To determine the least number of planks required to stop the bullet, we need to consider the amount of velocity lost after passing through each plank.

Let's assume the initial velocity of the bullet is V.

After passing through the first plank, the bullet loses 1/20th of its velocity. So, the velocity after passing through the first plank is (19/20)V.

After passing through the second plank, the bullet again loses 1/20th of its velocity. Therefore, the velocity after passing through the second plank is (19/20) * (19/20)V = (19/20)^2V.

Similarly, after passing through the third plank, the velocity becomes (19/20)^3V.

We can observe a pattern here:

After passing through the nth plank, the velocity becomes (19/20)^nV.

To stop the bullet, the velocity should become zero. So, we need to find the minimum value of n for which (19/20)^nV = 0.

Simplifying the equation, we get:

(19/20)^n = 0

Since any positive number raised to the power of n cannot be zero, this equation has no solution. Therefore, the bullet cannot be completely stopped by any finite number of planks.

However, if we consider a practical scenario where the velocity is reduced to a negligible value, we can determine the minimum number of planks required to achieve that.

Let's say we want the velocity to be reduced to 1/1000th of its initial value. In other words, we want (19/20)^nV = (1/1000)V.

Simplifying the equation, we get:

(19/20)^n = 1/1000

Taking the logarithm of both sides, we have:

n log(19/20) = log(1/1000)

Solving for n, we get:

n = log(1/1000) / log(19/20)

Using a calculator, we find that n ≈ 11.05.

Since the number of planks must be a whole number, the least number of planks required to reduce the velocity to a negligible value is 11.

Therefore, the correct answer is option C) 11.

To solve this problem, we need to understand the concept of velocity and how it is affected when passing through a plank.

1. Understanding Velocity Loss: When a bullet passes through a plank, it experiences a loss in velocity. In this case, the loss is given as 1/20th of its initial velocity. This means that after passing through one plank, the bullet's velocity reduces to 19/20th of its initial velocity.

2. Stopping the Bullet: In order to stop the bullet completely, its velocity needs to be reduced to zero. This can be achieved by passing the bullet through multiple planks, each reducing its velocity by 1/20th.

3. Calculation: Let's assume the initial velocity of the bullet is V. After passing through one plank, its velocity becomes (19/20)V. After passing through two planks, its velocity becomes (19/20)^2 * V. Similarly, after passing through n planks, its velocity becomes (19/20)^n * V.

4. Finding the Least Number of Planks: We need to find the value of n for which the bullet's velocity becomes zero. So, we set the equation (19/20)^n * V = 0 and solve for n.

(19/20)^n = 0

Taking the logarithm of both sides, we get:

n * log(19/20) = log(0)

Since the logarithm of zero is undefined, we conclude that the bullet's velocity cannot reach zero. Hence, the bullet cannot be completely stopped by passing it through multiple planks.

5. Least Number of Planks to Reduce Velocity: However, we can determine the least number of planks required to reduce the bullet's velocity to a negligible amount. Let's say we want the velocity to be reduced to less than 1/1000th of its initial velocity. So, we set the equation (19/20)^n * V ≤ 1/1000 * V and solve for n.

(19/20)^n ≤ 1/1000

Taking the logarithm of both sides, we get:

n * log(19/20) ≤ log(1/1000)

Simplifying the equation, we find:

n ≥ log(1/1000) / log(19/20)

Using a calculator, we can evaluate this expression to be approximately 10.77.

6. Rounding Up: Since we cannot have a fraction of a plank, we round up the value of n to the nearest whole number. Hence, the least number of planks required to reduce the bullet's velocity to less than 1/1000th of its initial velocity is 11.

Therefore, the correct answer is option C) 11.