SSC CHSL Tier 1 2009 Question Paper with Answers & Explanations

Explanation

The relationship between the first two terms is that of a problem and its remedy or solution. Hunger is satisfied or cured by consuming food. Applying the same analogy to the second pair, a disease is cured or treated by taking medicine.

Explanation

The relationship between the words in each pair is based on antonyms.

Thin is the opposite of Thick.

Similarly, Dwarf (written as Draft) is the opposite of Tall.

Explanation

The pattern is based on shifting each letter forward by one position (+1) in the English alphabetical order.

A + 1 = B N + 1 = O

Applying this same rule to LY: L + 1 = M Y + 1 = Z

Explanation

The positional values of the letters in the English alphabet are used to find the pattern. In the first pair, the letters of ACE are transformed into HIL by adding 7, 6, and 7 to their respective alphabetical positions: A (1) + 7 = H (8) C (3) + 6 = I (9) E (5) + 7 = L (12)

Applying this same pattern of adding 7, 6, and 7 to the letters of MOQ: M (13) + 7 = T (20) O (15) + 6 = U (21) Q (17) + 7 = X (24)

This yields the letter combination TUX.

Explanation

Each letter in the first group BDFH is shifted forward by 8 positions in the alphabetical order to obtain the second group JLNP. Specifically, B (2) + 8 = J (10), D (4) + 8 = L (12), F (6) + 8 = N (14), and H (8) + 8 = P (16).

Applying the same pattern of adding 8 positions to the third group RTVX yields R (18) + 8 = Z (26), T (20) + 8 = B (2), V (22) + 8 = D (4), and X (24) + 8 = F (6) using a circular alphabetical system. This results in the letter group ZBDF.

Explanation

The relationship in the first pair is that the second number is the square root of the first number: √400 = 20

Applying the same mathematical rule to the second pair: √484 = 22

Explanation

The relationship between the numbers in each pair follows the mathematical rule where the second number is twice the square of the first number.

y = 2x²

For the first pair, when x = 4: y = 2 × 4² = 2 × 16 = 32

Using the same relationship for the second pair, when x = 7: y = 2 × 7² = 2 × 49 = 98

Explanation

The relationship between the first pair of numbers is established by reversing the order of their digits. Reversing the digits of 624 gives 426. Applying the same logic to the second pair, reversing the digits of 745 yields 547.

Explanation

The given numbers are analyzed based on their basic mathematical properties to find the odd one out. Among the alternatives, the number 9 is a perfect square because it can be expressed as 3². In contrast, none of the other numbers in the options represent a perfect square of any integer. Specifically, 2 is a prime number, 28 is a composite number equal to 4 × 7, and 63 is a composite number equal to 9 × 7. Since 9 is the only perfect square in the set, it is the odd number.

Explanation

Option c) is the odd one out because it represents the value 0.09 and has 9 as its numerator, which is a single-digit number. Unlike the other choices, it does not feature the three-digit sequence of 9, 0, and 9 in its numerical structure.

Explanation

The pair 100-110 is the odd one because it does not consist of consecutive perfect squares. In this set of pairs, the relationship follows the pattern x² and (x + 1)². Since 100 is 10², the next consecutive perfect square must be 11², which is 121, rather than 110.

Explanation

The difference between the alphabetical positions of the letters in the pair XV is 2 (X = 24, V = 22), whereas for all other options, the difference between the alphabetical positions of the two letters is 3. This makes XV the odd pair.

Explanation

In the letter group SUW, the alphabetical positions of S, U, and W are 19, 21, and 23 respectively. The difference between the consecutive letters in this group is +2 (S + 2 = U and U + 2 = W). This differs from the pattern where the first and second letters have a difference of +3, and the second and third letters have a difference of +2.

Explanation

In HIXW, the first two letters HI are in ascending alphabetical order, while the last two letters XW are in descending alphabetical order. This differs from the other letter groups, where both pairs of letters consist of consecutive letters in descending alphabetical order.

Explanation

The given letter series is w_xw_x_ax_a_wa. By counting the number of blanks, we find there are 5 gaps to be filled.

When we place the letters of the sequence "aawwx" in these gaps sequentially, we get: w a x w a x w a x w a x w a

This forms a repeating pattern of the three-letter unit "wax". Thus, the sequence of letters that completes the series is aawwx.

Explanation

The series follows a pattern where the alphabetical positions of the letters in consecutive terms increase by 5.

Converting the letters of the given terms to their positions in the English alphabet: A = 1, E = 5 F = 6, J = 10 P = 16, T = 20

For the first letter of each term: A (1) + 5 = F (6) F (6) + 5 = K (11) K (11) + 5 = P (16)

For the second letter of each term: E (5) + 5 = J (10) J (10) + 5 = O (15) O (15) + 5 = T (20)

Matching the numerical positions 11 and 15 back to the alphabet yields K and O.

Explanation

The alphabetical positions of the letters in each term of the series follow a continuous arithmetic progression of even numbers with a common difference of 2.

The first term BDF corresponds to the 2nd, 4th, and 6th letters of the alphabet. The second term HJL corresponds to the 8th, 10th, and 12th letters. The third term NPR corresponds to the 14th, 16th, and 18th letters.

Following this pattern, the letters of the next term must correspond to the 20th, 22nd, and 24th positions of the English alphabet, which are T, V, and X.

Explanation

The pattern of the given series is based on multiplying the preceding number by 2 and subtracting successive odd numbers starting from 1.

9 × 2 - 1 = 17 17 × 2 - 3 = 31 31 × 2 - 5 = 57 57 × 2 - 7 = 107 107 × 2 - 9 = 205

Alternatively, the differences between consecutive terms double and decrease by 2 at each step: 17 - 9 = 8 31 - 17 = 14 (where 8 × 2 - 2 = 14) 57 - 31 = 26 (where 14 × 2 - 2 = 26) 107 - 57 = 50 (where 26 × 2 - 2 = 50) 205 - 107 = 98 (where 50 × 2 - 2 = 98)

Explanation

The sum of the ages of A, B, and C is calculated by multiplying their average age by the number of friends, which is 20 × 3 = 60 years.

Similarly, the sum of the ages of A and B is calculated by multiplying their average age by 2, which is 19 × 2 = 38 years.

The age of C is the difference between these two sums: Age of C = 60 - 38 = 22 years.

Explanation

Representing the running speeds using inequalities based on the given statements:

Arun runs faster than Elias, but not as fast as Dinesh, which gives: Dinesh > Arun > Elias

Dinesh runs faster than Chander, but not as fast as Bikram, which gives: Bikram > Dinesh > Chander

Combining these relations shows that Bikram runs faster than Dinesh, who is already faster than Arun, Elias, and Chander. This establishes Bikram as the fastest runner.

Explanation

Ramu's mother refers to her mother's son, which means her own brother (Ramu's maternal uncle). The son of this brother is Achyut, who is the son of Ramu's maternal uncle. Since the son of one's maternal uncle is a cousin, Achyut is Ramu's cousin.

Explanation

The word GLAZE contains the letters G, L, A, Z, and E. The word ZEAL is made up of the letters Z, E, A, and L. Because every letter required to spell ZEAL is present in GLAZE, it is the word that can be formed.

Explanation

The word CRUMBS can be formed using the letters of the word CIRCUMSCRIBE because each letter required to construct it is available in the original word. The letter inventory of CIRCUMSCRIBE includes three Cs, two Is, two Rs, one U, one M, one S, one B, and one E. Since the word CRUMBS requires exactly one C, one R, one U, one M, one B, and one S, all of its constituent letters are present in CIRCUMSCRIBE in sufficient quantities.

Explanation

The word FLASCO cannot be formed from the given word SIGNIFICANT because the letters L and O are not present in the word SIGNIFICANT.

Explanation

The word MISSILE contains the letter L, which is not present in the word COMMISSIONER. Therefore, this word cannot be formed using the letters of the given word.

Explanation

The coding scheme adds 1 to the numerical position of each letter in the standard English alphabet.

Under the standard alphabetical order, the positions of the letters are: A = 1, which is coded as 1 + 1 = 2 B = 2, which is coded as 2 + 1 = 3

For the word FACE, the standard alphabetical positions of the letters are F = 6, A = 1, C = 3, and E = 5. Applying the rule of adding 1 to each letter's position:

F = 6 + 1 = 7 A = 1 + 1 = 2 C = 3 + 1 = 4 E = 5 + 1 = 6

Combining these coded values in order gives 7246.

Explanation

In the given code, each letter is shifted one step back in the alphabet: T becomes S, I becomes H, G becomes F, E becomes D, and R becomes Q. Applying the same rule to HORSE, H becomes G, O becomes N, R becomes Q, S becomes R, and E becomes D, giving the code GNQRD.

Explanation

The equations are solved by rearranging the three single-digit numbers in each multiplication into a three-digit number. The rearrangement follows a specific pattern:

First number × Second number × Third number = (Third number)(First number)(Second number)

Applying this pattern:

For the equation 4 × 5 × 6, the digits are rearranged as 6, 4, and 5 to form 645.

For the equation 5 × 6 × 7, the digits are rearranged as 7, 5, and 6 to form 756.

For the equation 6 × 7 × 8, the digits are rearranged as 8, 6, and 7 to form 867.

For the equation 8 × 7 × 9, the digits are rearranged as 9, 8, and 7 to form 987.

Explanation

The logic of the puzzle lies in multiplying the three numbers in each column to obtain the product at the bottom of that column.

First column: 6 × 12 × 10 = 720

Second column: 8 × 9 × 5 = 360

Third column: 12 × 4 × x = 336 48 × x = 336 x = 336 ÷ 48 = 7

Explanation

Let the starting point be S. When Mrs. Kiran drives 6 km towards the west, she reaches point A. Turning to her right means she is now facing north. She drives 4 km in this direction to reach point B. Turning to her right again means she is now facing east. She drives 6 km in this direction to reach her final destination, point C.

The path traced by her movements forms three sides of a rectangle S-A-B-C, where SA = 6 km, AB = 4 km, and BC = 6 km. Since opposite sides of a rectangle are equal, the distance from her starting point S to her final position C is equal to the length of AB, which is 4 km.

Explanation

From the given conditions, we can determine the circular arrangement of the five boys:

Since C is sitting immediately to the left of E, E is to the immediate right of C.

Since A is sitting between D and E, the two neighbors of E must be C and A.

Consequently, because A is between D and E, the neighbors of A are E and D.

This gives us a consecutive sequence of four boys: D - A - E - C.

The only remaining seat in the five-member circle is between D and C, which must be occupied by the remaining boy, B.

The complete circular arrangement is therefore D - A - E - C - B (connecting back to D).

Since E is on the immediate right of C, the person sitting on the immediate left of C is B.

Explanation

To find the arrangement of the five boys sitting in a circle:

First, place E at a position. Since C is sitting immediately to the left of E, C is placed next to E on E's left side.

Next, since A is sitting between D and E, A must be adjacent to both E and D. Since C is already on E's left side, A must be on E's right side, and D must be on the other side of A. This gives the sequence C - E - A - D.

Finally, the only remaining boy, B, must occupy the seat between D and C to complete the circle, resulting in the circular arrangement C - E - A - D - B.

From this arrangement, the person sitting between B and A is D.

Explanation

The statement that some phones are watches means there is a common intersection between the set of phones and the set of watches. Since all watches are guns, the entire set of watches is contained within the set of guns. This means the intersection of phones and watches must also lie inside the set of guns. Therefore, there must be an intersection between guns and phones, which validates the conclusion that some guns are phones.

Explanation

The given statement establishes that learning in schools is determined by two essential factors. The phrase "as they are able to understand" indicates that learning relies on the students' individual comprehension and cognitive capacity, which directly validates that learning depends on their ability to learn. The phrase "what is taught to them" implies that learning is also contingent on the delivery, method, and quality of instruction, which directly validates that learning depends on how they are taught. Because both the students' capability and the teaching method are necessary components of the learning process described in the statement, both conclusions logically follow.

Explanation

The statement "Private firm workers are hardworking" implies that the entire group of private firm workers is contained within the larger group of hardworking people. Since all private firm workers are hardworking, it logically follows that there are at least some hardworking people who are private firm workers. Therefore, conclusion I is a direct and valid deduction from the given statement.

Explanation

Mahatma Gandhi's boycott of foreign goods was deeply tied to the concept of Swadeshi and self-reliance. By advocating for the rejection of British-made textiles and manufactured items, Gandhiji aimed to revive and promote traditional Indian cottage industries, particularly the hand-spinning of Khadi using the charkha. He believed that reviving these village-level and cottage industries was crucial for rebuilding the rural economy, providing employment to the impoverished masses, and achieving economic self-sufficiency at the grassroots level.

Explanation

According to Article 58 of the Constitution of India, a candidate must have completed the age of 35 years to be eligible for election as the President of India. The Constitution does not prescribe any upper or maximum age limit for holding this office, meaning a qualified citizen of any age above 35 years can be elected to the post.

Explanation

The Jawahar Rozgar Yojana was launched on April 1, 1989, by merging the National Rural Employment Programme and the Rural Landless Employment Guarantee Programme. Designed to promote decentralised governance and community participation, the primary responsibility for planning and implementing the scheme was entrusted to the Gram Panchayats. Under this framework, financial resources were pooled and a major portion of these funds was directly allocated to village-level institutions, bypassing intermediate bureaucratic layers. This arrangement empowered the Gram Panchayats to directly address local employment needs, build essential rural infrastructure, and manage community asset creation at the grassroots level.

Explanation

The phrase primus inter pares, meaning first among equals, refers to the Prime Minister in a parliamentary system of government. While all cabinet ministers hold a similar status and share collective responsibility under the constitution, the Prime Minister occupies a pre-eminent position as the head of the Council of Ministers. The Prime Minister directs and coordinates the work of the government, presides over cabinet meetings, and holds the ultimate authority to advise the head of state on the appointment and dismissal of other ministers.

Explanation

Bangalore is known as the Silicon Valley of India because of its role as the nation's leading hub for information technology. The city is home to numerous multinational technology companies, major Indian IT exporters, and prestigious research institutions. This concentration of technology enterprises and engineering talent resembles the Silicon Valley in California, making it the premier center for software development and IT services in India.

Explanation

Maulana Abul Kalam Azad, a distinguished nationalist leader, freedom fighter, and independent India's first Minister of Education, authored the autobiographical book India Wins Freedom. First published in 1959, the book offers an insightful first-hand account of the crucial political developments during the Indian independence movement, the challenges of partition, and Azad's personal experiences and reflections on the key political figures of that era.

Explanation

The Reserve Bank of India (RBI) issues currency notes under the Fixed Minimum Reserve System, which was adopted in 1957. Under this framework, the RBI is legally mandated to maintain a constant minimum reserve of ₹200 crore in its Issue Department at all times. Out of this total reserve, a minimum value of ₹115 crore must be kept in gold coins or gold bullion, while the remaining ₹85 crore is held in the form of foreign securities and foreign currencies. Once this minimum reserve requirement is met, the RBI has the flexibility to issue banknotes to any extent to meet the transactional and liquidity demands of the Indian economy.

Explanation

International Human Rights Day is celebrated annually on December 10th to commemorate the day in 1948 when the United Nations General Assembly adopted the Universal Declaration of Human Rights. This landmark document proclaimed the inalienable rights that every human being is inherently entitled to, regardless of race, colour, religion, sex, language, political or other opinion, national or social origin, property, birth, or other status.

Explanation

Karachi served as the first capital of independent Pakistan from 1947 until 1959. In 1959, the government decided to shift the capital to a newly planned city in the north, during which Rawalpindi became the temporary capital while Islamabad was being constructed.

Explanation

The Foreign Exchange Regulation Act (FERA) of 1973 was replaced by the Foreign Exchange Management Act (FEMA) of 1999. FERA had rigid regulations and treated violations of foreign exchange rules as criminal offences, which hindered economic growth after India opened its economy in 1991. To support economic liberalization, FEMA was introduced to shift the focus from conserving foreign exchange to facilitating external trade, payments, and maintaining an orderly foreign exchange market. Under FEMA, violations were classified as civil offenses instead of criminal ones. The act officially came into force on June 1, 2000.

Explanation

Ajantha Mendis, the mystery spinner from Sri Lanka, won the ICC Emerging Player of the Year award in 2008. He had a phenomenal debut year in international cricket, which included a legendary spell of 6 for 13 against India in the 2008 Asia Cup final and 26 wickets in his first three Test matches. His outstanding bowling performances across formats during the voting period earned him this prestigious global recognition.

Explanation

The term PC stands for Personal Computer, which refers to a multi-purpose microcomputer designed for individual use. It is configured to be operated directly by an end-user, rather than requiring a computer specialist or mainframe operator. Personal computers are commonly used for daily tasks such as word processing, internet browsing, gaming, and running productivity software in homes and offices.

Explanation

Nagaland adopted English as its official language in 1967 through the passage of the Nagaland State Official Language Act. Under Article 345 of the Constitution of India, state legislatures have the power to adopt any language in use in the state, or Hindi, as their official language. English serves as the administrative language of Nagaland to facilitate official communication and governance among its diverse tribes, who speak various mutually unintelligible languages.

Explanation

The Right to Information Act was passed by the Parliament of India in 2005 to secure for citizens access to information under the control of public authorities, promoting transparency and accountability in the working of the government. The bill received the assent of the President of India on 15 June 2005 and came into force on 12 October 2005.

Explanation

Navin Chawla succeeded N. Gopalaswami as the 16th Chief Election Commissioner of India. He took charge of the office on 21 April 2009 and served until 29 July 2010. During his tenure as the Chief Election Commissioner, he successfully supervised the conducting of the 2009 Indian general elections to the 15th Lok Sabha. Prior to his elevation to the post of Chief Election Commissioner, he had been serving as an Election Commissioner since June 2005.

Explanation

The 2009 Sultan Azlan Shah Cup, which is referred to as the Sultan Afzal Shah tournament in the question, was the 18th edition of the annual international men's field hockey tournament held in Ipoh, Malaysia, from 5 to 12 April 2009. The final was played on 12 April 2009 between India and the host nation, Malaysia. India won the match 3-1 to secure their fourth title in the history of the tournament. India's goals in the final were scored by Arjun Halappa, Prabhjot Singh, and Shivendra Singh, while Aslam Misron scored the lone goal for Malaysia.

Explanation

The 2011 ICC Cricket World Cup was originally planned to be co-hosted by India, Pakistan, Sri Lanka, and Bangladesh. However, in April 2009, the International Cricket Council stripped Pakistan of its hosting rights due to security concerns following the terrorist attack on the Sri Lankan national cricket team in Lahore in March 2009. As a result, the matches originally scheduled to be played in Pakistan were redistributed, and the tournament was co-hosted by India, Sri Lanka, and Bangladesh.

Explanation

Virender Sehwag was named the Wisden Leading Cricketer in the World for his outstanding performances in 2008, becoming the first Indian player to receive this prestigious honour since the award was established in 2004. In the 2008 calendar year, he scored 1462 Test runs at an exceptional strike rate of over 85. His brilliant form during this period included a remarkable innings of 319 off 304 balls against South Africa in Chennai, which stands as the fastest triple century in Test cricket history.

Explanation

G. Madhavan Nair served as the Chairman of the Indian Space Research Organisation (ISRO) and the Secretary to the Department of Space, Government of India, from September 2003 to October 2009. During his tenure as the chief of ISRO, India achieved significant milestones in space exploration, most notably the successful launch of India's first lunar mission, Chandrayaan-1, in October 2008.

Explanation

The value of money refers to its purchasing power, which is the amount of goods and services that can be bought with a unit of currency. As the general price level rises, a unit of money buys fewer goods and services, meaning the value of money decreases, which establishes an inverse relationship between the two.

Explanation

In national income accounting, the difference between any gross measure and its corresponding net measure is depreciation, which represents the consumption of fixed capital. The relationship is defined by the formula:

Net National Product = Gross National Product - Depreciation

Rearranging this formula to solve for depreciation yields:

Depreciation = Gross National Product - Net National Product

This represents the loss in value of capital assets due to wear and tear, obsolescence, and accidental damage during the production process over a given period.

Explanation

The classification of sectors into public and private is determined by the ownership of enterprises. In the public sector, the government owns and controls the assets and enterprises, prioritizing social welfare and public interest. In the private sector, the ownership of assets and businesses is held by private individuals or corporations, with the primary goal of generating profit.

Explanation

The Story of My Experiments with Truth is the autobiography of Mohandas Karamchand (M.K.) Gandhi, covering his life from early childhood through to 1921. It was originally written in Gujarati and published in weekly installments in his journal Navajivan from 1925 to 1929. The English translation, prepared primarily by Mahadev Desai, also appeared in installments in Gandhi's other journal, Young India, before being published as a book. The work details his spiritual, personal, and political development, outlining the origins of his philosophies of truth, non-violence, and satyagraha.

Explanation

Ratan Tata, then-Chairman of the Tata Group, was adjudged the Business Person of the Year 2008 by The Times of India Survey. This recognition highlighted his visionary leadership during a monumental year for the conglomerate, which was marked by the historic acquisition of the British luxury car brands Jaguar and Land Rover in June 2008, as well as the unveiling of the world's most affordable car, the Tata Nano, in January 2008.

Explanation

The Luni River is the most significant and largest river in the Thar Desert region of northwest India. It originates in the Pushkar Valley of the Aravalli Range near Ajmer at an elevation of about 550 meters. It flows southwest through the arid and semi-arid desert region of Rajasthan before terminating in the marshy lands of the Rann of Kutch in Gujarat. Due to its flow through a desert terrain with high evaporation and saline soil, it is an ephemeral river with highly saline water in its lower reaches, earning it the name Luni, which is derived from the Sanskrit word Lavanavari, meaning salt river.

Explanation

The Nagarjunasagar Dam is one of the largest and most prominent masonry dams in India, constructed across the Krishna River. Built between 1955 and 1967, the dam creates a massive reservoir that is one of the largest man-made lakes in the world. Named after the revered Buddhist philosopher and monk Acharya Nagarjuna, the dam serves as a vital source of water for irrigation and hydroelectric power generation, benefiting the agricultural lands of both Andhra Pradesh and Telangana.

Explanation

Contours, or contour lines, are imaginary lines drawn on a map connecting points of equal height or elevation above a reference datum, typically mean sea level. They are plotted at regular vertical intervals to effectively represent the three-dimensional topography and slopes of the terrain on a flat, two-dimensional map surface.

Explanation

Stagflation is an economic condition characterized by a combination of slow economic growth, high unemployment (which together constitute economic stagnation), and rising prices (inflation). The term itself is a portmanteau of stagnation and inflation, describing a challenging scenario where the inflation rate is high, the economic growth rate slows down, and unemployment remains steadily high, presenting a dilemma for macroeconomic policy.

Explanation

Khetri, located in the Jhunjhunu district of Rajasthan, is renowned for its rich copper deposits and is a major center of copper mining in India. The copper mines in this region have been actively worked since ancient times, dating back to the Indus Valley Civilization. Modern mining and processing facilities in Khetri are operated by Hindustan Copper Limited, a public sector undertaking. This region houses the Khetri Copper Complex, which comprises integrated facilities for copper mining, concentration, smelting, and refining.

Explanation

The Narmada River is a major west-flowing river in India that originates from the Amarkantak Plateau in Madhya Pradesh and flows through a rift valley between the Vindhya and Satpura ranges. Due to its passage through hard rocky terrain with a steep gradient, the river carries minimal sediment load. The high velocity of the river flow prevents the deposition of silt at its mouth, resulting in the formation of a deep, funnel-shaped estuary where it empties into the Gulf of Khambhat in the Arabian Sea.

Explanation

Charaka was a renowned physician in ancient India and is widely regarded as one of the principal contributors to Ayurveda. He served as the court physician of the Kushana king Kanishka, who ruled in the late 1st to early 2nd century CE. Charaka is celebrated for authoring the Charaka Samhita, one of the foundational Sanskrit texts on traditional Indian medicine, which comprehensively details anatomy, pathology, diagnostics, and medical ethics.

Explanation

The Great Stupa at Sanchi is one of the oldest stone structures in India and a prominent Buddhist monument. It is situated on a hilltop at Sanchi in the Raisen district of the state of Madhya Pradesh. Commissioned by the Mauryan Emperor Ashoka in the 3rd century BCE, the stupa was constructed to house and protect the sacred relics of Lord Buddha. It is renowned for its magnificent hemispherical dome and intricately carved gateways (toranas) that depict various stories from the Jataka tales and key events from the life of Buddha.

Explanation

Akbar was born on October 15, 1542, in Amarkot. Following the sudden demise of his father, Humayun, Akbar was crowned as the Mughal Emperor at Kalanaur in Punjab on February 14, 1556. At the time of this coronation, he was thirteen years and four months old. Due to his young age, his military commander Bairam Khan was appointed as his regent to run the affairs of the state until Akbar reached maturity.

Explanation

The ashrama system in ancient Aryan society divided the ideal human life of 100 years into four successive stages of 25 years each. The chronological sequence begins with Brahmacharya, which is the period of education, celibacy, and mental discipline. This is followed by Grihastha, the householder stage dedicated to marriage, family, and worldly duties. Next is Vanaprastha, the retirement phase where one begins to withdraw from societal bonds and focus on spiritual contemplation. The final stage is Sanyasa, representing complete renunciation of material life and dedication to attaining liberation or Moksha.

Explanation

Renewable resources are natural resources that replenish themselves naturally through ecological or physical processes over time. Because their rate of regeneration matches or exceeds their rate of consumption, they are virtually inexhaustible and can be utilized continuously, year after year, without the risk of depletion.

Explanation

The Malabar Coast constitutes the southwestern coastline of the Indian peninsula, lying primarily within the state of Kerala. This coastal region is bounded by the Arabian Sea on the west and the Western Ghats on the east. It is highly famous for its unique geographical features such as backwaters, lagoons, and estuaries, as well as its historical significance as a major global hub for the spice trade.

Explanation

Anantapur district is famous for gold mining, primarily due to the presence of the Ramagiri Gold Fields (RGF). This gold-bearing belt extends across a 13-kilometer-long stretch in the Ramagiri region of the district. Underground gold mining was extensively carried out here by British miners in the early twentieth century, and later by the government-owned Bharat Gold Mines Limited (BGML) until mining activities were suspended around 2001. The Ramagiri greenstone belt is well-known for its rich gold mineralization, making Anantapur a major gold-producing tract in Andhra Pradesh.

Explanation

Bahadur Shah II, popularly known as Bahadur Shah Zafar, was the twentieth and last Mughal emperor of India. He ascended the throne in 1837. During the Indian Rebellion of 1857, the rebel sepoys declared him the Emperor of Hindustan. After the British suppressed the uprising, he was tried for treason, deposed, and exiled to Rangoon in Burma, which brought a formal end to the Mughal Empire.

Explanation

Mangal Pandey was a sepoy in the 34th Bengal Native Infantry stationed at the Barrackpore cantonment near Calcutta. On March 29, 1857, he rebelled against the British officers over the introduction of the new Enfield cartridges, which were rumored to be greased with cow and pig fat. During this incident, he fired the first shot of the mutiny at Sergeant-Major James Hewson and subsequently attacked Lieutenant Baugh, marking the opening event that catalyzed the widespread Revolt of 1857.

Explanation

Bal Gangadhar Tilak coined the famous slogan "Swaraj is my birthright and I shall have it" during the Indian independence movement. He was a prominent nationalist, social reformer, and leader who strongly advocated for self-rule (Swaraj) as a fundamental and inherent right of every Indian to mobilize public consciousness and resistance against British colonial rule.

Explanation

The boiling point of a liquid is the temperature at which its vapor pressure equals the surrounding atmospheric pressure. As altitude increases on hills, the atmospheric pressure decreases because the air column above is shorter and less dense. With a lower external atmospheric pressure, water requires less heat energy to generate a vapor pressure that equals the surrounding pressure, causing it to boil at a temperature below the standard 100 °C.

Explanation

The Chauri Chaura incident occurred on 4 February 1922 in Gorakhpur district of the United Provinces, when a large group of protesters participating in the Non-Cooperation Movement clashed with local police. After police opened fire on the crowd, the demonstrators retaliated by setting fire to a police station, which resulted in the deaths of 22 policemen. Mahatma Gandhi, who was deeply committed to the principles of Ahimsa, felt that the movement was losing its strictly non-violent character and that the participants were not yet fully trained for peaceful resistance. Consequently, he decided to suspend the Non-Cooperation Movement nationwide on 12 February 1922 through the Bardoli resolution.

Explanation

Refrigeration preserves food by lowering the temperature, which significantly slows down the metabolic activities of bacteria and moulds, rendering them inactive. Low temperatures in a refrigerator do not kill or sterilize germs, but merely inhibit their growth and reproduction.

Explanation

Individuals with the AB blood group have both A and B antigens present on the membrane of their red blood cells. Consequently, their blood can only be safely transfused into individuals who also belong to the AB blood group, as AB recipients do not have anti-A or anti-B antibodies in their plasma to react against these antigens.

Explanation

Birds possess a highly specialized and exceptionally efficient respiratory system characterized by several extra air sacs distributed throughout their body cavity. These air sacs, typically numbering nine, act as bellows to pump air through the respiratory tract. They facilitate a continuous, unidirectional flow of fresh, oxygen-rich air through the lungs during both inhalation and exhalation.

Unlike mammals, whose bidirectional tidal breathing results in the mixing of fresh and stale air, this unidirectional system completely eliminates anatomical dead space. Consequently, the lungs are constantly supplied with fresh air for highly efficient crosscurrent gas exchange. This remarkable physiological adaptation enables birds to extract sufficient oxygen to sustain the high metabolic demands of flight even in the extremely thin, hypoxic conditions at high altitudes.

Explanation

The Sun is the ultimate and primary source of energy for almost all ecosystems on Earth. Solar energy is captured by autotrophic organisms, such as green plants, through the process of photosynthesis, where it is converted into chemical energy. This energy then flows through various trophic levels of the food chain, sustaining all life forms within the ecosystem.

Explanation

Tungsten is a heavy metal characterized by its exceptionally high melting point, high density, and extreme hardness. It is primarily utilized in the manufacture of high-speed tool steels, filaments for incandescent light bulbs, and heavy metal alloys designed to withstand extreme thermal and mechanical stress. Tungsten is not used in the manufacture of standard stainless steel, as it does not contribute to the corrosion resistance and metallurgical properties required for stainless steel alloys.

Explanation

Distilled water is a pure chemical compound represented by the formula H₂O. It consists of hydrogen and oxygen atoms chemically bonded in a fixed 2:1 ratio. Because its components are chemically combined in a definite proportion, it exhibits constant chemical and physical properties throughout and cannot be separated into its constituent elements by physical methods. This classification as a pure compound distinguishes it from mixtures, which consist of physically blended substances that retain their individual properties and can be separated by physical means.

Explanation

The relationship between the Celsius (C) and Fahrenheit (F) temperature scales is given by the formula:

F = 9/5 × C + 32

To find the point where the two scales read the same value, set F = C = T:

T = 9/5 × T + 32

Subtracting 9/5 × T from both sides gives:

-4/5 × T = 32

Solving for T:

T = 32 × (-5/4) = -40

This calculation demonstrates that -40° is the unique temperature at which the Celsius and Fahrenheit scales register the exact same numerical value.

Explanation

The preposition in is incorrect when referring to a beach. The correct preposition to use with beach is on or at, as a beach represents an open surface or a specific location rather than a three-dimensionally enclosed space. Therefore, the phrase in the beach should be corrected to on the beach or at the beach.

Explanation

The phrase has early in part (b) is grammatically incorrect and incomplete. The auxiliary verb has must be followed by a main verb in the past participle form, such as left, to form the present perfect tense has left early and convey a complete meaning.

Explanation

The verb told is a transitive verb that requires an indirect object representing the person being spoken to before a that-clause. For example, it must be written as told us that or told the students that. When no indirect object is specified, the reporting verb said must be used instead of told. Therefore, the phrase must be corrected to The teacher said that to be grammatically correct.

Explanation

The grammatical structure one of the is always followed by a plural noun because it represents one individual selected from a larger group. In part (b), the preposition of is missing after one, and the singular noun boy is incorrectly used instead of the plural noun boys. The correct construction is one of the tallest boys.

Explanation

The verb award is transitive and directly takes a direct object without requiring a preposition. In passive voice constructions, the pattern is subject + be awarded + object. Therefore, the preposition with is grammatically incorrect and redundant.

The corrected sentence is: He was awarded a doctorate degree for his new invention.

Explanation

The verb hamper means to hinder, impede, or make progress difficult. Heavy rainfall typically disrupts, slows down, or creates obstacles for outdoor activities, construction, or development projects, making hampered the most suitable word to describe how the progress of the works was affected by the rains.

Explanation

The word besides is a preposition that means in addition to or as well as. In this sentence, it is used to indicate that the person has knowledge of the Russian language in addition to French and German.

Explanation

The word tainted means damaged, tarnished, or contaminated, especially in a moral or qualitative sense. When applied to someone's reputation, it signifies that their standing or honor has been ruined or soiled. Foolish acts naturally lead to a loss of respect or damage to one's character, making tainted the grammatically and semantically correct choice to complete the sentence.

Explanation

The adjective best is the superlative form of good. In English grammar, superlative adjectives are preceded by the definite article the when modifying a singular noun to indicate a supreme or unique degree. Since the noun way in the sentence is singular, the definite article the must accompany the superlative adjective best to form the grammatically correct phrase the best way.

Explanation

The phrasal verb "call on" means to pay a visit to someone, especially in a formal or official capacity. In the given sentence, the Prime Minister of England paid a visit to the President of America, making "on" the correct preposition to complete the phrasal verb "called on".

Explanation

The word inadvertent describes an action, mistake, or occurrence that is not done deliberately, planned, or intended. It refers to something happening by accident, oversight, or lack of attention, which directly aligns with the meaning of unintentional.

Explanation

The word barren describes land or soil that is unproductive and unable to grow crops or sustain vegetation. It also refers to a living organism that is unable to produce offspring. The word infertile directly translates to this state of being sterile, unproductive, or incapable of reproduction, making it the closest synonym.

Explanation

The word abstain means to voluntarily restrain or hold oneself back from doing or enjoying something, especially from an action or practice. The word refrain similarly means to stop oneself from doing something, making it the most accurate synonym that expresses the exact same meaning.

Explanation

The word counterfeit is used to describe something that is made in imitation of something else with the intent to deceive, cheat, or defraud. Therefore, the word that best expresses its meaning is fake, which refers to an object or person that is not genuine.

Explanation

The word novice refers to a person who is new to a circumstances, field, or activity and lacks experience. It is derived from the Latin word novus, which means new. A beginner is also someone who is starting to learn or do something for the first time, making it the synonym that best expresses the meaning of novice.

Explanation

The word diminish means to make or become less in size, amount, intensity, or degree. The direct opposite of this action or state is to make or become greater in size, amount, intensity, or degree, which is the definition of the word increase.

Explanation

The word comply means to act in accordance with a rule, order, or request, representing submission and obedience. The opposite action is to resist, dispute, or defy authority. The word challenge means to call into question, oppose, or defy, making it the correct antonym.

Explanation

The word treacherous is defined as being guilty of or involving betrayal, deception, or disloyalty. Its direct antonym is faithful, which describes someone who is loyal, steadfast, and reliable in their allegiance or duties.

Explanation

The word inquisitive is used to describe someone who is curious, eager for knowledge, or highly interested in learning about things and inquiring into others' affairs. The opposite of being curious or interested is being indifferent, detached, or showing a lack of interest. Unconcerned directly represents this state of having a complete lack of interest, care, or curiosity, making it the antonym of inquisitive.

Explanation

The word affluence denotes a state of abundance, great wealth, or prosperity. Its direct antonym is poverty, which refers to the condition of having little or no money, goods, or means of support.

Explanation

The phrasal verb run down means to disparage, belittle, or speak ill of someone. In the context of the sentence, it means to criticise one's friends in public.

Explanation

The idiom "to make both ends meet" means to have enough money to cover basic living expenses, or to balance income and expenditure. It refers to the struggle of ensuring that one's outgoing expenses do not exceed their incoming revenue, which translates directly to living within one's income.

Explanation

The phrasal verb "pore over" means to read, study, or examine something with great care and attention. Similarly, the phrasal verb "go through" means to read, examine, or study something thoroughly from beginning to end. In the context of students studying their lessons attentively, "go through" accurately conveys this meaning of diligent and detailed examination.

Explanation

The idiom crossed swords means to engage in a dispute, argument, or confrontation with someone. Derived from the literal action of clashing swords in a duel, in modern figurative usage, particularly when referring to writers, intellectuals, or colleagues, it signifies having a strong disagreement or verbal conflict over opinions and ideas.

Explanation

The idiom or phrase standstill refers to a state of cessation of movement or activity, representing a situation where everything has stopped completely. In the context of traffic after a heavy downpour, coming to a standstill means that vehicles have completely stopped moving, resulting in a complete halt.

Explanation

Compound nouns containing a principal noun and a prepositional phrase form their plural by pluralizing the principal noun. In the compound noun mother-in-law, mother is the principal noun. Therefore, the correct plural form is mothers-in-law.

Explanation

The idiomatic expression run down is used to describe someone who is extremely tired, depleted of energy, or in a poor physical state, usually due to overwork, stress, or lack of rest. The word exhausted precisely captures this state of being completely drained of physical or mental strength, making it the most accurate and suitable replacement to convey the intended meaning of the sentence.

Explanation

The verb console means to comfort someone specifically at a time of grief, disappointment, or bereavement, such as after the death of a loved one. In the context of mourning and loss, consoled is the most precise and appropriate term to describe the act of trying to make the grieving old man feel less sad.

Explanation

The term fraudulent is the most appropriate adjective to modify means when describing the illegal or deceptive acquisition of confidential data. While wrong is grammatically acceptable, it is too informal and vague for a sentence involving top-secret information. Fraudulent means specifically indicates the use of deceit, dishonesty, or misrepresentation to bypass security and illegally acquire data, which matches the formal tone and context of the statement.

Explanation

The verb broadcast is irregular, and its past tense and past participle forms are traditionally broadcast. For a passive voice sentence referring to a specific time in the past like last Thursday, the simple past passive form was broadcast is grammatically correct and preferred in standard English.

Explanation

The word assent means to express official agreement, approval, or acceptance of a proposal, opinion, or request. It functions as a verb meaning to agree to a statement or decision, or as a noun representing the expression of such agreement.

Explanation

A recluse is a person who lives a solitary life and tends to avoid other people, typically choosing to withdraw from society to live in complete seclusion for personal, religious, or philosophical reasons.

Explanation

The term bibliophile is derived from the Greek words biblion, which means book, and philos, which means loving or friend. Therefore, a bibliophile is literally defined as a person who loves, collects, or has a great appreciation for books.

Explanation

The word sporadic is used to describe events, occurrences, or phenomena that happen occasionally, singly, or in scattered instances, without any regular pattern, consistency, or scheduled frequency in time.

Explanation

The word commemorate means to recall, honor, or preserve the memory of an extraordinary person or significant past event, typically through a ceremony, celebration, or monument. Derived from the Latin com- (together) and memorare (to bring to mind), it specifically describes the act of keeping a historical occurrence or prominent figure alive in the collective consciousness of people.

Explanation

Autumn is the correct spelling for the season between summer and winter. The word is of Latin origin and features a silent 'n' at the end, which is a common characteristic of English words ending with the 'mn' consonant cluster where the 'n' remains unpronounced.

Explanation

The word "premier" is correctly spelled. It functions as an adjective meaning first in importance, order, or position, and as a noun referring to a prime minister or other head of government.

Explanation

The word superintendent is derived from the Latin verb superintendere, which means to oversee or supervise. It is formed by combining the prefix super- (meaning over or above) with the root word intend and the noun suffix -ent, which denotes a person who performs a specific action. This combination yields the correct spelling s-u-p-e-r-i-n-t-e-n-d-e-n-t.

Explanation

The word dictionary is correctly spelled. It is a noun that refers to a reference source containing an alphabetical list of words with their explanations, meanings, pronunciations, and etymologies. The term originates from the Medieval Latin word dictionarium, which is derived from the Latin dictio, meaning speech, word, or expression.

Explanation

The word rehabilitation is correctly spelled as r-e-h-a-b-i-l-i-t-a-t-i-o-n. It originates from the Latin prefix re- meaning again, combined with habilitare meaning to make fit, and the suffix -ion which denotes an action or process. The word comprises six syllables: re-ha-bil-i-ta-tion, maintaining the h after the prefix and ending with the standard -tion suffix.

Explanation

The passage discusses how the physical environment and architectural layout of modern cities contribute directly to the occurrence of criminal activities. The sentence states that the actual design of a city acts as a factor or source that brings about crime, which means it is identified as one of the primary causes of crime.

Explanation

The verb published is the most appropriate fit for the blank because a researcher or academic makes their research findings available to the public by publishing them in a book. In this context, Oscar Newman has made the results of his study accessible to the public in his book titled Defensible Space.

Explanation

The noun effect is standardly paired with the preposition on to indicate the entity that is being influenced or impacted by a particular cause. In this sentence, the environment is the cause, and crime is the entity experiencing the impact. Therefore, the phrase effect of environment on crime correctly describes this relationship of influence.

Explanation

The sentence discusses how certain building designs discourage social intervention, leading residents to stand by and permit criminal activities to take place. In this context, the verb phrase "allow crimes to" is completed naturally by "happen", which means to occur or take place, indicating that the environment enables crimes to be committed without any interference.

Explanation

In the context of the sentence, the author highlights a paradox of modern urban living where crowded apartments bring people physically close but keep them psychologically disconnected. The adverb mentally provides the correct semantic contrast to the adverb physically. It accurately describes the state of being emotionally and psychologically detached or isolated from others, despite living in extreme physical proximity.

Explanation

The word essentially is the most appropriate fit for blank 146 as it means fundamentally or basically, describing how the residents live in what is in essence a single building with a shared entrance yet remain isolated from one another. Options like accidentally or deliberately do not make sense in this context.

Explanation

The adjective unconcerned is followed by the preposition with when it means having no interest, involvement, or connection with someone or something. In this context, the residents feel isolated and lack any social connection or involvement in the lives of their neighbours, making with the correct preposition to complete the sentence.

Explanation

The preposition over is used to denote duration or the passage of time. The phrase over a period of half an hour is the standard idiomatic construction to describe an action happening throughout that specific duration.

Explanation

The word observed fits the context of being a passive, inactive bystander. To observe means to watch, notice, or perceive a situation attentively without taking an active part in it. In this scenario, the residents of the building were aware of the violent crime taking place, yet they maintained a detached position and failed to intervene or contact the authorities. This passive act of witnessing a significant event unfold without participation is accurately conveyed by the verb observed.

Explanation

The phrase out of sight is a standard English idiom that means hidden from view or outside the area where things can be seen. In the context of the passage, spaces between buildings that are not visible to others (out of sight) provide convenient, secluded locations where criminals can act without fear of being detected or observed.

Explanation

We can express the base 256 as 4⁴: 256 = 4⁴

Using the exponent rule (aᵐ)ⁿ = aᵐ ˣ ⁿ: (256)⁰·¹⁶ = (4⁴)⁰·¹⁶ = 4⁴ ˣ ⁰·¹⁶ = 4⁰·⁶⁴

With d = 4, the expression becomes: 4⁰·⁶⁴ × 4⁰·³⁶

Using the product rule of exponents, aᵐ × aⁿ = aᵐ ⁺ ⁿ: 4⁰·⁶⁴ × 4⁰·³⁶ = 4⁰·⁶⁴ ⁺ ⁰·³⁶ = 4¹ = 4

Explanation

The sum of the cubes of the first n natural numbers is given by the formula: Sₙ = [n(n + 1) / 2]²

For the series of the first 10 natural numbers, where n = 10: 1³ + 2³ + 3³ + ... + 10³ = [10 × (10 + 1) / 2]² = [10 × 11 / 2]² = 55² = 3025

Explanation

Let the two numbers be 3x and 4x, where x is a positive integer representing their highest common factor.

The product of two numbers is always equal to the product of their HCF and LCM.

Product of the two numbers = 3x × 4x = 12x²

Since the product of their HCF and LCM is 2028: 12x² = 2028 x² = 2028 ÷ 12 x² = 169 x = 13

The sum of the two numbers is: 3x + 4x = 7x 7 × 13 = 91

Explanation

The given multiplication problem represents the product of two-digit numbers, written as a2 × 7a = 6396. Substituting the value 8 for the digit a yields the expression 82 × 78. Using the algebraic identity (x + y)(x - y) = x² - y², this product can be computed by setting x = 80 and y = 2. This results in (80 + 2) × (80 - 2) = 80² - 2² = 6400 - 4 = 6396. This confirms that the digit is indeed 8.

Explanation

The square root of 1000 lies between 31 and 32. Calculating the squares of these integers: 31² = 961 32² = 1024

To make 1000 a perfect square by subtraction, we must reduce it to the nearest lower perfect square, which is 961.

The required number to be subtracted is the difference between 1000 and this perfect square: 1000 - 961 = 39

Explanation

Let the two numbers be x and y.

We are given: Sum of the numbers, x + y = 11 Product of the numbers, xy = 18

The sum of their reciprocals is defined by the relation: 1/x + 1/y = (x + y)/xy

By substituting the given values of the sum and the product into the formula: 1/x + 1/y = 11/18

Explanation

The number of grapes eaten each day forms an arithmetic progression where the number of terms n = 5, the common difference d = 6, and the sum of the terms Sₙ = 100.

The sum of an arithmetic progression is given by the formula: Sₙ = (n/2) × [2a + (n - 1)d]

where a is the first term, representing the number of grapes eaten on the first day.

Substituting the values into the formula: 100 = (5/2) × [2a + (5 - 1) × 6] 100 = (5/2) × [2a + 24] 100 = 5 × (a + 12) 20 = a + 12 a = 8

Explanation

The given sequence follows a pattern where the square of consecutive odd integers is added to each preceding term to obtain the next term.

The first term is 5.

The second term is 5 + 1² = 6.

The third term is 6 + 3² = 15.

The fourth term, which is the missing number, is 15 + 5² = 40.

The fifth term is 40 + 7² = 89.

The sixth term is 89 + 9² = 170.

The seventh term is 170 + 11² = 291.

Explanation

Let the original number be x.

The student was required to find 0.72x but instead calculated 7.2x.

According to the given condition, the difference between these two products is 2592: 7.2x - 0.72x = 2592

Subtracting the coefficients on the left-hand side: 6.48x = 2592

Solving for x: x = 2592 / 6.48 x = 259200 / 648 x = 400

Explanation

The operator + in the expression represents the division operator ÷. Dividing 7,77,777 by 77 gives:

7,77,777 ÷ 77 = 10101

To verify this by long division: 77 ÷ 77 = 1 Bringing down the next digit 7, it is not divisible by 77, so we write 0 in the quotient. Bringing down the next digit 7 to make 77: 77 ÷ 77 = 1, making the quotient 101. Bringing down the next digit 7, it is not divisible by 77, so we write 0 in the quotient. Bringing down the final digit 7 to make 77: 77 ÷ 77 = 1, making the final quotient 10101.

We can also verify by multiplication: 10101 × 77 = 10101 × 7 × 11 = 70707 × 11 = 7,77,777

Explanation

If two pipes can fill a cistern separately in a and b hours, the time taken by both pipes working together to fill the cistern is given by the formula:

T = (a × b) / (a + b)

Substituting the given values, a = 10 hours and b = 15 hours:

T = (10 × 15) / (10 + 15) T = 150 / 25 T = 6 hours

Explanation

The product of the natural numbers from 1 to 100 is represented as 100! (100 factorial). The number of trailing zeroes in n! is determined by the exponent of the prime number 5 in its prime factorization, as there are always more than enough factors of 2 to pair with each 5 to form a 10.

Using Legendre's formula, the exponent of a prime p in n! is calculated as the sum of floor values of n divided by successive powers of p:

Number of zeroes = ⌊100/5⌋ + ⌊100/5²⌋ + ⌊100/5³⌋ + ...

Substituting the values gives:

Number of zeroes = ⌊100/5⌋ + ⌊100/25⌋ + ⌊100/125⌋

Number of zeroes = 20 + 4 + 0 = 24

Explanation

Let the total work be the least common multiple of 12 and 15, which is 60 units.

The efficiency of A is 60 / 12 = 5 units per day. The efficiency of B is 60 / 15 = 4 units per day.

Their combined efficiency is 5 + 4 = 9 units per day.

In the first 4 days, A and B work together and complete: 4 × 9 = 36 units of work

The remaining work is: 60 - 36 = 24 units

B alone completes this remaining work. The number of additional days required by B is: 24 / 4 = 6 days

Explanation

Let the side of the equilateral triangle be a. The area of the equilateral triangle is given by the formula Area = (√3/4)a².

By Viviani's theorem, the sum of the lengths of the perpendiculars from any interior point of an equilateral triangle to its sides is equal to the altitude (h) of the triangle. Therefore: h = 3 + 4 + 5 = 12 cm

The altitude of an equilateral triangle is also related to its side length a by the formula: h = (√3/2)a

Equating the two expressions for the altitude: (√3/2)a = 12 a = 24 / √3 a = 8√3 cm

Substituting the side length a into the area formula: Area = (√3/4) × (8√3)² Area = (√3/4) × 192 Area = 48√3 cm²

Explanation

According to the given condition, the area of the triangle is equal to the area of the circle. Using the standard formulas for these areas:

½ × base × altitude = π × radius²

Substituting the given base of 8 cm and radius of 8 cm into the equation:

½ × 8 × altitude = π × 8²

4 × altitude = 64π

altitude = 16π cm

Explanation

Let the radius of the base of the cone be r = 5x and its height be h = 12x.

The slant height l of a right circular cone is given by the formula: l = √(r² + h²) l = √((5x)² + (12x)²) = √(25x² + 144x²) = √(169x²) = 13x

The volume V of a cone is given by the formula: V = (1/3) × π × r² × h

We are given V = 314 2/7 cm³ = 2200/7 cm³. Using π = 22/7: 2200/7 = (1/3) × (22/7) × (5x)² × 12x 2200/7 = (1/3) × (22/7) × 25x² × 12x 2200/7 = (22/7) × 100x³

Multiplying both sides by 7/22: 100 = 100x³ x³ = 1 x = 1

Therefore, the slant height is: l = 13 × 1 = 13 cm

Explanation

When a solid metallic cone is melted and recast into a solid cylinder, the total volume remains conserved.

Let the base radius of both the cone and the cylinder be r, the height of the cone be h_cone, and the height of the cylinder be h_cyl.

The volume of the cone is given by: V_cone = ⅓ × π × r² × h_cone

The volume of the cylinder is given by: V_cyl = π × r² × h_cyl

Equating the two volumes because the material is conserved: ⅓ × π × r² × h_cone = π × r² × h_cyl

Canceling the common term π × r² on both sides yields: ⅓ × h_cone = h_cyl h_cone = 3 × h_cyl

Substituting the given height of the cylinder, h_cyl = 7 cm, we get: h_cone = 3 × 7 = 21 cm

Explanation

Using the successive discount formula, if the original price of an item is 100, the final price after three successive discounts of 20%, 25%, and 10% is calculated by multiplying the remaining percentages:

Final Price = 100 × (1 - 0.20) × (1 - 0.25) × (1 - 0.10) Final Price = 100 × 0.80 × 0.75 × 0.90 Final Price = 100 × 0.60 × 0.90 Final Price = 54

Since the final price of the item is 54, the total discount on the original price of 100 is:

Total Discount = 100 - 54 = 46%

Explanation

Using the successive percentage change formula, the net profit or loss percentage when an item is marked up by x% and then discounted by y% is given by x - y - xy/100.

Substituting the given values, where the markup percentage x = 20 and the discount percentage y = 20:

Net change = 20 - 20 - (20 × 20)/100 = -4%

The negative sign represents a net decrease, which means the seller bears a loss of 4%.

Explanation

Let the total work be 60 units.

The daily work rates are: One man's work rate = 60 ÷ 20 = 3 units per day One woman's work rate = 60 ÷ 30 = 2 units per day One boy's work rate = 60 ÷ 60 = 1 unit per day

To complete the entire work of 60 units in 2 days, the required total rate of work is: 60 ÷ 2 = 30 units per day

Let the number of boys required to assist be x. The combined daily work rate of 2 men, 8 women, and x boys is: (2 × 3) + (8 × 2) + (x × 1) = 30 6 + 16 + x = 30 22 + x = 30 x = 8 boys

Explanation

Let the sides of the right-angled triangle be represented by three consecutive integers: x, x + 1, and x + 2.

According to Pythagoras' theorem, the sum of the squares of the two shorter sides equals the square of the hypotenuse: x² + (x + 1)² = (x + 2)²

Expanding the terms: x² + x² + 2x + 1 = x² + 4x + 4

Rearranging the terms into a quadratic equation: x² - 2x - 3 = 0 (x - 3)(x + 1) = 0

Since the side length of a triangle must be a positive value, we take x = 3. This gives the side lengths of the triangle as 3 cm, 4 cm, and 5 cm.

The area of a right-angled triangle is calculated using the formula: Area = ½ × base × height

Substituting the two perpendicular sides: Area = ½ × 3 × 4 = 6 cm²

Explanation

For four numbers a, b, c, and d to become proportional after adding a constant value x to each, the value of x can be directly calculated using the relation:

x = (ad - bc) / ((b + c) - (a + d))

Given the numbers 6, 7, 15, and 17, we assign a = 6, b = 7, c = 15, and d = 17.

Substituting these values into the formula:

x = (6 × 17 - 7 × 15) / ((7 + 15) - (6 + 17))

x = (102 - 105) / (22 - 23)

x = -3 / -1 = 3

Adding 3 to each of the original numbers gives 9, 10, 18, and 20. The first ratio is 9/10 and the second ratio is 18/20, which simplifies to 9/10. Because these ratios are equal, the resulting numbers are in proportion.

Explanation

The total fare collected from any class is the product of the fare per passenger and the number of passengers traveling in that class.

Let the ratio of fares of first and second class be F₁ : F₂ = 4 : 1, and the ratio of the number of passengers be N₁ : N₂ = 1 : 40.

The ratio of revenue collected from first class and second class is: R₁ : R₂ = (F₁ × N₁) : (F₂ × N₂) R₁ : R₂ = (4 × 1) : (1 × 40) = 4 : 40 = 1 : 10

The total revenue collected corresponds to 1 + 10 = 11 parts. Given that the total collection is Rs. 1,100, we find the value of 1 part: 1 part = 1,100 ÷ 11 = Rs. 100

The revenue collected from first class passengers corresponds to 1 part, which is Rs. 100.

Explanation

The relationship between Marked Price (MP), Cost Price (CP), Gain percentage (G), and Discount percentage (D) is given by the formula:

MP/CP = (100 + G) / (100 - D)

Substituting G = 8 and D = 10:

MP/CP = (100 + 8) / (100 - 10) = 108/90 = 6/5

If no discount is allowed, the selling price equals the marked price. The new gain percentage is:

Gain % = (MP/CP - 1) × 100 = (6/5 - 1) × 100 = 1/5 × 100 = 20%

Explanation

Given that A = 4/5 * B and B = 5/2 * C, we can substitute B in terms of C into the first equation to get A = (4/5) * (5/2) * C = 2 * C. This simplifies to the ratio A:C = 2:1.

Explanation

The odd numbers less than 100 are 1, 3, 5, ..., 99. This sequence is an Arithmetic Progression with the first term being 1 and the last term being 99.

For any Arithmetic Progression, the average of the terms is given by the formula: Average = (First term + Last term) / 2

Substituting the values: Average = (1 + 99) / 2 = 50

Alternatively, the number of odd numbers less than 100 is 50. The average of the first n odd numbers is always equal to n. Therefore, the average of these 50 odd numbers is 50.

Explanation

The ratio of the incomes of A and B is 4 : 3, and the ratio of their expenses is 3 : 2.

Since savings equal income minus expenses, we can analyze the difference in ratio units for both individuals.

For A, the difference is 4 - 3 = 1 unit. For B, the difference is 3 - 2 = 1 unit.

Since both save the same amount, this 1 unit of difference corresponds directly to their individual savings: 1 unit = Rs. 60,000

The annual income of A is represented by 4 units in the ratio. Therefore, we calculate the annual income of A by multiplying: Income of A = 4 × 60,000 = Rs. 2,40,000

Explanation

We can solve this using the rule of alligation by focusing on the concentration of milk in each part.

In the first glass, the ratio of milk to water is 3:5, so the concentration of milk is 3/(3 + 5) = 3/8.

In the second glass, the ratio of milk to water is 6:1, so the concentration of milk is 6/(6 + 1) = 6/7.

In the final mixture, the required ratio of milk to water is 1:1, so the desired concentration of milk is 1/(1 + 1) = 1/2.

Applying the rule of alligation: Ratio of glass 1 quantity to glass 2 quantity = (Concentration in Glass 2 - Desired concentration) : (Desired concentration - Concentration in Glass 1)

Ratio = (6/7 - 1/2) : (1/2 - 3/8)

Subtracting the fractions: First term = (12 - 7) / 14 = 5/14 Second term = (4 - 3) / 8 = 1/8

Ratio = (5/14) : (1/8)

To find the ratio in simplest integer form, multiply both terms by 56, which is the least common multiple of 14 and 8: Ratio = (5/14 × 56) : (1/8 × 56) Ratio = 20 : 7

Explanation

The initial average age of the 11 players is 20 years.

The new average age after including the coach increases by 10%, which is 20 × 10% = 2 years. Therefore, the new average age for the 12 people (11 players + 1 coach) is 20 + 2 = 22 years.

The age of the coach can be directly calculated using the formula: Age of the coach = New Average + (Initial number of players × Increase in average) Age of the coach = 22 + (11 × 2) = 22 + 22 = 44 years.

Explanation

The combined average of two groups is calculated using the weighted average formula:

Weighted Average = (n₁A₁ + n₂A₂) / (n₁ + n₂)

Here, n₁ = 32 and A₁ = 60 for Section A, while n₂ = 40 and A₂ = 33 for Section B.

Substituting these values into the formula:

Weighted Average = (32 × 60 + 40 × 33) / (32 + 40) Weighted Average = (1920 + 1320) / 72 Weighted Average = 3240 / 72 Weighted Average = 45

Explanation

Four years ago, the sum of the ages of the husband and wife was 27 × 2 = 54 years.

Since each of them has aged by 4 years, the sum of their present ages is 54 + 4 + 4 = 62 years.

Presently, the average age of the family consisting of the husband, wife, and the newborn child is 21 years. The sum of their present ages is 21 × 3 = 63 years.

The present age of the child is the difference between these two sums: 63 - 62 = 1 year.

Explanation

Let the original price per kg of sugar be P. The quantity of sugar bought for Rs. 360 at the original price is 360/P.

With a 25% reduction, the new price per kg is 0.75P. The quantity of sugar bought for Rs. 360 at this reduced price is 360/0.75P, which simplifies to 480/P.

According to the question, the difference in the quantity bought is 7½ kg, which is 7.5 kg: 480/P - 360/P = 7.5 120/P = 7.5 P = 120 / 7.5 = 16

Explanation

Cost Price of 12 articles = Rs. P Cost Price of 1 article = P/12

Selling Price of 1 article = P/8

Profit per article = Selling Price - Cost Price = P/8 - P/12 = P/24

Profit percent = (Profit / Cost Price) × 100 Profit percent = (P/24) / (P/12) × 100 = (12/24) × 100 = 50%

Explanation

Let the cost price of the article be CP.

Selling price at 20% gain = CP × (1 + 20/100) = 1.20 × CP Selling price at 20% loss = CP × (1 - 20/100) = 0.80 × CP

The difference between these two selling prices is given as Rs. 60.

1.20 × CP - 0.80 × CP = 60 0.40 × CP = 60 CP = 60 / 0.40 = 150

Explanation

Let the selling price of 1 ball pen be x. Selling price of 1 dozen (12) ball pens = 12x. The profit earned is equal to the selling price of 4 ball pens, which is 4x. Cost price of 12 ball pens = Selling price - Profit = 12x - 4x = 8x. Profit percent = (Profit / Cost Price) × 100 = (4x / 8x) × 100 = 50%.

Explanation

Let the third number be 100.

Since x is 20% more than the third number, x = 120. Since y is 50% more than the third number, y = 150.

To find what percent x is of y, the formula is: Percentage = (x / y) × 100

Substituting the values: Percentage = (120 / 150) × 100 Percentage = (4 / 5) × 100 = 80%

Explanation

Let the annual salary in 2006 be S.

Since the annual salary in 2007 is 10% more than the annual salary in 2006, we can write the relation as: Salary in 2007 = S × (1 + 10/100) = 1.1 × S

Substitute the given 2007 salary of Rs. 8,80,000 into the formula: 1.1 × S = 8,80,000

Solving for S: S = 8,80,000 / 1.1 S = 8,00,000

This direct calculation yields his 2006 salary as Rs. 8,00,000.

Explanation

Let the original price of the T.V. set be P.

The reduction in price is given as 10% of the original price, which is equal to Rs. 1,650.

10% of P = 1,650

(10 / 100) × P = 1,650

P = 1,650 × 10 = 16,500

Explanation

When a quantity is decreased by x% and then increased by the same x%, the net percentage change is always a decrease given by the formula:

Net change = -x²/100 %

Substituting x = 25 into the formula:

Net change = -25²/100 % Net change = -625/100 % = -6.25%

The negative sign indicates a decrease, which means the new salary is 6.25% less than the original salary.

Explanation

When a train crosses a platform, the total distance covered is the sum of the length of the train and the length of the platform.

Using the relationship: Speed = (Difference in distance) ÷ (Difference in time)

Substitute the given values: Difference in distance = 162 - 120 = 42 m Difference in time = 18 - 15 = 3 s

Speed in m/s = 42 ÷ 3 = 14 m/s

To convert the speed from m/s to km/hr, multiply by the conversion factor 18/5: Speed in km/hr = 14 × 18/5 = 50.4 km/hr

Explanation

The simple interest formula is: SI = (P × R × T) / 100

Rearranging the formula to solve for time (T): T = (SI × 100) / (P × R)

Substitute the given values: Principal (P) = Rs. 3,000 Simple Interest (SI) = Rs. 1,080 Rate of interest (R) = 12% per annum

T = (1080 × 100) / (3000 × 12) T = 108000 / 36000 T = 3 years

Explanation

Let the number of boys and girls in the college be 300 and 200 respectively, making the total number of students 500.

Since 20% of the boys are adults, the remaining 80% of the boys are not adults. Number of non-adult boys = 80% of 300 = 240

Since 25% of the girls are adults, the remaining 75% of the girls are not adults. Number of non-adult girls = 75% of 200 = 150

Total number of students who are not adults = 240 + 150 = 390

Percentage of students who are not adults = (390 / 500) × 100 = 78%

Explanation

The speed of the jeep is 90 km/hr and the speed of the car is 75 km/hr.

Since both vehicles are moving in the same direction, the relative speed is the difference between their speeds: Relative speed = 90 - 75 = 15 km/hr

The initial distance between the jeep and the car is 5 km.

The time taken by the jeep to catch the car is calculated as: Time = Distance ÷ Relative speed = 5 / 15 = 1/3 hour

To convert this duration into minutes: Time = (1/3) × 60 = 20 minutes

Explanation

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

D = P × (R / 100)²

Substituting the given values, P = 1000 and R = 5:

D = 1000 × (5 / 100)² D = 1000 × (1 / 20)² D = 1000 × (1 / 400) D = 2.50