Given:

Total shops = 6

Condition: In each shop he spends (½ of what he had + ₹1)

At last he has ₹0 left

Formula used:

If money before entering a shop = M

Money spent = (M ÷ 2 + 1)

Money left = M − (M ÷ 2 + 1) = (M ÷ 2 − 1)

We work backward from last shop (final = 0)

Calculations:

After shop 6 = 0

⇒ Before shop 6 = (0 + 1) × 2 = 2

⇒ Before shop 5 = (2 + 1) × 2 = 6

⇒ Before shop 4 = (6 + 1) × 2 = 14

⇒ Before shop 3 = (14 + 1) × 2 = 30

⇒ Before shop 2 = (30 + 1) × 2 = 62

⇒ Before shop 1 = (62 + 1) × 2 = 126

∴ Sandeep received ₹126 from his father.

Given:

Total students = 45

Rahul's position from the top = 20

According to the question, if the students are arranged in the descending order of ranks:

Rahul's position from the bottom → Total students - Rahul's position from the top + 1

→ 45 - 20 + 1 = 26​

Hence, the correct answer is "Option 1".

The logic followed here is:

SUN is written as 54

And,

MOON is written as 57

Similarly,

STAR written

Hence, "Option 1" is the correct answer.

The logic followed here is:

means '+'

5#3=8 → 5 + 3 = 8

And

7#2=9 → 7 + 2 =9 

Similarly,

9#4 → 9 + 4 = 13

Hence, "Option 2" is the correct answer.

The logic followed here is:

​​Option 1) 11, 13, 17, 19 → Prime numbers

Option 2) 37, 41, 43, 47 → Prime numbers

Option 3) 23, 29, 31, 33 → Prime and composite numbers

Option 4) 2, 3, 5, 7 → Prime numbers

Hence, "Option 3" is the correct answer.

The logic followed here is:

Hence, "Option 1" is the correct answer.

Additional Information Prime numbers from 1 - 220:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211.

According to the question:

Hence, "Option 1" is the correct answer.

The logic followed here is:

A is to C

Similarly,

E is to

​

Hence, "Option 3" is the correct answer.

The logic followed here is:

Hence, "Option 3" is the correct answer.

Given: 

1. A is the mother of B

2. B is the father of C

Thus, A is C's grandmother.

Hence, the correct answer is "Option 2"