Mitigate means to make something less severe, harmful, or painful.

Diminish means to make something smaller, less important, or less intense.

Despite several setbacks the mission succeeded in its attempt to resolve the conflict.

Cost function: C(q) = 5q^2

Revenue function: R(q) = 50q (since the price per unit is 50)

Profit function: P(q) = R(q) - C(q) = 50q - 5q^2

derivative of the profit function:

P'(q) = 50 - 10q

derivative equal to zero and solve for q:

• 50 - 10q = 0

• q = 5

Verify that this is a maximum point:

• We can use the second derivative test. P''(q) = -10, which is negative. This indicates a maximum point.

Therefore, the number of units to be produced by the firm to maximize profit is 5.

Mark to all

D) This country’s expenditure on educational reforms is very less.

The correct form would be: "This country’s expenditure on educational reforms is very low."

"Less" is typically used for comparison, while "low" is used to describe a quantity.   

Bayes' theorem: P(A|B) = P(B|A) * P(A) / P(B)

Where:

• P(A|B) is the probability of A given B

• P(B|A) is the probability of B given A

• P(A) is the probability of A  

• P(B) is the probability of B

In our case:

• A is the event that the shock absorber is made by Y.

• B is the event that the shock absorber is reliable.

So, we need to find P(A|B), which is the probability that the shock absorber is made by Y given that it is reliable.

• P(A) = Probability of shock absorber being made by Y = 0.4

• P(B|A) = Probability of a shock absorber being reliable given it's made by Y = 0.72

• P(B|A') = Probability of a shock absorber being reliable given it's made by X = 0.96

• P(A') = Probability of shock absorber being made by X = 0.6

Now, we can calculate P(B) (probability of a shock absorber being reliable) using the law of total probability:

• P(B) = P(B|A) * P(A) + P(B|A') * P(A')

• P(B) = 0.72 * 0.4 + 0.96 * 0.6 = 0.84

Finally, we can apply Bayes' theorem:

• P(A|B) = (0.72 * 0.4) / 0.84 = 0.3429

Therefore, the probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is approximately 0.334.

So, the correct answer is (B) 0.334.

(D) Not gender-discriminatory             

• First letter: A, C, F, J. The difference between consecutive letters increases by 1 each time (2, 3, 4).

• Second letter: D, G, K, P. The difference between consecutive letters also increases by 1 each time (3, 4, 5).

Following the pattern:

• The next first letter will be 5 letters after J, which is O.

• The next second letter will be 6 letters after P, which is V.

Therefore, the next term in the sequence is OV.

Mean is the average of a set of numbers. It is calculated by summing all the numbers and dividing by the total count.

When you add a constant to each number in a dataset, you are essentially shifting the entire dataset by that constant value.

Since every number is increased equally, the overall center (mean) of the data also shifts by the same constant value.

Standard deviation measures the dispersion or spread of a dataset relative to its mean. It is not influenced by a constant shift in the data.

When you add a constant to every data point, the distance between each data point and the mean remains the same. This is because both the data points and the mean are shifted by the same amount. Consequently, the spread of the data (standard deviation) does not change.