Explanation

Total persons = 14  

Number of engineers = 4  

Number of non-engineers = 14 - 4 = 10  

We have to select a committee of 2 persons.

Total number of ways to select 2 persons out of 14 = 14C2  

14C2 = (14 x 13) / (2 x 1) = 91

Number of ways to select 2 engineers out of 4 = 4C2  

4C2 = (4 x 3) / (2 x 1) = 6

Probability = Favorable outcomes / Total outcomes  

Probability = 6 / 91

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Explanation

Total books if nothing was missing:

46 shelves × 28 books = 1288 books

Books missing:

17 shelves × 9 missing books each = 153 books

Books present now:

Total - Missing = 1288 - 153 = 1135 book

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Explanation

With 10 people, the middle positions are 5th and 6th.

Given:

1. B _ _ F 

2. DH together

3. E ≠ neighbor of B or F

4. J at 1 or 10

Let's check if we can fix position 5 or 6:

Possible B-F positions: (1,4), (2,5), (3,6), (4,7), (5,8), (6,9), (7,10)

Case 1: B=2, F=5 → then 5th = F  

Case 2: B=3, F=6 → then 6th = F  

Case 3: B=4, F=7 → then 5th and 6th could be DH or others  

Case 4: B=1, F=4 → then 5th,6th are not fixed

We can make multiple valid arrangements and the middle keeps changing.  

Example: J A B C D H G E F I → middle = D, H  

Example: A B C D E F G H I J → middle = E, F

So we cannot determine one exact person for the middle.

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Explanation

If two trains move on two straight lines with constant speeds, the distance between them changes over time unless the lines are parallel. 

The distance is 10 km at 12:00, 1:00, and 2:00. That is 3 different times. 

For the distance to stay exactly the same for 3 hours with different speeds of 100 km/h and 50 km/h, the trains must keep the same separation forever. 

This can only happen if the tracks are parallel and the trains move in the same direction. Then the faster train gains 50 km per hour but never gets closer because it started 10 km ahead.

If the tracks were non-parallel and intersected, the distance would have to change. It cannot be 10 km at 12, 1, and 2.

Therefore the statement "non-parallel" is false. The tracks must be parallel. 

The angle between parallel lines is 0°.

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Explanation

D's statement directly concerns whether B is lying.

If D tells the truth, B lies; if D lies, B tells the truth.

Therefore, B and D must have opposite identities.

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Explanation

• The chain ultimately loops back through the scholar's own family.
• The phrase "my father's only niece's male first cousin" resolves back to the scholar under normal bilateral family relationships.
• Therefore, the scholar and the male first cousin are the same person.

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Explanation

Two line segments that share an endpoint do not have another intersection.

Segment Alpha → Beta ends at Beta.

Segment Beta → Gamma begins at Beta.

Their only intersection is Beta itself (Kazungula).

If the author instead meant the intersection of the infinite lines extending those segments, that intersection is still Beta, because both lines pass through Beta.

The explanation then switches to a "center of gravity" or "center line" argument. That is not what the question asks. An intersection is a precise geometric concept; it is not a centroid or midpoint.

Nothing in the coordinates places Vatican City near the actual intersection.

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Explanation

Step 1: Find the capitals

Northernmost structural volcanic desert is in Iceland. Capital is Reykjavik.

Lowest point on land is the Dead Sea in Jordan and Israel. Capital is Amman.

Worlds deepest lake is Lake Baikal in Russia. Capital is Moscow.

Step 2: The rule

Count the letters in the capital city name. Then square that number. L squared.

Check:

Reykjavik has 9 letters. 9 squared = 81.

Amman has 5 letters. 5 squared = 25.

Step 3: Apply to Moscow

Moscow has 6 letters. 

6 squared = 36.

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Explanation

Key clues:

1. Sovereign enclave comprehensively landlocked by a solitary extraneous nation-state"  

   That describes only one country in the world: Lesotho → completely surrounded by South Africa.

2. The movements: 4000 km S, 4000 km W, 4000 km N, 4000 km E

   On a perfect sphere, if you started at the pole and did equal sides you’d return. But Earth is an oblate spheroid and we’re at mid-latitudes, not the pole.

   When you go 4000 km South, you’re on a larger circle of latitude.  

   Then 4000 km West covers fewer degrees of longitude than it would have further North.  

   Then 4000 km North brings you back to the same latitude you started at.  

   Then 4000 km East now covers more degrees of longitude than the West leg did, because you’re back at the original latitude.

   Net result: You end up East of where you started.

3. "Accounting strictly for real-world national boundaries"

   Starting inside Lesotho, going 4000 km in each direction puts you far outside Southern Africa. 4000 km S from Lesotho → into the Southern Ocean/Antarctic region. 4000 km W → into the Atlantic. 4000 km N → back near Central Africa. 4000 km E → into the Indian Ocean.

You cannot end in another country’s landmass with those distances from Lesotho, and you definitely don’t return to the start because of the spheroid geometry.

Answer: They terminate their journey East of their starting point, ending up in the Indian Ocean.

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Explanation

Ostriches are flightless birds and cannot fly.

All birds have wings, but not all birds can fly.

Therefore, "Ostrich can fly" is the incorrect statement.

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