SSC GD Constable Previous Year Paper (Held on: 13th December 2021 Shift 2)

Logic : 

• (4) is added to each letter's position value.

​So, 

• PARTH is coded as :

​

Similarly,

• Word for code ‘XVEHI’ - It will reverse i.e instead of adding (4), it will be subtracted.

​

Hence, "TRADE" is the correct answer.

Mistake Points "XVEHI" is the code itself, and we have to find its root word which is coded as XVEHI.

The figure that will replace the question mark (?) in the following figure series is shown below:

1. The line outside the star - It is shifting in the clockwise direction.

2. The line inside the star - It is shifting in the anti-clockwise direction.

Hence, "Option - (2)" is the correct answer.

Logic :

• (2) is multiplied by position value of each letter.
• With only letter 'E' first multiplied by (4) then added (2).

So,

• SLIDE is coded as :

Similarly,

• TREND is coded as :

Hence, "403622288" is the correct answer.

Logic : 

• (2) is added to each letter's position value in alternate order, starting with the first letter.
• (1) is subtracted from each letter's position value in alternate order, starting with the second letter.

So,

• SLEEPER is written as :

Similarly, 

• BEGUMPET is written as :

Hence, "DDITOOGS" is the correct answer.

According to the sequence in the dictionary.

1. Trimmer
2. Trinity
3. Trinket
4. Tripled
5. Triumph

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

The pattern followed here is :  Consecutive multiple of 5 are added.

Hence, "102" is the correct answer.

According to given conditions,

1) Keshav and Sumer are brothers. 

2) Sumer is the father-in-law of Sonu (male).

3) Gulab is the only nephew of Keshav. 

4) Pooja is the only sister of Gulab. 

Thus, according to the final family tree Pooja is the wife of Sonu.

Hence, "Wife" is the correct answer.

Given : 48 + 37 × 5 – 36 ÷ 12 = 274 

So, by interchanging the number according to question :

• Option - (1) : 37 and 48

​37 + 48 × 5 - 36 ÷ 12 = 274 

37 + 48 × 5 - 3 = 274

37 + 240 - 3 = 274

277 - 3 = 274

274 = 274 (LHS = RHS)

• Option - (2) : 12 and 5

​48 + 37 × 12 - 36 ÷ 5 = 274 

48 + 37 × 12 - 7.2 = 274

48 + 444 - 7.2 = 274

492 - 7.2 ≠ 274 (LHS ≠ RHS)

484.8 ≠ 274 (LHS ≠ RHS)

• Option - (3) : 12 and 36

​48 + 37 × 5 - 12 ÷ 36 = 274 

48 + 37 × 5 - 0.33 = 274

48 + 185 - 0.33 = 274

233 - 0.33 = 274

232.67 ≠ 274 (LHS ≠ RHS)

• Option - (4) : 48 and 12

12 + 37 × 5 - 36 ÷ 48 = 274 

12 + 37 × 5 - 0.75 = 274

12 + 185 - 0.75 = 274

197 - 0.75 = 274

196.25 ≠ 274 (LHS ≠ RHS)

Hence, "37 and 48" is the correct answer.

The faces opposite to each other are shown below:

⇒ As the alternate positions becomes opposite to each other and the remaining two faces becomes opposite to each other.

So, opposite pairs are:

• T → S
• Q → U
• P → R

Therefore,

• Option(1) → U and T ⇒ Not opposite (As U is opposite to Q and T is opposite to S)
• Option(2) → P and Q ⇒ Not opposite (As P is opposite to R and Q is opposite to U)
• Option(3) → S and R ⇒ Not opposite (As S is opposite to T and R is opposite to P)
• Option(4) → Q and U ⇒ Opposite

Hence, "Q and U" is the correct answer.

Given : U _ _ Q G _ X P _ _ UX _ _ G

By checking options :

1. XPUQGPQ → U X P Q G U X P Q G UX P Q G → (It follows the pattern of :  UXPQG - UXPQG - UXPQG)
2. XQPGUPQ → U X P Q G U X P Q G UX P Q G → (It doesn't Follows the pattern)
3. XPQUQGP → U X P Q G U X P Q G UX P Q G → (It doesn't Follows the pattern)
4. QPXUGQP → U X P Q G U X P Q G UX P Q G → (It doesn't Follows the pattern)

⇒Option - (1) gives the pattern of " U X P Q G - U X P Q G - UX P Q G "

Hence, "XPUQGPQ" is the correct answer.

The logic followed here is:

• Axe is a tool used for woodcutting.

Similarly,

• Sieve is a utensil used to filter.

Hence, the correct answer is "Filter".

Additional Information 

1. Flame - It is a hot glowing body of ignited gas that is generated by something on fire.
2. Filter - It is a process or assess (Items) in order to reject or remove those that are unwanted.
3. Grind - To reduce (something) to small particles or powder by crushing it.
4. Hold - Keep or sustain in a specified position.

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

Detailed Explanation:

• The line PQ is the mirror
• The word "EMPHASIS" the mirror is placed vertically instead of horizontally ⇒ Option 1 is eliminated.
• The word "EMPHASIS" the mirror is placed vertically instead of horizontally ⇒ Option 2 is eliminated..
• The word "EMPHASIS" the fifth letter is "A". So, the mirror image should be "A" instead of "I"⇒ Option 4 is eliminated.

Hence, the correct answer is "Option - (3)".

The image embedded in given figure is as shown below :

∴ Here, Option figure -(1) is not embedded in given figure.

Hence, the correct answer is "Option-(1)".

Given : 

• Six friends - A, B, C, D, E and F
• They are sitting in two lines, facing the north.
• Three persons are sitting in each line.

​Explanation:

1) F is sitting in the middle

There are two possibilities of the position of F i.e F is sitting either in row - (1) or in row - (2).

• Case - (1)

• Case - (2)

​

2) B is to the immediate left of F.

3) C is just behind B.

As C is just behind B, therefore C will be sitting in row - (2)

As B cannot be position in row -(1) therefore, case - (2) will be eliminated.

• Case - (1)

​

4) D is to the immediate right of E.

After positioning D and E only one position is left which will be occupied by the only person left i.e A.

• Case - (1)

​

Thus, according to the final arrangement 'B, F and A' and 'C, E and D' are sitting in row -(1) and row - (2) respectively.

Hence, "C, D and E" is the correct answer.

Logic :

• (2) is added to each position value of the first word in alternate order starting with first letter.
• (2) is subtracted from each position value of the first word in alternate order starting with second letter.

So,

• BACK : ZCAM

​

Similarly,

• REAR : ?

​

Hence, "PGYT" is the correct answer.

Given : sequence - '195, 188, 181, …..'

To find : First negative term of the given sequence.

Explanation :

The sequence - '195, 188, 181, …..' is in Arithmetic progression (A.P).

So,

Let 'n' be the first negative term of the sequence.

In A.P → Tn = a + (n - 1) d 

'n' < 0

Therefore, a + (n - 1) d < 0

According to the sequence :

a = 195 (First term)

d = (188 - 195) (Common difference)

d = (-7)

Now, putting the values in the equation :

a + (n - 1) d < 0

195 + (n - 1)(-7) < 0

195 - 7n + 7 < 0

202 - 7n < 0

n < 29

Hence, "29" is the correct answer.

The set of words that best represented by the given Venn diagram is shown below:

1. Jasmine, Flowers, Eggs - As Jasmine is one of the types of flower, there Jasmine will be inside the flowers. Eggs is food is not related to flowers or Jasmine.

2. Water, Liquid, Juice - Water and Juice are the types of liquid , therefore both water and juice will come inside the liquid ⇒ Option - 2 eliminated

3) Roses, Lilies, Flowers - Roses and lilies are the types of flowers, therefore both roses and lilies will come inside flowers ⇒ Option - 3 eliminated

4) Maize, Rice, Food - Maize and rice are the types of food, therefore both maize and rice will come inside food ⇒ Option - 4 eliminated

Hence, "Jasmine, Flowers, Eggs" is the correct answer.

According to given figure:

The figure will appear when it is opened as follows:

Hence, "Option - (3)" is the correct answer.

Logic : (Square of the second number × 2) = First number

So,

• 72 : 6

​$(6)^2$ × 2 = 72

36 × 2 = 72

72 = 72 (LHS = RHS)

• 128 : 8

​$(8)^2$ × 2 = 128

64 × 2 = 128

128 = 128 (LHS = RHS)

Similarly,

• ? : 7

​$(7)^2$ × 2 = ?

49 × 2 = ?

? = 98

Hence, "98" is the correct answer.

Logic :

• (2) is subtracted from position value of each first letter.
• (2) is added to position value of each second letter.

So,

Hence, "HD" is the correct answer.

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

Conclusions:

I. At least some backpacks are bags → Follow (As some trolley-bags are backpacks, some backpacks are suitcases and all suitcases are bags . So, it is definitely true)

II. Some bags are suitcases → Follow (As all suitcases are bags. So, it is definitely true)

∴ Here, both, conclusion I and II follow.

Hence, the correct answer is "Both, conclusion I and II follow.".

Logic : Square of the number in serial order is added starting with '1'.

 

Hence, "45" is the correct answer.

Given : 

• Eight persons - A, B, C, D, E, F, G and H
• They are sitting clockwise around a circular table in the same sequence at equal distances between them.
• All are facing the center of the table.

Explanation :

• E is sitting in the north-west :

​

Thus, according to the final arrangement, G is in the South-West direction.

Hence, "South-West" is the correct answer.

Logic : The pattern used here is column wise 

(Square of first number + Square of second number) = Square of third number

So,

• First column

$(9)^2$ + $(12)^2$ = $(15)^2$

81 + 144 = 225

225 = 225 (LHS = RHS)

• Second column

$(7)^2$ + $(24)^2$ = $(25)^2$

49 + 576 = 625

625 = 625 (LHS = RHS)

Similarly,

• Third column

$(12)^2$ + $(?)^2$ = $(37)^2$

144 + $(?)^2$ = 1369

$(?)^2$ = 1369 - 144

$(?)^2$ = 1225

? = 35

Hence, "35" is the correct answer.

Logic : Sum of the position of each letter is equal to 42.

So,

1) MDNK

2) GBTM

3) SFHJ

4) JLQC

Thus, the sum of position value of each letter of 'SFHJ' is 43, rest of them has sum value as 42.

Hence, "SFHJ" is the correct answer.

The correct answer is Punjab.

Key Points 

• Punjab was the first to try out modern methods of farming during the Green Revolution in India. 
• At independence, about 75% of the country’s population was dependent on agriculture.
• The stagnation in agriculture during the colonial rule was permanently broken by the green revolution.
• This refers to the large increase in production of food grains resulting from the use of high-yielding variety (HYV) seeds, especially for wheat and rice.
• The use of HYV seeds required the use of fertilizer and pesticide in the correct quantities as well as a regular supply of water; the need for these inputs in correct proportions is vital.
• The farmers who could benefit from HYV seeds required reliable irrigation facilities as well as the financial resources to purchase fertilizer and pesticides.
• As a result, in the first phase of the green revolution (the approximately mid-1960s up to mid-1970s), the use of HYV seeds was restricted to the more affluent states such as Punjab, Andhra Pradesh, and Tamil Nadu.
• Further, the use of HYV seeds primarily benefited the wheat-growing regions only.

Additional Information

• The Green Revolution was an endeavour initiated by Norman Borlaug in the 1960s.
• He is known as the 'Father of Green Revolution in the world.
• In India, the Green Revolution was mainly led by M.S. Swaminathan.
• For introducing high-yielding varieties of rice and wheat to increase food production in order to alleviate hunger and poverty.
• The Green Revolution was a period when agriculture in India was converted into an industrial system and was a change in crop pattern.
• White Revolution was started to make India self-dependent in milk production.
• The master brain behind the white revolution in India was Dr Verghese Kurien.
• Verghese Kurien is well known as the milkman of India.
• Operation flood is the code name given to the white revolution.
• The 'Brown Revolution' is focused on giving emphasis to an Increase in the production of raw leather.
• Hiralal Chaudri is considered the father of the Brown Revolution.
• The Brown Revolution is related to Visakhapatnam’s tribal areas.
• Yellow revolution is related to Oil seeds like mustard, groundnuts sesame, etc.
• Sam Pitroda is credited for the Yellow revolution.
• It also resulted in a sudden increase in the production of edible oil due to the production of Hybrid oil seeds.
• The Yellow revolution started in the year 1986-87.

The correct answer is Crystal Award.

Key Points

• Crystal Award  is given by World Economic Forum to artists who have used their art to improve the state of the world.
• The Crystal Awards celebrate the achievements of leading artists and cultural figures whose leadership inspires inclusive and sustainable change.
• Crystal Awards conferred for the achievements of leading artists and cultural figures whose leadership inspires inclusive and sustainable change.
• Theaster Gates, Jin Xing, and Lynette Wallworth named as 2020 Crystal Award recipients apart from Indian Deepika Padukone.
• Theaster Gates, Chicago, gets the award for his leadership in creating sustainable communities.
• Jin Xing, China, gets the award for her leadership in shaping inclusive cultural norms.
• Lynette Wallworth, Australia, gets the award for her leadership in creating inclusive narratives.

Additional Information

• The World Economic Forum (WEF), based in Geneva, Switzerland, is an international NGO, founded on 24 January 1971.
• The WEF hosts an annual meeting at the end of January in Davos in the eastern Alps region of Switzerland.
• The reports released by WEF
• Global Competitiveness Report
• The Global Information Technology Report
• The Global Gender Gap Report
• The Global Risks Report
• The Global Travel and Tourism Report
• The Financial Development Report
• The Global Enabling Trade Report

The correct answer is Chemistry.

Key Points

• Jennifer A Doudna and Emmanuelle Charpentier were awarded the Nobel Prize in Chemistry 2020 for their exemplary work in genome editing.
• Genome editing is the technology that allows the addition, alteration and removal of genetic material at particular locations in the genome.
• Specific changes in the DNA of a cell or organism are made.
• Clustered Regularly Interspaced Short Palindromic Repeats(CRISPR) technology is a gene-editing technology that can be used for the purpose of changing the genome of an Organism.

Additional InformationNobel Prize Winners 2020

The correct answer is 1765.

Key Points

• In 1765 the Mughal Emperor Shah Alam II appointed the English East India Company as the Diwan of the province of Bengal.
• Shah Alam II agreed to:
• Reside at Allahabad, to be ceded to him by the Nawab of Awadh, under the Company's protection.
• Issue a Farman granting the Diwani of Bengal, Bihar and Orissa to the East India Company in lieu of an annual payment of Rs 26 lakh.
• A provision of Rs 53 lakh to the Company in return for Nizamat functions (military defence, police, and administration of justice) of the said provinces.
• Robert Clive did not want to annex Awadh because it would have placed the Company under an obligation to protect an extensive land frontier from the Afghan and the Maratha invasions.

Additional Information

• The Treaty of Allahabad, 1765:
• Robert Clive concluded two important treaties at Allahabad in August 1765
• With the Nawab of Awadh and,
• With the Mughal Emperor, Shah Alam II.

The correct answer is 16.

Key Points Census of 2021

• It will be the 16th Census of India and the 8th Census of Independent India.
• The theme of Census 2021 is “Jan Bhagidari se Jan Kalyan”.
• Census 2021 will be completely paperless and the process of collection and classification of population data will be completely digital.
• A mobile app issued by the government will be used in the process of the census.
• Information can be given in 16 languages ​​through this app, this information will be verified by senior officials.
• The census work will be completed in two phases across the country.

Thus the correct answer is 16.

Additional Information   Census of India

• Census is conducted every 10 years in India.
• The first nationwide census was conducted in India in the year 1872 under British rule during the tenure of Lord Mayo.
• The Census of India is the largest project of its kind in the world.
• For the first time after independence, the caste census was conducted in the year 2011.

The correct answer is National income.

Key Points

• National Income is the total monetary value of goods and services produced within the territory of the country in a given period of time.
• National Income = C+I+G+ (X-M)

Here, 

C stands for Consumption

I stands for Total Investment

G stands for Total Government Expenditure

X stands for Export

M stands for Import

Additional Information

The correct answer is Speaker of the Lok Sabha.

Key Points

• A Bill is said to be a Money Bill if it only contains provisions related to taxation, borrowing of money by the government, expenditure from or receipt to the Consolidated Fund of India.
• Speaker of the Lok Sabha decides whether a particular bill is a Money Bill or not.

Additional Information 

Procedures of a Money Bill: 

• Money Bills can be introduced only in Lok Sabha.
• Money bills passed by the Lok Sabha are sent to the Rajya Sabha. The Rajya Sabha may not amend money bills but can recommend amendments. A money bill must be returned to the Lok Sabha within 14 days, or the bill is deemed to have passed both houses in the form it was originally passed by the Lok Sabha.
• When a Money Bill is returned to the Lok Sabha with the recommended amendments of the Rajya Sabha, it is open to the Lok Sabha to accept or reject any or all of the recommendations.
• A money bill is deemed to have passed both houses with any recommended amendments the Lok Sabha chooses to accept, and without any that it chooses to decline.
• The definition of "Money Bill" is given in Article 110 of The Constitution of India. A financial bill is not a Money Bill unless it fulfills the requirements of Article 110.
• The Speaker of the Lok Sabha certifies if a financial bill is a Money Bill or not.​

The correct answer is bamboo.

Key Points

• The Indian Forest (Amendment) Bill, 2017  amends this definition of the tree and removes the word bamboo.
• Since bamboo is defined as a tree under the Act, its inter-state movement requires permits when in transit in other states. Consequent to the amendment, felling or transportation of bamboos growing in non-forest areas will not require any permits.
• The government has called Bamboo ‘Green Gold’ and announced the launch of the Rs.1290- crore Restructured National Bamboo Mission, which is based on a cluster-based approach to address the complete bamboo value chain and promote the bamboo sector in a holistic manner.

Additional Information

• The Indian Forest (Amendment) Bill, 2017 was introduced in Lok Sabha by the Minister of Environment, Forest, and Climate Change on December 18, 2017.
• The Bills replaces the Indian Forest (Amendment) Ordinance, 2017 and amends the Indian Forest Act, 1927.
• The Act consolidates laws relating to forests, the transit of forest produce, and the duty to be levied on them.
• Under the Act, the definition of tree includes palms, bamboos, stumps, brush-wood, and canes.

The correct answer is Bhaichung Bhutia.

Key Points

• Bhaichung Bhutia is also known as the Sikkimese Sniper.
• He is a former Indian national footballer and is considered the epitome of the rise of Indian football.
• He was born on 15 December 1976 in Tinkitam, Sikkim, and played as a striker all his career.
• Bhutia is known for his powerful shots and his pinpoint accuracy in front of the goal.
• His hunger for goals and his passion for the game made him the father figure of Indian football.
• Bhaichung has also captained the national side and currently plays the role of manager at the Sikkim state football club.
• Bhutia has represented the following teams - India, East Bengal, JCT Mills, Bury, Mohun Bagan, Perak FA, Selangor MK Land, and United Sikkim.
• Bhaichung Bhutia made his club professional debut in 1993 for Calcutta-based East Bengal where he would make nine appearances, scoring 4 goals in the league.
• In 2008, He had refused to carry the Olympic torch to show support and solidarity for the people of Tibet and their struggle.

Additional Information

• Sandesh Jhingan has been named the AIFF men’s Footballer of the Year.
• Subrata Paul is an Indian professional footballer who plays as a goalkeeper for Indian Super League club ATK Mohun Bagan, on loan from Hyderabad.
• ​Sunil Chhetri, captain of the Indian football team, is one of the most active goal scorers in the country. 
• He is the leading goal scorer in international football for India as well as in domestic football tournaments.
• Sunil Chhetri appeared in 54 international matches for India so far and has scored 41 goals which is almost half of his total goals tally (84)

The correct answer is Mohenjo-daro.

Key Points

• The Great Bath was excavated from Mohenjo-Daro.
• Rakhigarhi is the largest Harappan site in the Indian subcontinent.
• The Great Granary was the largest building discovered at Mohenjodaro of Harappan Civilisation (also known as Indus Civilisation).
• It shows the importance of ritualistic bathing.
• There is no leakage or cracks in the construction of ‘The Great Bath'.
• It reflects the cleanliness of this culture.
• In addition to this, Great Granary, Assembly Hall, etc. were also excavated.
• The excavators were Rakhal Das Bannerji (1922), Mackay (1927) & Wheeler (1930).

Additional Information

• Indus Valley Civilization:
• It was one of the major civilizations of the ancient river valley civilizations of the world.
• It is also known as Harappan Civilization and Indus-Saraswati Civilization.
• It developed on the banks of the Indus and Ghaggar/Hakra (ancient Saraswati).
• Mohenjodaro, Kalibanga, Lothal, Dholavira, Rakhigarhi, and Harappa were its main centers.

The correct answer is the Moon.

Key Points

• Moon is the Non-Luminous body.
• Moon does not produce its own light and shines in the light reflected from the sun.
• The Luminous Body is an object which emits its own light and shines as a result of it.

Additional Information

• A luminous object is one that has its own light.
• While a non-luminous object reflects the light from a luminous body and thus shines.
• Sun is luminous body.
• Sun is a star in which the source of heat and light are the nuclear fusion reactions.
• The isotopes of hydrogen combine to form a helium nucleus which releases a huge amount of energy.

The correct answer is Piyush Goyal.

Key Points

• The G20 summit, which concluded on 31 October 2021, has adopted Rome Declaration.
• The member countries have agreed on mutual recognition of vaccines, strengthening of WHO to give faster approvals to vaccines, and suspending debt servicing for developing countries till December 2021.
• Union Minister Piyush Goyal was India's G20 Sherpa.

Additional Information 

• G20:
• The G20 or Group of Twenty is an intergovernmental forum comprising 19 countries and the European Union.
• It works to address major issues related to the global economy, such as international financial stability, climate change mitigation, and sustainable development.
• The members of the G20 are:
• Argentina.
• Australia.
• Brazil.
• Canada.
• China.
• France.
• Germany.
• India.
• Indonesia.
• Italy.
• Japan.
• Republic of Korea.
• Mexico.
• Russia.
• Saudi Arabia.
• South Africa.
• Turkey.
• United Kingdom.
• United States.
• European Union.

The correct answer is Rajasthan.

Key Points

• Rajasthan has the largest inland saline wetland.
• Sambhar Lake in Rajasthan is India's largest inland saline wetland system.
• It is located in Sambhar Lake-town near Jaipur.
• The lake has been designated as a Ramsar site.
• The lake has a catchment area of 5700 sq. km and receives water from five rivers:
• Medta,
• Samaod,
• Mantha,
• Rupangarh,
• Khari, and
• Khandela.

Additional Information

• A wetland is a distinct ecosystem that is flooded by water, either permanently (for years or decades) or seasonally (for weeks or months).
• Flooding results in oxygen-free (anoxic) processes prevailing, especially in the soils.
• The primary factor that distinguishes wetlands from terrestrial land forms or water bodies is the characteristic vegetation of aquatic plants, adapted to the unique anoxic hydric soils.
• Wetlands are considered among the most biologically diverse of all ecosystems, serving as home to a wide range of plant and animal species.
• Methods for assessing wetland functions, wetland ecological health, and general wetland condition have been developed for many regions of the world.

The correct answer is Sunrisers Hyderabad.

Key Points

• Afghan cricketer Rashid Khan played for Sunrisers Hyderabad in the Indian Premier League (IPL) 2021.
• At 19 years of age, Afghanistan leg-spinner Rashid Khan became the youngest captain in the history of international cricket.
• Rashid is also the youngest player to be ranked No.1 in the ICC's Player Rankings across formats.

Additional Information

• Sunrisers Hyderabad has won the IPL trophy so far only once I.e in the 2016 IPL season.
• 2016 IPL final was held between Sunrisers Hyderabad and Royal Challengers Bangalore at M. Chinnaswamy Stadium.
• The earlier name of the franchise was Deccan Chargeres and they won the trophy in 2009.

The correct answer is Sodium hydrogen carbonate.

Key Points

• The common name of sodium hydrogen carbonate is Baking soda.
• It is also called Sodium bicarbonate (NaHCO₃).
• It is used as a leavening agent, fungicide, pest control, mild disinfectant, fire extinguisher, neutralization of acids, and Cleaning agent, etc.

Additional Information

• Sodium Benzoate is a white odorless crystalline powder used to preserve tomato ketchup.
• It is also widely used in acidic foods like pickles, carbonate drinks, condiments, jams, and fruit juices.
• It is made by adding benzoic acid and sodium hydroxide.
• Benzoic acid is a natural preservative found in plants like tomato, clove, berry, apple, and cinnamon.
• The chemical formula of Sodium Benzoate is C7H5NaO2.
• Benzoic acid, in the form of sodium benzoate, is a widely used food preservative suitable for acid foods.
• It delays the fermentation of the juices.
• In the long run, benzoic acid may darken the product.
• It is commonly used in products which are having natural colors such as anthocyanin pigment.
• Sodium metabisulphite is used as an antioxidant agent in many pharmaceutical formulations.
• It is extensively used as a food preservative and disinfectant.
• It has been demonstrated that sulphite exposure can affect some organs.

The correct answer is Saudi Arabia.

Key Points

• The G20 Foreign Ministers' Extraordinary Meeting was convened by the current G20 Chair, the Kingdom of Saudi Arabia on 3rd September, 2020.
• Minister of Foreign Affairs of Kingdom of Saudi Arabia, His Highness Prince Faisal Bin Farhan Al-Saud, chaired the meeting. EAM Dr. S. Jaishankar represented India.

Additional Information

• ​The G20 or Group of Twenty is an intergovernmental forum comprising 19 countries and the European Union.
• It works to address major issues related to the global economy, such as international financial stability, climate change mitigation, and sustainable development.
• As of 2022, there are 20 members in the group: Argentina, Australia, Brazil, Canada, China, France, Germany, India, Indonesia, Italy, South Korea, Japan, Mexico, Russia, Saudi Arabia, South Africa, Turkey, the United Kingdom, the United States, and the European Union.
• ​The G20:
• Founder: G-7 countries
• Founded: 26 September 1999

The correct answer is Rose.

Key Points

• Roses are dicotyledon or dicots as they have two cotyledons, the first seed leaf, which is present in the embryo.
• Other characteristics are reticulate venation in leaves, monocots generally have parallel venation.
• The cotyledons act as a food store in plant seeds.
• Cotyledons are often fleshy and full of reserve food materials.
• Based on the number of cotyledons vascular plants can be classified as Monocot and Dicot.
• Cot word represents the cotyledons, which means an embryonic leaf

Additional Information

• Two different types of cotyledon are Monocotyledons and Dicotyledons.
• Monocot-
• Monocotyledons are the angiosperms or the flowering plants in which the seeds typically contain only one embryonic leaf or Cotyledon.
• Example- Ginger, onions, wheat, and grass.
• Dicot- 
• Dicotyledons are the angiosperms or the flowering plants in which the seeds contain two embryonic leaves or cotyledons.
• Example- All legumes including beans, lentils, pea, rose and peanuts

The correct answer is Nag.

Key Points

• DRDO successfully conducted the final trial of Nag missile anti-tank guided missile in Pokhran range in October 2020.
• The Nag missile, also called "Prospina'' for the land-attack version, is an Indian third-generation, all-weather, fire-and-forget, lock-on after launch, anti-tank guided missile (ATGM) with an operational range of 500 m to 20 km.
• It has a single-shot hit probability of 90% and a ten-year, maintenance-free shelf life.

Additional Information

• The Nag has five variants under development: a land version, for a mast-mounted system;
• The helicopter-launched Nag (HELINA) also known as Dhruvastra;
• A "man-portable" version (MPATGM);
• An air-launched version which will replace the current imaging infra-red (IIR) to millimetric-wave (mmW) active radar homing seeker
• The Nag Missile Carrier (NAMICA) "tank buster"
• Development of the Nag is part of the Integrated Guided Missile Development Program (IGMDP), run by Defence Research and Development Organisation (DRDO).
• It is manufactured by Bharat Dynamics Limited (BDL).
• The Man-Portable Anti-tank Guided Missile (MP-ATGM) is an Indian-made third-generation anti-tank guided missile derived from the Nag missile.Recently Drdo confirmed its production to start in 2021.

The correct answer is Gonds.

Important Points

• Rani Durgawati, who ruled over on behalf of her five-year-old son Bir Narain belonged to Gonds.
• Rani Durgawati was a Chandel princess.
• She was the daughter of the king of Chandel Keerat Rai.
• She was married to Dalpat Shah, the eldest son of the king of Gondwana kingdom, Sangram Shah in 1542.
• Dalpat Shah died in 1550. She was the ruling Queen of Gondwana from 1550  to 1564.
• Durgawati moved the capital of Gondwana from Singorgarh fort to Chauragarh.
• She killed herself on the battlefield on 24 June 1564.
• Her martyrdom day (24 June 1564) is commemorated as "Balidan Diwas".

Additional Information

• Gond is one of the largest tribes in India.
• Gonds are found in Madhya Pradesh, Maharashtra, Chhattisgarh, Uttar Pradesh, Telangana, Andhra Pradesh, Bihar, and Odisha.
• Gonds worship a high god known as Baradeo, whose alternate names are Budha Dev, Thakur Dev, Dulha Dev, Sri Shambu Mahadeo, etc.
• Gond women from Chattisgarh perform the Sua dance which is performed after Diwali to honor Shiva and Parvati.

The correct answer is 10 lakhs and 1 crore.

Important Points

• 'Stand-up India' Scheme's purpose is To encourage entrepreneurship among the SC/STs and women entrepreneurs.
• Stand up India is one of the core parts of the Start-up India scheme in order to encourage individuals to bring their ideas to life.
• The Stand up India scheme aims at promoting entrepreneurship among women and scheduled castes and tribes.
• The scheme is anchored by Department of Financial Services (DFS), Ministry of Finance, Government of India.
• Stand-Up India Scheme facilitates bank loans between Rs 10 lakh and Rs 1 Crore to at least one Scheduled Caste (SC) or Scheduled Tribe (ST) borrower and at least one woman borrower per bank branch for setting up a greenfield enterprise.

The correct answer is Ghana Vadya.

Key Points

• Ghana Vadya or Idiophones/Solid instruments which do not require tuning-
• The earliest instruments invented by man are said to be the Ghana Vadya.
• Once constructed, this variety of instrument do not need special tuning prior to playing.
• They are principally rhythmic in function and are best suited as accompaniment to folk and tribal music and dance.
• E.g - Jal Tarang, Ghatam etc

Additional Information

• Instruments have been listed below.
• Avanaddha Vadya or Membranophones/Percussion instruments -
• In the Avanaddha Vadya category of instruments, the sound is produced by striking the animal skin which has been stretched across an earthern or metal pot or a wooden barrel or frame.
• E.g - Tabla, Mridangam, Nagara, Damaru etc.
• Sushira Vadya or Aerophones/Wind instruments -
• In the Sushira Vadya group, the sound is produced by blowing air into a hollow column.
• The pitch of the note is determined by controlling the air passage and the melody is played by using the fingers to open and close the instrument.
• E.g - Flutes, Shehnai, Nadaswaram, etc.
• Tata Vadya or Chordophones/Stringed instruments - 
• ​The tata vadya is a category of instruments in which sound is produced by the vibration of a string or chord.
• These vibrations are caused by plucking or by bowing on the string which has been pulled taut.
• E.g - Veena, Sitar, Sarangi etc.

The correct answer is Arabic was the language of administration under the Delhi Sultans.

Important Points

• Persian was the language of administration under the Delhi Sultans.
• Tarikh and Tawarikh, sources of information on Delhi Sultans, were written in Persian.
• It was also the language for administration.
• Turkish rulers who ascended the throne of Delhi made the Persian language popular.
• Hence statement 1 is INCORRECT.
• Delhi first became the capital of a kingdom under the Tomara Rajputs, who were defeated in the middle of the twelfth century by the Chauhans (also referred to as Chahamanas) of Ajmer.
• It was under the Tomaras and Chauhans that Delhi became an important commercial centre.
• Many rich Jaina merchants lived in the city and constructed several temples.
• Coins minted here, called Dehliwal, had a wide circulation.
• Hence statement 2 and 3 is CORRECT.
• Qutb al-Din Aibak ruled over Delhi from 1206 - 1210.
• Time period: 1206-1210
• He was the slave of Muhammad Gori.
• He was the founder of the Slave dynasty.
• He constructed Quwwat Ul Islam Masjid in Delhi and Adhai Din Ka Jhonpra in Ajmer.
• Hence statement 4 is CORRECT.

The correct answer is Five.

Key Point

• Five sportspersons won the Rajiv Gandhi Khel Ratna Award in 2020.
• Winners in 2020:
• Wrestler Vinesh Phogat
• Women's hockey captain Rani Rampal
• Table tennis star Manika Batra
• Para-athlete Mariyappan Thangavelu
• Batsman Rohit Sharma
• 12 sportspersons will be honoured with the Major Dhyan Chand Khel Ratna Award (former Rajiv Gandhi Khel Ratna) 2021.

Additional Information

• Rajiv Gandhi Khel Ratna Award: It is the highest sporting award of the Republic of India.
• It was named after former prime minister Rajiv Gandhi.
• It was given by the Ministry of Youth Affairs and Sports for the spectacular and most outstanding performance in the field of sports by a sportsperson over a period of four years.
• The award comprises of Medallion and Cash prize of 25 lakh rupees.
• Award was instituted in 1991-92.
• First awardee: Viswanath Anand.

The correct answer is Mahabalipuram, Tamil Nadu.

Key Points

• A monument called Descent of the Ganges, also referred to as Arjuna's Penance locally may be found in the Indian state of Tamil Nadu's Chengalpattu district in Mahabalipuram on the Coromandel Coast of the Bay of Bengal.
• Arjuna’s Penance, a mammoth architecture with finely carved rock sculptures, serves as a venue for the Mamallapuram Dance Festival, in the backdrop of the Bay of Bengal.
• It is a massive open-air rock relief that is 96 by 43 feet (29 by 13 metres) in size and carved onto two monolithic rock boulders.
• The legend illustrated in the relief tells the tale of Bhagiratha leading the sacred river Ganges as it descended from the sky to the land.
• Stone carvings at the Pallava historic site depict the Ganges' descent and Arjuna's penance.

Additional Information

• Mahabalipuram was registered under UNESCO Heritage Site in 1984.
• A World Heritage Site is a landmark or area with legal protection by an international convention administered by the United Nations Educational, Scientific and Cultural Organization (UNESCO).
• World Heritage Sites are designated by UNESCO to be of cultural, historical, scientific, or any other type of importance.
• As of July 2021, a total of 1,154 World Heritage sites are located in 167 State Parties (countries that adhere to the World Heritage Convention, including non-member states of the Holy See), of which 897 are cultural, 218 are natural. And there are 39 mixed properties.​

The correct answer is slash and burn.

Key Points

• Shifting cultivation is an agricultural practice in which a piece of land is farmed on, only to be abandoned later after initial use.
• It is prohibited in India as shifting cultivation was believed to be responsible for the alarming rate of deforestation of Indian forests.
• Shifting cultivation, also referred to as Jhum or slash-and-burn cultivation.

Additional Information

• Shifting cultivation is called as
• Roca in Brazil
• Jhumming in India
• Ladang in Indonesia and Malaysia
• Milpa in Central America and Mexico

Given:

⇒ $\frac{{3of5\frac{1}{2} + 6 \div 5 - 2of3 \div 4}}{{1 + \frac{3}{{1 + \frac{1}{4}}}of5 - 3\frac{1}{3}of2 \div 5}}$

Formula used:

Calculation:

⇒$\frac{{3of\frac{11}{2} + 6 \div 5 - 2of3 \div 4}}{{1 + \frac{3}{{1 + \frac{1}{4}}}of5 - 3\frac{1}{3}of2 \div 5}}$ 

⇒ $\frac{{{33\over2} + {6\over5} - 2\times3 \div 4}}{{1 + \frac{3}{{1 + \frac{1}{4}}}of5 - {10\over3}of2 \div 5}}$

⇒ $\frac{{{33\over2} + {6\over5} - 2\times3 \div 4}}{{1 + \frac{12}{5}of5 - {10\over3}of\frac{2}{5}}}$

⇒ $\frac{{{33\over2} + {6\over5} - 2\times3 \div 4}}{{1 + (\frac{12}{5}\times5) - ({10\over3}\times\frac{2}{5}})}$

⇒ $\frac{{\frac{33}{2} +\frac{6} 5 - \frac 3 2}}{{13 - \frac{4}{3}}}$

⇒ $\frac{{\frac{162}{10} }}{{ \frac{35}{3}}}$

⇒ $\frac{{243}}{{175}}$

Hence, the value of expression is 243/175.

Given:

The average of 19 numbers = 58

The average of the first 12 numbers = 63.6

The average of the last 8 numbers = 55.1

Formula used:

Average= (Sum of all observations)/(Total number of observations)

Calculation:

The average of 19 numbers = 58

∴ Sum of 19 numbers = 19 × 58 = 1102

The average of the first 12 numbers = 63.6

∴ Sum of first 12 numbers = 12 × 63.6 = 763.2

The average of the last 8 numbers = 55.1

∴ Sum of last 8 numbers = 8 × 55.1 = 440.8

⇒ 12^th number = {(763.2 + 440.8) – 1102} = 102

According to the question

The 12th number from the beginning is excluded.

The sum of the remaining numbers = 1102 – 102 = 1000

The average of the 18 remaining numbers = $1000\over18$ = $500\over9$ = ${55}{5\over9}$ 

 ∴ The average of the 18 remaining numbers is ${55}{5\over9}$.

Given:

The Numbers 341, 434, and 620 

Their HCF is x

Concept used:

The full form of HCF in Maths is the Highest Common Factor.

HCF of two or more numbers is the greatest factor that divides the numbers.

For example:

4 = 2 × 2

6 = 2 × 3

⇒ 2 is the HCF of 4 and 6.

Calculation:

Prime factorization of the numbers are:

341 = 11 × 31

434 = 2 × 7 × 31

And 620 = 2² × 5 × 31

So, HCF = 31

∴ x = 31 and it lies between 30 and 35.

Shortcut Trick

Initial Ratio (Alcohol : Water) = 4 : 3 (Total 7 units)

7 units = 350 mL ⇒ 1 unit = 50 mL. So, Alcohol = 200 mL, Water = 150 mL.

Final Ratio = 5 : 6. Since only water is added, alcohol remains 200 mL.

5 units = 200 mL ⇒ 1 unit = 40 mL. Final water = 6 × 40 = 240 mL.

Water added = 240 − 150 = 90 mL.

∴ The correct answer is 90 mL.

Alternate Method

Given: Initial volume = 350 mL, Initial ratio = 4 : 3, Final ratio = 5 : 6.

Formula: Quantity of component = (Ratio part / Total parts) × Total Volume

⇒ Initial Alcohol = (4/7) × 350 = 200 mL

⇒ Initial Water = (3/7) × 350 = 150 mL

⇒ Let x mL of water be added.

⇒ New ratio of Alcohol to Water = 200 / (150 + x) = 5 / 6

⇒ 200 × 6 = 5 × (150 + x)

⇒ 1200 = 750 + 5x

⇒ 5x = 450

⇒ x = 90 mL

∴ The correct answer is 90 mL.

Additional Information

Constant Component Rule

When one component is added to a mixture, the quantity of the other component remains unchanged. Use this to equate the constant part across both ratios.

Alligation Method

Mixture problems can also be solved using Alligation by taking the concentration of water in the initial mix (3/7) and the added pure water (1/1) to reach the target concentration (6/11).

Ratio Balancing

Multiply the ratios to make the non-changing part equal. If Alcohol is 4:3 and later 5:6, multiply the first by 5 and the second by 4 to get Alcohol as 20 in both.

Given:

Rate of interest = 6.4%

Time in the first situation = ${3}{3\over4}$ years = $15\over4$ years

Time in the second situation = ${6}{1\over4}$ years = $25\over4$ years

Simple interest = Rs. 1896

Formula used:

S.I. = (P × R × T)/100

Amount = Principal + S.I.

Where, P = Principle, R = Rate of interest

T = Time and S.I. = Simple interest

Calculation:

Simple interest = (P × R × T)/100

⇒ 1896 = $(P×6.4×15)\over(4×100)$ 

⇒ P = $(1896×4×100)\over(6.4×15)$ 

⇒ P = (1896 × 400)/96 = Rs. 7900

Simple interest on the same rate in ${6}{1\over4}$ years.

Simple interest = (P × R × T)/100

⇒ S.I = $(7900×6.4×25)\over(4×100)$ 

⇒ S.I. = (79 × 160)/4 = Rs. 3160

Amount = Principal + S.I

⇒Amount = (7900 + 3160) = Rs. 11060

∴ Hence, the amount is Rs. 11060.

Given:

Reshma's expenditure = 84%

Increase in her income = 30%

Increase in her savings = 40%

Formula used:

Income = Expenditure + Savings 

Calculation:

Let Reshma's income be Rs. 100

∴ Expenditure of Reshma = 100 × 84/100 = 84

Savings of Reshma = 100 - 84 = 16

According to the question,

Increased income of Reshma = 130/100 × 100

∴ Increased income = 130

Increased savings of Reshma = 140 × 16/100 

∴ Increased savings = 22.4

Expenditure = Income - Savings

∴ Increased expenditure = 130 - 22.4 = 107.6

⇒ % Increase in expenditure = (107.6 - 84)/84 × 100

⇒ 28.1% (approx)

∴ Hence, the increase in her expenditure is 28.1%.

Given:

The average score of 35 students = 46

Wrong entries = 33, 33, 30

Correct entries = 23, 23, 36

Formula used:

Average = Sum of all the terms/Total number of terms

Calculation:

Sum of scores of 35 students = 46 × 35

⇒ Sum of scores of 35 students = 1610

Sum of wrong entries = 33 + 33 + 30 = 96

Sum of correct entries = 23 + 23 + 36 = 82

∴ Actual Sum = 1610 - 96 + 82 = 1596

Actual average score = 1596/35 = 45.6

∴ The Actual average score is 45.6.

Given: 

Marked price is 35% more than cost price 

Discount = 5%

Formula used:

$P\% = \frac{(SP - CP)× 100}{(CP)}$

Where, SP = Selling price, P = Profit

And CP = Cost price

Calculation:

Let CP be 100 

∴ Marked price = 100 + (100 × 35/100) 

⇒ Marked price = 135

Selling price = MP - Discount

∴ SP = 135 - (135 × 5)/100

⇒ SP = 128.25

∴ Profit % = [(128.25 - 100)/100] × 100

⇒ Profit % = 28.25

Hence, the Profit of Shyamlal is 28.25%.

Given:-

Copper : Zinc = 5 : 4

Quantity (Q) of zinc Q_z = 20 kg

Concept used:-

Unitary Method-

Copper : Zinc = Q_C : Q_Z

Calculation:-

According to question-

⇒ 5 : 4 = Q_C : 20

⇒ 4Q_C = 20 × 5

⇒ Q_C = 100/4

⇒ Q_C= 25 kg

∴ Quantity of copper is 25Kg.

Shortcut Trick Prime factors: 34 = 2 × 17; 38 = 2 × 19; 85 = 5 × 17; 95 = 5 × 19. LCM = 2 × 5 × 17 × 19 = 10 × 323 = 3230. Average = (34 + 38 + 85 + 95) ÷ 4 = 252 ÷ 4 = 63. Remainder = 3230 mod 63 ⇒ 3230 = (63 × 51) + 17. ∴ The correct answer is 17.

Alternate Method Given: The numbers are 34, 38, 85, and 95. Formula Used:

1. Average = (Sum of all observations) ÷ (Total number of observations)
2. LCM = Product of the highest powers of all prime factors involved.
3. Dividend = (Divisor × Quotient) + Remainder

Step 1: Calculate the Average of the numbers. ⇒ Sum = 34 + 38 + 85 + 95 = 252 ⇒ Average = 252 ÷ 4 = 63 Step 2: Calculate the LCM of 34, 38, 85, and 95. ⇒ 34 = 2 × 17 ⇒ 38 = 2 × 19 ⇒ 85 = 5 × 17 ⇒ 95 = 5 × 19 ⇒ LCM = 21 × 51 × 171 × 191 = 3230 Step 3: Find the Remainder when 3230 is divided by 63. ⇒ 3230 ÷ 63 ⇒ 63 × 50 = 3150 ⇒ 3230 − 3150 = 80 ⇒ 80 − 63 = 17 ⇒ 3230 = (63 × 51) + 17 ∴ The correct answer is 17.

Additional Information Least Common Multiple (LCM) LCM is the smallest quantity that is exactly divisible by each of two or more given quantities. It is found by taking the highest power of each prime factor present in the numbers. Arithmetic Mean The average or mean is the central value of a set of data, calculated by summing all values and dividing by the count of those values: Σx ÷ n. Division Algorithm For any two integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < |b|. Here, r is the remainder.

Shortcut Trick

Let MP = 100% i.e 1250 → 100%

∴ 1150 → 1150/1250 × 100 = 92

% Discount = 100 - 92 = 8%

Hence, The discount allowed is 8%.

Alternate Method 

Given:-

MP = Rs.1250

SP = Rs.1150

Formula used:-

Discount% = {(MP - SP) × 100}/MP

Calculation:-

Discount% = {(1250 - 1150) ×100}/1250

⇒ (100 × 100)/1250

⇒ 10000/1250

⇒ 8% 

∴ The discount percentage allowed by the shopkeeper is 8%

Alternate Method

Calculations:

Marked Price = 1250

Let Selling price be x % of MP

∴ 1150 = x × 1250/100

⇒ x = (1150/1250) × 100 = 92

Discount % = 100 - 92 = 8 %.

∴ The discount percentage allowed by the shopkeeper is 8%

Given:-

Total Interest = Rs.11880

Total time = 4 years

R₁ = 7%, R₂ = 9%, and R₃ = 11%

Formula used:-

SI = (P × R × T)/100

Where P = Principle, R = Rate of interest

T = Time, and SI = Simple Interest

Calculation:-

Let the total sum be x

According to question:-

P₁ = 3x/7, P₂ = 2x/5, And 

P₃ = [1 - (3x/7 + 2x/5)] = 6x/35

Total Interest = ∑ (P × R × T)/100

⇒ 11880 = $\large{\frac{3x× 7× 4}{7 × 100}}$ + $\large{\frac{2x × 9 × 4}{5 × 100}}$ + $\large{\frac{6x × 11 × 4}{35 × 100}}$

⇒ 11880 = $\large{\frac{4}{100}× [\frac{21x}{7} + \frac{18x}{5} + \frac{66x}{35}]}$]

⇒ 1188000/4 = $\large{\frac{105x + 126x + 66x}{35}}$  

⇒ 297x = 297000 × 35

⇒ x = 10395000/297

⇒ x = 35000

∴ The total sum invested is Rs.35000

Shortcut Trick

 

Combined efficiency (A + B + C) = 6

∴ Efficiency of C = 6 - 3 - 2 = 1 unit

Time taken by C = Total work/ Efficiency of C

Time taken by C = 24/1 = 24 days.

Hence, Time taken by C to complete the work is 24 days.

Alternate Method

Given:

Time taken by A = 8 days 

Time taken by B = 12 days

Time taken by A, B, and C together = 4 days

Formula used:

Total work = Time taken × Efficiency

Calculation:

Let the total work be x

A's one-day work = x/8

B's one-day work = x/12

A + B + C's one-day work = x/4

∴ C's efficiency (C's one-day work) = x/4 - (x/8 + x/12)

⇒ C's efficiency = x/4 - 5x/24

⇒ C's efficiency = (6x - 5x)/24

⇒ C's Efficiency = x/24

Time taken by C = Total work/Efficiency

Time taken by C = x/(x/24) = 24 days.

Hence, Time taken by C to complete the work is 24 days.

Shortcut Trick

Sum the ratios: a²+b² + b²+c² + c²+a² = 34 + 61 + 45 = 140.

Then a²+b²+c² = 140 ÷ 2 = 70.

Individual squares: a² = 70 − 61 = 9, b² = 70 − 45 = 25, c² = 70 − 34 = 36.

Roots: a = 3, b = 5, c = 6.

Required ratio: (3+5) : (5+6) : (6+3) = 8 : 11 : 9.

∴ The correct answer is 8 : 11 : 9.

Alternate Method

Given: (a² + b²) : (b² + c²) : (c² + a²) = 34 : 61 : 45

Calculations:

⇒ Let a² + b² = 34k, b² + c² = 61k, and c² + a² = 45k.

⇒ Adding all three: 2(a² + b² + c²) = (34 + 61 + 45)k = 140k.

⇒ a² + b² + c² = 70k.

⇒ a² = (a² + b² + c²) − (b² + c²) = 70k − 61k = 9k → a = 3√k.

⇒ b² = (a² + b² + c²) − (c² + a²) = 70k − 45k = 25k → b = 5√k.

⇒ c² = (a² + b² + c²) − (a² + b²) = 70k − 34k = 36k → c = 6√k.

⇒ a + b = 3√k + 5√k = 8√k.

⇒ b + c = 5√k + 6√k = 11√k.

⇒ c + a = 6√k + 3√k = 9√k.

⇒ (a + b) : (b + c) : (c + a) = 8√k : 11√k : 9√k = 8 : 11 : 9.

∴ The correct answer is 8 : 11 : 9.

Additional Information

Sum of Ratios Property

For equations involving sums of pairs like x+y, y+z, and z+x, adding all equations and dividing by 2 gives the total sum x+y+z.

Ratio to Square Root

When terms are in square form, the ratio of the variables is found by taking the square root of the ratio constants, provided the numbers are positive.

Compound Ratio

The ratio of the sums (a+b):(b+c):(c+a) is derived from individual values calculated through the method of substitution or comparison from the total sum.

Shortcut Trick

When Profit% = Cost Price (CP), use the formula: CP = 10 × [√(25 + SP)] − 50.

Given Selling Price (SP) = 375.

CP = 10 × [√(25 + 375)] − 50

CP = 10 × [√400] − 50 ⇒ 10 × 20 − 50

CP = 200 − 50 = 150.

∴ The correct answer is Rs. 150.

Alternate Method

Given: Selling Price (SP) = Rs. 375, Profit% = CP.

Formulas: SP = CP × (100 + Profit%) ÷ 100

⇒ Let Cost Price be x. Then Profit% is also x%.

⇒ 375 = x × (100 + x) ÷ 100

⇒ 37500 = 100x + x²

⇒ x² + 100x − 37500 = 0

⇒ x² + 250x − 150x − 37500 = 0

⇒ x(x + 250) − 150(x + 250) = 0 ⇒ (x − 150)(x + 250) = 0

⇒ x = 150 (Since CP cannot be negative).

∴ The correct answer is Rs. 150.

Additional Information

Verification via Options

If CP = 150, then Profit% = 150%. SP = 150 + 150% of 150 = 150 + 225 = 375. This matches the given SP.

Loss Case

If Loss% = CP, the formula becomes CP = 10 × [50 ± √(2500 − 100 × SP)] ÷ 10.

Given:

Discount = 10%

Market price = 30% above cost price

Formula used:

Discount % = (MP - SP)/MP × 100

Gain% = (SP - CP)/CP × 100

Calculation:

Let the cost price be Rs.100

⇒ MP = 130/100 × 100 = Rs.130

Discount offered = 10%

⇒ 10 = (130 - SP)/130 × 100

⇒ 13 = 130 - SP 

⇒ SP = Rs.117

Gain% = (117 - 100)/100 × 100

⇒ Gain % = 17

∴ The gain percentage is 17%.

Shortcut Trick

For the largest cone inscribed in a cube of edge a, the radius is a/2 and the height is a.

Direct formula for Volume = πa³ ÷ 12

Volume = (22/7 × 12³) ÷ 12 = 22/7 × 144

Volume = 3168 ÷ 7 ≈ 452.57 cm³

∴ The correct answer is 452.57 cm³.

Alternate Method

Given:

Edge of the cube (a) = 12 cm

Concept Used:

To cut the largest right circular cone from a cube, the base of the cone must perfectly fit within one face of the cube, and its height must span directly to the opposite face.

h = 12 cm

r = 6 cm

a = 12 cm

a = 12 cm

Calculations:

⇒ Diameter of the cone's base = Edge of the cube = 12 cm

⇒ Radius (r) = 12 ÷ 2 = 6 cm

⇒ Height of the cone (h) = Edge of the cube = 12 cm

⇒ Volume of the cone = 1/3 × π × r² × h

⇒ Volume = 1/3 × (22/7) × 6² × 12

⇒ Volume = 1/3 × (22/7) × 36 × 12

⇒ Volume = (22/7) × 12 × 12

⇒ Volume = (22/7) × 144 = 3168 ÷ 7

⇒ Volume ≈ 452.57 cm³

∴ The correct answer is 452.57 cm³.

Additional Information

Largest Cone inscribed in a Cube

The base diameter and height of the cone are equal to the edge of the cube (a). Volume = πa³ ÷ 12.

Largest Sphere inscribed in a Cube

The diameter of the sphere is exactly equal to the edge of the cube. Volume = πa³ ÷ 6.

Largest Cube inside a Sphere

The body diagonal of the cube spans the entire diameter of the circumscribing sphere (2R = a√3).

Surface Area of Cone

Curved Surface Area (CSA) = πrl and Total Surface Area (TSA) = πr(r + l), where slant height l = √(r² + h²).

Shortcut Trick

Interest for 5 years = 990 − 715 = 275

Interest for 1 year = 275 ÷ 5 = 55

Interest for 3 years = 55 × 3 = 165

Principal (Sum) = Amount_{3 yrs} − Interest_{3 yrs} = 715 − 165 = 550

∴ The correct answer is Rs. 550.

Alternate Method

Given:

Amount after 3 years (A₁) = Rs. 715

Amount after a further 5 years (total 8 years) (A₂) = Rs. 990

Formula Used:

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

Amount (A) = Principal (P) + Simple Interest (SI)

Calculations:

⇒ Total duration for second amount = 3 + 5 = 8 years

⇒ Interest for (8 − 3) years = Rs. (990 − 715)

⇒ Interest for 5 years = Rs. 275

⇒ Yearly Interest = 275 ÷ 5 = Rs. 55

⇒ Interest for first 3 years = 55 × 3 = Rs. 165

⇒ Principal (Sum) = Amount after 3 years − Interest for 3 years

⇒ Principal = 715 − 165 = Rs. 550

∴ The correct answer is Rs. 550.

Additional Information

Simple Interest Concept

In Simple Interest, the interest remains constant every year because it is always calculated on the original Principal (P).

Amount Formula

The total Amount (A) is the sum of the principal and the interest earned over time T: A = P + (P × R × T) ÷ 100.

Rate Calculation

If required, the Rate of Interest (R) can be found using R = (SI × 100) ÷ (P × T). For this problem, R = (55 × 100) ÷ (550 × 1) = 10%.

Given:

⇒ 96 - 4 of (18 - 13) + 4 × 7

Calculation:

⇒ 96 - 4 of 5 + 4 × 7

⇒ 96 - 20 + 4 × 7

⇒ 96 - 20 + 28

⇒ 124 - 20

⇒ 104

∴  104 is the correct  Answer.

Given:

Time taken to fill the tank = 3 hours

Ratio of efficiency of A and C = 6 : 1

Ratio of efficiency of A and B = 2 : 1

Formula used:

Work = Efficiency × Time

Calculation: 

We have A : B = 2 : 1

Multiplying with 3 on both sides

A : B = (2 : 1) × 3 = 6 : 3

and A : C = 6 : 1

∴ Efficiency ratio of A : B : C = 6 : 3 : 1

Total efficiency = 6 + 3 + 1 = 10 units

Total Work = 10 × 3 = 30 units

Efficiency of B & C pipe = 3 + 1 = 4 units

∴ Time taken by B and C = 30/4 = 7$1 \over 2$ hour

Hence, pipe B & C can fill the whole tank in 7$1 \over 2$ hours.

Concept used:

 

Calculation:

Here, 45% of 360 + 30% of 400 = 25% of x

⇒ (45 × 360/100) + (30 × 400/100) = (25 × x)/100

⇒ 162 + 120 = x/4

⇒ x/4 = 282

⇒ x = 1128

∴ The correct answer is 1128.

Shortcut Trick

When a square is inscribed in a circle, Diameter of circle = Diagonal of square.

Diagonal of square = side × √2 = (6√2) × √2 = 12 cm.

Radius (r) = Diameter ÷ 2 = 12 ÷ 2 = 6 cm.

Required Area = Area of Circle − Area of Square = (π × 6²) − (6√2)².

Area = 113.14 − 72 = 41.14 ≈ 41 cm².

∴ The correct answer is 41 cm².

Alternate Method

Given: Side of the inscribed square = 6√2 cm

Formula: Area of Circle = πr² | Area of Square = side²

⇒ Diagonal of square = √2 × side = √2 × 6√2 = 12 cm

⇒ Diameter of the circle = Diagonal of the square = 12 cm

⇒ Radius (r) of the circle = 12 ÷ 2 = 6 cm

⇒ Area of the circle = (22/7) × 6 × 6 = 792 ÷ 7 = 113.1428 cm²

⇒ Area of the square = (6√2) × (6√2) = 36 × 2 = 72 cm²

⇒ Remaining Area = 113.1428 − 72 = 41.1428 cm²

⇒ Rounded to nearest integer = 41 cm²

∴ The correct answer is 41 cm².

Additional Information

Circumcircle of a Square

When a circle circumscribes a square of side 'a', the radius (R) is half of the diagonal: R = a√2 ÷ 2 = a ÷ √2.

Incircle of a Square

When a circle is inscribed within a square of side 'a', the radius (r) is half of the side: r = a ÷ 2.

Ratio of Areas

The ratio of the area of an inscribed square to the area of the circumscribing circle is 2 : π.

Given:

A man takes 2 hours to swim 25 km downstream

He swims 19 km upstream in the same time.

Concept used:

Speed = Distance/time

Speed of the current = (Downstream - Upstream)/2

Calculation:

Downstream speed = 25/2

⇒ 12.5 km/h

Upstream Speed = 19/2

⇒ 9.5 km/h

Speed of the current = (Downstream - Upstream)/2

⇒ (12.5 - 9.5)/2

⇒ 3/2 = 1.5 km/h

∴ The Required speed of the current is 1.5 km/h.

Shortcut Trick

Net loss % when Selling Price (SP) is same: [100(x + y) + 2xy] ÷ [200 + x + y] where x and y are gain/loss with signs.

Here x = +17 and y = −19. Sum (x+y) = −2, Product (xy) = −323.

Net % = [100(−2) + 2(−323)] ÷ [200 + 17 − 19] = [−200 − 646] ÷ 198 = −846 ÷ 198.

Net loss % = 4.2727...% ≈ 4.3%.

∴ The correct answer is 4.3%.

Alternate Method

Given → SP₁ = SP₂ = Rs. 631.80. Gain₁ = 17%, Loss₂ = 19%. Formulas: CP = SP × 100 ÷ (100 ± Gain/Loss%) | Loss% = (Total CP − Total SP) ÷ Total CP × 100.

⇒ CP₁ = 631.80 × 100 ÷ 117 = Rs. 540. ⇒ CP₂ = 631.80 × 100 ÷ 81 = Rs. 780. ⇒ Total CP = 540 + 780 = Rs. 1320. ⇒ Total SP = 631.80 × 2 = Rs. 1263.60. ⇒ Total Loss = 1320 − 1263.60 = Rs. 56.40. ⇒ Loss % = (56.40 ÷ 1320) × 100 = 4.272...% ≈ 4.3%.

∴ The correct answer is 4.3%.

Additional Information

Same Selling Price - Equal Gain and Loss

If two articles are sold at the same price, one at a gain of x% and another at a loss of x%, there is always a net loss = (x ÷ 10)² %.

Calculation Accuracy

When values are not equal, use the total CP and total SP method or the combined percentage formula for precision.

Shortcut Trick

Total distance is the sum of an Arithmetic Progression (AP) where the first hour distance a = 55, common difference d = 4, and number of terms n = 13.

Sum S_n = (n/2) × [2a + (n − 1)d]

S₁₃ = (13/2) × [2(55) + (12 × 4)] = (13/2) × [110 + 48] = 13 × 79

S₁₃ = 1027 km.

∴ The correct answer is 1027 km.

Alternate Method

Given:

Distance in 1^st hour (a) = 55 km

Increase in speed every hour (d) = 4 km/hr

Total time (n) = 13 hours

Formula Used:

Total Distance (S_n) = (n/2) × [2a + (n − 1)d]

Calculations:

⇒ Distance in the 13^th hour = a + (n − 1)d

⇒ Distance in the 13^th hour = 55 + (13 − 1) × 4 = 55 + 48 = 103 km

⇒ Total Distance = (n/2) × [First hour + Last hour]

⇒ Total Distance = (13/2) × [55 + 103]

⇒ Total Distance = (13/2) × 158

⇒ Total Distance = 13 × 79

⇒ Total Distance = 1027 km

∴ The correct answer is 1027 km.

Additional Information

Arithmetic Progression (AP)

A sequence where the difference between consecutive terms is constant. The n^th term is T_n = a + (n − 1)d.

Sum of AP Terms

The sum can also be calculated as S_n = (n/2) × (a + l), where 'l' is the last term of the series.

Average Speed in AP

For a constant time interval, the average speed is the arithmetic mean of the initial and final speeds: (a + l) / 2.

The correct answer is 'gives a lots of'.

Key Points

• The right form should be 'gives a lot of' because 'lots of' is informal and is not appropriate to be used in formal/written language.
• Example- That's a lot of money.

Additional Information

• Words like 'lot of', 'many', 'much' are called quantifiers and they are used to talk about quantities, amount and degree.
• Example- There are many trees in our orchard.
• Example- There was not much to do about it.
• Example- There would be a lot of people at the concert.

The correct answer is 'could not went'.

Key Points

• The sentence is in Simple Past tense.
• As the auxiliary 'could' is already in its V2 (can-could) form so the main verb should have been 'go' instead of 'went'.
• The correct sentence should be: I could not go for my sister's wedding in Rajasthan as I had my final examination at that time.

Additional Information

• 'Would' (will) and 'should' (shall) are other auxiliary verbs used in Past tense sentences.
• Example- I thought we would be late.
• Example- I should have brought an umbrella.

The correct answer is 'lavish'.

Key Points

• Lavish means luxurious or rich. 
• Example- Weddings in India are generally lavish affairs.
• Among the options given, 'Lavish' is the most appropriate option.

Additional Information

• Lucky means having or bringing good luck.
• Example- She is a lucky girl because she is the only one who got selected.
• Lonely means sad because of not having friends or company.
• Example- She grew lonely after her husband passed away.
• Light means something that is not heavy or sombre.
• Example- You must pack light because it's only for two days.

The correct answer is 'Deterioration'.

Key Points

• Betterment means the progression of becoming something better.
• Example- They believed their work was for the betterment of society.
• Deterioration means the progression of becoming worse.
• Example- There was deterioration in the condition of the patient.
• Clearly 'deterioration' is the opposite in meaning while other options are quite similar to the meaning of 'betterment'.

Additional Information

• Progress means developing gradually.
• Example- I can see progress in his health.
• Prosperity means the process of being successful.
• Example- This will bring prosperity to the country.
• Advancement means development or improvement.
• Example- The advancement in Medical Science is commendable.

The correct answer is 'inflammable'.

Key Points

• Inflammable means a substance that can easily be set on fire or burnt. 
• Example- Alcohol is an inflammable substance.
• So clearly this word is the most appropriate choice for the given group of words.

Additional Information

• Incredible means something that is difficult to believe or unbelievable.
• Example- The crowd at Ratha Yatra was incredible.
• Invisible means something that is not seen.
• Example- 'Mr.India' movie is about an invisible man.
• Indelible means making marks that cannot be removed.
• Example- Her memories have an indelible effect on me.