To answer this question, we need to understand the relationship between the radius and the area of a circle.

The formula for the area of a circle is given by:

[ A = \pi r^2 ]

Where A is the area and r is the radius of the circle.

Now, let's consider the effect of diminishing the radius by 10%.

If the radius is diminished by 10%, it means the new radius is 90% of the original radius. Mathematically, we can express this as:

[ \text{New radius} = 0.9 \times \text{Original radius} ]

Now, let's find the new area of the circle using the new radius.

[ \text{New area} = \pi \times (\text{New radius})^2 ] [ \text{New area} = \pi \times (0.9 \times \text{Original radius})^2 ] [ \text{New area} = \pi \times 0.81 \times (\text{Original radius})^2 ]

Now, let's calculate the ratio of the new area to the original area.

[ \frac{\text{New area}}{\text{Original area}} = \frac{\pi \times 0.81 \times (\text{Original radius})^2}{\pi \times (\text{Original radius})^2} ] [ \frac{\text{New area}}{\text{Original area}} = 0.81 ]

Therefore, if the radius of a circle is diminished by 10%, its area is diminished by 0.19 or 19%.

Option B) 0.19 - This option is correct because it represents the correct percentage decrease in the area of the circle when the radius is diminished by 10%.

The correct answer is B) 0.19.

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To solve this question, let's consider the distance traveled by both trains.

Let's assume the average speed of the freight train is 'x' km/hr.

The freight train leaves Delhi 2 hours before the passenger train. So, in those 2 hours, the freight train travels a distance of 2x km.

After 4 hours, the passenger train overtakes the freight train. In those 4 hours, the passenger train travels a distance of 16 × 4 = 64 km.

Since the passenger train overtakes the freight train, the distance traveled by both trains must be equal.

Therefore, we can set up the equation:

2x + 64 = 4x

Now, let's solve this equation:

2x = 64

Dividing both sides by 2:

x = 32

Therefore, the average speed of the freight train is 32 km/hr.

The correct answer is option A) 40.

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• Wrong explanation

To solve this problem, we need to find the distance travelled by train.

Given that Dinesh travelled 1200 km by air, which formed 2/5 of his trip, we can find the total distance of his trip by multiplying 1200 km by 5/2.

Total distance of the trip = (1200 km) * (5/2) = 3000 km.

Next, we are told that one-third of the whole trip, Dinesh travelled by car. To find the distance travelled by car, we can multiply the total distance of the trip by 1/3.

Distance travelled by car = (3000 km) * (1/3) = 1000 km.

Finally, the distance travelled by train is the remaining distance after subtracting the distance travelled by air and the distance travelled by car from the total distance of the trip.

Distance travelled by train = Total distance of the trip - Distance travelled by air - Distance travelled by car = 3000 km - 1200 km - 1000 km = 800 km.

Therefore, the distance travelled by train is 800 km, which corresponds to option C.

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• Wrong explanation

To solve this problem, let's break it down into smaller parts and analyze each piece of information given.

Let's assume the original speed of the train is "v" miles per hour and the time it takes to cover the distance between the two stations is "t" hours.

1) First, we are given that after traveling for an hour at the original speed, the train goes at 3/5th of the original speed. This means that the new speed of the train is (3/5)v miles per hour. The time taken to cover the remaining distance at this reduced speed is (t + 2) hours.

2) Next, we are told that if the fault had occurred after traveling another 50 miles, the train would have reached the destination 40 minutes earlier. This means that the time taken to cover the remaining distance would be (t - 40/60) hours.

Now, let's use these pieces of information to form equations and solve for the distance between the two stations.

Distance = Speed × Time

1) Using the information given in point 1, we can write the equation as: (v × 1) + ((3/5)v × (t + 2)) = v × t

2) Using the information given in point 2, we can write the equation as: (v × 1) + ((3/5)v × (t - 40/60)) = v × (t - 2)

Simplifying these equations will give us the value of "t" and subsequently the distance between the two stations.

Let's solve these equations step by step:

1) v + (3/5)v(t + 2) = vt 5v + 3v(t + 2) = 5vt 5v + 3vt + 6v = 5vt 8v + 3vt = 5vt 8v = 2vt 4v = vt

2) v + (3/5)v(t - 40/60) = vt - 2v 5v + 3v(t - 2/3) = 5vt - 10v 5v + 3vt - 2v = 5vt - 10v 3vt + 3v = 5vt - 5v 3v = 2vt - 5v 5v = 2vt

From equation 1) and equation 2), we can see that 4v = 5v. This implies that v = 0, which is not possible.

Hence, there is no valid solution for this problem.

Therefore, the given question is incorrect, and none of the options provided (A, B, C, D) are correct.

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• Wrong explanation