means that 2x – 1 is a factor of f(x)

Hence,

Using factor theorem,

(x – a) will be a factor of f(x) if f(a) = 0 and hence,

f() 0

Hence,

= 5a = -35

a = -7

Thus, the value of a is -7