SSC GD Constable Previous Year Paper (Held on: 30th November 2021 Shift 3)

The logic followed here is:

Similarly,

Hence, 'SFIUPN' is the correct answer.

An amount of ₹870 is divided between Urmi and Kripa in the ratio of 18 : 11

• Amount of money Urmi got = 18 / (18 + 11) × 870 = 18 / 29 × 870 = 540
• Amount of money Kripa got = 870 - 540 = 330

An amount of ₹960 is divided between Poorvi and Mrinal in the ratio of 5 : 7

• Amount of money Poorvi got = 5 / (5 + 7) × 960 = 5 / 12 × 960 = 400
• Amount of money Mrinal got = 960 - 400 = 560

Clearly, Mrinal gets the maximum amount of money among all four.

Hence, 'Mrinal' is the correct answer.

The correct option that indicates the arrangement of the given words in the order in which they appear in an English dictionary is:

2. Caring
3. Carpet
4. Carrot
5. Creamy
6. Creek

Hence, '2, 1,  3, 4, 5' is the correct answer.

BODMAS rule:

Given expression: 82 A 126 B 16 D 112 C 73 

After replacing the letters by their meaning, we get:

82 + 126 × 16 ÷ 112 - 73

= 82 + 126 × 1/7 - 73

= 82 + 18 - 73

= 100 - 73

= 27

Hence, '27' is the correct answer.

The paper when unfolded will appear as shown below:

Hence, 'option 1' is the correct answer.

The logic followed here is:

Similarly,

Hence, 'ACDTE' is the correct answer.

The logic followed here is:

Hence, '127' is the correct answer.

The logic followed here is:

​

Similarly,

Hence, 'OFMRTAOISN' is the correct answer.

The mirror image of the given combination when the mirror is place at the right side is as shown below :

• The line PQ is the mirror.
• The given word "detA9P" has third letter "t", so the mirror image should be "

" ⇒ Option 2 is eliminated.

• The given word "detA9P" has first letter "P" and fourth letter "A", so the mirror image should be "

" and "

" ⇒ Option 3 is eliminated.

• The given word "detA9P" has sixth letter "b", so the mirror image should be "

" ⇒ Option 4 is eliminated.

Hence, 'option 1' is the correct answer.

The logic followed here is:

1. NRV → N + 4 = R; R + 4 = V
2. QVB → Q + 5 = V; V + 6 = B
3. SXD → S + 5 = X; X + 6 = D
4. YDJ → Y + 5 = D; D + 6 = J

Hence, 'NRV' is the odd one out.

The logic followed here is

(First number + 4) × (2/5) = Second number

6 : 4 ⇒

(6 + 4) × (2/5) = 10  × (2/5) = 2 × 2 = 4

And

16 : 8 ⇒

(16 + 4) × (2/5) = 20  × (2/5) = 4 × 2 = 8

Similarly,

11 : ? ⇒

(11 + 4) × (2/5) = 15  × (2/5) = 3 × 2 = 6

Hence, the correct answer is "6".

The logic followed here is:

• 'Ammeter’ is related to ‘Current’ → An ammeter is a measuring instrument used to measure the current in a circuit.

Similarly,

• ‘Anemometer’ is related to ‘________’ → An anemometer is an instrument that measures wind speed and direction.

Hence, 'Wind Speed and Direction' is the correct answer.

LOGIC: (First number × second number)/3 = Third number

(12, 14, 56) → (12 × 14)/3 = 4 × 14 = 56

Now, check each option,

1) (16, 18, 96) → (16 × 18)/3 = 16 × 6 = 96 

2. (24, 16, 214) → (24 × 16)/3 = 8 × 16 = 128 ≠ 214

3. (10, 16, 82) → (10 × 16)/3 = 160/3 = 53.33 ≠ 82

4. (14, 20, 145) → (14 × 20)/3 = 280/3 = 93.33 ≠ 145

Hence, the correct answer is (16, 18, 96).

The pattern followed here is:

1) 

 is shift right side middle in second figure, then shift left side middle in third figure then shift upper side in the middle in fourth figure at last shift right side middle in fifth figure.

2. Square and circle interchange their position in every figure.

3. Arrow shift upper side in the middle in second figure, then shift right side middle in the third figure, then shift left side in the fourth figure at last shift upper side in the middle of the figure.

4) 

 shift left side middle of the figure in second figure, then shift upper middle of the figure in third figure, then shift right side middle in the figure in fourth figure, at last shift left side middle of the figure. 

Hence, the correct answer is "Option 1".

The paper when folded to form a dice, the faces that will be opposite to each other is shown below:

Clearly, B will be the face opposite to D.

Hence, 'B' is the correct answer.

In a cafeteria, seven customers (B, G, H, K, L, M and N) sit on three different benches (X, Y and Z). 

Each bench must have at least two customers sitting on it.

1. Customer K sits on Bench X with his best friends. 2. Customer H sits on Bench Z.

3. Customer B sits only with customer N.

• As B sits only with N, they are sitting on bench Y as bench Y is vacant and no one else sits on it.

4. Customer G does not sit with customers K, L and M

• Customer G sits with H on bench Z as G does not sit with customers K, L and M.
• Also, L and M sits on bench X with K.

Clearly, on bench X, there are three customers.

Hence, 'Only Bench X' is the correct answer.

Given sequence: D Q _ R _ D _ M R _ D _ M _ T

1. M Q T T Q R → D Q M R Q - D T M R T - D Q M R T
2. M T Q R Q T → D Q M R T - D Q M R R - D Q M T T
3. M T Q T R Q → D Q M R T - D Q M R T - D R M Q T
4. M T Q T Q R → D Q M R T - D Q M R T - D Q M R T

• In option 4, DQMRT is repeated.

Hence, 'M T Q T Q R' is the correct answer.

The least possible Venn diagram is:

Conclusions:

I. No court is a garden. → Follow (As, All gardens are resorts and No resort is a court)

II. No garden is a park. → Follow (As, All gardens are resorts, No resort is a court and All parks are courts)

Hence, Both the conclusions follow.

The image embedded in given figure is as shown below:Hence,

option 4' is the correct answer.

The logic followed here is:

Logic: Every alphabet coded with different number.

Similarly,

Hence, '96551499' is the correct answer.

Six friends, Govardan, Sarayu, Rekha, Shyamala, Hema and Ganesh, are standing in a queue at a ticket counter.

1. Only one person is standing ahead of Govardan.

____ > Govardan > ____ > ____ > ____ > ____

2. Ganesh who is fourth from the back end of the row, is between Govardan and Hema.

____ > Govardan > Ganesh > Hema > ____ > ____

3. There are two persons between Sarayu and Hema.

Sarayu > Govardan > Ganesh > Hema > ____ > ____

4. Rekha is between Hema and Shyamala.

Sarayu > Govardan > Ganesh > Hema > Rekha > Shyamala

Clearly, Govardan and Ganesh are the two persons standing between Sarayu and Hema.

Hence, 'Govardan and Ganesh' is the correct answer.

The set of classes whose relationship between them is best represented by the given Venn diagram is shown below:

• All mothers are women.
• Some mothers and women are lawyers.

Hence, 'mothers, women, lawyers' is the correct answer.

The logic followed here is:

Hence, '278' is the correct answer.

The logic followed here is:

Hence, 'NQU' is the correct answer.

By using the symbols in the table given below, we can draw the following family tree:

Clearly, Roshan is brother of Pramila.

Hence, 'Brother' is the correct answer.

The correct answer is Brahmaputra.

Key Points

• Brahmaputra river originates in the Chemayungdung glacier of the Kailash range near Mansarovar lake.
• India's largest river flows through Tibet, India and Bangladesh.
• In Tibet it is known as Tsangpo while entering India in Arunachal Pradesh it is called the Dihang river, it came to know as Bramhaputra in Assam and in Bangladesh its name is Jamuna.
• It is well known for floods, channel shifting and bank erosion.
• While flowing from the slope of Namcha Barwa mountains in Arunachal Pradesh it has the highest Hydroelectric Potential.
• Majuli the largest riverine island in the world is created by it.
• Its major tributaries are Dibang, Lohit, Subansiri, Kameng and Manas.

Additional Information

The correct answer is A day after the full moon.

Key Points

• Holi is typically celebrated at the end of winter, on the day after the full moon in the Hindu month of Phalguna, which usually falls in late February or early March.
• The night before Holi is known as Holika Dahan or Choti Holi, during which bonfires are lit to signify the burning of the evil Holika.
• The next day, which is the main day of Holi celebrations, is often called Dhulandi or Rangwali Holi, where people play with colours and water.

Additional InformationImportant festival of India

• Diwali - It is a festival of lights and one of the biggest festivals in India.
• Dussera -  It is the story of the triumph of Rama, an avatar of Vishnu, over the 10-headed demon king Ravana. It is celebrated as the symbol of the triumph of good over evil.

The correct answer is Chola​

Key Points

• The Kadamai tax was a type of land revenue that the peasants had to pay to their landlords or king.
• During the Chola administration, there were around 400 different types of taxes.
• Vetti also called forced labour and Kadamai also called land revenue.
• Land revenue and trade tax were the main source of income, The Chola rulers.

 Additional Information

• The Chola Empire was a Southern Indian Tamil family and is one of the longest-ruling dynasties in the history of the world.
• The dynasty emerged from the valley of the wealthy Kaveri (Cauvery) River. Its oldest capital is Uraiyur (now Tiruchchirappalli).
• Vijayalaya was the founder of the Chola dynasty.
• The Chola Dynasty reached its peak under Rajaraja Chola I (985 – 1014 AD) and his son, Rajendra Chola (1014 – 1044 AD).
• Chola rulers used the symbol of a tiger as their royal emblem.
• The medieval Cholas are best known for the construction of the magnificent Brihadisvara temple at Thanjavur.
• Rajendra I was the first to venture to the banks of the Ganges.
• He was popularly called the Victor of the Gange.

Important Points

• Kushan-Kushan Dynasty was established by Kujula Kadphises.
• Gupta - Founded by Sri Gupta, the dynasty rose to fame with rulers like Chandragupta-I, Samudragupta, etc.
• Chalukya dynasty-Jayasimha was the first ruler of the Chalukyas.
• Founded the empire with his capital at **Vatapi.**​

The correct answer is Sapru Committee.

Key Points

• The Sapru Committee Report was published in 1945
• The Sapru Committee 21 recommendations pertaining to constitutional questions that concerned the governance and politics of India.
• The Sapru Committee Report rejected the proposal for the division of the Indian sub-continent into the two states of India and Pakistan.​
• The Sapru Committee consisted of thirty members

Additional Information

• About Tej Bahadur Sapru.
• Born in Aligarh on 8th December 1875.
• He attended the 1892 session of the Indian national congress and was a member of the India congress committee.
• He was knighted in 1922 and after receiving his Knighthood, he was known as Sir Tej Bahadur supra.
• He is a member of the Muddiman committee in 1924.
• He helped Draft the Nehru Committee Report on constitutional reforms.
• Died 20 January 1949.

Important Points

• Zakir Hussain Committee- Dr Zakir Hussain formulated the scheme of basic education in India(1937).
• Sardar Patel Committee-The aim of this committee was to distribute Princely States seats in the Assembly according to the Cabinet Mission Plan, 1946
• Balvant Rai Mehta committee- it is related to Panchayati raj(1957).

The correct answer is rock.

Key Points

• The Perseverance rover has collected 11 scientifically-compelling rock core samples and one atmospheric sample.
• A core from Jezero Crater is slightly thicker than a pencil.

 Additional Information

• NASA, or the National Aeronautics and Space Administration, was created by President Dwight Eisenhower in 1958.
• Soviet Union's Mars 3, which landed in 1971, was the first successful Mars landing.
• The Indian Mars Orbiter Mission, also called Mangalyaan, is a space probe orbiting Mars since 24 September 2014.
• India became the first Asian country to successfully send a probe to Mars in 2014.​

The correct answer is $574.

Key Points

• The foreign exchange reserve is the foreign currency held by the Reserve Bank of India.
• India's foreign reserve includes Foreign assets, Gold reserve, Special drawing rights, and Reserve with IMF.
• It helps in managing crises, and rupee appreciation and boosts the confidence of investors.
• As of August 2022, India's Foreign reserve is $572.978 billion.

Additional Information

• Important terms related to Forex Reserve
• Special Drawing Rights  
• It is not a currency but a potential claim on the freely usable currencies of IMF members.
• It is an international reserve asset, created by the IMF in 1969.
• Foreign Currency Assets
• They are the largest part of forex reserves.
• They are value-based currencies expressed in Dollars.

The correct answer is Akbar.

Key Points

• Akbar was born on October 15, 1542, in Umarkot (now in Sindh Province, Pakistan).
• Akbar was the son of Humayun and the grandson of Babur.
• Akbar got enthroned at a very early stage of 14 years.
• Akbar ruled from 1556 to 1605.
• Akbar got the title of ‘Shahenshah’ because of his kindness, fearlessness, and bravery.
• Akbar started a system called Mansabdari to organize his military.
• Illahabad, Allahabad (now Prayagraj) was named by Akbar.
• The most notable wife of Akbar was Jodha Bai, Princess of Jaipur.
• Important battle of Akbar
• Battle of Thanesar (9 April 1567).
• The second battle of Panipat (5 November 1556).

Additional Information

• Muhammad Husain al-Katib (Zarrin Qalam), is one of the most celebrated calligraphers of Emperor Akbar’s time.
• Muhammad Husayn al-Katib (active India, ca. 1560–1620).​

The correct answer is The socio-economic condition of the people was very favourable.

Key Points

• On 29th August 1947, the Constituent Assembly through a resolution appointed a Drafting Committee.
• The Drafting Committee had seven members: Alladi Krishnaswami Ayyar, N. Gopalaswami; B.R. Ambedkar, K.M Munshi, Mohammad Saadulla, B.L. Mitter and D.P. Khaitan.
• At its first meeting on 30th August 1947, the Drafting Committee elected B.R Ambedkar as its Chairman.

Additional Information

• The Constituent Assembly took almost three years (two years, eleven months and seventeen days to be precise) to complete its historic task of drafting the Constitution for Independent India.
• The Constitution of India was adopted on 26 November 1949 and the hon'ble members appended their signatures to it on 24 January 1950.
• The Constitution of India came into force on 26 January 1950.

The correct answer is To clap.

Key Points

• The medulla oblongata is the lower part of the brain.
• It is tube or funnel-shaped.
• Its function is to regulate breathing, heartbeat, and digestion.
• It connects our brain with the spinal cord, pons, and cerebral cortex.

Additional Information About Human Brain

• The brain can be divided into three parts the forebrain, the midbrain, and the hindbrain.
• The brain sends and receives chemical and electrical signals throughout the body.
• It controls the voluntary movements, and balance of the body, (functioning of vital involuntary organs lungs, heart, and kidneys).
• The forebrain consists of the cerebrum, thalamus, and hypothalamus.
• The hindbrain comprises the pons, cerebellum, and medulla.

The correct answer is the United Kingdom.

Key Points

• Indian Prime Minister addressed the 47th G7 Summit 2021 through video conferencing.
• The last G-7 summit was in **France in 2019.**​

Additional Information

• About G7
• It is an intergovernmental organisation that was formed in 1975.​
• The country meets annually to discuss issues of common interest like global economic governance, international security and energy policy.
• The G7 countries are the UK, Canada, France, Germany, Italy, Japan and the US.
• The G7 does not have a formal constitution or a fixed headquarters.
• India is not part of the G7 country.
• India was invited to G7 because its agenda is 'deep and diverse.
• 48th G7 summit held in Germany.

The correct answer is Allahabad Bank (now Indian Bank).

Key Points

• Joint Stock Bank is a bank having more than one shareholder.
• Allahabad is the oldest Joint stock bank established in the year 1865.
• The first variety of joint-stock banks was the Bank of Bombay, established in 1720 in Bombay.

Additional Information

• Types of banks in India
• RBI- Central Bank of India and apex regulatory body.
• Schedule banks - These are regulated by RBI, Schedule Commercial banks, and Scheduled cooperative bank
• Schedule Commercial bank
• Public sector banks, private sector banks, Regional Rural banks, and others.
• Schedule cooperative bank
• ​Urban cooperative bank and State cooperative bank.
• Non-Schedule banks - RBI does not regulate these.

The correct answer is Bihar.

Key Points

• The Census is the collecting, compiling, analyzing and disseminating of demographic, economic and social data on basis of population.
• It is conducted by the Office of the Registrar General and Census Commissioner, Ministry of Home Affairs.
• Its significance is in providing administration, planning, demarcation of constituency and policy-making to the government.
• According to the census of 2011, Bihar has the highest population density in India.
• Bihar has a population density of 1,106 persons per square kilometre as per the census of 2011.

Additional Information

• Population density is the number of people per square km in a geographical area.
• 1st census was conducted in 1872 by Viceroy Lord Mayo.
• Census 2021 was postponed owing to the outbreak of the Covid-19 pandemic.

Important Points

• As per the 2011 census
• Arunachal Pradesh has the lowest population density in India.
• Uttar Pradesh is the highest populous state.
• Sikkim is the less populous state.
• Kerala has the highest sex ratio and Haryana with lowest sex ratio.

The correct answer is Solids can be compressed easily.

Key Points

• Solid is a form of matter that has structural rigidity and a firm shape which cannot be changed easily.
• It has a fixed shape and volume.
• The intermolecular force of attraction is strong as molecules of particles are closely attached.
• There is less Intermolecular space between particles.
• They are not easily compressible.
• It is difficult to change the shape of solids, so they are hard.​

Additional Information

The correct answer is Billy Jin King Cup

Key Points

• The Billie Jean King Cup (or the BJK Cup) is the premier international team competition in women's tennis
• Fed cup is the oldest name of the Billie Jean King Cup.
• It is the first major Team tournament to be named after a woman.
• changed name in September 2020 in honour of former World No,1 Billie Jean King.

Additional Information

• About ITF (International tennis federation).
• Formation-1 March,1913.
• Headquarters- Landon(England).
• President-David Haggerty.

Important Points

The correct answer is Mithali Raj.

Key Points

• Mithali Raj was born on 3 December 1982, in Jodhpur district, Rajasthan.
• She is the 1st Indian woman cricketer to play 200 One Day International Matches.
• She is also the 1st and only woman cricketer to participate in the 6 world cup.
• She is the all-time leading run-scorer for India in Test, ODI, and  T20. As of August 2022.
• She has received many awards for her contribution and performance in cricket.
• Wisden Leading Woman Cricketer in the World in 2017, Arjuna Award in 2003, the Padma Shri in 2015, and Major Dhyan Chand Khel Ratna in 2021.
• She has taken retirement from all forms of cricket in June 2022.

Additional Information

The correct answer is Awadh was captured by the British East India Company.

Key Points

• The Company annexed the state of Awadh in 1856 on the charges of misgovernance by the Nawab of Awadh.
• It was captured on the order of Lord Dalhousie under the Doctrine of lapse.
• Wajid Ali Shah was the ruler of Awadh during the annexation and was later deported to Garden Reach in Metiabruz, Kolkata.

Additional Information

• About the Doctrine of lapse
• It is an annexation policy, that a princely state in which the ruler did not have a legal male heir would be annexed by the company.
• It was started by Lord Dalhousie, then Governor General of India.
• Annexed state- Satara (1848), Jaitpur (1849), Sambalpur (1849), Bhagat 1850, Udaipur (1852), Jhansi (1853) and Nagpur (1854).​

Important Points

• Events in 1856
• Passing of Hindu Widows' Remarriage Act, 1856.
• Charles Canning became the Governor General of India.
• Bal Gangadhar Tilak was born on 23 July 1856.

The correct answer is 1980.

Key Points

• The Forest (Conservation) Act in India was enacted by the parliament for the conservation and protection of forest resources.
• It limits the state government, except for prior permission from the central government to take any decisions.
• The objective of these acts is to protect its flora, and fauna and prevent deforestation for cultivation, grazing and other purposes.

Additional Information

• About Forests in India
• According to the India State of Forest Report (ISFR), 2021 total forest and tree cover is 24.62% present in India.
• Madhya Pradesh has the largest area under forest followed by Arunachal Pradesh, Chhattisgarh and Odisha.
• Percentage-wise Mizoram(84.53%) has the highest % of forest cover followed by Arunachal Pradesh (79.33%),  Meghalaya (76.00%) and Manipur (74.34%).
• There is a gain in forest cover in Andhra Pradesh,  Telangana, Odisha and Karnataka.
• Loss of forest cover found in the states of  Arunachal Pradesh, Manipur, Nagaland, Mizoram and Meghalaya.​​

The correct answer is MERI SAHELI.

Key Points

• ‘Meri Saheli’ initiative was launched as Pilot Project by Railway Protection Force (RPF) across the South Eastern Railway to secure women passengers in trains originating in that zone.
• Meri Saheli Initiative was launched to provide safety and security to lady passengers travelling by trains for their entire journey from originating station to the terminating station.
• Section 58 of the Railways Act, 1989 provides for the earmarking of accommodation for female passengers in trains.​

Additional Information

• The Indian railways came into existence long back in 1853 on 16 April.
• The first passenger train ran between Mumbai’s Bori Bandar and Thane, covering 34 kilometres.
• Indian Railways is the world’s 4th largest railway network, followed by the US, China and Russia.
• India possesses the world’s longest platform, 1,366 metres in length, at the Gorakhpur Railway Station in Uttar Pradesh.
• Indian Railway is constructing the world’s highest rail arch bridge with steel and concrete over the Chenab river.
• Pir Pranjal Is India’s Longest Rail Tunnel.
• Railway Zones and Divisions in The Country.
• At present, there are 17 Railway Zones and 68 Divisions in the country.

The correct answer is Thumri.

Key Points

• Girija Devi is a classical singer and represents Banaras Gharana.
• She was born on 8 May 1929, in Varanasi, Uttar Pradesh.
• She is also called Queen of Thumri.
• She has won Padma Shree (1972), Padma Bhushan (1989), and Padma Vibhushan (2016) for her contribution to classical music.

Additional Information

• Hindustani Classical Music is a part of Indian classical music practised in north India.
• The Hindustani branch adopted a scale of Shudha Swara Saptaka or the Octave of Natural notes.
• Tabla, Sarangi, Sitar, Santoor, Flute, and violin are its instruments.
• Chaturanga, Ragasagar, Tarana,Sargam,Dhrupad, Dhamar, Hori, Khayal,Tappa and Thumri are its main singing style.​

The correct answer is Delhi crime.

Key Points

• The 48th International Emmy Awards 2020 was held in Hammerstein Ballroom, New York City.
• International Emmy Awards was formed in 1946 and in 1949 presented the first Emmys.
• It derives its name from Immy, a nickname for image orthicon, which is used as a camera tube in television.
• The awards were made by the National Academy of Television Arts and Sciences.
• The awards are given in the following categories which are dramatic series, comedy series, special drama, limited series, and variety, music, or comedy.
• Delhi Crime became the 1st Indian web series to receive an award in Drama-Series.

Additional Information

Emmy Award winner in 2020

Emmy Award winner in 2021

The correct answer is 2015.

Key Points

• ​Pradhan Mantri Jeevan Jyoti Bima Yojana has completed seven years.
• It is a one-year life insurance scheme offering coverage for death for any reason.
• It provides 2 Lakh life cover against a premium of Rs 436 per year.
• The age group between 18-50 years is covered under this scheme.

Additional Information

• The cumulative enrolments under the scheme have been more than 12.76 crores.
• An amount of Rs. 11,522 crores has been paid for 5.76 lakh claims.
• Out of the 12.76 crore cumulative enrolments, over 38% are PM Jan Dhan Yojana account holders, 49% are women account holders and 70% are people from rural areas.

The correct answer is honey hunting.

Key Points

• Honey hunting has an integral part of the Arunachal Pradesh, Shetukpen community.
• The documentary is made by independent filmmaker Kezang D Thongdok.

Additional Information

• The Dadasaheb Phalke Award is India's highest award in the field of cinema.
• It is presented annually at the National Film Awards ceremony by the Directorate of Film Festivals.
• Presented first in 1969, the award was introduced by the Government of India.
• The award comprises a Swarna Kamal (Golden Lotus) medallion, a shawl, and a cash prize of ₹10 lakh.
• The first recipient of the award was actress Devika Rani.
• Rajinikanth October 25 received the prestigious 51st Dadasaheb Phalke Award at the 67th National Film Awards ceremony (2021).​

The correct answer is Lonar Lake, Maharashtra.

Key Points

• Lonar lake is a saline lake located in Buldhana district, Maharashtra.
• It is formed after a meteorite impact led to crater formation.
• It has been designated as a Ramsar site by wetland international in the year 2020.
• The colour of the lake is pink due to the presence of Haloarchaea microbes.
• It is a notified National Geo-heritage Monument due to its culturally significant offering insight into earth’s evolution.

Additional Information

The correct answer is Gyanendra Malla.

Key Points

• Gyanendra Malla is an Nepali right-handed batsman.
• Gyanendra Malla was a part of the Nepal Under-15 and Under-19 squads before joining the senior side.
• Gyanendra Malla born 16 September 1990).

 Additional Information

• Sandeep Lamichhane is the present (2022) captain of the Nepal cricket team.
• Nepal capital**-Kathmandu**
• Currency- Nepalese rupee
• Prime Minister-Sher Bahadur Deuba.
• Uttarakhand, Uttar Pradesh, Bihar, West Bengal and Sikkim border touched with Nepal.

The correct answer is bacteria.

Key Points

• Unicellular organisms are made up of single cells. 
• They may be eukaryotic or prokaryotic.
• They can survive in any environment.
• They are so small cannot be seen with the naked eye.
• They reproduce asexually.
• Some unicellular organisms are bacteria, protists, and yeast.

Additional Information

• Multicellular organism
• These are the organism are consist of more than one cell.
• They are only eukaryotic.
• Reproduction takes place sexually as well as asexually.
• Plants, animals, and birds are examples.
• They are both microscopic and macroscopic.

Given: 

A sum amounts to 7 times itself in 3 years

Formula used:

Amount = Principal ×(1 +Rate/100)ⁿ

Where n = number of years

Calculation:

Let P be the sum of money and R = rate %

Amount after 3 years,

7P = P(1 + R/100)³

⇒ 7 = (1 + R/100)³      ---(1)

Let after 't' years amount becomes 2401 times of sum

2401 × P = P(1 + R/100)^t 

⇒ 2401 = (1 + R/100)^t 

⇒ 7⁴ = (1 + R/100)^t      ---(2)

On comparing (1) and (2) we get,

(1 + R/100)¹² = (1 + R/100)^t

⇒ t = 12

∴ After 12 years the sum will become 2401 times of itself.

Alternate Method 

In the first 3 years, the amount becomes 7 times of principal

In the next 3 years, the amount becomes (7 × 7) 0r 7² times of principal

Hence, the amount becomes 7⁴ times of the principal in = 4 × 3 = 12 years

∴ The sum becomes 2401 times itself in 12 years.

Shortcut Trick

Average speed of the journey = 1 ÷ [(2/3 ÷ 70) + (1/3 ÷ 50)] = 1050/17 km/h.

Total Distance = Average Speed × Total Time = (1050/17) × (34/5) = 420 km.

New Time = Total Distance ÷ New Speed = 420 ÷ 56 = 7.5 hours.

∴ The correct answer is 7(1/2) hr.

Alternate Method

Given: First speed (s₁) = 70 km/h, Second speed (s₂) = 50 km/h, Total time (T) = 6(4/5) hr = 34/5 hr.

Formula Used: Time = Distance ÷ Speed

Let the total distance be D km.

⇒ Total Time = Time₁ + Time₂

⇒ 34/5 = [(2/3)D ÷ 70] + [(1/3)D ÷ 50]

⇒ 34/5 = 2D/210 + D/150

⇒ 34/5 = D/105 + D/150

⇒ 34/5 = (10D + 7D) ÷ 1050

⇒ 34/5 = 17D ÷ 1050

⇒ D = (34 × 1050) ÷ (17 × 5) = 2 × 210 = 420 km

⇒ New Time = Total Distance ÷ New Speed

⇒ New Time = 420 ÷ 56 = 15/2 = 7.5 hr

∴ The correct answer is 7(1/2) hr.

Additional Information

Average Speed for Different Distances

When distances are unequal, Average Speed = Total Distance ÷ Total Time taken.

Distance Constant Relationship

If the distance is constant, speed is inversely proportional to time: S₁/S₂ = T₂/T₁.

Unit Conversion

To convert speed from km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Calculation:

A + B + C = 4500 + 5600 + 4800 = 14900      -----(1)

A + C = 2 × 4800 = 9600      -----(2)

⇒ (1) - (2)

⇒ B = 14900 - 9600 = 5300

∴ Monthly income of B is Rs. 5300.

Alternate Method

Given: 

Average monthly income of A and B = Rs. 4500

Average monthly income of B and C = Rs. 5600

Average monthly income of A and C = Rs. 4800

Formula used:

Average of N terms = Sum of N terms/N 

Calculation:

A + B = 2 × 4500 = 9000

B + C = 2 × 5600 = 11200

C + A = 2 × 4800 = 9600      -----(1)

⇒ A + B + C = 29800/2 = 14900      -----(2)

⇒ (2) - (1)

⇒ B = 14900 - 9600 = 5300

∴ Monthly income of B is Rs. 5300.

Given:

The price of sugar is increased by 10%

Formula used:

Expenditure = Price × Quantity

Percentage reduction in a Quantity = (Old quantity - New quantity)/Old quantity × 100

Calculation:

If Price is increased in ratio a : b

Then, to keep the expenditure same 

The quantity should be reduced in the ratio b : a

Here, price is increaseby 10% 

Ratio of price change = 10 : 11

⇒ Ratio of quantity = 11 : 10

Reduction in quantity = (11 - 10)/11 = 1/11

Percent reduction in quantity = 1/11 × 100 = $9\frac{1}{11}$%

∴ Percentage decrease in the consumption of sugar so as to not increase the expenditure is $9\frac{1}{11}$%.

Alternate Method Let the price of sugar be 100

Increase price of sugar = 100 × 1.1 = 110 (∵ 10% increase)

Let the initial quantity of sugar purchased = 10

Old expenditure on sugar = 100 × 10 = 1000

New expenditure = Increased price × New quantity

Keeping the expenditure same

⇒ 1000 = 110 × New quantity

⇒ New quantity = 100/11

Percentage Reduction in quantity = (10 - 100/11)/10 × 100 

⇒ (110 - 100)/110 × 100

⇒ 1/11 × 100

⇒ $9\frac{1}{11}$%

∴ Percentage decrease in consumption is $9\frac{1}{11}$%.

Shortcut Trick

Assume the Original Marked Price = 100 units.

Varun's Cost Price (CP) = 100 − 20% = 80 units.

New Marked Price = 100 + 20% = 120 units.

Selling Price (SP) = 120 − 10% discount = 108 units.

Profit % = [(108 − 80) ÷ 80] × 100 = 35%.

∴ The correct answer is 35%.

Alternate Method

Given:

Discount on Marked Price (MP) for purchase = 20%

Increase in original MP for markup = 20%

Discount offered to customer = 10%

Let the Original Marked Price be 100.

⇒ Cost Price (CP) for Varun = 100 − 20% of 100 = 80.

⇒ New Marked Price = 100 + 20% of 100 = 120.

⇒ Selling Price (SP) = 120 − 10% of 120 = 120 − 12 = 108.

⇒ Profit = SP − CP = 108 − 80 = 28.

⇒ Profit Percentage = (Profit ÷ CP) × 100

⇒ Profit % = (28 ÷ 80) × 100 = (7 ÷ 20) × 100 = 35%.

∴ The correct answer is 35%.

Additional Information

Profit and Loss Formula

Profit % = (Profit ÷ Cost Price) × 100. Always calculate profit or loss on the cost price unless specified otherwise.

Discount and Marked Price

Selling Price = Marked Price × (100 − Discount%) ÷ 100. Discounts are always offered on the Marked Price.

Successive Percentage Change

If a value is changed by a% and then by b%, the net change is given by (a + b + ab/100)%.

Given:

One-fifth of three-eights of two-thirds of a number = 20

Calculation:

Let the required number be X

Then according to question,

1/5 × 3/8 × 2/3 × X = 20

⇒ X/20 = 20

⇒ X = 400

Now,

60% of X = 60/100 × 400 = 240

∴ 60% of the required number is 240.

Shortcut Trick

New weight = Old weight + (Number of persons × Average increase)

New weight = 45 + (6 × 1.5)

New weight = 45 + 9 = 54 kg

∴ The correct answer is 54 kg.

Alternate Method

Given: weight of replaced person = 45 kg, total number of persons = 6, average increase = 1.5 kg.

⇒ Total weight increase of the 6 persons = 6 × 1.5 kg = 9 kg.

⇒ When a new person replaces the one weighing 45 kg, the total weight of the group increases by 9 kg.

⇒ Weight of new person = weight of the person who left + total increase in weight.

⇒ Weight of new person = 45 + 9 = 54 kg.

∴ The correct answer is 54 kg.

Additional Information

Average Weight Concept

Average weight = Total weight of all persons ÷ Total number of persons.

Replacement (Decrease) Formula

If the average weight decreases, the new person's weight = weight of replaced person − (number of persons × average decrease).

Total Sum Calculation

Total Sum = Average × Number of entities. Any change in total weight is directly equal to the difference between the incoming and outgoing value.

Shortcut Trick

Use the Product of Extremes = Product of Means rule for any proportion a : b :: c : d.

Here, the extremes are 0.35 and 6, and the means are x and 5.

Calculation: 5 × x = 0.35 × 6

x = (0.35 × 6) ÷ 5 ⇒ x = 0.07 × 6 = 0.42

∴ The correct answer is 0.42.

Alternate Method

Given: The proportion is 0.35 : x :: 5 : 6.

Formula Used: In a proportion a : b :: c : d, the relationship is expressed as a/b = c/d.

Step-by-step Calculation:

⇒ 0.35 ÷ x = 5 ÷ 6

⇒ 5 × x = 0.35 × 6

⇒ 5x = 2.10

⇒ x = 2.10 ÷ 5

⇒ x = 0.42

∴ The correct answer is 0.42.

Additional Information

Properties of Proportion

In any proportion a : b :: c : d, the values a and d are called Extremes, while b and c are called Means. The fundamental property states that a × d = b × c.

Fourth Proportional

If three numbers a, b, and c are given, their fourth proportional x is found using the ratio a : b = c : x, which results in x = (b × c) ÷ a.

Continued Proportion

Three quantities a, b, and c are in continued proportion if a : b = b : c, which leads to the formula b² = ac or b = √(ac), where b is the mean proportional.

Shortcut Trick

If two successive discounts say D1% and D2% are given, then the direct formula to calculate the equivalent discount is

D% = D1 + D2 - D1 × D2/100 

Here, D1% = 25%, D2% = 10%

D% = 25 + 10 - 25 × 10/100

⇒ D% = 32.5%

∴ The single discount equivalent is 32.5%.

Alternate MethodGiven:

The two successive discounts are 25% and 10%

Calculation:

Let the Mark Price be 100

Selling Price after two discounts = 100 × 0.75 × 0.90 = 67.5

Total Discount = 100 - 67.5 = 32.5

∴ The single discount equivalent to two successive discounts of 25% and 10% is 32.5%

Important PointsDiscount % is always calculated on Mark Price

Discount = (Mark price - Selling price)/Mark price × 100

Profit % is always calculated on the Cost price

Profit = (Selling price - Cost price)/Cost price × 100

Given:

Compound interest for two years = Rs. 85

Simple interest for two years = Rs. 80

Formula used

Simple interest (SI) = (P × R × T) ÷ 100

Where P = Principal amount, R = Rate, T = Time 

Concept used:

Simple interest (SI) is the rate percent of the principal amount

In compound interest, the principal modifies every year. The interest of the previous year becomes the principal for the following year.

For example,  

Let SI (for 1 year) = Rs. X, Rate % = R

Then, CI (for 2 years) = X + X + R % of X

Or, CI (for 2 years) = SI for 2 years + R % × SI for 1 year

Calculation:

SI for 1 year = 80 ÷ 2 = Rs. 40

CI (for 2 years) = SI for 2 years + R % × SI for 1 year

85 = 80 + R % × 40

⇒ R % × 40 = 5

⇒ R × 40 ÷ 100 = 5

⇒ R = $\frac{25}{2}$    

⇒ R = 12.5 %

∴ The rate of interest per annum is 12.5%.

Given:

Time taken by pipe A = 18 hrs

Time taken by pipe B = 27 hrs

Formula used:

Efficiency = Total work done/ total time taken

Calculation:

Let the total volume of the tank be the LCM of 18 and 27 i.e. 54 unit

The efficiency of A = 54/18 = 3

Efficiency of B = 54/27 = 2

Tank filled by both pipes together in 2 days (A starts the work) = 3 +2 = 5 unit

Tank filled by both pipes together in 20 days = 50 unit

Now, on the 21^st day, A will fill 3 units of tank

Total tank filled till now = 53 unit

On the 22^nd day, B will work and will fill 2 units of the tank, but we need only 1 unit of more work. Hence B will work only half a day

Total number of days taken = $21\frac{1}{2}$ days

∴ The total number of days taken by A and B together to fill the tank completely is $21\frac{1}{2}$ days

Alternate Method

Total Capacity = 54

Tank filled in 2 days = 3 + 2 = 5

Tank filled in 20 days = 50

Tank filled in 21 days = 50 + 3 = 53

The remaining 1 unit tank will be filled by Pipe B in 1/2 day

Total time taken = 21 + 1/2 days = $21\frac{1}{2}$ days

∴ The total number of days to fill the tank completely is $21\frac{1}{2}$ days.

Shortcut TrickIf Discount % and Profit % of a person is given,

Then we can directly use the formula,

(100 - D%)/(100 + P%) = CP/MP

Where,

D% = Discount %

P% = Profit %

From the above formula we can directly find out the ratio between MP and CP

(100 - 10)/(100 + 8) = CP/MP

⇒ 90/108 = CP/MP

⇒ CP/MP = 5/6

⇒ Markup % = (6 - 5)/5 × 100

⇒ Markup % = 20%

∴ The trader marks his goods 20% above the cost price.

Alternate Method

Given:

Discount = 10%

Profit = 8%

Formula used:

Markup % = (MP - CP)/CP × 100

Calculation:

Let Mark Price (MP) be 100

Selling price (SP) = 0.9 × 100 = 90 

Cost price × 1.08 = 90

⇒ Cost price (CP) = 250/3

Markup % = (MP - CP)/CP × 100

Markup % = $\frac{100 - \frac{250}{3}}{250/3} × 100$

Markup % = 20%

∴ The trader marks his goods 20% above the cost price.

Shortcut Trick

Capacity of a hemispherical bowl = (1/12) × π × d³

Volume = (1/12) × 3.1416 × 9³ ≈ (3.1416 × 729) ÷ 12 ≈ 190.85 cm³.

To convert to litres, divide by 1000: 190.85 ÷ 1000 ≈ 0.19085 litres.

Rounding to three decimal places, we get 0.191 litres.

∴ The correct answer is 0.191 litres.

Alternate Method

Given:

Diameter (d) of the hemisphere = 9 cm

Formula Used:

Volume of Hemisphere = (2/3) × π × r³

Conversion: 1 litre = 1000 cm³

Calculations:

⇒ Radius (r) = Diameter ÷ 2 = 9 ÷ 2 = 4.5 cm

⇒ Volume = (2/3) × (22/7) × 4.5 × 4.5 × 4.5

⇒ Volume ≈ (2/3) × 3.14159 × 91.125

⇒ Volume ≈ 2 × 3.14159 × 30.375

⇒ Volume ≈ 190.85175 cm³

⇒ Capacity in litres = 190.85175 ÷ 1000

⇒ Capacity ≈ 0.19085 litres

∴ The correct answer is 0.191 litres.

Additional Information

Volume of a Sphere

A hemisphere is exactly half of a sphere. The volume of a complete sphere is given by V = (4/3) × π × r³.

Surface Area of Hemisphere

The Curved Surface Area (CSA) = 2πr² and the Total Surface Area (TSA) including the flat base = 3πr².

Metric Volume Conversions

1 litre = 1000 cm³ = 1 dm³. Also, 1 m³ = 1000 litres = 1,000,000 cm³.

Shortcut Trick

Directly multiply the initial ratio parts by the percentage growth factors.

New Ratio = (2 × 115%) : (7 × 120%)

⇒ New Ratio = (2 × 115) : (7 × 120)

⇒ New Ratio = 230 : 840 = 23 : 84

∴ The correct answer is 23 : 84.

Alternate Method

Given:

Initial ratio of Girls to Boys = 2 : 7

Increase in Girls = 15%

Increase in Boys = 20%

Formula Used:

New Value = Original Value × (100 + Increase %)/100

Calculations:

Let the number of girls be 200 and the number of boys be 700 (maintaining the 2:7 ratio).

⇒ New number of girls = 200 + 15% of 200

⇒ New number of girls = 200 + (15/100) × 200 = 200 + 30 = 230

⇒ New number of boys = 700 + 20% of 700

⇒ New number of boys = 700 + (20/100) × 700 = 700 + 140 = 840

⇒ New Ratio = 230 : 840

⇒ New Ratio = 23 : 84

∴ The correct answer is 23 : 84.

Additional Information

Ratio Multiplication

If components of a ratio a:b are increased by x% and y% respectively, the new ratio is a(1 + x/100) : b(1 + y/100).

Percentage Growth Factor

An increase of k% is equivalent to multiplying the base value by (100 + k)/100. This is the fastest way to handle percentage changes in ratios.

Compound Ratio

The compound ratio of two ratios (a : b) and (c : d) is found by multiplying the corresponding terms: (a × c) : (b × d).

Given:

Total Profit = Rs. 2600

The ratio of investment of A and B = 3 : 4

A invested for 10 months

B invested for 12 months

Formula used:

Profit of Investment = Investment Amount × Time of Investment

Calculation:

Let the investment of A is 3X

And the investment of B is 4X

Profit of A = 10 × 3X

Profit of B = 12 × 4X

Total Profit = 30X + 48X = 78X

Now, according to question,

78X = 2600

⇒ X = 2600/78

Profit of A = 10 × 3 × 2600/78 = 1000

∴ A's share of Profit is Rs. 1,000.

Given:

Savings = 12%

Formula used:

Income = Savings + Expenditure

Calculation:

Let the income be 100

Savings = 0.12 × 100 = 12 (∵ 12% of Income)

Expenditure = 100 - 12 = 88

Increased Income = 1.25 × 100 = 125 (∵ 25% increase) 

Still he saves the same amount i.e. 12

New Expenditure = 125 - 12 = 113

Percentage Hike in Expenditure = (New Expenditure - Initial Expenditure)/Initial Expenditure

⇒ Percentage Hike in Expenditure = (113 - 88)/88 × 100

⇒ 25/88 × 100 =  28.4%

∴ Percentage hike in his Expenditure is 28.4%.

Given:

$\frac{\frac{2}{5} of 7\frac{1}{2} ÷ \frac{3}{4} - \frac{3}{4} × 1\frac{1}{2} ÷ 2\frac{1}{4}}{5\frac{1}{2} ÷ 3\frac{2}{3} of \frac{3}{8}}$

Concept used:

Follow the BODMAS rule according to the given table

Calculation:

(2/5 of $7\frac{1}{2}$ ÷ 3/4 - 3/4 × $1\frac{1}{2}$ ÷ $2\frac{1}{4}$)/($5\frac{1}{2}$ ÷ $3\frac{2}{3}$ of 3/8)

⇒ (2/5 of 15/2 ÷ 3/4 - 3/4 × 3/2 ÷ 9/4)/(11/2 ÷ 11/3 of 3/8)

⇒ (3 ÷ 3/4 - 3/4 × 3/2 ÷ 9/4)/(11/2 ÷ 11/8)

⇒ (4 - 3/4 × 2/3)/4

⇒ (4 - 1/2)/4

⇒ (8 - 1)/(2 × 4)

⇒ 7/(2 × 4)

⇒ 7/8

∴ The value of the given fraction is 7/8​

Given:

Investment amount = Rs. 9000

Time = 3 years

Rate of compound interest = 2%

Formula used:

Compound rate of interest for 3 years if Rate % is same for each year = 3R + 3R²/100 + R³/10000 

where R = Rate % for each year

Amount = Principal (1 + Rate/100)ⁿ

Where n = time period

Calculation:

Compound rate of interest for 3 years = (3 × 2) + (3 × 2²)/100 + 2³/10000

⇒  6 + 0.12 + 0.0008

⇒ 6.1208

∴ Compound rate of interest for 3 years = 6.1208

Amount = 9000 × (1 + 6.1208/100)

⇒ 9000 × 106.1208/100 = 9550.87

⇒ Amount = Rs. 9550.87

∴ Karthik will get Rs. 9550.87 on maturity of his fixed deposit.

Alternate Method Amount = 9000 × (1 + 2/100)³

⇒ Amount = 9000 × (51/50)³

⇒ Amount = 9000 × 132651/125000

⇒ Amount = 9550.87

∴ Karthik will get an amount of Rs. 9550.87 on the maturity of the fixed deposit.

Given:

85 ÷ 17 of 4 - [65 ÷ 13 of 2 - 14 × (19 - 25) ÷ 12 - 10] of 2/3

Concept Used:

Follow the BODMAS rule according to the table given below:

Calculation:

85 ÷ 17 of 4 - [65 ÷ 13 of 2 - 14 × (19 - 25) ÷ 12 - 10] of 2/3

⇒ 85 ÷ 17 of 4 - [65 ÷ 13 of 2 - 14 × (-6) ÷ 12 - 10] of 2/3

⇒ 85 ÷ 17 of 4 - [65 ÷ 13 of 2 + 7 -10] of 2/3

⇒ 85 ÷ 17 of 4 - [65 ÷ 26 +7 - 10] of 2/3

⇒ 85 ÷ 17 of 4 - [5/2 +7 - 10] of 2/3

⇒ 85 ÷ 17 of 4 - [5/2 - 3] of 2/3

⇒ 85 ÷ 17 of 4 + 1/2 of 2/3

⇒ 85 ÷ 68 + 1/3

⇒ 5 ÷ 4 + 1/3

⇒ 19/12

∴ The value of 85 ÷ 17 of 4 - [65 ÷ 13 of 2 - 14 × (19 - 25) ÷ 12 -10] of 2/3 is 19/12

Given:

Ratio of radii of cones C and D is 2 : 3

Ratio of Heights of cones C and D is 3 : 2

Formula used:

Volume of cone = 1/3 × π × r² × h

⇒ Volume ∝ r² × h

where, r = radius of cone

h = height of cone

Calculation:

Let radius of cone C = 2x, Height of cone C = 3y

⇒ Volume of cone C ∝ (2x)² × (3x)

Radius of cone D = 3x, height of cone D = 2y

⇒ Volume of cone D ∝ (3x)² × (2x)

⇒ Volume of cone D : volume of cone C = 18x²y : 12x²y = 3 : 2

∴ The ratio of cone D to that of cone C is 3 : 2

Shortcut Trick

Use the direct proportionality formula: (Quantity₁ × SP%₁) / Price₁ = (Quantity₂ × SP%₂) / Price₂

Where SP% = 100 − Loss% or 100 + Profit%.

⇒ (90 × 70) / 1557 = (n × 118) / 708

⇒ 6300 / 1557 = 118n / 708 ⇒ n = (6300 × 708) / (1557 × 118)

⇒ n = (6300 × 6) / 1557 = 37800 / 1557 ≈ 24

∴ The correct answer is 24.

Alternate Method

Given:

⇒ Selling Price (SP₁) of 90 pens = ₹1557

⇒ Loss percentage = 30%

⇒ New Selling Price (Total) = ₹708

⇒ Desired Profit percentage = 18%

Calculations:

⇒ Cost Price (CP) of 1 pen = 1557 / (90 × 0.70)

⇒ CP of 1 pen = 1557 / 63 = 519 / 21 = ₹(173/7)

⇒ Required Selling Price (SP_{per pen}) for 18% profit = (173/7) × (118 / 100)

⇒ SP_{per pen} = (173 × 118) / 700 = 20414 / 700 ≈ ₹29.16

⇒ Number of pens to be sold for ₹708 = 708 ÷ SP_{per pen}

⇒ Number of pens = 708 ÷ (20414 / 700)

⇒ Number of pens = (708 × 700) / 20414 = 495600 / 20414 ≈ 24.27

⇒ Taking the nearest integer value based on standard transaction units:

∴ The correct answer is 24.

Additional Information

Basic Profit and Loss Relation

Selling Price (SP) = Cost Price (CP) × (100 ± Profit or Loss %)/100. This is the fundamental relation used to switch between CP and SP.

Price and Quantity Inverse Rule

When the total expenditure or revenue is constant, the Quantity of items is inversely proportional to the Price per item. n₁ × P₁ = n₂ × P₂.

Combined Proportionality

In problems involving changing rates and changing total values, use: (Price₁) / (Quantity₁ × Rate₁) = (Price₂) / (Quantity₂ × Rate₂).

Given:

Given numbers are 15, 24 and 36

Formula used:

The Least common multiple  (LCM) of two or more numbers is the least number which is exactly divisible by each of those numbers.

Calculation:

The least number which is divisible by each of 15, 24 and 36 will be the LCM of 15, 24 and 36

LCM of 15, 24, and 36 

15 = 3 × 5

24 = 3 × 2 × 2 × 2

36 = 2 × 2 × 3 × 3

LCM of 15, 24, and 36 = 2 × 2 × 2 × 3 × 3 × 5 = 360

Clearly, we can see that to make 360 a perfect square number we have to multiply it by 2 and 5, then we get

⇒ 360 × 2 × 5 = 3600

∴ The least number which is a perfect square and is divisible by each of 15, 24, and 36 is 3600.

Shortcut Trick

Calculate distance in blocks of 3 hours based on speed increments.

Block 1 (0−3 hr): 60 km/h × 3 = 180 km

Block 2 (3−6 hr): 80 km/h × 3 = 240 km

Total distance in 6 hours = 180 + 240 = 420 km. Remaining = 470 − 420 = 50 km.

Speed for the next block = 100 km/h. Time for remaining distance = 50 ÷ 100 = 1/2 hr.

∴ The correct answer is 6 (1)/(2) hr.

Alternate Method

Given:

Initial speed = 60 km/h

Speed increment = 20 km/h after every 3 hours

Total distance = 470 km

Formula Used:

Distance = Speed × Time

Calculations:

⇒ Distance covered in first 3 hours = 60 × 3 = 180 km

⇒ Speed for the next 3 hours = 60 + 20 = 80 km/h

⇒ Distance covered in next 3 hours = 80 × 3 = 240 km

⇒ Total distance covered in 6 hours = 180 + 240 = 420 km

⇒ Remaining distance = 470 − 420 = 50 km

⇒ Speed after 6 hours = 80 + 20 = 100 km/h

⇒ Time taken to cover remaining 50 km = 50 ÷ 100 = 0.5 hours (or 1/2 hr)

⇒ Total time taken = 3 + 3 + 0.5 = 6.5 hours

∴ The correct answer is 6 (1)/(2) hr.

Additional Information

Average Speed

Average Speed = Total Distance ÷ Total Time. In this case, 470 ÷ 6.5 ≈ 72.31 km/h.

Uniform Speed vs Variable Speed

When speed changes at specific intervals, calculate the distance for each segment independently using D = S × T.

Speed-Time Conversion

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Given:

(9987693 × 6432 × 7695)/10

Concept: 

If a Product is divided by '10', then the unit digit of the product will be the remainder 

Similarly, if it is divided by '100', then the last two digits will be the remainder

Calculation:

Unit digit of the given product will be

Unit digit = 3  × 2 × 5 = 0

On dividing the given product by 10, the remainder will be '0'

∴ The remainder will be zero.

Shortcut Trick

Total Work (LCM of 32, 48) = 96 units.

Efficiency: Rohit = 96 ÷ 32 = 3; Raj = 96 ÷ 48 = 2.

Since Rohit left 8 days before completion, Raj worked alone for the last 8 days.

Work done by Raj alone = 8 × 2 = 16 units; Work done together = 96 − 16 = 80 units.

Days worked together = 80 ÷ (3 + 2) = 16 days.

∴ The correct answer is 16 days.

Alternate Method

Given: Rohit can complete work in 32 days; Raj can complete it in 48 days.

Formula Used: Total Work = Efficiency × Time

⇒ Let the total time to complete the work be x days.

⇒ Rohit worked for (x − 8) days and Raj worked for x days.

⇒ Total Work = (Rohit efficiency × Rohit days) + (Raj efficiency × Raj days)

⇒ 96 = 3 × (x − 8) + 2 × x

⇒ 96 = 3x − 24 + 2x

⇒ 96 + 24 = 5x

⇒ 5x = 120

⇒ x = 24 days

⇒ Days worked together = Days Rohit worked = 24 − 8 = 16 days.

∴ The correct answer is 16 days.

Additional Information

Work and Efficiency

Efficiency is inversely proportional to the time taken to complete the work. If person A is twice as efficient as B, A takes half the time B takes.

Leaving Before Completion

If a person leaves n days before completion, their work is added to the total work for calculation purposes, or the remaining person is assumed to work alone for those n days.

Combined Work Formula

If A and B work together, their combined efficiency is the sum of their individual efficiencies: Total Efficiency = E_A + E_B.

The erroneous segment is "at his"

Key Points

• The usage of the preposition is incorrect in the given sentence.
• We need to use the preposition "from".
• We use the preposition "from" to give a reason for something.
• Example: Rohit was on sick leave last week as he was recovering from Covid-19.
• In the given sentence we are being told the reason for his huge profit so we need to use the preposition "from".

The correct sentence is: Mohit is expecting a huge profit from his recent investment. 

Hence, the correct answer is option 1.

The erroneous spelling is "Abandan"

Key Points

• Let's look at the correct spelling and meaning of the word.
• Abandon: cease to support or look after (someone); desert.
• ​Example: She was abandoned by her mother in childhood due to poverty and drug abuse.
• ​​All the other words are spelled correctly.

​​Hence, the correct answer is option 4.

The erroneous spelling is "Pretanse"

Key Points

• Let's look at the meaning of the given words.
• Pretense: an attempt to make something that is not the case appear true.
• ​Example: Ranjith said, "You know there is no pretense with me when it comes to financial matters"
• ​​All the other words are spelled correctly.

​Hence, the correct answer is option 1.

The correct answer is "Harmful"

Key Points

• Let's look at the meaning of the given word.
• Beneficial: resulting in good; favourable or advantageous.
• Let's look at the meaning of the given words.
• ​Careful: making sure to avoid potential danger, mishap, or harm; cautious.
• Fearful: feeling or showing fear or anxiety.
• Hopeful: feeling or inspiring optimism about a future event.
• Harmful: causing or likely to cause harm.
• ​As per the meaning of the given words, "harmful" is the antonym of the word "beneficial".
• ​Example: Watching TV for long hours without maintaining an adequate distance from the screen is harmful to our eyes.

​Hence, the correct answer is option 4.

The correct answer is "Vulnerable"

Key Points

• Let's look at the meaning of given words.
• Vulnerable: exposed to the possibility of being attacked or harmed, either physically or emotionally.
• Available: able to be used or obtained; at someone's disposal.
• Accessible: (of a place) able to be reached or entered.
• Flexible: able to be easily modified to respond to altered circumstances.
• ​As per the meaning of the given words, "vulnerable" is the one-word substitute for the given group of words.
• ​Example: After his chemotherapy, his body became vulnerable to all sorts of ailments.

Hence, the correct answer is option 1.

The correct answer is "Collect"

Key Points

• Let's look at the meaning of the given word.
• Compose: form (a whole) by ordering or arranging the parts, especially in an artistic way.
• Let's look at the meaning of the given options.
• ​Clutch: grasp (something) tightly.
• Confuse: make (someone) bewildered or perplexed.
• Collect: bring or gather together (a number of things).
• Cuddle: hold close in one's arms as a way of showing love or affection.
• ​As per the meaning of the given words, "collect" is the synonym of the word "compose".
• ​Example: I want to collect some historical records of the Siraiki community for my research work.

​Hence, the correct answer is option 3.

The correct answer is "Pile".

Key Points

• Let's look at the meaning of the given words.
• Batch: a quantity or consignment of goods produced at one time.
• Group: a number of people or things that are located, gathered, or classed together.
• Pile: a heap of things laid or lying one on top of another.
• Load: a heavy or bulky thing that is being carried or is about to be carried.
• ​As per the meaning of the given words, "pile" is the one-word substitute for the given group of words.
• Example: Her mother shouted at her after finding the pile of smelly clothes lying on the floor.

Hence, the correct answer is option 3.