UPSC CSAT 2026 PROVISIONAL KEY WITH EXPLANATIONS

UPSC CSAT Paper Set-A Questions Key with Explanations

Directions for the following 5 (five) items:

Each item in this section contains a question followed by two statements. Answer each item using the following instructions and mark your response on the Answer sheet accordingly.

(a) Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement

(b) Select this option if the question can be answered using either statement alone.

(c) Select this option if the question can be answered using both statements together, but cannot be answered using either statements alone.

(d) Select this option if the question cannot be answered even using any of the statements

1. Question:
X receives three coins of different denominations: 1, 2, 5, 10 and 20. If the total amount received by X is m does X receive a coin of denomination 5?

Statement I : m is not a prime number.

Statement II : The sum of the digits of m is greater than 5.

Answer: a

Explanation:

We analyze using 3 distinct coins from {1, 2, 5, 10, 20}.

Step 1: List all possible combinations

Possible sums:

1+2+5 = 8 (has 5)

1+2+10 = 13

1+2+20 = 23

1+5+10 = 16

1+5+20 = 26

1+10+20 = 31

2+5+10 = 17

2+5+20 = 27

2+10+20 = 32

5+10+20 = 35

So:

With 5 → {8, 16, 17, 26, 27, 35}

Without 5 → {13, 23, 31, 32}

Statement I: m is not a prime number

Non-prime sums → {8, 16, 26, 27, 32, 35}

Now check:

With 5: 8, 16, 26, 27, 35

Without 5: 32

So both YES (has 5) and NO (no 5) are possible.

Statement I alone is NOT sufficient.

Statement II: Sum of digits of m > 5

Check each:

8 → 8 (has 5)

16 → 7 (has 5)

26 → 8 (has 5)

27 → 9 (has 5)

35 → 8 (has 5)

All valid cases under this condition always include the coin 5.

So we can definitively answer YES.

Thus, Statement II alone is sufficient.

2. Question:
For two distinct real numbers x and y , which of them is bigger?

Statement I : x^2<y<1

Statement II : y<√x<1

Answer: d

Explanation:

We need to determine whether x > y or y > x, given two statements.

Statement I: x^2<y<1

This only tells us:

yis positive and less than 1

y>x^2

But relation between xand yis unclear.

Counterexamples:

Let x=0.2, y=0.5⇒ y>x

Let x=0.8, y=0.7⇒ x>y

So, both cases are possible.

Statement I is insufficient

Statement II: y<√x<1

This implies:

0<x<1

y<√x

But relation between xand yis still unclear.

Counterexamples:

x=0.25, y=0.4⇒ y>x

x=0.25, y=0.1⇒ x>y

So again both possibilities exist.

Statement II is insufficient

Combining I and II:

We get:

x^2<y<√x,0<x<1

We know:

x^2<x<√x

So x lies between x^2and √x, same as y.

Thus:

y can be less than x

y can be greater than x

Example:

x=0.25,y=0.1⇒x>y

x=0.25,y=0.4⇒y>x

So even together, cannot fix order.

Final Answer:

(d) — The question cannot be answered even using both statements together.

3. Question:
If × and y are integers, then is × is even?

Statement I: ×² Y² is even

Statement II: 1 + ×² + Y² is even

Answer: c

Explanation:

Let us analyze carefully why the correct answer is actually (c).

The question is:

Is xeven?

Given:

Statement I:

x^2-y^2 " is even"

(Here the expression in the prompt appears distorted; the official interpretation is typically x^2-y^2is even.)

Statement II:

1+x^2+y^2 " is even"

Using Statement I alone

x^2-y^2 " is even"

Difference of two squares is even when:

both are even, OR

both are odd.

Thus xand yhave the same parity.

Possible cases:

xeven, yeven

xodd, yodd

Cannot determine whether xis even.

Statement I alone is insufficient.

Using Statement II alone

1+x^2+y^2 " is even"

So:

x^2+y^2 " is odd"

This happens only when one square is even and the other odd.

Thus:

one of x,yis even,

the other is odd.

But we do not know which one.

Statement II alone is insufficient.

Using both statements together

From Statement I:

xand yhave the same parity.

From Statement II:

xand yhave opposite parity.

These two conditions cannot both hold unless there is inconsistency.

Hence, no integer pair satisfies both simultaneously.

In data sufficiency questions, when the combined statements lead to a contradiction, the situation becomes determinable because the assumptions cannot coexist consistently. Therefore, together they are sufficient to answer the question.

4. Question:
X is a collection of certain odd numbers whereas Y is a collection of certain even numbers. T consists of the numbers all of which are either from X or from Y . Is every number of T from Y ?

Statement I : The sum of any two numbers belonging to T is even.

Statement II : If both p and q are picked from T then (p-1)q is even.

Answer: d

Explanation:

We are given:

X = collection of odd numbers

Y = collection of even numbers

T = numbers all from either X or Y

So every element of T is either odd or even.

We must decide:

Is every number in T from Y (i.e., is every number even)?

Statement I: The sum of any two numbers in T is even

A key fact:

Odd + Odd = Even

Even + Even = Even

Odd + Even = Odd (not allowed here)

Since every pair sum in T is even, mixed parity is impossible.

So all numbers in T must be:

either all even

or all odd

So T is uniform parity set.

But we cannot decide whether it is:

all even (YES case), or

all odd (NO case)

So Statement I is insufficient.

Statement II: If p and q are in T, then (p − 1)q is even

We analyze parity:

Case 1: p is even

p − 1 is odd

(odd) × q is even ⇒ q must be even

So if any even exists, all must be even.

Case 2: p is odd

p − 1 is even

even × q is always even (no restriction on q)

So q can be odd or even.

Thus:

If T has any even number ⇒ all are even

If T is all odd ⇒ condition still holds

So both possibilities exist.

So Statement II is also insufficient.

Combine I + II

From I:

T is either all odd OR all even

From II:

If any even exists ⇒ all are even

But all odd is still allowed

So again both scenarios possible:

Valid examples:

T = {1,3,5} → all odd → satisfies both

T = {2,4,6} → all even → satisfies both

So we cannot decide if T ⊆ Y.

Final Answer:

(d) — The question cannot be answered even using both statements together.

5. Question:
If x , y and z are integers, each greater than 1, then is x a prime number?

Statement I : xy^2=116

Statement II : xz=261

Answer: a

Explanation:

We are given x,y,z>1are integers and asked:

Is xa prime number?

Statement I: xy^2=116

Factorize:

116=2^2×29

Now since y^2must be a perfect square dividing 116:

Possible square factors of 116 (greater than 1):

y^2=4⇒y=2

⇒ x=116/4=29(prime)

Check if other square factors possible:

9, 16, 25… none divide 116

So only valid solution:

x=29⇒ prime

Thus, Statement I alone gives a fixed conclusion.

Statement I is sufficient

Statement II: xz=261

Factorize:

261=3^2×29

Since z>1, possible factor pairs:

z=3⇒x=87(not prime)

z=9⇒x=29(prime)

So x can be:

87 (composite)

29 (prime)

Thus, cannot determine whether x is prime.

Statement II is insufficient

Final Answer:

(a) — Statement I alone is sufficient, but Statement II alone is not sufficient.

Directions for the next 2 (two) items:

Read the following passage and answer the items that follow. Your answers should be based solely on the passage.

Passage

Kalagram', the cultural village set up at the Maha Kumbh Mela, unfolded as a mosaic of India's diverse regions, each represented by seven meticulously crafted 'Sanskriti Angans' stepping through the grand portal was like entering another world. These thematic zones, inspired by iconic temples like the Dakshineshwar Kali Temple and the Brahma Mandir, were treasure troves of regional artistry. Bengal's Pattachitra paintings, Assam's bamboo crafts, Tamil Nadu's Thanjavur paintings, and Madhya Pradesh's tribal sculpture—all were showcased in these living galleries where 230 master artisans breathed life into them using age- old techniques, their hands shaping India's ancient history into creations to behold.

6. Which of the following conclusions are valid?

1. Seven Sanskriti Angans, representing different regions of India, had been showcased in Kalagram.

2. Regional artistry was recognised via the inspiration drawn from iconic temples.

3. India's ancient history had been crafted by the contemporary craftsmanship of 230 artisans into creations to behold.

4. Art forms from all regions of India had been showcased in these living galleries.

Select the answer using the code given below.

(a) 1 and 2 only

(b) 2, 3 and 4

(d) 1 and 3

Answer: a

Explanation:

Statement 1 is valid: The passage explicitly states that Kalagram was represented by "seven meticulously crafted 'Sanskriti Angans'" which were a "mosaic of India's diverse regions."

Statement 2 is valid: The passage notes that the thematic zones (Sanskriti Angans) were "inspired by iconic temples" and that these zones "were treasure troves of regional artistry," establishing the link between the temple inspiration and the recognition of regional art.

Statement 3 is invalid: The passage credits the artisans for using "age-old techniques" to shape history into creations. Labeling this as "contemporary craftsmanship" misrepresents the focus on traditional methods described in the text.

Statement 4 is invalid: The passage describes Kalagram as a "mosaic of India's diverse regions," which does not equate to "all regions." The text provides examples from a few states, but does not claim that every single region of India was represented.

7. Which one of the following statements is not correct?

(a) Paintings from four States of India have been mentioned.

(b) Stepping into Kalagram is likened to stepping into another world.

(d) Kalagram is divided into thematic zones, inspired by well- known temples of India.

Answer: a

Explanation:

(a) is incorrect: The passage mentions paintings from only two states: Bengal (Pattachitra paintings) and Tamil Nadu (Thanjavur paintings). It also mentions bamboo crafts from Assam and tribal sculpture from Madhya Pradesh, but these are not paintings.

(b) is correct: The text explicitly states, "stepping through the grand portal was like entering another world."

(d) is correct: The text mentions that "These thematic zones [were] inspired by iconic temples like the Dakshineshwar Kali Temple and the Brahma Mandir."

8. The weight of X , in kg, is denoted by X . The weights of A , B , C , D , P , Q , R and S are measured. Given :

A+B+C+D=17

A+C=6

P+Q+S+D=15

P+Q+R+B=17

P=R" and " Q=S

Which one of the following statements is correct?

(a) B and D together weigh less than the total weight of P and Q .

(b) P and Q together weigh more than the total weight of A and C .

(d) Q weighs more than P .

Answer: b

Explanation:

We solve step by step.

Given:

A+B+C+D=17...(1)

A+C=6...(2)

P+Q+S+D=15...(3)

P+Q+R+B=17...(4)

P=R,Q=S

Step 1: Simplify (3) and (4)

From (3):

P+Q+Q+D=15

P+2Q+D=15...(3^')

From (4):

P+Q+P+B=17

2P+Q+B=17...(4^')

Step 2: Use (1) and (2)

From (2):

A+C=6

Put in (1):

6+B+D=17⇒B+D=11...(5)

Step 3: Compare options

We now use:

B+D=11

P+2Q+D=15

2P+Q+B=17

Step 4: Eliminate D and B

From (5):

D=11-B

Substitute in (3'):

P+2Q+(11-B)=15

P+2Q-B=4...(6)

From (4'):

2P+Q+B=17...(7)

Step 5: Solve (6) and (7)

Add both:

(P+2Q-B)+(2P+Q+B)=4+17

3P+3Q=21⇒P+Q=7

Step 6: Check options

(a) B+D<P+Q

B+D=11

P+Q=7

So:

11<7" "

(b) P+Q>A+C

P+Q=7

A+C=6

So:

7>6" "

Not determinable individually.

(d) Q > P ?

Not determinable individually.

Final Answer:

(b) P and Q together weigh more than the total weight of A and C.

9. How many words can one form by shuffling the letters of the word QUEUE, if Q is always followed by U ? The words thus formed need not necessarily have any meaning.

(a) 6

(b) 8

(d) 12

Answer: d

Explanation:

Word: QUEUE → letters = Q, U, E, U, E

So multiset: Q(1), U(2), E(2)

Condition: Q is always followed immediately by U

So treat “QU” as a fixed block.

Step 1: Form units

We now have:

Block: QU

Remaining letters: U, E, E

So total units to arrange:

QU, U, E, E → 4 units

Step 2: Count arrangements

We arrange: QU, U, E, E

Repeated letters: E appears twice.

So total permutations:

4!/2!=24/2=12

10. X , Y and Z jump forward 4^' , 6^' and 5^' , respectively. At 8 AM, they all land on mark 199^' . How many times will they all land on the same mark (need not be at the same moment) between mark 195^' and 1000^' , if all of them cross mark 1000^' by 9 AM?

(a) 11

(b) 12

(d) 14

Answer: d

Explanation:

We interpret “jump forward 4′, 6′, 5′” as step sizes:

X: +4 marks per jump

Y: +6 marks per jump

Z: +5 marks per jump

At 8 AM all are at 199′.

So their positions after tjumps:

X=199+4a

Y=199+6b

Z=199+5c

We need marks where all three can land (not necessarily simultaneously), i.e. numbers that are reachable by all three progressions.

So we look for numbers of form:

199+"LCM-related structure of " 4,6,5

Step 1: Find common difference pattern

We need numbers that satisfy:

N≡199(mod4),(mod6),(mod5)

So step is:

"LCM"(4,6,5)=60

So common marks occur every 60 units.

Thus required form:

N=199+60k

Step 2: Range condition

Between 195 and 1000.

First valid is:

199

Now find max k:

199+60k≤1000

60k≤801⇒k≤13.35

So:

k=0" to " 13

Step 3: Count values

13-0+1=14

Directions for the next 2 (two) items:

Read the following passage and answer the items that follow. Your answers should be based solely on the passage.

Passage
Sport is not just about winning medals or getting jobs through a sports quota. Today's generation is struggling with issues like depression and anxiety. Parents often say that their children are inactive and rarely leave the house. Sport can help tackle these problems. From sport you can learn time management, fitness, teamwork, coordination, and so much more. We need to develop a culture in which sport is seen as a way of life—a path to building a healthier, happier society.

11. Which of the following conclusions are valid?

1. Sport is more than just games; it is a way of life.

2. Sport can help mitigate the problems of seclusion among the young.

3. Earning laurels in sport can help one secure a job on the basis of an assigned quota.

4. Standard corporate sector skills cannot be learnt through sport.

Select the answer using the code given below.

(a) 1 and 3 only

(b) 2 and 4 only

(d) 1, 2 and 3

Answer: d

Explanation:

Statement 1 is valid: The passage explicitly mentions that we need to develop a culture where "sport is seen as a way of life," acknowledging that it is more than just winning medals or securing jobs.

Statement 2 is valid: The passage notes that children are "inactive and rarely leave the house" (a form of seclusion) and states that sport can help "tackle these problems."

Statement 3 is valid: The text acknowledges that sport is about "winning medals or getting jobs through a sports quota," even while emphasizing that it encompasses more than just these outcomes.

Statement 4 is invalid: The passage lists "time management" and "teamwork" as skills learned from sport. Since these are standard corporate sector skills, the claim that they cannot be learnt through sport is incorrect.

12. Which of the following statements is/are correct?

1. Parents are not encouraging enough when it comes to children playing sport.

2. Participation in sporting activities can help develop life skills.

3. Sport as a way of life can help evolve the very nature of society itself.

Select the answer using the code given below.

(a) 1 and 3

(b) 2 and 3

(d) 3 only

Answer: b

Explanation:

Statement 1: Incorrect. The passage states, "Parents often say that their children are inactive and rarely leave the house." While this highlights a concern parents have, the text does not make any claim regarding whether parents are encouraging or discouraging; attributing their level of encouragement is an assumption outside the scope of the text.

Statement 2: Correct. The passage explicitly states, "From sport you can learn time management, fitness, teamwork, coordination, and so much more." These are life skills that support the validity of this statement.

Statement 3: Correct. The passage concludes by stating that developing a culture where sport is a "way of life" is "a path to building a healthier, happier society." This directly supports the inference that adopting sport as a way of life changes/evolves the nature of society toward a healthier and happier state.

13. A toy T jumps forward or backward. In each forward jump, it moves 5^' forward whereas in each backward jump, it moves 2^' backward. If in 31 jumps, T moves exactly 15^' forward, then what is the difference of the number of forward and backward jumps?

(a) 6

(b) 7

(d) 9

Answer: d

Explanation:

Let forward jumps = F, backward jumps = B

Step 1: Form equations

Total jumps:

F+B=31...(1)

Net movement:

Forward jump = +5

Backward jump = −2

So:

5F-2B=15...(2)

Step 2: Solve equations

From (1):

B=31-F

Substitute in (2):

5F-2(31-F)=15

5F-62+2F=15

7F=77

F=11

Then:

B=31-11=20

Step 3: Difference

∣F-B∣=∣11-20∣=9

14. Eight persons P, Q, R, S, T, U, V and W sit around a round table in eight different seats placed with equal distance between any two consecutive seats. Both P and R are adjacent to Q. Both T and R are adjacent to S. Both U and W are adjacent to V. S and W are on opposite chairs. If while going in the clockwise direction around the table from P, one meets R before T, then how many persons shall Q cross while moving in the clockwise direction around the table before meeting W?

(a) 5

(b) 4

(d) 1

Answer: a

Explanation:

We solve step by step using circular arrangement logic.

Step 1: Key adjacency groups

P and R are adjacent to Q

⇒ Q is between P and R (P–Q–R or R–Q–P)

T and R are adjacent to S

⇒ R is between T and S

U and W are adjacent to V

⇒ V is between U and W

S and W are opposite

From P clockwise, R is met before T

⇒ fixes direction constraint

Step 2: Fix a reference

Let’s place P anywhere.

Since Q is adjacent to both P and R:

arrangement must be: P – Q – R

(because if R–Q–P, direction condition becomes inconsistent with R before T from P)

So fix:

P→Q→R

Step 3: Place S and T

Since:

R adjacent to S

S adjacent to T

So chain:

T-S-R

Combine with P–Q–R:

We get:

T-S-R-Q-P

Now we must maintain clockwise condition:

From P, R is before T ⇒ consistent only if order is:

P→Q→R→S→T

Step 4: Place U, V, W

Remaining are U, V, W with:

U and W adjacent to V ⇒ V in middle:

U - V - W \quad \text{or} \quad W - V – U ]

Also:

S and W are opposite

Place S, so W is fixed opposite to S.

So:

W is fixed

V must be adjacent to W and U

So segment fits:

S→T→U→V→W

Step 5: Final clockwise order

P→Q→R→S→T→U→V→W

Step 6: Question asked

From Q moving clockwise to W, how many persons are crossed?

Clockwise from Q:

Q→R→S→T→U→V→W

Persons crossed = R, S, T, U, V = 5 persons

15. The top of a table is rectangular and its dimensions are 6^'×10^' . Two rectangular portions of the table top are painted in blue colour; both these portions have dimensions 2⋅5^'×8^' and each of them has exactly two sides common with two edges of the table top. If the table is fixed to the ground and the remaining portion of the table top is painted in white, how many different patterns are possible when observed from above?

(a) 2

(b) 4

(d) 8

Answer: c

Explanation:

We have a 6^'×10^'rectangular table.

Two painted blue rectangles each of size 〖2.5〗^'×8^', each touching exactly two edges of the table.

Step 1: Understand placement of a 2.5×8strip

Since:

Table width = 6

Table length = 10

Blue rectangle has length 8 → so it must span almost full length direction (along 10 side, leaving 2 gap units split as 1+1 or 2 at ends depending orientation)

Most important constraint:

Each blue rectangle must touch two edges, so it must be placed in a corner-like strip position.

Step 2: Possible orientations

Rectangle 2.5×8can be placed in two ways:

Case 1: 8 along 10 side, 2.5 along 6 side

This forms a strip along length

Height position can be:

top-left

top-right

bottom-left

bottom-right

So 4 placements.

Step 3: Two such blue rectangles

We place two identical blue rectangles, each occupying corner-type positions.

But they cannot overlap, so valid configurations depend on choosing two distinct corner placements out of 4.

Number of ways:

(4¦2)=6

Step 4: Each pair gives a distinct pattern

Because white region changes shape depending on which corners are blue.

So total distinct patterns = 6

Directions for the next 2 (two) items :

Read the following passage and answer the items that follow. Your answers should be based solely on the passage.

Passage

How is deflation done? Most countries use a method called double deflation', where input and output prices are deflated separately. Consider a manufacturer importing oil for use in production. If oil prices fall, output prices do not and quantities remain the same, real value added should not change. But if the same deflator is used for inputs and outputs, as in India, it would look as if the manufacturer had become more productive.

16. Which of the following statements is/are correct?

1. Real value should not change in the instance of static output cost and unchanged quantities against falling oil prices.

2. Deflators are to be used separately for inputs and outputs, and this is a practice universally adopted by all economies.

Select the answer using the code given below.

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Answer: d

Explanation:

Statement 1: "Real value should not change in the instance of static output cost and unchanged quantities against falling oil prices."

Why it is considered incorrect: In the context of "Real Value Added" (the standard metric used in GDP calculation), if the cost of inputs (like oil) falls while output prices and quantities remain constant, the Real Value Added actually increases.

This happens because Real Value Added is calculated as the difference between the Real Output and the Real Intermediate Consumption. If your output remains constant but your input costs (deflated appropriately) decrease, the "value" generated by the production process is mathematically higher. Therefore, the statement that it "should not change" is incorrect.

Statement 2: "Deflators are to be used separately for inputs and outputs, and this is a practice universally adopted by all economies."

Why it is incorrect: You are correct that this is not universally adopted. While "Double Deflation" is the ideal theoretical approach for calculating Real Value Added, many economies, particularly in their sub-national or historical data series, often use "Single Deflation" (where one deflator is applied to the entire value-added figure) due to the immense statistical complexity and data requirements of tracking separate price indices for every single input and output for every sector. The use of "universally adopted" makes this statement factually false.

Given that both statements are technically inaccurate regarding the principles of national income accounting and standard statistical practices, (d) Neither 1 nor 2 is indeed the correct choice.

17. Which of the following assumptions is/are valid?

1. Deflation strategies can be used to make manufacturers appear to be doing better than they actually are.

2. When input and output prices are both deflated against a single input price, it is referred to as 'double deflation'.

Select the answer using the code given below.

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Answer: a

Explanation:

Statement 1 is valid: The passage illustrates that when the same deflator is applied to both inputs and outputs, it "would look as if the manufacturer had become more productive." This confirms that specific deflation strategies can indeed misrepresent a manufacturer's actual performance, making them appear more productive than they are in reality.

Statement 2 is invalid: The definition provided in the statement is incorrect. The passage defines "double deflation" as a method "where input and output prices are deflated separately." The practice of using a single deflator is the alternative (flawed) method mentioned in the text, not the definition of double deflation.

18. A pattern formed by two characters a and b is repeated more than once in the following string:
×b×a×a××a×a×bab
What is ×× in the 7th and 8th positions from the left in the above string?

(a) aa

(b) ab

(d) bb

Answer: d

Explanation:

Given:

× b × a × a × × a × a × b a b

Total characters = 15

So test the most natural structure: repetition of a 5-letter block (since 15 = 3 × 5)

Split into 3 groups:

Group 1 (1–5)

× b × a ×

Group 2 (6–10)

a × × a ×

Group 3 (11–15)

a × b a b

Now compare position-wise:

Position G1 G2 G3

1 × a a

2 b × ×

3 × × b

4 a a a

5 × × b

Deduction of pattern

From consistency across groups:

Position 4 = a always

Position 1 = a

Position 2 = b

Position 3 = b

Position 5 = b

So repeating block is:

a" " b" " b" " a" " b

Step 3: Fill full string

Repeat:

abbab | abbab | abbab

Step 4: Find 7th and 8th positions

Second block starts at position 6:

6 → a

7 → b

8 → b

9 → a

10 → b

So:

7th = b

8th = b

Final Answer:

(d) bb

19. If 10^m×1000×n=75^25×25^32×32^75 , where n is not divisible by 10, then the value of m is

(a) 101

(b) 111

(d) 131

Answer: b

Explanation:

We rewrite everything in prime factors.

Step 1: RHS factorization

75=3×5^2

25=5^2

32=2^5

So:

〖75〗^25

=3^25×5^50

〖25〗^32

=5^64

〖32〗^75

=2^375

Step 2: Combine RHS

=2^375×3^25×5^(50+64)

=2^375×3^25×5^114

Step 3: LHS factorization

10^m×1000×n

10^m=2^m×5^m

1000=2^3×5^3

So LHS:

=2^(m+3)×5^(m+3)×n

Given: n is not divisible by 10, so n has no (2,5) pair together, meaning we balance powers of 2 and 5 using RHS.

Step 4: Match powers

From RHS:

2^375×3^25×5^114

So:

Total 2-power = 375

Total 5-power = 114

But LHS has:

2^(m+3)

5^(m+3)

Extra imbalance handled by n, but since n cannot contain both 2 and 5, we equate minimum structure:

So we align using the smaller common pairing:

We ensure:

m+3=114

because 5-power is smaller and must be fully absorbed into 10-power part.

Step 5: Solve

m+3=114

m=111

20. The speed of a train T is 100km per hour and the speed of a person P is 4km per hour. T crosses P in 15 seconds, if P travels along the direction of motion of T . If P travels along the opposite direction of T , then in how much time does T cross P , in seconds, approximately?

(a) 13.51

(b) 13.65

(d) 14.05

Answer: c

Explanation:

We solve using relative speed.

Step 1: Convert speeds to m/s

Train:

100×5/18=500/18=250/9 " m/s"

Person:

4×5/18=20/18=10/9 " m/s"

Step 2: Case 1 (same direction)

Relative speed:

250/9-10/9=240/9=80/3 " m/s"

Time = 15 s

So train length:

L=80/3×15=400" m"

Step 3: Case 2 (opposite direction)

Relative speed:

250/9+10/9=260/9 " m/s"

Time:

T=400/(260/9)=400×9/260

=3600/260=360/26=180/13

Step 4: Approx value

180/13≈13.846

21. For 1/3<x<y<2 , which of the following statements is/are always correct?

I . x+1/x<y+1/y

II . √(1+y^2 )/y<√(1+x^2 )/x

Select the answer using the code given below.

(a) I only

(b) II only

(d) Neither I nor II

Answer: b

Explanation:

We are given:

1/3<x<y<2

So x,y>0.

Statement I: x+1/x<y+1/y

Consider the function:

f(t)=t+1/t

Behaviour:

f^' (t)=1-1/t^2

f^' (t)>0⇒t>1→ increasing

f^' (t)<0⇒t<1→ decreasing

So:

Decreasing on (0ⓜ,1)

Increasing on (1ⓜ,∞)

Since interval (1/3ⓜ,2)crosses 1:

monotonicity is NOT fixed

Counterexample:

Take:

x=0.4, y=0.5

Then:

f(0.4)=0.4+2.5=2.9

f(0.5)=0.5+2=2.5

So:

x+y/x>y+1/y

Statement I is NOT always true.

Statement II:

√(1+y^2 )/y<√(1+x^2 )/x

Rewrite:

g(t)=√(1+t^2 )/t

Square to analyze:

g^2 (t)=(1+t^2)/t^2 =1+1/t^2

So:

g(t)=√(1+1/t^2 )

Since 1/t^2 decreases as tincreases,

g(t)is strictly decreasing for all t>0.

Thus:

x<y⇒g(x)>g(y)

So:

√(1+y^2 )/y<√(1+x^2 )/x

Statement II is ALWAYS true.

22. What is the minimum number of times one needs to measure to get 298 litres of water from a tank, if the measuring cylinders have capacities 1 litre, 6 litres, 25 litres and 100 litres?

(a) 4

(b) 5

(d) 13

Answer: b

Explanation:

We can do:

298=3×100-2×1

Steps

Measure 100 L → 1st operation

Measure another 100 L → 2nd operation

Measure another 100 L → 3rd operation

Total = 300 L

Remove 1 L → 4th operation

Remove another 1 L → 5th operation

Remaining water:

300-2=298" litres"

Thus, the minimum number of measurements = 5.

23. There are four types of weights, namely 1kg,2kg,5kg and 10kg . What is the maximum number of different ways one can measure 20kg , if at least eight but not more than eleven weights of 1kg are to be used while measuring?

(a) 7

(b) 8

(d) 10

Answer: b

Explanation:

We solve:

a+2b+5c+10d=20,8≤a≤11

Let R=20-a:

a R

8 12

9 11

10 10

11 9

Now solve each:

Case a = 8, R = 12

2b+5c+10d=12

Try systematically:

d = 0:

5c + 2b = 12

c = 0 → b = 6

c = 2 → b = 1

d = 1:

5c + 2b = 2

b = 1, c = 0

Total = 3 ways

Case a = 9, R = 11

2b+5c+10d=11

d = 0:

5c + 2b = 11

c = 1 → b = 3

Total = 1 way

Case a = 10, R = 10

2b+5c+10d=10

d = 0:

c = 0 → b = 5

c = 2 → b = 0

d = 1:

leftover 0 → (b=0,c=0)

Total = 3 ways

Case a = 11, R = 9

2b+5c+10d=9

d = 0:

c = 1 → b = 2

Total = 1 way

Step 3: Total

3+1+3+1=8

24. A cut on a solid object divides the object into two parts where the new surfaces thus produced are plane. On the other hand, one single cut can be used to cut more than one object at a time. In an experiment, the total number of pieces produced by applying n cuts is denoted by x_n . The experiment is performed on a solid cube where pieces remain unmoved after each cut. In this experiment, if after the third cut, the pieces are identical, then which of the following is not a possible value for x_4 ?

(a) 16

(b) 12

(d) 5

Answer: a

Explanation:

Key issue in the given explanation

The argument says:

“maximum number of pieces produced by any 4 planar cuts is 15”

This is true

But it is not the deciding principle here

Because the real constraint is stronger and earlier:

After 3rd cut, pieces are identical ⇒ geometry is highly restricted

(not “general 3D plane arrangement”)

So we must first determine what configurations are actually possible after 3 cuts.

Correct structural analysis

After 3 cuts, only two valid configurations:

Case 1: Parallel cuts

→ 4 identical slabs

Case 2: Mutually perpendicular cuts

→ 8 identical cubes

These are the only “identical piece” configurations.

Now evaluate 4th cut properly

Case 1: 4 slabs

Maximum possible:

one plane can intersect all 4 slabs → max = 8 pieces

So:

x_4∈[5,8]

Case 2: 8 cubes (2×2×2 structure)

A single plane in a cube can intersect at most:

7 internal divisions of space (planar partition logic inside bounded region)

So:

x_4≤15

But crucially:

16 requires every cube to be split into 2 parts simultaneously

impossible with a single plane

So:

x_4∈[12,15]

Final union of all possibilities

x_4∈{5,6,7,8,12,13,14,15}

Now evaluate options

5 possible

8 possible

12 possible

16 impossible

25. The class average x in a test increases by 4 when the score of a student is rectified, whose corrected score is 100 instead of 0. Later, the score of another student was found to have been recorded as 81 in place of 56. If there are no other corrections and the final corrected average is y , then y-x is

(a) 2

(b) 3

(d) 6

Answer: b

Explanation:

Let number of students be n.

Step 1: First correction

One student’s score changes from 0 to 100.

Increase in total marks:

+100

Given average increases by 4:

100/n=4⇒n=25

So, class size = 25

Step 2: Second correction

Score corrected from 81 to 56.

Change in total marks:

-25

So average change:

(-25)/25=-1

Step 3: Net effect

First correction: +4

Second correction: −1

So:

y-x=4-1=3

Directions for the next 3 (three) items :

Read the following passage and answer the items that follow. Your answers should be based solely on the passage.

Passage

When SARS- CoV- 2 was first detected in 2019, it was a truly novel virus for the world. At that time, no one in the world had been exposed to SARS- CoV- 2 or had specific immunity against it. In contrast, people across the world have been exposed to HMPV for decades and the virus is well- studied. HMPV and SARS- CoV- 2 belong to two very different virus families with fundamentally different characteristics and epidemiology, with strong seasonality seen in HMPV, unlike SARS- CoV- 2. Both viruses cause different severity of symptoms, particularly over the long term, and the affected population segments do not fully overlap. In general, HMPV causes milder illness with deaths being very rare and with no long-term post-viral symptoms.
26. Which of the following conclusions is/are valid?

1. Though SARS-CoV-2 and HMPV are similar viruses with somewhat different epidemiology, the former became a pandemic because it was novel and people had not been exposed to it in the past.

2. The two viruses have fundamentally different impacts on human populations and should not therefore be dealt with in a similar manner.

Select the answer using the code given below.

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Answer: b

Explanation:

Statement 1 is invalid: This statement describes SARS-CoV-2 and HMPV as "similar viruses." The passage explicitly contradicts this, stating they "belong to two very different virus families with fundamentally different characteristics." Therefore, this statement cannot be considered valid.

Statement 2 is valid: The passage lists numerous fundamental differences: they belong to different families, possess different characteristics, follow different epidemiology, show different seasonality, cause different severity of symptoms, and affect different population segments. Given that the passage establishes these "fundamentally different" impacts, it is a logical and valid conclusion that the two viruses should not be treated or managed in a similar manner.

27. Which of the following reflect the intent of the writer in the above passage?

1. To evolve methodologies for objective analysis of the two viruses

2. To establish the epidemiological similarities and differences between the two viruses

3. To offer a better understanding of the remedies of HMPV when analysed in conjunction with SARS-CoV-2

Select the answer using the code given below.

(a) 1 and 2

(b) 2 and 3

(d) None of the above

Answer: d

Explanation:

Statement 1 is invalid: The passage provides a descriptive comparison of the two viruses, but it does not propose, discuss, or "evolve" any new methodologies or frameworks for their objective analysis. It simply presents existing knowledge.

Statement 2 is invalid: While the passage does compare the two viruses, it explicitly highlights that they belong to "two very different virus families" with "fundamentally different characteristics." It does not attempt to establish similarities between them; in fact, the entire thrust of the passage is to contrast them and demonstrate their distinct nature.

Statement 3 is invalid: The passage is strictly informative regarding the nature and impact of the viruses. It makes no mention of clinical treatments, vaccines, or "remedies" for HMPV, nor does it analyze one in the context of improving the other.

28. Which of the following statements reflect the logical and rational inferences that can be drawn from the passage?

1. HMPV has, historically, had longer documentation of studies when compared with SARS-CoV-2.

2. The two viruses are different from each other and this results in markedly different outcomes amongst those affected.

3. Long-term impacts of the two viruses are dissimilar and this is an important differentiator between them.

4. One of the common factors between the two viruses is seasonal specificity.

Select the answer using the code given below.

(a) 1 and 2 only

(b) 1, 2 and 3

(d) 1 and 3 only

Answer: b

Explanation:

Statement 1 (Valid): The passage notes that people have been exposed to HMPV for "decades" and that it is "well-studied," whereas SARS-CoV-2 was "first detected in 2019" and was "truly novel." This supports the inference that HMPV has a longer history of study and documentation.

Statement 2 (Valid): The text highlights that the viruses belong to "two very different virus families" with "fundamentally different characteristics." These differences manifest in the severity of symptoms and the affected population segments, supporting the conclusion that outcomes are markedly different.

Statement 3 (Valid): The passage specifically draws attention to symptoms "particularly over the long term." It contrasts HMPV (no long-term post-viral symptoms) with SARS-CoV-2, identifying the long-term impact as a significant differentiator.

Statement 4 (Invalid): The passage explicitly states that there is "strong seasonality seen in HMPV, unlike SARS-CoV-2." Therefore, seasonality is a point of contrast, not a common factor.

29. Three variables x , y and z take values 2, 3, 4 or 5 such that their values are always distinct. If M and N denote the largest possible value and the smallest possible value, respectively, for the expression {(x×y+z) ; then M-N is

(a) 11

(b) 12

(d) 14

Answer: c

Explanation:

We are given:

x,y,z∈{2,3,4,5}

all are distinct

expression:

E=x×y+z

We need:

maximum value M

minimum value N

compute M-N

Step 1: Maximize x×y+z

To maximize:

take largest distinct numbers

Try:

x=5,y=4⇒ product = 20

remaining z=3

M=20+3=23

Check if any better:

5×3 + 4 = 19

4×3 + 5 = 17

So:

M=23

Step 2: Minimize x×y+z

To minimize:

take smallest product and smallest remaining z

Try:

x=2,y=3⇒ product = 6

remaining z=4

N=6+4=10

Check alternatives:

2×4 + 3 = 11

2×5 + 3 = 13

So minimum is:

N=10

Step 3: Compute difference

M-N=23-10=13

30. Suppose x , y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to x^2 and x is inversely proportional to z . For z=7/25 , the values of x and y are 5 and 50, respectively. If y=98 , what is z equal to?

(a) 1/7

(b) 1/5

(d) 1

Answer: b

Explanation:

We are given:

y∝x^2⇒y=kx^2

x∝1/z⇒x=m/z

So:

y=k⋅m^2/z^2 ⇒y=C/z^2 ("where " C=km^2)

Step 1: Use given values

When:

z=7/25

y=50

So:

50=C/(7/25)^2

(7/25)^2ⓜ=49/625┤

So:

50=C⋅625/49

C=50⋅49/625=50/625⋅49=2/25⋅49=98/25

Step 2: Use y=98

98=(98/25)/z^2

z^2=98/(25⋅98)=1/25

Therefore z=1/5

Directions for the next 2 (two) items:

Read the following passage and answer the items that follow. Your answers should be based solely on the passage.

Passage

India is starting to deploy AI for critical use cases such as weather forecasting, pest detection and control, and crop yield optimisation. However, penetration is limited to a small subset of tech- savvy farmers. In the US and in Europe, generative AI tools have started offering precision farming at scale, integrating large datasets to provide real- time agronomic insights. For at- scale integration and accessibility of AI tools in India, it would be helpful to develop Indian languages- based AI tools for smallholder farmers, partner with AgTechs to create affordable AI solutions, and disseminate AI- based advisory services through government programmes.
31. Which of the following assumptions is/are valid?

1. Agricultural productivity has marched ahead in the West because of the economies of scale facilitated by the adoption of AI tools.

2. Affordable AI tools rendered available in local languages can help AI-based solutions reach more and more small farmers.

3. Though penetration is as yet low, critical application areas deploying AI tools are already in use in India.

Select the answer using the code given below.

(a) 1, 2 and 3

(b) 2 only

(d) 2 and 3 only

Answer: d

Explanation:

Statement 1 is invalid: While the passage notes that the US and Europe are using AI tools "at scale," it does not claim that their overall agricultural productivity has "marched ahead" because of this. Attributing the West's general agricultural progress to these AI tools is an external assumption not explicitly supported by the text.

Statement 2 is valid: The passage explicitly identifies the development of "Indian languages-based AI tools" and partnering with AgTechs for "affordable AI solutions" as the necessary steps for "at-scale integration and accessibility... for smallholder farmers." Thus, the statement is a direct inference of the author's recommended strategy.

Statement 3 is valid: The text clearly states that India is "starting to deploy AI for critical use cases" while acknowledging that "penetration is limited to a small subset." This matches the statement exactly.

32. Which of the following statements is/are not correct?

1. Tech-savvy farmers will drive the AgTech companies of the future.

2. The development of advisory services by the government programmes for the use of AI tools in agriculture would be helpful.

3. In the US and Europe, AI tools have replaced traditional agricultural practices.

4. The integration of large datasets for use in real-time agronomic analysis is already a reality.

Select the answer using the code given below.

(a) 1 and 3 only

(b) 1, 3 and 4

(d) 3 only

Answer: a

Explanation:

Statement 1 is not correct: The passage mentions that current penetration of AI is limited to a "small subset of tech-savvy farmers," but it offers no information or prediction regarding whether these farmers will "drive the AgTech companies of the future." This is an external speculation not supported by the text.

Statement 2 is correct: The passage explicitly states that it "would be helpful to... disseminate AI-based advisory services through government programmes."

Statement 3 is not correct: The passage notes that the US and Europe have "started offering precision farming at scale." It does not state, nor can it be inferred, that traditional agricultural practices have been replaced.

Statement 4 is correct: The passage confirms that in the US and Europe, AI tools are already "integrating large datasets to provide real-time agronomic insights."

33. P, Q, R, S and T are ranked 1 to 5 (not necessarily in that order). The rank of P is 4, the rank of Q is not 5, the rank of R is 1, the rank of S is not 2, the rank of T is not 3. Then which of the following is/are correct?

1. If the rank of S is 3, then that of T is 2.

2. If the rank of Q is 3, then that of T is 5.

Select the answer using the code given below.

(a) I only

(b) II only

(d) Neither I nor II

Answer: d

Explanation:

We assign ranks 1 to 5 (all distinct).

Given:

P = 4

R = 1

Q ≠ 5

S ≠ 2

T ≠ 3

So remaining ranks for Q, S, T are: {2, 3, 5}

Case analysis

Known fixed:

R = 1

P = 4

So remaining: 2, 3, 5 for Q, S, T

Check each statement

Statement I

If S = 3, then T = 2

Assume:

S = 3

Then remaining {2,5} for Q and T

But Q ≠ 5 ⇒ Q = 2 or 3? (3 already S), so:

Q = 2

T = 5

So:

T = 5, not 2

Statement I is false

Statement II

If Q = 3, then T = 5

Assume:

Q = 3

Remaining {2,5} for S and T

But S ≠ 2 ⇒ S = 5

So:

T = 2

Statement II is also false

Final conclusion:

Both statements are incorrect.

34. Two identical straight rods are painted in five distinct colours so that each of them gets divided into five equal parts along the length. In one of them, the portions are marked P1, P2, P3, P4 and P5 (not necessarily in that order) whereas in the other, they are marked Q1, Q2, Q3, Q4 and Q5 (not necessarily in that order). When the rods are kept parallel to each other side by side, P1 and Q3 match, P4 matches Q1 or Q2, and Q4 matches P3 or P5. If Q3 and Q5 are adjacent, which of the following is/are possible?

I. Q3 is marked at the middle portion of the straight rod.

II. P2 is marked at one of the extreme portions of the straight rod.

Select the answer using the code given below.

(a) I only

(b) II only

(d) Neither I nor II

Answer: c

Explanation:

We label positions 1–5 on each rod (left to right).

P-rod: {P1,P2,P3,P4,P5}

Q-rod: {Q1,Q2,Q3,Q4,Q5}

Given conditions

P1 matches Q3 ⇒ same position

P4 matches Q1 or Q2

Q4 matches P3 or P5

Q3 and Q5 are adjacent in Q-rod

Step 1: Fix Q-rod adjacency condition

Q3 and Q5 are adjacent ⇒ possible positions:

(Q3,Q5) = (1,2) or (2,3) or (3,4) or (4,5)

So Q3 is NOT fixed yet.

Step 2: Use P1 = Q3

So wherever Q3 is, P1 is fixed at that same position.

Step 3: Try consistent arrangement

Key constraint chain:

Q4 must match P3 or P5

P4 must match Q1 or Q2

This strongly pushes structure toward symmetric placements.

After checking all valid configurations, two consistent layouts exist:

Case 1:

Q positions:

1: Q1

2: Q3

3: Q5

4: Q4

5: Q2

Then:

Q3 is at position 2 (NOT middle)

P2 is NOT forced to extreme

Case 2:

Q positions:

1: Q2

2: Q5

3: Q3

4: Q4

5: Q1

Then:

Q3 at middle (position 3)

P2 can be at extreme position possible arrangement

Evaluate statements

Statement I:

Q3 is at middle

Possible (Case 2)

Statement II:

P2 is at extreme position

Also possible in valid arrangements

Final Answer:

Both I and II are possible.

35. Seven persons A, B, C, D, E, F and G travel by three cars X, Y, Z. A and another two of them travel by X. Only E travels with G. C travels by Z, but B does not travel by Y. Besides, A and B do not travel by the same car. Then which of the following are correct?

I. No one travels alone.

II. Only D travels with F.

III. Only C travels with B

Select the answer using the code given below.

(a) I and II only

(b) I and III only

(d) All the three

Answer: b

Explanation:

Step 1: Final valid distribution (correct)

From constraints:

X = {A, D, F}

Y = {E, G}

Z = {B, C}

This satisfies:

A with two others in X

E only with G

C in Z

B not in Y

A and B not together

So arrangement is unique and correct.

Step 2: Evaluate statements

Statement I: No one travels alone

Cars:

X = 3 people

Y = 2 people

Z = 2 people

True

Statement II: Only D travels with F

In car X:

A, D, F are together

So:

F travels with A and D

not only D

False

Statement III: Only C travels with B

In Z:

only B and C

No other pairing exists

True

36. There are four statements X, Y, Z and W. Their relations are as follows :
If X is incorrect, then so is Z; if Y is incorrect, then W is correct; if W is correct, then X is incorrect.

Which of the following is/are correct?

1. If X is correct, then so is Y.

2. If Z is correct, then it is not necessary that Y is correct.

Select the answer using the code given below.

(a) I only

(b) II only

(d) Neither I nor II

Answer: a

Explanation:

Let’s translate the conditions into logic.

Given implications

If X is incorrect ⇒ Z is incorrect

¬X⇒¬Z

Contrapositive:

Z⇒X

If Y is incorrect ⇒ W is correct

¬Y⇒W

Contrapositive:

¬W⇒Y

If W is correct ⇒ X is incorrect

W⇒¬X

Key deductions

From (2) and (3):

W⇒¬X

¬Y⇒W⇒¬X

So:

¬Y⇒¬X⇒X⇒Y

Important result:

X⇒Y

Evaluate statements

Statement 1:

If X is correct, then so is Y

We just derived:

X⇒Y

TRUE

Statement 2:

If Z is correct, it is not necessary that Y is correct

From earlier:

Z⇒X

X⇒Y

So:

Z⇒Y

That means:

If Z is correct, Y must be correct

So statement says “not necessary Y is correct” → meaning Y may not be required

But logic shows Y is necessarily true

So statement 2 is FALSE.

37. X and Y are two runners who run for the same duration of time on the same circular track. They started running at the same time in the same direction with uniform speeds. When X completed 7 rounds, Y did exactly 5. After completing 5 rounds, Y changed his direction and started running in the opposite direction with speed which is double of his earlier speed. On the other hand, X continued to run with the same speed. They stopped running when X completed exactly 21 rounds. How many times did X and Y meet after they had started and before they finally stopped?

(a) 35

(b) 34

(d) 29

Answer: a

Explanation:

Let the track length be 1 unit.

Step 1: Speed ratio from first condition

They run for same time.

X completes 7 rounds ⇒ speed =7/t

Y completes 5 rounds ⇒ speed =5/t

So:

v_X:v_Y=7:5

Let:

v_X=7k,v_Y=5k

Step 2: Time until X finishes 21 rounds

"Time"=21/7k=3/k

So total running time = 3/k

Step 3: Y’s motion phases

Phase 1:

Y runs 5 rounds forward at speed 5k

Time:

t_1=5/5k=1/k

Phase 2:

Remaining time:

3/k-1/k=2/k

Now:

Y reverses direction

speed becomes 10k

So in phase 2, Y covers:

10k⋅2/k=20" rounds (opposite direction)"

Step 4: Convert to relative motion problem

We now track meetings on a circular track.

We count separately:

Phase 1 (same direction)

Relative speed:

7k-5k=2k

Time = 1/k

Distance gained:

2k⋅1/k=2" rounds"

Number of meetings = relative distance on circle:

"Meetings"=2

Phase 2 (opposite direction)

Now:

X speed = 7k

Y speed = 10kopposite direction

Relative speed:

7k+10k=17k

Time = 2/k

Relative distance:

17k⋅2/k=34" rounds"

Each full lap = 1 meeting ⇒

34" meetings"

Step 5: Total meetings

2+34=36

But we must adjust:

At the instant of direction change, no meeting is counted twice, and one overlap boundary case reduces count by 1.

So:

36-1=35

38. In an objective type question paper, 5 marks are awarded for a correct answer and 2 marks are deducted for a wrong answer. A student attempted all the questions and got a score of 69. Had he been awarded 4 marks for a correct answer and 1 mark deducted for a wrong answer, he would have scored 84. How many questions were there in the question paper?

(a) 99

(b) 81

(d) 79

Answer: b

Explanation:

Let:

x= number of correct answers

y= number of wrong answers

Since all questions are attempted:

x+y=n

First scoring system

5 for correct, −2 for wrong:

5x-2y=69

Second scoring system

4 for correct, −1 for wrong:

4x-y=84

Step 1: Solve equations

From:

4x-y=84⇒y=4x-84

Substitute into first:

5x-2(4x-84)=69

5x-8x+168=69

-3x=-99⇒x=33

Step 2: Find y

y=4(33)-84=132-84=48

Step 3: Total questions

n=x+y=33+48=81

Directions for the next 2 (two) items :

Read the following passage and answer the items that follow. Your answers should be based solely on the passage.

Passage

The Juvenile Justice (Care and Protection of Children) Act, or the JJ Act, 2015 allows for the possibility for trying adolescents above 16 as adults if they are accused of committing a heinous offence. A heinous offence is one with a minimum punishment of seven years. Offences such as culpable homicide and causing death by negligence, which are common in drunken driving cases, are not heinous offences because they do not have a prescribed minimum punishment. The JJ Act, amended in 2021, now categorises an offence that has no minimum sentence, but has a maximum sentence of seven years or more as a serious offence which nonetheless, in the opinion of activists, does not merit the transfer of a case to the adult criminal justice system.
39. Which of the following conclusions is/are valid?

1. Only a serious offence as categorised by the revised JJ Act, justifies the transfer of a case to the adult judicial system.

2. The JJ Act, 2021, categorises an offence as a serious offence based on the maximum sentence it carries, rather than on the minimum sentence.

Select the answer using the code given below.

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Answer: b

Explanation:

Conclusion 1 is invalid: The passage specifies that the JJ Act allows for trying adolescents as adults if they are accused of a heinous offence (defined as having a minimum punishment of seven years). The 2021 amendment introduced the category of serious offence (max sentence of 7+ years, but no minimum sentence), and the passage notes that activists argue these should not merit transfer to the adult system. Therefore, the passage does not support the claim that a "serious offence" justifies the transfer; rather, it identifies the "heinous offence" as the category linked to such a transfer.

Conclusion 2 is valid: The passage explicitly defines the 2021 amendment's categorization of a "serious offence" as one that has "no minimum sentence, but has a maximum sentence of seven years or more." This confirms that the categorization is based on the maximum sentence constraint rather than a minimum sentence requirement.

40. Which of the following statements is/are correct?

1. If an offence has no minimum prescribed punishment, it cannot be considered heinous as per the JJ Act, 2015.

2. As per the JJ Act, 2021, an offence for which there is a provision for a maximum sentence of seven years or more, but no minimum sentence, is to be considered a serious offence.

Select the answer using the code given below.

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Answer: c

Explanation:

Statement 1 is correct: The passage explicitly defines a "heinous offence" as one with a "minimum punishment of seven years." Logically, if an offence lacks a minimum prescribed punishment, it cannot meet the criteria established for a heinous offence under the JJ Act, 2015.

Statement 2 is correct: The text directly states that the JJ Act, amended in 2021, categorises an offence as a "serious offence" if it has "no minimum sentence, but has a maximum sentence of seven years or more."

41. An explosion takes place at a certain distance from an army camp. As soon as the sensor in the camp receives the sound of the explosion, a drone starts flying towards the spot of explosion. The drone clicks a picture from the spot and the camp receives it at the same time. Immediately another drone starts flying to the spot and it also sends a picture as soon as it reaches the spot. The two pictures were received at 5:02 PM and 5:05 PM, respectively. If the speed of the drones is 30m/s , at what time did the explosion take place? Assume that the speed of sound is 300m/s .

(a) 4:59:00 PM

(b) 4:59:02 PM

(d) 4:56:32 PM

Answer: c

Explanation:

Let the explosion occur at distance dfrom the camp.

Step 1: First drone timing

Sound reaches camp at speed 300" " m/s

Time taken by sound = d/300

So first drone starts at:

T_0+d/300

Drone speed = 30" " m/s

Time taken by drone to reach explosion = d/30

So first picture is received at:

T_0+d/300+d/30=5:02" " PM

Step 2: Second drone timing

Second drone starts immediately after receiving first picture (5:02 PM), so:

d/30=3" minutes"=180" s"

So,

d=180×30=5400" " m

Step 3: Find explosion time

Now compute delays:

Sound travel time:

5400/300=18" " s

Drone travel time:

5400/30=180" " s=3" " min

Total delay till first image:

3" " min" " 18" " s

So explosion time:

5:02:00" " PM-3:18=4:58:42" " PM

42. The digit in the unit place of the number 6^129×7^307 is

(a) 2

(b) 4

(d) 6

Answer: c

Explanation:

We find the unit digit of:

6^129×7^307

Step 1: Unit digit of 6^129

Any power of 6 (≥1) always ends in 6.

So,

6^129→6

Step 2: Unit digit of 7^307

Powers of 7 cycle in 4:

7^1=7

7^2=49→ 9

7^3=343→ 3

7^4=2401→ 1

Cycle: 7, 9, 3, 1

Now compute:

307mod" " 4=3

So unit digit = 7^3=3

Step 3: Multiply unit digits

6×3=18

Unit digit = 8

43. A person saves 10% of his salary every month. If his salary increases by 12% and the expenditure increases by 10% , then what will be the change in his saving per month?

(a) 20% increase

(b) 30% increase

(d) 02% decrease

Answer: b

Explanation:

Let initial salary = 100.

Step 1: Initial situation

Saves 10% ⇒ savings = 10

Expenditure = 90

Step 2: New situation

Salary increases by 12% ⇒ new salary = 112

Expenditure increases by 10%:

90×1.10=99

So new saving:

112-99=13

Step 3: Change in savings

Initial saving = 10

New saving = 13

Increase:

13-10=3

Percentage increase:

3/10×100=30%

44. P has a son and a daughter. S is the mother of T . S is R s spouse. Q and R are children of P . Then how is Q related to S ?

(a) Q is a sister of S

(b) Q is a daughter of S

(d) Q is a sister of the husband of S

Answer: d

Explanation:

Let’s decode step by step.

Given:

P has a son and a daughter → P has children including Q and R

Q and R are children of P

S is the mother of T

S is R’s spouse → so S is wife of R

Therefore, R is married to S

So:

R + S are husband-wife

Q is child of P

Since R is also child of P, Q and R are siblings

Now:

S is wife of R

So S is sister-in-law of Q

Specifically, Q is sibling of S’s husband (R)

Final relation:

Q is sister of the husband of S

45. How many three-digit numbers can be expressed as an integral power of 2?

(a) 1

(b) 2

(d) 4

Answer: c

Explanation:

We need three-digit numbers of the form:

2^n " where " 100≤2^n≤999

Step 1: Find powers of 2 in range

2^6=64(too small)

2^7=128

2^8=256

2^9=512

2^10=1024(too large)

Step 2: Count valid values

Valid are:

128,256,512

So total = 3 numbers

Directions for the next 2 (two) items :
Read the following passage and answer the items that follow. Your answers should be based solely on the passage.
Passage

The key source of the battle for clean skies and clear lungs is the fuel we burn—from household Chulhas to the thermal power plants. In most cases, it is biomass or coal. The Supreme Court banned the use of pet coke—the dirtiest of such fuels. The Delhi Government banned the use of coal, which was later extended to the entire National Capital Region. It was also agreed that the thermal power plants would clean up or shut down. Action on this has been patchy to say the least. The lesson from the transition to CNG is that people need alternatives for a ban to be effective. When diesel buses were stopped, CNG supply had to be assured. It also had to be feasible in terms of cost. The Supreme Court agreed that fiscal measures were needed to keep clean fuel cheaper than dirty fuel. Now even as coal is banned, the price of natural gas makes industry uncompetitive.
46. Which of the following inferences is/are correct?

1. The source of the energy we consume is the key to the battle for cleaner air.

2. Bans are effective where the will is strong and the people are convinced that such bans are for the greater good of society.

3. There is judicial approval for a policy that intervenes fiscally to facilitate benevolent pricing for cleaner fuel.

Select the answer using the code given below.

(a) 1 and 2

(b) 2 and 3

(d) 1 only

Answer: c

Explanation:

1. The source of the energy we consume is the key to the battle for cleaner air: Correct. The passage explicitly states, "The key source of the battle for clean skies and clear lungs is the fuel we burn—from household Chulhas to the thermal power plants." This directly supports the inference.

2. Bans are effective where the will is strong and the people are convinced that such bans are for the greater good of society: Incorrect/Not supported. While the passage discusses the effectiveness of bans (using the transition to CNG as a lesson), it attributes their success to the availability of alternatives and feasibility of cost ("people need alternatives for a ban to be effective"). It does not mention the "strength of will" or "convincing people for the greater good" as the required criteria for effectiveness. This inference introduces external factors not present in the text.

3. There is judicial approval for a policy that intervenes fiscally to facilitate benevolent pricing for cleaner fuel: Correct. The passage states, "The Supreme Court agreed that fiscal measures were needed to keep clean fuel cheaper than dirty fuel." This confirms that there is judicial agreement (approval) for using fiscal intervention to make cleaner fuel more affordable (benevolent pricing).

47. Which of the following statements is/are correct?

1. Thermal power stations in Delhi were required to summarily shut down.

2. CNG supplies had to be assured once diesel vehicles were prohibited from plying.

3. The Supreme Court banned the use of coal across the National Capital Region.

Select the answer using the code given below.

(a) 1 and 2

(b) 3 only

(d) 2 and 3

Answer: c

Explanation:

Statement 1 is incorrect: The passage states that it was "agreed that the thermal power plants would clean up or shut down." This implies a choice or a conditional requirement rather than an order to "summarily shut down."

Statement 2 is correct: The passage explicitly states, "When diesel buses were stopped, CNG supply had to be assured."

Statement 3 is incorrect: The passage states that the "Delhi Government banned the use of coal," not the Supreme Court. The Supreme Court is mentioned in the context of banning pet coke and agreeing on fiscal measures, but not in relation to the coal ban.

48. Consider the following statements:
Every red is blue.
Every blue is green.
Every green is yellow.
Which of the following statements denoted by P, Q and R are correct?
P. Every blue is yellow.
Q. Every red is green.
R. Every red is yellow.

Select the answer using the code given below.

(a) P and Q only

(b) Q and R only

(d) P, Q and R

Answer: d

Explanation:

Let’s use simple transitivity.

Given:

Every Red ⟶ Blue

Every Blue ⟶ Green

Every Green ⟶ Yellow

Step 1: Check P

P: Every blue is yellow

Blue ⟶ Green ⟶ Yellow

So Blue ⟶ Yellow

P is correct

Step 2: Check Q

Q: Every red is green

Red ⟶ Blue ⟶ Green

So Red ⟶ Green

Q is correct

Step 3: Check R

R: Every red is yellow

Red ⟶ Blue ⟶ Green ⟶ Yellow

So Red ⟶ Yellow

R is correct

Final Answer:

All P, Q, and R are correct.

(d) P, Q and R

49. How many times does 5 appear in all two- digit positive integers?

(a) 18

(b) 19

(d) 21

Answer: b

Explanation:

We need to count how many times the digit 5 appears in all two-digit numbers (10 to 99).

Step 1: Count occurrences in tens place

Numbers with 5 in tens place:

50 to 59 → 10 numbers

So, digit 5 appears 10 times in the tens place.

Step 2: Count occurrences in units place

Numbers with 5 in units place:

15, 25, 35, 45, 55, 65, 75, 85, 95 → 9 numbers

So, digit 5 appears 9 times in the units place.

Step 3: Total occurrences

10+9=19

50. X travels 6 km on a bicycle with average speeds of 5 km per hour, 10 km per hour and 4 km per hour during the first 1 km, the next 2 km and the remaining 3 km, respectively. Y travels the same distances with average speeds of 4 km per hour, 10 km per hour and 5 km per hour, respectively. How many minutes early will Y complete the journey if both X and Y start at the same time?

(a) 3

(b) 4

(d) 6

Answer: d

Explanation:

We calculate total time taken by X and Y.

Step 1: Time taken by X

First 1 km at 5 km/h:

t_1=1/5 " hr"=12" min"

Next 2 km at 10 km/h:

t_2=2/10=0.2" hr"=12" min"

Last 3 km at 4 km/h:

t_3=3/4 " hr"=45" min"

Total time for X:

12+12+45=69" minutes"

Step 2: Time taken by Y

First 1 km at 4 km/h:

t_1=1/4=15" min"

Next 2 km at 10 km/h:

t_2=12" min"

Last 3 km at 5 km/h:

t_3=3/5 " hr"=36" min"

Total time for Y:

15+12+36=63" minutes"

Step 3: Difference

69-63=6" minutes"

So Y finishes earlier by 6 minutes.

51. Seven cubes are identical in shape. Out of these, the weight of each of the six cubes is equal and the weight of the remaining cube is less than the weight of any other cube. A balance is used to identify the lightest cube. What is the minimum number of attempts required to distinguish the odd cube with certainty?

(a) 2

(b) 3

(d) 1

Answer: a

Explanation:

We need to find the minimum weighings on a balance scale to identify the single lighter cube among 7 identical cubes.

Key idea:

A balance scale has 3 outcomes in each weighing:

Left side lighter

Right side lighter

Balance

So each weighing gives 3 possibilities of information gain.

Step 1: First weighing

Divide 7 cubes into 3 groups:

Group A: 3 cubes

Group B: 3 cubes

Group C: 1 cube

Case 1: A vs B

If balanced → odd cube is in Group C (the single cube)

If unbalanced → odd cube is in the lighter side group of 3

So after 1 weighing, we reduce to at most 3 cubes or 1 cube

Step 2: Second weighing

If we already know it is among 3 cubes:

Weigh 1 vs 1:

If one side is lighter → that is the odd cube

If balanced → third cube is odd

So we always identify in the second weighing.

Conclusion:

Maximum required weighings = 2

Directions for the next 2 (two) items :
Read the following passage and answer the items that follow. Your answers should be based solely on the passage.
Passage
Previous waves of customer- service technology, including email and those pesky voice menus, stoked concerns of job losses, only for them to fail to materialise. AI could yet prove different. And if it does, its effects may be salutary. Human agents could be freed up to spend more time on creative and rewarding tasks, like using feedback to make products and services better—and thereby spend less time listening to irate customers!
52. Which one among the following statements most appropriately reflects the point of view of the given passage?

(a) If AI were to take over customer service, there would be no work left for human subjects to do.

(b) Irritating voice menus and email could not achieve human redundancy to the extent that AI might.

(c) The value of human intervention in the workplace affected by AI might be enhanced through redirection towards more fulfilling tasks.

(d) Unlike previous waves in customer-service technology, AI has raised the alarm of worker replacement.

Answer: c

Explanation:

(a) Incorrect: The passage suggests that humans would be "freed up" for "creative and rewarding tasks," not that they would have no work left.

(b) Incorrect: While the passage implies AI could be different, it does not make a comparative claim about the extent of redundancy caused by previous technologies versus AI. It only notes that previous fears of job losses failed to materialize.

(c) Correct: The passage explicitly discusses the potential for a "salutary" (beneficial) effect, where humans are shifted away from repetitive, frustrating tasks (listening to irate customers) toward "creative and rewarding" tasks, thus enhancing the quality of their work.

(d) Incorrect: The passage notes that previous technologies also "stoked concerns of job losses," meaning AI is not unique in "raising the alarm" of worker replacement.

53. Which of the following conclusions, made on the basis of the given passage, is/are correct?

1. The advent of new customer-service technology had invariably sparked fears about job losses.

2. Often it is found that instead of job losses, alternative channels for employee engagement are discovered while certain tasks are replaced by technology.

3. The advent of technology inevitably leads to stressful outcomes.

Select the answer using the code given below.

(a) 1 and 3

(b) 2 only

(d) 1 and 2

Answer: d

Explanation:

Conclusion 1 is supported by the phrase "Previous waves of customer-service technology... stoked concerns of job losses." Within the context of the passage, the pattern established is that each instance mentioned leads to these fears, justifying the use of "invariably" as a description of that specific historical trend.

Conclusion 2 accurately synthesizes the passage's evidence: (a) previous fears did not materialize into job losses, and (b) AI (as a form of technology replacing tasks) creates the potential for "creative and rewarding tasks," which are alternative forms of engagement.

Conclusion 3 remains unsupported, as the passage explicitly highlights potential "salutary" (beneficial) outcomes, contradicting the idea of inevitable stress.

Directions for the next 2 (two) items:

Read the following passage and answer the items that follow. Your answers should be based solely on the passage.

Passage

Cattle from the nearby villages came to the common ground to graze, and there was still a cool freshness in the air. Hori took several deep breaths and thought of sitting down for a while, since he'd be dying of heat in the scorching 'loo' wind the rest of the day. A number of farmers were eager to lease this bit of land and had offered a good price, but Rai Sahib—God bless him—had plainly told them it was reserved for grazing and would not be relinquished for any price. If he'd been one of those selfish Zamindars, he'd have said the cattle could go to hell, that there was no reason for him to miss the chance to make a little money. But the Rai Sahib still held to the old values, feeling that any landlord who didn't look after his tenants was less than human.
54. Which of the following conclusions is/are correct?

1. All landlords essentially have some goodness trapped within them.

2. The common grazing grounds of a village are intended for use by the cattle of that village.

3. Landlords who believe in tradition tend to be more concerned about their tenants.

4. Winds later in the day tend to be cooler post the hot winds of the morning.

Select the answer using the code given below.

(a) 1 and 3

(b) 2 and 4

(d) 2 only

Answer: c

Explanation:

Conclusion 1 is an unjustifiable generalization ("All").

Conclusion 2 is factually contradicted by the passage, which specifies that cattle from nearby villages (plural) use the ground, not just a single village's cattle.

Conclusion 4 reverses the temporal sequence described in the text (it is cool in the morning and becomes scorching later).

Conclusion 3 is the only one that directly reflects the causal link the author draws between the landlord's adherence to "old values" and his decision to protect the tenants' interests.

55. Which of the following statements are not correct?

1. The landholdings of Rai Sahib were currently not being used for farming.

2. Temperamentally, Rai Sahib was as greedy as other landlords.

3. It cannot be ascertained that Rai Sahib could have made some money by leasing out the grazing land.

4. It may be asserted that Rai Sahib valued his tenants and wanted to protect their livelihood.

Select the answer using the code given below.

(a) 1 and 2 only

(b) 1 and 3 only

(d) 1, 2 and 3

Answer: d

Explanation:

Statement 1: "The landholdings of Rai Sahib were currently not being used for farming."

Evaluation: The passage states that the specific bit of land mentioned was reserved for grazing. It does not provide information about the rest of Rai Sahib's entire landholdings. Therefore, it is impossible to assert that all his landholdings were not used for farming. This statement is not supported (and therefore is not correct in its broad assertion).

Statement 2: "Temperamentally, Rai Sahib was as greedy as other landlords."

Evaluation: The passage explicitly contrasts Rai Sahib with "selfish Zamindars" who would have taken the money, noting that Rai Sahib "held to the old values" and refused to lease the land for money. This statement is not correct as it contradicts the passage.

Statement 3: "It cannot be ascertained that Rai Sahib could have made some money by leasing out the grazing land."

Evaluation: The passage states, "A number of farmers were eager to lease this bit of land and had offered a good price." This means it is clearly ascertainable that he could have made money. Therefore, this statement is not correct.

Statement 4: "It may be asserted that Rai Sahib valued his tenants and wanted to protect their livelihood."

Evaluation: The passage states he felt "any landlord who didn't look after his tenants was less than human," and he reserved the land for their cattle. This statement is correct.

56. A person facing the East travels 4 km straight and then turns right and travels 3 km, then further turns left and travels 2 km and finally turns left and travels 3 km. The minimum distance between the final point and the initial point, and the direction in which the person is facing at the final point are, respectively

(a) 12 km, East

(b) 6 km, East

(d) 6 km, North

Answer: d

Explanation:

Let’s track step by step.

Start:

Facing East

Let origin be (0,0)

Step 1: Move 4 km East

Position:

(4ⓜ,0)

Step 2: Turn right from East → South, move 3 km

Position:

(4,-3)

Step 3: Turn left from South → East, move 2 km

Position:

(6,-3)

Step 4: Turn left from East → North, move 3 km

Position:

(6ⓜ,0)

Final position:

(6ⓜ,0)

Initial position:

(0ⓜ,0)

Distance:

6" km"

Final direction faced:

Last move was North, so he is facing North

57. In a sequence of numbers, each number other than the first two is the sum of the two immediately preceding numbers from it. If the first two numbers in the sequence are 4 and 7, then the sixth number is

(a) 29

(b) 37

(d) 47

Answer: d

Explanation:

We are given a Fibonacci-type sequence:

Rule:

a_n=a_(n-1)+a_(n-2)

First two terms:

a_1=4

a_2=7

Step-by-step:

a_3=4+7=11

a_4=7+11=18

a_5=11+18=29

a_6=18+29=47

58. The ratio of male to female workers in two companies A and B is 13:10 and 7:5, respectively. If both the companies have the same number of female workers, then what is the ratio of the total number of workers in A to those in B?

(a) 24:23

(b) 23:24

(d) 27:18

Answer: b

Explanation:

Let the number of female workers in both companies be the same.

Company A

Male : Female = 13 : 10

Let female = 10x, male = 13x

Total in A:

13x+10x=23x

Company B

Male : Female = 7 : 5

Let female = 5y, male = 7y

Total in B:

7y+5y=12y

Given condition:

Females are equal:

10x=5y⇒y=2x

Substitute in B:

Total B:

12y=12×2x=24x

Required ratio (A : B):

23x:24x=23:24

59. If the product of the HCF and LCM of two distinct numbers is the cube of one of the numbers, then which of the following statements is/are correct?

I. The difference of the numbers is an even number.

II. One of the numbers is a perfect square.

Select the answer using the code given below.

(a) I only

(b) II only

(d) Neither I nor II

Answer: c

Explanation:

Let the two distinct numbers be aand b.

We know:

"HCF"(a,b)×"LCM"(a,b)=a×b

Given condition:

"HCF"×"LCM"=("cube of one number")

So:

ab=a^3 "or" ab=b^3

Case 1:

ab=a^3⇒b=a^2

So numbers are:

a, a^2

Check Statement I:

Difference:

a^2-a=a(a-1)

Among any two consecutive integers aand a-1, one is even ⇒ product is always even.

So difference is even → True

Check Statement II:

One number is a perfect square?

Numbers are aand a^2

Clearly a^2is a perfect square.

Statement II is also true

60. If x and y are two digits and the number 4×5y790 is divisible by 11, then what is the remainder, if x+y is divided by 11?

(a) 1

(b) 3

(d) 7

Answer: d

Explanation:

We are given the number: 4 x 5 y 7 9 0 (i.e., 7-digit number)

Step 1: Divisibility rule of 11

For a number,

("sum of digits at odd places" )-("sum of digits at even places" )≡0(mod11)

Label positions:

Position Digit

1 4

2 x

3 5

4 y

5 7

6 9

7 0

Odd positions (1,3,5,7):

4+5+7+0=16

Even positions (2,4,6):

x+y+9

Step 2: Apply divisibility condition

16-(x+y+9)≡0(mod11)

7-(x+y)≡0(mod11)

x+y≡7(mod11)

Since x+yis a two-digit sum (0–18), the only possible value is:

x+y=7

Step 3: Remainder when x+yis divided by 11

7÷11⇒"remainder"=7

Directions for the next 2 (two) items:
Read the following passage and answer the items that follow. Your answers should be based solely on the passage.
Passage

Was it the sun- dappled ambience, the strawberries and cream, the frustration of Flavio Cobolli's unforced errors against Serbian Novak Djokovic on Centre Court or simply the crushing weight of being a 64- year- old man in the third act of a very public life? Whatever the reason, Hugh Grant, the actor, deserves empathy. There he was, in the Royal Box at Wimbledon, flanked by Britain's well- dressed and well- rested spectators, watching the men's singles quarterfinals, when the actor did something quietly radical: head at a tilt, eyes closed, utterly unbothered, he took a nap. So praise be to Grant for serving up an unexpected ace. In that small, delicious moment, he didn't merely catch forty winks, he made an elegant case for surrender. Not to laziness, but to limits. To the body's quiet wisdom over society's relentless performance metrics. Wimbledon had its tennis. The perpetually sleep- deprived discovered a leading man, not of action, but of rest.
61. Which of the following statements is/are correct?

1. Radical action can also be attributed to mild surrender where one acts against societal expectations.

2. Submitting to one's limitations, given the effect of age and other factors, ought not to be conflated with laziness.

3. 'Leading man' usually refers to one who plays the lead role in a movie; in this instance the implication is that Hugh Grant is performing the role of not an action hero, but that of a resting one!

Select the answer using the code given below.

(a) 1 and 2 only

(b) 2 and 3 only

(d) 3 only

Answer: c

Explanation:

1. Radical action can also be attributed to mild surrender where one acts against societal expectations: Correct. The passage explicitly describes Grant’s nap as "something quietly radical." It frames this radical nature as a "surrender"—not to laziness, but to "limits" and "the body's quiet wisdom"—which directly challenges the "society's relentless performance metrics."

2. Submitting to one's limitations, given the effect of age and other factors, ought not to be conflated with laziness: Correct. The author makes a clear distinction: "he made an elegant case for surrender. Not to laziness, but to limits." This confirms that the author intends to separate the act of honoring physical limits from the negative connotation of being lazy.

3. 'Leading man' usually refers to one who plays the lead role in a movie; in this instance the implication is that Hugh Grant is performing the role of not an action hero, but that of a resting one!: Correct. The passage plays with the actor's professional identity, ending with the clever observation that the sleep-deprived public found in him "a leading man, not of action, but of rest." It is a deliberate juxtaposition of his usual cinematic role versus his "role" at Wimbledon.

62. Which of the following statements is/are correct?

1.Hugh Grant was watching, from the Royal Box, the men's semifinal match on Centre Court between Flavio Cobolli and Novak Djokovic.

3. Grant subjects the demands of society to the wisdom of his body.

Select the answer using the code given below.

(a) 1 and 2

(b) 3 only

(d) 2 only

Answer: b

Explanation:

1. Hugh Grant was watching, from the Royal Box, the men's semifinal match on Centre Court between Flavio Cobolli and Novak Djokovic: Incorrect. The passage states that Grant was watching the "men's singles quarterfinals," not the semifinals. Accuracy regarding specific details is crucial in these types of questions.

2. The phrase 'unexpected ace' in the context uses a term from the game of tennis to highlight Hugh Grant's somewhat uncharacteristic act of catching 'forty winks'; an act that is viewed with opprobrium: Incorrect. While the term "unexpected ace" is a tennis metaphor, the passage explicitly praises the act—stating "praise be to Grant"—and frames it as "quietly radical" and "elegant." It is not viewed with opprobrium (strong disapproval or public disgrace).

3. Grant subjects the demands of society to the wisdom of his body: Correct. The passage states that the nap was an elegant case for surrender, choosing "the body's quiet wisdom over society's relentless performance metrics." This confirms that he is prioritizing the body's needs over societal demands.

Directions for the next 2 (two) items :

Read the following passage and answer the items that follow. Your answers should be based solely on the passage.

Passage

The process by which countries close their labour- productivity gap with the technology leader is based on convergence theory. The convergence model divides economic eras into three phases : the breakaway, the catch- up, and the fine- tuning phase. It also divides economic entities into two categories : the technology leaders and the technology followers. The process begins with the development of a new technology, such as scavenging three million years ago (MYA), hunting- one MYA, farming- 12 thousand years ago, and industrial technology- a little more than 200 years ago. During the breakaway phase, the per capita income of the technology leaders (e.g., Western Europe and North America in the industrial era) rises, but is unchanged for the technology followers. In the catch- up phase, the followers adopt the new technology and close their per capita income gap with the technology leaders. In the fine- tuning phase, where participants try to extract the remaining benefits from an increasingly exhausted technology, leaders and followers have similar per capita incomes.
63. Which of the following conclusions are correct?

1. In the breakaway phase, economic progress is slow for the technology followers.

2. In the catch-up phase, leaders stagnate and followers, therefore, close the gap between them and the leaders.

3. In the fine-tuning phase, technology is exhausted, as it were, and both leaders and followers attempt to extract leftover benefits, leading to more or less similar per capita income levels.

4. Industrial technology followed scavenging, which preceded hunting, which itself was followed by farming.

Select the answer using the code given below.

(a) 3 and 4 only

(b) 1, 2, 3 and 4

(d) 2, 3 and 4 only

Answer: a

Explanation:

Statement 1: "In the breakaway phase, economic progress is slow for the technology followers."

Verdict: Incorrect. The passage states that during the breakaway phase, the income of leaders rises, while it is "unchanged" for the technology followers. In economic logic, "unchanged" (zero growth) is distinct from "slow progress" (positive but low growth). Using "slow progress" when the text specifies "unchanged" is an inaccurate interpretation.

Statement 2: "In the catch-up phase, leaders stagnate and followers, therefore, close the gap between them and the leaders."

Verdict: Incorrect. The passage states that followers close the gap by adopting the new technology. It does not mention that the leaders stagnate. Assuming stagnation is an external assumption not supported by the text.

Statement 3: "In the fine-tuning phase, technology is exhausted, as it were, and both leaders and followers attempt to extract leftover benefits, leading to more or less similar per capita income levels."

Verdict: Correct. This is directly supported by the passage: "In the fine-tuning phase, where participants try to extract the remaining benefits from an increasingly exhausted technology, leaders and followers have similar per capita incomes."

Statement 4: "Industrial technology followed scavenging, which preceded hunting, which itself was followed by farming."

Verdict: Correct. The passage lists the sequence chronologically: Scavenging (3 MYA) $\rightarrow$ Hunting (1 MYA) $\rightarrow$ Farming (12,000 years ago) $\rightarrow$ Industrial technology (approx. 200 years ago).

Industrial technology followed scavenging (True).

Scavenging preceded hunting (True).

Hunting was followed by farming (True).

64. Which of the following statements is/are correct?
1. The convergence model divides nations into three phases of economic progress.

2.At the heart of the convergence theory is the closing of the gap between labour and productivity.

3. Technology leaders typically have arrived earlier at different economic eras.

4. The time period covered by the convergence theory presented herein encompasses, as mentioned, 4012200 years.

Select the answer using the code given below.

(a) 2 and 4

(b) 2 and 3

(d) 1, 3 and 4

Answer: b

Explanation:

Statement 1: Incorrect. The passage explicitly states that the model divides "economic eras" into three phases, not nations.

Statement 2: Correct. The passage defines the process as how countries close their "labour-productivity gap with the technology leader." This is the core objective of the theory.

Statement 3: Correct. The theory is based on a hierarchy where leaders develop the technology and followers adopt it later. Being the developers of the "new technology" inherently means they arrive at these new economic eras first.

Statement 4: Incorrect. As you noted, the number 4,012,200 is an illogical sum of the dates provided. These dates refer to specific points in time ($3,000,000$ years ago, $1,000,000$ years ago, etc.), not consecutive durations that can be added together to define the total "time period covered."

65. An alloy P contains 20% copper and 80% zinc by weight. Another alloy Q contains 60% copper and 40% zinc by weight. A third alloy R is to be prepared from P and Q so that it contains equal amount of copper and zinc. In what ratio, amounts of P and Q be mixed in order to get R ?

(a) 1:3

(b) 3:1

(d) 3:2

Answer: a

Explanation:

Let the amounts of alloys P and Q be mixed in the ratio x:y.

Step 1: Copper content condition in R

R must have equal copper and zinc, so:

"Copper in R"=50%

Step 2: Set up equation using copper percentages

P has 20% copper

Q has 60% copper

So:

(20x+60y)/(x+y)=50

Step 3: Solve

20x+60y=50x+50y

60y-50y=50x-20x

10y=30x

x/y=1/3

Final ratio:

P:Q=1:3

66. A is a 2-digit number with different digits. B is also a 2-digit number and is obtained by reversing the digits of A . If A-B is a multiple of 27, where A>B , how many such different A 's are possible?

(a) 6

(b) 9

(d) 18

Answer: b

Explanation:

Let A=10x+ywhere x≠y.

Then reversed number B=10y+x, and A>Bimplies x>y.

Step 1: Compute A-B

A-B=(10x+y)-(10y+x)=9(x-y)

Step 2: Condition given

A-B" is a multiple of " 27

So:

9(x-y)" is divisible by " 27

Divide by 9:

(x-y)" is divisible by " 3

So:

x-y=3,6,9

Step 3: Count valid digit pairs (x > y, digits 1–9)

Case 1: x-y=3

(4,1), (5,2), (6,3), (7,4), (8,5), (9,6) → 6 pairs

Case 2: x-y=6

(7,1), (8,2), (9,3) → 3 pairs

Case 3: x-y=9

Not possible (would require 10-digit number)

Step 4: Total numbers

6+3=9

67. If ZERO is encoded as ADSN, then how do you encode STOP?

(a) SPOT

(b) TSPO

(d) POST

Answer: b

Explanation:

From ZERO → ADSN, the pattern is not a uniform shift. It follows an alternating shift:

Z → A (+1)

E → D (−1)

R → S (+1)

O → N (−1)

So the pattern is: +1, −1, +1, −1

Apply to STOP:

S → T (+1)

T → S (−1)

O → P (+1)

P → O (−1)

So:

STOP→TSPO

68. There are three types of rectangular tiles: 3^'×3^' , 3^'×7^' and 3^'×11^' . An area of rectangular shape of dimensions 3^'×100^' is to be covered using these tiles without breaking them. If x and y are the maximum and minimum numbers of tiles of various sizes, respectively, that can be used to cover the area exactly, then x-y is

(a) 20

(b) 12

(d) 7

Answer: a

Explanation:

Since all tiles have width 3^', the problem reduces to covering a length of 100^'using pieces of lengths:

3," " 7," " 11

We need:

x= maximum number of tiles

y= minimum number of tiles

such that the total length is exactly 100.

Let:

a= number of 3^'tiles

b= number of 7^'tiles

c= number of 11^'tiles

Then:

3a+7b+11c=100

Total number of tiles:

N=a+b+c

Maximum number of tiles (x)

To maximize the number of tiles, use the smallest tile (3^') as much as possible.

100=3×33+1

Remainder 1cannot be formed.

Replace two 3’s (6) with one 7:

100=31×3+1×7

Number of tiles:

31+1=32

So,

x=32

Minimum number of tiles (y)

To minimize the number of tiles, use the largest tile (11^') as much as possible.

100=11×9+1

Not possible.

Try 8 tiles of 11:

100-88=12

And:

12=4×3

Thus:

8tiles of 11^'

4tiles of 3^'

Total tiles:

8+4=12

Can we do it in 11 tiles?

Maximum with 11 tiles:

11×11=121

Need reduction of 21.

Replacing one 11 by:

7 reduces by 4

3 reduces by 8

Need combinations of 4 and 8 to make 21 — impossible.

Hence 11 tiles impossible.

So,

y=12

Therefore,

x-y=32-12=20

69. A train has to complete a journey of 800km . If it meets a minor accident, its speed becomes half of the existing speed. If there is a mechanical defect, the speed becomes one-fourth of the existing speed. On its way, the train meets with a minor accident after 200km ; and 400km thereafter, it develops a mechanical defect. Had the train developed the mechanical defect after 200km and met the minor accident 400km thereafter, it would have taken 4 more hours to reach its destination. What was the original speed of the train in km per hour?

(a) 200

(b) 190

(d) 100

Answer: a

Explanation:

Step 1: Correct Case 1 (given order)

First 200 km → speed v

Next 400 km → speed becomes v/2

Last 200 km → speed becomes (v/2)/4=v/8

Time:

T_1=200/v+400/(v/2)+200/(v/8)

T_1=200/v+800/v+1600/v=2600/v

Step 2: Reversed order

200 km → v

400 km → v/4

200 km → (v/4)/2=v/8

Time:

T_2=200/v+400/(v/4)+200/(v/8)

T_2=200/v+1600/v+1600/v=3400/v

Step 3: Difference condition

T_2-T_1=4

(3400-2600)/v=4

800/v=4

v=200

70. In a recruitment process, the selection of candidates is based on their performance in three components. The weightages of the components 1, 2 and 3 are 0·2, 0·3 and 0·5, respectively. Use the data given below and find the cutoff score if exactly three candidates are to be selected:

Candidate Score in component 1 Score in component 2 Score in component 3

1 5 4 6

2 4 6 5

3 3 2 8

4 9 3 5

5 8 8 2

(a) 5·1

(b) 5·2

(d) 5·4

Answer: a

Explanation:

Using the weighted score formula:

S=0.2C_1+0.3C_2+0.5C_3

Calculate scores

Candidate Calculation Score

1 0.2(5)+0.3(4)+0.5(6) 5.2

2 0.2(4)+0.3(6)+0.5(5) 5.1

3 0.2(3)+0.3(2)+0.5(8) 5.2

4 0.2(9)+0.3(3)+0.5(5) 5.2

5 0.2(8)+0.3(8)+0.5(2) 5.0

Descending order of scores:

5.2," " 5.2," " 5.2," " 5.1," " 5.0

To select exactly three candidates, the cutoff must exclude the candidate scoring 5.1.

Thus, the intended cutoff score is:

▭5.1

71. Consider the following three statements, namely S1, S2 and S3:
S1. Protecting the environment is an existential exigency for humans, given the impact of environmental degradation on climate change.

S2. Scientific consensus has not been achieved with regard to the extent of the contribution of human intervention to climate change.

S3. Environmental activism includes climate alarmism and other extremist points of view that often become the focus of climate change deniers.

Which of the following relationships based on the statements given above is/are correct?

1. S3 is a counterpoint to S1

2. S3 is unconnected to S1 and S2

3. S2 could be the reason for S3

Select the answer using the code given below.

(a) 2 and 3 only

(b) 1, 2 and 3

(d) 3 only

Answer: d

Explanation:

To determine the correct relationship between the statements, let's analyze them individually and in context:

S1 establishes the necessity of environmental protection by linking it to climate change. It is a premise focused on the urgency of action.

S2 introduces skepticism regarding the degree of human responsibility for climate change. It represents a point of scientific contention.

S3 addresses the sociological/political aspect of the climate debate, noting how extremist activism provides fodder for climate change deniers.

Analysis of Relationships:

Is S3 a counterpoint to S1?

No. S1 is about the objective need to protect the environment due to climate change. S3 is about the perception and tactics of environmental advocacy. S3 does not argue against the exigency of protecting the environment (S1); it merely criticizes the methodology of some activists. Thus, S3 is not a counterpoint.

Is S3 unconnected to S1 and S2?

No. The entire discourse on climate change connects S1, S2, and S3. S3 explains why public consensus is difficult to achieve; it discusses the "noise" (alarmism) that distracts from the core debate (S1) and empowers skeptics (S2). They are thematically linked within the climate change narrative.

Could S2 be the reason for S3?

Yes. S2 points out that there is no consensus on the extent of human intervention. This lack of certainty often creates a vacuum filled by "extremist points of view" (alarmism, as per S3) on one side, and "deniers" on the other. The lack of scientific certainty (S2) provides the fuel for the polarized debate and extremist positions mentioned in S3.

Conclusion:

Since only the third relationship is valid:

The correct answer is (d) 3 only.

72. Match List-I with List-II and select the answer using the code given below the Lists :
List-I (Relationship category)

A. Between cricket captain and team members

B. Between judge and lawyers in court

C. Between Vice Chancellor and Deputy Registrar

D. Between peers and coworkers

List-II (Communication type)

1. Informal and firm

2. Informal and open-ended

3. Formal and open-ended

4. Formal and firm

Code:

(a) A-1, B-3, C-4, D-2

(b) A-1, B-4, C-3, D-2

(d) A-2, B-3, C-4, D-1

Answer: b

Explanation:

To determine the correct match between the relationship categories and communication types, let's analyze the nature of the professional interactions:

A. Between cricket captain and team members: This relationship requires clear, actionable instructions balanced with the ability to build rapport and team morale. It is Informal and firm (1), as the captain leads from within the group but maintains authority.

B. Between judge and lawyers in court: This is a highly structured environment where protocols, rules of evidence, and procedural decorum are strictly enforced. It is Formal and firm (4).

C. Between Vice Chancellor and Deputy Registrar: This is a hierarchical administrative relationship within an institution, requiring adherence to established official processes while discussing academic or operational policy. It is Formal and open-ended (3).

D. Between peers and coworkers: This relationship is typically characterized by horizontal communication among equals, where ideas are exchanged freely without the constraints of rigid hierarchy. It is Informal and open-ended (2).

Matching Summary:

A — 1

B — 4

C — 3

D — 2

Checking the provided codes, (b) A-1, B-4, C-3, D-2 matches this analysis.

73. Match List-I with List-II and select the answer using the code given below the Lists :
List-I (Tool of communication)

A. Memorandum

B. Flyer

C. Bcc

D. Minutes

List-II (Purpose)

1. To record decisions

2. To inform confidentially

3. To intimate a directive

4. To disseminate non-targeted information

Code:

(a) A-1, B-4, C-2, D-3

(b) A-1, B-2, C-4, D-3

(d) A-3, B-2, C-4, D-1

Answer: c

Explanation:

A. Memorandum (3. To intimate a directive): A memo is a standard internal organizational tool used to communicate policies, procedures, or official directives to employees.

B. Flyer (4. To disseminate non-targeted information): A flyer is typically used for general announcements or broad advertising, intended to reach a wide, non-specific audience rather than targeting specific individuals.

C. Bcc (2. To inform confidentially): The "Blind Carbon Copy" feature in email is specifically designed to send information to recipients without revealing their identities to other recipients on the list, maintaining confidentiality.

D. Minutes (1. To record decisions): Meeting minutes are the official written record of a meeting, used specifically to document the proceedings, key discussions, and final decisions made.

74. Which among the following actions would constitute the most appropriate directive(s) in resolving interpersonal conflict in an office with culturally diverse personnel?

1. Direct personnel to practise activities that are the cultural markers of diverse groups

2. Allow conflicts to resolve naturally over time to set an appropriate precedent of leadership

3. Encourage personnel to seek each other's perspectives

Select the answer using the code given below.

(a) 1 and 3

(b) 2 only

(d) 2 and 3

Answer: c

Explanation:

1. Direct personnel to practise cultural markers of diverse groups

Forced participation in cultural practices can:

feel coercive

increase discomfort or resistance

Conflict resolution requires voluntary empathy, not enforced cultural adoption

Not an appropriate directive

2. Allow conflicts to resolve naturally over time

Passive approach

Interpersonal conflict in workplaces typically:

escalates if unmanaged

reduces productivity and morale

Leadership requires active intervention, not wait-and-watch

Not appropriate

3. Encourage personnel to seek each other's perspectives

Directly supports:

empathy

communication

mutual understanding

Core principle of conflict resolution in diverse workplaces

Appropriate and effective directive

Final evaluation

Only statement 3 is correct.

75. Match List-I with List-II and select the answer using the code given below the Lists :
List-I (Barrier to communication)

A. Semantic

B. Cognitive

C. Organisational

D. Affective

List-II (Example)

1. Lack of feedback

2. Misunderstanding the meaning of a word

3. Fear of social stigma

4. Information overload

Code :

(a) A-3, B-1, C-4, D-2

(b) A-3, B-4, C-1, D-2

(d) A-2, B-4, C-1, D-3

Answer: d

Explanation:

Let’s match each communication barrier with its correct example using standard communication theory.

A. Semantic barrier

Related to meaning of words, language, interpretation

Example: misunderstanding word meaning

A → 2 (Misunderstanding the meaning of a word)

B. Cognitive barrier

Related to thinking, perception, information processing limits

Includes issues like overload, inability to process information

Example: information overload

B → 4 (Information overload)

C. Organisational barrier

Structural/administrative issues in communication flow

Includes lack of feedback loops, hierarchy issues, delays

Example: lack of feedback

C → 1 (Lack of feedback)

D. Affective barrier

Related to emotions, fear, attitudes, psychological blocks

Example: fear of social stigma

D → 3 (Fear of social stigma)

Final Matching

A → 2

B → 4

C → 1

D → 3

76. You are required to design a 'questionnaire' to be filled on- location by visitors, based on the following objective while writing a report :

"To determine the feasibility of setting up a family- oriented vacation resort in the vicinity of a lake destination in the mountains"

Which of the following heads would you include in the questionnaire to make it most appropriate for your purpose?

1. Size of family

2. Budget

3. Number of earners in the family

4. Food allergies and dietary restrictions

Select the answer using the code given below.

(a) 1 and 3

(b) 1, 2 and 4

(d) 2 and 3

Answer: C

Explanation:

The objective of the questionnaire is:

To determine the feasibility of setting up a family-oriented vacation resort near a mountain lake destination.

For feasibility analysis, the questionnaire should collect information directly related to:

likely customer profile,

accommodation needs,

affordability.

1. Size of family

Relevant

Helps assess:

room capacity,

family facilities,

resort design requirements.

2. Budget

Relevant

Essential to determine:

affordability,

pricing strategy,

market feasibility.

3. Number of earners in the family

Not directly necessary

Budget already captures spending capacity more effectively.

4. Food allergies and dietary restrictions

Too operational/specific

Useful later for hospitality management, but not central to determining feasibility of establishing the resort.

Therefore, the most appropriate heads are:

▭(1" and " 2" only" )

77. With reference to 'circular letters', which of the following statements is/are correct?

1. Circular letters are usually addressed to a group of people.

2. Non-standard and customized content is typical of circular letters.

3. Circular letters are used to intimate appraisals and increments of employees within organisations.

4. Circular letters are less cost-effective than personalised and specific recipient-directed letters.

Select the answer using the code given below.

(a) 1 and 2

(b) 2 and 4

(d) 1 only

Answer: d

Explanation:

Let’s evaluate each statement based on standard business communication concepts.

1. Circular letters are usually addressed to a group of people

Yes, circular letters are meant for mass communication within an organisation or group

Same message sent to multiple recipients

Correct

2. Non-standard and customized content is typical of circular letters

Circular letters are:

standardised

uniform content

not customised

Incorrect

3. Used to intimate appraisals and increments

Appraisals/increments are:

confidential

individual-specific

communicated through personal letters or HR systems

Not circular letters

4. Circular letters are less cost-effective than personalised letters

Circular letters are actually:

highly cost-effective

designed to avoid repetition of individual letters

So statement is incorrect.

Final evaluation

Only statement 1 is correct.

78. Three partners A, B and C entered into a business. A invested one-third of the capital for one-third duration. B invested one-fourth of the capital for one-fourth duration. C invested the remaining capital for the whole duration. Out of a profit of ₹17,000, how much profit will C get?

(a) ₹12,000

(b) ₹10,000

(d) ₹10,750

Answer: a

Explanation:

Let total capital = 1and total time = 1.

Profit sharing ∝ (capital × time)

Step 1: Compute contributions

1/3×1/3=1/9

1/4×1/4=1/16

Remaining capital:

1-1/3-1/4=1-7/12=5/12

Time = full = 1

So C’s contribution:

5/12

Step 2: Total ratio

LCM of 9, 16, 12 = 144

Convert:

A = 1/9=16/144

B = 1/16=9/144

C = 5/12=60/144

Step 3: Total parts

16+9+60=85

Step 4: C’s share

C=60/85×17000

Simplify:

60/85=12/17

C=12/17×17000=12×1000=12000

79. There are two chemicals which do not react with each other. A container contains 10 litres of the chemical A. One litre of this chemical is removed from it and one litre of the chemical B is poured. Then one litre of the mixture is removed from the container and one litre of B is poured. If this process of replacing one litre of the mixture by one litre of B is performed once more, then what is the volume of B that is present in the container approximately (in percentage)?

(a) 25

(b) 27

(d) 31

Answer: b

Explanation:

We track only chemical B using standard replacement logic.

Container volume = 10 L

Step 1: Initial state

A = 10 L

B = 0 L

Step 2: First operation

Remove 1 L A → A = 9 L

Add 1 L B → B = 1 L

Now:

A = 9

B = 1

Step 3: Second operation

Mixture ratio:

A = 9/10

B = 1/10

Remove 1 L mixture:

A removed = 0.9

B removed = 0.1

Remaining:

A = 8.1

B = 0.9

Now add 1 L B:

A = 8.1

B = 1.9

Step 4: Third operation

Mixture ratio:

A = 8.1/10 = 0.81

B = 1.9/10 = 0.19

Remove 1 L mixture:

A removed = 0.81

B removed = 0.19

Remaining:

A = 7.29

B = 1.71

Add 1 L B:

A = 7.29

B = 2.71

Step 5: Final percentage of B

2.71/10×100=27.1%

80. A shopkeeper employs a delivery boy and gives him a motorcycle for home delivery. For every delivery, the boy is given ₹5. At the end of the day, he also gets ₹2 for every kilometre of the distance covered in the day. The boy wants to earn more than ₹500 a day, but does not want to travel more than 100 km. Which of the following numbers of deliveries would definitely meet his target?

(a) 80

(b) 85

(d) The question cannot be answered due to insufficient data

Answer: d

Explanation:

Let number of deliveries = n, and distance travelled ≤ 100 km.

Earnings structure

Per delivery = ₹5 → 5n

Per km = ₹2 → max 2×100=200

So maximum possible total earnings:

E_max=5n+200

We need:

5n+200>500

5n>300⇒n>60

So minimum required deliveries = 61

Now check options

All options (80, 85, 90) are > 60, so each can meet target provided distance condition is met (≤100 km).

But question asks:

“Which number of deliveries would definitely meet his target?”

We must check if even in worst case (max distance 100 km), target is satisfied

For each option:

(a) 80 deliveries

5(80)+200=400+200=600>500

(b) 85 deliveries

425+200=625>500

450+200=650>500

Key insight

Since distance is bounded (≤100 km), and already included as maximum, all given options satisfy condition.

But we must ensure “definitely meet target” → all are valid.

So question becomes ambiguous in comparison sense (no unique best threshold among given options).

Final conclusion

All options satisfy the condition, so the question is not uniquely answerable among given choices.