Correct Answer: 4, 3, 5, 1, 2

Solution : Given:
1. Puritan   2. Purpose   3. Purge   4. Purgatory   5. Purify

Step 1: The first, second, and third letters of each word are the same, so move on to the next letter.
Step 2: The fourth letter of each word is: i, p, g, g, i. Based on the alphabetical order of these letters, we can arrange them: Purge, Purgatory, Puritan, Purify, Purpose.
Step 3: Compare the fifth letter of (Purge, Purgatory), and (Puritan, Purify). Purgatory will come before Purge in the sequence as a comes before e in the alphabetical system. Similarly, Purify will come before Puritan in the sequence as f comes before t in the alphabetical system.

So, the sequence is Purgatory, Purge, Purify, Puritan, Purpose, or 43512. Hence, the fourth option is correct.

Correct Answer: 8500

Solution : From the pie chart, the population of Village D is 17% of the total population. 
Population of Village D = $\frac{17}{100}$ × 50000 = 8500
Hence, the correct answer is 8500.

Correct Answer: back out

Solution : The correct answer is the fourth option.

This phrase means to withdraw from a commitment or agreement, and it fits the context of the sentence. If someone backs out after signing an agreement, it implies that he decided not to proceed with the commitment they initially agreed to.

The meanings of the other options are as follows:

• Back up: This phrase means to support or provide assistance.

• Back in: It refers to returning to a location or situation.

• Back it: It is not a common expression related to signing agreements or commitments.

Therefore, the correct sentence is: "Once he has signed the agreement, he won't be able to back out."

Correct Answer: resileince

Solution : The fourth option is the correct answer.

The incorrectly spelled word is "resileince"; the correct spelling is "resilience," which refers to the ability to recover from or adjust to adversity.

The meanings of other options are as follows:

• Livelihood is the means of securing the necessities of life, often in terms of employment or income.
• Diversifying means making or becoming more diverse or varied.
• Appropriate means suitable or fitting for a particular purpose or situation.

Therefore, the correct answer is resileince.

Correct Answer:

Solution : Train, chair, and school are not related to each other in any way, so all three of them will have separate circles and they would not intersect with each other.

The Venn diagram will be –

Hence, the first option is correct.

Correct Answer: 3

Solution : The error is in the third option "in which he was".

The correct sentence is: "Despite the speed at which he was driving, he couldn't reach on time."

The phrase "despite the speed at which he was driving" is a prepositional phrase. It modifies the verb "couldn't reach." It tells us why he couldn't reach on time.

Correct Answer: 10%

Solution : Let the cost price of the item be 100.
The shopkeeper increases the cost price by 50% so,
Marked Price = 100 + 0.5 × 100 = 150
The shopkeeper offers a discount of 40% on the marked price
⇒ Discounted Price = 150 − 0.4 × 150 = 90
Loss = Cost Price − Discounted Price = 100 – 90 = 10
Now,
Loss Percentage = $\frac{\text{Loss}}{\text{Cost Price}} × 100=\frac{10}{100} × 100 = 10\%$
Hence, the correct answer is 10%.

Correct Answer: crude

Solution : The correct answer is crude.

The crude birth rate signifies the number of live births within a year per 1,000 individuals in a population estimated at midyear. Calculating the rate of natural increase involves subtracting the crude death rate from the crude birth rate. This figure represents the rate of population change exclusive of migration, reflecting the overall growth or decrease in the population due to natural factors such as births and deaths.

Correct Answer: 3, 2, 4, 5, 1

Solution : Given:
1. Flint 2. Flec 3. Flaw  4. Fleet 5. Flight

Step 1: Compare the first and second letters of each word. Since all the words start with the same letter F and are followed by l, then move on to the next letter.
Step 2: The third letter of each word is a, e, or i. Based on the alphabetical order of these letters, we can arrange them – Flaw, Flec, Fleet, Flint, Flight
Step 3: Compare the fourth letter of (Flec, Fleet). Flec will come before Fleet in the sequence as c comes before e in the alphabetical system. 
Step 4: Compare the fourth letter of (Flint, Flight). Flight will come before Flint in the sequence as g comes before n in the alphabetical system.

So, the sequence is Flaw, Flec, Fleet, Flight, Flint, or 3, 2, 4, 5, 1. Hence, the third option is correct.

Correct Answer: 125

Solution : Given:
64 × 8 ÷ 24 – 5 + 3 = ?

On interchanging the mathematical sign, we get –
= 64 ÷ 8 + 24 × 5 – 3
= 8 + 24 × 5 – 3
= 8 + 120 – 3
= 125

So, 125 is the required answer. Hence, the second option is correct.