HPAS Prelims 2020 CSAT (Paper II) with Answers & Explanations

Explanation

The passage explicitly states that a right by itself is incomplete and cannot last long if the obligations which accompany that right are absent. This directly implies that rights cannot endure without their corresponding obligations.

Explanation

According to the passage, thinking too much in terms of rights and privileges and too little in terms of obligations weakens a nation and causes people to become merely decriers who grumble without contributing anything positive. Since a decrier is someone who publicly denounces or expresses strong disapproval of something, this corresponds directly to becoming critics.

Explanation

The passage explicitly states that even if the government dislikes the liberties taken by the press and considers them dangerous, it is wrong to obstruct the freedom of the press. Since impeding means to obstruct or hinder, this directly aligns with the writer's assertion that restricting the press is incorrect and counterproductive because suppressing its public manifestation only causes the underlying thoughts to spread further.

Explanation

The passage explicitly states in its final sentence that imposing restrictions or constraints does not change anything but merely suppresses the public manifestation of certain issues. Consequently, this suppression causes the underlying ideas and thoughts to spread even further.

Explanation

The phrase low levels of is grammatically correct and contextually appropriate. In India, despite rapid smartphone penetration, digital literacy, particularly in rural and semi-urban areas, remains significantly low. This digital divide and lack of fundamental digital skills among a large section of the population have been major areas of concern for the Government of India, leading to the launch of targeted initiatives such as the Pradhan Mantri Gramin Digital Saksharta Abhiyaan to bridge this gap.

Explanation

The adverb scarcely is grammatically paired with the conjunction when to connect two closely succeeding events. When a sentence begins with a negative or restrictive word like scarcely, hardly, or barely, subject-verb inversion occurs (did Mohan step), and the subsequent clause is introduced by when to indicate that the second action happened immediately after the first.

Explanation

A mendicant is a member of a religious order, or more generally any individual, who relies solely on charitable donations and alms for survival. The word originates from the Latin mendicans, meaning begging, which is derived from menda, meaning physical defect or fault. In both Christian and Eastern religious traditions, mendicant practices are associated with asceticism, spiritual devotion, and the renunciation of material wealth.

Explanation

The adjective acquainted is followed by the preposition with when expressing familiarity or a personal relationship with someone or something. In this sentence, acquainted with me correctly conveys that Jaya is not very familiar with or does not know me well.

Explanation

The verb gesticulate means to make dramatic or expressive gestures, particularly with the hands and arms, while speaking to emphasize one's words or feelings. It comes from the Latin word gesticulatus, which refers to making expressive movements.

Explanation

The pronoun whom is the objective form of who, used when the pronoun acts as the object of a verb or preposition. In the noun clause whom I can trust, the pronoun serves as the direct object of the transitive verb trust, while I is the subject of the clause. This grammatical relationship corresponds to the use of the objective pronoun him in the statement I can trust him.

Explanation

Latin comparative adjectives ending in -ior, such as superior, inferior, senior, junior, prior, anterior, and posterior, are always followed by the preposition to rather than than. Therefore, both blanks in the sentence must be filled with to.

Explanation

The preposition besides means in addition to or as well as. Using besides in this sentence correctly conveys that, in addition to his uncle, the person has six other male relations.

Explanation

In this sentence, the pronoun I is the main subject, and John serves as an appositive noun phrase that provides additional information about the subject. In English grammar, the verb must agree in person and number with the primary subject of the sentence rather than the appositive. Since the subject I is first-person singular, it requires the corresponding first-person singular present form of the verb to be, which is am. This maintains proper subject-verb agreement.

Explanation

The noun aircrew is a collective noun that is treated as a singular unit. In the present perfect tense, which is indicated by the adverb yet, the singular collective noun aircrew requires the singular auxiliary verb has followed by the past participle verb come.

Explanation

The word superior is an adjective of Latin origin. Adjectives ending in -ior, such as superior, inferior, senior, junior, and prior, possess an inherent comparative meaning. Consequently, they cannot be modified by more or most, and they are always followed by the preposition to instead of than to establish a comparison. Therefore, superior to is the grammatically correct formulation to compare the two nouns.

Explanation

The adverbial phrase no sooner is grammatically paired with the conjunction than to form a correlative conjunction. This structure is used to indicate that one event happens immediately after another. When a sentence begins with no sooner, it is followed by an auxiliary verb and the subject (inversion), and the second clause is introduced by than.

Explanation

Let the supply of the product be S, the demand be D, and the capacity of the industry be C.

According to the definitions given: Supply as a percentage of demand, S/D = x% = x/100 Demand as a percentage of capacity, D/C = y% = y/100

We can express supply in terms of capacity as: S = D × (x / 100) S = (C × (y / 100)) × (x / 100) S = C × (xy / 10000)

Given that the product supply for the year 2005 is 6000 kg, and the capacity is 12500 kg: 6000 = 12500 × (xy / 10000) 6000 = 1.25 × xy xy = 6000 / 1.25 = 4800

Since all values in the chart are multiples of 5, we can choose x = 60% and y = 80% (or x = 80% and y = 60%), both of which are multiples of 5 and satisfy xy = 4800.

This gives: Demand = S / 60% = 6000 / 0.60 = 10000 kg Capacity = D / 80% = 10000 / 0.80 = 12500 kg

This fits the conditions perfectly.

Explanation

From the bar chart the two percentages for each year are Supply (as % of demand) and Demand (as % of capacity): 2003 = 65%, 80%; 2004 = 70%, 90%; 2005 = 60%, 80%; 2006 = 90%, 65%. With the capacity fixed at 10,000 kg, the actual supply each year = (Supply% / 100) x (Demand% / 100) x capacity. This gives 2003: 0.65 x 0.80 x 10000 = 5200 kg; 2004: 0.70 x 0.90 x 10000 = 6300 kg; 2005: 0.60 x 0.80 x 10000 = 4800 kg; 2006: 0.90 x 0.65 x 10000 = 5850 kg. Average supply = (5200 + 6300 + 4800 + 5850) / 4 = 22150 / 4 = 5537.5 kg. As the question asks for the approximate average, the nearest given value is 5375 kg, so the answer is B.

Explanation

Let the supply of the product be S, the demand be D, and the industry capacity be C.

The bar chart presents two percentages: The supply as a percentage of demand, which can be represented as X: X = (S / D) × 100 From this, the demand D can be expressed as: D = (S / X) × 100

The demand as a percentage of capacity, which can be represented as Y: Y = (D / C) × 100 From this, the capacity C can be expressed as: C = (D / Y) × 100

Substituting the expression for D into the equation for C: C = ((S / X) × 100 × 100) / Y C = (10000 × S) / (X × Y)

Since the product supply S remains unchanged (constant) for the given period, the relationship simplifies to: C ∝ 1 / (X × Y)

The values of X and Y represent the percentages shown in the bar chart for each year. Because the values of X and Y vary from year to year over the given period, their product (X × Y) also varies. Since the industry capacity C is inversely proportional to this product, it fluctuates over the given period.

Explanation

Here the demand is taken as 10,000 kg for every year. Since demand is a percentage of capacity, capacity = demand / (Demand% / 100); and since supply is a percentage of demand, supply = (Supply% / 100) x 10000. Using the chart values (Supply%, Demand%) = 2003 (65, 80), 2004 (70, 90), 2005 (60, 80), 2006 (90, 65): difference (capacity - supply) = 2003: 12500 - 6500 = 6000; 2004: 11111 - 7000 = 4111; 2005: 12500 - 6000 = 6500; 2006: 15385 - 9000 = 6385. The year-on-year increase in this difference is 2004: 4111 - 6000 = -1889; 2005: 6500 - 4111 = +2389; 2006: 6385 - 6500 = -115. The highest increase over the previous year occurs in 2005, so the answer is C.

Explanation

Let S be the supply of the product, D be the demand, and C be the capacity of the industry.

The two bar chart percentages are defined as: x = Supply as a percentage of demand = (S / D) × 100 y = Demand as a percentage of capacity = (D / C) × 100

From the first percentage, we can express demand as: D = 100 × S / x

From the second percentage, we can express capacity as: C = 100 × D / y

Substituting the expression for D into the equation for C: C = 100 × (100 × S / x) / y C = 10000 × S / (x × y)

Since the supply S is constant across all the given years, the capacity C is inversely proportional to the product of the two percentages: C ∝ 1 / (x × y)

To find the year with the highest capacity C, we must identify the year that has the lowest product of the two percentages, x × y. In the year 2005, the product of supply as a percentage of demand and demand as a percentage of capacity reaches its minimum value.

Explanation

The profit figures for each year are calculated by subtracting the cost from the sales revenue.

For the year 2007: Estimated Profit = 1281 - 986 = 295 Actual Profit = 1326 - 988 = 338 Here, the actual profit of 338 is greater than the estimated profit of 295.

For the year 2008: Estimated Profit = 1452 - 1051 = 401 Actual Profit = 1286 - 1076 = 210 Here, the actual profit of 210 is less than the estimated profit of 401.

For the year 2009: Estimated Profit = 1228 - 1024 = 204 Actual Profit = 1452 - 1068 = 384 Here, the actual profit of 384 is greater than the estimated profit of 204.

Thus, there are exactly 2 years (2007 and 2009) in which the actual profit is more than the estimated profit.

Explanation

The measure of forecasting is given by the ratio of Estimated Sales to Actual Sales. Let this ratio be R = Estimated Sales / Actual Sales.

Computing the ratio R for each year:

For 2007: R = 1281 / 1326 ≈ 0.966

For 2008: R = 1452 / 1286 ≈ 1.129

For 2009: R = 1228 / 1452 ≈ 0.846

A lower ratio indicates a better forecasting. Comparing the calculated ratios, 0.846 is the lowest value, which corresponds to the year 2009.

Explanation

The formula for the maximum possible profit is given by: Maximum Possible Profit = Max(Estimated Revenue, Actual Revenue) - Min(Estimated Cost, Actual Cost)

For 2007, the maximum possible profit is calculated as Max(1281, 1326) - Min(986, 988) = 1326 - 986 = 340.

For 2008, the maximum possible profit is calculated as Max(1452, 1286) - Min(1051, 1076) = 1452 - 1051 = 401.

For 2009, the maximum possible profit is calculated as Max(1228, 1452) - Min(1024, 1068) = 1452 - 1024 = 428.

Comparing the values from all three years, the overall maximum possible profit derived using this forecasting method is 428.

Explanation

Sum of percentages of asylum applications for the 15 listed countries in 2010 is: 15 + 13 + 11 + 3 + 9 + 6 + 6 + 6 + 4 + 3 + 3 + 4 + 3 + 3 + 3 = 92%

Percentage of asylum applications received by countries not mentioned in the table is: 100% - 92% = 8%

Given that USA received 15% of the total applications in 2010, which equals 72800: 15% of total applications = 72800

To find the applications received by other countries (8%): Number of applications = 72800 × 8 / 15 = 582400 / 15 ≈ 38826.67

This is approximately equal to 38800.

Explanation

To find the number of years where the sum of the percentage of applications received by the top three ranked countries is greater than that of the remaining countries in the table, we calculate the sums for each year:

In 2007, the top three countries are USA (15%), Sweden (11%), and France (9%). Sum of top three = 15 + 11 + 9 = 35% Sum of remaining countries = 86 - 35 = 51% Here, 35% is less than 51%.

In 2008, the top three countries are USA (13%), Canada (10%), and France (9%). Sum of top three = 13 + 10 + 9 = 32% Sum of remaining countries = 87 - 32 = 55% Here, 32% is less than 55%.

In 2009, the top three countries are USA (13%), France (11%), and Canada (9%). Sum of top three = 13 + 11 + 9 = 33% Sum of remaining countries = 89 - 33 = 56% Here, 33% is less than 56%.

In 2010, the top three countries are USA (15%), France (13%), and Germany (11%). Sum of top three = 15 + 13 + 11 = 39% Sum of remaining countries = 92 - 39 = 53% Here, 39% is less than 53%.

In 2011, the top three countries are USA (17%), France (12%), and Germany (10%). Sum of top three = 17 + 12 + 10 = 39% Sum of remaining countries = 93 - 39 = 54% Here, 39% is less than 54%.

In all five years, the sum of the top three countries is less than the sum of the remaining countries, which gives 0 years.

Explanation

To find the sum of ranks of Germany, we determine its rank in each year by arranging the countries in descending order of their application share using standard competition ranking.

In 2007, the percentages are USA (15%), Sweden (11%), France (9%), UK (8%), Canada (8%), Greece (8%), and Germany (6%). USA gets Rank 1, Sweden gets Rank 2, France gets Rank 3, and UK, Canada, and Greece tie for Rank 4. Because six countries are ranked ahead of Germany, Germany receives Rank 7.

In 2008, the percentages are USA (13%), Canada (10%), France (9%), Italy (8%), UK (8%), Germany (6%), and Sweden (6%). USA gets Rank 1, Canada gets Rank 2, France gets Rank 3, and Italy and UK tie for Rank 4. Because five countries are ranked ahead of Germany, Germany receives Rank 6.

In 2009, the percentages are USA (13%), France (11%), Canada (9%), UK (8%), and Germany (7%). Arranging them in descending order gives Rank 1 for USA, Rank 2 for France, Rank 3 for Canada, Rank 4 for UK, and Rank 5 for Germany.

In 2010, the percentages are USA (15%), France (13%), and Germany (11%), which gives Rank 1 for USA, Rank 2 for France, and Rank 3 for Germany.

In 2011, the percentages are USA (17%), France (12%), and Germany (10%), which gives Rank 1 for USA, Rank 2 for France, and Rank 3 for Germany.

Summing Germany's ranks across the given duration: 7 + 6 + 5 + 3 + 3 = 24

Explanation

Let T₂₀₀₇, T₂₀₀₈, T₂₀₀₉, T₂₀₁₀, and T₂₀₁₁ be the total number of asylum applications received globally in the years 2007, 2008, 2009, 2010, and 2011 respectively.

The total number of applications received by the USA between 2007 and 2011 is represented by the equation: 0.15 T₂₀₀₇ + 0.13 T₂₀₀₈ + 0.13 T₂₀₀₉ + 0.15 T₂₀₁₀ + 0.17 T₂₀₁₁ = 278800

The total number of applications received by France during the same period is: 0.09 T₂₀₀₇ + 0.09 T₂₀₀₈ + 0.11 T₂₀₀₉ + 0.13 T₂₀₁₀ + 0.12 T₂₀₁₁

Since we only have one equation with five variables (T₂₀₀₇, T₂₀₀₈, T₂₀₀₉, T₂₀₁₀, and T₂₀₁₁), the individual yearly totals cannot be uniquely determined. Consequently, the total number of applications received by France cannot be calculated from the given data.

Explanation

In 2007, the percentage shares of applications received by the countries are: USA: 15% Sweden: 11% France: 9% UK, Canada, Greece: 8% each Germany: 6% Italy, Austria: 4% each Belgium, Switzerland: 3% each Turkey, Netherlands, Norway: 2% each Australia: 1%

USA had the highest share of 15% in 2007, giving it the 1st rank.

In 2011, the percentage shares of applications received are: USA: 17% France: 12% Germany: 10% Italy: 8% Sweden: 7% Belgium, UK, Canada: 6% each Switzerland, Turkey: 4% each Austria, Netherlands, Australia: 3% each Greece, Norway: 2% each

USA had the highest share of 17% in 2011, keeping it at the 1st rank.

Since USA held the 1st rank in both 2007 and 2011, the variation in its ranking is 0, which is the minimum possible variation.

Explanation

The total number of students in 2001 is 35,000 and in 2002 is 40,000.

For Agriculture: Number of students in 2001 = 7% of 35,000 = (7 ÷ 100) × 35,000 = 2,450 Number of students in 2002 = 5% of 40,000 = (5 ÷ 100) × 40,000 = 2,000

This shows a decrease of 450 students from 2001 to 2002.

For comparison, calculations for other faculties show increases: Arts: 12% of 35,000 = 4,200 in 2001 to 11% of 40,000 = 4,400 in 2002 Medicine: 11% of 35,000 = 3,850 in 2001 to 10% of 40,000 = 4,000 in 2002 Science: 24% of 35,000 = 8,400 in 2001 to 22% of 40,000 = 8,800 in 2002 Pharmacy: 6% of 35,000 = 2,100 in 2001 to 9% of 40,000 = 3,600 in 2002 Commerce: 22% of 35,000 = 7,700 in 2001 to 24% of 40,000 = 9,600 in 2002 Engineering: 18% of 35,000 = 6,300 in 2001 to 19% of 40,000 = 7,600 in 2002

Explanation

To find the ratio of the number of students studying pharmacy in 2001 to those in 2002, we determine the number of pharmacy students in each year using the total number of students and their respective percentages.

For 2001, the total number of students is 35000, and the percentage of pharmacy students is 7%. Number of pharmacy students in 2001 = 7% of 35000 = (7 ÷ 100) × 35000 = 2450

For 2002, the total number of students is 40000, and the percentage of pharmacy students is 9%. Number of pharmacy students in 2002 = 9% of 40000 = (9 ÷ 100) × 40000 = 3600

The ratio between the number of pharmacy students in 2001 and 2002 is: Ratio = 2450 ÷ 3600 = 245 ÷ 360 = 49 ÷ 72

Explanation

Engineering students in 2001 = 20% of 35,000 = 7,000; in 2002 = 19% of 40,000 = 7,600. Percentage increase = (7,600 - 7,000) / 7,000 × 100 = 600/7,000 × 100 ≈ 8.57% ≈ 9%, which is option C.

Explanation

We are given that 3x + 7y is a multiple of 11. To find the expression that is divisible by 11, we can multiply this given expression by a suitable integer such that the resulting coefficients can be simplified modulo 11 to match the correct expression.

Multiplying the expression 3x + 7y by 5 gives: 5(3x + 7y) = 15x + 35y

Since 3x + 7y is a multiple of 11, the expression 15x + 35y must also be a multiple of 11. We can rewrite the coefficients 15 and 35 by separating out the multiples of 11: 15x = 11x + 4x 35y = 44y - 9y

Substituting these values back into the expression: 15x + 35y = (11x + 4x) + (44y - 9y) 15x + 35y = 11(x + 4y) + (4x - 9y)

Since the left-hand side 15x + 35y is a multiple of 11, and the term 11(x + 4y) is also a multiple of 11, the remaining term 4x - 9y must be divisible by 11.

Explanation

The fundamental relationship between two numbers, their Highest Common Factor (HCF), and their Least Common Multiple (LCM) is given by the formula:

Product of the two numbers = HCF × LCM

Let the other number be x. Substituting the given values into the formula:

77 × x = 11 × 693

x = (11 × 693) / 77

x = 693 / 7

x = 99

Explanation

For any two positive numbers x and y, the product of their Least Common Multiple (LCM) and Highest Common Factor (HCF) is equal to the product of the two numbers themselves. This is represented by the formula:

LCM(x, y) × HCF(x, y) = x × y

Given that the product of the LCM and HCF is 24, the product of the two numbers is:

x × y = 24

We are also given that the difference between the two numbers is 2:

x - y = 2

Expressing x in terms of y gives x = y + 2. Substituting this into the product equation:

(y + 2) × y = 24

y² + 2y - 24 = 0

Solving this quadratic equation by factoring:

(y + 6)(y - 4) = 0

Since the numbers are positive integers, we take the positive root, y = 4.

Substituting y = 4 back into the difference equation gives:

x = 4 + 2 = 6

Therefore, the two numbers are 6 and 4.

Explanation

To find the fraction of workers without children, we first calculate the total fraction of workers who have children.

The fraction of women in the office is 1/3. The fraction of women who have children is: 1/3 × 1/2 × 1/3 = 1/18

Since 1/3 of the workers are women, the fraction of men is: 1 - 1/3 = 2/3

The fraction of men who have children is: 2/3 × 3/4 × 2/3 = 12/36 = 6/18

Adding these two values gives the total fraction of workers with children: 1/18 + 6/18 = 7/18

Subtracting this from the total workforce of 1 gives the fraction of workers without children: 1 - 7/18 = 11/18

Explanation

Let the number of keepers be K.

The total number of heads is calculated by summing the heads of all animals and keepers: Total Heads = 50 + 45 + 8 + K = 103 + K

The total number of feet is calculated by multiplying each group by their respective number of feet (hens and keepers have 2 feet each, while goats and camels have 4 feet each): Total Feet = 50 × 2 + 45 × 4 + 8 × 4 + K × 2 = 100 + 180 + 32 + 2K = 312 + 2K

Given that the total number of feet is 224 more than the number of heads, we set up the equation: Total Feet = Total Heads + 224 312 + 2K = 103 + K + 224 312 + 2K = 327 + K K = 15

Explanation

Let S be the original number of sections. Since 3 new sections were started to make a total of 16 sections, the original number of sections is S = 16 - 3 = 13.

Initially, there were 24 students in each of the 13 sections, giving: Original number of students = 13 × 24 = 312

Currently, there are 21 students in each of the 16 sections, giving: Final number of students = 16 × 21 = 336

The number of new students admitted is the difference between the final and original number of students: New students admitted = 336 - 312 = 24

Explanation

The net profit percentage can be calculated directly using the successive percentage change formula:

Net Percentage Change = x + y + xy/100

Here, the price is first marked up by 25% (x = +25) and then a discount of 16% is offered (y = -16).

Substituting these values:

Net Profit % = 25 - 16 + (25 × -16)/100 Net Profit % = 9 - 4 Net Profit % = 5%

Alternatively, if the Cost Price (CP) is ₹100, the Marked Price (MP) including a 25% profit markup is ₹125. Offering a discount of 16% on the Marked Price yields the Selling Price (SP):

SP = 125 × (1 - 0.16) = 125 × 0.84 = ₹105

The actual profit is SP - CP = 105 - 100 = ₹5, which represents an actual profit of 5%.

Explanation

To find the least square number exactly divisible by 10, 12, 15, and 18, we first find the Least Common Multiple (LCM) of these numbers.

The prime factorizations are: 10 = 2 × 5 12 = 2² × 3 15 = 3 × 5 18 = 2 × 3²

The LCM of 10, 12, 15, and 18 is calculated by taking the highest power of each prime factor: LCM = 2² × 3² × 5 = 180

In the prime factorization of 180, the prime factors 2 and 3 have even exponents, but the prime factor 5 has an odd exponent of 1. To make 180 a perfect square, we must multiply it by 5 to pair the factor of 5.

Required least square number = 180 × 5 = 900

Explanation

Total hours taken by A to complete the work = 7 days × 9 hours/day = 63 hours

Total hours taken by B to complete the work = 6 days × 7 hours/day = 42 hours

Rate of work per hour: A's 1-hour work = 1/63 B's 1-hour work = 1/42

Combined work done by A and B in 1 hour = 1/63 + 1/42 = (2 + 3) / 126 = 5/126

Total time required to complete the work together = 126/5 hours

With the daily working schedule of 8 ⅖ hours per day (which is 42/5 hours per day): Number of days required = (126/5) ÷ (42/5) = 126/42 = 3 days

Explanation

First, convert the speeds from kmph to m/s by multiplying by 5/18.

Speed of the train = 54 × 5/18 = 15 m/s. Speed of the man = 6 × 5/18 = 5/3 m/s.

When the train passes the man walking in the same direction, the relative speed of the train with respect to the man is: Relative speed = 15 - 5/3 = 40/3 m/s.

The distance covered to pass the man is equal to the length of the train. Using the relation Distance = Speed × Time: Length of the train = 40/3 × 12 = 160 meters.

When the train passes the platform, the total distance covered is the sum of the length of the train and the length of the platform. Total distance = Speed of train × Time Length of train + Length of platform = 15 × 20 160 + Length of platform = 300 Length of platform = 300 - 160 = 140 meters.

Explanation

Let the speed of the man in still water be x kmph and the speed of the current be y kmph. The upstream speed is x - y and the downstream speed is x + y.

Using the relation Time = Distance / Speed, the given conditions can be represented as: 40/(x - y) + 55/(x + y) = 13 30/(x - y) + 44/(x + y) = 10

Substituting u = 1/(x - y) and v = 1/(x + y): 40u + 55v = 13 30u + 44v = 10

To solve this system, multiply the first equation by 3 and the second by 4: 120u + 165v = 39 120u + 176v = 40

Subtracting the first of these from the second yields: 11v = 1 v = 1/11

Substituting v = 1/11 back into the equation 30u + 44v = 10: 30u + 4 = 10 30u = 6 u = 1/5

This gives: x - y = 5 x + y = 11

Solving this pair of linear equations by adding them gives: 2x = 16 x = 8 kmph

Subtracting the first equation from the second gives: 2y = 6 y = 3 kmph

Explanation

For compound interest, when a sum of money P amounts to A₁ after t years and to A₂ after 2t years, the relationship between the sum and the amounts is given by the formula:

P = A₁² / A₂

In this problem, the time periods are 3 years and 6 years (which is 2 × 3 years), so we can apply this formula directly with A₁ = 6690 and A₂ = 10035:

P = (6690 × 6690) / 10035

Dividing 10035 and 6690 by their common factor 3345 gives 3 and 2 respectively:

P = 6690 × 2/3 P = 2230 × 2 P = 4460

Explanation

The given equations can be solved using successive substitution under two standard interpretations.

First, interpreting the relations as exponential equations: a = bˣ b = cʸ c = aᶻ

Substituting the second equation into the first: a = (cʸ)ˣ = cˣʸ

Substituting the third equation into this result: a = (aᶻ)ˣʸ = aˣʸᶻ

Since a¹ = aˣʸᶻ, comparing the powers on both sides gives: xyz = 1

Second, interpreting the relations as multiplication: a = bx b = cy c = az

Substituting the second equation into the first: a = (cy)x = cxy

Substituting the third equation into this result: a = (az)xy = axyz

Dividing both sides by a (assuming a ≠ 0): 1 = xyz

Explanation

The area of a trapezium is given by the formula Area = ½ × (sum of parallel sides) × height.

In this case, the parallel sides of the canal's cross-section are its top width and bottom width, which are 12 m and 8 m respectively. Let the depth (height) of the canal be h.

Substituting the given values into the formula:

840 = ½ × (12 + 8) × h

840 = ½ × 20 × h

840 = 10 × h

h = 84 m

Explanation

The volume of a cone with base radius r₁ and height h₁ is given by the formula V₁ = ⅓ × π × r₁² × h₁. The volume of a cylinder with base radius r₂ and height h₂ is given by the formula V₂ = π × r₂² × h₂.

The ratio of the volume of the cone to the volume of the cylinder is calculated as: V₁ / V₂ = (⅓ × π × r₁² × h₁) / (π × r₂² × h₂) V₁ / V₂ = (r₁² × h₁) / (3 × r₂² × h₂)

Substituting the given values r₁ = 3 cm, h₁ = 5 cm, r₂ = 2 cm, and h₂ = 4 cm into the relation: V₁ / V₂ = (3² × 5) / (3 × 2² × 4) V₁ / V₂ = (9 × 5) / (3 × 4 × 4) V₁ / V₂ = 45 / 48

Simplifying the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3, yields: V₁ / V₂ = 15 / 16

Explanation

Time elapsed on the incorrect clock from 5 a.m. on the first day to 10 p.m. on the fourth day is calculated as follows: From Day 1, 5 a.m. to Day 4, 5 a.m. is 3 days, which equals 3 × 24 = 72 hours. From Day 4, 5 a.m. to Day 4, 10 p.m. is 17 hours. Total elapsed time on the incorrect clock = 72 + 17 = 89 hours.

The clock loses 16 minutes in 24 hours. This means 23 hours and 44 minutes of this incorrect clock is equal to 24 hours of a correct clock. Converting 23 hours 44 minutes to hours: 23 + 44/60 = 23 + 11/15 = 356/15 hours.

Therefore, 356/15 hours on the incorrect clock = 24 hours on the true clock. To find the equivalent of 1 hour on the incorrect clock: 1 hour on the incorrect clock = 24 × 15/356 = 360/356 = 90/89 hours on the true clock.

Now, for 89 hours on the incorrect clock: True time elapsed = 89 × 90/89 = 90 hours.

Since the true clock has run for 90 hours while the incorrect clock has run for 89 hours, the true clock is exactly 1 hour ahead. Adding 1 hour to 10 p.m. gives 11 p.m.

Explanation

To find the sitting arrangement of the seven friends from left to right (positions 1 to 7):

T sits fourth to the left of V, and W sits to the immediate left of T, forming the sequence W T _ _ _ V. Since V cannot be at an extreme end, there must be a position to the right of V, giving the template: W T _ _ _ V _.

Q sits third to the right of W (position 1), placing Q at position 4: W T _ Q _ V _.

R is not a neighbor of Q, so R cannot be at position 3 or 5, placing R at the right extreme (position 7): W T _ Q _ V R.

S is not a neighbor of V, so S cannot be at position 5, placing S at position 3: W T S Q _ V R.

The remaining position 5 is occupied by P, completing the arrangement as: W, T, S, Q, P, V, R. This places W at the left extreme and R at the right extreme.

Explanation

Based on the given clues, let the seven positions from left to right be 1 to 7. Since T is fourth to the left of V and W is to the immediate left of T, their relative sequence is W-T-x-x-x-V. Because V cannot sit at the extreme end (position 7), V must sit at position 6, placing T at position 2 and W at position 1.

Q sits third to the right of W, which puts Q at position 4. Since R is not an immediate neighbor of Q (positions 3 and 5), R must sit at position 7. Since S is not an immediate neighbor of V (positions 5 and 7), S must sit at position 3. This leaves position 5 for P.

The complete arrangement from left to right is W, T, S, Q, P, V, R. As S sits at position 3, the person sitting second to his right (position 5) is P.

Explanation

The linear arrangement of the seven friends facing north is determined step-by-step. Since T is fourth to the left of V, and W is to the immediate left of T, this forms a block of W T _ _ _ V. V does not sit at an extreme end of the line, meaning V cannot be at the seventh position. Therefore, the block must occupy the first six positions from the left: W at position 1, T at position 2, and V at position 6.

Since Q is sitting third to the right of W, Q must be at position 4. R is not an immediate neighbor of Q, which means R cannot sit at position 3 or 5, so R must sit at position 7. S is not an immediate neighbor of V, so S cannot sit at position 5. This places S at position 3. Consequently, the remaining person, P, must occupy position 5.

The final sequence from left to right is W, T, S, Q, P, V, R. Based on this arrangement, S sits exactly between T and Q.

Explanation

By analyzing the given conditions, the seating arrangement of the seven friends facing north from left to right can be determined step-by-step.

Since V does not sit at an extreme end of the line and T is sitting fourth to the left of V, V cannot be at the seventh position (extreme right). W is sitting to the immediate left of T, which means T cannot sit at the first position (extreme left) because there must be space for W. Thus, the only possible positions for T and V are the second and sixth positions respectively, placing W at the first position.

Since Q is sitting third to the right of W, and W is at the first position, Q must be at the fourth position.

R is not an immediate neighbor of Q, so R cannot sit at the third or fifth positions. This leaves the seventh position for R.

S is not an immediate neighbor of V, so S cannot sit at the fifth position. This leaves the third position for S.

The only remaining fifth position is occupied by P.

The final seating arrangement from left to right is W, T, S, Q, P, V, R.

The person at the fourth position (the exact middle) has three people sitting to their left (W, T, S) and three people sitting to their right (P, V, R). Q is at the fourth position.

Explanation

By analyzing the given clues, the exact sitting positions from left to right (positions 1 to 7) can be determined.

T is sitting fourth to the left of V, and W is to the immediate left of T. This means V cannot be at position 5 because that would place T at position 1 and leave no space for W on its left. Since V cannot sit at an extreme end, V is not at position 7. Therefore, V must sit at position 6, placing T at position 2 and W at position 1.

Q is sitting third to the right of W, so Q sits at position 4.

R is not an immediate neighbor of Q, meaning R cannot be at positions 3 or 5. Thus, R must sit at position 7.

S is not an immediate neighbor of V, which means S cannot sit at position 5. Therefore, S sits at position 3.

The remaining person, P, sits at position 5.

The final arrangement from left to right is W, T, S, Q, P, V, R. The person sitting third to the left of V (position 6) is S (position 3).

Explanation

Total number of persons in the row = 30 Position of the first person from the left (L) = 9 Position of the second person from the right (R) = 16

Since the sum of the positions from both ends, L + R = 9 + 16 = 25, is less than the total number of persons, 30, the two individuals do not overlap in the row.

The number of persons sitting between them is given by the formula: Number of persons = Total - (L + R)

Substituting the values: Number of persons = 30 - (9 + 16) = 30 - 25 = 5

Explanation

Ramesh's father's father is Ramesh's paternal grandfather. The daughter of Ramesh's paternal grandfather is Ramesh's father's sister, which makes her Ramesh's paternal aunt. The son of Ramesh's paternal aunt is Amit, which means Amit is Ramesh's cousin.

Explanation

Sangita is Madan's sister. Therefore, Sangita's brother can either be Madan himself or another brother of Madan. If Sangita's brother refers to Madan himself, then Nandani, who is the daughter of this brother, is Madan's daughter. If Sangita's brother refers to another brother of Madan, then Nandani is the daughter of Madan's brother, which makes her Madan's niece. Thus, Nandani is either Madan's niece or daughter.

Explanation

A candidate must select exactly 3 subjects out of {A, B, C, D, E, F} subject to the given conditions.

According to condition (i), subjects A and B must be chosen together or not chosen at all. This gives two cases:

In the first case, both A and B are selected. To complete the set of 3 subjects, one more subject must be chosen from {C, D, E, F}. Under condition (ii), choosing A means E cannot be chosen, which leaves {C, D, F} as the options for the third subject. Under condition (iii), a candidate who offers C or D cannot offer F. Since we are choosing only one additional subject from {C, D, F}, this constraint is satisfied for each choice because we will not have F alongside C or D. Thus, the three valid combinations in this case are {A, B, C}, {A, B, D}, and {A, B, F}.

In the second case, neither A nor B is selected. This means all 3 subjects must be chosen from {C, D, E, F}. The possible combinations of 3 subjects from this set are {C, D, E}, {C, D, F}, {C, E, F}, and {D, E, F}. Condition (iii) states that a candidate choosing C or D cannot choose F. This makes {C, D, F}, {C, E, F}, and {D, E, F} invalid because they all contain F alongside C or D. Only {C, D, E} satisfies the condition since F is not selected. Thus, there is only one valid combination in this case.

Adding the valid combinations from both cases yields 3 + 1 = 4 permitted combinations.

Explanation

Let us determine the valid combinations of three subjects that a candidate can choose under the given conditions.

First, since anyone who offers A must offer B and vice-versa, any combination containing A must also contain B, and any combination containing B must also contain A. Thus, A and B are always taken together.

Second, a candidate offering A (and therefore B) cannot offer E. So the combination {A, B, E} is invalid.

Third, a candidate offering C or D cannot offer F. This means F cannot be combined with C or D.

Fourth, each candidate must select exactly three subjects.

Let us find the valid three-subject combinations: Candidates who choose A and B can choose their third subject from {C, D, F} (since E is excluded). This gives three valid combinations: {A, B, C}, {A, B, D}, and {A, B, F}. Candidates who do not choose A and B must choose three subjects from {C, D, E, F}. Since F cannot be combined with C or D, any combination containing F from this group is invalid because we cannot form a group of three without C or D. Therefore, the only valid combination without A and B is {C, D, E}.

Let: x be the number of candidates choosing {A, B, C} y be the number of candidates choosing {A, B, D} z be the number of candidates choosing {A, B, F} w be the number of candidates choosing {C, D, E}

Using the given distribution data: Candidates choosing E: w = 70 Candidates choosing F: z = 35 Candidates choosing C: x + w = 90. Since w = 70, x = 90 - 70 = 20 Candidates choosing D: y + w = 85. Since w = 70, y = 85 - 70 = 15

We can verify this with the count for A (or B): Candidates choosing A: x + y + z = 20 + 15 + 35 = 70, which matches the given data.

The total number of candidates who appeared for the examination is the sum of candidates in all four mutually exclusive groups: Total candidates = x + y + z + w = 20 + 15 + 35 + 70 = 140.

Explanation

Let the candidate counts for each valid combination of three subjects be represented as follows:

c₁: Candidates offering the combination A + B + C c₂: Candidates offering the combination A + B + D c₃: Candidates offering the combination A + B + F c₄: Candidates offering the combination C + D + E

According to condition (i), candidates who offer A must also offer B, and vice-versa, meaning A and B are always taken together.

According to condition (ii), A and E cannot be offered together, which rules out any combination containing A, B, and E.

According to condition (iii), any candidate offering C or D cannot offer F. Thus, any candidate who offers F cannot offer C or D. Since F cannot be paired with C or D, and cannot be paired with E alone (as each candidate must offer exactly three subjects), any candidate offering F must choose the combination A + B + F.

This leaves C + D + E as the only permissible combination for candidates who do not offer A and B.

Using the given distribution of candidates: The total count of candidates offering F is 35. Since F is only in the combination A + B + F, we have: c₃ = 35

The total count of candidates offering E is 70. Since E is only in the combination C + D + E, we have: c₄ = 70

The total count of candidates offering C is 90. Candidates offering C are in either A + B + C or C + D + E: c₁ + c₄ = 90 c₁ + 70 = 90 c₁ = 20

The total count of candidates offering D is 85. Candidates offering D are in either A + B + D or C + D + E: c₂ + c₄ = 85 c₂ + 70 = 85 c₂ = 15

To verify, the total count of candidates offering A (and B) is: c₁ + c₂ + c₃ = 20 + 15 + 35 = 70

This perfectly matches the given count of 70 for both A and B. Thus, the number of candidates who offered the combination A + B + C is 20.

Explanation

Every candidate must select exactly three subjects under the given constraints.

First, according to condition (i), A and B must always be taken together.

Second, according to condition (ii), A and E cannot be taken together, which also means B and E cannot be taken together.

Third, according to condition (iii), C or D cannot be taken with F.

Let us analyze the subject F. Any candidate taking F cannot take C or D. To complete a set of three subjects without C or D, the candidate must choose from A, B, and E. Since E cannot be taken with A and B, the only possible combination of three subjects containing F is {A, B, F}. Since there are 35 candidates taking F, exactly 35 candidates chose the combination {A, B, F}.

Now analyze the subject E. Any candidate taking E cannot take A (and thus B). To complete a set of three subjects, they must choose from C, D, and F. Since F cannot be taken with C or D, the candidate cannot take F because that would leave them with only two subjects. Thus, the only possible combination of three subjects containing E is {C, D, E}. Since there are 70 candidates taking E, exactly 70 candidates chose the combination {C, D, E}.

The candidates who combined C with D are those who took both C and D together. Looking at the valid combinations, the only combination containing both C and D is {C, D, E}. The number of candidates with this combination is 70.

Explanation

By condition (i), subjects A and B must always be taken together. Any candidate taking A must take B, and vice-versa.

By condition (ii), anyone taking A cannot take E. Since A and B are taken together, this means the combination (A, B, E) is not possible.

By condition (iii), anyone taking C or D cannot take F. This means combinations containing (C, F) or (D, F) are not allowed.

If a candidate chooses to offer subject F, they cannot offer C or D. Thus, to choose three subjects, the remaining two subjects must be chosen from {A, B, E}. However, if they choose E, they cannot choose A, and consequently they cannot choose B, leaving them with only two subjects (E and F), which is invalid. Thus, they cannot choose E.

Therefore, any candidate who offers F must choose A and B as their other two subjects. This means the only possible three-subject combination containing F is (A, B, F).

Since all candidates who offered F must have offered the combination (A, B, F), the number of candidates who offered B with F is exactly equal to the total number of candidates who offered F, which is 35.

Explanation

We are given five cities: L, M, N, O, and P.

First, we identify the three industrial cities. The problem states that N and O are not industrial cities. Since there are five cities in total and three of them are industrial, the industrial cities must be L, M, and P.

Second, we determine which cities have universities. We are given that there are three universities in total, and two of these are in industrial cities. The problem also states that M is a port city and no port city has a university. Therefore, M cannot have a university. This means the two industrial cities with universities must be L and P.

Since M is one of the three industrial cities, is a port city, and does not have a university, it satisfies all the conditions of having industries as well as a port but not having a university.

Explanation

To determine the characteristics of each city, we can analyze the given conditions systematically.

There are five cities (L, M, N, O, P) and three of them are industrial cities. Since we are given that N and O are not industrial cities, the three industrial cities must be L, M, and P.

There is only one hill station, which is specified as O. Since none of the industrial cities is a hill station, this is consistent. Every hill city has a university, which means O has a university.

We are given that P has a university, and also that two industrial cities have universities. Since the industrial cities are L, M, and P, and M is a port city which cannot have a university, the two industrial cities with universities must be L and P. This accounts for all three universities, which belong to L, O, and P.

Since no port city can have a university, the two port cities must be M and N.

Evaluating the characteristics of city N, we find that N is a port city, which means N is not an industrial city, does not have a university, and is not a hill station.

Explanation

To find the two port cities, we can analyze the given conditions systematically.

There are five cities: L, M, N, O, and P.

First, we identify the industrial cities. There are three industrial cities. Since N and O are not industrial cities, the three industrial cities must be L, M, and P.

Next, we identify the cities with universities. There are three cities with universities. Since O is a hill station and every hill city has a university, O has a university. P is also given to have a university. Since two industrial cities have universities, and the industrial cities are L, M, and P (with P already having a university), either L or M must have the other university.

We are given that M is a port city. Since no port city has a university, M cannot have a university. Therefore, L must be the second industrial city with a university.

Thus, the three cities with universities are O, P, and L.

Since no port city has a university, the two port cities must be selected from the cities that do not have universities, which are M and N.

Explanation

Amandeep is an Indian citizen, satisfying condition (i). With a birth date of 2nd February, 1974, his age on 5th September, 1997 is 23 years, which is within the 21-50 years age group, satisfying condition (ii). As a graduate, he meets the minimum education criteria of being a Matriculate, satisfying condition (iii). He has been living in Delhi since 1987, satisfying the requirement of residing in Delhi for at least 5 years preceding the application, fulfilling condition (iv). His father is the sole earner drawing Rs. 800 per month, making the annual family income Rs. 9,600 (800 × 12), which is well below the Rs. 50,000 limit and satisfies condition (v). Since he is an unemployed graduate, conditions (vi) and (vii) are waived as per condition (ix). Thus, all requirements are satisfied, and he is selected.

Explanation

Under condition vi, an applicant must not hold any dealership in any oil company. Kishan Gopal already has a dealership in Tamsha Oil Company, which directly violates this requirement. Although condition ix allows for the waiver of condition vi for unemployed graduates, Kishan Gopal is only a matriculate and does not qualify for this waiver. Consequently, he fails to meet the selection criteria.

Explanation

Balvinder Singh satisfies the following standard conditions: (i) Indian nationality ✓; (ii) Age 23 years — within the 21–50 range ✓; (iii) Graduate, which exceeds the minimum of Matriculate ✓; (iv) Resident of Delhi for 7 years, which is not less than the required 5 years ✓; (vi) No personal oil dealership ✓; (vii) No close relative as dealer/distributor ✓. His family income is Rs. 60,000 per annum, which exceeds the Rs. 50,000 limit under condition (v). However, Balvinder works in a State Corporation (owned/controlled by state government). Condition (viii) explicitly provides that the annual income restriction is NOT applicable to such persons, but their cases must be referred to the Managing Director. Since the only obstacle — the income limit — is overridden by condition (viii), and that condition mandates a referral, the correct action is to refer the case to the Managing Director. Answer: C.

Explanation

Chaluka satisfies all primary eligibility conditions: he is an Indian national, he is 21 years of age on 5th September, 1997, he is a matriculate, his annual family income is Rs. 20,000, and he has no dealerships or close relatives associated with any oil company. However, he is a resident of Mumbai instead of Delhi. Since he belongs to the Scheduled Caste (SC) category and is not a resident of Delhi, condition (x) is triggered, which states that his case must be referred to the Chairman.

Explanation

Naresh Saini satisfies all the necessary criteria for selection as a distributor: He is an Indian national, fulfilling condition (i). At 27 years of age, he falls within the 21-50 age range, fulfilling condition (ii). As a graduate, he exceeds the minimum educational requirement of matriculation, satisfying condition (iii). He has resided in Delhi since 1988, which is more than the required 5 years, satisfying condition (iv). His annual family income of Rs. 16,000 is well below the maximum limit of Rs. 50,000, fulfilling condition (v). As an unemployed graduate, conditions (vi) and (vii) regarding oil dealerships and close relatives are waived for him under condition (ix).

Explanation

Pran Chaturvedi satisfies all the primary criteria except the annual family income limit, as his family income of Rs. 75,000 exceeds the maximum limit of Rs. 50,000 specified in condition (v). However, since he works in the Haryana State Corporation, which is a state government-controlled corporation, condition (viii) applies. According to condition (viii), the annual income restriction is not applicable to employees of state government-owned or controlled corporations, and their cases must be referred to the Managing Director. All other conditions, including citizenship, age (24 years on 5th September, 1997), education (Senior Secondary), residence in Delhi (5 years), and lack of any oil company dealership or distribution connection, are fully satisfied. Thus, his case must be referred to the Managing Director.

Explanation

Maninder Vohra satisfies several conditions: (i) Indian nationality ✓; (ii) Age 33 years — within 21–50 ✓; (iii) Unemployed graduate — above Matriculate ✓; (iv) Resident of Delhi for 12 years — not less than 5 years ✓; (vi) No personal oil dealership (not stated to have one) ✓; (vii) No close relative as dealer/distributor (not stated) ✓. His family income is Rs. 55,000 per annum, which exceeds the Rs. 50,000 ceiling set by condition (v). Condition (ix) relaxes only conditions (vi) and (vii) for unemployed graduates; it does NOT waive the income limit in condition (v). Condition (viii), which waives the income restriction, applies only to persons employed in state-government-owned or controlled corporations — Maninder is unemployed, so (viii) does not apply. Since he fails condition (v) with no applicable exemption, he is not selected. Answer: B.

Explanation

Ashok Garg satisfies the age criterion as he is 20 years old as of September 1, 1994, which is above the minimum required 18 years. He can pay the required admission fees of Rs.20000, fulfilling criterion (iv). In his XIIth Std. Science examination with Biology, he scored 90% marks, which is greater than the 60% required in criterion (i). Although he does not satisfy criterion (iii) because his entrance test score of 60% is less than the required 70%, he meets the sub-condition (v) by having obtained 90% marks in the XIIth Std. Science examination. Consequently, his case must be referred to the Principal.

Explanation

Asha Thakur satisfies all the primary criteria required for admission as of September 1, 1994:

First, she secured 68% marks in her XIIth Std. Science examination with Biology, which satisfies the requirement of at least 60% marks in criterion (i).

Second, born on October 20, 1975, she is 18 years and 10 months of age as on September 1, 1994, which satisfies the age requirement of being at least 18 years of age in criterion (ii).

Third, she secured 75% marks in the entrance test, satisfying the requirement of obtaining at least 70% marks in criterion (iii).

Fourth, she can pay the required admission fee of Rs. 20000, satisfying criterion (iv).

Since all the primary eligibility criteria are met, she must be admitted.

Explanation

Pankaj Goel was 17 years old on September 11, 1993. This means he will complete 18 years of age and turn 18 only on September 11, 1994. Consequently, as of September 1, 1994, he is less than 18 years old. Since he does not satisfy the age criterion (ii) requiring a student to be 18 years of age as on September 1, 1994, and there is no provision for relaxing the age requirement under the exception clauses, he fails to qualify for admission.

Explanation

To determine the admission decision for Rakesh Yadav, we evaluate his credentials against the given criteria.

Under criterion (i), he secured 85% marks in his XIIth Std. Science examination with Biology, which is well above the required 60% marks.

For criterion (ii), while his exact birth year is not specified, the age requirement of 18 years is assumed to be met since there is no option for inadequate data.

Under criterion (iii), he scored 80% marks in the entrance test, which satisfies the requirement of at least 70% marks.

Under criterion (iv), he cannot pay the full Rs. 20000 admission fee because he can only pay Rs. 15000.

According to clause (vi), an exemption is provided for candidates who meet all other criteria except the payment amount under (iv). It states that if a candidate can pay at least Rs. 10000 at the time of admission, they are eligible for provisional admission. Since Rakesh satisfies all other requirements and can pay Rs. 15000, which is greater than the Rs. 10000 threshold, his case satisfies this exemption.

Explanation

To qualify for admission, a candidate must be at least 18 years of age as on September 1, 1994. Meeta Chandra was born on November 7, 1978. As of September 1, 1994, her age is 15 years, 9 months, and 25 days, which is less than the required minimum age of 18 years. Since she fails to satisfy this age criterion and there is no alternative sub-clause or exemption provided for it, she cannot be admitted.

Explanation

To find the order of arrival, we can represent the four couples by their arrival positions 1st, 2nd, 3rd, and 4th.

From statement iv, we have a consecutive block of three couples: Ashutosh's couple → Rinku's couple → Jewellery-dealing couple

From statement i, Rajiv's couple arrived immediately after the Garments-dealing couple and immediately before Rupu's couple, which gives another consecutive block: Garments-dealing couple → Rajiv's couple → Rupu's couple

If Ashutosh's couple arrived 2nd, Rinku's couple would be 3rd, and the Jewellery-dealing couple 4th. This arrangement leads to contradictions with other statements regarding Pappu dealing in Books and the position of Prem's couple.

Thus, Ashutosh's couple must have arrived 1st: 1st Couple: Ashutosh (husband) 2nd Couple: Rinku (wife) 3rd Couple: Jewellery-dealing couple

Now, fitting the second block (Garments → Rajiv → Rupu), Rajiv's couple must be 3rd so that Rinku's couple (at 2nd position) deals in Garments (which is consistent with Rinku not dealing in Furniture). This gives: 2nd Couple: Garments-dealing couple (husband Prem, wife Rinku) 3rd Couple: Rajiv's couple (husband Rajiv, wife Rosy, dealing in Jewellery) 4th Couple: Rupu's couple (husband Pappu, wife Rupu, dealing in Books)

By elimination, Nitu is married to Ashutosh, and they deal in Furniture: 1st Couple: Ashutosh and Nitu (Furniture) 2nd Couple: Prem and Rinku (Garments) 3rd Couple: Rajiv and Rosy (Jewellery) 4th Couple: Pappu and Rupu (Publishing/Books)

Since Ashutosh arrived with the 1st couple, the 2nd couple consisting of Prem and Rinku arrived immediately after them. Therefore, Rinku came after Ashutosh.

Explanation

To find the business Rosy deals in, we can determine the sequence of arrival for the four couples at positions 1, 2, 3, and 4.

We have two overlapping sequences of consecutive arrivals. According to clue four, Ashutosh arrived immediately before Rinku, who arrived immediately before the couple dealing in Jewellery. This forms the sequence: Ashutosh → Rinku → Jewellery. According to clue one, Rajiv arrived immediately after the couple dealing in Garments and immediately before Rupu. This forms the sequence: Garments → Rajiv → Rupu.

Combining these two sequences reveals the exact arrival order: Position 1 is Ashutosh. Position 2 is Rinku, whose couple deals in Garments. Position 3 is Rajiv, whose couple deals in Jewellery. Position 4 is Rupu.

Now we can match the remaining individuals to their respective positions. According to clue three, Pappu deals in Books. Since the couple at position 4 is the only one left that can deal in Books (as positions 2 and 3 deal in Garments and Jewellery, and Rinku does not deal in Furniture), Pappu must be at position 4 and is married to Rupu.

According to clue two, Prem arrived immediately before Rosy. Since Rinku is at position 2 and Rupu is at position 4, the female Rosy must be at either position 1 or position 3. For Prem to arrive immediately before Rosy, Prem must be at position 2 and Rosy must be at position 3. This means Prem is married to Rinku at position 2, and Rosy is married to Rajiv at position 3, leaving Nitu to be married to Ashutosh at position 1.

Since Rajiv and Rosy are at position 3, they are the couple dealing in Jewellery.

Explanation

We determine the arrival order of the four couples using the given clues.

Clue (iv) establishes a chain of three consecutive arrivals: Ashutosh's couple → Rinku's couple → Jewellery couple. Clue (i) establishes another chain: Garments couple → Rajiv's couple → Rupu's couple.

With only four positions available, Ashutosh's three-person chain must begin at position 1 (if it started at 2, positions 2–4 would be taken, leaving no room for Rajiv's chain starting before position 2): Position 1: Ashutosh's couple Position 2: Rinku's couple Position 3: Jewellery couple

Fitting Rajiv's chain into the remaining positions gives: Position 2: Garments couple → Rinku's couple deals in Garments (consistent with 'Rinku does not deal in Furniture') Position 3: Rajiv's couple → Rajiv's couple deals in Jewellery Position 4: Rupu's couple

Clue (iii): Pappu deals in Books. The businesses at positions 2 (Garments) and 3 (Jewellery) are assigned; position 1 gets Furniture (the only remaining business among 4). Pappu must be at position 4 (Books), so Pappu and Rupu are the couple at position 4.

Clue (ii): Prem arrived immediately before Rosy. The only male unplaced is Prem. The unplaced female at position 3 must be Rosy, so Prem is at position 2 and Rosy is at position 3. This makes Prem and Rinku the couple at position 2.

The remaining female, Nitu, belongs to Ashutosh's couple at position 1.

Final arrangement: Position 1: Ashutosh + Nitu (Furniture) Position 2: Prem + Rinku (Garments) Position 3: Rajiv + Rosy (Jewellery) Position 4: Pappu + Rupu (Books)

The female dealing in Furniture is Nitu (arrived with couple 1); the female dealing in Garments is Rinku (arrived with couple 2). Therefore their respective arrival orders are 1 and 2. Answer: A.

Explanation

Based on the given clues, we can determine the sequence of arrival (from 1st to 4th) for the four couples:

From clue i, we have a consecutive sequence of three couples: Garments couple → Rajiv's couple → Rupu's couple.

From clue iv, we have another consecutive sequence: Ashutosh's couple → Rinku's couple (not Furniture) → Jewellery couple.

To combine these two sequences into four slots: If Ashutosh is 1st, Rinku's couple is 2nd, and the Jewellery couple is 3rd. The other sequence (Garments → Rajiv → Rupu) can only fit if the Garments couple is 2nd, Rajiv's couple is 3rd, and Rupu's couple is 4th. This matches perfectly as Rinku's couple (2nd) deals in Garments (which is not Furniture).

This gives us the following structure: 1st Couple: Ashutosh (Husband) 2nd Couple: Prem/Pappu (Husband), Rinku (Wife), Garments (Business) 3rd Couple: Rajiv (Husband), Jewellery (Business) 4th Couple: Prem/Pappu (Husband), Rupu (Wife)

Since Pappu deals in Books (clue iii) and the 3rd couple deals in Jewellery, Pappu must belong to the 4th couple, meaning Prem is the husband of the 2nd couple.

From clue ii, Prem (2nd couple) arrived immediately before Rosy, which means Rosy is the wife of the 3rd couple (Rajiv's wife).

Finally, the remaining wife, Nitu, belongs to the 1st couple (Ashutosh's wife), and their business is Furniture.

The final arrangement is: 1st Couple: Ashutosh and Nitu (Furniture) 2nd Couple: Prem and Rinku (Garments) 3rd Couple: Rajiv and Rosy (Jewellery) 4th Couple: Pappu and Rupu (Books)

Therefore, Rosy is the wife of Rajiv.

Explanation

The total number of children in the row is 35. M is positioned 15th from the right end. Since there are 10 children between M and R, R can be positioned either to the right or to the left of M.

If R is to the right of M, R's position from the right end is 15 - 10 - 1 = 4th. Using the relation that Position from left = Total - Position from right + 1, R's position from the left end is 35 - 4 + 1 = 32nd.

If R is to the left of M, R's position from the right end is 15 + 10 + 1 = 26th. Using the same formula, R's position from the left end is 35 - 26 + 1 = 10th.

Since two distinct and valid positions from the left end are possible for R, a single unique position cannot be determined with the given information.

Explanation

Let the heights of Roshan, Hardik, Susheel, Niza, and Harry be represented by R, H, S, N, and Hy respectively.

According to the first statement, Roshan is taller than Hardik (R > H) and Hardik is shorter than Susheel (S > H).

The second statement states that Niza is taller than Harry but shorter than Hardik (H > N > Hy).

The third statement establishes that Susheel is shorter than Roshan (R > S).

By combining these inequalities, the complete descending order of height is R > S > H > N > Hy, which establishes Roshan as the tallest individual.

Explanation

Since A's father has a son B, A and B are siblings. B has an aunt C, meaning C is the sister of A and B's father (or mother). X is the husband of C. Y is the father-in-law of X, which means Y is the father of X's wife, C. Since C is the sister of A's father (or mother), her father Y is also the father of A's father (or mother). Therefore, Y is the grandfather of A.

Explanation

Let the lady in the photograph be denoted as L. The speaker states that she is the only daughter of L, and L's son is Pramod's maternal uncle.

Since L's son is the speaker's brother, and this same son is Pramod's maternal uncle (mother's brother), the mother of Pramod must be a daughter of L. Because the speaker is the only daughter of L, she must be the mother of Pramod.

As the speaker is Pramod's mother, she is the wife of Pramod's father.

Explanation

The pattern of the given series is based on the relation where each subsequent term is obtained by squaring the preceding term and subtracting 1:

Tₙ = Tₙ₋₁² - 1

Applying this formula to each term step-by-step: First term = 2 Second term = 2² - 1 = 3 Third term = 3² - 1 = 8 Fourth term = 8² - 1 = 63 Fifth term = 63² - 1 = 3969 - 1 = 3968

The fifth term given in the series is 3962, whereas it should be 3968.

Explanation

Ajay starts task A at 9 a.m. Since task A takes 2 hours, it is completed at 11 a.m. Task B can only begin after task A is finished and requires 1 hour, meaning it starts at 11 a.m. and is completed at 12 noon. Work on task C can start only after both A and B are completed. Thus, task C starts at 12 noon. Since task C takes 1 hour to complete, Ajay will complete task C at 1 p.m.

Explanation

The initial start time is 9:00 am. Task A starts immediately at 9:00 am and takes 2 hours, completing at 11:00 am.

Task B starts after Task A is completed, which is at 11:00 am. Since Task B takes 2 hours, it is completed at 1:00 pm.

Task C can only start after both A and B are complete, which is at 1:00 pm. Since Task C takes 1 hour, it is completed at 2:00 pm.

Task D runs in parallel with tasks B and C. Therefore, Task D starts at the same time as Task B at 11:00 am. Since Task D takes 3 hours, it is completed at 2:00 pm.

Task E can only begin once all preceding tasks A, B, C, and D are complete. Since both C and D are finished by 2:00 pm, Task E can start at 2:00 pm.

Explanation

The scheduling of the tasks proceeds as follows starting at 9:00 AM:

Task A begins at 9:00 AM and takes 2 hours, completing at 11:00 AM.

Task B can only start after Task A is complete. Therefore, Task B runs from 11:00 AM to 12:00 PM.

Task C can start after both Task A and Task B are complete. Since Task B finishes at 12:00 PM, Task C runs from 12:00 PM to 1:00 PM.

Task D can be performed concurrently alongside Task B and Task C. It starts as soon as Task A is complete at 11:00 AM. Since it requires 3 hours, Task D runs from 11:00 AM to 2:00 PM.

Task E can only start once all previous tasks (A, B, C, and D) are completed. The last of these tasks to finish is Task D, which concludes at 2:00 PM. Therefore, Task E starts at 2:00 PM and, requiring 1 hour, finishes at 3:00 PM.

Explanation

Track movements step by step, treating the starting house as the origin (0, 0), where x increases East and y increases North.

Step 1 — 15 m North: position moves to (0, 15). Step 2 — 10 m West: position moves to (−10, 15). Step 3 — 5 m South: position moves to (−10, 10). Step 4 — 10 m East: position moves to (0, 10).

The final position is (0, 10). Relative to the starting point (0, 0), the x-coordinate is unchanged (net East-West displacement = 0) and the y-coordinate is +10, meaning the person is 10 m directly to the North of the house. Answer: A (North).

Explanation

Starting from the South direction, each right turn represents a 90° clockwise rotation.

First right turn: From South, rotating 90° clockwise leads to the West direction. Second right turn: From West, rotating 90° clockwise leads to the North direction. Third right turn: From North, rotating 90° clockwise leads to the East direction.

This sequence of three consecutive right turns successfully changes the direction from South to East.

Explanation

The letters represent unique integers from 1 to 9. We are given that P = 4.

The difference between P and T is 5, which is represented as |P - T| = 5. Substituting P = 4 gives |4 - T| = 5. This yields two possible values: T = 4 + 5 = 9 T = 4 - 5 = -1

Since the integers must be between 1 and 9, T must be 9.

The difference between N and T is 3, which is represented as |N - T| = 3. Substituting T = 9 gives |N - 9| = 3. This yields two possible values: N = 9 - 3 = 6 N = 9 + 3 = 12

Since the integers must be between 1 and 9, N must be 6.

Explanation

Communication is a fundamental soft skill. Soft skills represent interpersonal, character-based, and non-technical abilities that govern how an individual interacts and works with others. Effective communication, which includes speaking, active listening, presentation, and writing, is essential for building professional relationships, collaborating within teams, and resolving conflicts in any workplace environment.

Explanation

To apply for leave, a formal written record is required so that the request is documented and can be processed through official channels. Among the four options: a Poster is a public mass-communication tool used for announcements, not private formal requests; a Blog is a public online publishing medium unsuitable for official workplace communication; a Newsletter is a periodic publication for distributing information to a group, not for individual formal requests. E-mail is the standard, widely accepted medium for formal workplace communication — it allows a direct, dated, written request to the relevant authority (e.g., supervisor or HR), creates a verifiable paper trail, and is appropriate for formal procedures such as leave applications. Answer: D (E-mail).

Explanation

An upright body posture, characterized by standing or sitting straight with the shoulders back and the head held high, is a primary form of non-verbal communication that conveys confidence. Keeping the spine straight and shoulders relaxed indicates self-assurance, readiness, and attentiveness, which helps project a positive and secure image during interpersonal interactions.

Explanation

Impersonal communication occurs when we interact with others based on their roles, functions, or as mere instruments to accomplish a task, rather than as unique individuals. This type of communication is mechanical and lacks personal warmth, depth, or emotional connection. It happens when people are treated like objects or things, such as in routine transactions where the parties only interact to fulfill a specific, non-personal purpose.

Explanation

The passage explicitly states that the maximum losses suffered by these pesticide formulation units are through poor housekeeping, sub-optimal operating practices, and a lack of proper opportunities for recycling waste. The given inference claims that poor housekeeping is not reflected due to maximum losses, which directly contradicts the facts provided in the text. Since the inference is in direct opposition to the stated facts, it is definitely false.

Explanation

The passage explicitly states that the maximum losses suffered by smaller pesticide formulation units are due to poor housekeeping, sub-optimal operating practices, and a lack of proper opportunities for recycling waste. It further emphasizes the need to reduce or eliminate these losses through innovative and sustainable waste minimization techniques. Since the lack of waste recycling is a primary cause of their maximum losses, adopting modern recycling techniques will directly address this major issue and offset a large part of the losses they incur. This makes the inference definitely true based on the provided information.

Explanation

The passage highlights that smaller pesticide formulation units operate under heavy constraints, specifically pointing out that their small scale of operation and low operating profit margins leave them vulnerable to minor adverse conditions. This strongly suggests that scale is a major factor limiting their financial health. While the passage also mentions that smaller units can reduce losses through waste minimization and better housekeeping, a larger scale of operation would likely provide the necessary economies of scale and resources to remain economically viable. Thus, the inference that pesticide units should be on a large scale to be economically viable is highly likely and probably true, though not definitively the only solution.

Explanation

The inference to evaluate is: 'Waste management process in India needs modernization.'

The passage states that smaller pesticide formulation units in India operate under heavy constraints including 'obsolete technology' and 'lack of proper opportunities for recycling waste.' It further states that losses should be reduced 'through innovative and sustainable waste minimization techniques.' These statements directly and explicitly indicate that current waste management practices rely on outdated technology and insufficient recycling mechanisms, and that newer, innovative approaches are needed.

Because the passage itself explicitly cites obsolete technology and the absence of modern recycling opportunities as core problems — and calls for innovative, sustainable techniques — the inference that the waste management process needs modernization is not merely probable but is definitively established by the passage. The inference is therefore 'definitely true.' Answer: A.

Explanation

The passage highlights that smaller pesticide formulation units operate under heavy constraints and have very low operating profit margins, which makes them highly vulnerable to even minor adverse conditions. It also states that these units suffer maximum losses through poor housekeeping. Since these units are in a severely constrained financial position, it is highly probable that a lack of funds leads to the neglect of housekeeping, as they cannot allocate sufficient resources to maintain it. However, because the text does not explicitly state this direct causal link, the inference is probably true rather than definitely true.