SSC CGL 2021 Tier-I (Held On : 12 April 2022 Shift 1) (Previous Year Paper)

Given :- C _ B N _ _ V_ _ H C _ B _ H

By checking options and substituting accordingly.

1) VHCBNVN → C V B N H - C V B N H - C V B N H

• Here "CVBNH" is repeated.

2) HVCNBVN → C H B N V - C V N B H - C V B N H

3) VCBHNVN → C V B N C - B V H N H - C V B N H

4) VHBNCHV → C V B N H - B V N C H - C H B V H

• Option (1) gives the pattern of :- C V B N H - C V B N H - C V B N H

Hence, the correct answer is "VHCBNVN".

The logic followed here is :-

In a column (Second number + First number) × (Second number - First number) = Third number ​

Column 1) :

= (14 + 11) × (14 - 11)

= 25 × 3

= 75

Column 2) :

= (16 + 15) × (16 - 15)

= 31 × 1

= 31

Column 3) :

⇒ (? + 9) × (? - 9) = 88

⇒ ?² - 9² = 88

⇒ ?2 = 88 + 81

⇒ ?2 = 169

⇒ ? = √ 169

⇒ ? = 13

Hence, the correct answer is "13".

The logic followed here is :-

By using BODMAS RULE :

Option 1) : 22 + 11 × 8 ÷ 3 = 19 

After interchanging the symbols '+' and '÷' the equation is as follows : 22 ÷ 11 × 8 + 3 = 19

⇒ 22 ÷ 11 × 8 + 3 = 19

⇒ 2 × 8 + 3 = 19

⇒ 16 + 3 = 19

⇒ 19 = 19

LHS = RHS

Option 2) : 24 – 12 ÷ 6 + 3 = 20

After interchanging the symbols '+' and '÷' the equation is as follows : 24 - 12 + 6 ÷ 3 = 20

⇒ 24 - 12 + 6 ÷ 3 = 20

⇒ 24 - 12 + 2 = 20

⇒ 26 - 12 = 20

⇒ 14 ≠ 20

LHS ≠ RHS

Option 3) : 12 + 4 – 8 ÷ 3 = 11 

After interchanging the symbols '+' and '÷' the equation is as follows : 12 ÷ 4 - 8 + 3 = 11

⇒ 12 ÷ 4 - 8 + 3 = 11

⇒ 3 - 8 + 3 = 11

⇒ 6 - 8 = 11

⇒ - 2 ≠ 11

LHS ≠ RHS

Option 4) : 16 + 4 × 8 ÷ 3 = 45 

After interchanging the symbols '+' and '÷' the equation is as follows : 16 ÷ 4 × 8 + 3 = 45

⇒ 16 ÷ 4 × 8 + 3 = 45

⇒ 4 × 8 + 3 = 45

⇒ 32 + 3 = 45

⇒ 35 ≠ 45

LHS ≠ RHS

Hence, the correct answer is "22 + 11 × 8 ÷ 3 = 19".

In the second and third dice 1, and 3 are common in both dice.

The second dice is rotated 1800 clockwise on the other adjacent side of 1, 3 is '4'.

In the first and third dice 1, and 4 are common in both dice.

The first dice rotated 90⁰ anti-clockwise the other adjacent side of 1,4 is '3'.

The opposite faces of given cubes are :

∴ Here, the opposite face of '5' is '1'.

Hence, the correct answer is "1".

The logic followed here is :-

Hence, the correct answer is "JXWE".

PEN is written as 17717.

Similarly,

CAP will be written as :

Hence, the correct answer is "4319".

The logic followed here is :-

By using BODMAS RULE :

A denotes ‘addition’, B denotes ‘multiplication’, C denotes ‘subtraction’, and D denotes ‘division’,

Given equation : 46 C (6 A 7) B 5 A 24 D 6 B (27 D (9 D 3))

After inserting the symbols in given equation the equation is as follows : 46 - (6 + 7) × 5 + 24 ÷ 6 × (27 ÷ (9 ÷ 3))

= 46 - (6 + 7) × 5 + 24 ÷ 6 × (27 ÷ (9 ÷ 3))

= 46 - (6 + 7) × 5 + 24 ÷ 6 × (27 ÷ 3)

= 46 - 13 × 5 + 24 ÷ 6 × 9

= 46 - 13 × 5 + 4 × 9

= 46 - 65 + 36

= 82 - 65

= 17

Hence, the correct answer is "17".

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some leaves are rotten → True (As All rotten are fruits and All fruits are leaves so, Some leaves are rotten is true)

II. Some mangoes are fruits → True (As All rotten are fruits and Some mangoes are rotten so, Some mangoes are fruits is true)

III. All leaves are either rotten or mangoes → False (As All rotten are fruits and All fruits are leaves and Some mangoes are rotten so, All leaves are either rotten or mangoes is false)

∴ Here, Only conclusions I and II are true.

Hence, the correct answer is "Only conclusions I and II follow".

The logic followed here is :-

The mailing process from the given sentences are arranged in order is as shown below :

3. Start computer
4. Open email account
5. Compose email
6. Enter email address
7. Write the content
8. Send the mail

Hence, the correct answer is "3, 1, 2, 4, 5, 6".

After unfolding the paper the figure formed is as shown below :

Hence, the correct answer is "Option 2".

The logic followed here is :-

1) UWZBI

2) NPSWB

3) ACFJO

4) TVYCH

∴ Here, 'UWZBI' is different from other three alternatives.

Hence, the correct answer is "UWZBI".

The figure that replace the ? in the given series is as shown below :

• The inner polygon of first figure moved to outer polygon of second figure and repeats same until fourth figure.

Hence, the correct answer is "Option 3".

Preparing the family tree using the following symbols:

According to the given information,

The given expression is : 

‘G # M # T % S @ H & R & W @ U’, → G is father of M, M is the father of T, T is mother of S, S is sister of H, H is the son of R, R is the son of W, W is the sister of U.

1) G is the paternal grandfather of T → True (As G is father of M and M is the father of T so, G is the paternal grandfather of T is true)

2) W is the maternal grandmother of H → False (As S is sister of H and H is the son of R and R is the son of W so, W is the paternal grandmother of H hence W is the maternal grandmother of H is false)

3) M is the maternal grandfather of S → True (As M is the father of T and T is mother of S so, M is the maternal grandfather of S is true)

4) R is the husband of T → True (As T is mother of S, S is sister of H, H is the son of R so, R is the husband of T is true)

Hence, the correct answer is "W is the maternal grandmother of H".

Given A is 25 years younger than B.

⇒ A = B - 25 ............. (i)

Age of B would be double the age of C after 15 years.

⇒ (B + 15) = 2(C + 15)

⇒ B + 15 = 2C + 30 ............ (ii)

The current age of B is three times the current age of C.

⇒ B = 3C ........... (iii)

By solving equations (ii) & (iii) we get,

⇒ 3C + 15 = 2C + 30

⇒ C = 15 years

∴ From equation (iii), B = 3C

⇒ B = 3 × 15

⇒ B = 45 years

By substituting B age in equation (i) we get,

⇒ A = B - 25

⇒ A = 45 - 25

⇒ A = 20 years

∴ Here, the age of A is 20 years.

Hence, the correct answer is "20 years".

The logic followed here is :-

SOUP is written as TNVO.

Similarly,

BOWL will be written as :

Hence, the correct answer is "CNXK".

The image not embedded in given figure is as shown below :

Hence, the correct answer is "Option 3".

The logic followed here is :-

Hence, the correct answer is "107".

The correct mirror image of the given combination when the mirror is placed at PQ is as shown below :-

Detailed Explanation:

• The line PQ is the mirror.
• The word "cxYLRgb" the last letter is "b". So, the mirror should be "

" ⇒ Option 1 is eliminated.

• The word "cxYLRgb" the second last letter is "g". So, the mirror image should be "

" ⇒ Option 4 is eliminated.

• The word "cxYLRgb" the third last letter is "R". So, the mirror image should be "

" ⇒ Option 2 is eliminated.

Hence, the correct answer is "Option 3".

The logic followed here is :-

Consonants are added + 1.

Vowels are subtracted - 1.

FRONTIER : GSNOUHDS

Similarly,

CLOSING : ?

Hence, the correct answer is "DMNTHOH".

The logic followed here is :-

∴ Here, Srinija is '11km' from her initial position.

Hence, the correct answer is "11km".

The logic followed here is :-

In 52 ∶ 91 →

= (13 × 4) : (13 × 7) 

Similarly;

In 72 ∶ ? →

= (18 × 4) : (18 × 7) 

= 72 : 126.

Hence, the correct answer is "126".

The least possible Venn diagram for the given relation is as shown below :

• Mars and Venus are planets in solar system.

Hence, the correct answer is "Option 4".

The logic followed here is :-

Hence, the correct answer is "113".

Eight north-facing restaurants named P, Q, R, S, T, U, V and W are located in a straight line.

1) S is second to the left of T and S is third to the left of V.

2) T is between P and V.

3) W is third to the left of P and W is to the immediate right of U.

4) R is third to the right of P.

∴ Here, 'R' is located fourth to the right of S.

Hence, the correct answer is "R".

The logic followed here is :-

∴ Here, 'pay' is coded as 'ruw'.

Hence, the correct answer is "ruw".

The correct answer is Doha.

Key Points

• Asian games are also called Asiad and it is held every four years among athletes from all over Asia.
• The first Asian Games was hosted by New Delhi.

Important Points 

The correct answer is Petiole.

Key Points

• Petiole is like a stem that attaches the leaf blade to the stem.
• Long thin flexible petioles allow leaf blades to flutter in wind, thereby cooling the leaf and bringing fresh air to leaf surface.

​

Additional Information

• Pistil: The pistil is the innermost part of the flower. It is the female part of the flower.
• Stamen: The stamen is the male part of the flower.
• Petals: The petal is the coloured part of the flower that gives it a unique shape.
• Sepals: These are leaf-like structures attached to the outside of the flower. They're very similar to petals.
• The schematic diagram of the flower is as follows:

The correct answer is Hima Das.

Key Points

• Indian Sprinter Hima Das was appointed by the Assam government as the Deputy Superintendent of Police.
• In 400 meters with a timing of 50.79 s, she holds the new Indian national record that she clocked at the 2018 Asian Games in Jakarta, Indonesia.
• She is the first Indian athlete to win a gold medal at the IAAF World U20 Championships in a track meet.
• Currently training at the NIS-Patiala, the 21-year-old from Assam, referred to as 'Dhing Express' referring to the town near her native village, and she qualified for the Tokyo Olympics.
• Also, part of the gold-winning women's 400m relay and mixed 400m relay quartets in the quadrennial event in Jakarta was the reigning world junior 400m champion, who won a silver in women's 400m at the 2018 Asian Games.

The correct answer is Twenty-fourth Amendment.

Key Points

• The Twenty-fourth Amendment of the Constitution of India, officially known as The Constitution (Twenty-fourth Amendment) Act, 1971, enables Parliament to dilute Fundamental Rights through Amendments of the Constitution.
• It also amended Article 368 to provide expressly that Parliament has the power to amend any provision of the Constitution.
• The 24th Amendment modified Articles 13 and 368 to authorize Parliament to freely amend the Fundamental Rights. 
• **Article 13 stated that any law which was inconsistent with the Fundamental Rights was invalid.**​

Important Points

• In the Golak Nath case, the Supreme Court ruled that the word ‘law’ also included constitutional amendments; as a result, any constitutional amendment which violated the Fundamental Rights was invalid.
• So Parliament would not be able to use constitutional amendments to curtail the Fundamental Rights.
• The 24th Amendment inserted clause (4) to Article 13, which stated that Article 13 would not apply to any constitutional amendments, effectively overturning Golak Nath.
• Article 368 lays down the procedure to amend the Constitution.
• Under the original Constitution, any constitutional amendment would only come into force if two conditions were met:
• first, if two-thirds of the members of each House of Parliament voted in its favour;
• second if it received the assent of the President, who had the option of withholding assent.
• The Amendment modified the second condition, to provide that the President was bound to give his assent to the Bill - they had no choice.
• The 24th Amendment was partially overturned in 1973 when the Supreme Court held in Kesavananda Bharati v. State of Kerala that Parliament could not amend the 'basic structure' of the Constitution.
• In this case, 11 judges held that certain basic or essential features of the Constitution were beyond the scope of Parliament’s amending powers.
• Both Articles 13 and 368 continue to exist in their amended form. However, through various causes, the Courts have strived to not allow these Articles to undermine the basic structure of the Constitution.

The correct answer is Maize.

Key Points

• Maize is a crop that is used both as food and fodder.
• It is a Kharif crop that requires a temperature between 21°C to 27°C and grows well in old alluvial soil.
• In some states like Bihar maize is grown in the rabi season also.
• The use of modern inputs such as HYV seeds, fertilisers and irrigation have contributed to the increasing production of maize.
• Major maize-producing states are Karnataka, Madhya Pradesh, Uttar Pradesh, Bihar, Andhra Pradesh and Telangana.

Additional Information

• Kharif Crops: Paddy, Jowar, Bajra, Maize, Ragi, Arhar(Tur), Moong, Urad, Cotton, Groundnut, Sunflower Seed, Soybean Black, Sesamum, Nigerseed.
• Rabi crops: Wheat, Barley, Masur (Lentil), Rapeseed/Mustard, Safflower, Toria.
• Other Crops: Copra, De-Husked Coconut, Jute, Sugarcane.

The correct answer is Pranab Mukherjee.

Key Points

• Pranab Mukherjee gave assent to the 100th Amendment of the Constitution of India.
• The 100th amendment of the Indian constitution deals with the Land Boundary Agreement.
• In the Agreement exchange of certain enclave territories with Bangladesh and the conferment of citizenship rights to residents of those enclaves took place between India and Bangladesh.
• The Land Boundary Agreement was signed in Bangladesh in the year 2015.

Additional Information

• Pranab Kumar Mukherjee was an Indian politician and statesman.
• He served as the 13th President of India from 2012-to 2017.
• He was preceded by Pratibha Patil and was succeeded by Ram Nath Govind.
• He received Padma Vibhushan in the year 2008 and Bharat Ratna in the year 2019.
• Books: Challenges Before the Nation: A Saga of Struggle and Sacrifice, Beyond Survival: Emerging Dimensions of the Indian Economy.

The correct answer is The Tughlaq dynasty.

Key Points

• Tamerlane or Timur marched into India with his army and reached Delhi in the year 1398.
• Attacking the Delhi Sultanate ruled by Sultan Nasir-ud-Din Mahmud Shah Tughluq.
• He started his journey from Samarkand. After crossing the Sindh river, he entered Punjab.
• He crossed Indus and captured Multan, and just walked over to Delhi without much resistance.
• Hence Tughlaq dynasty is the answer.

Additional Information

• Five dynasties ruled over the Delhi Sultanate sequentially:
• Mamluk dynasty (1206–1290)
• Khalji dynasty (1290–1320)
• Tughlaq dynasty (1320–1414)
• Sayyid dynasty (1414–1451)
• Lodi dynasty (1451–1526)

The correct answer is Seven.

Key Points

• The government has unveiled a scheme for setting up mega textile parks in the country.
• Finance Minister Nirmala Sitharaman made the announcement while presenting the Budget 2021-22 in Parliament.
• A scheme of mega-investment textile parks will be launched in addition to the production-linked incentive (PLI) scheme.
• 7 mega textile parks will be launched in 3 years as part of the scheme.

Additional Information

• The Union Budget is presented by Union Finance Minister.
• The union budget comes under Article 112.
• The Budget has to be passed by the Lok Sabha before it can come into effect.
• The Union Budget is also known as the Annual Financial Statement.

The correct answer is 97.

Important Points

• 97 percent (nearest to integer) of the total water on the surface of the earth is accounted for by the oceans.
• Earth is called the "Blue Planet" because it looks blue from space due to the presence of water on its surface.
• Around 71% of the Earth's surface is covered with water.
• While the other 29% consists of continents and islands.

Additional Information

• Total water on earth is majorly divided into two parts:
• Freshwater (2.5%)
• Saline water (97.4%)
• Freshwater is again divided into four parts:
• Icecaps and glaciers (68.7%)
• Groundwater (30.1%)
• Surface water (0.3%) (lakes, ponds, rivers, streams, etc.)
• Others (0.9%) (soil moisture, atmospheric moisture, etc.)

The correct answer is bacteria.

Key Points

• The foul smell from a body especially during a sultry summer is due to the action of bacteria on sweat.
• Sweat glands are small tubular structures of the skin that produce sweat.
• Sweat glands are used to regulate temperature and remove waste by secreting water, sodium salts, and nitrogenous waste (such as urea) onto the skin surface.

Additional Information

• Human sweat contains Lactic acid.
• Sweat contains water, minerals, lactate, and urea.
• Sweating is produced by sweat glands. There are two to four million sweat glands distributed all over our bodies.

The correct answer is  Dhruva​.

Main points

• Rulers of the Rashtrakuta dynasty.
• Dhruva (c. 780−793 CE)
• During his reign, the kingdom expanded into an empire that included all the territory between the Kaveri River and central India.
• Govind III (c.793−814 CE)
• It was Dhruvaputra who took the Rashtrakutas to greater heights. He became the winner in the tripartite struggle.
• Amoghavarsha I (c.814−878 CE)
• The most famous of the Rashtrakutas, he built the new capital city of Manyakheta (modern Malkhed).
• He defeated the invading Eastern Chalukyas at Vingavalli and earned the title Veeranarayana.
• Krishna III (c.939−967 CE) 
• The last great Rashtrakuta ruler, consolidated the empire so that it extended from the Narmada river to the Kaveri river and included the northern Tamil country (Thondaimandalam) and paid tribute to the king of Ceylon.

The correct answer is 1991.

Key Points

• The Government of National Capital Territory of Delhi (Amendment) Bill, 2021 was introduced in Lok Sabha on March 15, 2021.
• The Bill amends the Government of National Capital Territory of Delhi Act, 1991.
• The Act provides a framework for the functioning of the Legislative Assembly and the government of the National Capital Territory (NCT) of Delhi.

 Important Points

• The Bill amends certain powers and responsibilities of the Legislative Assembly and the Lieutenant Governor.
• Restriction on laws passed by the Assembly: 
• The Bill provides that the term “government” referred to in any law made by the Legislative Assembly will imply Lieutenant Governor (LG).
• Rules of Procedure of the Assembly: 
• ​The Act allows the Legislative Assembly to make Rules to regulate the procedure and conduct of business in the Assembly.
• The Bill provides that such Rules must be consistent with the Rules of Procedure and Conduct of Business in the Lok Sabha.
• Inquiry by the Assembly into administrative decisions: 
• The Bill prohibits the Legislative Assembly from making any rule to enable itself or its Committees to:
• (i) consider the matters of the day-to-day administration of the NCT of Delhi.
• (ii) conduct an inquiry in relation to administrative decisions.
• Assent to Bills:
• The Act requires the LG to reserve certain bills passed by the Legislative Assembly for the consideration of the President.
• These Bills are those:
• (i) which may diminish the powers of the High Court of Delhi.
• (ii) which the President may direct to be reserved.
• (iii) dealing with the salaries and allowances of the Speaker, Deputy Speaker, and members of the Assembly and the Ministers.
• (iv) relating to official languages of the Assembly or the NCT of Delhi. The Bill requires the LG to also reserve those Bills for the President that incidentally cover any of the matters outside the purview of the powers of the Legislative Assembly.
• LG’s opinion on executive actions: 
• The Act specifies that all executive action by the government, whether taken on the advice of the Ministers or otherwise, must be taken in the name of the LG.
• The Bill adds that on certain matters, as specified by the LG, his opinion must be obtained before taking any executive action on the decisions of the Minister/ Council of Ministers.

The correct answer is rice.

Key Points

• As part of Mission Sagar-IV, Indian Naval Ship Jalashwa arrived at Port Anjouan, Comoros on 14 March 2021 to deliver 1,000 Metric Tonnes of rice.
• An official ceremony for handing over the food aid from the Government of India to the Government of Comoros was held on 15 March 2021.
• The Indian side was represented by Captain Pankaj Chauhan, Commanding Officer INS Jalashwa.
• This is the second visit of an Indian Navy ship to the island country within a span of one year.
• Earlier, as part of Mission Sagar-I, in May-June 2020, the Indian Navy had delivered essential medicines to the nation.
• INS Jalashwa, the largest amphibious ship of the Indian Navy, has been specially sent to Comoros due to its large carrying capacity.
• Comoros and India have always enjoyed close and friendly relations and have similarities of view on regional and global issues. ‘Mission Sagar’, builds on the excellent relations existing between the two countries and deployment also resonates with the vision of our Prime Minister of Security and Growth for All in the Region ‘SAGAR’ and highlights the importance accorded by India to relations with the countries of the IOR.
• The operation is being progressed in close coordination with the Ministries of External Affairs, and other agencies of the Government of India

The correct answer is Indian Rupee.

Key Points

• PIB publishes the value of the GDP in the Indian Rupee.
• Real GDP or Gross Domestic Product (GDP) in the year 2020-21 is estimated at Rs135.13 lakh crore, as against the First Revised Estimate of GDP for 2019-20 of Rs.145.69 lakh crore.
• The growth in GDP during 2019-20 is estimated at -7.3 per cent.
• Nominal GDP or GDP at current prices in the year 2020-21 is estimated to attain a level of Rs197.46 lakh crore against the First Revised Estimates of Rs 203.51 lakh crore in 2019-20, showing a change of -3.0 per cent.
• The GDP of India has expanded by 2.47 times from 2004-to 05.
• According to the IMF World Economic Outlook (April - 2021).
• India's nominal GDP in 2021 is projected at $3,050 billion at current prices.
• This projection would make India the 6th largest economy globally, one position down compares to the 5th spot in 2019.
• India attained the highest 5th rank in 2019 and the lowest 17th in 1991.
• India contributes 3.25% of the entire world's GDP.
• India's share of the world economy increased from 1.08 per cent in 1993 to the current estimate of 3.27 per cent in 2019.
• India is in 3rd position after China and Japan among Asian Countries.
• India shares around 9% of the total of Asia's GDP (nominal).
• Based on PPP, India's economy in 2021 is projected at 10,207 billion international dollars**, 3rd highest in the world, behind the United States and China.**
• India contributes 7.19% of the entire world's GDP (PPP).
• India shares over 16 per cent of the total of Asia's GDP (PPP).

Important Points

• According to the Press Information Bureau (PIB), here is some recent data on India's GDP: 
• 2024-25
• Nominal GDP is estimated to be ₹77.31 lakh crore, a 9.7% increase from Q1 of 2023-24. Real GVA is estimated to be ₹40.73 lakh crore, a 6.8% increase from 2023-24.
• India's real GDP is projected to grow between 6.5–7%. The IMF has upgraded its GDP forecast to 7% for FY24-25.
• 2023-24
• Real GDP is estimated to be ₹173.82 lakh crore, an 8.2% increase from 2022-23. Nominal GDP is estimated to be ₹295.36 lakh crore, a 9.6% increase from 2022-23.
• The Central Statistics Office (CSO) releases six estimates of India's annual GDP over a period of two years and 10 months.

The correct answer is Beri beri.

Key Points

• Beriberi is easily treated with thiamine supplements. Hence, do not need a vaccine.
• The doctor may prescribe a thiamine shot or pill. For severe cases, a healthcare professional will administer intravenous thiamine.
• Beri-beri refers to a deficiency of thiamine pyrophosphate, the biologically active form of the **vitamin known as thiamine or vitamin B-1.**​

Additional Information

• Measles
• Measles is an acute viral respiratory illness.
• It's symptoms include:
• Fever (as high as 105°F) and malaise, cough, coryza, and conjunctivitis -the three “C”s -, pathognomonic enanthema (Koplik spots) followed by a maculopapular rash.
• The rash usually appears about 14 days after a person is exposed.
• Measles can be prevented with the MMR vaccine.​
• Typhoid
• ​Typhoid fever is a bacterial infection that can spread throughout the body, affecting many organs.
• It's caused by a bacterium called Salmonella typhi.
• Parenteral Vi polysaccharide and oral Ty21a are both acceptable forms of typhoid vaccine.
• Rabies
• ​Rabies is a fatal but preventable viral disease.
• It can spread to people and pets if they are bitten or scratched by rabid animals like bats, raccoons, skunks, and foxes.
• The rabies vaccine is an active immunizing agent used to prevent infection caused by the rabies virus.

The correct answer is David Ricardo.

Key Points

• David Ricardo first argued in the face of high deficits, people save more.
• The law of comparative advantage is popularly attributed to English political economist David Ricardo.
• His book “On the Principles of Political Economy and Taxation” was written in 1817.
• Comparative advantage is an economy's ability to produce a particular good or service at a lower opportunity cost than its trading partners.
• A comparative advantage gives a company the ability to sell goods and services at a lower price than its competitors and realize stronger sales margins.

Additional Information

• Adam Smith was a Scottish economist also known as the Father of economics or the Father of Capitalism.
• Amartya Sen is a world-renowned economist awarded the 1998 Nobel Prize.
• He has propounded "the concept of public welfare economics".
• Good Economics for a Hard Time was written by Abhijit V Banerjee and Esther Duflo.
• In this book Nobel laureates Abhijit Banerjee and Esther Duflo debunk myths about migration.

The correct answer is Jay Shah.

Key Points

• Jay Shah was elected as the President of the Asian Cricket Council (ACC) in January 2021.
• He will take over the reins from Mr Nazmul Hassan, President of, the Bangladesh Cricket Board.

Additional Information

• The Asian Cricket Council was formed in New Delhi on 19th September 1983, as the Asian Cricket Conference.
• The aims and objectives as stated in the original constitution were "organizing, developing and promoting the game of cricket in Asia."
• The founding members of the ACC were Bangladesh, India, Malaysia, Pakistan, Singapore, and Sri Lanka.

The correct answer is Louise Gluck.

Key Points

• Louise Glück was awarded the Nobel prize in Literature.​
• She won Nobel Prize in Literature 2020 for "her unmistakable poetic voice that with austere beauty makes individual existence universal".

Additional Information Nobel Prize Winners 2020:

The correct answer is Second law of motion.

Key Points

• Newton’s Second Law:
• The rate of change in linear momentum of a body is directly proportional to the external force applied to the body and this change takes place always in the direction of the applied force.
• If a body of mass m moves with velocity $\vec v$ then its linear momentum can be given by $\vec p = mv$ and if force $\vec F$ is applied to a body, then
• $\therefore \vec F = m a$
• Where F = Force, m = mass  and a = acceleration
• From the above concept, it is clear that Newton's Second law of motion provides the definition of force.
• The correct option is 1.

Additional Information

• Newton’s First law:
• A body continues to be in its state of rest or of uniform motion along a straight line unless it is acted upon by some external force to change the state.
• If no net force acts on a body, then the velocity of the body cannot change i.e. the body cannot accelerate.
• Newton’s first law defines inertia and is rightly called the law of inertia.
• Newton’s Third Law:
• To every action, there is always an equal (in magnitude) and opposite (in direction) reaction.
• When a body exerts a force on any other body, the second body also exerts an equal and opposite force on the first.
• Forces in nature always occur in pairs. A single isolated force is not possible.
• The universal law of gravitation:
• The universal law of gravitation was propounded by Sir Isaac Newton.
• Newton used the universal law of gravity to prove that the moon is accelerating towards Earth just as a body on Earth is falling towards Earth.
• According to the Universal law of gravitation, the force between two bodies is directly proportional to their masses and inversely proportional to a square of the distance.
• The law was given in the year 1687.

The correct answer is Assam.

Key Points

• Me Dam Me Phi is a festival celebrated in the state of Assam.
• The Ahoms celebrate this festival in a common place to worship their ancestors on 31st January every year with all traditional costumes and fanfare.
• It is the most important Ancestor worship communal festival in the Ahom religion celebrated by the Ahom people.

Additional Information

• Other festivals of Assam:
• Kherai Puja of the Bodos,
• Baikhu and Pharkantis of the Rabhas,
• Ali-ai-ligang and Parag of the Mishing tribe,
• Sagra-misawa wansawa and
• Laghun of the Tiwas.

The correct answer is Rakhigarhi.

Key Points

• Rakhigarhi site of Indus valley civilisation situated at Rakhigarhi village in Hisar district.
• The site is located in the Sarasvati river plain, some 27 km from the seasonal Ghaggar river.
• The Global Heritage Fund declared Rakhigarhi one of the 10 most endangered heritage sites in Asia.
• A team of Indian and South Korean researchers carried out excavations in Rakhigarhi.
• The team unearthed a fire altar, parts of a city wall, drainage structures as well as a hoard of semi-precious beads.

Additional Information

Important Sites of Harappan Civilization:

The correct answer is Odisha.

Key Points

• The Deomali (1672m) mountain peak is situated on the Eastern Ghat in Odisha.
• It is the highest peak of Odisha.
• Deomali is a mountain peak in the Chandragiri-Pottangi subrange of the Eastern Ghats.
• It is located near Koraput town in the Koraput district of southern Odisha, India.

Additional Information 

The correct answer is Kalbelia.

Key Points

• UNESCO has inscribed Kalbelia folk songs and dance in the Representative List of the Intangible Cultural Heritage of Humanity in 2010.
• Kalbelia is a folk dance performed by women of the Kalbelia tribe of Rajasthan.
• The costumes and dance movements are similar to that of serpents.
• ‘Been’ is a popular musical instrument of this folk dance.

Additional Information

• Bhangra and Gidhdha are the folk dances of Punjab.
• The Dalkhai dance of Odisha is usually performed to please Goddess Durga.

The correct answer is oxygen.

Important Points

• Ozone is an allotrope of oxygen.

• Ozone also is known as Trioxygen which is a triatomic molecule consisting of three oxygen.

• Oxygen is insoluble in acidic pyrogallol.

• Oxygen is denser than air.

• Ozone is created by the action of daylight on oxygen.

• Ozone at a ground level is considered a pollutant.

The correct answer is Earth Hour.

Key Points

• Earth Hour is switching off the moment observed worldwide on the last Saturday of March every year.
• This environment event is observed by switching off all lights at homes, business establishments, landmarks and so on for an hour.
• It was first observed in 2007 by the World Wildlife Fund in Sydney.
• People switch off the lights of their premises for an hour at 8:30 pm (according to their local time) on the last Saturday of March.
• It is a symbolic action that connects with people and draws their attention to the climate crisis.

Additional Information

• World Environment Day was established by the United Nations General Assembly in 1972 on the first day of the Stockholm Conference on the Human Environment.
• World Environment Day is celebrated on the 5th of June of every year.
• Earth Day Network (EDN), the organization that leads Earth Day worldwide, has chosen the theme of Earth Day-2018, "End Plastic Pollution".
• Earth Day is an annual event held on 22 April to demonstrate support for environmental protection.
• Earth Day is observed on April 22 since 1970.

Given:

Radius of each circle = 7 cm

BD = transverse common tangent between two circles = 48 cm

Concept used:

Length of direct transverse tangents = √(Square of the distance between the circle - Square of sum radius of the circles)

Length of the direct common tangents =√(Square of the distance between the circle - Square of the difference between the radius of circles)

Calculation:

AC = Length of the direct common tangents

BD = Length of direct transverse tangents

Let, the distance between two circles = x cm

So, BD = √[x² - (7 + 7)²]

⇒ 48 = √(x2 - 142)

⇒ 48² = x2 - 196  [Squaring on both sides]

⇒ 2304 = x2 - 196

⇒ x2 = 2304 + 196 = 2500

⇒ x = √2500 = 50 cm

Also, AC = √[502 - (7 - 7)2]

⇒ AC = √(2500 - 0) = √2500 = 50 cm

∴ The length of BD is 48 cm, length of AC is 50 cm

Given:

AB = 12 cm, BC = 18 cm and AC = 15 cm

Calculation:

Here, the bisector of ∠B in ΔABC meets AC at D

So, BC/AB = CD/AD

⇒ 18/12 = CD/AD

⇒ CD/AD = 3/2

Let CD and AD be 3x and 2x respectively

Given, AC = 15 cm

AD + CD = 15

⇒ 2x + 3x = 15

⇒ x = 3

So, AD = 2x = 6 cm

∴ The length of AD (in cm) is 6 cm

Given:

cotB = $\frac{12}{5}$

Formula used:

Pythagoras Theorem,

h = $\sqrt{p^2+b^2}$p2+b2−−−−−−√p2+b2−−−−−−√p2+b2−−−−−−√p2+b2

Where, h = Hypotenuse, p = Perpendicular, and b = Base

Calculation:

Here, cotB = $\frac{12}{5}$ = $b\over p$ 

Using Pythagoras Theorem,

h = $\sqrt{p^2+b^2}$

⇒ h = $\sqrt{12^2+5^2}$ 

⇒ $\sqrt{144 + 25}$ = $\sqrt{169}$ = 13

⇒ h = 13

then, secB = $h\over b$ = $13\over 12$

∴ The value of secB is $13\over 12$.

Given:

The total marks of the test = 30

Calculation:

The two-third of the total marks = 30 × (2/3) = 20

The number of students who scored less than 20 = 2 + 8 + 7 + 8 = 25

∴ The total number of 25 students has scored less than two-thirds of the total marks.

Shortcut Trick

We know that a³ + b³ + c³ = 3abc if a + b + c = 0

703 + 203- 903

= 703 + 203 + (- 90)3

= 3 × 70 × 20 × (- 90)  [∵ 70 + 20 + (- 90) = 0]

= - 378000

∴ The value of the given expression is - 378000

Alternate Method

Given:

The given expression = 703 + 203- 903

Calculation:

703 + 203- 903

= 343000 + 8000 - 729000

= 351000 - 729000

= - 378000

∴ The value of the given expression is - 378000

Given:

The average of 9 consecutive numbers = 20

Formula used:

Average = Sum of the terms/Number of the terms

Calculation:

Let, the 9 consecutive numbers are x, (x + 1), (x + 2), (x + 3), (x + 4), (x + 5), (x + 6), (x + 7), (x + 8)

So, [x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) + (x + 7) + (x + 8)]/9 = 20

⇒ (9x + 36)/9 = 20

⇒ 9x + 36 = 180

⇒ 9x = 180 - 36 = 144

⇒ x = 144/9 = 16

∴ The smallest of these numbers is 16

 

Alternate Method 

Average of Consecutive Numbers = 1/2 × (First Term + Last Term)

Here, in the question let the First term be x and the last term will be x + 8

According to the question,

(1/2) × (x + x + 8) = 20

⇒ 2x + 8 = 40

⇒ 2x = 32

∴ x = 16

The smallest number is 16

Shortcut Trick For such trigonometric equations, checking standard angle values like 30°, 45°, or 60° gives the fastest result. Let's substitute θ = 45°: 3sec245° + tan45° - 7 ⇒ 3(√2)2 + 1 - 7 = 6 + 1 - 7 = 0. Thus, θ = 45° satisfies the equation. Now substitute θ = 45° in the required expression: (2sin45° + 3cos45°) ÷ (cosec45° + sec45°) ⇒ [2(1/√2) + 3(1/√2)] ÷ (√2 + √2) = (5/√2) ÷ 2√2 = 5/4. ∴ The correct answer is 5/4.

Alternate Method Given: 3sec2θ + tanθ - 7 = 0 Formula Used: sec2θ = 1 + tan2θ

Calculations: ⇒ 3(1 + tan2θ) + tanθ - 7 = 0 ⇒ 3 + 3tan2θ + tanθ - 7 = 0 ⇒ Let tanθ = x ⇒ 3x2 + x - 4 = 0 ⇒ 3x2 + 4x - 3x - 4 = 0 ⇒ x(3x + 4) - 1(3x + 4) = 0 ⇒ (x - 1)(3x + 4) = 0 ⇒ x = 1 or x = -4/3 ⇒ Since 0° < θ < 90°, tanθ must be positive. Therefore, tanθ = 1 ⇒ θ = 45° ⇒ Expression to calculate = (2sinθ + 3cosθ) ÷ (cosecθ + secθ) ⇒ (2sin45° + 3cos45°) ÷ (cosec45° + sec45°) ⇒ [2 × (1/√2) + 3 × (1/√2)] ÷ (√2 + √2) ⇒ (5/√2) ÷ 2√2 ⇒ 5 ÷ (√2 × 2√2) ⇒ 5 ÷ 4 ∴ The correct answer is 5/4.

Additional Information Trigonometric Identities The fundamental Pythagorean trigonometric identities are: sin2θ + cos2θ = 1, sec2θ - tan2θ = 1, and cosec2θ - cot2θ = 1. Values at 45° For a 45° angle, sin45° = cos45° = 1/√2, tan45° = cot45° = 1, and sec45° = cosec45° = √2. Quadrant Rule (ASTC) In the first quadrant (0° < θ < 90°), all six trigonometric ratios hold positive values. This allows us to reject negative algebraic roots.

Given:

Remainder each time = 5

Calculation:

LCM of 8, 9, 12, and 15 = 360

Let, the number is (360k + 5), which is multiple of 7

Put k = 1

⇒ (360 × 1 + 5) = 365

⇒ 365/7 → Remainder = 1

Put k = 2

⇒ (360 × 2 + 5) = 725

⇒ 725/7 → Remainder = 4

Put k = 3

⇒ (360 × 3 + 5) = 1085

⇒ 1085/7 → Remainder = 0

∴ The required answer is 1085

Shortcut Trick

SI for 4 years (10 − 6) = 72,000 − 59,200 = 12,800

SI for 1 year = 3,200 ⇒ Principal (P) = 59,200 − (3,200 × 6) = 40,000

Original Rate (R) = (3,200 ÷ 40,000) × 100 = 8%

New Rate = 8% + 2% = 10%

New SI required = 76,000 − 40,000 = 36,000

Required Time = 36,000 ÷ (40,000 × 10%) = 9 years

∴ The correct option is (A).

Alternate Method

Given:

Amount after 6 years (A₁) = Rs. 59,200

Amount after 10 years (A₂) = Rs. 72,000

New Interest Rate = Original Rate + 2%

Target Amount = Rs. 76,000

Formula Used:

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

Amount (A) = Principal (P) + SI

P

A1 (6 yrs) 59,200

A2 (10 yrs) 72,000

Diff = 12,800 (4 yrs)

SI/yr = 3,200

Calculations:

⇒ SI for (10 − 6) years = 72,000 − 59,200

⇒ SI for 4 years = 12,800

⇒ SI for 1 year = 12,800 ÷ 4 = 3,200

⇒ SI for 6 years = 3,200 × 6 = 19,200

⇒ Principal (P) = A₁ − SI₆ = 59,200 − 19,200 = 40,000

⇒ Original Rate (R) = (3,200 × 100) ÷ 40,000 = 8%

⇒ New Rate (R') = 8% + 2% = 10%

⇒ New SI for target amount = 76,000 − 40,000 = 36,000

⇒ Required Time (T) = (36,000 × 100) ÷ (40,000 × 10)

⇒ T = 360,000 ÷ 40,000 = 9 years

∴ The correct option is (A).

Additional Information

Effective Rate of Interest

When rate increases by r%, the additional interest earned is (P × r × T) ÷ 100.

SI vs CI Difference

For 2 years, the difference is P(R ÷ 100)². For SI, interest remains constant every year.

Relation between Amount and Principal

A = P × [1 + (R × T) ÷ 100]. This can be used to directly find P if A, R, and T are known.

Given:

The angle of elevation of the top of the tower from the top of the pole = 60º

The angle of depression of the bottom of the tower from the top of the pole = 30º

Calculation:

Here, ∠BEC = ∠ABE = 30°

The height of the pole (AE) = 24 m

Also, BC = 24 m

Let, CD = x m

So, the height of the tower (BD) = (24 + x) cm

In ΔABE, tan 30° = AE/AB

⇒ 1/√3 = 24/AB

⇒ AB = 24√3 m

In ΔCED, tan 60° = CD/AB

⇒ √3 = CD/24√3

⇒ CD = √3 × 24√3 = 72 m

∴ BD = 24 + 72 = 96 m

∴ The height of the tower (in m) is 96 m

Given:

The following bar graph shows the total number of youth (in lakhs) and the number of employed youth (in lakhs) in states A, B, C, D and E.

Calculation:

The number of youth in states A, C, and E (in lakhs) = 12 + 11.5 + 9 = 32.5

The number of employed youth in states B, C, and D (in lakhs) = 7 + 10 + 7.5 = 24.5

The ratio = 32.5 : 24.5 = 325 : 245 = 65 : 49

∴ The ratio of the number of youth in states A, C and E taken together to the number of employed youth in states B, C and D taken together is 65 : 49

Given:

The given expression = $\frac{5-35\div 5 \times 15 + 5}{12-2}$

Calculation:

$\frac{5-35\div 5 \times 15 + 5}{12-2}$

= $\frac{5-7 \times 15 + 5}{10}$

= (5 - 105 + 5)/10

= - 95/10

= - 9.5

∴ The value of the expression is - 9.5

Given:

The price of petrol before hike = Rs. 82/litre

Hike of petrol price = 5%

Total distance covered by the man every month = 3045 km

The mileage of his car = 15 km/litre

Calculation:

Total petrol required every month = 3045/15 = 203 litres

The petrol price hike = 82 × (5/100) = Rs. 4.1

Increase in monthly expenditure = 203 × 4.1 = Rs. 832.30 ≈ Rs. 832 (to the nearest Rs.)

∴ The increase in the monthly expenditure (to the nearest Rs.) is Rs. 832

Given:

The difference between the two perpendicular sides of a right-angled triangle = 17 cm

The area of the right-angled triangle = 84 cm2

Concept used:

Hypotenuse = √(Perpendicular² + Base²)

Area of a right angle triangle = 1/2 × Perpendicular × Base

The perimeter of a right angle triangle = Hypotenuse + Perpendicular + Base

Calculation:

Let, the base = x cm

The perpendicular = (x + 17) cm

So, 1/2 × x × (x + 17) = 84

⇒ x² + 17x = 168

⇒ x2 + 24x - 7x - 168 = 0

⇒ x (x + 24) - 7 (x + 24) = 0

⇒ (x - 7) (x + 24) = 0

⇒ x + 24 = 0 

⇒ x = - 24  ["-" is neglected]

⇒ x - 7 = 0

⇒ x = 7

∴ The base = 7 cm

the perpendicular = (7 + 17) cm = 24 cm

Hypotenuse = √(242 + 72)

⇒ √(576 + 49)

⇒ √625 = 25 cm

The perimeter of the right-angle triangle = 25 + 24 + 7 = 56 cm

∴ The perimeter (in cm) of the triangle is 56 cm

Shortcut Trick This question can be solved if we know the triplet of 7, 24, and 25

If we use value-putting, 

⇒ Area of triangle = 1/2 × 7 × 24 = 84 cm²

And difference = 24 - 7 = 17 cm

hence the triplet satisfies the given conditions

Now,

⇒ The perimeter = 7 + 24 + 25 = 56cm

∴ The perimeter (in cm) of the triangle is 56 cm

Given:

The ratio of the speeds of two trains = 2 : 7

The first train runs 250 km in 5 hours

Formula used:

Speed = Distance/Time

Calculation:

Let, the speed of the first train = 2x

The speed of the second train = 7x

So, 2x = 250/5 = 50

⇒ x = 50/2 = 25

∴ The speed of the first train = 2 × 25 = 50 km/h

Also, the speed of the second train = 7 × 25 = 175 km/h

The sum of both speed = 50 + 175 = 225 km/h

∴ The sum of the speeds (in km/h) of both the trains is 225 km/h

Given:

The initial selling price = Rs. 425

Loss = 15%

Required profit = 5%

Formula used:

C.P. = 100/(100 - Loss%) × S.P.

S.P. = (100 + Profit%)/100 × C.P.

Where. C.P. = Cost price; S.P. = Selling price

Calculation:

The cost price of the article = 100/(100 - 15) × 425

= (100/85) × 425

= Rs. 500

The required selling price = (100 + 5)/100 × 500

= (105/100) × 500

= Rs. 525

∴ The trader should sell the article at Rs. 525

Given:

PT = 10.5 cm

PA = 7 cm

Concept used:

Tangent secant theorem: When a tangent and secant segment are drawn to a circle from an exterior point, the square of the tangent segment's measure equals the product of the secant segment's and its external secant segment's measurements.

Calculation:

Let, AB = x cm

By tangent secant theroem, PT² = PA × PB

⇒ (10.5)² = 7 × PB

⇒ 110.25 = 7 × PB

⇒ PB = 110.25/7 = 15.75 cm

Here, AB = PB - PA

⇒ x = 15.75 - 7 = 8.75 cm

∴ The length (in cm) of the chord AB is 8.75 cm

Given:

Total angle for the spent on rent = 60°

Concept used:

The total angle of a circle around the center = 360°

Calculation:

The percentage of spending on rent = (60/360) × 100

= 100/6 %

= $16\frac{2}{3}$%

∴ The percentage of family earnings spent on rent is $16\frac{2}{3}$%

Given:

x + y + z = 11

xy + yz + zx = -6

x3 + y3 + z3 = 1604

Formula used:

(a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca)

a3 + b3 + c3 - 3abc = (a + b + c) (a2 + b2 + c2 - ab - bc - ca)

Calculation:

x + y + z = 11

⇒ (x + y + z)² = 11²  [Squaring on both sides]

⇒ x2 + y2 + z2 + 2 (xy + yz + zx) = 121

⇒ x2 + y2 + z2 + 2 × (- 6) = 121

⇒ x2 + y2 + z2 = 121 + 12

⇒ x2 + y2 + z2 = 133 .....(1)

Also, x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2 - xy - yz - zx)

⇒ x3 + y3 + z3 - 3xyz = (x + y + z) [(x2 + y2 + z2) - (xy + yz + zx)

⇒ 1604 - 3xyz = 11 × [133 - (- 6)] [∵ x2 + y2 + z2 = 133]

⇒ 1604 - 3xyz = 11 × (133 + 6)

⇒ 3xyz = 1604 - (11 × 139)

⇒ 3xyz = 1604 - 1529 = 75

⇒ xyz = 75/3 = 25

∴ The value of xyz is 25

Alternate Method Formula used:

a³ + b³ + c³ - 3abc = (a + b + c)×{(a + b + c) ² - 3(ab + bc + ac)}

⇒ x3 + y3 + z3 - 3xyz = (x + y + z){(x + y + z)² - 3(xy + yz + zx)}

⇒ 1604 - 3xyz = 11{121 - 3(- 6)}

⇒ 1604 - 1529 = 3xyz

⇒ xyz = 75/3

⇒ xyz = 25

∴ The value of xyz is 25.

Given:

There are three numbers 335, 608 and 853

Concept used:

We have to multiply all the remainder from the given numbers by dividing them all differently by the divisor and also if the result will be greater than the divisor, we should divide the remainder by the divisor to find the final resultant remainder.

Calculation:

335 ÷ 13 ⇒ Remainder = 10

608 ÷ 13 ⇒ Remainder = 10

853 ÷ 13 ⇒ Remainder = 8

So, 10 × 10 × 8 = 800

Then, 800 ÷ 13 ⇒ Remainder = 7 (concept used)

∴ The remainder when the product of 335, 608 and 853 is divided by 13 is 7

Given:

The given bar graph shows exports of cars of type A and B (in Rs millions) from 2014 to 2018.

Calculation:

The total exports of cars of type A in 2014 and 2018 (in Rs millions) = 200 + 300 = 500

The total exports of cars of type B in 2015 and 2017 (in Rs millions) = 250 + 275 = 525

The ratio = 500 : 525 = 20 : 21

∴ The ratio of the total exports of cars of type A in 2014 and 2018 to the total exports of cars of type B in 2015 and 2017 is 20 : 21

Shortcut Trick

Ratio of efficiency of A : B : C = 1/8 : 1/10 : 1/12

Multiply by LCM(8, 10, 12) = 120 → Efficiency Ratio = 15 : 12 : 10

Total ratio units = 15 + 12 + 10 = 37 units

37 units = ₹5,550 → 1 unit = 150

Share of B = 12 × 150 = ₹1,800

∴ The correct answer is ₹1800.

Alternate Method

Given:

Time taken by A = 8 days

Time taken by B = 10 days

Time taken by C = 12 days

Total amount received = ₹5,550

Formula Used:

Efficiency = Total Work ÷ Time

Share of a person = (Individual Efficiency ÷ Total Efficiency) × Total Amount

Calculations:

⇒ Total Efficiency of A, B and C = 15 + 12 + 10 = 37 units

⇒ Total amount to be distributed = ₹5,550

⇒ Share of B = (Efficiency of B ÷ Total Efficiency) × Total Amount

⇒ Share of B = (12 ÷ 37) × 5550

⇒ Share of B = 12 × 150

⇒ Share of B = ₹1,800

∴ The correct answer is ₹1800.

Additional Information

Work and Wages Relationship

Wages are distributed in the ratio of the work done by each person. If everyone works for the same duration, the ratio of work done is equal to the ratio of their efficiencies.

Efficiency and Time Inverse Rule

Efficiency is inversely proportional to the time taken. If time ratio is x:y, then efficiency ratio is y:x for the same amount of work.

Total Work Assumption

The most common method to solve Time and Work problems is by assuming the LCM of given time periods as the Total Work units.

Given:

The radius of the sphere = 7 cm

The radius of the cone = 7 cm

The height of the cone = 10 cm

Formula used:

The volume of a sphere = (4/3) × π × (Radius)³

The volume of a cone = (1/3) × π × (Radius)² × Height

Calculation:

The difference in volume = [(4/3) × π × 73] - [(1/3) × π × 72 × 10]

= [(4/3) × (22/7) × 343] - [(1/3) × (22/7) × 49 × 10]

= [(7 × 22)/3] (28 - 10)

= (154/3) × 18

= 924 cm3

∴ The difference in the volume (in cm3) is 924 cm3

Given:

The marked price = Rs. 625

Discount = 32%

Profit = Rs. 25

Formula used:

C.P. = S.P. - Profit

S.P. = (100 - Discount%)/100 × M.P.

Profit% = Profit/C.P. × 100

Where, C.P. = Cost price; S.P. = Selling price; M.P. = Marked price

Calculation:

The selling price of the article = (100 - 32)/100 × 625 = (68/100) × 625 = Rs. 425

The cost price = 425 - 25 = Rs. 400

The percentage of profit = (25/400) × 100 = 6.25% ≈ 6% (correct to the nearest integer)

∴ TThe profit percentage (correct to the nearest integer) is 6%

Shortcut Trick

Age difference remains constant at 8 years.

4 years ago, Ratio A : B = 1 : 2. Difference = 2 − 1 = 1 unit.

1 unit = 8 years → B's age 4 years ago = 2 × 8 = 16 years.

Present age of B = 16 + 4 = 20 years.

∴ The correct answer is 20 years.

Alternate Method

Given: Present age difference = 8 years. Ratio 4 years ago = 1 : 2.

Formula: Age = Ratio unit × Value + Time elapsed.

⇒ Let ages 4 years ago be x and 2x.

⇒ Difference = 2x − x = 8

⇒ x = 8

⇒ B's age 4 years ago = 2 × 8 = 16 years.

⇒ B's Present age = 16 + 4 = 20 years.

∴ The correct answer is 20 years.

Additional Information

Constant Age Difference

The numerical difference between the ages of two persons never changes regardless of the number of years passed or gone by.

Ratio Proportionality

If ages are in ratio a : b and the difference is D, then one unit equals D ÷ (b − a).

The correct answer is '4' i.e. my sister .

Key Points

• The sentence compares the house of the speaker with "my sister," which is incorrect. The comparison should be made between similar entities, i.e., "my house" and "my sister's house."
• The grammatical error lies in the fourth segment, "my sister," as it does not provide a proper comparison for "my house."
• To correct the sentence, the possessive form should be used to compare the two houses. Instead of "my sister," it should be "my sister's house."

Correct sentence: My house is more spacious than my sister's house.

Additional Information

• Comparison Rules:
• When comparing two entities, ensure that they are of the same type (e.g., house vs. house, car vs. car).
• Use the possessive form (e.g., "my sister's house") if the comparison involves ownership.
• Common Errors in Comparison:
• Avoid vague or incomplete comparisons like "my sister" instead of "my sister's house."
• Ensure the adjective used (e.g., "spacious") is appropriate for both entities being compared.

The erroneous part is 'and punished'.

Key Points

• ​In a compound sentence, both the auxiliary verbs and main verbs should be mentioned separately if they differ in number, form or voice.
• For example:
• The criminal surrendered before the Judge and sent to prison. (incorrect)
• The criminal surrendered before the Judge and was sent to prison. (correct)
• Similarly, in this context, the auxiliary verb and the main verb should be mentioned separately. Hence, 'was' must be placed before 'punished'.

Therefore, the correct answer is: He was late for school and was punished.

The correct answer is 'Pair'.

Key Points

• The most appropriate synonym of the given word 'Duo' is 'Pair'.
• Duo: two people playing music or singing together. (एक साथ प्रदर्शन करने वाले गायकों या वादकों की जोड़ी; युगलगान, युगलवादन)
• Example: The comedy duo will perform tonight.
• Pair: two things of the same type that are used or worn together. (एक ही प्रकार की दो वस्‍तुएँ जिनको साथ-साथ प्रयोग किया या पहना जाता है; जोड़ा, युग्‍म)
• Example: a pair of shoes/gloves/earrings...
  

Correct Answer: Pair.

Additional Information

• Let's look at the meaning of other words:
• Debt: an amount of money that you owe to somebody. (कर्ज़, ऋण)
• Loan: money, etc. that somebody/something lends you. (उधार, ऋण)
• Bond: something that joins two or more people or groups of people together, such as a feeling of friendship. [दो व्‍यक्तियों या जनसमूहों को बाँधने या जोड़ने वाली शक्ति, भावना आदि (जैसे मैत्री या बंधुत्‍व); बंधन, संबंध]

The correct answer is 'Unfair or dishonest behaviour'.

Key Points

• The most appropriate meaning of the given idiom 'Foul play' is 'Unfair or dishonest behaviour'.
• Foul play: a criminal act that results in serious damage or injury, especially murder. (एक आपराधिक कृत्य जिसके परिणामस्वरूप गंभीर क्षति या चोट लगती है, विशेष रूप से हत्या)
• Example: It is not clear what caused the explosion, but the police do not suspect foul play.
  

Correct Answer: Unfair or dishonest behaviour.

The correct answer is 'BCAD'.

Key Points

• The given question is an example of a Para Jumble.
• We know that the first statement of a para jumbled question is usually an independent general statement, a noun, a universal fact, starting of an incident, or it starts with 'most' or 'once'.
• Sentence B will be the first sentence because it is an introductory sentence and talks about the cold desert of 'Ladakh'.
• Sentence C will be the next sentence because the previous sentence talks about the cold desert and Sentence C further tells us what is the source of water for the people in Ladakh.
• Sentence A will be the next sentence because it is connected with the previous sentence.
• Lastly, Sentence D will be used.
• Thus, the correct sequence is:
• B: Ladakh is a cold desert with a low average annual rainfall.
• C: Thus, glaciers have been the main source of water for the people.
• A: However, when areas in Leh began to experience water shortages, life didn’t grind to a halt.
• D: This was because Chewang Norphel, a retired civil engineer came up with the idea of artificial glaciers.
  

Correct Sequence: Ladakh is a cold desert with a low average annual rainfall. Thus, glaciers have been the main source of water for the people. However, when areas in Leh began to experience water shortages, life didn’t grind to a halt. This was because Chewang Norphel, a retired civil engineer came up with the idea of artificial glaciers.

The correct answer is 'Abolish'.

Key Points

• The most appropriate word for the given group of words is 'Abolish'.
• It means 'to end a law or system officially'. (किसी क़ानून या प्रथा को आधिकारिक रूप से समाप्‍त करना)
• Example: When was capital punishment abolished here?
  

Correct Answer: Abolish.

Additional Information

• Let's look at the meaning of other words:
• Stop: to finish moving or make something finish moving. [रुकना या (किसी को) रोकना (गतिमान न रहना या न रहने देना)]
• Destroy: to damage something so badly that it can no longer be used or no longer exists. (किसी वस्‍तु को इस तरह हानि पहुँचाना कि वह इस्‍तेमाल न हो सके या समाप्‍त हो जाए, नष्‍ट करना)
• Kill: to make somebody/something die. (किसी को मारना, किसी का मारा जाना)

The correct answer is 'had listened'.

Key Points

• The underlined part in the given sentence is grammatically incorrect.
• Here, 'had listened' should be used instead of 'were listening'.
• The structure of these kinds of sentences is: wish + past perfect is used to express regret, or that we want a situation in the past to be different,
• Example: I wish I hadn’t eaten so much. (I ate a lot)
• Thus, the correct answer is Option 4.
  

Correct Sentence: I wish I had listened to my parents.

The correct answer is 'Am I trusted by you?'.

Key Points

• The given sentence is in Active Voice. As per the given question we have to change it into Passive Voice.
• The process of transformation is as follows: 
• The given sentence starts with a helping verb.
• Hence, in 'active to passive' transformation 'do' is changed into 'am'.
• 'trust' will be changed into 'trusted'.
• Lastly, the preposition 'by' will be added.
• Thus, the correct answer is Option 2.
  

Correct Sentence: Am I trusted by you?

The correct answer is 'does she'.

Key Points

• The most appropriate option for the given blank is 'does she'.
• A positive statement is followed by a negative question tag.
• Example: Mary can speak English, can't she?
• A negative statement is followed by a positive question tag.
• Example: They aren't funny, are they?
• In the given sentence 'hardly' is a negative word.
• Hence, it should be followed by a positive question tag.
• Thus, the correct answer is Option 3.
  

Correct Sentence: She hardly works on weekends, does she?

The correct answer is 'Distrustful'.

Key Points

• The most appropriate synonym of the given word 'Paranoid' is 'Distrustful'.
• Paranoid: wrongly believing that other people are trying to harm you or are saying bad things about you. (इस मिथ्‍या संदेह से ग्रस्‍त कि अन्‍य लोग हानि पहुँचाना चाहते हैं या दुर्व्यवहार कर रहे हैं)
• Example: I guess I was just being paranoid.
• Distrustful: feeling or showing distrust of someone or something. (किसी या किसी चीज़ के प्रति अविश्वास महसूस करना या दिखाना)
• Example: I have grown up to be distrustful of men.
  

Correct Answer: Distrustful.

Additional Information

• Let's look at the meaning of other words:
• Trustful: having or marked by a total belief in the reliability, truth, or ability of someone. (किसी की विश्वसनीयता, सच्चाई या क्षमता में पूर्ण विश्वास होना या होना)
• Convinced: completely sure about something. (किसी विषय में पूर्णतया आश्‍वस्‍त)
• Committed: prepared to give a lot of your time and attention to something because you believe it is right or important. [(किसी उचित या महत्वपूर्ण लगने वाले कार्य में) संलग्‍न, प्रतिबद्घ]

The correct answer is 'Distrust'.

Key Points

• The most appropriate antonym of the given word 'Rely' is 'Distrust'.
• Rely: to trust somebody/something to work or behave well. [किसी पर भरोसा या विश्‍वास करना (किसी काम के लिए)]
• Example: Can I rely on you to keep a secret?
• Distrust: the feeling that you cannot believe somebody/something; a lack of trust. (किसी पर भरोसा न कर सकने का भाव; अविश्‍वास)
• Example: She distrusts him because he lied to her once before.
  

Correct Answer: Distrust.

Additional Information

• Let's look at the meaning of other words:
• Await: to wait for somebody/something. (किसी की प्रतीक्षा करना)
• Depend: be able to trust; rely on. (भरोसा करने में सक्षम हो; पर भरोसा)
• Move: to change position or to put something in a different position. (स्‍थान बदलना या किसी वस्‍तु को अन्‍य स्‍थान पर ले जाना, हिलना या हिलाना; खिसकना या खिसकाना)

The erroneous part is 'It was a surprising'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'It was surprising' should be used instead of 'It was a surprising'.
• An article is a short word like "a" or "the" that goes before a noun to make it clear what the noun refers to.
• We should use an article with a singular countable noun like a person, house, apple, or book.
• Articles are sometimes (but not always) needed before plural nouns, proper nouns, or uncountable nouns.
• Example: This is a waste of time!
• In the given sentence 'surprising' is 'adjective'. Which is used with the linking verb "was"
• Thus, the correct answer is Option 4.
  

Correct Sentence: It was surprising to receive the gift from my brother.