Explanation : 

Religious denominations

Q1: Correct Answer – (c) Religious denominations tend to ignore the unity of man.
Explanation – The most logical assumption from the passage is © Religious denominations tend to ignore the unity of man.

This option suggests that different religious denominations may focus on their own beliefs and practices rather than recognizing the commonalities among all people. In other words, religious denominations may overlook the fact that all humans share a common bond and instead focus on their differences.

Explanation : 

10th October 2027 Day ?

We know that, 10th October 2021 is a Sunday. (The day of UPSC CSE, 2021 Preliminary exam)

So, 10th October 2022 will be Sunday + 1, i.e. Monday.
10th October 2023 will be Monday + 1, i.e. Tuesday.
10th October 2024 will be Tuesday + 2, i.e. Thursday. We added 2, as 2024 is a leap year.
10th October 2025 will be Thursday + 1, i.e. Friday.
10th October 2026 will be Friday + 1, i.e. Saturday.
10th October 2027 will be Saturday + 1, i.e. Sunday.

Explanation : 

Given Information:

1. Statement 1: Month ends on Wednesday

2. Statement 2: Third Saturday is on 17th

Using Statement 1 alone:
– Only knows last day is Wednesday
– Month could be 30 or 31 days
– First day could vary
– Cannot determine 14th day
– Not sufficient

Using Statement 2 alone:
– Third Saturday = 17th
– Second Saturday = 10th
– First Saturday = 3rd
– Working backwards:
1st day must be Thursday
14th must be Wednesday
– Sufficient to answer

Using Both Statements:
– Statement 2 alone gives the answer
– Statement 1 not needed

Answer: (b) Statement 2 alone is sufficient

The 14th of the month is Wednesday, determined solely from Statement 2.

Explanation : 

Half of the villagers of a certain village

The correct answer is (b) Some villagers under 25 years of age are literate. This is because the given information states that one-third of the villagers are literate and four-fifth of the villagers are under 25 years of age.

Therefore, it is possible that some villagers who are under 25 years of age are also literate because one third is larger than one-fifth.

Explanation :

Hour hand and Minute hand of the clock

Let’s solve this step by step:

1) When hands make 180°, they point in opposite directions.

2) At 7:00:
– Hour hand moves (7/12 × 360°) = 210° from start
– Minute hand at 0°
– Angle = 210° (not 180°)

3) In 1 hour:
– Hour hand moves 30°
– Minute hand moves 360°

4) In 1 minute:
– Hour hand moves 0.5°
– Minute hand moves 6°

5) At 7:05:
– Hour hand: 210° + (5 × 0.5°) = 212.5°
– Minute hand: 5 × 6° = 30°
– Angle = 182.5° (not 180°)

6) Between 7:05 and 7:10, at approximately 7:06, the hands form exactly 180°.

Therefore, the answer is (d) Between 7:05 hours and 7:10 hours.

Explanation : 

MATHEMATICS – CHEMISTRY

According to the pattern:
For odd positions (1,3,5,7,9,11): Subtract 1
For even positions (2,4,6,8,10): Add 1

MATHEMATICS → LBSIDNZUHDR
CHEMISTRY → BIDLHTSSX

Therefore, answer is (c) BIDLHTSSX

Explanation : 

P scored 40 marks more than Q in an examination

Given:
– P scored x marks
– P scored 40 marks more than Q
– Q scored 10% less than P

Step 1: Initial Equations
– Q’s marks = x – 40 (40 less than P)
– Q’s marks = 0.9x (10% less than P)

Step 2: Solve for x
– x – 40 = 0.9x
– x – 0.9x = 40
– 0.1x = 40
– x = 400

Final Scores:
– P scored 400 marks
– Q scored 360 marks (400 – 40)

Explanation : 

The given series is: _b_a_ba_b_abab_aab

The pattern being followed in the above series is: abb, then aab. Again abb, and then aab, and so on.
The blanks have been highlighted below:
a b b / a a b / a b b / a ab / ab b / aab

Explanation : 

Three points P,Q and R on straight line

CASE – 1
Assuming PQ = 3x, QR = 5x and PR = PQ + QR, we get
PQ : PR = 3x : (3x + 5x)
⇒ PQ : PR = 3 : 8

CASE – 2
Assuming PQ = 3x, QR = 5x and PR = QR – PQ, we get
PQ : PR = 3x : (5x – 3x)
⇒ PQ : PR = 3 : 2

So, we have n = 2 possible values.

Explanation : 

X & Y Age Relationship Analysis

Given:
– X’s present age = 42 years
– At Y’s birth, X was twice Y’s current age
– Let Y’s present age = y

Step 1: Initial Equation
– 42 – y = 2y (X’s age at Y’s birth = 2 × Y’s current age)
– 42 = 3y
– Therefore, y = 14 (Y’s current age)

Step 2: Testing Statement 1 (8 years ago)
– X’s age: 42 – 8 = 34
– Y’s age: 14 – 8 = 6
– Check: 34 ≠ 5 × 6 (30)
– Result: Statement 1 is false

Step 3: Testing Statement 2 (14 years later)
– X’s age: 42 + 14 = 56
– Y’s age: 14 + 14 = 28
– Check: 56 = 2 × 28
– Result: Statement 2 is true

Answer: Only Statement 2 is correct.