Explanation : 

To determine how the word “ARENA” is encoded, let’s analyze the given examples:

1. POT → ATOP
Original Word: POT
Reversed: TOP
Encoded: A + TOP = ATOP

2. TRAP → APART
Original Word: TRAP
Reversed: PART
Encoded: A + PART = APART

From these examples, the pattern is clear:
– Add an “A” at the beginning
– Reverse the original word and append it after the “A”

Applying this pattern to “ARENA”:

Original Word: ARENA
Reversed: ANERA
Encoded: A + ANERA = AANERA

Answer: d) AANERA

Explanation : 

To determine how “IJKL” is encoded, let’s analyze the given examples:

1. ABCD:
A = 1, B = 2, C = 3, D = 4
Product: 1 x 2 x 3 x 4 = 24

2. EFGH:
E = 5, F = 6, G = 7, H = 8
Product: 5 x 6 x 7 x 8 = 1680

The pattern involves taking the numerical value of each letter (A=1, B=2, …, Z=26) and multiplying them together.

3. IJKL:
I = 9, J = 10, K = 11, L = 12
Product: 9 x 10 x 11 x 12 = 11880

Answer: a) 11880

Explanation : 

Statement 1: “If 2x is not less than 3y AND 3x equals 4z, then 9y is greater than 8z”

Analysis:
1. From 3x equals 4z, we can say x equals 4z/3
2. Putting this in first condition: 2(4z/3) is not less than 3y
3. Simplifying: 8z/3 is not less than 3y
4. Multiplying both sides by 3: 8z is not less than 9y
5. Therefore: 9y is less than or equal to 8z
6. But statement claims 9y is greater than 8z
7. This is a contradiction

Statement 2: “If x is less than 2y AND y is not greater than z, then x is not greater than z”

Analysis:
1. From first condition: x < 2y
2. From second condition: y ≤ z
3. Putting these together: x < 2z
4. However, x < 2z does not guarantee that x ≤ z
5. Counter example: Let z = 1, y = 1, x = 1.9
– Here x < 2y is true (1.9 < 2)
– y ≤ z is true (1 ≤ 1)
– But x ≤ z is false (1.9 is not ≤ 1)

Therefore, both statements are false.

Explanation : 

Original Expression:
10 + 30 – 100 x 50 / 25

Replacing each operator simultaneously:
The plus sign (+) becomes minus (-)
The minus sign (-) becomes multiply (x)
The multiply sign (x) becomes divide (/)
The divide sign (/) becomes plus (+)

After replacing all operators at once, the expression becomes:
10 – 30 x 100 / 50 + 25

Now let’s solve this expression following standard order of operations:

First step: Work out multiplication
30 x 100 equals 3000

Second step: Work out division
3000 / 50 equals 60

Third step: The expression is now
10 – 60 + 25

Fourth step: Work from left to right with subtraction and addition
10 minus 60 equals -50
-50 plus 25 equals -25

Therefore, the final answer is -25

Explanation : 

Given main statement: Pradeep becomes either a Director or a Producer

Let’s define:
D = Pradeep is a Director
P = Pradeep is a Producer
R = Not Director
S = Not Producer

Analyzing statement pairs:

1. S implies P:
– If S is true (Not Producer)
– From main statement (must be Director or Producer)
– Then D must be true (Director)
This is valid

2. R implies Q:
– If R is true (Not Director)
– From main statement (must be Director or Producer)
– Then P must be true (Producer)
This is valid

Both pairs are logically valid based on the main statement that Pradeep must be either Director or Producer.

Answer: c) Both SP and RQ are valid implications.

Explanation : 

Given:
– P and Q are two-digit ages
– P = 10a + b
– Q = 10b + a where a and b are digits (1-9)

Statement I: P is greater than Q

– This means 10a + b > 10b + a
– Simplifies to a > b
– Multiple values possible
– Not sufficient alone

Statement II: Sum of ages is 11/6 times their difference

– (P + Q) = 11/6 × (P – Q)
– (10a + b) + (10b + a) = 11/6 × [(10a + b) – (10b + a)]
– 11a + 11b = 11/6 × (9a – 9b)
– 66(a + b) = 99(a – b)
– 5b = a

Since a and b must be single digits:
– Only possible solution is a = 5, b = 1
– Therefore P = 51 and Q = 15
Statement II alone is sufficient.

Answer: a) The question can be answered using Statement II alone, but cannot be answered using Statement I alone.

Explanation : 

Statement I Alone:

– Knowing only the size (12 MB) isn’t enough to find download time
– Need transfer rate to calculate time

Statement II Alone:

– Knowing only transfer rate (2.4 KB/s) isn’t enough
– Need file size to calculate time

Both Statements Together:
1. Convert 12 megabytes to kilobytes:
12 MB = 12 × 1024 = 12,288 KB

2. Calculate time:
Time = Size ÷ Rate
= 12,288 KB ÷ 2.4 KB/s
= 5,120 seconds
= 1 hour, 25 minutes, 20 seconds

Explanation : 

Statement I Alone:

1. Rearranging m + n > mn gives (m-1)(n-1) < 1
2. Since m and n are natural numbers, and m > n:
– n must equal 1
– m can be any natural number > 1
This alone doesn’t give unique values.

Statement II Alone:

1. Factors of 24 give these pairs:
(1,24), (2,12), (3,8), (4,6), (6,4), (8,3), (12,2), (24,1)
This alone doesn’t give unique values.

Both Statements Together:
1. From Statement I, n must be 1
2. From Statement II, mn = 24
3. Substituting n = 1:
m × 1 = 24
Therefore m = 24

The unique solution is m = 24 and n = 1.

Answer: c) The question can be answered using both statements together, but cannot be answered using either statement alone.

Explanation : 

Conclusion-I: India is the world’s largest exporter of milk.
Analysis: Being largest producer doesn’t mean largest exporter. Production and export are different metrics. India might consume most milk domestically rather than export.

Conclusion-II: India does not import milk.
Analysis: Being largest producer doesn’t mean no imports. A country can both produce and import based on various factors like regional demand and quality requirements.

Answer: d) Neither Conclusion-I nor Conclusion-II follows

Explanation : 

Analyzing Statement I Alone:

P + Q = R + S
This only shows sum of P and Q equals sum of R and S.
Examples:
P = 7, Q = 5, R = 4, S = 8 → P > Q
P = 6, Q = 6, R = 5, S = 7 → P = Q
P = 5, Q = 7, R = 4, S = 8 → P < Q
Statement I alone insufficient.

Analyzing Statement II Alone:

P + S > Q + R
Shows P and S together score more than Q and R.
Examples:
P = 7, S = 5, Q = 5, R = 4 → P > Q
P = 3, S = 6, Q = 4, R = 3 → P < Q
Statement II alone insufficient.

Combining Statements:

From I: P + Q = R + S → P = R + S – Q
From II: P + S > Q + R → S > Q
Substituting: P = R + (S – Q)
Examples:
If R = 35, S = 60, Q = 50 → P = 45 → P < Q
If R = 41, S = 60, Q = 50 → P = 51 → P > Q
Combined statements still insufficient.

Answer: d) The Question cannot be answered even by using both the Statements together.