To solve this problem, we need to understand the concepts of vena contracta, coefficient of velocity, and coefficient of discharge.

1. Vena Contracta:
The vena contracta is the point in a fluid jet where the diameter is the smallest. In this case, the vena contracta diameter is given as 90mm.

2. Coefficient of Velocity (Cv):
The coefficient of velocity is the ratio of the actual velocity of the fluid to the theoretical velocity of the fluid. It is denoted by Cv and is given as 0.95 in this problem.

3. Coefficient of Discharge (Cd):
The coefficient of discharge is the ratio of the actual discharge to the theoretical discharge. It is denoted by Cd and is what we need to find.

Now, let's solve the problem step by step:

Step 1: Calculate the theoretical velocity (Vt) at the nozzle exit using the vena contracta diameter.
- Given nozzle diameter = 100mm
- Given vena contracta diameter = 90mm

The ratio of the vena contracta diameter to the nozzle diameter is given by the equation:
Vt/V = (d/D)^0.5

Substituting the values:
Vt/V = (90/100)^0.5 = 0.9487

Therefore, the theoretical velocity is 0.9487 times the velocity at the nozzle exit.

Step 2: Calculate the actual velocity (Va) at the nozzle exit using the coefficient of velocity.
- Given coefficient of velocity (Cv) = 0.95

The actual velocity is given by the equation:
Va = Cv * Vt

Substituting the values:
Va = 0.95 * 0.9487 = 0.9013

Therefore, the actual velocity at the nozzle exit is 0.9013 times the velocity at the nozzle exit.

Step 3: Calculate the coefficient of discharge (Cd) using the actual velocity and the vena contracta diameter.
- Given vena contracta diameter = 90mm

The coefficient of discharge is given by the equation:
Cd = (Va^2 * Aa) / (V^2 * A)

where Aa is the area at the vena contracta and A is the area at the nozzle exit.

Since the areas are proportional to the squares of the diameters:
Cd = (Va^2 * (d^2/D^2)) / (V^2 * 1)

Substituting the values:
Cd = (0.9013^2 * (90^2/100^2)) / (1^2 * 1)
= (0.8118 * 0.81)
= 0.6588

Therefore, the coefficient of discharge for the nozzle is 0.6588.

The correct answer is not given in the options provided. The correct answer should be 0.6588, not 0.7695.