HPAS Prelims 2013 CSAT (Paper II) with Answers & Explanations

Explanation

The passage highlights that post-graduate instruction in regional languages often constricts the range of literature available to students, thereby diluting the content of education. To resolve these impediments and ensure access to advanced academic literature, the author supports the approach where education is facilitated through a library language, specifically mentioning English as a library language to ensure students have no difficulties of comprehension while engaging with advanced global resources.

Explanation

The passage directly states that when the range of literature a student is exposed to at the post-graduate level is constricted by regional language barriers, the content of education gets diluted. Since this dilution of content directly impacts the quality of education, the intervention of regional voices demanding regional mediums of instruction has a diluting effect on the quality of higher education.

Explanation

The author presents a detailed evaluation of how regionalism affects higher education in India. Through a structured argument, the text examines the educational implications of transitioning the medium of instruction at the post-graduate level to regional languages. It highlights critical challenges such as the scarcity of advanced academic literature in local languages, the consequent dilution of academic standards, and the cascading effect of this dilution on future generations of teachers. The author also assesses the proposed solution of teaching English as a library language, analyzing its practical viability. This balanced and objective evaluation of the issues, causes, and consequences constitutes a thorough critical analysis of the situation.

Explanation

The passage highlights that the medium of instruction at the post-graduate level must be chosen with great care because any dilution in the quality of education at this stage has far-reaching consequences. The students who receive post-graduate education are the ones who subsequently become teachers for future generations. If their education is compromised due to a poorly chosen medium of instruction, the resulting deficiencies will be passed on to their students, creating a long-lasting and damaging cycle across succeeding generations.

Explanation

The passage explains that teaching a "library language" like English helps students access advanced literature in higher education. It states that this approach is highly beneficial and unobjectionable if the library language is taught intensively from an early stage of schooling. Introducing the language early ensures that students develop strong comprehension skills, enabling them to reap the maximum benefits of higher education without facing language barriers at later stages.

Explanation

The passage highlights a paradigm shift in how we perceive the natural world. It begins by describing the long-held, conditioning beliefs that viewed evolution solely as a ruthless struggle for existence and a gladiator's show. It then presents modern evidence showing that cooperation and mutual aid are actually the most crucial factors in the survival and evolution of species from protozoa to human beings. By contrasting the outdated competitive clichés with this new cooperative understanding, the passage invites the reader to look at the process of evolution from a new, updated perspective. Therefore, understanding evolution afresh is the most fitting title.

Explanation

The passage draws a clear distinction between "the struggle for life" and "the struggle for the life of others". By contrasting these two concepts, the author implies that the traditional term "struggle for life" refers to an organism's struggle for its own individual survival.

Explanation

According to the passage, our belief in our babies has been destroyed by the general Freudian atmosphere, which supports the old idea of the original sin. The concept of original sin is equivalent to the primordial idea that man is born a sinner, which portrays even infants as being possessed by jealousy and hate.

Explanation

The author of the passage questions and challenges the classical nineteenth-century biological theories of evolution that emphasize the struggle for existence and the survival of the fittest. By highlighting modern evidence which shows that cooperation and mutual aid are the most important factors in the survival of animal groups, the author expresses a doubting attitude toward the traditional competitive model of evolution.

Explanation

The passage highlights how traditional evolutionary concepts such as the struggle for existence and the survival of the fittest have historically dominated human thinking, leading to the belief that conflict and competition are inevitable. It presents contemporary scientific evidence showing that cooperation and mutual aid are far more crucial to the survival and evolution of species from protozoa to humans. By challenging these established biological clichés and emphasizing co-operation over competition, the author actively calls for a reassessment of the dominant, older scientific views on evolution.

Explanation

The word perceptive means having or showing keen insight, understanding, and intuition, which is an essential trait for an administrator to understand complex situations. The word sagacity refers to the quality of having or showing keen mental discernment, sound judgment, and wisdom. In this context, having the sagacity to know when to do a particular thing perfectly describes the timely decision-making and wisdom required of a good administrator.

Explanation

The word ventured fits the first blank as it represents the cautious step of embarking on a significant and revered task, which is imparting knowledge to disciples. The word profound is the most suitable adjective to collocate with import, referring to matters of deep, immense, and sacred significance, aligning with the ancient teachers requiring strict discipline beforehand.

Explanation

The word borders refers to the dividing lines or separations between different academic disciplines or fields of study. In scientific research, traditional divisions between separate fields like physics, chemistry, and biology are not rigid; they frequently overlap to form interdisciplinary areas of study. Thus, these borders are constantly—meaning continuously and without interruption—being dissolved or broken to foster collaborative discoveries. This combination of words accurately conveys the evolving, integrated, and dynamic nature of contemporary scientific inquiry.

Explanation

The sentence describes drawing a realistic picture where any pessimism that arises is naturally built-in or a fundamental part of the current state of affairs, making inherent the most appropriate word for the first blank. Since pessimism is a negative condition, the responsibility lies with us to amend, improve, or put the situation right, which is precisely defined by the action to rectify it.

Explanation

The sentence discusses the production of electricity or energy from atomic disintegration, which is standardly referred to as the generation of power. Additionally, nuclear fission is a physical occurrence scientifically classified as a phenomenon. Since the singular verb was is used at the end of the sentence, the singular noun phenomenon is grammatically correct to complete the clause.

Explanation

An obsessive concern with perfection is a behavioral trait associated with perfectionism, micro-management, or obsessive-compulsive tendencies. While it can cause operational stress and inefficiencies within an organization, it is a task-oriented dysfunction rather than one of the ego-driven, manipulative, and self-serving behaviors that characterize the dark side of charismatic leadership.

Explanation

In social psychology, attitude similarity is defined as the degree to which two individuals share the same attitudes, beliefs, values, or interests across various topics. This concept is a major predictor of interpersonal attraction, as sharing similar viewpoints provides validation for an individual's own beliefs, reduces the likelihood of conflict, and fosters smoother communication and mutual liking.

Explanation

Terror management theory is a social psychology framework that posits that the unique human awareness of the inevitability of death creates a potential for overwhelming existential terror. To manage this deep anxiety, individuals rely on cultural worldviews and self-esteem, which provide a sense of personal value, order, and symbolic or literal immortality, thereby buffering the psychological dread associated with mortality.

Explanation

In adult attachment theory, individuals with a secure attachment style have a positive view of both themselves and others. Ravi exhibits respect for himself, which represents high self-esteem and a positive self-model. Simultaneously, his belief in the competence of others and his willingness to trust and be trusted reflect a positive model of others. This combination of self-confidence and interpersonal trust allows him to form stable, healthy, and cooperative relationships in the workplace.

Explanation

Power represents the capacity to control, direct, or influence the behavior of others and the allocation of resources. In behavioral psychology, an individual with a high need for power seeks dominance, authority, and comprehensive oversight of information flow. Hari's lack of personal concern for his peers, combined with his desire to monitor their resources, activities, and participation, demonstrates a drive to establish dominance and authority through the control of information and resources.

Explanation

The cognitive component of an attitude represents the beliefs, knowledge, thoughts, and opinions held by an individual about an attitude object. The statement "Punjabi food is the best of Asian Cuisine" represents a subjective belief, judgment, or cognitive evaluation regarding the attribute and quality of the cuisine, which constitutes the cognitive dimension of the attitude.

Explanation

Including significant issues, unresolved problems, or negative complications in a persuasive communication message creates cognitive dissonance, confusion, and skepticism among the audience. For effective persuasion and successful technology adoption, the communication must be clear, simple, and focused on relative advantages and solutions rather than highlighting barriers. Presenting significant issues directly undermines the message's appeal and decreases the audience's confidence, hindering the adoption of the new technology.

Explanation

Problem-focused coping involves taking direct, active steps to manage, alter, or eliminate the underlying source of stress. Rather than merely addressing the emotional distress generated by a stressful situation, an individual utilizing this coping mechanism focuses on altering the external environment or the stressor itself, thereby resolving the problem at its root.

Explanation

Negotiation is a process of dialogue where parties with differing views exchange ideas, put forth proposals, make counter-offers, and offer mutual concessions to resolve a conflict or reach a mutually acceptable agreement. This exchange can take place directly between the concerned individuals or through their designated representatives.

Explanation

Attachment styles refer to the systematic patterns of expectations, needs, and behaviors that individuals develop in the context of close relationships, which are initially shaped during infancy through interactions with primary caregivers. Formulated by John Bowlby and Mary Ainsworth, attachment theory posits that the responsiveness and sensitivity of a caregiver teach an infant whether they are worthy of love and whether other people are reliable and trustworthy. These early experiences form internal working models—cognitive frameworks comprising mental representations for understanding the self and others—that establish the foundation for self-worth, a sense of security, and interpersonal trust, persisting throughout the lifespan into adult relationships.

Explanation

The implicit bystander effect is a social psychological phenomenon where the activation of a group setting or the presence of a social circle diminishes an individual's likelihood of taking action to help. Even though Nikhil is fundamentally a helpful person, being in the presence of his close group of friends triggers a subconscious diffusion of responsibility. The social context of the group implicitly suppresses his individual altruistic impulses and personal accountability, leading to passive behavior and a failure to initiate assistance for the accident victim.

Explanation

The Focus Theory of Normative Conduct, often referred to as normative focus theory, was developed by Robert Cialdini, Raymond Reno, and Carl Kallgren in 1990. The theory suggests that social norms do not influence human behavior constantly or universally. Instead, they direct behavior primarily when they are salient, prominent, or focal in the consciousness of an individual at the exact moment of decision-making. If a norm is not activated or brought to attention at the time of the action, its influence on behavior remains negligible. This makes situational cues and attention-focusing mechanisms critical for motivating norm-consistent actions, such as litter reduction or recycling.

Explanation

Pluralistic ignorance is a social psychological phenomenon wherein individuals in a group privately reject a particular norm, belief, or attitude but falsely assume that everyone else in the group accepts it. Consequently, people conform to the perceived norm under the mistaken belief that their own private attitude is different from the majority. This collective misinterpretation leads people to hide their true attitudes, reinforcing the illusion of a unanimous group consensus that does not actually exist.

Explanation

In social psychology, the situation describes the black-sheep effect, where group members evaluate a deviant in-group member more harshly than an out-group member exhibiting the same behavior. Sanjay acts as a deviant whose negative behavior threatens the positive social identity and reputation of his group. To protect and preserve their collective identity, the other members distance themselves from his actions by expressing strong disapproval and passing derogatory remarks, defining his position within the group as that of a black-sheep.

Explanation

Distributive justice refers to the perceived fairness of the allocation of outcomes and rewards within a group or social relationship. Rooted in equity theory, it occurs when individuals evaluate whether the benefits they receive are proportionate to the inputs and contributions they have made, such as effort, time, and skill, compared to others. When people perceive that their share of rewards matches their relative contribution, they experience a sense of distributive justice.

Explanation

Persuasion is a process of communication through which an individual attempts to influence and change the attitudes, beliefs, values, or behaviors of another person. It involves presenting targeted messages, arguments, reasoning, or emotional appeals designed to convince the receiver to voluntarily adopt the communicator's perspective. When Shankar uses different types of messages and arguments to alter Piyush's mindset, he is employing persuasive communication to achieve attitude change.

Explanation

Social influence is driven by two primary human motivations: the desire to be accurate and the desire to be socially accepted. The fundamental assumption is that people expect a shared objective reality, assuming that others perceive the world as it is. When an individual's perception differs from the consensus, they experience cognitive conflict, fearing that they are either incorrect or will face social disapproval and appear foolish. Consequently, they conform to the perceptions of others to align their view of the world with the collective and to avoid the social cost of deviance.

Explanation

Internalization is the deepest level of conformity, occurring when an individual is genuinely persuaded by a group's position and adopts their beliefs or behaviors both publicly and privately. This process involves a true cognitive reorganization where the individual integrates the new views into their personal belief system because they perceive them to be intrinsically rewarding, logical, and correct. This results in a permanent and independent change in attitude that persists even when the group is no longer present.

Explanation

Pluralistic ignorance is a social psychological phenomenon where individuals in a group privately hold one belief or attitude but incorrectly assume that the rest of the group holds a different one. Because of this incorrect assumption, individuals conform to the perceived majority norm in their public behavior. Consequently, everyone in the group misinterprets the public behavior of others as a reflection of their true private beliefs, and then uses that misinterpretation as evidence to conclude what must be true.

A classic example occurs in emergency situations where a bystander is unsure if help is needed. The bystander looks at other onlookers to gauge the severity of the event. Since everyone else is also holding back to avoid looking foolish, the bystander misinterprets their outward calm as evidence that the situation is not an emergency, thereby confirming a false reality.

Explanation

Egocentric bias is a cognitive bias in which individuals rely heavily on their own perspective, experiences, and behaviors to interpret the world. One prominent manifestation of egocentric bias is the false consensus effect, wherein people overestimate the typicality, commonness, and prevalence of their own beliefs, opinions, and behaviors. This occurs because individuals naturally use their own responses as a primary reference point, assuming that others would act and think in the same manner under similar circumstances.

Explanation

Alternating +5/−7 pattern gives the 6th term as 72 (71→76→69→74→67→72), but 72 is absent from all four options — this is an exam printing error. No listed option is mathematically correct; A is retained as the original exam key answer.

Explanation

The series follows a pattern where each term is calculated by multiplying the preceding term by 2 and then subtracting 2. This relation can be represented by the formula Tₙ = 2 × Tₙ₋₁ - 2.

Applying this formula to each successive term: First term = 8 Second term = 2 × 8 - 2 = 14 Third term = 2 × 14 - 2 = 26 Fourth term = 2 × 26 - 2 = 50

The fourth term is given as 48 instead of 50, which makes it the incorrect term. If we continue the pattern with the correct term 50: Fifth term = 2 × 50 - 2 = 98 Sixth term = 2 × 98 - 2 = 194 Seventh term = 2 × 194 - 2 = 386

Explanation

The pattern of the series is determined by adding 15 to the alphabetical position of each letter in the previous term, using modulo 26 arithmetic.

By mapping the letters to their numerical positions in the alphabet (A = 1, B = 2, ..., Z = 26):

For the first letter of each term: e (5) + 15 = 20 (t) t (20) + 15 = 35 ≡ 9 (i) i (9) + 15 = 24 (x) x (24) + 15 = 39 ≡ 13 (m)

For the second letter of each term: j (10) + 15 = 25 (y) y (25) + 15 = 40 ≡ 14 (n) n (14) + 15 = 29 ≡ 3 (c) c (3) + 15 = 18 (r)

For the third letter of each term: o (15) + 15 = 30 ≡ 4 (d) d (4) + 15 = 19 (s) s (19) + 15 = 34 ≡ 8 (h) h (8) + 15 = 23 (w)

Combining these results gives the next term in the series as mrw.

Explanation

Marie Curie discovered and isolated the radioactive element radium. Similarly, the Polish biochemist Casimir Funk discovered and coined the term vitamins, establishing the vital connection between these essential organic compounds and the prevention of deficiency diseases.

Explanation

The waxy cuticle serves as the outer protective covering on the leaves of a lotus, preventing them from water logging and decay in an aquatic environment. Similarly, scales form the outer protective covering on the body of a fish, protecting its skin and internal organs while aiding its survival in water. Both represent the primary protective outer layer of the respective aquatic organisms.

Explanation

Sitar, Guitar, and Tanpura are all classified as stringed instruments, also known as chordophones, which produce sound through the vibration of stretched strings. The violin is similarly a stringed instrument that generates sound from vibrating strings, placing it in the same category of musical instruments.

Explanation

Weevils, borers, and beetles are all destructive insect pests that tunnel into, feed on, and damage wood, crops, and stored agricultural products. Termites share this exact characteristic, as they are wood-boring social insect pests notorious for destroying timber, wooden structures, and agricultural plants by feeding on cellulose.

Explanation

The coding scheme shifts each letter of the word forward by 4 positions in the alphabetical sequence.

Applying this logic to CASUAL: C + 4 = G A + 4 = E S + 4 = W U + 4 = Y A + 4 = E L + 4 = P

By applying the same shift of +4 to each letter of PEOPLE: P + 4 = T E + 4 = I O + 4 = S P + 4 = T L + 4 = P E + 4 = I

This yields the coded word TISTPI.

Explanation

In the given coding scheme, each letter of the original word is shifted one position forward in the alphabetical sequence to generate the code. For example, in POPULAR, P becomes Q, O becomes P, P becomes Q, U becomes V, L becomes M, A becomes B, and R becomes S.

To find the word that corresponds to the code GBNPVT, we apply the reverse logic by shifting each letter of the code one position backward in the alphabetical sequence.

G shifted one position backward is F B shifted one position backward is A N shifted one position backward is M P shifted one position backward is O V shifted one position backward is U T shifted one position backward is S

Combining these letters yields the word FAMOUS.

Explanation

The code for CRAPE is obtained by direct letter-to-digit mapping from the words ROPE and CHAIR:

C is coded as 7 (from CHAIR) R is coded as 6 (from ROPE and CHAIR) A is coded as 4 (from CHAIR) P is coded as 2 (from ROPE) E is coded as 1 (from ROPE)

Combining these digits in order gives 76421.

Explanation

A farmer draws water from a well. According to the given coding rules, a well is called an island. Therefore, in this code language, the farmer will draw water from an island.

Explanation

The total number of females in the family is determined by counting each female category:

The grandmother represents 1 female. The mother represents 1 female. The wives of the four sons represent 4 females. The daughters of the four sons, with 2 daughters for each of the 4 sons, represent 4 × 2 = 8 females.

Summing these values gives the total number of females: 1 + 1 + 4 + 8 = 14 females.

Explanation

Neelam is the daughter of Deepak, which means Neelam's father is Deepak. Since Deepak is the third child of Ramlal, Ramlal is the parent of Deepak. Rekha, who is the younger sister of Deepak, is also a child of Ramlal. Given that Rekha is the mother of Deepika, Ramlal is the parent of Deepika's mother. This makes Ramlal the grandfather of Deepika.

Explanation

The pinna is the visible, external part of the ear, which is made of elastic cartilage and skin rather than bone. This makes it structurally distinct as a cartilaginous feature, whereas the other elements are bones of the human skeleton.

Explanation

Simmer is the odd one out because it refers to the state of heating or cooking liquid just below the boiling point, which relates to temperature and heat rather than light or shining.

Explanation

Since S is ranked sixth, the scenario where R scores the highest (first) and T gets the lowest (seventh) must be active.

We are given that Q is ranked fifth. We also know that V always scores more than P, and P always scores more than Q (V > P > Q). Since Q is fifth, V and P must occupy two of the remaining positions among the second, third, and fourth ranks (since first is R, and sixth and seventh are S and T).

This leaves the fifth, sixth, and seventh ranks occupied by Q, S, and T respectively, and the first rank occupied by R. The remaining three ranks (second, third, and fourth) must be shared among V, P, and U.

Since V must score higher than P, the possible assignments for the second, third, and fourth ranks are: V is second, P is third, and U is fourth V is second, P is fourth, and U is third V is third, P is fourth, and U is second

In these valid scenarios, U can be ranked second, third, or fourth. Therefore, it is possible for U to be ranked third or fourth.

Explanation

When R scores the highest, it is ranked 1st. Based on the given rules, if R gets the highest marks, T must get the lowest marks, placing T at 7th.

We are given the relative ranking condition V > P > Q. This means there must be at least two students, P and Q, ranked below V.

If we try to place V at the 5th rank, the only ranks below V are 6th and 7th. Since T already occupies the 7th rank, there is only one rank (6th) available below V. This makes it impossible to place both P and Q below V.

Thus, V can be ranked no lower than 4th. When V is 4th, P can be 5th, and Q can be 6th, which satisfies all the conditions. Therefore, V should be ranked not lower than Fourth.

Explanation

Since R is ranked second, the scenario where R scores highest and T lowest is not possible. Thus, the alternative scenario must hold: S is ranked first and either U or Q is ranked seventh. Since Q is ranked fifth, U must be ranked seventh.

The positions determined so far are S (first), R (second), Q (fifth), and U (seventh). This leaves the third, fourth, and sixth ranks vacant for V, P, and T. Since V and P always score higher than Q, they must occupy the vacant ranks higher than fifth, which are the third and fourth ranks. Since V scores higher than P, V must be third and P must be fourth. The remaining student, T, must therefore occupy the sixth rank.

Explanation

When S is ranked second, the alternate case where S scores the highest cannot be true. Therefore, the case where R scores the highest (1st rank) and T gets the lowest (7th rank) must apply.

With R in 1st place, S in 2nd place, and T in 7th place, the remaining ranks of 3rd, 4th, 5th, and 6th must be shared among U, V, P, and Q. Since V must always score more than P, and P must score more than Q, we must maintain the order V > P > Q.

We can satisfy all conditions by placing U in 3rd place, V in 4th place, P in 5th place, and Q in 6th place. In this valid ranking order, U (3rd) gets more than V (4th).

Explanation

We are given the ranking order V > P > Q.

If V is ranked fifth, the only available ranks lower than fifth are sixth and seventh. Since P must score higher than Q, P must be ranked sixth and Q must be ranked seventh.

There are two possible scenarios for the highest and lowest ranks: First scenario: R is highest and T is lowest. This is impossible here because Q is already lowest. Second scenario: S is highest and either U or Q is lowest. Since Q is indeed the lowest, this scenario must occur, which means S must score the highest.

Explanation

The first statement establishes that Manas belongs to the category of players. The second statement asserts that the entire group of players is contained within the category of tall people. Since Manas is a player, and every single player is tall, it logically follows that Manas must be tall.

Explanation

The second statement is a particular affirmative proposition (Some mammals are vertebrates). In formal logic, any proposition of the form "Some A are B" can be directly converted to "Some B are A". Therefore, the statement "Some mammals are vertebrates" immediately and logically implies its converse, "Some vertebrates are mammals." This makes the conclusion valid based on the second statement alone.

Explanation

Based on the rules of syllogism and set theory, the given statements can be represented as:

All men are dishonest: This means the set of Men (M) is a subset of the set of Dishonest persons (D), or M ⊆ D. Some men are fraudulent: This means the intersection of the set of Men (M) and the set of Fraudulent persons (F) is non-empty, or M ∩ F ≠ ∅.

Since M ∩ F is non-empty, there exists at least one individual x who is both a man and fraudulent (x ∈ M and x ∈ F).

Because all men are dishonest (M ⊆ D), this individual x must also be dishonest (x ∈ D). Thus, x is both dishonest and fraudulent, meaning the intersection of dishonest persons and fraudulent persons is non-empty (D ∩ F ≠ ∅).

From this, two direct logical deductions follow: Some dishonest persons are fraudulent (which represents the intended meaning of option d, where the second instance of the word dishonest is a typographical variation of fraudulent). Some fraudulent persons are dishonest.

Furthermore, because the existence of dishonest persons is established, the statement "Some dishonest persons are dishonest" is a trivially true logical tautology. Therefore, option d logically follows under both the literal interpretation and the corrected logical translation of the term.

Explanation

According to the rules of formal logic and the Square of Opposition, the statement "Some teachers are not learned" is a particular negative (O) proposition.

When an O-proposition is false, its contradictory, which is the universal affirmative (A) proposition "All teachers are learned", must be true.

Since "All teachers are learned" is true, the particular affirmative (I) proposition "Some teachers are learned" is also true by subalternation.

By conversion of this true particular affirmative proposition, "Some learned beings are teachers" must also be true.

A universal affirmative proposition "All S are P" cannot be simply converted to "All P are S". Therefore, the statement "All learned beings are teachers" does not logically follow and is false.

Explanation

To find the country that lost the most number of matches, we can count the number of losses for each country based on the given information:

When India defeated Australia twice, Australia registered 2 losses.

When West Indies defeated India twice, India registered 2 losses.

When Australia defeated West Indies twice, West Indies registered 2 losses.

When India defeated West Indies and New Zealand twice each, West Indies registered 2 losses and New Zealand registered 2 losses.

Summing up the losses for each country: India: 2 losses Australia: 2 losses New Zealand: 2 losses West Indies: 2 + 2 = 4 losses

West Indies lost the highest number of matches.

Explanation

The four vocalists are Jalaja, Vanaja, Shailaja, and Tanuja. We are given that two of these vocalists are also violinists. Since Jalaja and Shailaja do not play the violin, the two vocalists who play the violin must be Vanaja and Tanuja. Furthermore, the problem states that Shailaja and Tanuja are among the dancers. Since Tanuja is a dancer and has been established as a violinist, she is both a dancer and a violinist.

Explanation

Let the birth year of Kadambari be 1915.

Since Kadambari is older than Kalyani by 5 years, Kalyani is younger than Kadambari by 5 years. Therefore, Kalyani was born 5 years after Kadambari: Birth year of Kalyani = 1915 + 5 = 1920

Kamayani is younger than Kalyani by 5 years, which means Kamayani was born 5 years after Kalyani: Birth year of Kamayani = 1920 + 5 = 1925

Kumud is younger than Kalyani (or Kadambari) by 5 years. If Kumud is younger than Kalyani, her birth year is 1925. If she is younger than Kadambari, her birth year is 1920.

In either case, the youngest sister (the person with the latest birth year) was born in 1925.

Explanation

Replacing the mathematical operators in the given expression as per the instructions: × becomes +

• becomes ÷ becomes × ÷ becomes -

The original expression: 40 × 12 + 3 - 6 ÷ 60

After substitution, the expression becomes: 40 + 12 ÷ 3 × 6 - 60

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

First, perform the division: 12 ÷ 3 = 4 The expression becomes: 40 + 4 × 6 - 60

Next, perform the multiplication: 4 × 6 = 24 The expression becomes: 40 + 24 - 60

Next, perform the addition: 40 + 24 = 64 The expression becomes: 64 - 60

Finally, perform the subtraction: 64 - 60 = 4

Explanation

According to the rules of mathematical operations, the signs are substituted as follows:

• is replaced by ÷ ÷ is replaced by - is replaced by × × is replaced by +

Substituting these signs into the given expression: 48 + 16 ÷ 4 - 2 × 8

We get: 48 ÷ 16 - 4 × 2 + 8

Applying the BODMAS rule (Division, Multiplication, Addition, Subtraction): First, perform the division: 48 ÷ 16 = 3

Next, perform the multiplication: 4 × 2 = 8

Substitute these results back into the expression: 3 - 8 + 8 = 3

Explanation

According to the given definition, the mathematical operators are substituted as follows: × is replaced by + is replaced by ÷ ÷ is replaced by ×

Substituting these values into the given expression: 3 × 6 - 12 × 1 - 2 ÷ 3

We get: 3 + 6 ÷ 12 + 1 ÷ 2 × 3

Applying the BODMAS rule, division and multiplication are solved first from left to right: 6 ÷ 12 = ½ 1 ÷ 2 = ½

Now substitute these values back into the expression: 3 + ½ + ½ × 3

Next, perform the multiplication: ½ × 3 = 1.5

The expression becomes: 3 + 0.5 + 1.5

Finally, perform the addition: 3 + 0.5 + 1.5 = 5

Explanation

The total amount of ₹2,800 is divided in the ratio of 5:6:3.

The sum of the ratio terms is 5 + 6 + 3 = 14.

The value of each ratio unit is 2800 / 14 = 200.

The initial shares of Amit, Sumit, and Vinit are: Amit's share = 5 × 200 = 1000 Sumit's share = 6 × 200 = 1200 Vinit's share = 3 × 200 = 600

Adding ₹200 to each of their shares gives: Amit's new share = 1000 + 200 = 1200 Sumit's new share = 1200 + 200 = 1400 Vinit's new share = 600 + 200 = 800

The new ratio of their shares is 1200 : 1400 : 800. Dividing each term by 200 simplifies the ratio to 6:7:4.

Explanation

The numbers between 100 and 1000 are 3-digit numbers. A 3-digit number has three positions to be filled: the hundreds place, the tens place, and the units place.

Since each digit can only be either 2 or 9, there are exactly 2 choices for each of the three positions. Using the fundamental multiplication principle of counting, the total number of such 3-digit numbers is:

2 × 2 × 2 = 2³ = 8

These 8 numbers are 222, 229, 292, 299, 922, 929, 992, and 999, all of which lie strictly within the range of 100 and 1000.

Explanation

Sum of monthly incomes of Deepa and Sandhya = 2 × 25,000 = 50,000.

Given the ratio of their incomes is 7:3, Deepa's monthly income is: Deepa's income = (7 / (7 + 3)) × 50,000 = (7 / 10) × 50,000 = 35,000.

Supriya's monthly income is twice Deepa's monthly income: Supriya's income = 2 × 35,000 = 70,000.

Since Rs. 70,000 is not listed in the other options, the correct choice is None of the above.

Explanation

In a race of 600 m, when A covers 600 m, B covers 550 m. Ratio of speeds A : B = 600 / 550 = 12 / 11

In a race of 500 m, when B covers 500 m, C covers 440 m. Ratio of speeds B : C = 500 / 440 = 25 / 22

To find the ratio of speeds of A and C: A / C = (A / B) × (B / C) = (12 / 11) × (25 / 22) = 300 / 242 = 150 / 121

In a race of 400 m, when A covers 400 m, C covers x m. 150 / 121 = 400 / x x = (400 × 121) / 150 = 968 / 3 = 322⅔ m

The distance by which A beats C is: 400 - 322⅔ = 77⅓ m

Explanation

The rate of work of an individual is the total work done divided by the total time taken.

X's rate of copying = 80 pages / 20 hours = 4 pages per hour

Combined rate of X and Y copying together = 135 pages / 27 hours = 5 pages per hour

Y's rate of copying = Combined rate - X's rate = 5 pages per hour - 4 pages per hour = 1 page per hour

Time required for Y to copy 20 pages = Total pages / Y's rate = 20 pages / 1 page per hour = 20 hours

Explanation

Average Cost = (Total Cost) / (Total Quantity)

Total cost of the mixture = (5 kg × Rs. 8) + (3 kg × Rs. 6) = Rs. 40 + Rs. 18 = Rs. 58

Total quantity of the mixture = 5 kg + 3 kg = 8 kg

Average cost of the mixture = Rs. 58 / 8 = Rs. 7.25 per kg

Explanation

In a parallelogram, any two adjacent angles are supplementary, meaning their sum is 180°.

Let the given angle be A = 26°. Its adjacent angle B is calculated as: B = 180° - 26° = 154°

The difference between these two adjacent angles is: B - A = 154° - 26° = 128°

Explanation

The perimeter of a rectangle is given by the formula: P = 2(l + b)

Let the length (l) and breadth (b) of the rectangular plot be 7x and 6x respectively.

Substituting these values into the perimeter formula: 208 = 2(7x + 6x) 208 = 26x x = 8

Using the value of x, the dimensions of the rectangular plot are: l = 7 × 8 = 56 meters b = 6 × 8 = 48 meters

The area (A) of a rectangle is given by the formula: A = l × b

Substituting the dimensions: A = 56 × 48 = 2688 sq. m

Explanation

The total number of possible outcomes when selecting an integer from 1 to 100 is 100.

The number of integers between 1 and 100 that are divisible by 7 is determined by dividing 100 by 7 and taking the integer part of the quotient: n = floor(100 / 7) = 14

The probability of selecting a number divisible by 7 is: P = 14 / 100

The probability that the selected number is not divisible by 7 is the complement of this probability: P' = 1 - P = 1 - 14/100 = 86/100 = 43/50

Explanation

Let the two numbers be x and y, where x is the larger number and y is the smaller number.

According to the given conditions: x + y = 12 x - y = 6

Adding these two equations gives: 2x = 18 x = 9

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

The ratio of the smaller number to the larger number is: y/x = 3/9 = 1/3

Explanation

Using the standard relation for correcting a mean:

Correct Mean = Incorrect Mean + (Correct Value - Incorrect Value) / n

Substituting the given values, where the incorrect mean is 200, the correct value is 50, the incorrect value is 250, and the total number of observations (n) is 100:

Correct Mean = 200 + (50 - 250) / 100 Correct Mean = 200 - 200 / 100 Correct Mean = 200 - 2 Correct Mean = 198

Explanation

Let the present ages of the two persons be represented as 5x and 7x. After 14 years, their ages will be 5x + 14 and 7x + 14.

According to the given condition, the ratio of their ages after 14 years is 7 : 9. This gives the equation:

(5x + 14) / (7x + 14) = 7 / 9

By cross-multiplying, we get: 9 × (5x + 14) = 7 × (7x + 14) 45x + 126 = 49x + 98 49x - 45x = 126 - 98 4x = 28 x = 7

Substituting the value of x back into the expressions for their present ages: First person's age = 5 × 7 = 35 years Second person's age = 7 × 7 = 49 years

Alternatively, using the ratio method, the ratio changes from 5 : 7 to 7 : 9 over a span of 14 years. Since the difference in parts for both persons is 2 units (7 - 5 = 2 and 9 - 7 = 2), these 2 units directly correspond to 14 years. Thus, 1 unit equals 7 years. Multiplying the original ratio parts by 7 gives the present ages as 35 and 49 years.

Explanation

Let the number of coins of each type be x.

The total value of these coins is the sum of the values of the individual coin types: Value of 1 rupee coins = 1 × x = x rupees Value of 50 paise coins = 0.50 × x = 0.50x rupees Value of 25 paise coins = 0.25 × x = 0.25x rupees

Adding these values together gives the total amount: x + 0.50x + 0.25x = 70 1.75x = 70

Representing 1.75 as the fraction 7/4: 7/4 x = 70 x = 70 × 4 / 7 x = 10 × 4 x = 40

Explanation

To find the individual shares, we combine the given ratios: Son : Wife = 3 : 1 Wife : Daughter = 3 : 1

To make the share of the wife common in both ratios, we multiply the first ratio by 3: Son : Wife : Daughter = 9 : 3 : 1

Let the shares of the son, wife, and daughter be 9x, 3x, and x respectively. Total worth of the property = 9x + 3x + x = 13x

The difference between the son's share and the daughter's share is given as Rs. 20,000: 9x - x = 20,000 8x = 20,000 x = 2,500

Substituting the value of x to find the total worth of the property: Total worth = 13 × 2,500 = 32,500

Explanation

Using the principle of inclusion-exclusion for two sets, the total number of unique elements in the union of two sets J (Java programmers) and C (C++ programmers) is given by the formula:

n(J ∪ C) = n(J) + n(C) - n(J ∩ C)

Substitute the given values into the formula:

n(J) = 32 n(C) = 28 n(J ∩ C) = 15

n(J ∪ C) = 32 + 28 - 15 = 45

To satisfy the hiring requirements, the company must hire at least 45 engineers, consisting of 17 who work only on Java, 13 who work only on C++, and 15 who work on both.

Explanation

The mode (or modal size) of a dataset is the value that appears most frequently. Counting the frequency of each shirt size in the given list:

Size 85 appears 1 time. Size 90 appears 4 times. Size 95 appears 3 times. Size 100 appears 2 times. Size 105 appears 1 time. Size 110 appears 1 time. Size 115 appears 1 time.

Since the size 90 has the highest frequency of occurrence, it is the modal size.

Explanation

Given the equation: mⁿ = 144

Since m and n are whole numbers, we can express 144 as a power: 144 = 12²

Comparing mⁿ with 12² gives: m = 12 n = 2

The expression (m - 1)ⁿ⁺¹ represents: (12 - 1)²⁺¹ = 11³

Evaluating this power: 11³ = 11 × 11 × 11 = 1331

Explanation

Using the standard algebraic identity: (a + b)² + (a - b)² = 2(a² + b²)

By setting a = 49 and b = 21, the numerator of the expression simplifies directly: (49 + 21)² + (49 - 21)² = 2(49² + 21²)

Substituting this into the given equation: x = 2(49² + 21²) / (49² + 21²)

The term (49² + 21²) in the numerator and denominator cancels out, which simplifies the expression to: x = 2

Explanation

The even numbers from 1 to 200 form an arithmetic progression: 2, 4, 6, ..., 200.

The number of terms, n, in this sequence is 200 ÷ 2 = 100.

The sum of the first n even natural numbers is given by the formula: Sₙ = n(n + 1)

Substituting n = 100 into the formula yields: S₁₀₀ = 100 × (100 + 1) = 100 × 101 = 10100

Explanation

Let the original positive number be x.

The candidate was asked to find ⅞ of x, but calculated ⁷⁄₁₈ of x instead. The difference between these two values is 770:

(⅞)x − (⁷⁄₁₈)x = 770

Factoring out 7: 7 × (x/8 − x/18) = 770 x/8 − x/18 = 110

Finding a common denominator (LCM of 8 and 18 is 72): 9x/72 − 4x/72 = 110 5x/72 = 110

Solving for x: x = 110 × 72 / 5 x = 7920 / 5 x = 1584

The original number is 1584, which corresponds to option A.

Explanation

The mean (x̄) of a grouped frequency distribution is calculated using the formula:

x̄ = ∑(fᵢ × xᵢ) / ∑fᵢ

First, calculate the sum of the products of each value and its corresponding frequency:

∑(fᵢ × xᵢ) = (10 × 3) + (15 × 2) + (20 × 5) + (25 × 4) + (30 × 6) ∑(fᵢ × xᵢ) = 30 + 30 + 100 + 100 + 180 ∑(fᵢ × xᵢ) = 440

Next, find the total frequency:

∑fᵢ = 3 + 2 + 5 + 4 + 6 ∑fᵢ = 20

Substituting these values into the mean formula gives:

x̄ = 440 / 20 x̄ = 22

Explanation

For an even number of observations, n, arranged in ascending order, the median is calculated as the average of the (n/2)th and ((n/2) + 1)th terms:

Median = ((n/2)th term + ((n/2) + 1)th term) / 2

In the given data set of 10 observations, the 5th term is 34 and the 6th term is x. Substituting these values into the formula:

Median = (34 + x) / 2

Given that the median is 35:

35 = (34 + x) / 2

70 = 34 + x

x = 36

Explanation

Let the work rates of A, B, and C per day be A, B, and C respectively.

The given combined rates are: A + B = 1/12 B + C = 1/15 C + A = 1/20

Summing these equations: 2 × (A + B + C) = 1/12 + 1/15 + 1/20 2 × (A + B + C) = (5 + 4 + 3) / 60 2 × (A + B + C) = 12/60 = 1/5 A + B + C = 1/10

The individual rate of C is found by subtracting the rate of A and B from the total combined rate: C = (A + B + C) - (A + B) C = 1/10 - 1/12 C = (6 - 5) / 60 = 1/60

Since C's rate of work is 1/60 per day, the total time required for C to clean the shed alone is 60 days.

Explanation

To find where a line meets the y-axis, we substitute x = 0 into its equation, since every point on the y-axis has x-coordinate equal to zero.

For the first line 2x − y = 1, substituting x = 0: 2(0) − y = 1 −y = 1 y = −1 So the first line meets the y-axis at the point (0, −1).

For the second line x + 2y = 8, substituting x = 0: 0 + 2y = 8 2y = 8 y = 4 So the second line meets the y-axis at the point (0, 4).

The coordinates are (0, −1) and (0, 4) respectively, which corresponds to option C.

Explanation

To find the greatest four-digit number exactly divisible by 12, 15, 20, and 35, we first determine their Least Common Multiple (LCM).

The prime factorization of each number is: 12 = 2² × 3 15 = 3 × 5 20 = 2² × 5 35 = 5 × 7

LCM(12, 15, 20, 35) = 2² × 3 × 5 × 7 = 420

The greatest four-digit number is 9999. Dividing this number by 420: 9999 ÷ 420 = 23 with a remainder of 339

Subtracting the remainder from 9999 gives the greatest four-digit number that is a multiple of 420: 9999 − 339 = 9660

Explanation

Let the height of the vertical standing portion of the tree be h, and the length of the broken portion leaning against the ground be L.

These two portions, along with the ground, form a right-angled triangle. In this triangle, the base is the distance from the foot of the tree to where the top touches the ground, which is 10 meters. The angle of elevation is 45 degrees.

Using the tangent trigonometric ratio: tan(45°) = perpendicular / base = h / 10 Since tan(45°) = 1, we have: h = 10 meters

Using the cosine trigonometric ratio: cos(45°) = base / hypotenuse = 10 / L Since cos(45°) = 1 / √2, we have: 1 / √2 = 10 / L L = 10√2 meters

The entire length of the tree is the sum of the standing portion and the broken portion: Total height = h + L = 10 + 10√2 = 10(1 + √2) meters

Explanation

When two trains run in the same direction, their relative speed is the difference between their individual speeds.

Relative speed = 46 - 36 = 10 km/h

Converting the speed to meters per second: 10 × 5/18 = 25/9 m/s

Let the length of each train be L meters. The total distance covered when the faster train completely passes the slower train is the sum of their lengths: Total distance = L + L = 2L

Using the formula for distance: Distance = Speed × Time 2L = 25/9 × 36 2L = 25 × 4 2L = 100 L = 50 meters

Explanation

Initial quantity of milk is 30 × 7/10 = 21 litres, and the initial quantity of water is 30 × 3/10 = 9 litres.

Since only water is added to the mixture, the quantity of milk remains constant at 21 litres.

In the new mixture, the ratio of milk to water is 3 : 7. Since the milk portion represents 3 parts of the new ratio, we can equate 3 parts to 21 litres. This means 1 part equals 7 litres.

The new quantity of water represents 7 parts of the ratio, which equals 7 × 7 = 49 litres.

The amount of water to be added is the difference between the new water quantity and the initial water quantity, which is 49 - 9 = 40 litres.

Explanation

Let the cost price of the article be x. Since the profit percentage is numerically equal to the cost price, the profit percentage is x%.

Using the standard selling price formula: Selling Price = Cost Price × (1 + Profit Percentage / 100)

Substituting the given values into the formula: 39 = x × (1 + x/100) 39 = x + x²/100 3900 = 100x + x² x² + 100x - 3900 = 0

Factoring the quadratic equation: (x + 130)(x - 30) = 0

Since the cost price cannot be negative, we take the positive root: x = 30

Alternatively, testing the cost price of 30 directly gives a profit of 30% of 30, which is 9. Adding this profit to the cost price yields a selling price of 30 + 9 = 39, matching the given selling price.

Explanation

The plot is 10 m long and 5 m broad. A path ½ m wide is paved around the outside.

Step 1 — Find the area of the path. The outer rectangle (including the path) has dimensions: Length = 10 + 2 × ½ = 11 m Width = 5 + 2 × ½ = 6 m Outer area = 11 × 6 = 66 m²

Inner area (the plot itself) = 10 × 5 = 50 m²

Area of path = 66 − 50 = 16 m²

Step 2 — Convert to square centimetres. 16 m² = 16 × 10,000 cm² = 160,000 cm²

Step 3 — Find the area of one tile. Each tile has a side of 2.5 cm. Area of one tile = 2.5 × 2.5 = 6.25 cm²

Step 4 — Find the number of tiles. Number of tiles = 160,000 ÷ 6.25 = 25,600

The required number of tiles is 25,600, which corresponds to option B.

Explanation

To find the smallest perfect square divisible by 15, 18, and 25, we first determine their Least Common Multiple (LCM).

The prime factorization of the given numbers is: 15 = 3 × 5 18 = 2 × 3² 25 = 5²

The LCM is found by taking the highest power of each prime factor present: LCM = 2¹ × 3² × 5² = 450

For a number to be a perfect square, all exponents in its prime factorization must be even. In the prime factorization of 450, the prime factor 2 has an odd power of 1. To make it a perfect square, we multiply 450 by 2 to complete the pair: 450 × 2 = 900

900 is a perfect square (30²) and is the smallest such number divisible by 15, 18, and 25.