UKPSC Prelims 2025 CSAT (Paper II) with Answers & Explanations

Explanation

Constructive thinking in leadership involves actively listening to feedback, demonstrating emotional intelligence, and proactively seeking a collaborative resolution. By calling a meeting to discuss the subordinate's feedback regarding emotional well-being, the leader acknowledges the concern directly, promotes an open and transparent work culture, and fosters a supportive environment to find a mutually beneficial solution.

Explanation

In classical formal logic, the statement "All birds can fly" is a universal affirmative proposition, traditionally represented as A in the Square of Opposition.

The contradictory of a universal affirmative proposition of the form "All S are P" is the particular negative proposition "Some S are not P", represented as O. According to the rules of contradictory relations, two contradictory statements must have opposite truth values; they cannot both be true and cannot both be false.

Therefore, if the universal affirmative statement "All birds can fly" is false, its contradictory particular negative statement "Some birds can not fly" is logically guaranteed to be true. Since it must be true, it can certainly be true.

Explanation

The middle position between the 13ᵗʰ and 25ᵗʰ letters in any linear arrangement is the average of their positions:

Middle Position = (13 + 25)/(2) = 19

Therefore, the letter in the middle corresponds to the 19ᵗʰ letter in the reverse alphabetical order.

The position of any letter in the standard alphabetical order (p) and its position in the reverse alphabetical order (r) are related by the formula:

p + r = 27

Substituting r = 19 into the formula:

p = 27 - 19 = 8

The 8ᵗʰ letter in the standard English alphabet is H.

Explanation

The first letters of the terms in the series follow the consecutive sequence of English vowels: A, E, and I. Following this alphabetical pattern, the first letter of the next term in the series must be the next vowel, which is O. The word OLD starts with the letter O, completing the series.

Explanation

Emotional intelligence and self-regulation are critical competencies for an effective administrator. When faced with a highly stressful administrative scenario that causes frustration, taking a brief pause to breathe deeply helps in physiological calming, reducing the immediate surge of anger. Channeling that energy into other productive tasks allows the administrator to regain composure, maintain a professional demeanor, and approach the underlying issue of staff inexperience and inefficiency with a calm, rational, and constructive problem-solving mindset later on.

Explanation

In professional and administrative scenarios, the most constructive and professional reaction to strict monitoring or micromanagement is to maintain focus on one's core duties. Concentrating completely on your work and consistently delivering high-quality results demonstrates competence, diligence, and commitment. Over time, high performance and reliability shift the focus from strict oversight to proven results, establishing professional trust and reducing the supervisor's need for continuous, hands-on checks without creating unnecessary workplace confrontation or friction.

Explanation

Iconic memory is the sensory memory register specific to the visual domain. It is responsible for retaining a highly detailed, fleeting visual representation of a stimulus for a very brief duration, typically lasting for about 250 to 500 milliseconds. This form of memory acts like a temporary buffer that preserves visual input, such as the trailing light of a moving sparkler, allowing the brain a fraction of a second to process and recognize the visual information before it decays completely.

Explanation

The angle θ between the hour hand and the minute hand of a clock at H hours and M minutes is given by the formula:

θ = |30H - ¹¹⁄₂M|

For the time 40 minutes past 3, we have H = 3 and M = 40. Substituting these values:

θ = |30(3) - ¹¹⁄₂(40)|

θ = |90 - 220| = |-130| = 130°

Explanation

Let the order of reading the newspaper from first to last be represented by positions 1 to 5.

The person who reads first gives it to C, which means C is in the 2nd position.

The person who reads last takes it from A, which means A is in the 4th position.

Since E is neither first nor last, E must be in the 3rd position, as the 2nd and 4th positions are already occupied.

There are two persons between B and A. Since A is in the 4th position, B must be in the 1st position so that there are exactly two readers (in positions 2 and 3) between them.

The remaining position 5 is occupied by D.

The complete order of readers from first to last is B, C, E, A, D. Therefore, B, who is the first to read, gives the newspaper to C.

Explanation

To find the unit digit of the product 459 × 46 × 28⊗ × 484, we only need to multiply the unit digits of each of the individual numbers. Let the digit in place of ⊗ be x. The unit digits of the numbers in the product are 9, 6, x, and 4.

The product of these unit digits is: 9 × 6 × x × 4

Multiplying the known digits: 9 × 6 × 4 = 216

The unit digit of 216 is 6. Therefore, the unit digit of the entire product is determined by the unit digit of the product of 6 and x: 6 × x

We are given that the unit digit of the product is 2. This means: 6 × x ≡ 2 10

Solving for the single-digit integer x: If x = 2, 6 × 2 = 12, which has a unit digit of 2. If x = 7, 6 × 7 = 42, which has a unit digit of 2.

Among the given options, the digit 7 is present, which satisfies the condition.

Explanation

Using modular arithmetic, the remainder of the expression when divided by 8 can be determined by evaluating each term modulo 8.

First, express 9 modulo 8: 9 ≡ 1 8

Raising this relation to the power of 6: 9⁶ ≡ 1⁶ 8 ≡ 1 8

Adding 1 to this result: (9⁶ + 1) 8 ≡ (1 + 1) 8 ≡ 2 8

Explanation

The term non-divisible numbers in this context refers to prime numbers. Let the three prime numbers be p₁, p₂, and p₃ such that:

p₁ + p₂ + p₃ = 100

All prime numbers except 2 are odd. Since the sum of three odd numbers is always odd, and the sum of these three numbers is 100 (which is an even number), one of the three prime numbers must be even. The only even prime number is 2.

Let p₁ = 2. The sum of the remaining two prime numbers is:

p₂ + p₃ = 100 - 2 = 98

We are also given that one of these numbers exceeds another by 36:

p₃ - p₂ = 36

Adding these two equations together:

(p₂ + p₃) + (p₃ - p₂) = 98 + 36

2p₃ = 134

p₃ = 67

Now, solving for p₂:

p₂ = 98 - 67 = 31

Both 31 and 67 are prime numbers, satisfying all the given conditions. Thus, the three numbers are 2, 31, and 67.

Explanation

Let the number of cows be C and the number of hens be H.

Each cow has 1 head and 4 legs, while each hen has 1 head and 2 legs.

The total number of heads is: Heads = C + H

The total number of legs is: Legs = 4C + 2H

According to the given condition, the total number of legs is 14 more than twice the total number of heads: Legs = 2(Heads) + 14

Substituting the expressions for Legs and Heads into this relation: 4C + 2H = 2(C + H) + 14

Expanding the right side: 4C + 2H = 2C + 2H + 14

Subtracting 2H from both sides: 4C = 2C + 14

Subtracting 2C from both sides: 2C = 14 C = 7

Solving this equation gives the number of cows as 7.

Explanation

The total number of students in a class when a single person's rank is known from both ends is calculated using the formula:

Total = R_top + R_bottom - 1

Here, R_top is Rahul's rank from the top, which is 9, and R_bottom is his rank from the bottom, which is 38.

Substituting these values into the formula:

Total = 9 + 38 - 1 = 46

Subtracting 1 is necessary because Rahul's position is counted twice, once from the top and once from the bottom.

Explanation

Let the starting position of Babita be represented by the coordinates (0, 0) on a Cartesian plane, where the x-axis represents the West-East direction and the y-axis represents the South-North direction.

First, Babita walks 5 meters East, moving her position to (5, 0).

Next, turning left directs her North, and walking 6 meters changes her coordinates to (5, 6).

Then, turning right directs her East, and walking 9 meters updates her coordinates to (5 + 9, 6) = (14, 6).

Finally, turning right directs her South, and walking 6 meters brings her coordinates to (14, 6 - 6) = (14, 0).

The straight-line distance from her starting point (0, 0) to her final position (14, 0) is 14 meters.

Explanation

The general term of the series is: Tₙ = n - ⁿ⁄₅₁ = n (1 - ¹⁄₅₁) = ⁵⁰⁄₅₁ n

To find the sum of the first 51 terms, we calculate the sum of Tₙ from n = 1 to 51: S₅₁ = ∑ₙ₌₁⁵¹ Tₙ = ∑ₙ₌₁⁵¹ ⁵⁰⁄₅₁ n = ⁵⁰⁄₅₁ ∑ₙ₌₁⁵¹ n

Using the standard formula for the sum of the first N natural numbers, ∑ₙ₌₁ᴺ n = (N(N+1))/(2), we substitute N = 51: S₅₁ = ⁵⁰⁄₅₁ × (51 × 52)/(2)

Simplifying the terms: S₅₁ = 50 × 26 = 1300

Explanation

The given series can be written as: S = 2² + 4² + 6² + … + 50²

Taking 2² common from each term of the series: S = 2² (1² + 2² + 3² + … + 25²) S = 4 ₖ₌₁²⁵ k²

The formula for the sum of the squares of the first n natural numbers is: ₖ₌₁ⁿ k² = (n(n + 1)(2n + 1))/(6)

Substituting n = 25 into the formula: ₖ₌₁²⁵ k² = (25 × 26 × 51)/(6) ₖ₌₁²⁵ k² = 25 × 13 × 17 ₖ₌₁²⁵ k² = 5525

Now, multiplying by 4 to find the total sum: S = 4 × 5525 S = 22100

Explanation

To find the required number, we first determine the least common multiple (LCM) of the divisors 6, 9, 15, and 18.

The prime factorizations are: 6 = 2 × 3 9 = 3² 15 = 3 × 5 18 = 2 × 3²

Thus, LCM(6, 9, 15, 18) = 2 × 3² × 5 = 90.

Any number that leaves a remainder of 4 when divided by these numbers must be of the form: N = 90m + 4

We need to find the smallest positive integer m such that N is a multiple of 7. Representing 90 in terms of multiples of 7: 90m + 4 = (84 + 6)m + 4 = 84m + (6m + 4)

Since 84m is always divisible by 7, the term (6m + 4) must also be divisible by 7. Testing small positive integers for m: For m = 1: 6(1) + 4 = 10 (not divisible by 7) For m = 2: 6(2) + 4 = 16 (not divisible by 7) For m = 3: 6(3) + 4 = 22 (not divisible by 7) For m = 4: 6(4) + 4 = 28 (divisible by 7)

Substituting m = 4 back into the general form gives: N = 90 × 4 + 4 = 364

Explanation

A natural number is divisible by both 2 and 3 if and only if it is divisible by their Least Common Multiple (LCM). Since 2 and 3 are prime, their LCM is: LCM(2, 3) = 2 × 3 = 6

To find the number of natural numbers between 1 and 200 that are divisible by 6, we identify the first and last terms of the arithmetic progression within this range. The first multiple of 6 is 6, and the largest multiple of 6 less than 200 is 198.

Using the formula for the n-th term of an arithmetic progression: aₙ = a + (n - 1)d

Substituting the first term a = 6, the common difference d = 6, and the last term aₙ = 198: 198 = 6 + (n - 1)6 198 = 6n n = 33

Explanation

Let Mohal's birth year be Y_M and his mother's birth year be Y_Mₒ.

According to Statement-I, Mohal is 25 years younger than his mother. This gives the relation: Y_M = Y_Mₒ + 25 This single equation has two variables, making Statement-I alone insufficient.

According to Statement-II, Mohal's brother was born in 1964 and is 35 years younger than his mother. This allows us to calculate the mother's birth year: Y_Mₒ = 1964 - 35 = 1929 Since Statement-II contains no information about Mohal, it is alone insufficient.

By combining both Statement-I and Statement-II, the mother's birth year obtained from Statement-II can be substituted into the relation from Statement-I: Y_M = 1929 + 25 = 1954 This uniquely determines that Mohal was born in 1954, meaning both statements together are sufficient.

Explanation

An ogive is a cumulative frequency polygon. When the "less than" cumulative frequency curve and the "more than" cumulative frequency curve are plotted on the same coordinate axes, they intersect at a specific point.

The x-coordinate of this point of intersection represents the median of the given data distribution, which is the value that divides the dataset into two equal halves.

Among the various partition values, the median is mathematically identical to the second quartile (Q₂), the fiftieth percentile (P₅₀), and the fifth decile (D₅). Since deciles divide a distribution into ten equal parts, the fifth decile marks the point below which exactly 50% of the observations fall, aligning precisely with the median. Thus, the point of intersection of the two ogives represents the 5th decile.

Explanation

The range of a grouped dataset is calculated using the formula: Range = Uₘₐₓ - Lₘᵢₙ where Uₘₐₓ is the upper class limit of the highest class interval and Lₘᵢₙ is the lower class limit of the lowest class interval.

According to Statement-I, the class intervals are from 10-20 to 60-70. This provides the lower limit of the lowest class interval (Lₘᵢₙ = 10) and the upper limit of the highest class interval (Uₘₐₓ = 70). Substituting these values into the formula gives: Range = 70 - 10 = 60 Therefore, Statement-I alone is sufficient to determine the range.

Statement-II specifies the class interval with the highest frequency. Since the distribution of frequencies across class intervals does not affect the range of the dataset, Statement-II is not sufficient.

Explanation

The difference between each divisor and its corresponding remainder is constant: 5 - 3 = 2 7 - 5 = 2 13 - 11 = 2

This implies that when 2 is added to the required number N, the resulting number is perfectly divisible by 5, 7, and 13. Therefore, N + 2 must be a multiple of the Least Common Multiple (LCM) of 5, 7, and 13.

Since 5, 7, and 13 are prime numbers, their LCM is: LCM(5, 7, 13) = 5 × 7 × 13 = 455

The general form of the required number is: N = 455a - 2 (where a is a positive integer)

To find the smallest 4-digit number, we substitute successive integers for a: For a = 1: N = 455(1) - 2 = 453

For a = 2: N = 455(2) - 2 = 908

For a = 3: N = 455(3) - 2 = 1363

Explanation

To find the sum of the terms of the ratio of the LCM and HCF of the numbers 12, 18, and 30, we first determine their prime factorizations:

12 = 2² × 3¹ 18 = 2¹ × 3² 30 = 2¹ × 3¹ × 5¹

The Highest Common Factor (HCF) is obtained by multiplying the lowest powers of the common prime factors: HCF = 2¹ × 3¹ = 6

The Least Common Multiple (LCM) is obtained by multiplying the highest powers of all prime factors involved: LCM = 2² × 3² × 5¹ = 4 × 9 × 5 = 180

The ratio of the LCM to the HCF in its simplest form is: (LCM)/(HCF) = ¹⁸⁰⁄₆ = ³⁰⁄₁

This gives the ratio as 30 : 1.

The sum of the terms of this ratio is: 30 + 1 = 31

Explanation

The given series can be simplified by expressing each radical in its simplest form: T₁ = √2 T₂ = √8 = 2√2 T₃ = √(18) = 3√2 T₄ = √(32) = 4√2

This is an arithmetic progression where the nth term is: Tₙ = n√2

The sum of the first n terms, Sₙ, is given by factoring out √2: Sₙ = √2 (1 + 2 + 3 + … + n)

Using the formula for the sum of the first n natural numbers, ᵢ₌₁ⁿ i = ⁿ⁽ⁿ⁺¹⁾⁄₂: Sₙ = √2 × ⁿ⁽ⁿ⁺¹⁾⁄₂

For n = 16: S₁₆ = √2 × (16 × 17)/(2) = 136√2

Explanation

The average of a set of numbers is given by the formula:

Average = (Sum of the numbers)/(Total count of numbers)

Here, the total count of numbers is N = 5.

According to Statement-I, the sum of these five numbers is 225. Substituting these values into the formula:

Average = ²²⁵⁄₅ = 45

This provides a unique and definite value for the average, making Statement-I alone sufficient to answer the question.

According to Statement-II, the largest number is 60. Knowing only the value of one number does not provide the sum of all five numbers, which is necessary to determine the average. Therefore, Statement-II alone is not sufficient.

Explanation

The average of a set of values is given by the formula:

Average = (Sum of all values)/(Total number of values)

For the five months from January to May, the average is 40. Therefore, the sum of the values for these five months is:

Sum = 40 × 5 = 200

The sum of the values for January, February, March, and May is:

30 + 45 + 35 + 50 = 160

To find the missing value for April, subtract the sum of the four known months from the total sum of the five months:

April = 200 - 160 = 40

Explanation

The central angle corresponding to any category in a pie chart is determined by the formula:

θ = (Value of the category)/(Total value) × 360°

First, calculate the total number of graduates in the company:

Total graduates = 300 + 700 + 500 = 1500

Next, substitute the value for Science graduates and the total value into the formula:

θ = ³⁰⁰⁄₁₅₀₀ × 360° = ⅕ × 360° = 72°

Explanation

Statement-II states that the 17th day of the month is Saturday. Since the days of the week repeat in a fixed cycle of 7 days, the day of the week for any date in this month can be uniquely determined. The 14th of the month is exactly 3 days before the 17th. Subtracting 3 days from Saturday gives Wednesday. Thus, Statement-II alone is sufficient to find the day on the fourteenth. Statement-I is insufficient on its own because the last day of a month could be the 28th, 29th, 30th, or 31st, leading to different possible days for the 14th.

Explanation

To find the individual proportion of profit distributed among Ajit, Krishna, and Amrish, we need to determine the ratio of their individual shares of profit, which can be represented as A : K : Am.

From Statement-I, Ajit gets 2/5 of the total profit, which means Krishna and Amrish together receive the remaining 3/5 of the profit. However, this statement does not provide any information about how the remaining profit is divided between Krishna and Amrish.

From Statement-II, Krishna and Amrish together make 75% of the total investment, which implies Ajit makes the remaining 25% of the investment. Even if profit is distributed in proportion to investment, this statement only gives the combined share of Krishna and Amrish and does not disclose their individual investments or profit shares.

Even when combining both statements, we only have information regarding Ajit's individual share and the combined share of Krishna and Amrish. Since there is no data to separate the individual shares of Krishna and Amrish, the exact ratio A : K : Am cannot be determined. Therefore, both Statements-I and II together are not sufficient to answer the question.

Explanation

The percentage of any sector in a pie-chart is determined by the ratio of its central angle to the total angle of the circle, which is 360 degrees, multiplied by 100.

Percentage of the sector = (θ)/(360°) × 100%

For a sector with an angle θ = 75°:

Percentage = (75°)/(360°) × 100%

Percentage = ⁵⁄₂₄ × 100%

Percentage = ¹²⁵⁄₆% ≈ 20.83%

Explanation

The average yearly increase is calculated using the formula:

Average Yearly Increase = (Total Increase in Sales)/(Total Period of Time)

The total increase in sales is the difference between the final sales and the initial sales:

Total Increase in Sales = 200 - 100 = 100 units

The total period of time over which this increase occurs is 5 years. Substituting these values into the formula yields:

Average Yearly Increase = ¹⁰⁰⁄₅ = 20 units per year

This represents the constant amount by which the sales increase each year under a linear growth model.

Explanation

The relationship in this analogy is based on the primary optical phenomenon associated with each medium. When light waves strike a highly polished and opaque surface like a mirror, they bounce back, which is known as reflection. Similarly, when light waves travel through a transparent medium like water, they change speed and bend as they pass from air into the denser water medium. This bending of light waves is known as refraction. Just as reflection is the characteristic optical process of a mirror, refraction is the characteristic optical process associated with water.

Explanation

An island is a landform completely surrounded by a vast body of water, which is the ocean. In the exact same manner, an oasis is a fertile, water-bearing area of land completely surrounded by a vast expanse of dry land, which is the desert. Both analogies represent a distinct, isolated geographic feature characterized by the presence of one element (land or water) situated entirely within a massive surrounding environment of the opposite element.

Explanation

The numbers in each triad, represented as (a, b, c), follow a specific logical relationship where the difference between the first and second numbers, when its digits are reversed, yields the third number.

For the first given triad, (60, 12, 84): a - b = 60 - 12 = 48 Reversing the digits of 48 gives 84, which is the third number c.

For the second given triad, (115, 20, 59): a - b = 115 - 20 = 95 Reversing the digits of 95 gives 59, which is the third number c.

Similarly, for the analogous triad, (64, 8, 65): a - b = 64 - 8 = 56 Reversing the digits of 56 gives 65, which is the third number c.

Explanation

The logic of the coding scheme is that the code for each word is calculated by multiplying the sum of the alphabetical positions of its letters (where A = 1, B = 2, ..., Z = 26) by the total number of letters in the word.

For the word HIGH: Numerical positions of the letters are H = 8, I = 9, G = 7, H = 8. Sum of positions = 8 + 9 + 7 + 8 = 32. Number of letters in HIGH = 4. Code = 32 × 4 = 128.

For the word LOW: Numerical positions of the letters are L = 12, O = 15, W = 23. Sum of positions = 12 + 15 + 23 = 50. Number of letters in LOW = 3. Code = 50 × 3 = 150.

Applying the same logic to the word FAR: Numerical positions of the letters are F = 6, A = 1, R = 18. Sum of positions = 6 + 1 + 18 = 25. Number of letters in FAR = 3. Code = 25 × 3 = 75.

Explanation

To find the time taken by a train to cross a pole, we use the formula:

t = (L)/(v)

where t is the time, L is the length of the train, and v is the speed of the train.

First, convert the speed of the train from km / h to m / s:

v = 120 × ⁵⁄₁₈ = ¹⁰⁰⁄₃m / s

Substituting the length of the train L = 600m and the converted speed into the formula:

t = (600)/(100){3} = 600 × ³⁄₁₀₀ = 18seconds

Explanation

Roof is a singular noun representing a specific physical component of a structure. In contrast, the other words in the group represent plural nouns or broader, abstract concepts.

Explanation

The relationship in the first pair is that of synonyms. Vigilant and alert are synonymous terms that both mean watchful, awake, and attentive to danger. Similarly, viable and feasible are synonyms. Viable describes something that is capable of working successfully, is practicable, or is doable, which is the exact definition of feasible.

Explanation

The logical and chronological sequence of actions starts with using a Key to open a Lock. Unlocking the lock allows you to open the Door, which provides access to enter the Room. Once inside the room, the final action is to Switch on the lights or appliances. This logical progression of actions directly yields the sequence of Key (1), Lock (3), Door (2), Room (4), and Switch on (5).

Explanation

The coding pattern shifts each letter forward in the alphabetical order by a decreasing sequence of integers starting from +6 down to +1.

Applying this numerical shift pattern to the letters of the word ENOUGH:

E (5) + 6 = 11, which represents K N (14) + 5 = 19, which represents S O (15) + 4 = 19, which represents S U (21) + 3 = 24, which represents X G (7) + 2 = 9, which represents I H (8) + 1 = 9, which represents I

Combining these coded letters gives KSSXII.

Explanation

The letter-coding pattern involves shifting each letter of the word one position backward in the English alphabetical order.

The letter L is coded as K because K is the letter immediately preceding L. The letter I is coded as H because H is the letter immediately preceding I. The letter O is coded as N because N is the letter immediately preceding O. The letter N is coded as M because M is the letter immediately preceding N.

Applying this exact decrement of one position to each letter of the word TIGER: T shifts back to S I shifts back to H G shifts back to F E shifts back to D R shifts back to Q

Combining these letters yields SHFDQ.

Explanation

Apply the given substitutions throughout the expression: ÷ means +, − means ÷, × means −, and + means ×.

Numerator: (36 × 4) − 8 × 4 Replacing × with − and − with ÷: (36 − 4) ÷ 8 − 4 = 32 ÷ 8 − 4 = 4 − 4 = 0

Denominator: 4 + 8 × 2 + 16 ÷ 1 Replacing + with ×, × with −, and ÷ with +: 4 × 8 − 2 × 16 + 1 = 32 − 32 + 1 = 1

So the value of the expression = 0 / 1 = 0.

Explanation

The sequence follows a systematic pattern which can be identified by analyzing the differences between consecutive terms. Let the terms of the sequence be a₁, a₂, a₃, …, a₇.

The differences between successive terms are: a₂ - a₁ = 9 - 5 = 4 a₃ - a₂ = 16 - 9 = 7 a₄ - a₃ = 29 - 16 = 13 a₅ - a₄ = 54 - 29 = 25 a₆ - a₅ = 103 - 54 = 49

The sequence of these differences is 4, 7, 13, 25, 49. By looking at the second-tier differences (the differences of the differences), we get: 7 - 4 = 3 13 - 7 = 6 25 - 13 = 12 49 - 25 = 24

The second-tier differences double at each step, forming a geometric progression: 3, 6, 12, 24. Following this pattern, the next difference in this progression is 24 · 2 = 48.

To find the next first-tier difference: 49 + 48 = 97

Adding this difference to the sixth term of the sequence gives the seventh term: 103 + 97 = 200

Alternatively, the sequence can also be defined by the recurrence relation aₙ = 2 aₙ₋₁ - (n - 1) for n ≥ 2. Using this formula: a₇ = 2 a₆ - 6 = 2 · 103 - 6 = 206 - 6 = 200

Explanation

The standard relation between the first number x and the second number y in the pairs is defined by the formula y = 3x + 1. In the pair 8:27, this pattern is violated because 8 × 3 + 1 = 25, which is not equal to 27.

Explanation

Chalk is a tool used specifically for writing or drawing on a blackboard. Similarly, an ink-pen is a tool used for writing on paper. Both pairs represent the relationship of a writing instrument and its corresponding writing surface.

Explanation

The coding scheme represents each letter by its numerical position in the English alphabetical order.

For the word DOG: The alphabetical position of D is 4. The alphabetical position of O is 15. The alphabetical position of G is 7. Combining these values yields 4157.

For the word CAT: The alphabetical position of C is 3. The alphabetical position of A is 1. The alphabetical position of T is 20. Combining these values yields 3120.

Explanation

By rearranging the jumbled letters of each option, we obtain the names of various clothing garments: THRSI rearranges to SHIRT, AOTC to COAT, EOUBSL to BLOUSE, and KTRIS to SKIRT. Among these, a skirt is a garment worn on the lower part of the body, whereas a shirt, coat, and blouse are all garments worn on the upper part of the body. This distinguishes KTRIS from the other three options.

Explanation

From the statement "All windows are carpets", the set of windows is entirely contained within the set of carpets. This does not guarantee that all carpets are windows, meaning conclusion (II) does not follow.

From the statement "Some carpets are rats", there is only a partial overlap between the set of carpets and the set of rats. This does not mean that all rats are carpets, so conclusion (I) does not follow.

Furthermore, because there is no specified relationship linking the set of windows directly to the set of rats through the subset of carpets, no definite conclusion can be drawn between windows and rats. Thus, neither conclusion (III) nor conclusion (IV) follows.

Explanation

According to the rules of immediate inference in syllogisms, a particular affirmative proposition of the form Some A are B can be converted to its logically equivalent converse form Some B are A. Applying this rule to the first statement, Some teachers are advocates converts directly to Some advocates are teachers. This directly validates conclusion (III), which means it logically follows from the premises.

Explanation

Substituting the given operator symbols into the expression 6a7b8c8d2a50 gives:

6 + 7 - 8 × 8 ÷ 2 + 50

According to the BODMAS rule, the operations must be performed in the order of Division, Multiplication, Addition, and Subtraction.

First, division is carried out: 8 ÷ 2 = 4

This simplifies the expression to: 6 + 7 - 8 × 4 + 50

Next, multiplication is performed: 8 × 4 = 32

This simplifies the expression to: 6 + 7 - 32 + 50

Finally, addition and subtraction are executed from left to right: 6 + 7 - 32 + 50 = 13 - 32 + 50 = -19 + 50 = 31

Explanation

Neither conclusion logically follows from the given statement.

Conclusion (I) is invalid because designating a specific day as World Yoga Day is meant for global awareness and celebration. It does not restrict the practice of Yoga to that single day, making the use of the word only logically incorrect.

Conclusion (II) is also invalid because promoting a tradition globally means it is being recognized and practiced worldwide. It does not mean that people must travel to India to practice it, nor does the statement provide any data or direct link regarding an increase in tourist inflow to India for this purpose.

Explanation

The number 110001 is a six-digit number. To check its divisibility by 111, we can express it as:

110001 = 111000 - 999

Since 111000 is a multiple of 111 (111 × 1000) and 999 is also a multiple of 111 (111 × 9), their difference must be divisible by 111. This can be written as:

110001 = 111 × 1000 - 111 × 9 = 111 × (1000 - 9) = 111 × 991

This confirms that 110001 is divisible by 111.

Explanation

E is the daughter of B, and D is the brother of E, which means D is the son of B. Since A is the sister of B, A is the sister of D's mother. The sister of one's mother is their maternal aunt, commonly known as Mausi. Therefore, A is the maternal aunt of D.

Explanation

The statement that all flowers are trees indicates that the set of flowers is entirely contained within the set of trees. The statement that no fruits are trees means that the set of fruits has no overlap with the set of trees. Since the set of flowers is fully inside the set of trees, and fruits have no intersection with trees, fruits can have no overlap with flowers. This validates conclusion (I) that no fruits are flowers. Furthermore, since all flowers are trees, it inherently follows that at least some portion of the category of trees is made up of flowers. This validates conclusion (II) that some trees are flowers. Therefore, both conclusions logically follow.

Explanation

Reducing the academic curriculum is a deliberate administrative action typically intended to alleviate the learning pressure on students. Since mathematics is often perceived as a rigorous and demanding subject, cutting down the syllabus directly aims to make the workload more manageable, thereby directly addressing and minimizing student stress and burden. Consequently, assumption (II) is a logical and direct expectation behind the institute's decision.

Conversely, a reduction in the syllabus does not guarantee that students will score higher marks. Academic performance depends on multiple other factors such as the difficulty level of the examination, evaluation standards, and individual student effort. Thus, the expectation of higher marks is not an implicit assumption behind the decision.

Explanation

Orientation programs directly address the lack of awareness among teachers by training and educating them on modern pedagogical techniques and tools. This is a constructive, feasible, and direct solution to bridge the gap between traditional and modern teaching methods.

Explanation

Let the present ages of A, B, and C be represented by A, B, and C respectively.

According to the third statement, after four years, A will be 31 years old: A + 4 = 31 A = 27

According to the first statement, A is three times as old as B: A = 3B 27 = 3B B = 9

According to the second statement, four years ago, C was twice as old as A: C - 4 = 2(A - 4) C - 4 = 2(27 - 4) C - 4 = 2(23) C - 4 = 46 C = 50

To find the sum of the present ages of B and C: B + C = 9 + 50 = 59

Explanation

By stating that concerted efforts will be made for the upliftment of poor farmers alongside announcing an annual pension for them, the government directly indicates that it acknowledges the vulnerable state of poor farmers and recognizes that their condition requires active, immediate intervention. Therefore, conclusion (I) logically flows from the statement. Conversely, the statement only addresses the specific measures taken for poor farmers and does not provide any information regarding policies, benefits, or announcements for other sections of society, meaning conclusion (II) cannot be inferred.

Explanation

Graphical representation of data translates complex numerical and qualitative datasets into visual formats, such as charts, graphs, and plots. Human visual perception processes images and spatial patterns much faster than text or numbers. Consequently, visual diagrams enable immediate recognition of trends, patterns, correlations, and outliers. This rapid cognitive processing allows decision-makers to grasp the overall scenario and draw key insights almost instantaneously, facilitating timely and informed actions in time-critical situations.

Explanation

The decision-making process systematically begins with the identification of a problem, which is defined as a discrepancy between an existing state of affairs and a desired state. Recognizing this gap is the necessary initial step because it establishes the purpose and direction for the entire decision-making cycle. Without identifying a specific problem or opportunity to address, there is no trigger to define criteria, develop alternatives, or make a choice.

Explanation

When faced with multiple options, determining the most effective one requires an objective and systematic evaluation of the alternatives. Logical reasoning provides a structured framework to analyze facts, assess risks, evaluate feasibility, and project outcomes based on empirical evidence and rational analysis. By prioritizing logical reasoning, an individual can make an informed and optimal decision that reliably achieves the desired goal.

Explanation

Argument (I) is weak because it presents an extreme view. Making school education free is not the sole or exclusive method to enhance literacy rates. Other parallel measures, such as developing high-quality infrastructure, hiring trained educators, and running adult education drives, also play critical roles.

Argument (II) is strong as it highlights a highly realistic and practical economic challenge. Offering completely free school education to the entire population of India would demand immense financial resources, which would directly increase the fiscal pressure on the national and state exchequers.

Explanation

Both arguments are strong because they present realistic, practical, and highly valid advantages of their respective family structures. Argument (I) is strong because living in a joint family provides a robust emotional and financial safety net, while the sharing of daily chores and responsibilities naturally eases the workload for individual members. Argument (II) is also strong because nuclear families have fewer constraints and less external interference, which directly fosters personal privacy, independence, and greater individual freedom in decision-making. Since both points are logically sound and address significant social realities, both arguments hold strong merit.

Explanation

In the event of a severe railway accident where multiple coaches have derailed and blocked both tracks, the railway authorities must prioritize both the clearing of the accident site and the management of ongoing rail traffic. Action I is a necessary restorative measure because sending personnel and machinery immediately to clear the tracks is the direct way to restore normal operations and ensure the safety and rescue of any affected passengers. Action II is also an essential operational measure because diverting oncoming trains to alternative routes prevents further gridlock on the blocked line, ensures passenger safety, and maintains the continuity of the rail network while the recovery work is ongoing. Thus, both actions are logical, constructive, and immediate solutions to the problem.

Explanation

Emotional Intelligence is defined as the capability to recognize, understand, manage, and reason with emotions, both in oneself and in others. Popularized by psychologist Daniel Goleman, it comprises core components such as self-awareness, self-regulation, empathy, motivation, and social skills. By developing these attributes, individuals are better equipped to navigate social complexities, resolve conflicts, build empathy, and maintain healthy, collaborative interpersonal connections.

Explanation

Self-efficacy is a psychological concept introduced by Albert Bandura as part of his social cognitive theory. It refers to an individual's belief in their own capability to execute behaviors necessary to produce specific performance attainments and succeed in various tasks. Rather than being a core dimension of emotional intelligence frameworks, self-efficacy is a distinct cognitive self-belief system centered on personal capability, agency, and confidence in managing specific situations.

Explanation

Critical thinking involves the intellectually disciplined process of actively and skillfully analyzing, evaluating, and synthesizing information gathered from observation, experience, or reflection. Open-mindedness is a fundamental characteristic of this process because it enables individuals to remain receptive to new ideas, alternative perspectives, and different viewpoints. An open-minded thinker is willing to examine all evidence objectively, recognize personal cognitive biases, and revise their beliefs or conclusions when presented with sound logical arguments and valid data. This flexibility and willingness to explore diverse possibilities are essential for fair-minded and objective inquiry.

Explanation

Accepting constructive criticism and being made aware of one's shortcomings or mistakes is a vital trait for professional growth, ethical conduct, and emotional intelligence. A batchmate who points out these lapses acts as a well-wisher, offering an honest perspective that allows for self-reflection, correction of errors, and personal improvement. Showing gratitude towards such feedback fosters accountability and integrity in public service and professional relationships.

Explanation

India is a democratic republic where supreme power is vested in the people. In a representative democracy, citizens exercise this power by electing representatives through periodic, free, and fair elections based on universal adult suffrage. These elected representatives form the government and make laws on behalf of the public. Therefore, the assertion that the people of India elect their own representatives is true, and it is directly explained by the fact that India is a democracy.

Explanation

The temperature of a place depends significantly on its altitude. Within the troposphere, temperature decreases with an increase in altitude, a phenomenon known as the normal lapse rate, which is approximately 6.5 degrees Celsius for every 1000 meters of ascent. Shimla is located at an elevation of about 2206 meters above sea level in the Himalayas, whereas Delhi is situated in the plains at an altitude of only about 216 meters. Because of this substantial difference in elevation, Shimla experiences a much cooler climate than Delhi. Thus, both statements are factually correct, and the higher altitude of Shimla is the direct reason for its colder temperature.

Explanation

The Assertion is correct because the Indian Constitution ensures the independence of the judiciary from the executive through various provisions, such as security of tenure for judges, salaries being charged on the Consolidated Fund of India, and Article 50 which directs the State to separate the judiciary from the executive. The Reason is incorrect because the judiciary is an independent organ of the state whose role is to interpret the Constitution, protect fundamental rights, and perform judicial review of legislative and executive actions, rather than assisting the government in implementing its policies.

Explanation

दिए गए अपठित गद्यांश का मुख्य केंद्रबिंदु इच्छाओं को दबाने के बजाय उन्हें सही दिशा देना अर्थात उनका उदात्तीकरण करना है। गद्यांश के अनुसार, इच्छाओं का उदात्तीकरण ही वह प्रक्रिया है जिसके द्वारा व्यक्ति व्यक्तिगत स्वार्थ और संकीर्णताओं से ऊपर उठकर परोपकार, जनसेवा तथा उच्च आदर्शों के प्रति समर्पित होता है। लेखक ने स्पष्ट किया है कि मनुष्य को अपनी कामनाओं का दमन करने की आवश्यकता नहीं है, बल्कि उन्हें एक जन-कल्याणकारी मार्ग प्रदान करना है, जिसे गद्यांश में इच्छाओं का उदात्तीकरण कहा गया है।

Explanation

दिए गए गद्यांश के अनुसार, इच्छा, असन्तोष और लोभ इत्यादि के कारण समाज में शोषण, कुटिलता, अत्याचार, भोगवृत्ति एवं अशांति को प्रोत्साहन मिलता है। गद्यांश की दूसरी पंक्ति में यह स्पष्ट रूप से वर्णित है कि वास्तव में इन विकारों के कारण ही समाज में शोषण की प्रवृत्ति बढ़ती है।

Explanation

गद्यांश के अनुसार, साधक पदोन्नति, धन अथवा सत्ता की प्राप्ति व्यक्तिगत इच्छा की तृप्ति के लिए नहीं करता है। गद्यांश में स्पष्ट रूप से उल्लेखित है कि यदि साधक पदोन्नति, धन अथवा सत्ता प्राप्त करता है तो वह व्यक्तिगत इच्छा की तृप्ति के लिए नहीं, प्रत्युत् परोपकार के लिए, मानवमात्र की सेवा के लिए और ईश्वर की प्रसन्नता के लिए करता है। इस प्रकार, साधक द्वारा धन और सत्ता प्राप्त करने का उद्देश्य मानवमात्र की सेवा करना है।

Explanation

प्रस्थान शब्द में 'प्र' उपसर्ग का प्रयोग हुआ है। यहाँ मूल शब्द 'स्थान' है, जिसके पूर्व में 'प्र' उपसर्ग जोड़ने से 'प्रस्थान' शब्द का निर्माण होता है। व्याकरण के नियमों के अनुसार 'प्र' उपसर्ग का अर्थ आगे, अधिक, ऊपर या बाहर होता है, और जब इसे 'स्थान' के साथ मिलाया जाता है, तो इसका अर्थ किसी स्थान से रवाना होना या आगे बढ़ना होता है। इस संयोग में मूल शब्द और उपसर्ग स्पष्ट रूप से पृथक दिखाई देते हैं।

Explanation

'अत्युत्तम' शब्द का संधि-विच्छेद 'अति + उत्तम' होता है।

यहाँ संधि के नियमानुसार प्रथम पद के अंत में 'इ' और द्वितीय पद के आरंभ में भिन्न स्वर 'उ' का मेल हो रहा है। यण स्वर-संधि का नियम है कि यदि ह्रस्व या दीर्घ 'इ/ई', 'उ/ऊ' या 'ऋ' के बाद कोई असमान स्वर आता है, तो 'इ/ई' का 'य्', 'उ/ऊ' का 'व्' और 'ऋ' का 'र्' हो जाता है।

अति (इ) + उत्तम (उ) के योग से 'इ' का परिवर्तन आधा व्यंजन 'त्' के साथ मिलकर 'यु' में हो जाता है, जिससे 'अत्युत्तम' शब्द का निर्माण होता है।

Explanation

लोकोक्ति भरी गगरिया चुपके जाय का अर्थ ज्ञानी आदमी गम्भीर होता है होता है। यह प्रसिद्ध लोकोक्ति अधजल गगरी छलकत जाए, भरी गगरिया चुपके जाय का उत्तरार्ध है। जिस प्रकार पानी से आधा भरा हुआ घड़ा चलते समय हिलने-डुलने से बहुत अधिक आवाज करता है, उसी प्रकार कम ज्ञान या योग्यता रखने वाला व्यक्ति अत्यधिक दिखावा और अहंकार करता है। इसके विपरीत, जो घड़ा पानी से पूरी तरह भरा होता है, वह बिना किसी शोर-शराबे के शांत भाव से जाता है। यह इस बात का प्रतीक है कि जो व्यक्ति वास्तव में ज्ञानी, विद्वान और गुणवान होते हैं, वे सदैव गंभीर, शांत और शालीन बने रहते हैं तथा अपने ज्ञान का व्यर्थ प्रदर्शन नहीं करते हैं।

Explanation

लघु का सही विलोम शब्द गुरु या दीर्घ होता है, जबकि स्थूल का सही विलोम शब्द सूक्ष्म होता है। चूँकि विलोम शब्द सदैव सजातीय और समान कोटि के होने चाहिए, इसलिए लघु और स्थूल आपस में एक-दूसरे के विपरीतार्थक शब्द नहीं हैं और यह एक त्रुटिपूर्ण विलोम शब्द-युग्म है।

Explanation

'सेनापति' शब्द का समास विग्रह 'सेना का पति' होता है, जिसका अर्थ सेना का स्वामी या सेनाध्यक्ष है। इस पद में दोनों शब्दों के बीच सम्बन्ध कारक के विभक्ति चिह्न 'का' का लोप हुआ है। जिस तत्पुरुष समास में सम्बन्ध कारक के चिह्न (का, की, के) का लोप होता है, उसे सम्बन्ध तत्पुरुष समास कहते हैं।

Explanation

देशज शब्द उन शब्दों को कहा जाता है जिनकी उत्पत्ति के मूल स्रोत का कोई स्पष्ट प्रमाण नहीं मिलता है और जो स्थानीय बोलियों, क्षेत्रीय भाषाओं या जनसाधारण की आवश्यकता के अनुसार स्वतः विकसित होकर हिंदी भाषा में घुल-मिल गए हैं। हिंदी व्याकरण में खिचड़ी इसी श्रेणी का एक अत्यंत प्रसिद्ध शब्द है क्योंकि इसकी उत्पत्ति का स्रोत संस्कृत या किसी विदेशी भाषा में नहीं मिलता, बल्कि यह विशुद्ध रूप से भारतीय जनमानस की बोलचाल से उपजा एक लोक शब्द है।

Explanation

पठनीय शब्द में मूल शब्द और प्रत्यय का विभाजन इस प्रकार है: पठ् (मूल धातु) + अनीय (प्रत्यय) = पठनीय

अनीय संस्कृत का एक प्रमुख कृत् प्रत्यय (कृदंत) है जो क्रिया या धातु के अंत में जुड़कर नए विशेषण शब्दों का निर्माण करता है। इसका प्रयोग योग्य या चाहिए के अर्थ में होता है। पठ् धातु के साथ अनीय प्रत्यय के जुड़ने से पठनीय शब्द बनता है, जिसका अर्थ पढ़ने योग्य होता है।

Explanation

धन शब्द का पर्यायवाची शब्द द्रव्य है। द्रव्य के अन्य पर्यायवाची शब्दों में वित्त, सम्पत्ति, सम्पदा, दौलत, विभूति और लक्ष्मी शामिल हैं, जो सभी धन और आर्थिक समृद्धि को दर्शाते हैं।

Explanation

'उज्ज्वल' शब्द का अर्थ प्रकाशमान, चमकीला, या स्वच्छ होता है। इसका सटीक विपरीतार्थक (विलोम) शब्द 'धूमिल' है, जिसका अर्थ धुंधला, मंद, या मलीन होता है।

Explanation

दिए गए गद्यांश के अनुसार, सत्पुरुष उज्ज्वल भविष्य के लिए योजना बनाकर प्रयत्न करते हुए महोच्च आदर्शों को अपनी आँखों से ओझल नहीं होने देते हैं। गद्यांश की पंक्ति सत्युरुष उज्ज्वल भविष्य के लिए योजना बनाकर प्रयत्न करते हुए महोच्च आदशों को आँखों से ओझल नहीं होने देते से यह स्पष्ट रूप से प्रमाणित होता है।

Explanation

The passage directly establishes a comparison in its opening sentence by stating that there is a certain analogy between action control and political liberty. It elaborates on this comparison by explaining how having control over our actions gives us independence within nature, much like a free government or state grants its citizens political liberty and a share in determining their own lives.

Explanation

The passage draws a direct analogy between action control and political liberty, comparing the way humans live within the universe to how citizens live within a free state. It explains that just as a free government allows its citizens a measure of political liberty and a share in determining their own path, nature similarly does not entirely dictate human actions but instead leaves a part of our lives for us to direct, thereby granting humans a measure of liberty.

Explanation

The passage states that having some degree of control over our lives provides humans with a certain independence within nature. It explicitly highlights that this is an independence that sticks, stones, and even the lower animals do not possess. This indicates that, unlike animals, humans possess a level of agency and control to direct their own lives and determine what happens to them.

Explanation

The word loquacious is derived from the Latin root loqui, which means to speak. It is used to describe a person who is exceptionally talkative, chatty, or wordy, and who has a tendency to speak continuously or at great length.

Explanation

A fallacy is a mistaken belief, misconception, or erroneous reasoning that leads to an unsound argument. It refers to an idea or view that is logically invalid or factually incorrect, making a false opinion its direct synonym.

Explanation

The word relinquish means to voluntarily give up, surrender, let go, or yield a possession, right, or claim. Its direct antonym is possess, which means to have, own, keep, or retain control and custody over something. While relinquishing involves parting with or releasing ownership, possessing represents the act of holding and maintaining ownership.

Explanation

The word dearth refers to a lack, shortage, or inadequate supply of something, which makes scarcity its closest synonym. It historically evolved from Middle English to denote dearness or high cost, typically arising when goods and resources are in extremely short supply. Today, it is commonly used to describe an insufficient quantity of resources, food, or abstract qualities like information or talent.