Step 1: Understand the relationship -
Taciturn (meaning reserved or saying little) is the antonym (opposite) of Garrulous (meaning excessively talkative).

Step 2: Apply the logic -
Insolvent (meaning unable to pay one's debts) needs its opposite. The most accurate term is Solvent (meaning having assets in excess of liabilities; able to pay one's debts). Quick Tip: This is an analogy question based on Antonyms. Always identify the relationship in the first pair before looking at the second.

Step 1: Analyze the sentence structure -
The sentence uses a third conditional structure ("would not have secured") which indicates a hypothetical situation in the past.

Step 2: Check the options -
"Had it not been for" is a formal inversion of "If it had not been for." It is used to indicate that if a specific event had not happened, the result would have been different.

Step 3: Conclusion -
Option 4 correctly completes the conditional clause. Quick Tip: "Had it not been for" = "If it had not been for". It is a standard way to express a condition that was essential for an outcome.

Step 1: Identify the comparison -
The sentence compares the "bureaucratic system" to a "labyrinth" (a maze).

Step 2: Determine the type -
Since the comparison is direct (it says the system *was* a labyrinth) without using the words "like" or "as", it is a Metaphor.

Step 3: Define "Red Tape" -
"Red tape" is also a metaphor for excessive regulations or rigid conformity to formal rules. Quick Tip: Simile uses "like" or "as" (e.g., as busy as a bee). Metaphor states one thing *is* another (e.g., time is money).

Step 1: Define the target word -
"Recondite" means little known, abstruse, or obscure.

Step 2: Analyze the context -
The sentence says the texts were "accessible only to a handful of scholars," which implies they are specialized or difficult to understand.

Step 3: Match the synonym -
"Esoteric" means intended for or likely to be understood by only a small number of people with a specialized knowledge. This is a perfect match for "recondite". Quick Tip: Context clues like "accessible only to a handful" often help define difficult vocabulary words in a sentence.

Step 1: Calculate completed years -
We take completed years up to 1946. Total = 1600 years + 300 years + 46 years.

Step 2: Calculate odd days in centuries -
1600 years have 0 odd days. 300 years have 1 odd day.

Step 3: Calculate odd days in 46 years -
In 46 years, there are 11 leap years and 35 ordinary years. Total odd days = \((11 \times 2) + (35 \times 1) = 22 + 35 = 57\) days.

Step 4: Simplify odd days - \(57 \div 7\) leaves a remainder of 1. So, odd days in 46 years = 1. Total odd days till 1946 = \(1 + 1 = 2\).

Step 5: Calculate odd days in 1947 till Aug 15 -
Jan(3), Feb(0), Mar(3), Apr(2), May(3), Jun(2), Jul(3), Aug(15). Total = 31 days. \(31 \div 7\) leaves a remainder of 3.

Step 6: Final Total -
Total odd days = \(2 (till 1946) + 3 (in 1947) = 5\).
According to the code, 5 represents Friday. Quick Tip: Standard Odd Day Codes: 0-Sun, 1-Mon, 2-Tue, 3-Wed, 4-Thu, 5-Fri, 6-Sat.

Step 1: Identify the year type -
2007 is an ordinary year. To find a matching calendar, the target year must also be an ordinary year.

Step 2: Check the leap year relation -
2007 is \((2004 + 3)\) or \((Leap + 3)\).

Step 3: Apply the repetition rule -
For a \((Leap + 2)\) or \((Leap + 3)\) year, the calendar repeats after 11 years.

Step 4: Calculate the year - \(2007 + 11 = 2018\).
Since 2018 is also an ordinary year, the calendars match perfectly. Quick Tip: Repetition Rules: \(Leap \to +28\) years, \(Leap+1 \to +6\) years, \(Leap+2/+3 \to +11\) years.

Step 1: Calculate total hours elapsed -
From Monday 6 AM to Tuesday 6 AM = 24 hours.

Step 2: Add remaining hours -
From Tuesday 6 AM to Tuesday 6 PM = 12 hours. Total elapsed time = \(24 + 12 = 36\) hours.

Step 3: Calculate total time lost -
Loss per hour = 5 minutes. Total loss = \(36 \times 5 = 180\) minutes.

Step 4: Convert minutes to hours -
180 minutes = \(180 / 60 = 3\) hours.

Step 5: Adjust the clock time -
At 6 PM (correct time), the clock will be 3 hours slow.
Clock time = 6 PM - 3 hours = 3 PM. Quick Tip: Always double-check if the clock is "slow" (subtract loss) or "fast" (add gain) relative to the correct time.

Step 1: Find the first difference - \(7 - 5 = 2\), \(13 - 7 = 6\), \(25 - 13 = 12\), \(45 - 25 = 20\).

Step 2: Find the second difference (difference of differences) - \(6 - 2 = 4\), \(12 - 6 = 6\), \(20 - 12 = 8\).

Step 3: Identify the pattern in second difference -
The second differences are 4, 6, 8. This is a sequence of even numbers. The next difference should be 10.

Step 4: Calculate the next first difference -
Next difference = \(20 + 10 = 30\).

Step 5: Find the missing number -
Missing number = \(45 + 30 = 75\). Quick Tip: If the first level of differences doesn't show a clear pattern, always check the "difference of differences" (Step-deviation).

Step 1: Calculate initial factorials - \(1! = 1\), \(2! = 2\), \(3! = 6\), \(4! = 24\), \(5! = 120\).

Step 2: Observe the pattern -
Starting from \(5!\), every factorial ends with the digit 0 because it contains at least one factor of 2 and one factor of 5 (\(5 \times 2 = 10\)).

Step 3: Sum the unit digits -
We only need to sum the unit digits of factorials up to \(4!\), as the rest are 0.

Sum \(= Unit digit of (1 + 2 + 6 + 24)\).

Sum \(= Unit digit of (33)\).

Step 4: Final Digit -
The unit digit is 3. Quick Tip: Any factorial \(n!\) where \(n \geq 5\) will always have 0 as its unit digit.

Step 1: Use the Harmonic Mean formula -
When equal distances are covered at different speeds (\(v_1, v_2, v_3\)), Average Speed \(= \frac{3}{\frac{1}{v_1} + \frac{1}{v_2} + \frac{1}{v_3}}\).

Step 2: Substitute the values -
Average Speed \(= \frac{3}{\frac{1}{10} + \frac{1}{20} + \frac{1}{60}}\).

Step 3: Find the LCM of denominators -
LCM of 10, 20, and 60 is 60.

Average Speed \(= \frac{3}{\frac{6 + 3 + 1}{60}} = \frac{3}{\frac{10}{60}}\).

Step 4: Calculate the final value -
Average Speed \(= \frac{3 \times 60}{10} = 3 \times 6 = 18\) km/h. Quick Tip: Average speed is NOT the simple arithmetic mean of speeds. Use \(\frac{2xy}{x+y}\) for two equal distances and the Harmonic Mean for more.

Step 1: Use the fundamental relationship -
Product of two numbers \(= HCF \times LCM\).

Step 2: Substitute the given values - \(1800 = 15 \times LCM\).

Step 3: Solve for LCM - \(LCM = \frac{1800}{15}\).

Step 4: Calculate - \(LCM = 120\). Quick Tip: This formula \(n_1 \times n_2 = HCF \times LCM\) is only valid for exactly two numbers.

Step 1: Total possible outcomes -
Since there are two dice, total outcomes \(= 6 \times 6 = 36\).

Step 2: List outcomes where Red \(>\) Blue - \((2,1), (3,1), (3,2), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3), (5,4), (6,1), (6,2), (6,3), (6,4), (6,5)\).

Step 3: Filter those where the sum is prime (2, 3, 5, 7, 11) -
- Sum 3: \((2,1)\)

- Sum 5: \((3,2), (4,1)\)

- Sum 7: \((4,3), (5,2), (6,1)\) (Wait, let's check: \((4,3)\) is Red > Blue, sum 7. Yes.)

- Sum 11: \((6,5)\)

Wait, let's re-verify:

Pairs (R,B) where R > B and sum is prime:
\((2,1)\) [Sum 3]
\((3,2)\) [Sum 5]
\((4,1)\) [Sum 5]
\((4,3)\) [Sum 7]
\((5,2)\) [Sum 7]
\((6,1)\) [Sum 7]
\((6,5)\) [Sum 11]

Total favorable outcomes = 7. (Correction: Based on typical exam options, please re-count carefully).

Step 4: Final Probability -
Probability \(= \frac{Favorable}{Total} = \frac{7}{36}\).
(Note: If the result is 5/36 in your source, check if the prime number 7 was excluded or a specific condition was different). Quick Tip: In dice problems, drawing a \(6 \times 6\) table helps to quickly identify pairs that meet multiple conditions.