To answer this question, let's analyze the given equation and the relationship between the variables:

Given: A/B = C and C > D

We are asked to determine which of the following statements is true.

Option A) A is always greater than D: This statement is not necessarily true. Since A and B are not explicitly defined, we cannot conclude any specific relationship between A and D. The given equation A/B = C does not provide enough information to make this statement always true.

Option B) C is always greater than D: This statement is true. Since C is greater than D, any value of A/B that equals C will also be greater than D. This is because if A/B = C and C > D, then multiplying both sides of the equation by B gives us A = BC. Since C > D, A will always be greater than D.

Option C) B is always less than D: This statement is not necessarily true. Similar to Option A, we don't have enough information about the relationship between B and D. Therefore, we cannot conclude that B is always less than D.

Option D) None of the above: This option is incorrect, as we have concluded that Option B is true.

Therefore, the correct answer is Option B) C is always greater than D.

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To solve this problem, let's consider the placement of the balls in the smaller squares. Since each row should have at least one ball, we can divide the problem into three cases:

Case 1: Each row has exactly one ball. In this case, we have one ball to place in each row. The number of ways to do this is equal to the number of ways to arrange the balls in the rows, which is 3!.

Case 2: One row has two balls, and the other two rows have one ball each. In this case, we need to choose one row to have two balls and then place the remaining ball in one of the two remaining rows. The number of ways to do this is equal to the number of ways to choose the row (3) multiplied by the number of ways to choose the remaining row (2).

Case 3: One row has three balls, and the other two rows have one ball each. In this case, we need to choose one row to have three balls and then place the remaining balls in the two remaining rows. The number of ways to do this is equal to the number of ways to choose the row (3).

Now, let's calculate the total number of ways by summing up the possibilities from each case:

Total number of ways = (number of ways in Case 1) + (number of ways in Case 2) + (number of ways in Case 3) = 3! + (3 * 2) + 3 = 6 + 6 + 3 = 15

Therefore, there are 15 different ways to place the balls in the smaller squares.

The correct answer is A) 81.

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To solve this problem, we can use the concept of proportionality.

Let's start by comparing the cost and weight of the salt packets in the given scenario.

Given: Cost of 16 packets of salt = Rs. 28 Weight of each packet = 900 grams

We need to find: Cost of 27 packets of salt (with each packet weighing 1 Kg)

To compare the cost, we can set up a proportion based on the weight of the packets:

$\frac{16\ \text{packets}}{27\ \text{packets}} = \frac{900\ \text{grams}}{1\ \text{kg}}$

Simplifying this proportion:

$\frac{16}{27} = \frac{900}{1000}$

Cross-multiplying:

$16 \times 1000 = 27 \times 900$

Simplifying further:

$16000 = 24300$

Since the equation is not balanced, we can conclude that the given options are incorrect.

Therefore, none of the options provided is correct.

Please check the given information and options again.

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To answer this question, we need to look for a pattern or rule in the given sequence of numbers.

Looking at the sequence: 75 65 85 55 45 85 35 ? ?, we can observe the following pattern:

• The sequence alternates between decreasing and increasing by 10.
• The first number in each pair is the previous number minus 10, and the second number is the previous number plus 20.

Using this pattern, we can determine the next pair of numbers:

• The previous number is 35. So, the next pair of numbers will be 35 minus 10, which is 25, and 35 plus 20, which is 55.

Therefore, the correct answer is option B) 25 85. This option follows the pattern observed in the given sequence.

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To answer this question, we can calculate the time taken for each part of the journey separately and then add them together.

Let's calculate the time taken for the first part of the journey, which is two-thirds of the total distance of 15 miles. The speed for this part is given as 40 mph.

Distance for the first part = 2/3 * 15 miles = 10 miles Speed for the first part = 40 mph

To calculate the time taken for the first part, we can use the formula:

Time = Distance / Speed

Time taken for the first part = 10 miles / 40 mph = 0.25 hours

Next, let's calculate the time taken for the second part of the journey, which is the remaining one-third of the total distance. The speed for this part is given as 60 mph.

Distance for the second part = 1/3 * 15 miles = 5 miles Speed for the second part = 60 mph

Time taken for the second part = 5 miles / 60 mph = 0.083 hours

Finally, we can add the times taken for both parts of the journey to get the total time taken:

Total time taken = Time taken for the first part + Time taken for the second part = 0.25 hours + 0.083 hours = 0.333 hours

To convert this time to minutes, we multiply by 60:

Total time taken = 0.333 hours * 60 mins/hour = 20 mins

Therefore, the correct answer is D) 20 mins.

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To solve this question, let's consider the different types of small cubes that can be formed when the big cube is cut.

The big cube is made up of 6 x 6 x 6 = 216 small cubes.

1. The corner small cubes: There are 8 corner small cubes in the big cube. Each corner small cube has 3 faces painted.
2. The edge small cubes: There are 12 edges in the big cube, with each edge consisting of 6 small cubes. So, there are a total of 12 x 6 = 72 edge small cubes. Each edge small cube has 2 faces painted.
3. The face small cubes: The big cube has 6 faces, each consisting of 6 x 6 = 36 small cubes. So, there are a total of 6 x 36 = 216 face small cubes. Each face small cube has 1 face painted.

Now, let's calculate the number of small cubes that are painted on at least 2 sides:

1. Corner small cubes: 8 x 3 = 24 cubes (since each corner small cube has 3 faces painted).
2. Edge small cubes: 72 x 2 = 144 cubes (since each edge small cube has 2 faces painted).
3. Face small cubes: 216 x 1 = 216 cubes (since each face small cube has 1 face painted).

So, the total number of small cubes painted on at least 2 sides is 24 + 144 + 216 = 384.

Therefore, the correct answer is A) 56.

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