SSC CHSL Tier 1 2008 Question Paper with Answers & Explanations

Explanation

The analogy is based on the relationship between a profession and its primary tool. A mechanic uses a spanner as a tool to perform their tasks. Similarly, a carpenter uses a saw as a primary tool to cut wood and perform their tasks.

Explanation

The analogy compares animals to their primary respiratory organs. Since fish breathe through gills, humans (for which Min is a typographical error for Man) breathe through lungs.

Explanation

The relationship in this analogy is based on storage. Just as grains are stored and accumulated in a warehouse, water is collected and stored in a dam.

Explanation

The relationship in each group is based on opposite letter pairs (where the sum of the numerical positions of the two letters from the start and end of the alphabet is 27) and a forward shift.

In AZBY, the opposite pairs are A (1st) and Z (26th), and B (2nd) and Y (25th).

In CXDW, the opposite pairs are C (3rd) and X (24th), and D (4th) and W (23rd). The first letter shifts forward by two positions (A to C), and the third letter also shifts forward by two positions (B to D).

Applying the same logic to HSIR: The opposite pairs are H (8th) and S (19th), and I (9th) and R (18th).

Shifting the first letter forward by two positions gives H (8) + 2 = J (10th), and its opposite is Q. Shifting the third letter forward by two positions gives I (9) + 2 = K (11th), and its opposite is P. This yields the sequence JQKP.

Explanation

The relationship between the terms is a constant alphabetical shift of +2 positions for each letter.

Applying this shift to the second pair: H + 2 = J Q + 2 = S Z + 2 = B I + 2 = K

Applying the same +2 shift to each letter of DMVE: D + 2 = F M + 2 = O V + 2 = X E + 2 = G

This yields the sequence FOXG.

Explanation

The given relationship follows the pattern of x² : (x + 3)².

For the first pair: 16 = 4² 49 = (4 + 3)² = 7²

Applying the same pattern to the second pair: 100 = 10² (10 + 3)² = 13² = 169

Explanation

A niece is a collateral relative, meaning she belongs to a parallel line of descent (being the daughter of a sibling) rather than the direct lineal line of descent. This distinction in family lineage places her in a separate genealogical category compared to direct descendants.

Explanation

February is the only month among the choices that contains 28 days in a standard year and 29 days in a leap year, whereas January, July, and December each consist of 31 days.

Explanation

Stupid is the only word that conveys a negative quality, signifying a lack of intelligence, reasoning, or mental sharpness. The other three words all represent positive, desirable attributes associated with intellect, clarity, and knowledge. This makes stupid the odd one out in the group.

Explanation

In the letter series HFDC, the alphabetical positions of the letters are H = 8, F = 6, D = 4, and C = 3. The differences between consecutive letters are 8 - 6 = 2, 6 - 4 = 2, and 4 - 3 = 1. This variation in the gap, specifically the difference of 1 between D and C, makes this combination different because the other combinations maintain a constant difference of 2 between each consecutive letter.

Explanation

MONJK is characterized by having five completely unique and distinct letters with no repetitions.

Explanation

The number 19 is a prime number and is not a perfect square of any integer, unlike the remaining numbers which are all perfect squares.

Explanation

The pairs of numbers follow a pattern of the form (n² + 1, n³ + 1) for a natural number n.

For C), the first number is 10, which can be expressed as 3² + 1 (where n = 3). To follow the pattern, the second number should be 3³ + 1 = 28. Since the second number is 27, this pair fails to follow the rule.

Explanation

In this series, the common pattern of differences between consecutive numbers is +7 followed by +11. In the set 18 - 25 - 34, the difference between the first and second number is 7 (25 - 18 = 7), but the difference between the second and third number is 9 (34 - 25 = 9), which deviates from the standard +7 and +11 pattern of the other sets.

Explanation

The correct biological and chronological order represents the developmental stages of human life from conception to growth.

An embryo (4) is the earliest stage of development, occurring post-fertilization up to about eight weeks of gestation.

A neonate (1) refers to a newborn infant in the first four weeks (28 days) of life after birth.

An infant (3) is a young baby, typically spanning from the end of the neonatal period up to one year of age.

A child (2) represents the stage of development succeeding the infancy stage, covering the period from toddlerhood up to puberty.

This establishes the sequential progression as 4, 1, 3, 2.

Explanation

The correct chronological order of building construction and finishing is starting with the foundation, followed by erecting the walls, putting up the ceiling, plastering the surfaces, and finally painting them. This sequence corresponds to 3, 4, 5, 1, 2, which is option D.

Explanation

The series follows three distinct patterns for the first letter, the middle number, and the last letter of each term:

First letter pattern: The first letters decrease by 3 steps each time in alphabetical order: Z (26) - 3 = W (23) W (23) - 3 = T (20) T (20) - 3 = Q (17) Q (17) - 3 = N (14)

Middle number pattern: The middle numbers increase by consecutive integers starting from 2: 3 + 2 = 5 5 + 3 = 8 8 + 4 = 12 12 + 5 = 17

Last letter pattern: The first and last letters of each term are opposite pairs in the English alphabet, meaning the sum of their positional values is 27: Z (26) and a (1) sum to 27 (26 + 1 = 27) W (23) and d (4) sum to 27 (with W5a containing a typographical error where d is printed as a) T (20) and g (7) sum to 27 (20 + 7 = 27) Q (17) and j (10) sum to 27 (17 + 10 = 27) N (14) and m (13) sum to 27 (14 + 13 = 27)

Explanation

The series follows a pattern where each subsequent letter increases by 2 positions in alphabetical order.

For the first letter of each term: D (4) + 2 = F (6) F (6) + 2 = H (8) H (8) + 2 = J (10) J (10) + 2 = L (12)

For the second letter of each term: G (7) + 2 = I (9) I (9) + 2 = K (11) K (11) + 2 = M (13) M (13) + 2 = O (15)

For the third letter of each term: J (10) + 2 = L (12) L (12) + 2 = N (14) N (14) + 2 = P (16) P (16) + 2 = R (18)

Combining the letters L, O, and R gives the next term.

Explanation

The series decreases by doubling the difference subtracted at each step.

321 - 20 = 301 301 - 40 = 261 261 - 80 = 181 181 - 160 = 21

The differences form a geometric progression with a common ratio of 2: 20, 40, 80, 160. Subtracting 40 from 301 yields the missing number 261.

Explanation

The terms in the series are obtained by dividing the preceding term by 4, which is equivalent to multiplying by 4 when moving from right to left.

11 × 4 = 44 44 × 4 = 176 176 × 4 = 704 704 × 4 = 2816

Explanation

When two people in a row exchange their positions, the change in position for both individuals remains identical.

Harish moves from the 11th position to the 13th position from the left. Increase in Harish's position = 13 - 11 = 2

Since Mahesh undergoes the same shift, his new position is calculated by adding this increase to his initial position from the right. New position of Mahesh from the right = 17 + 2 = 19

Alternatively, this can be solved by finding the total number of children in the row. Since Harish's new position (13th from the left) is the same physical spot as Mahesh's old position (17th from the right), the total number of children is: Total = 13 + 17 - 1 = 29

Mahesh's new position is Harish's old position (11th from the left). Thus, Mahesh's new position from the right is: New position = Total - Position from left + 1 = 29 - 11 + 1 = 19

Explanation

B and C are sisters, which means they share the same mother, E. Since D is the son of E, D is the brother of both B and C. A is the son of B. Since D is the brother of A's mother, D is the maternal uncle of A.

Explanation

Each letter in the word BOMBAY is shifted forward by four positions in the alphabet to obtain its code FSQFEC: B + 4 = F O + 4 = S M + 4 = Q B + 4 = F A + 4 = E Y + 4 = C

Applying the reverse process to decode the word from QCWSVI, each letter of the code must be shifted backward by four positions: Q - 4 = M C - 4 = Y W - 4 = S S - 4 = O V - 4 = R I - 4 = E

This yields the word MYSORE.

Explanation

The coding scheme calculates the average of the alphabetical positions of the letters in the word.

For D, the alphabetical position is 4, and the number of letters is 1, giving 4 / 1 = 4.

For READ, the alphabetical positions of the letters are R = 18, E = 5, A = 1, and D = 4. The sum of these values is 18 + 5 + 1 + 4 = 28. Dividing this sum by the number of letters, which is 4, gives 28 / 4 = 7.

Applying the same logic to HEAR, the alphabetical positions of the letters are H = 8, E = 5, A = 1, and R = 18. The sum of these values is 8 + 5 + 1 + 18 = 32. Dividing this sum by the number of letters, which is 4, gives 32 / 4 = 8.

Explanation

The pattern in the given equations is that the digits of the two numbers being multiplied are written in reverse order to form the result.

For 72 × 96, the sequence of digits is 7, 2, 9, 6. Reversing this sequence gives 6, 9, 2, 7, which forms the number 6927.

For 58 × 87, the sequence of digits is 5, 8, 8, 7. Reversing this sequence gives 7, 8, 8, 5, which forms the number 7885.

Following the same system for 79 × 86, the sequence of digits is 7, 9, 8, 6. Reversing this sequence gives 6, 8, 9, 7, which forms the number 6897.

Explanation

The given operators are decoded according to the rules:

• represents ÷ × represents - represents + ÷ represents ×

Applying these substitutions to the expression 20 + 4 × 6 - 5 ÷ 7, we get: 20 ÷ 4 - 6 + 5 × 7

According to the BODMAS rule, we solve the division first: 20 ÷ 4 = 5

Next, we solve the multiplication: 5 × 7 = 35

Finally, we perform the addition and subtraction: 5 - 6 + 35 = 34

Explanation

The pattern in each row is to multiply the square roots of the outer numbers to obtain the middle number.

For the first row: √144 × √121 = 12 × 11 = 132

Applying the same pattern to the second row: √64 × √100 = 8 × 10 = 80

Explanation

According to the given instructions, the mathematical operators are substituted as follows: Subtraction (-) is replaced by division (÷) Division (÷) is replaced by addition (+) Addition (+) is replaced by multiplication (×) Multiplication (×) is replaced by subtraction (-)

Substituting these operations into the original expression: 175 - 25 ÷ 5 + 20 × 3 + 10

We obtain the modified expression: 175 ÷ 25 + 5 × 20 - 3 × 10

Following the BODMAS rule, perform division first: 175 ÷ 25 = 7

This simplifies the expression to: 7 + 5 × 20 - 3 × 10

Next, perform the multiplications: 5 × 20 = 100 3 × 10 = 30

The expression simplifies further to: 7 + 100 - 30

Finally, performing the addition and subtraction: 107 - 30 = 77

Explanation

The movement of Rana is traced as follows: Starting from point O, Rana travels 10 km North to reach point A. He then turns left and travels 4 km West to reach point B. From point B, he turns right and travels 5 km North to reach point C. Finally, he turns right and travels 4 km East to reach point D.

Since the Westward distance AB of 4 km is equal to the Eastward distance CD of 4 km, point D lies directly in line with the starting point O along the North direction. The total distance from the starting point O to the final point D is the sum of the two Northward segments: OA + BC = 10 km + 5 km = 15 km.

Explanation

The statement establishes that a significant proportion of language specialists engage in writing novels. Writing a novel is a creative and literary endeavor that fundamentally requires a strong command, precision, and mastery over language. Because language specialists possess deep expertise in vocabulary, grammar, syntax, and style, their specialized knowledge serves as an asset that facilitates literary creation. This clear correlation indicates that having a specialty in language is highly beneficial and supportive when it comes to the complex task of drafting novels.

Explanation

The statement "Industries destroy the natural resources" indicates that industrial activities have a destructive impact on natural resources.

Conclusion I does not follow because it is an extreme generalization. The given statement describes a general consequence of industrial activity but does not imply that every single natural resource in existence is destroyed by industries.

Conclusion II does not follow because it introduces the concept of environmental pollution, which is completely absent from the statement. Furthermore, it assumes that industries are the sole cause of environmental pollution, whereas pollution can arise from various other sources.

Explanation

Under the Seventh Schedule of the Constitution of India, the power to levy taxes is divided between the Centre and the States. Entry 82 of the Union List (List I) empowers the Central Government to levy taxes on income other than agricultural income. Meanwhile, Entry 46 of the State List (List II) vests the authority to levy taxes on agricultural income exclusively with the State Governments. As a result, agricultural income tax is a state subject and does not serve as a source of revenue for the Central Government.

Explanation

Operation Flood, launched in 1970 by the National Dairy Development Board, is the world's largest dairy development program. Spearheaded by Dr. Verghese Kurien, who is widely regarded as the Father of the White Revolution, this initiative aimed to create a nationwide milk grid. By implementing a cooperative model modeled after Amul, it empowered rural milk producers, increased dairy farmer incomes, and successfully transformed India from a milk-deficient country into the largest producer of milk in the world.

Explanation

Under Section 22 of the Reserve Bank of India Act, 1934, the Reserve Bank of India has the sole right to issue banknotes of all denominations in India. Although one-rupee notes and coins are minted and issued by the Government of India, their distribution and the management of the overall currency system are entirely controlled by the Reserve Bank of India, making it the supreme authority for paper currency issuance and circulation in the country.

Explanation

Under the principles of market equilibrium, the price of a commodity is determined by the interaction of market demand and supply. A fall in demand shifts the demand curve to the left, creating a market surplus at the original price level. To clear this excess stock, sellers reduce prices. Similarly, a rise in supply shifts the supply curve to the right, creating a surplus where the quantity supplied exceeds the quantity demanded at the initial price. This excess supply forces producers to lower their prices to attract buyers, resulting in a decrease in the market price of the commodity.

Explanation

The Planning Commission of India was established on 15 March 1950 through a cabinet resolution of the Government of India. It was set up as a non-constitutional and advisory body to formulate India's Five-Year Plans for effective and balanced utilization of the country's resources, with the Prime Minister serving as its ex-officio Chairman.

Explanation

The Constitution of India envisages three types of emergencies under Part XVIII, spanning from Article 352 to Article 360. The first is a National Emergency under Article 352, which can be declared due to war, external aggression, or armed rebellion. The second is President's Rule or State Emergency under Article 356, which is imposed due to the failure of constitutional machinery in a state. The third is a Financial Emergency under Article 360, which can be declared if the financial stability or credit of India or any part of its territory is threatened.

Explanation

Under Article 108 of the Constitution of India, the President of India is empowered to summon a joint sitting of both Houses of Parliament. This mechanism is used to resolve a deadlock between the Lok Sabha and the Rajya Sabha over the passage of a bill. A deadlock is deemed to have occurred if a bill passed by one House is rejected by the other, if the Houses disagree on amendments, or if more than six months elapse without the bill being passed by the other House.

Explanation

Upon returning from South Africa, Mahatma Gandhi initially founded the Satyagraha Ashram on 25 May 1915 at Kochrab Bungalow in Ahmedabad. However, due to a plague outbreak and the need for more open land to carry out activities like farming, cattle-rearing, and Khadi production, the ashram was relocated to its permanent site on the banks of the Sabarmati River on 17 June 1917. It was after this relocation that it became widely known as the Sabarmati Ashram.

Explanation

Under Article 75(3) of the Constitution of India, the Union Council of Ministers is collectively responsible to the House of the People, which is the Lok Sabha. This constitutional provision means that the government stays in power only as long as it commands the confidence of the majority of members in the Lok Sabha. Consequently, a No-Confidence Motion can only be introduced, debated, and voted upon in the Lok Sabha, in accordance with Rule 198 of the Rules of Procedure and Conduct of Business in the Lok Sabha.

Explanation

The 44th Amendment Act, passed in 1978, deleted the Right to Property from the list of Fundamental Rights. Prior to this amendment, the Right to Property was protected under Article 19(1)(f) and Article 31. The amendment removed these provisions from Part III of the Constitution and reclassified the Right to Property as a legal right under Article 300A in Part XII. Consequently, while property remains a legal right that cannot be deprived without the authority of law, it is no longer a Fundamental Right.

Explanation

The Chola rulers were ardent patrons of Shaivism, making Shiva the central deity of their religious and architectural endeavors. The vast majority of the grand temples constructed during the Chola period, including the magnificent Brihadisvara Temple at Thanjavur, the Gangaikonda Cholapuram Temple, and the Airavatesvara Temple at Darasuram, were built to honor and worship Shiva.

Explanation

The first session of the Indian National Congress was held from 28 to 31 December 1885 at Gokuldas Tejpal Sanskrit College in Bombay. It was attended by 72 delegates from all over India and was presided over by Womesh Chandra Bonnerjee. Allan Octavian Hume, a retired British civil servant, played a key role in organizing this historic meeting, which was originally scheduled to take place in Poona but had to be shifted to Bombay due to an outbreak of cholera.

Explanation

The Gupta Empire is distinguished in ancient Indian history for issuing the largest number of gold coins, known as Dinars. These coins are highly regarded for their outstanding craftsmanship, aesthetic beauty, and realistic portraiture. The abundance of these gold coins reflects the economic prosperity, flourishing trade, and stable financial administration of the empire, particularly during the reigns of monarchs like Samudragupta, Chandragupta II, and Kumaragupta I.

Explanation

In the Vedic period, Bali was the term used for the tax or tribute paid by the people to the king. During the Early Vedic (Rigvedic) period, it was a voluntary offering made by the members of the tribe to their chieftain, consisting of grain, cattle, or other domestic products. In the Later Vedic period, as the institution of kingship became stronger and more institutionalized, Bali evolved into a compulsory tax collected regularly by officers to support the royal administration and state activities.

Explanation

After attaining enlightenment, Gautama Buddha traveled to Sarnath, near Varanasi, where he preached his first sermon to his five former companions at the Deer Park. This momentous event is known in Buddhist tradition as the Dharmachakrapravartana, which translates to the Turning of the Wheel of Dharma or Law, marking the beginning of the propagation of his teachings.

Explanation

Fiords are long, deep, and narrow inlets of the sea bordered by steep cliffs, which are formed through glacial action rather than underground water processes. During ice ages, glaciers carve deep U-shaped valleys as they move toward the sea. When these glaciers retreat and melt, the rising sea levels submerge these steep-sided glacial valleys, creating fiords. This makes them landforms of glacial erosion.

Explanation

The Pampas are extensive, fertile plains located in South America, primarily covering parts of Argentina, Uruguay, and Brazil. These temperate grasslands feature a flat topography, a moderate climate, and nutrient-rich soils that make them highly suitable for agriculture and cattle ranching.

Explanation

The continental shelf is the shallow, gently sloping region of the ocean floor that extends from the coast of a continent. It is structurally a part of the continental crust rather than the oceanic crust, meaning it is fundamentally a submerged extension of the mainland. It is formed over geological time through the erosion of the land and the accumulation of river-borne sediment, maintaining the same geological composition and structure as the adjacent landmass.

Explanation

An anemometer is a meteorological instrument designed to measure wind velocity and speed. Derived from the Greek word anemos, meaning wind, it is used to calculate the rate of air movement in the atmosphere.

The most common type is the cup anemometer, which features horizontally rotating cups. The rotation speed of these cups is directly proportional to the velocity of the wind, allowing meteorologists and researchers to determine wind velocity accurately.

Explanation

The Mariana Trench is situated in the western Pacific Ocean, to the east of the Mariana Islands. It is the deepest known trench on Earth, formed by the geological process of ocean-to-ocean subduction, where the Pacific Plate is pushed beneath the Mariana Plate. Its deepest point, known as the Challenger Deep, reaches a depth of approximately 11,000 meters.

Explanation

Brain cells, specifically neurons, have the least regenerative power in the human body because they are terminally differentiated cells. During early development, these cells specialize and permanently exit the active cell cycle to enter the G₀ phase. Consequently, mature neurons lose the capacity to undergo cell division or mitosis. While minimal neurogenesis is limited to very specific regions like the hippocampus, the brain as a whole lacks the regenerative machinery to replace lost or damaged neurons, making injuries to the central nervous system permanent and irreversible.

Explanation

Potatoes are rich in starch, which is a polymeric carbohydrate. The standard chemical test for detecting the presence of starch is the iodine test. Iodine solution itself is normally brown or yellow-brown. When a few drops of this iodine solution are applied to the freshly cut surface of a potato, the iodine molecules slip into the helical structure of the amylose component of starch. This interaction forms a starch-iodine coordination complex, which causes a highly visible and distinct color change from brown to deep blue-black, confirming the abundant presence of starch in the potato tuber.

Explanation

The question contains a typographical error and meant to ask for the number of valves (or chambers) in a human heart. The human heart has four valves (tricuspid, pulmonary, mitral, and aortic) and four chambers, making option A the correct answer.

Explanation

Lymphocytes are a type of white blood cell crucial for the adaptive immune system. Specifically, B-lymphocytes (or B cells) are the cells responsible for humoral immunity. Upon encountering specific foreign antigens, B-lymphocytes mature and differentiate into plasma cells, which synthesize and secrete large quantities of antibodies. These antibodies circulate in the blood and lymphatic system, binding to and neutralizing pathogens such as bacteria and viruses.

Explanation

The enzyme diastase, also widely known as amylase, is produced by the salivary glands in the oral cavity. It is an amylolytic enzyme responsible for initiating the process of carbohydrate digestion by breaking down complex starches and glycogen into simpler, absorbable sugars such as maltose and glucose.

Explanation

Mycoplasma, specifically Mycoplasma pneumoniae, is a bacterium that causes respiratory tract infections in humans. It is a primary causative agent of primary atypical pneumonia, often referred to as walking pneumonia. Because Mycoplasma species lack a cell wall, they can easily attach to the ciliated epithelial cells lining the respiratory tract. This attachment leads to the destruction of these cells, causing inflammation and damage to respiratory organs such as the trachea, bronchi, and lungs, resulting in symptoms like persistent cough and breathing difficulties.

Explanation

Water has an exceptionally high specific heat capacity of approximately 4184 J/(kg·K) or 1 cal/(g·°C) due to its extensive hydrogen bonding. In liquid water, molecules are held together by a strong network of hydrogen bonds. When heat is absorbed, much of the energy is first consumed to break or disrupt these hydrogen bonds before the kinetic energy of the molecules can increase and raise the temperature. As a result, water can absorb or release a large amount of heat energy with minimal change in its own temperature.

Explanation

Sonar, which stands for Sound Navigation and Ranging, is the technology used to detect, locate, and measure the distance of submerged objects under the sea. Sound waves, particularly ultrasonic waves, are highly effective in water because electromagnetic waves are rapidly absorbed and attenuated by seawater. Sonar systems emit acoustic pulses that travel through the water, strike a submerged object, and bounce back as an echo. By measuring the time interval between the emission of the pulse and the reception of the reflected echo, and knowing the speed of sound in water, the precise distance and depth of the submerged object can be determined using the formula:

Distance = (v × t) / 2

where v represents the speed of sound in water and t represents the total round-trip travel time of the sound pulse.

Explanation

Silver possesses the highest electrical conductivity of all metals. This exceptional conductivity is due to its unique electronic configuration, which features a single valence electron in its outermost shell (5s) that is highly mobile and experiences minimal resistance as it moves through the metallic crystal lattice. At room temperature, silver has an electrical conductivity of approximately 6.30 × 10⁷ S/m, making it the most efficient conductor of electricity.

Explanation

The boiling point of a liquid is the temperature at which its vapour pressure equals the external pressure of the surrounding environment, which is typically atmospheric pressure. At this specific pressure and temperature, the liquid transition to a gas occurs throughout the entire volume of the liquid rather than just at the surface. The vapour pressure of the liquid becomes strong enough to overcome the atmospheric pressure holding it in the liquid phase, allowing bubbles of vapour to form within the bulk of the liquid and rise to the surface, causing the liquid to boil.

Explanation

Seaweeds are multicellular marine algae that naturally concentrate minerals from their marine environment, making them an exceptionally rich source of iodine. They absorb iodine directly from seawater and accumulate it in high concentrations. Iodine is a crucial micronutrient required by the human body to synthesize thyroid hormones, which regulate metabolism, growth, and cognitive development. Brown seaweeds, such as kelp, are especially recognized for their extremely high iodine content, which makes seaweeds highly beneficial in preventing iodine deficiency disorders.

Explanation

Heavy water, or deuterium oxide (D₂O), is utilized in nuclear reactors to slow down the fast neutrons produced during the fission process. To sustain a controlled nuclear chain reaction, these neutrons must be decelerated to thermal velocities, where they are much more likely to induce further fission in uranium-235 nuclei. Deuterium possesses a very low neutron capture cross-section, which allows it to efficiently reduce the kinetic energy of neutrons through elastic collisions without absorbing them.

Explanation

Malaria is a parasitic infection caused by protozoa of the genus Plasmodium, which are transmitted to humans through the bites of infected female Anopheles mosquitoes. Chloroquine is a classic antimalarial drug utilized extensively for both the prophylaxis and treatment of malaria. It works by diffusing into the lysosome of the parasite inside infected red blood cells, preventing the detoxification of toxic heme produced from hemoglobin digestion, which ultimately leads to the death of the parasite.

Explanation

Tear gas, formally known as a lachrymatory agent, primarily consists of chlorine-containing organochlorine compounds. The most commonly used tear gases by law enforcement forces for crowd and riot control are o-chlorobenzylidene malononitrile (commonly called CS gas) and phenacyl chloride (chloroacetophenone, commonly called CN gas).

The chemical formulas for these principal agents are C₁₀H₅ClN₂ for CS gas and C₈H₇ClO for CN gas. In both of these formulations, chlorine is a key structural constituent. When these agents are dispersed, they irritate the corneal nerves of the eyes, resulting in heavy tear production, severe stinging pain, and temporary blindness, alongside irritation of the mucosal linings in the respiratory tract.

Explanation

HTTP stands for Hypertext Transfer Protocol. It is an application-layer protocol used for transmitting hypermedia documents, such as HTML, over the internet. Designed to facilitate communication between web browsers and web servers, it enables the retrieval of resources and forms the foundation of data exchange on the World Wide Web.

Explanation

National Aluminium Company Ltd. (NALCO) is currently a Navaratna public sector enterprise, having been conferred this status in 2008. Among the other options, Steel Authority of India Ltd. (SAIL) and Oil India Ltd. (OIL) have been elevated to Maharatna status, while MMTC Ltd. holds Miniratna status.

Explanation

World AIDS Day is observed globally on 1st December each year. First designated in 1988, this day serves to raise public awareness about HIV/AIDS, show support for people living with the virus, and remember those who have died from AIDS-related illnesses. It was established as the first-ever global health day by the World Health Organization to foster international cooperation and solidarity in addressing the pandemic.

Explanation

Devika Rani was the first recipient of the Dadasaheb Phalke Award, which was introduced in 1969 by the Government of India to commemorate Dadasaheb Phalke's contribution to Indian cinema. Widely known as the first lady of Indian cinema, she received this prestigious honor at the 17th National Film Awards for her pioneering work as an actress and co-founder of the legendary studio Bombay Talkies.

Explanation

Meandering Pastures of Memories is an autobiographical book written by the renowned Kathak dancer and Padmashri awardee Shovana Narayan. Published in 2007, the book chronicles her journey, dedication, and accomplishments in the field of classical dance, while also touching upon her experiences as a senior officer in the Indian Audit and Accounts Service. It provides an intimate reflection on her artistic evolution, family, and philosophical outlook.

Explanation

Rajasthan is a landlocked state situated in northwestern India. It shares an international land border with Pakistan to the west and northwest, and domestic land borders with the Indian states of Punjab, Haryana, Uttar Pradesh, Madhya Pradesh, and Gujarat. Since Rajasthan is completely situated inland and does not touch any sea, gulf, or ocean, it does not have a coastline or any maritime boundary.

Explanation

The internationally recognized slogan "Just Do It" is a trademark of Nike, the American multinational sportswear and footwear corporation. Introduced in 1988, the campaign was created by the advertising agency Wieden+Kennedy to appeal to a broad demographic, emphasizing fitness, motivation, and determination. The slogan became a cornerstone of the brand's global marketing success.

Explanation

Dr. Sarvepalli Radhakrishnan is deeply associated with An Idealist View of Life, Bhagavad Gita, and Hindu View of Life. He authored Hindu View of Life in 1927, which was based on his Upton Lectures at Manchester College, Oxford, in 1926. He wrote An Idealist View of Life in 1932, containing his Hibbert Lectures delivered in 1929. Furthermore, he published a widely acclaimed translation, introductory essay, and commentary on the Bhagavad Gita in 1948.

Explanation

The International Court of Justice is the principal judicial organ of the United Nations, established in June 1945 by the Charter of the United Nations. The permanent seat of the court is located at the Peace Palace in The Hague, Netherlands, where it officially began its work in April 1946.

Explanation

The Subroto Cup is a prestigious international inter-school football tournament held annually in New Delhi, India. Initiated in 1960, the tournament is named after the first Indian Chief of Air Staff, Air Marshal Subroto Mukerjee, who envisioned promoting the game at the grassroots level. It is organized by the Subroto Mukerjee Sports Education Society with the active support of the Indian Air Force.

Explanation

Alam Ara is India's first sound or talkie film, directed by Ardeshir Irani. It was released on 14 March 1931 at the Majestic Cinema in Bombay (now Mumbai). The film marked a major milestone in Indian cinema by transitioning from the silent era to talkies. It also featured the very first song in Indian cinematic history, De de khuda ke naam pe, sung by Wazir Mohammed Khan.

Explanation

Sachin Tendulkar holds the record for the highest number of aggregate runs in One-day Cricket World Cup history, with a total of 2,278 runs. He also held the record for the most runs scored in a single tournament, with 673 runs in the 2003 World Cup.

Explanation

Ustad Bismillah Khan was a legendary Indian musician who single-handedly elevated the status of the shehnai from a traditional ceremonial instrument played in temples and weddings to the classical concert stage. Through his exceptional mastery and expressive playing, he brought global recognition to this Indian wind instrument, eventually earning India's highest civilian honor, the Bharat Ratna, in 2001.

Explanation

The Bara Imambara, also known as the Asafi Imambara, is a famous monument located in Lucknow, Uttar Pradesh. It was constructed in 1784 by Asaf-ud-Daula, the Nawab of Awadh, primarily as a famine-relief project to provide employment and livelihood to the local population during a severe drought.

Designed by the architect Kifayatullah, the monument is a masterpiece of Mughal and Awadhi architecture. Its central hall is globally renowned as one of the largest vaulted chambers in the world, uniquely built without the support of any external pillars, beams, or columns. The complex is also widely celebrated for the Bhool Bhulaiya, an intricate labyrinth of interconnected corridors and passages located on its upper floors.

Explanation

Open Market Operations refer to the sale and purchase of government securities and treasury bills by the Reserve Bank of India in the open market. This is a monetary policy tool used by the central bank to regulate the money supply and liquidity in the economy. When there is excess liquidity, the RBI sells securities to absorb cash from the banking system. When liquidity is tight, the RBI buys securities from the market, injecting money into the economy to facilitate credit flow.

Explanation

World Consumer Rights Day is celebrated globally every year on 15th March to raise awareness about consumer rights and needs. This special day was inspired by US President John F. Kennedy, who sent a historic message to the US Congress on 15th March 1962. In his address, he formally defined and spoke about consumer rights, making him the first world leader to do so. The international consumer movement first observed this day on 15th March 1983, and it has been celebrated annually ever since to promote solidarity and highlight consumer protection across the globe.

Explanation

The correct idiomatic expression is free of charge, which means without cost or payment. The adverb freely means in a free or unrestricted manner, which is incorrect in this context. Therefore, freely should be replaced with the adjective free to make the sentence grammatically correct.

Explanation

The phrase "returned back" contains a redundancy error. The verb "return" already means to go or come back to a place. Therefore, using the word "back" after "returned" is superfluous. The sentence should be corrected by removing the word "back" to read "and returned to his village".

Explanation

The verb comprise is a transitive verb that means to consist of or to be composed of. In the active voice, it takes a direct object and must not be followed by a preposition. Therefore, the use of the preposition of after comprises is grammatically incorrect. The sentence should instead use comprises without of, or be rephrased using consists of or is comprised of.

Explanation

The sentence is a conditional sentence where the subordinate clause introduced by unless uses the simple present tense thinks. In a standard first conditional structure, the main clause should express future possibility, which requires the future tense modal verb will. Therefore, does not spend must be replaced with will not spend to make the sentence grammatically correct.

Explanation

When two singular subjects are connected by the correlative conjunctions neither... nor, the verb that follows must be singular. In this sentence, the subjects my sister and my brother are both singular, so they require the singular verb is instead of the plural verb are to maintain correct subject-verb agreement.

Explanation

The sentence describes a hypothetical, imaginary, or counterfactual situation in the present, which is structured as a second conditional sentence. In English grammar, the subjunctive mood is used to express such unreal conditions, and the subjunctive form of the verb "to be" is "were" for all subjects, including the first-person singular pronoun "I". This structure represents an impossible or unlikely condition in the present, followed by "would" and the base form of the verb in the main clause.

Explanation

The conjunction yet is used to introduce a statement that adds something surprising or expresses a contrast with what has just been mentioned. In this sentence, despite the state of being weak, the person performs a significant amount of work, which is an unexpected contrast that is properly joined by yet.

Explanation

The word aptitude refers to a natural ability, talent, or suitability for acquiring a particular skill or performing a specific type of activity. Showing an aptitude for sports at a very early stage means demonstrating an inherent capacity or natural talent for athletic activities from a young age, which perfectly fits the grammatical and contextual requirement of the sentence.

Explanation

The expression "for heaven's sake" is a standard English idiom used to express surprise, annoyance, impatience, or strong emphasis. Grammatically, this phrase requires the possessive form "heaven's" to modify the noun "sake", which means "for the sake of heaven".

Explanation

The verb capitulate means to surrender or yield, typically under agreed-upon conditions, or to cease resisting an opponent. In a military context, it refers to an army surrendering to its enemy. Grammatically, this verb is followed by the preposition to, which perfectly fits the structure of the sentence.

Explanation

The word supersede means to set aside, override, or take the place of something previously in authority or use. In legal, statutory, and administrative contexts, to supersede an existing rule, law, or authority means to annul or replace it, rendering the previous version obsolete. This aligns with the meaning of repeal, which refers to revoking, rescinding, or formally annulling a legislative act or regulation so that it is no longer in force.

Explanation

The word perilous refers to something that is full of danger, hazard, or risk. It originates from the noun peril, which denotes serious and immediate danger. Therefore, dangerous is the correct synonym as it means likely to cause problems, harm, injury, or damage.

Explanation

Affluence refers to the state of having a great deal of money, wealth, or material goods. It denotes prosperity, abundance, and richness. Therefore, richness is the most appropriate synonym as it directly conveys the state of being wealthy or possessing an abundant supply of resources.

Explanation

The word bifurcated is derived from the Latin prefix bi- (meaning two) and furca (meaning fork). It is used to describe something that is split, branched, or divided into two distinct branches or parts.

Explanation

Consensus denotes a general agreement or shared collective opinion among a group of people. Unanimity likewise represents a state of complete, undivided agreement or consensus among all members of a group, making it the most accurate synonym for the given word.

Explanation

The word salient is defined as most noticeable, prominent, or of primary importance. Its direct antonym is insignificant, which describes something that is minor, trivial, or lacking in importance and noticeability.

Explanation

The word dormant means lying asleep, inactive, or latent (hidden and undeveloped). The word reveal means to make known, disclose, or bring to light something that was hidden or concealed. Therefore, reveal acts as the opposite in meaning to dormant, representing the action of bringing a latent state into view.

Explanation

The word camouflage means to disguise, conceal, or hide the true identity or appearance of something so that it blends in with its surroundings. The opposite of concealing or hiding is to expose, uncover, or make something visible and known. The word reveal means to make previously unknown or hidden information known, or to allow something to be clearly seen, making it the direct antonym.

Explanation

The word latent refers to something that is hidden, concealed, or present but not yet visible, active, or developed. The word evident means clearly visible, obvious, plain, or easily understood and recognized. Because evident describes something that is manifest and easily seen, it is the direct opposite in meaning to latent.

Explanation

The word ample means plentiful, abundant, or more than enough in size, quantity, or capacity. Its direct antonym is meagre, which refers to something that is deficient in quantity, thin, scanty, or inadequate.

Explanation

The idiom "gift of the gab" refers to the ability to speak easily, eloquently, and persuasively. It represents a natural talent for verbal communication, enabling a person to express their thoughts clearly and engage an audience effortlessly.

Explanation

The idiom "go a long way" means to be very helpful, contribute significantly, or make a major difference toward achieving a specific outcome. In this context, the teacher's extra hours of coaching made a significant positive impact and helped considerably in improving the student's performance.

Explanation

The phrasal verb "cope with" means to deal effectively with something difficult or to manage a challenging situation or person. In this context, it refers to the administration's struggle to manage, control, or deal with the striking employees, making "handle" the most accurate and direct synonym.

Explanation

The idiom "at the eleventh hour" refers to the very last possible moment before it is too late to make a change or take action. It originates from the biblical Parable of the Workers in the Vineyard in the Gospel of Matthew, where laborers hired at the eleventh hour of a twelve-hour workday received the same pay as those who started early in the morning. In the context of the sentence, the criminal received a pardon at the final moment just before the execution was carried out.

Explanation

The idiom "maiden speech" refers to the first public speech made by a person, especially a newly elected member of a parliament or legislature. In this context, the word "maiden" is used metaphorically to mean "first" or "earliest," similar to how a ship's first journey is called its "maiden voyage."

Explanation

In medical and clinical contexts, the standard and formally accepted term for officially allowing a patient to leave a hospital after treatment is discharged. While released conveys a general sense of being set free, discharged is the precise professional term used by medical institutions to indicate that a patient's stay and treatment at the facility have concluded.

Explanation

The verb "mellow" means to become less bright, intense, or harsh, and instead become softer, warmer, and more pleasant. When used in the context of light or colors, especially during a sunset, "mellowed" is the most precise and appropriate word to describe how the vibrant colors of the sky became softer and gentler as the sun went down.

Explanation

The word considerate means showing kindly awareness or regard for another's feelings, circumstances, or needs. In the context of describing a soft-spoken manager's polite and empathetic demeanor towards others, considerate is the appropriate adjective to convey thoughtfulness and respect.

Explanation

The verb hang has two distinct past tense forms depending on its meaning. When referring to suspending or attaching an object like a picture, painting, or portrait to a wall, the correct past tense and past participle form is hung. The form hanged is reserved exclusively for the act of executing or killing someone by suspending them by the neck. Since the sentence refers to placing a portrait in the main hall, the appropriate past tense form to use is hung.

Explanation

The phrasal verb call on means to pay a visit to someone. In the context of the sentence, it correctly conveys the meaning that they were unable to visit because of the rains. Since the original sentence is grammatically correct and uses the appropriate phrasal verb, no improvement or correction is needed.

Explanation

The word deprecate is defined as to feel or express disapproval of, or to protest against, someone or something. It originates from the Latin word deprecari, which means to plead against or ward off by prayer. In vocabulary and grammar, it is the precise one-word substitution for the act of voicing strong disapproval or criticism.

Explanation

The term illegible refers to handwriting, print, or characters that are impossible or extremely difficult to read, typically because they are scribbled, untidy, faded, or poorly formed.

Explanation

The term amphibian is derived from the Greek words amphi, meaning both, and bios, meaning life. It refers to a class of cold-blooded vertebrate animals that are ecologically and physiologically adapted to live both on land and in water. Typically, they start their life cycle in water as larvae breathing through gills and undergo metamorphosis to develop lungs and limbs for terrestrial living as adults.

Explanation

The term gullible is used to describe a person who is easily persuaded, tricked, or cheated because they are overly trusting, naive, or lack critical judgment. It is the direct one-word substitution for being easily duped or fooled.

Explanation

Hydrophobia is the extreme or irrational fear of water. The term originates from the Greek words hydro, meaning water, and phobos, meaning fear. It is commonly used to describe a psychological aversion to water as well as a clinical symptom of rabies in humans, where the infection causes painful throat spasms that trigger a dread of swallowing liquids.

Explanation

Dilapidated is correctly spelt. It is an adjective that refers to a building, vehicle, or object that has fallen into a state of ruin, decay, or disrepair due to age, wear, or neglect. Its standard dictionary spelling is d-i-l-a-p-i-d-a-t-e-d.

Explanation

The word prosperous is spelt correctly. It is an adjective used to describe someone or something that is financially successful, flourishing, or thriving. The spelling follows the standard pattern of adding the adjectival suffix -ous to the root verb prosper to denote possessing the quality of prosperity.

Explanation

The word "requisite" is spelt correctly, meaning made necessary by particular circumstances or regulations. The word "reprimand" (Option A) is also spelt correctly, but "requisite" is widely accepted as the primary correct choice in this specific exam question where other options contain spelling errors (resplendent and repository).

Explanation

The word prudent is spelt correctly. It is an adjective used to describe someone who acts with or shows care, wisdom, and good judgment, especially in practical matters or when planning for the future.

Explanation

The word exuberance is spelled correctly as e-x-u-b-e-r-a-n-c-e. Derived from the Latin verb exuberare, which means to abound or grow luxuriously, it refers to the state of being full of energy, excitement, and cheerfulness. It is formed by joining the prefix ex- meaning out or thoroughly, the root uber meaning fertile or abundant, and the standard noun-forming suffix -ance.

Explanation

The sentence highlights a contradiction between a widespread belief about ostriches and their actual behavior. Since the text asserts that the ostrich does not bury its head in the sand, this fact stands in opposition to the popular myth. The prepositional phrase contrary to is used to introduce a statement that limits, opposes, or contradicts a belief or expectation, making it the grammatically and contextually correct choice to start the passage.

Explanation

The collocation common belief is a standard English phrase used to refer to a widely held opinion, idea, or myth among the general public. In this context, the passage addresses the widespread but incorrect notion that ostriches bury their heads in the sand to avoid danger, characterizing this popular myth as a common belief.

Explanation

The correct word to fill in the blank is avoid, as the common myth is that ostriches bury their heads in the sand to escape or prevent themselves from seeing danger. The other options, such as encounter or face, contradict the meaning of trying to escape from danger.

Explanation

The preposition at is standardly used to indicate a specific rate, speed, or measurement. In English, the phrase at a speed of is the correct idiomatic construction used to denote the velocity at which an animal, person, or vehicle travels.

Explanation

The phrase miles per hour is the standard English expression used to measure and express speed, indicating the number of miles traveled in each hour. In this context, the preposition per functions to mean for each or in every, which correctly connects the distance metric to the unit of time.

Explanation

The verb peck (option A) means to strike or bite something with a beak. In the given context, it describes how an ostrich defends itself by running fast, kicking powerfully, and pecking aggressively with its beak (written as break in the passage).

Explanation

The preposition with is used to indicate the instrument, tool, or body part used to perform an action. In this passage, the ostrich uses its beak (written as break in the text) to perform the aggressive action, making with the correct preposition to describe this physical means of defense.

Explanation

The blank requires a superlative adjective because it is preceded by the definite article the and is grammatically paired with the superlative adjective fastest to describe the ostrich in comparison to all other birds in the world. The superlative form of the adjective large is largest, which maintains parallel structure with fastest.

Explanation

The passage is written in the simple present tense to describe general facts about the ostrich, as seen in verbs like does not bury and can run. For blank 149, the subject pronoun it refers to the ostrich, which requires a third-person singular verb. Since the context of the sentence explains that the ostrich is highly capable of defending itself by running fast and kicking powerfully, it has no requirement to hide its head. Therefore, the negative present tense auxiliary contraction doesn't is the correct grammatical and semantic fit to precede the base verb need.

Explanation

The passage debunks the common myth that ostriches bury their heads in the sand to avoid danger. By highlighting the physical capabilities of the ostrich, such as its speed and power, the text concludes that the bird has no actual need to perform this rumored action. Therefore, the verb bury is the most contextually fitting word for blank 150 because it directly refers back to the central myth of the ostrich burying its head.

Explanation

To find the value of the given expression, we first rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator, which is (2 + √3):

((2 + √3) × (2 + √3)) / ((2 - √3) × (2 + √3))

Using the algebraic identities (a + b)² = a² + b² + 2ab and (a - b)(a + b) = a² - b²:

= (2² + (√3)² + 2 × 2 × √3) / (2² - (√3)²)

= (4 + 3 + 4√3) / (4 - 3)

= 7 + 4√3

Substituting the given value of √3 = 1.732:

= 7 + 4 × 1.732

= 7 + 6.928

= 13.928

Explanation

To evaluate the expression, simplify the term under the nested square root, 7 - 2√10, by expressing it as a perfect square of the form (a - b)² = a² + b² - 2ab.

Comparing the terms: a² + b² = 7 2ab = 2√10, which gives ab = √10

By choosing a = √5 and b = √2, both equations are satisfied since: (√5)² + (√2)² = 5 + 2 = 7 (√5)(√2) = √10

Thus, the nested term can be rewritten as: 7 - 2√10 = (√5 - √2)²

Taking the square root of this perfect square: √(7 - 2√10) = √5 - √2

Substituting this back into the original expression: √2 + √(7 - 2√10) = √2 + √5 - √2 = √5

Explanation

Let the required number be x. The relationship is given by the equation:

x + 0.01 = 1.1

To find the value of x, subtract 0.01 from 1.1:

x = 1.1 - 0.01

By aligning the decimal points and performing the subtraction:

1.10 0.01

1.09

Explanation

The given sequence is an alternating series consisting of two interleaved arithmetic progressions.

The terms at the odd positions (1st, 3rd, and 5th) are 25, 30, and 35. This progression increases by 5 at each step: 25 + 5 = 30, and 30 + 5 = 35.

The terms at the even positions (2nd, 4th, and 6th) are 50, 45, and 40. This progression decreases by 5 at each step: 50 - 5 = 45, and 45 - 5 = 40.

The required term is the 7th term in the overall sequence, which continues the first progression. Therefore, the next term is 35 + 5 = 40.

Explanation

The expression represents the sum of the series of products of consecutive integers from 1 to 10. The term 3×4×5 is a typographical notation for 3×4 + 4×5.

The general formula for the sum of products of consecutive integers is: S = ∑[n=1 to N] n(n+1) = N(N+1)(N+2)/3

Substituting N = 10 into the formula: S = 10 × 11 × 12 / 3 S = 10 × 11 × 4 S = 440

Explanation

Applying the exponent rule x⁻¹ = 1/x:

The first term is: (7⁻¹ - 8⁻¹)⁻¹ = (1/7 - 1/8)⁻¹ To subtract the fractions, find a common denominator: 1/7 - 1/8 = (8 - 7)/56 = 1/56 Taking the reciprocal: (1/56)⁻¹ = 56

The second term is: (3⁻¹ - 4⁻¹)⁻¹ = (1/3 - 1/4)⁻¹ Subtracting the fractions: 1/3 - 1/4 = (4 - 3)/12 = 1/12 Taking the reciprocal: (1/12)⁻¹ = 12

Subtracting the second term from the first term: 56 - 12 = 44

Explanation

For real numbers, the square of any number is always non-negative, which means that for any real values, the squared terms (x - 3)², (y - 4)², and (z - 5)² are all greater than or equal to zero.

The sum of non-negative terms can only be equal to zero if each individual term is itself equal to zero. This gives:

(x - 3)² = 0 → x = 3 (y - 4)² = 0 → y = 4 (z - 5)² = 0 → z = 5

Substituting these values into the required expression:

x + y + z = 3 + 4 + 5 = 12

Explanation

The sum of the squares of the first n natural numbers is given by the formula Sₙ = n(n + 1)(2n + 1)/6.

For the first 10 natural numbers (n = 10), the sum of their squares is: S₁₀ = 10 × (10 + 1) × (2 × 10 + 1) / 6 S₁₀ = 10 × 11 × 21 / 6 = 385

The given series starts from 2² instead of 1². Therefore, the sum is obtained by subtracting 1² from the sum of the first 10 natural numbers: Required sum = S₁₀ - 1² = 385 - 1 = 384.

Explanation

Let a = 137 and b = 133.

We can simplify the given expression using the algebraic identity for the difference of two cubes: a³ - b³ = (a - b)(a² + ab + b²)

The expression is written in the algebraic form: (a² + ab + b²) / (a³ - b³)

By substituting the identity for the difference of cubes into the denominator, we get: (a² + ab + b²) / [(a - b)(a² + ab + b²)] = 1 / (a - b)

Substituting the values a = 137 and b = 133: 1 / (137 - 133) = 1/4

Explanation

Let the two numbers be x and y.

We are given: xy = 120 x² + y² = 289

Using the standard algebraic identity: (x + y)² = x² + y² + 2xy

Substitute the given values: (x + y)² = 289 + 2 × 120 (x + y)² = 289 + 240 (x + y)² = 529

Taking the square root on both sides: x + y = √529 x + y = 23

Explanation

The product P is given by: P = 2 × 4 × 6 × ... × 200

Since there are 100 even terms, we can factor out 2 from each of the 100 terms to rewrite the expression as: P = 2¹⁰⁰ × (1 × 2 × 3 × ... × 100) P = 2¹⁰⁰ × 100!

The number of trailing zeros in P is determined by the number of factors of 10 in its prime factorization, which is equal to the exponent of 5 since the exponent of 2 is much larger.

Using Legendre's formula, the exponent of 5 in 100! is: E₅(100!) = ⌊100/5⌋ + ⌊100/25⌋ E₅(100!) = 20 + 4 = 24

Since 2¹⁰⁰ contains no factors of 5, the total exponent of 5 in the product is 24.

Explanation

Let the time taken by A to complete the work be t days.

Since A takes twice as much time as B, the time taken by B is t/2 days. Similarly, since A takes three times as much time as C, the time taken by C is t/3 days.

In one day, the fraction of work completed by each is: Work done by A = 1/t Work done by B = 2/t Work done by C = 3/t

They complete the entire work together in 1 day. Therefore, the sum of their individual one-day work rates equals 1: 1/t + 2/t + 3/t = 1

Simplifying this equation: 6/t = 1 t = 6

This gives the time taken by A alone to complete the work as 6 days.

Explanation

Let the work rate of a man be M and that of a woman be W. Since the total work remains constant, we can equate the total work done in both cases:

14 × (2M + 1W) = 8 × (2M + 4W)

28M + 14W = 16M + 32W

12M = 18W

M/W = 18/12 = 3/2

The ratio of their work efficiencies is M : W = 3 : 2. Since daily wages are distributed in proportion to daily work efficiency, the ratio of the daily wage of a man to that of a woman is 3 : 2.

Given the standard daily wage of a man in this problem is ₹600:

Daily wage of a woman = (2 / 3) × ₹600 = ₹400

Explanation

The sides of the triangle are 6 cm, 8 cm, and 10 cm. Since 6² + 8² = 36 + 64 = 100 = 10², the given triangle is a right-angled triangle where the greatest side of 10 cm is the hypotenuse.

In any right-angled triangle, the midpoint of the hypotenuse acts as the circumcenter of the triangle. This means the distance from the vertex containing the right angle to the midpoint of the hypotenuse, which represents the median to the greatest side, is equal to the circumradius. The circumradius of a right-angled triangle is always equal to half the length of its hypotenuse.

Length of the median = Hypotenuse / 2 = 10 / 2 = 5 cm.

Explanation

The circumference of a circle is given by the formula C = 2πr. Given that the circumference is 11 cm, we can find the radius r:

2 × (22/7) × r = 11 44/7 × r = 11 r = (11 × 7) / 44 r = 7/4 cm

The area of a sector with central angle θ is given by the formula: Area = (θ/360°) × πr²

Substituting θ = 60° and r = 7/4 cm: Area = (60/360) × (22/7) × (7/4)² Area = (1/6) × (22/7) × (49/16) Area = (1/6) × 22 × (7/16) Area = 154/96 Area = 77/48 Area = 1 29/48 cm²

Explanation

The perimeter of a rhombus is 4s, where s is the length of each side. Given that the perimeter is 100 cm: 4s = 100 s = 25 cm

The diagonals of a rhombus, d₁ and d₂, bisect each other at right angles. This creates four right-angled triangles where the hypotenuse is the side s, and the legs are d₁/2 and d₂/2.

Given that one diagonal d₁ = 14 cm, its half-length is 7 cm. Applying the Pythagorean theorem: s² = (d₁/2)² + (d₂/2)² 25² = 7² + (d₂/2)² 625 = 49 + (d₂/2)² (d₂/2)² = 576 d₂/2 = 24 d₂ = 48 cm

The area of a rhombus is calculated using the formula: Area = ½ × d₁ × d₂ Area = ½ × 14 × 48 = 336 cm²

Explanation

The surface area S of a sphere with radius r is given by the formula S = 4πr². Therefore, the ratio of the surface areas of two spheres is the ratio of the squares of their radii: S₁/S₂ = (r₁/r₂)²

Given that this ratio is 4/9, taking the square root gives the ratio of their radii: r₁/r₂ = √(4/9) = 2/3

The volume V of a sphere is given by the formula V = 4/3 πr³. Therefore, the ratio of the volumes of the two spheres is the ratio of the cubes of their radii: V₁/V₂ = (r₁/r₂)³

Substituting the ratio of the radii into this equation: V₁/V₂ = (2/3)³ = 8/27

Explanation

The volume of similar cones is proportional to the cube of their respective heights. Let H be the height of the original cone, which is 30 cm, and h be the height of the smaller cone cut off from the top.

The ratio of the volume of the smaller cone (v) to the volume of the larger cone (V) is: v/V = (h/H)³

Given that v/V = 1/27, we can substitute the values into the relation: 1/27 = (h/30)³

Taking the cube root on both sides: 1/3 = h/30 h = 10 cm

The section is made at a height above the base equal to the difference between the total height and the height of the smaller cone: Height above base = H - h = 30 - 10 = 20 cm

Explanation

The single equivalent discount for successive discounts of d₁, d₂, and d₃ is given by the formula:

Equivalent Discount % = [1 - (1 - d₁/100) × (1 - d₂/100) × (1 - d₃/100)] × 100

Substituting the given discounts d₁ = 10, d₂ = 20, and d₃ = 40 into the formula:

Equivalent Discount % = [1 - (1 - 0.1) × (1 - 0.2) × (1 - 0.4)] × 100 = [1 - 0.9 × 0.8 × 0.6] × 100 = [1 - 0.432] × 100 = 0.568 × 100 = 56.8%

Explanation

Using the standard formula:

Time = Distance ÷ Speed

First, convert the distance from kilometers to meters: Distance = 4/5 km = 4/5 × 1000 m = 800 m

Next, convert the speed from km/hr to m/s by multiplying with 5/18: Speed = 45 × 5/18 m/s = 25/2 m/s = 12.5 m/s

Now, substitute these values into the time formula: Time = 800 m ÷ 12.5 m/s = 64 seconds

Explanation

The relation between Marked Price (MP) and Cost Price (CP) when profit percentage (p) and discount percentage (d) are given is:

MP / CP = (100 + p) / (100 - d)

Substituting the given values, where CP = 100, p = 20, and d = 4:

MP / 100 = (100 + 20) / (100 - 4)

MP / 100 = 120 / 96

MP = (120 / 96) × 100

Simplifying the fraction 120 / 96 to 5 / 4 gives:

MP = (5 / 4) × 100 = 125

Explanation

To find the combined ratio A:B:C, the term representing B must be made equal in both given ratios.

The value of B in the ratio A:B is 5, and in B:C is 4. The least common multiple of 5 and 4 is 20.

Multiply the terms of the ratio A:B = 3:5 by 4: A:B = (3 × 4) : (5 × 4) = 12 : 20

Multiply the terms of the ratio B:C = 4:7 by 5: B:C = (4 × 5) : (7 × 5) = 20 : 35

Combining these ratios yields A:B:C = 12:20:35.

Explanation

Let a/2 = b/3 = c/5 = k.

From this relation, we can express a, b, and c in terms of k: a = 2k b = 3k c = 5k

Substituting these values into the expression (a + b + c)/c: (2k + 3k + 5k) / 5k = 10k / 5k = 2.

Explanation

Let the quantity of sugar costing Rs. 20 per kg be x kg, and the quantity of sugar costing Rs. 15 per kg be y kg.

Since there is neither loss nor gain when selling the mixture at Rs. 16 per kg, the cost price of the mixture is equal to its selling price.

Total Cost Price = 20x + 15y Total Selling Price = 16(x + y)

Equating the cost price and the selling price: 20x + 15y = 16(x + y) 20x + 15y = 16x + 16y 4x = y x/y = 1/4

So, the ratio of the quantities of sugar costing Rs. 20 per kg and Rs. 15 per kg is 1:4.

Explanation

The ratio of A's share to B's share is given by A : B = 100 : 90 = 10 : 9. The ratio of B's share to C's share is given by B : C = 100 : 110 = 10 : 11.

To combine these ratios into A : B : C, we make B's term equal in both ratios by multiplying the first ratio by 10 and the second ratio by 9. A : B = 100 : 90 B : C = 90 : 99 Therefore, A : B : C = 100 : 90 : 99.

Let the individual shares be 100x, 90x, and 99x. The sum of their shares is 100x + 90x + 99x = 289x. Equating this to the total sum of Rs 86,700: 289x = 86,700 x = 300

B's share is 90x: 90 × 300 = Rs 27,000

Explanation

To find the ratio in which the two alloys should be mixed, we can use the rule of alligation on the proportion of gold in each alloy.

In the first alloy, the fraction of gold is 7 / (7 + 22) = 7/29. In the second alloy, the fraction of gold is 21 / (21 + 37) = 21/58. In the required mixture, the fraction of gold is 25 / (25 + 62) = 25/87.

The denominators of the gold fractions are 29, 58, and 87. The Least Common Multiple (LCM) of these denominators is 174.

Converting each gold fraction to have the common denominator of 174: First alloy: (7 × 6) / 174 = 42/174 Second alloy: (21 × 3) / 174 = 63/174 Required mixture: (25 × 2) / 174 = 50/174

Using the numerators for the alligation method: First alloy value: 42 Second alloy value: 63 Mean mixture value: 50

By the rule of alligation, the ratio of the first alloy to the second alloy is: (63 - 50) : (50 - 42) = 13 : 8

Explanation

For nine consecutive odd numbers, the average is equal to the middle (5th) term.

Let the nine consecutive odd numbers be: x, x + 2, x + 4, x + 6, x + 8, x + 10, x + 12, x + 14, x + 16

The average of these numbers is: Average = x + 8

Given that the average is 53: x + 8 = 53 x = 53 - 8 = 45

Explanation

The average age of a combined group can be calculated using the weighted average formula:

Combined Average = (n₁ × A₁ + n₂ × A₂) / (n₁ + n₂)

Here, the number of girls n₁ is 20 and their average age A₁ is 15 years. The number of boys n₂ is 25 and their average age A₂ is 24 years.

Substituting these values into the formula:

Combined Average = (20 × 15 + 25 × 24) / (20 + 25)

Combined Average = (300 + 600) / 45

Combined Average = 900 / 45

Combined Average = 20 years

Explanation

The present average age of P, Q, and R is 25 + 5 = 30 years. Thus, the sum of their present ages is 30 × 3 = 90 years.

Similarly, the present average age of Q and R is 20 + 7 = 27 years. Thus, the sum of the present ages of Q and R is 27 × 2 = 54 years.

The present age of P is calculated by subtracting the sum of the present ages of Q and R from the sum of the present ages of P, Q, and R. This gives 90 - 54 = 36 years.

Explanation

Let A, B, and C represent the individual per day incomes of A, B, and C.

The sum of the per day incomes of A, B, and C is calculated from their average: A + B + C = 450 × 3 = 1350

The sum of the per day incomes of A and B is: A + B = 400 × 2 = 800

The sum of the per day incomes of B and C is: B + C = 430 × 2 = 860

Adding the combined incomes of (A + B) and (B + C) gives: A + 2B + C = 800 + 860 = 1660

Subtracting the total income of all three individuals (A + B + C) from this sum isolates the per day income of B: B = (A + 2B + C) - (A + B + C) B = 1660 - 1350 B = 310

Explanation

Let the Cost Price (CP) of the article be 100%.

Selling at a loss of 20% means the first selling price is 80% of the CP. Selling at a gain of 5% means the second selling price is 105% of the CP.

The difference between the two selling prices is: 105% - 80% = 25% of the CP

This percentage difference corresponds to the actual price difference of Rs. 50: 25% of CP = Rs. 50

Multiplying both sides by 4 to find 100% of the CP: CP = Rs. 50 × 4 = Rs. 200

Explanation

Let CP be the cost price of one watch.

The total selling price of 14 watches is equal to the total cost price of 14 watches plus the profit earned.

Total Selling Price = Total Cost Price + Profit

Given that the selling price of one watch is Rs. 450, the total selling price for 14 watches is 14 × 450. The total cost price of 14 watches is 14 × CP. The profit is equal to the cost price of 4 watches, which is 4 × CP.

Substituting these values into the equation: 14 × 450 = 14 × CP + 4 × CP 14 × 450 = 18 × CP CP = (14 × 450) / 18 CP = 14 × 25 CP = 350

Explanation

Cost Price (CP) of one article is calculated by dividing the total cost by the number of articles: CP = 5110 / 73 = Rs. 70

Selling Price (SP) of one article is calculated by dividing the total selling price by the number of articles: SP = 5607 / 89 = Rs. 63

Since the Cost Price is greater than the Selling Price, there is a loss in the transaction.

Loss percentage is given by the formula: Loss % = ((CP - SP) / CP) × 100 Loss % = ((70 - 63) / 70) × 100 Loss % = (7 / 70) × 100 = 10%

Explanation

Total disbursement of loans of all banks together in 1997 is 45 + 18 + 22 + 28 = 113 crores.

Total disbursement of loans of all banks together in 1998 is 30 + 41 + 17 + 32 = 120 crores.

Increase in disbursement of loans from 1997 to 1998 = 120 - 113 = 7 crores.

Percentage increase = (7 / 113) × 100% = 700/113% = 6 22/113 %

Explanation

Net percentage change when a value is successively changed by x% and y% is given by the formula: Net Change = x + y + xy/100 %

For a 10% reduction followed by a 10% increase: x = -10 % y = +10 %

Substituting these values into the formula: Net Change = -10 + 10 + (-10 × 10)/100 % Net Change = -1 %

The negative sign indicates a decrease, meaning the new salary is 1% less than the original salary.

Alternatively, assuming the original salary is ₹100: After a 10% reduction, the salary becomes: 100 - 10 = ₹90

When this reduced salary is increased by 10%, the increase is: 10% of 90 = 9

So, the new salary becomes: 90 + 9 = ₹99

This is ₹1 less than the original ₹100, which corresponds to a 1% decrease.

Explanation

Revenue is the product of the number of seats and the cost of each ticket. When two quantities are multiplied, the net percentage change in their product due to percentage changes a% and b% in the individual quantities can be calculated using the successive percentage change formula:

Net percentage increase = a + b + (a × b)/100

Given that the number of seats is increased by a = 25% and the cost of each ticket is increased by b = 10%, the net change in revenue collection is:

Net percentage increase = 25 + 10 + (25 × 10)/100 Net percentage increase = 35 + 250/100 Net percentage increase = 35 + 2.5 Net percentage increase = 37.5%

Explanation

Let the monthly salary be S.

Expenditure on food is 40% of S, which leaves a remaining amount of 60% of S, or 0.6S.

Expenditure on transport is ⅓ of the remaining amount: ⅓ × 0.6S = 0.2S

The balance after spending on food and transport is: 0.6S - 0.2S = 0.4S

The monthly savings of Rs. 4,500 is equal to half of this balance: Savings = ½ × 0.4S = 0.2S

Setting this equal to the savings amount: 0.2S = 4500 S = 4500 ÷ 0.2 = 22500

Explanation

Let the required number be x.

According to the given condition, 80% of the number added to 80 results in the number itself. This relation can be written as:

80% of x + 80 = x

Converting the percentage into a decimal equivalent:

0.8x + 80 = x

Rearranging the terms to solve for x:

x - 0.8x = 80 0.2x = 80 x = 80 / 0.2 x = 400

Explanation

Let the speed of the truck be x km/hr. Since both vehicles are moving in the same direction, their relative speed is (45 - x) km/hr.

The formula for relative speed is: Relative speed = Distance / Time

Given that the distance is 150 meters and the time is 30 seconds, the relative speed in meters per second is: Relative speed = 150 / 30 = 5 m/s

To convert this relative speed into kilometers per hour, we multiply by 18/5: Relative speed = 5 × 18/5 = 18 km/hr

Equating the two expressions for relative speed: 45 - x = 18 x = 45 - 18 x = 27

Explanation

Let L be the length of the train in meters. When crossing a pole, the train covers a distance equal to its own length. Thus, the speed of the train is: speed = L / 15

When crossing a 100-meter platform, the total distance covered is the sum of the train's length and the platform's length. Thus, the speed is: speed = (L + 100) / 25

Since the speed of the train remains constant, we equate the two expressions: L / 15 = (L + 100) / 25

Simplifying by dividing the denominators by 5: L / 3 = (L + 100) / 5

Cross-multiplying: 5L = 3(L + 100) 5L = 3L + 300 2L = 300 L = 150 meters

Explanation

Let the principal sum of money be P. Since the sum becomes double of itself, the final amount is 2P, which means the simple interest earned is SI = 2P - P = P.

Using the standard simple interest formula, SI = (P × R × T) / 100, where R is the annual interest rate and T is the time in years:

P = (P × 15 × T) / 100

By canceling P from both sides:

1 = 15T / 100

T = 100 / 15

Reducing the fraction yields:

T = 20/3 = 6 2/3 years

Explanation

The difference (D) between compound interest and simple interest on a principal sum (P) for 2 years at an annual interest rate (R%) is given by the standard formula:

D = P × (R / 100)²

Given that the difference D = 768 and the rate R = 8%, we substitute these values into the formula:

768 = P × (8 / 100)²

768 = P × (64 / 10000)

P = (768 × 10000) / 64

Dividing 768 by 64 gives 12:

P = 12 × 10000 = 1,20,000

The sum of money is Rs 1,20,000.

Explanation

For yearly compounding: The total time is 1 year and ¼ year. The interest rate for the full year is 8%, and for the remaining ¼ year, it is 8% × ¼ = 2%. Amount (A₁) = 5000 × (1 + 8/100) × (1 + 2/100) = 5000 × 1.08 × 1.02 = 5508 Compound Interest (CI₁) = 5508 - 5000 = Rs. 508

For half-yearly compounding: The half-yearly rate of interest is 8% / 2 = 4%. The total time of 1¼ years (15 months) consists of 2 complete half-years (12 months) and one 3-month period (which is half of a half-year). The interest rate for the remaining 3-month period is 4% / 2 = 2%. Amount (A₂) = 5000 × (1 + 4/100)² × (1 + 2/100) = 5000 × 1.0816 × 1.02 = 5516.16 Compound Interest (CI₂) = 5516.16 - 5000 = Rs. 516.16

The difference between the compound interests is: Difference = CI₂ - CI₁ = 516.16 - 508 = Rs. 8.16