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Given:

A man walks 3 km west, then turns north and walks 4 km.

By applying the Pythagoras Theorem:

(AB)² = (AC)2 + (BC)2

(AB)2 = (4)2 + (3)2

(AB) = √(16 + 9)

(AB) = √(25)

(AB) = 5 km

Thus, the man is 5 km far from the starting point.

Hence, the correct answer is "Option 4".

Given: Six friends A, B, C, D, E, and F are sitting in a row.

1) F is sitting at one of the ends.

Case 1)

Case 2)

2) D is not at any end.

3) B is sitting between D and E.

4) C is sitting to the immediate right of A. 

4) D is not an immediate neighbor of neither A nor F.

Case 1)

Case 2)

Thus, D is sitting to the immediate left of B.

Hence, "Option 3" is the correct answer.

According to the question:

A can do a job in = 10 days

B can do a job in = 15 days

Work done by A and B together per day = (\(\frac{1}{10}\) + \(\frac{1}{15}\)) = (\(\frac{3}{30}\) + \(\frac{2}{30}\)) → \(\frac{1}{6}\)

Time taken to finish the work together = 1 ÷ Combined work rate.

= 1 ÷ \(\frac{1}{6}\) → 6 days

Hence, "Option 2" is the correct answer.

The logic followed here is:

​

Hence, "Option 3" is the correct answer.

Alternate Method

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

(1) Some smart people are not dull. → Follow (As some smart people are creative and no creative person is dull. So some part of smart is common with creative which cannot be dull, therefore it s true)

(2) Some engineers are creative. → Does not follow (As all engineers are smart and some smart people are creative. So it is possible but nit definite)

(3) Some dull people are smart. → Does not follow (As some smart people are creative and no creative person is dull. So it is possible but nit definite)

(4) No engineer is dull. → Does not follow (As all engineers are smart, some smart people are creative and no creative person is dull. So no direct relation is given between engineers and dull, therefore it is false.)

∴ Here, Only (1) follow.​

Hence, the correct answer is "Option 1".

Given: Introducing a boy, a girl said, "He is the son of the daughter of my father's brother."

Thus, the boy is girl's nephew.

Hence, the correct answer is "Option 2".

The conditions are as follows:

Thus, Neeraj will be referred to the principal.

Hence, "Option 4" is the correct answer.

Given: A says to B, "You are the daughter of the only son of my father."

Thus, A is B's father.

Hence, the correct answer is "Option 1".

Given: Sum of two consecutive odd numbers is 24.

Let the 2 consecutive odd numbers be = (p) and (p + 2)

According to the question:

p + (p + 2) = 24

2p + 2 = 24

2p = 22

p = 11

So, putting the value of 'p'

11 + 2 = 13

∴ The two consecutive odd numbers are 11 and 13.

Thus, the larger odd number is 13.

Hence, "Option 4" is the correct answer.

Decoding signs:

Given: 25 - 3 ÷ 5 +10 = ?

25 - 3 ÷ 5 +10 = ? ⇒ 25 × 3 + 5 - 10 = ?

⇒ 25 × 3 + 5 - 10 = ?

⇒ 75 + 5 - 10 = ?

⇒ 80 - 10 = ?

⇒ 70 = ?

Hence, "Option 2" is the correct answer.