Minimum value of x/y:

• To get the smallest possible value for x/y, we need the smallest value for x and the largest value for y.

• So, the minimum value of x/y is 3/11.

Maximum value of x/y:

• To get the largest possible value for x/y, we need the largest value for x and the smallest value for y.

• So, the maximum value of x/y is 5/8.

Therefore, the correct inequality is:

3/11 ≤ x/y ≤ 5/8

The Headmaster want to speak to you. incorrect

"Wants" is the correct form of the verb to use with the singular subject "The Headmaster."

C) he displayed modesty in his interactions.

This option directly addresses Gandhi's humility, which is the core of the question.

• Humility is synonymous with modesty.

• Gandhi was renowned for his simple lifestyle and respectful demeanor, reflecting his humble nature.

The part "how to do computation" is not appropriate. For consistency and conciseness, it should simply be "computation."

Correct - All engineering students should learn mechanics, mathematics and  computation.

Water flow inside the pipe and electricity flow inside wire

We can set up two inequalities based on the given conditions:

32 ≤ v ≤ 64

Putting values 

32 ≤ 80 - 32t  

-48 ≤ -32t

t ≤ 1.5

80 - 32t ≤ 64

-16 ≤ -32t

t ≥ 0.5

The velocity is between 32 m/s and 64 m/s when both conditions are met. So, the time interval is:

0.5 seconds ≤ t ≤ 1.5 seconds

A: The component is defective.

B: The component was manufactured by M2.

Given Probabilities

• P(B) = Probability that a component is manufactured by M2 = 40% = 0.4

• P(B') = Probability that a component is manufactured by M1 = 60% = 0.6

• P(A|B) = Probability that a component is defective given it was manufactured by M2 = 3% = 0.03

• P(A|B') = Probability that a component is defective given it was manufactured by M1 = 2% = 0.02

We need to find P(B|A), the probability that the component was manufactured by M2 given that it is defective.

We can use Bayes' theorem for this:

P(B|A) = (P(A|B) * P(B)) / P(A)

To find P(A), we can use the law of total probability: P(A) = P(A|B) * P(B) + P(A|B') * P(B')

Substituting the given values: P(A) = (0.03 * 0.4) + (0.02 * 0.6) = 0.012 + 0.012 = 0.024

Now, we can calculate P(B|A): P(B|A) = (0.03 * 0.4) / 0.024 = 0.5

The total number of tourists visiting India in 2011 was 13500. One-third of this number would be 4500 tourists. As you can see from the table, no single country sent even close to this number of tourists.

If we combine tourists of England and france 

3500+1000 = 4500

We have the equation: |−2x + 9| = 3

This equation can be split into two cases:

Case 1: -2x + 9 = 3

• x = 3

Case 2: -2x + 9 = -3

• x = 6

Now, we need to find the value of |−x| − x² for both values of x.

For x = 3:

• |−x| − x² = |-3| - 3² = 3 - 9 = -6

For x = 6:

• |−x| − x² = |-6| - 6² = 6 - 36 = -30

Therefore, the possible values of |−x| − x² are -6 and -30.