Logical And Analytical Reasoning Skills

Let’s break down the information step-by-step:
The problem states that a person was born on the fifth Monday of February in a particular year. To get to the correct answer, we need to analyze the distribution of the days in February in that year. Step 1: Determine the conditions for five Mondays in February.
- February typically has 28 or 29 days, depending on whether the year is a leap year.
- If a person is born on the fifth Monday of February, then February must have at least five Mondays.
- In order for a month to have five Mondays, the month must have 29 days (February in a leap year) because if February has only 28 days, it can have at most four Mondays.
- So, the year must be a leap year for the person to be born on the fifth Monday.
Step 2: Understand the distribution of the dates.
In a leap year, February has 29 days. To have five Mondays, the first Monday must fall on February 1\textsuperscript{st}, and the remaining Mondays will fall on: - 1\textsuperscript{st}, 8\textsuperscript{th}, 15\textsuperscript{th}, 22\textsuperscript{nd}, and 29\textsuperscript{th}. Step 3: Determine the day of the week for February 2\textsuperscript{nd.}
- Since February 1\textsuperscript{st} is a Monday, the next day, February 2\textsuperscript{nd}, must be a Tuesday.
This is the key to answering the question because the statement in option (A) says "The 2\textsuperscript{nd} February of that year is a Tuesday", which is true based on the above calculations. Step 4: Analyze the other options.
- Option (B) suggests that there will be five Sundays in the month of February. Since February has only 29 days and we already know the distribution of Mondays, February can only have four Sundays, not five. Thus, option (B) is incorrect. - Option (C) claims that the 1\textsuperscript{st} of February is a Sunday. However, as we have already determined, February 1\textsuperscript{st} is a Monday, so option (C) is incorrect. - Option (D) states that all Mondays of February have even dates. The Mondays of February are 1\textsuperscript{st}, 8\textsuperscript{th}, 15\textsuperscript{th}, 22\textsuperscript{nd}, and 29\textsuperscript{th}. As we can see, February 1\textsuperscript{st} is an odd date, so option (D) is also incorrect. Step 5: Conclusion.
Thus, the only correct statement is (A), "The 2\textsuperscript{nd} February of that year is a Tuesday."

In this passage, the fish species S has ultra-black skin that offers advantages and disadvantages. The ultra-black skin helps them avoid predators and sneakily attack prey, which gives them a distinct advantage in terms of camouflage and hunting ability. However, the extra pigment layer also leads to lower collagen levels, making their skin more fragile. This creates a disadvantage for species S in terms of the structural integrity of their skin. Step 1: Analyze the context of the passage.
The passage explains the dual nature of the ultra-black skin of species S. On one hand, it provides protection from predators and helps with hunting, but on the other hand, it leads to a fragility in the skin due to lower collagen. Step 2: Evaluate the options.
- Option (A): “Having ultra-black skin is only advantageous to species S.” This is incorrect because the passage clearly mentions that ultra-black skin has both advantages and disadvantages. The disadvantages are related to the fragility caused by lower collagen in their skin. - Option (B): “Species S with lower collagen in their skin are at an advantage because it helps them avoid predators.” This is incorrect. The passage explains that lower collagen makes the skin more fragile, not that it helps in avoiding predators. The ultra-black skin helps them avoid predators, not the collagen content. - Option (C): “Having ultra-black skin has both advantages and disadvantages to species S.” This is the correct answer. The passage explicitly mentions that the ultra-black skin provides benefits such as avoiding predators and aiding in hunting, but also has the disadvantage of making the skin more fragile due to reduced collagen. - Option (D): “Having ultra-black skin is only disadvantageous to species S but advantageous only to their predators.” This is incorrect. While the passage acknowledges the fragility of the skin, it does not suggest that the ultra-black skin is solely disadvantageous to species S or that it only benefits predators. Step 3: Conclusion.
The correct logical inference based on the passage is that the ultra-black skin of species S provides both advantages (camouflage and hunting) and disadvantages (fragility due to lower collagen). Hence, the correct answer is (C).

Let the total production for the past days be units. After today's production of 180 units, the total production becomes . The average production for days is given as 110 units. Therefore, we can set up the equation for the average: Multiplying both sides by to eliminate the denominator: Expanding the right side: Now, subtract and from both sides: Simplifying: Solving for : Thus, the value of is 7.

Let's break down the journey step-by-step: Step 1: From R to S.
- The person starts at 7 AM from city R.
- Trains from R to S start at 7 AM and run every 60 minutes.
- Since the person starts at 7 AM, they can catch the first train to S at 7 AM itself.
- The travel time from R to S is 1 hour, so the person reaches S at 8 AM.
Step 2: From S to Q.
- At city S, the first train to Q departs at 8 AM with a frequency of 45 minutes.
- The person arrives at 8 AM, so they can catch the 8 AM train to Q.
- The travel time from S to Q is 1 hour, so the person reaches Q at 9 AM.
Step 3: From Q to P.
- At city Q, the first train to P departs at 5 AM with a frequency of 120 minutes.
- Since the person arrives at 9 AM, they will have to wait for the 10 AM train.
- The travel time from Q to P is 1 hour, so the person reaches P at 11 AM.
Step 4: From P to R.
- At city P, the first train to R departs at 8 AM with a frequency of 90 minutes.
- Since the person arrives at 11 AM, they will have to wait for the 11:30 AM train.
- The travel time from P to R is 1 hour, so the person reaches R at 12:30 PM.
Step 5: Total Time Calculation.
- The person starts the journey at 7 AM and returns to R at 12:30 PM.
- The total time taken is from 7 AM to 12:30 PM, which is 6 hours and 30 minutes.
Final Answer:
The minimum time required is 6 hours and 30 minutes.

We are given a square sheet of paper with a side length of 1 cm. The area of the square sheet is: Now, let’s analyze the two cases. Case M: In case M, four equal-sized circles are shaded inside the square. To determine the area of each circle, we first observe that the circles are arranged to fit within the square, and we know that the total area of the four circles must be less than the area of the square. Let the radius of each circle be . The total area of the four circles is: The four circles are arranged in such a way that their combined area is equal to the area of the square. Therefore, the area of the unshaded region in case M is: Case N: In case N, nine equal-sized circles are shaded inside the square. Similarly, let the radius of each circle in case N be . The total area of the nine circles is: Again, the combined area of the nine circles must fit within the area of the square. Therefore, the unshaded area in case N is: Step 1: Relating the areas of the circles.
Since the circles are packed differently in each case, we must determine the relation between the radii and . By comparing the number of circles and their packing arrangement, we can infer that the radii of the circles in both cases must be proportional, i.e., . Step 2: Comparing the unshaded areas.
The unshaded area ratio can now be calculated as: Substituting into the equation, we find that the ratio simplifies to 1 : 1. Thus, the ratio of the areas of unshaded regions of case M to case N is .

We are asked to find the area bounded by the function on the interval .
Step 1: Simplify the function.
We start by simplifying the given function: Thus, .
Step 2: Set up the integral.
The area under the curve from to is given by the definite integral: Step 3: Evaluate the integral.
The integral of is: Evaluating from to : Step 4: Conclusion.
Thus, the area bounded by is 2.

Step 1: Initial Setup
The students are initially arranged in the following order:

Step 2: After the 1^st Round
The 4^th student behind P leaves the game.
Starting from P and counting clockwise: Q (1), R (2), S (3), T (4). So, T leaves the game.
The new arrangement is:

Step 3: After the 2^nd Round
The 5^th student behind Q leaves the game.
Starting from Q: R (1), S (2), U (3), V (4), W (5). So, W leaves the game.
The new arrangement is:

Step 4: After the 3^rd Round
The 3^rd student behind V leaves the game.
Starting from V: P (1), Q (2), R (3). So, R leaves the game.
The new arrangement is:

Step 5: After the 4^th Round
The 4^th student behind U leaves the game.
Starting from U: V (1), P (2), Q (3), S (4). So, S leaves the game.
The final arrangement is:

Step 6: Conclusion
The students left in the game after the 4^th round are: P, Q, U, and V.

Step 1: Analyzing the iterative process.
In the first iteration (Iteration 0), the length of the curve is 1. In each subsequent iteration, the number of segments increases, and the length of each segment decreases by a factor of .

Step 2: Finding the total length after each iteration.
After each iteration, the total length of the curve increases by a factor of , because each segment is scaled by a factor of and there are 5 times as many segments. Thus, the total length after 'Iteration n' is:

We are given the following data for the five nations:

Step 1: Calculate the total number of medals won by each nation.
USA: medals
Canada: medals
Japan: medals
Australia: medals
France: medals

Step 2: Analyzing the statements.

(A) France will occupy the third place if the list were made on the basis of the total number of medals won.
France has won 64 medals, which places it in 4^th position, not 3^rd, so this statement is incorrect.

(B) The order of the top two nations will not change even if the list is made on the basis of the total number of medals won.
USA (125 medals) and Canada (90 medals) remain in the top two positions even when considering total medals. This statement is correct.

(C) USA and Canada together have less than 50% of the medals awarded to the nations in the above table.
Total medals awarded:
USA and Canada together have medals.
Percentage:
Since 57.2% is greater than 50%, this statement is incorrect.

(D) Canada has won twice as many total medals as Japan.
Canada has 90 medals, and Japan has 45 medals.
, so this statement is correct.

Let the maximum consulting fee be .

The overhead is calculated as:
For , overhead = .
For , overhead = ₹1,00,000 + .

Also, the GST is 18% on the total amount (consulting fee + overhead). The client can pay a maximum of ₹10,00,000.

Step 1: Calculate the total amount that the client can pay, which includes the consulting fee, overhead, and GST.
The total amount is:

Given that the total amount cannot exceed ₹10,00,000, we can set up the following equation:


Step 2: Apply the formula for overhead and solve for .
For , the overhead is:

Thus, the total amount becomes:

Simplifying:


Conclusion:
The maximum consulting fee that the employee can charge is ₹7,24,961.