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"

According to the question:

Distance upstream = 40 km

Time upstream = 4 hrs

Time downstream = 2 hr

So, 

Speed upstream = 40/4 ⇒ 10 km/hr

Speed downstream = 40/2 ⇒ 20 km/hr

Now,

let the speed of the boat be = b

let the speed of the stream be = s

Upstream = b - s ⇒ 10 km/hr

Downstream = b + s ⇒ 20 km/hr

Solving both the equation we get:

2b = 30

b = 15 km/hr

∴ b - s = 10 

s = 5 km/hr

Hence, "Option 4" is the correct answer.

The logic followed here is:

Hence, "Option 3" is the correct answer.

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

Conclusions:

1. All books are trees → Follow (As all books are papers and all papers are trees. As whole books comes in papers which whole comes in trees, therefore it is true.)
2. Some trees are books → Follow (As all books are papers and all papers are trees. As whole books comes in papers which whole comes in trees, therefore it is true.)

∴ Here, Both I and II follow.​

Hence, the correct answer is "Option 3".

Correct Answer: Option (4) – Can't be determined

Nishant’s M.Sc. result is pending, and without his final post-graduation percentage, it is impossible to verify if he meets the complete educational eligibility. Since the specific recruitment guidelines for "result awaited" candidates are not provided, a definitive decision cannot be made.

The logic followed here is:

For capital letter → Place value × 2 

For small letter → 1 is positioned ahead of place value → '1' ' Place value'

"A" is coded as 2

"B" as 4

"a" as 11

"b" as 12

Similarly,

"Hi" is coded as

For 'H'

For 'i'

Hence, "Option 4" is the correct answer.

Given:

A man walks 10 meters south, then turns left and walks 15 meters.

Thus, facing in the east direction now.

Hence, "Option 2" is the correct answer.

Given:

8 people are seated in a row.

3 people sit next to each other

Formula:

Ways of arranging n distinct things taken all at a time = n!

Explanation:

So, the number of ways 8 people be seated in a row such that 3 people sit next to each other = 3! × 6 ⇒ 36

Hence, "Option 2" is the correct answer.

Given: 

5 people are seated in a row.

A and B are not next to each other.

Formula:

Ways of arranging n distinct things taken all at a time = n!

Explanation:

So, the number of ways 5 people be seated in a row such that A and B are not next to each other = 3! × 4C2 ⇒ 72

Hence, "Option 3" is the correct answer.

The logic followed here is:

Hence, "Option 3" is the correct answer

The logic followed here is:

Roll numbers ending with an even digit belong to Batch 1

Roll numbers ending with an odd digit belong to Batch 2.

Option 2) E2894 and F3917 

E2894 → Ends with an even digit

F3917 → Ends with an odd digit

Hence, "Option 2" is the correct answer.