SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 2) (Previous Year Paper)

The pattern followed here is:

Logic: (First number × Second number) = Third number.

1. (11, 13, 143)

⇒ (11 × 13) = 143

And,

2. (17, 11, 187)

⇒ (17 × 11) = 187

Similarly,

3. (3, 4, 12)

⇒ (3 × 4) = 12

Hence, the correct answer is "Option 3".

The position of the English alphabet letters is given below:

Logic: Addition of place value of letter + 4 = Code.

1. 'GOLF' is coded as '44'

⇒ G(7) + O(15) + L(12) + F(6) + 4 = 44

And,

2. 'BALL' is coded as '31'

⇒ B(2) + A(1) + L(12) + L(12) + 4 = 31

Similarly,

3. 'PLAY' is coded as '?'

⇒ P(16) + L(12) + A(1) + Y(25) + 4 = 58

Hence, the correct answer is "58".

The pattern followed here is:

Logic: If one side is similar in both figures then the other two sides of both figures are opposite to each other.

Taking dice of figure numbers (1) and (2)

Here, 4 and 2 are common in both the dice and 3 is opposite to 6.

Taking dice numbers (2) and (3)

Here, 4 and 6 are common in both the dice and 2 is opposite to 5.

Opposite pairs are:

⇒ 3 - 6

⇒ 2 - 5

⇒ 4 - 1

Clearly, 1 is the opposite of 4.

Hence, the correct answer is 4.

The pattern followed here is:

1)  Elements placed in the left diagonal, interchanged their positions and other elements shifted their position in an anti-clockwise direction.

2. The Elements placed in the outer square rotated their positions in a clockwise direction.  The Elements placed in the inner square interchanged their positions.in 

These two unique methods follow alternatively.

3. As same as step 1.

4)   As same as step 2.

Hence, the correct answer is "Option 4".

The pattern followed here is:

Interchanged :+ and ×, 5 and 4

I. 4 + 6 × 5 - 7 ÷ 1

After interchanging the sign and number we get the:

⇒ 5 × 6 + 4 - 7 ÷ 1

⇒ 5 × 6 + 4 - 7 

⇒ 30 + 4 - 7

⇒ 34 - 7 

⇒ 27

II. 5 × 3 - 4 + 8 ÷ 2

After interchanging the sign and number we get the:

⇒ 4 + 3 - 5 × 8 ÷ 2

⇒ 4 + 3 - 5 × 4

⇒ 4 + 3 - 20

⇒ 7 - 20

⇒ - 13

Hence, the correct answer is "27, -13".

The pattern followed here is:

Equation solved with the help of the BODMAS Rule.

Let's check the options one by one.

Option 1) ÷, +, ×, +, =

⇒ 99 ÷ 33 + 66 × 22 + 44 = 50

⇒ 3 + 66 × 22 + 44 = 50

⇒ 3 + 1452 + 44 = 50

⇒ 1499 ≠ 50 (Incorrect)

Option 2) +, -, ÷, -, =

⇒ 99 + 33 - 66 ÷ 22 - 44 = 50

⇒ 99 + 33 - 3 - 44 = 50

⇒ 132 - 3 - 44 = 50

⇒ 132 - 47 = 50

⇒ 85 ≠ 50 (Incorrect)

Option 3) ÷, +, ÷, +, =

⇒ 99 ÷ 33 + 66 ÷ 22 + 44 = 50

⇒ 3 + 3 + 44 = 50

⇒ 50 = 50 (Correct)

Option 4) ÷, -, +, ×, =

⇒ 99 ÷ 33 - 66 + 22 × 44 = 50

⇒ 3 - 66 + 22 × 44 = 50

⇒ 3 - 66 + 968 = 50

⇒ 971 - 66 = 50

⇒ 905 ≠ 50 (Incorrect)

Hence, the correct answer is "÷, +, ÷, +, =".

The pattern followed here is:

Logic:

The first and Second alphabet are opposite to each other.

Second alphabet - 3 = Third alphabet.

Let's check each option one by one.

Option 1) EVS

Option 2) IRP

Option 3) VEB

Option 4) GTQ

Hence, the correct answer is "IRP".

The pattern followed here is:

Arrange the given word according to the English dictionary order.

6. Fundament 2. Funerary 4. Funicular 5. Fuscous 7. Fuselage 3. Fusion 1. Fustian

Hence, the correct answer is "6, 2, 4, 5, 7, 3, 1".

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

Given relation code:

Given: A + B & C - D + E

A is the father of B, B is the son of C, C is the Mother of D, D is the father of E

Clearly, A is the Father's father of E.

Hence, the correct answer is Father's father.

The pattern followed here is:

Given: 

Hence, the correct answer is "Option 3".

The pattern follows here is:

The first word belongs to the female group and the second word belongs to the male group.

Pen : Cob

Pen → The female swan is called a Pen.

Cob → The male swan is called a Cob.

Similarly,

sorceress : sorcerer

Sorceress → The female magician is called a sorceress.

Sorcerer → The male magician is called a Sorcerer.

Hence, sorceress: sorcerer is the correct answer.

Additional Information 1) adult : infant 

Adult: a person or an animal that is fully grown.

Infant: a baby or very young child

2) banyan: tree

Banyan: an Indian tree with branches that put out roots that grow downwards till they reach the ground

Tree: a tall plant that can live for a long time.

3) pig: piglet

Pig: a fat pinkish animal with short legs and a short tail.

Piglet: a young pig.

The correct mirror image of the given figure when the mirror is held on the right side.

Detailed Explanation:

• The correct mirror image of the given figure is "

" the second alphabet of the given image is 'J' and the correct mirror image of this alphabet is '

' but it is wrongly given in Option 1 and Option 3 so it is eliminated.

• The correct mirror image of the given figure is "

" the first letter of the given image is '

' and the correct mirror image of this alphabet is '

' but it is wrongly given in Option 2 so it is eliminated.

 

Hence, the correct answer is "Option 4".

Additional Information

1. In the mirror image left side and right side changed vice-versa where the top and bottom remain the same.

2. In a real given mirror image the farthest number or alphabet appears closest in the mirror image.

The position of the English alphabet letters is given below:

Hence, the correct answer is "RJN".

The pattern followed here is:

1. Alphabet A shifted the left upper side and add +1, then B shifted the left bottom side and add +1, and finally, C shifted the right bottom side and add + 1.

2. Alphabet Z shifted the right bottom side and subtract -1, then Y shifted the right upper side and subtract - 1, and X finally shifted the right upper side and subtract - 1.

3. Middle circle is blank in the first figure, and colored with black colored in the second figure, and again blank circle in the third figure, finally colored with black colored in the final figure.

Hence, the correct answer is "Option 3".

The pattern followed here is:

1. CONTROL : NOCTRLO

And,

2. MISTAKE : SIMTAEK

Similarly,

3. JOURNAL : ?

Hence, the correct answer is "UOJRNLA".

The pattern followed here is:

Logic: (Second number + Third number + 2) =  First number.

1. (15, 9, 4)

⇒ (9 + 4 + 2) = 15

And,

2. (7, 2, 3)

⇒ (2 + 3 + 2) = 7

Similarly,

3. (19, 13, 4)

⇒ (13 + 4 + 2) = 19

Hence, the correct answer is "(19, 13, 4)".

The pattern followed here is:

Logic:

(First number × 10) = Second number.

(Second number - 10) = Third number.

Let's check each option one by one.

Option 1) (6 - 60 - 50)

⇒ (6 × 10) = 60

⇒ (60 - 10) = 50

Option 2) (7 - 70 - 68)

⇒ (7 × 10) = 70

⇒ (70 - 10) = 60 ≠ 68 

Option 3) (8 - 80 - 70)

⇒ (8 × 10) = 80

⇒ (80 - 10) = 70

Option 4) (9 - 90 - 80)

⇒ (9 × 10) = 90

⇒ (90 - 10) = 80

Hence, the correct answer is "(7 - 70 - 68)".

The pattern followed here is:

The least possible Venn diagram is shown below according to the given information.

Statements :

Some grasses are trees.

Some trees are branches.

Some branches are dogs.

Conclusions :

I. Some grasses are branches → False (As some grasses are trees and some trees are branches. So, some grasses are branches is possible but not definitely followed.)

II. Some trees are dogs →  False (As some trees are branches and some branches are dogs. So, some trees are dogs is possible but not definitely followed.)

III. Some grasses are dogs → False (As some grasses are trees, some trees are branches, and some branches are dogs. So some grasses are dogs is possible but not definitely followed.)

IV. Some branches are grasses →  False (As some grasses are trees and some trees are branches. So, some branches are grasses is possible but not definitely followed.)

Hence, the correct answer is "None of the conclusions follows".

The pattern followed here is:

Interchanged : × and +, 9 and 6

Check all options one by one.

Option 1) 7 × 6 ÷ 3 + 9 - 8 = 17

After interchanging the sign and number we get the:

⇒ 7 + 9 ÷ 3 × 6 - 8 = 17

⇒ 7 + 3 × 6 - 8 = 17

⇒ 7 + 18 - 8 = 17

⇒ 25 - 8 = 17

⇒ 17 = 17 (Correct)

Option 2) 6 × 8 - 9 ÷ 3 + 5 = 50

After interchanging the sign and number we get the:

⇒ 9 + 8 - 6 ÷ 3 × 5 = 50

⇒ 9 + 8 - 2 × 5 = 50

⇒ 9 + 8 - 10 = 50

⇒ 17 - 10 = 50

⇒ 7 ≠ 50 (Incorrect)

Option 3) 7 + 6 × 4 ÷ 9 - 8 = 8

After interchanging the sign and number we get the:

⇒ 7 × 9 + 4 ÷ 6 - 8 = 8

⇒ 7 × 9 + 0.6 - 8 = 8

⇒ 63 + 0.6 - 8 = 8

⇒ 63.6 - 8 = 8

⇒ 55.6 ≠ 8 (Incorrect)

Option 4) 9 × 7 + 4 ÷ 1 - 6 = 7

After interchanging the sign and number we get the:

⇒ 6 + 7 × 4 ÷ 1 - 9 = 7 

⇒ 6 + 7 × 4 - 9 = 7

⇒ 6 + 28 - 9 = 7

⇒ 34 - 9 = 7

⇒ 25 ≠ 7 (Incorrect)

Hence, the correct answer is "Option 1".

The pattern followed here is:

Hence, the correct answer is "410".

The logic followed here is:

Hence, the correct answer is "BUZ".

The pattern followed here is:

Logic: Subtraction of -1 in all the letters

'DENTIST' is written as 'CDMSHRS'

And,

'TOOTH' is written as 'SNNSG'

 

Similarly,

'HEALING' be written as '?'

Hence, the correct answer is "GDZKHMF".

The pattern followed here is:

The least possible Venn diagram is shown below according to the given information.

Statements :

I. All A are H.

II. No B is A.

Conclusion :

I. Some A are not B → Follow → As all A are H and No B is A. So some are not B is definitely followed.

II. No B is H → Does not follow → As all A are H and No B is A. No B is H is not definitely true because there is a possibility as Some B are H. So it is not followed.

Hence, the correct answer is "Option 4".

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

Given: 

‘A ÷ B’ means ‘A is the father of B’.

‘A × B’ means ‘A is the mother of B’.

‘A + B’ means ‘A is the Brother of B’.

Find:- expression shows that Q is the daughter of P?

Let's check each option one by one.

Option 1) P ÷ Q × R

(P is the father of Q, and Q is the mother of R.)

Here, Q is the daughter of P. (Correct)

Option 2) P ÷ Q + R

(P is the father of Q, and Q is the brother of R)

Here, Q is the son of P. (Incorrect)

Option 3) P × Q ÷ R

(P is the mother of Q and Q is the father of R)

Here, Q is the son of P. (Incorrect)

Option 4) P + Q ÷ R

(P is the brother of Q and Q is the father of R)

Here, Q is the brother of P. (Incorrect)

Hence, the correct answer is "Option 1".

The pattern follows here is:

(First number + 7 ) × 7 : Second number

→  21: 196 

= ( 21 + 7) × 7 

= 28 × 7 

= 196

→ 38: 315

= (38 + 7) × 7

= 45 × 7

= 315

Similarly,

→ 29:?

= (29 + 7 ) × 7

= 36  × 7

= 252

Hence the correct answer is 252.

The correct answer is Manipuri.

Key Points

• The Manipuri dancers and exponents Guru Bipin Singh and Guru Kalavati Devi are the parents of Bimbavati Devi.
• At a very young age, she was introduced to the world of dance and music.
• She has received instruction in pung (Manipuri mridang) playing and the fundamentals of Thang Ta in addition to dancing (Manipuri martial art).
• She was a performing and solo performer of Manipuri Nartanalaya.

Additional Information

• Chhau:
• Eastern Indians have a practice known as Chhau dance.
• It recreates scenes from epics like the Mahabharata and the Ramayana as well as regional folklore and abstract ideas.
• The Chhau dance in the region of Jharkhand, West Bengal and Odisha.
• Kathakali:
• ​A significant type of classical Indian dance is Kathakali.
• It belongs to the "story play" art form.
• Kathakali comes from southwestern India, around the state of Kerala.
• Odissi:
• ​The important ancient dance known as Odissi was created in the temples of Odisha.

Important Points

• The classical Dance forms of India:-

The correct answer is sovereignty.

Key Points

• Article 51-A of the Constitution contains a list of all eleven essential duties.
• On the basis of the Swaran Singh Committee's recommendations, they were added to Part IV-A of the Constitution by the 42^nd Constitutional Amendment Act of 1976.
• In addition to the original 10 duties, one additional was added by the 86^th Constitutional Amendment Act of 2002.
• One of the primary duties is to "uphold and protect the sovereignty, unity, and integrity of India."​​

Additional Information

• 51 A Fundamental duties: It shall be the duty of every citizen of India:
• to uphold the Constitution's ideals and institutions, as well as the national anthem and flag.
• to cherish and follow the noble ideals that inspired the national struggle for freedom.
• defending the nation and performing national service as required.
• In order to uphold the dignity of women, it is important to establish harmony and a sense of common brotherhood among all Indians, regardless of their differences in language, geography, or religion.
• to respect and uphold the rich cultural history of the nation as a whole.
• to exhibit compassion for all living things and to preserve and enhance the natural environment, including woods, lakes, rivers, and wildlife
• to foster humanism, a scientific mindset, and a spirit of reform.
• to protect public property and abstain from violence.
• to pursue excellence in all areas of personal and societal endeavour in order for the country to progressively reach greater heights of endeavour and success.
• should give his ward or child, between the ages of six and fourteen, chance for education (added by the 86^th Constitutional Amendment Act, 2002).

The correct answer is Option 4.

Key Points

• The Vice-President holds office for a term of five years from the date on which he enters his office. Hence statement 3 is correct.
• However, he can resign from his office at any time by addressing the resignation letter to the President.
• He can also be removed from office before the completion of his term.
• A formal impeachment is not required for his removal.
• He can be removed by a resolution passed by a majority of all the then members of the Rajya Sabha and agreed to by the Lok Sabha. Hence statement 4 is incorrect.
• This means that this resolution should be passed in the Rajya Sabha by an effective majority and in the Lok Sabha by a simple majority.
• It must be noted here that the effective majority in India is only a type of special majority and not a separate one.
• Further, this resolution can be introduced only in the Rajya Sabha and not in the Lok Sabha.
• But, no such resolution can be moved unless at least 14 days advance notice has been given.
• Notably, no ground has been mentioned in the Constitution for his removal.
• The Vice-President can hold office beyond his term of five years until his successor assumes charge.
• Members of the State legislature do not take part in his elections. Hence statement 1 is correct.
• He is also eligible for re-election to that office.
• He may be elected for any number of terms.

Additional Information

• Important articles of Vice President:
• ARTICLE 63: There shall be a Vice-President of India.
• ARTICLE 64: The Vice-President shall be ex-officio Chairman of the Council of States and shall not hold any other office of profit. Hence statement 2 is correct.
• ARTICLE 65: The Vice-President shall act as President in the event of the occurrence of any vacancy in the office of the President by reason of this death, resignation or removal, or otherwise.
• ARTICLE 66: Election of Vice President.
• ARTICLE 93: There will Lok Sabha speaker and deputy speaker of the house.

The correct answer is Carnatic Music.

Key PointsCarnatic music:

• A musical style called Carnatic music is frequently linked to South India.
• It is one of two main subgenres of Indian classical music that evolved from ancient Hindu texts and traditions, particularly the Samaveda.
• Carnatic music is used to accompany the classical Kuchipudi dance.
• The recital is in Telugu, and Carnatic music is used to accompany the dance.
• The entire male group performed the traditional Kuchipudi.
• In Angivastra, also known as Bagalbandi, a dancer portraying a masculine character would dress in a dhoti.

Additional Information

• Kajri:
• Kajari is a folk song and dance genre in India.
• It is a type of Hindustani classical music that is performed in rainy weather.
• Chaiti:
• Chaiti is Indian-born, semi-classical melodies that are performed during the Chait month of the Hindu calendar.
• Hindustani Music:
• The classical music of the northern parts of the Indian subcontinent is known as Hindustani.

The correct answer is 2005-06.

Key Points

• India began producing a gender budget concurrently with its Union budget in 2005.
• The gender budget is a project that uses a gendered perspective to track and distribute public expenditures.
• The emphasis is on enhancing women's welfare through legislative initiatives.
• The entire budgetary allotment for gender-responsive budgeting (GRB) in the Union budget for FY 2021–22 was reduced by 26% from the Revised Estimates of FY 2020–21.
• The gender budget was increased in the Revised Estimates for 2020–21 due to the pandemic's disproportionate impact on women.
• However, the gender budget for the current fiscal year was just 4.4% of the entire Union budget for FY 2021–2022.

Additional Information

• The Union Budget of India also referred to as the Annual Financial Statement in Article 112 of the Constitution of India, is the annual budget of the Republic of India.
• The Government presents it on the first day of February so that it could be materialised before the beginning of the new financial year in April.
• Until 2016 it was presented on the last working day of February by the Finance Minister in Parliament.
• The budget division of the department of economic affairs (DEA) in the finance ministry is the nodal body responsible for producing the budget.
• It is presented by means of the Finance bill and the Appropriation bill has to be passed by Lok Sabha before it can come into effect on 1 April, the start of India's financial year.
• Since 1947, there have been a total of 73 annual budgets, 14 interim budgets and four special budgets, or mini-budgets.

The correct answer is 1 December 2022.

Key Points

• On tobacco products made, imported, or packaged on or after December 1, 2022, a new display graphic with the warning "Tobacco causes painful death" will be printed, according to the Union Health Ministry.
• Until November 30, 2022, the current health warning will remain in effect.
• Another display graphic will be used starting on December 1, 2023, with the warning "Tobacco users die Younger." stated beneath it.
• The 2008 Cigarettes and Other Tobacco Products (Packaging and Labelling) Rules have been updated by the Ministry.
• The public was informed of these changes on July 21, 2022.
• Any person involved directly or indirectly in the manufacture**, production, import, supply, or distribution of any tobacco products** is required to make sure that all tobacco product packaging has specific health warnings.

Additional Information

• According to the Global Adult Tobacco Survey (GATS) 2016-2017, Maharashtra is the Indian state with the lowest prevalence of tobacco use.
• More than 91% of Indian smokers think smoking causes significant illnesses.
• 10.7% of adults in India smoke tobacco, compared to 28.6% of persons who use tobacco in a smokeless or smoking form.
• According to Tobacco Free Union, more than 1 million people die in India each year as a result of tobacco-related ailments.

The correct answer is Calcutta.

Key Points

• Ishwarchandra Vidyasagar
• Ishwarchandra Vidyasagar, a Bengali reformer, actively raised the issues related to women.
• He was an active proponent of the education of girl children as he believed that lack of education was the real cause underlying all their problems.
• With the help of an Englishman named Bethune, he set up many schools devoted especially to girl children.
• He forcefully attacked child marriage and polygamy.
• He was a strong advocate of widow remarriage.
• It was due to his active mobilization of support that the Widows’ Remarriage Act was passed in 1856 legalizing all widow remarriages.
• His graduation college, Sanskrit College, Calcutta gave him the title; Vidyasagar”, due to his excellent performance in Sanskrit studies and philosophy.
• He arranged many such remarriages.
• He set a personal example when his son Narayan also married a widow.
• Ishwar Chandra Vidyasagar was a person of wide knowledge or learning from Bengal India and a key figure of the Bengal Renaissance.
• He was an academic educator, philosopher, publisher, entrepreneur, philanthropist, writer, translator, printer, and reformer.
• He simplified and modernized Bengali prose. Hence considered the "Father of Bengali prose".
• Also rationalized and simplified the Bengali alphabet and type, which had remained unchanged since Charles Wilkins and Panchanan Karmakar had cut the first (wooden) Bengali type in 1780.
• His graduation college, Sanskrit College, Calcutta gave him the title “Vidyasagar”, due to his excellent performance in Sanskrit studies and philosophy.

The correct answer is two years.

Key Points

• ​In British India, there was a law known as the Rowlatt Act.
• On March 18, 1919, the Imperial Legislative Council in Delhi passed a legislative council statute.
• The Defence of India Act of 1915, passed during the First World War, extended the emergency provisions of preventative indefinite detention, imprisonment without trial, and judicial review indefinitely.
• The Rowlatt Committee's recommendations were adopted, and it was given that name in honour of Sir Sidney Rowlatt, the committee's chairman.
• The act effectively authorized the colonial British government to imprison any person suspected of terrorism living in British India for up to two years.
• It gave the colonial authorities the power to deal with all revolutionary activities.

Additional Information

• Jallianwala Bagh Massacre:
• Due to rioting and rallies against the Rowlatt Act, the situation in Punjab was worrying.
• When martial law was imposed in Punjab, it was forbidden for groups of more than four persons to congregate anywhere.
• A group of peaceful protestors had congregated in Jallianwala Bagh in Amritsar on April 13, 1919, the day of the Baisakhi festival.
• The solely limited entry to the garden was shut when General Dyer arrived with his troops.
• He then abruptly ordered his soldiers to open fire on the defenceless crowd, which also included children.
• This resulted in the deaths of at least 1000 people and injured more than 1500 people.

The correct answer is Loo - Hot wind.

Key Points

• The Loo is a strong, dusty, gusty, hot, and dry summer wind from the west which blows over the western Indo-Gangetic Plain region of North India and Pakistan.
• Loo winds originate over the Iranian, Baloch, and Thar deserts.
• It is especially strong in the months of May and June.
• Due to its very high temperatures (45 °C–50 °C or 115 °F–120 °F), exposure to it often leads to fatal heatstrokes.
• Since it causes extremely low humidity and high temperatures, the Loo also has a severe drying effect on vegetation leading to widespread browning in the areas affected by it during the months of May and June.
• In tropical regions particularly in northern India during the summer season, local winds called 'loo' are the outcome of the advection process.
• Winds are a result of advection, while air currents are a result of convection.

Additional Information

• Kaal Baisakhi:
• ​It is a local rainfall and thunderstorm that occurs in Assam and West Bengal and in India or Bangladesh.
• It occurs in the summer season.
• It harms life and money and generally occurs in the month of Baisakh (April-May), hence it is known as 'Kaal Baisakhi'.
• It originated from Chota Nagpur Plateau.
• Since It is caused by winds coming from the northwest direction, they are also called 'northwestern'.
• Trade winds:
• ​Trade winds ate winds that blow westward and towards the Equator from the sub-tropical high-pressure belts towards the Intertropical Convergence Zone (ITCZ).
• They blow from the subtropical high-pressure zone to the equatorial low-pressure zone.
• They can be found about 30 degrees north and south of the equator.
• Around 30 degrees in both hemispheres, air begins to descend towards the surface in sub-tropical high-pressure belts known as subtropical ridges.

The correct answer is Sikkim.

Key Points

• The scheme, "Bahini", aims at providing 100 percent access to free and safe sanitary pads to secondary and senior secondary school going girls.
• This scheme was launched by Sikkim government.
• The Sikkim government will implement the 'Aama Yojna' for non-working mothers and 'Bahini' scheme for girl students.
• Under the 'Aama Yojna' scheme, all non-working mothers in the state will receive Rs 20,000 each annually in their bank accounts.
• In the 'Bahini' scheme the state government will provide free sanitary napkins to girl students studying in class 9 and above.

Additional Information 

• Sikkim is a state in northeast India, bordered by Bhutan, Tibet and Nepal.

• About Sikkim:

• Capital: Gangtok

• Governor:  Lakshman Acharya

• Chief minister: Prem Singh Tamang

The correct answer is 150.

Key Points

• The Competition (Amendment) Bill, 2022 proposes to reduce the timeline for the CCI to pass an order on transactions from 210 days to 150 days.
• It seeks to amend the Competition Act, 2002.
• The Act prohibits any person or enterprise from entering into a combination which may cause adverse effect on competition.
• Combinations mean mergers, acquisitions, or amalgamation of enterprises.
• The Act defines control as control over the affairs or management by one or more enterprises over another enterprise or group.
• The Act specifies that any combination shall not come into effect until the CCI has passed an order or 210 days have passed from the day when an application for approval was filed.
• CCI may initiate proceedings against enterprises on grounds of entering into anti-competitive agreements and abuse of dominant position.
• The Act empowers the central government to appoint a Director General to CCI.
• It states required qualification of members of CCI.
• The Bill changes the nature of punishment for certain offences from imposition of fine to penalty.

Additional Information

• Competition Commission of India
• ​The objectives of the Act are sought to be achieved through the Competition Commission of India, which has been established by the Central Government with effect from 14^th October 2003.
• The Competition Commission of India's goal is to create and sustain fair competition in the economy that will provide a ‘level playing field’ to the producers and make the markets work for the welfare of the consumers.
• CCI consists of a Chairperson and 6 Members appointed by the Central Government.
• It is the duty of the Commission to eliminate practices having an adverse effect on competition, promote and sustain competition, protect the interests of consumers and ensure freedom of trade in the markets of India. Hence, option 4 is correct.
• The Commission is also required to give an opinion on competition issues on a reference received from a statutory authority established under any law and to undertake competition advocacy, create public awareness and impart training on competition issues.

The correct answer is Amritsar to Kolkata.

Key Points

• The Grand Trunk Road is one of South Asia's oldest and longest major roads.
• The road often called the "Gernaili Sadak" (the Generals' Road) and Sadak-e-Azam ('The Grand Road') covers a distance of over 2,500 kilometers (1,600 mi).
• During the British rule of colonial India, the road was renamed as the Grand Trunk Road.
• At present, the Grand Trunk Road extends from Amritsar to Kolkata in India.

Additional Information

• The Grand Trunk Road, built by Sher Shah Suri, a ruler of the Indian subcontinent in the 16^th century AD, starts in Kabul, Afghanistan.
• The road continues to Pakistan near Peshawar through the famous Khyber Pass. This famous international mountain pass, at an elevation of 1,070 m (3,510 ft) above the sea level, is one of the oldest known passes in the world, and connects Afghanistan and Pakistan, cutting through the northeastern part of the Spin Ghar mountains.
• 'GT', as it's often called, was built about 500 years ago to connect the east and western regions of the Indian subcontinent.

The correct answer is 8.81 inches - 9 inches.

Key Points

• 8.81 inches - 9 inches is the average circumference of the standard cricket ball in international cricket.
• A cricket ball is a hard, solid ball used to play cricket.
• The weight of a cricket ball is 159.9gram. – 163gram.
• A cricket ball consists of a cork core wound with string then a leather cover stitched on, and manufacture is regulated by cricket law at first-class level.
• The trajectory of a cricket ball when bowled, through movement in the air, and off the ground, is influenced by the action of the bowler and the condition of the ball and the pitch, while working on the cricket ball to obtain optimal condition is a key role of the fielding side.
• Cricket balls are harder and heavier than baseballs.

Additional Information 

• The first official cricket test match was played in the year 1877 between Australia and England in Melbourne.
• The First One Day International cricket match was played in the year 1971 between England and Australia in Melbourne.
• The first World Cup of one-day matches was played in 1975 in London.
• The apex institution of world cricket is the International Cricket Council (ICC) and its headquarters are now in Dubai.
• Earlier it was in Lords (England).
• The ICC was founded in 1909.
• The Board of Control for Cricket in India (BCCI) was formed in 1928.
• Terminologies used in cricket are Toss, Run, Wicket, Bails, Crease, Pavilion, Maiden Over, Follow-on, Bowled, Stump Out, Run Out, L.B.W. Hit Wicket, No ball, Wide ball, Dead ball, Overthrow, Bye, Leg bye, Cover drive, Late cut, Hook, Glance, Stroke, Spot, Pull, Sixer, Followthrough, Googly, Cover, Gully, Long on, Silly point, Midwicket, Mid on, Forward short leg
• The first slip is a position behind the batsman.

The correct answer is Hampi Festival.

Key Points

• Hampi Festival is known as Vijaya Utsav.
• Hampi Utsava also called Vijaya Utsav is celebrated for 2 or 3 days and captures the pomp, splendour, and glory of the Vijayanagara empire.
• Karnataka State Government holds the Hampi Utsava to recreate the grandeur of the erstwhile Vijayanagara Empire.
• It is believed that the Utsav is celebrated since the time of the Vijayanagara Empire and hence might be one of the oldest celebrations/festivals in India.

Additional Information

• Ganga-Sagar Mela is one of such festival of India celebrated on the occasion of Mankar Sankranti, during 13^th – 15^th January every year in West Bengal, which draws thousands of pilgrims from all over the world.
• The hosting state of West Bengal organises this fair with great pride and devout.
• Pushkar fair is one of India's biggest cattle (camel) fair.
• Pushkar fair is also known as Pushkar Camel Fair or locally Kartik Fair.
• It is an annual fair that is also known as Kartik Mela or Pushkar ka Mela.
• It is held in the Pushkar city of Ajmer district of Rajasthan.
• Konark Dance Festival is a five-day dance festival held every year in the month of December in the backdrop of the Sun Temple in Konark, Odisha, India.
• It is organized from 1 to 5 December every year since 1986.
• The festival will showcase dance forms like **Bharatanatyam, Kathak, Odissi, Kathakali, Manipuri, Kuchipudi and many more.**​

The correct answer is Temperate evergreen forest.

Key Points Temperate Evergreen Forests: These forests are located in the mid-latitudinal coastal region.

• Temperate evergreen forests are found predominantly in areas with warm summers and cool winters.
• Region: Eastern margin of the continents like in South-East USA, South China, and South-East Brazil.
• Trees: Hard and softwood trees like oak, pine, and eucalyptus.

Additional Information

• Tropical Evergreen Forests:
• These forests are also called tropical rainforests.
• These thick forests occur in the regions near the equator and close to the tropics.
• Region: Amazon Basin, Congo Basin
• These regions are hot and receive heavy rainfall throughout the year.
• There is no particular dry season so the trees do not shed their leaves altogether.
• Trees: Hardwood trees like rosewood, ebony, and mahogany.
• Tropical Deciduous Forests:
• Tropical deciduous is the monsoon forests.
• Region: Large part of India, Northern Australia, and Central America
• These regions experience seasonal changes.
• Trees shed their leaves in the dry season to conserve water.
• Trees: Hardwood trees like sal, teak, and neem
• Temperate Deciduous Forests:
• Temperate deciduous forests are found in higher latitudes above the tropics.
• Region: Northeastern part of the USA, China, New Zealand, Chile, and coastal regions of Western Europe
• They shed their leaves in the dry season.
• Trees: Oak, ash, beech

The correct answer is 24 September 2020.

Key Points

• On 24 September 2020, Prime Minister, Narendra Modi integrate selected fitness enthusiasts of the country in the first session of 'Fit India Dialogue' as a part of the 'Fit India Movement'.
• PM Narendra Modi will interact with fitness influencers and citizens during a nationwide online Fit India Dialogue on 24 September 2020.
• The dialogue is being organised to celebrate the first anniversary of the Fit India Movement.

Additional Information

• Prime Minister Narendra Modi launched the 'Fit India Age Appropriate Fitness Protocols' during an online Fit India Dialogue.
• It was done to celebrate the first anniversary of the Fit India Movement.
• The fitness protocols have been prepared with the help of fitness enthusiasts for three age categories, from 5-18 years, 18-65 years, and 65 plus age category.
• The online interaction will see participants sharing anecdotes and tips of their own fitness journey.
• Virat Kohli and Milind Soman will also participate.

The correct answer is Muharram.

Key Points

• Muharram is the most important festival celebrated by the Muslim community in India to mark the beginning of the Islamic New Year.
• Muharram is celebrated as the advent of the Islamic New Year by participating Muslims around the globe.
• It is regarded as a pious and important festival by the community.

Additional Information

• Eid al-Fitr marks the end of Ramzan, the Muslim holy month of fasting, and is celebrated during the first three days of Shawwal, the 10^th month of the Islamic calendar
• Shab-e-Miraj or The Night of Ascent is one of the most celebrated dates of the Islamic calendar.
• Id-ul-Zuha (Bakr-Id), is a festival of great rejoice, special prayers, and exchange of greetings and gifts mark this festival of Muslims.
• Id-ul-Zuha, the festival of sacrifice is celebrated with traditional fervor and gaiety in India and the world.
• Milad-un-nabi festival is celebrated to mark the birth anniversary of Prophet Muhammad.
• This day is celebrated in the month of Rabi’ al-awwal (Third month of the Islamic calendar).

The correct answer is 1782.

Key Points

• The First Anglo-Maratha War was won by Marathas and ended with the Treaty of Salbai.
• The Treaty of Salbai was signed on 17 May 1782, representing the Maratha Empire and the British East India Company after long negotiation to settle the outcome of the First Anglo-Maratha War II was signed between Warren Hastings and Mahadaji Scindia.
• Salbal is situated in Gwalior, MP.
• The Treaty of Salbai resulted in 20 years of relative peace between the Maratha Empire and the East India Company.
• Under the terms of this treaty, the British retained control of Broach and Salsette and acquired a guarantee that the Marathas would retake territories in the Carnatic by defeating Hyder Ali of Mysore.

Additional Information

• Anglo-Maratha War:
• The Second Anglo-Maratha War (1803-1805). 
• Treaty of Surji Anjangaon in 1803.
• Treaty of Deogaon in 1803
• Treaty of Rajghat in 1805.
• Third Anglo-Maratha War (1817-1818).
• Treaty of Gwalior in 1817.
• Treaty of Mandsaur in 1818.

The correct answer is Calcium carbonate.

Key Points

• Calcium Carbonate is a chemical compound with the formula CaCO_3.
• It is a common substance found in rocks as the minerals calcite and aragonite (most notably as limestone, which is a type of sedimentary rock consisting mainly of calcite) and is the main component of eggshells, snail shells, seashells and pearls.
• Mineral calcite and aragonite form limestone.
• Minerals calcite and aragonite are different crystal forms of calcium carbonate.
• When these minerals precipitate out of water containing dissolved calcium, limestone is formed.

Additional Information

• Calcium Oxide (CaO), commonly known as quicklime or burnt lime, is a widely used chemical compound.
• It is a white, caustic, alkaline, crystalline solid at room temperature.
• Calcium phosphate [Ca₃(PO₄)₂] is fundamental to the formation of teeth and bone.
• Calcium phosphate is a calcium salt of phosphoric acid. It is also known as Calcium phosphate tribasic or Tricalcium Phosphate.
• Calcium Hydroxide [Ca(OH)₂] is also known as Slaked lime.
• It is a white powder or colourless crystal which is obtained when quicklime (calcium oxide) is mixed with water.

The correct answer is Harshavardhana's court poet was Harishena.

Key Points

• Banabhatta was the court poet of king Harshavardhana. Banabhatta wrote Harshvardhan's biography Harshacharita in Sanskrit.
• Harshavardhana was born in 590 AD.
• He belonged to the Vardhana dynasty.
• He ruled North India from 606 AD to 647 AD.
• Kannauj city, present-day Uttar Pradesh was his capital.
• The Chinese Traveller Xuanzang visited the king and wrote about his reign.
• Emperor Samudragupta's court poet was Harisena.

Additional Information

• Harshavardhana was defeated by the south Indian emperor Pulkesin II of the Chalukya Dynasty in the Battle of Narmada.
• Harsha is widely believed to be the author of three Sanskrit plays "Ratnavali, Nagananda and Priyadarshika "
• The Chinese traveller Hiuen Tsang visited India during his reign.
• Harshavardhana established a large centre of knowledge which was called Bhadra Vihar at Kannauj.
• Banabhatta's Harshacharita and an account of Hieun Tsang was the major source of information about Harsha's period

The correct answer is Third.

Key Points

• The Third 5-Year Plan symbolizes the 1^st phase in a system of enduring expansion extending over the next 1the 5 years or so.
• In the course of this period, India's economy must not only enlarge swiftly but must, in unison, become independent and self-generating.
• The focus was on agriculture and improvement in the production of wheat.
• The Third 5 year Plan focused on agriculture enhancement in the production of wheat, but the succinct Sino - Indian War in the year 1962 exposed flaws in the economy and shifted the spotlight towards the Defence industry.
• The target growth rate was 5.6% and the actual growth rate only achieved 2.4%.
• This indicated a miserable failure of the Third Plan, and the government had to declare "Plan Holidays" (1966-67, 1967-68, and 1968-69).

Additional Information

• The Five Year Plans were formulated, implemented and regulated by a body known as the Planning Commission.
• The First Five Year Plan laid the thrust of economic development in India.
• It was presented by the first Indian Prime Minister, Jawaharlal Nehru to the Parliament of India.
• The Planning Commission was replaced by a think tank called NITI AAYOG in 2015.
• Chairman of NITi AYOG - Prime Minister of India ( Sh Narendra Modi)
• Vice Chairman - Shri Suman Bery
• CEO of NITI AYOG - Shri B.V.R. Subrahmanyam

Confusion Points

• The Fourth Five-Year Plan, spanning from 1969 to 1974, was implemented during the tenure of Indira Gandhi as Prime Minister, aimed at rectifying past shortcomings.
• It was developed following the Gadgil Formula and prioritized achieving growth with stability, as well as promoting self-reliance.

The correct answer is Net primary productivity and gross primary productivity.

Key Points

• Primary production is defined as the amount of biomass or organic matter produced per unit area over a time period by plants during photosynthesis.
• It is expressed in terms of gm^–2 yr ^–1 or (kcal m^–2 ) yr ^–1 to compare the productivity of different ecosystems
• It can be divided into gross primary productivity (GPP) and net primary productivity (NPP).
• The gross primary productivity of an ecosystem is the rate of production of organic matter during photosynthesis
• Net primary productivity, or NPP, is gross primary productivity excluding the rate of energy loss to metabolism and maintenance.
• Net primary productivity is the rate at which energy is stored as biomass by plants or other primary producers and made available to consumers.
• GPP – R = NPP ( R represents the Respiration losses)

Additional Information

• Primary productivity depends on the plant species inhabiting a particular area.
• Secondary productivity is defined as the rate of formation of new organic matter by consumers.
• The annual net primary productivity of the whole biosphere is approximately 170 billion tons (dry weight) of organic matter.
• Despite occupying about 70 per cent of the surface, the productivity of the oceans is only 55 billion tons.

The correct answer is Hydrochloric acid creates an acidic medium which facilitates the action of the enzyme pepsin.

Key Points

• The glands of the stomach are called gastric glands.
• Gastric glands secrete hydrochloric acid, a protein digestive enzyme called pepsin.
• Hydrochloric acid helps in the breakdown, digestion, and absorption of nutrients such as protein. It also kills germs and viruses in the stomach, keeping your body state from infection.
• Without adequate HCI secretion, larger fragments of proteins enter the small intestine and may compromise the efficacy of digestive processes.
• HCI provides an acidic pH of 1.8 optimal for pepsin.
• HCI activates pepsinogen into the enzyme pepsin which helps digestion by breaking the bonds linking amino acids. This process is known as Proteolysis.
• Pepsin is produced by the cells that are present in the stomach lining.
• It is a very important enzyme as it breaks down the complex proteins found in daily food into smaller peptides.
• Pepsin works best in an acidic condition which is why the stomach also produces acid to help break down proteins.

Additional Information

• Gastric glands also secrete Renin which helps to break down the caseinogen into Casein found in milk.
• As soon as the food reaches the duodenum bile juice from the lever combines with it. Bile juice is alkaline and it turns the acidic medium of food into alkaline.
• Pancreas also secretes three types of juices that help in digestion.
• Trypsin - It converts the protein and peptone into polypeptides and amino
• Analyse - It converts the starch into double sugar.
• Lipase - It converts emulsified fats into glycerol and fatty acids.

The correct answer is Herbert C Brown.

Key Points

• The 1979 Nobel Prize for Chemistry has been awarded jointly to Georg Wittig of the University of Heidelberg and Herbert C. Brown of Purdue University for their separate work in organic synthesis
• Wittig's major achievement was the development of a highly specific method for the synthesis of olefins
• Brown found major new routes to add substituents to olefins selectively
• Both employed elements that had found little previous use in organic synthesis, and both prospered by following up on unexpected observations.

Additional Information

• The Noble Prize award was conferred in 1901.
• It is given in the name of Alfred Noble who was a Swedish Inventor.
• The Nobel Prize is awarded yearly to the individual or organization who do an extraordinary job in the field of Physics, Chemistry, Literature, Peace, Physiology, and Economics.
• All the Noble Prizes are given in Stockholm, Sweden except for the Noble Peace prize which is awarded in Oslo, Norway.

The correct answer is 82.14 percent.

Key Point

• The literacy rate at all Indian levels was 74.04%.
• The literacy rate for females is 65.46 % and for males is 82.14%.
• The literacy rate of females in rural areas has observed an improvement in literacy rate of about 24%.
• The male and female literacy rate was higher in Kerala and lower in Bihar.
• The gap in literacy rates between females and males was low in Meghalaya, Kerala, and Mizoram.
• The gap was higher in Rajasthan, Jharkhand, Dadra & Nagar Haveli, Jammu and Kashmir, Uttar Pradesh, and Chattisgarh.​

Additional Information

• A census is official data on the population.
• Indian census includes demographic, social, and economic data.
• It is held periodically after every tenth year.
• The first census took place in 1872.

Given:

In an election between two candidates, the defeated candidate secured 42% of the valid votes polled and lost the election by 7,68,400 votes. 

82,560 votes were declared invalid and 20% of people did NOT cast their votes.

Calculation:

Percentage of total valid votes that winning candidate secured = (100 - 42) = 58%

% difference between the winning and defeated candidate = 58 - 42 = 16%

So, the total number of valid votes = 768400 ÷ 16% = 4802500

Total number of votes (both valid and invalid) = 4802500 + 82560 = 4885060

Total number of voters = 4885060 ÷ (100 - 20)% = 6106325

Number of people who didn't case vote = 6106325 × 20% = 1221265

Now, % = (82560/1221265) × 100% = 6.7602% ≈ 6.8%

∴ The invalid votes were 6.8% of the votes which people did NOT cast.

Given:

The side of an equilateral triangle is 24 cm.

Concept used:

Area of an equilateral triangle = $\frac {\sqrt3a^2}{4}$ (a = measure of each side)

Calculation:

Area of the equilateral triangle

⇒ $\frac {\sqrt3 \times 24^2}{4}$

⇒ 144 $\sqrt3$ cm2

∴ The area of the equilateral triangle is 144 $\sqrt3$ cm2.

Calculation:

Total quantity of P1 in all drugs = 5 + 3 + 4 + 6 = 18 mg

Total quantity of P2 in all drugs = 4 + 5 + 3 + 3 = 15 mg

Total quantity of P3 in all drugs = 4 + 5 + 3 + 4 = 16 mg

∴ P1 substance is most used in terms of quantity in all drugs.

Concept used:

1. Sum of the squares of first n natural numbers = $\frac {n(n +1)(2n +1)}{6}$
2. Sum of n natural numbers = $\frac {n(n +1)}{2}$

Calculation:

First n natural numbers = 1, 2, 3, ...., n

Their corresponding weights respectively = 1, 2, 3, ...., n

Now, the weighted arithmetic mean of the first 'n' natural numbers

⇒ $\frac {1 \times 1 + 2 \times 2 +3 \times 3 + ..... + n \times n}{1 + 2 + 3 + .... + n}$

⇒ $\frac {1^2 + 2^2 + 3^2 + .... + n^2}{1 + 2 + 3 + .... + n}$

⇒ $\frac {\frac {n(n +1)(2n +1)}{6}} {\frac {n(n +1)}{2}}$

⇒ $\rm \frac{{(2n + 1)}}{3}$

∴ The weighted arithmetic mean of the first 'n' natural numbers is $\rm \frac{{(2n + 1)}}{3}$.

Given:

A district has 10,24,000 inhabitants.

The population increases at the rate of 2.5% per annum.

Concept used:

In case of the compound interest,

Amount = P(1 + R/100)^N

CI = P(1 + R/100)^N - P

where

P = Principal amount

R = Rate of interest per year

N = Time in years

Calculation:

Now, the number of inhabitants at the end of three years

⇒ 1024000(1 + 2.5%)³

⇒ 11,02,736

∴ The number of inhabitants at the end of three years is 11,02,736.

Given:

A takes twice as much time as B and thrice as much time as C to finalise a task.

Working together, they can complete the task in 8 days.

Concept used:

If three workers can complete a task in P, Q, and R days respectively, then working together they can complete the work in = $\frac {pqr}{pq + qr + pr}$ days

Calculation:

Let's suppose, A, B, and C take 6q, 3q, and 2q days respectively.

​According to the concept,

$\frac {6q × 3q × 2q}{18q^2 + 6q^2 + 12q^2}$ = 8

⇒ $\frac {36q^3}{36q^2}$ = 8

⇒ q = 8

So, A finalises the work in = 6 × 8 = 48 days

So, B finalises the work in = 3 × 8 = 24 days

So, C finalises the work in = 2 × 8 = 16 days

∴ The time taken by A, B, and C, respectively, to complete the task is 48 days, 24 days, and 16 days.

Given:

$\rm X + \frac{{{y^2}}}{x} = 5$

Calculation:

$\rm \frac{{{x^2} + 2x + {y^2}}}{{{x^3} - 5{x^2}}}$

⇒ $\frac{ \frac { {x^2} + 2x + {y^2} }{x}} { \frac {{x^2} (x - 5)}{x} }$

⇒ $\frac{{ {x} + 2 + \frac {y^2}{x} }} {x \times \frac {-y^2}{x}}$ (From given)

⇒ $\frac{{ 5 + 2}} {-y^2}$ (From given)

⇒ $\rm -\frac{7}{y^2}$

∴ The simplified answer is $\rm -\frac{7}{y^2}$.

Given:

The diameter of a hemisphere is 28 cm.

Concept used:

1. Volume of a hemisphere = 2πR3/3 (R = Radius)
2. Diameter = Radius × 2

Calculation:

Radius of the hemisphere = 28/2 = 14 cm

Now, the volume of the hemisphere

⇒ $\frac {2π × 14^3}{3}$

⇒ 17248/3 cm3 ≈ 5749.33 cm3

∴ The volume of the hemisphere is 5749.33 cm3.

Given:

a + b = 5 and ab = 6

Concept used:

a² + b² = (a + b)² - 2ab

Calculation:

3(a2 + b2)

⇒ 3{(a + b)² - 2ab}

⇒ 3{5² - 2 × 6}

⇒ 39

∴ The required value is 39.

Given:

In ΔABC, AB = AC, O is the point on BC such that BO = CO and OD is perpendicular to AB and OE is perpendicular to AC.

∠BOD = 60°

Concept used:

1. In an isosceles triangle, we have one angle bisector that is also a median and an altitude. 2. All internal angles of a triangle sum up to 180°.

Calculation:

ΔOBD is a right-angled triangle at D and ∠BOD = 60°

So, ∠OBD = 90° - 60° = 30° 

Since in ΔABC, AB = AC, ∠OBD = ∠ACB = ∠ABC = 30°

So, ∠BAC = 180° - 2 × 30° = 120°

Since BO = OC, AO is a median.

​According to the concept,

∠BAO = ∠OAC = ∠OAE = 120/2 = 60°

Since OE is perpendicular to AC, ΔOEA is a right-angled triangle at E.

∠AOE = 90° - 60° = 30°

∴ The measure of ∠AOE is 30°.

Given:

The reduction of 20% in the price of rice enables a person to obtain 50 kg more for Rs. 450.

Concept used:

Incremented/Reduced value = Initial value (1 ± change%)

Calculation:

Let's suppose, originally for Rs. 450, one could get Q kg rice.

Now, for Rs. 450, one can get (Q + 50) kg rice.

​According to the question,

$\frac {450}{Q} × (1 - 20\%) = \frac {450}{Q + 50}$

⇒ $\frac {1}{Q} × 0.8 = \frac {1}{Q + 50}$

⇒ $\frac {1}{Q} × \frac {4}{5} = \frac {1}{Q + 50}$

⇒ 4Q + 200 = 5Q

⇒ Q = 200

Now, the original price of rice (per kg) = 450/200 = Rs. 2.25

∴ The original price of rice per kg is Rs. 2.25.

Shortcut Trick

​We know, 20% = 1/5,

Consumption difference (5 - 4) = 1 unit → 50 kg

Then, 4 unit → 50 × 4 = 200 kg

Now, price of 200 kg is 450

Then price of 1 kg is 450/200 = Rs.2.25

Given:

The surface area of a cube is 864 cm2. 

Concept used:

1. Surface area of a cube = 6 × (Side)²
2. Volume of a cube = (Side)³

Calculation:

Let the measure of each side of the cube be A cm.

​According to the question,

6A² = 864

⇒ A² = 144

⇒ A = 12

Now, the volume of the cube = 12³ = 1728 cm³

∴The volume of the cube is 1728 cm³.

Given:

In a class of students, the first student has 2 toffees, the second has 4 toffees, the third has 6 toffees, and so on.

Concept used:

1. Number of terms of an AP = (L - A)/D + 1
2. Sum of N terms of an AP = (L + A)/2 × N
3. N^th term = A + (N - 1) × D

(Where L = Last Term, A = First Term and D = Common Difference)

Calculation:

The number of toffees according to the number of students is in an Arithmetic Progression where

2 = First Term

(4 - 2) = (6 - 4) = ... = 2 = Common Difference

So, the number of toffees 25^th student will get = 2 + (25 - 1) × 2 = 50

Now, the total number of toffees

⇒ (2 + 50)/2 × 25

⇒ 26 × 25

⇒ 2 × 5² × 13

∴ The total number of toffees is divisible by 5 and 13.

Given:

A laptop is sold for Rs. 65,520 after a discount of 25%. 

Concept used:

Selling Price = Marked Price × (1 - Discount%)

Calculation:

Marked price of the laptop

⇒ 65520 ÷ (1 - 25%)

⇒ Rs. 87,360

∴ The marked price of the laptop is Rs. 87,360.

Shortcut Trick

25% discount means MP = 4 and SP = 3

Here, 3 unit → 65520 then, 4 unit → 65520/3 × 4 = 87360

Given:

Numbers given = 15, 18, 25, 32

Concept used:

LCM is the smallest common multiple of two or more numbers.

Calculation:

LCM (15, 18, 25, 32)

⇒ 7200

⇒ 2 × 3600

∴ The least number which when doubled will be exactly divisible by 15, 18, 25 and 32 will be 3600.

Given:

The distance covered by a train in (5y - 1) hours is (125y3 - 1) km. 

Concept used:

a³ - b³ = (a - b)(a² + ab + b²)

Calculation:

Speed of the train

⇒ (125y3 - 1) ÷ (5y - 1)

⇒ $\frac {(5y)^3 - 1}{(5y - 1)}$

⇒ $\frac {(5y - 1)(25y^2 + 5y + 1)}{(5y - 1)}$

⇒ (25y2 + 5y + 1) km/h

∴ The speed of the train is (25y2 + 5y + 1) km/h.

Given:

The sides of a triangle are in the ratio 4 ∶ 6 ∶ 8. 

Concept used:

The triangle is an obtuse triangle if the sum of the squares of the smaller sides is less than the square of the largest side.

Calculation:

Let the sides of the triangle be 4x, 6x, and 8x respectively.

Now,

(4x)² + (6x)² < (8x)²

⇒ 52x² < 64x²

So, the triangle is an obtuse-angled triangle.

∴ The triangle is obtuse-angled.

Calculation:

% of marks obtained by A in subject P = $\frac {150}{900} \times 100\%$ ≈ 16.67%

∴ A obtained 16.67% of marks in subject P.

Given:

In ΔABC, right-angled at B, AB = 7 cm and AC - BC = 1 cm.

Concept used:

1. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
2. A² - B² = (A + B)(A - B)
3. sin θ = perpendicular ÷ Hypotenuse

Calculation:

AC - BC = 1      ....(1)

​According to the concept,

AB² + BC² = AC²

⇒ 7² = AC² - BC² (∵ AB = 7)

⇒ (AC + BC)(AC - BC) = 49 

⇒ (AC + BC) = 49 (∵ AC - BC = 1)

Solving, (1) and (2) we get, AC = 25 and BC = 24.

Now, sin C = $\frac {7}{25}$

∴ The value of sin C is $\frac {7}{25}$.

Shortcut Trick

In the right-angled triangle one side AB = 7 and the other two sides difference is 1

Now, the only triplet 7,24,25 holds, so sin c = 7/25

Given:

In a 400-metre race, A runs at a speed of 16 m/sec.

A gives B a start of 15 metres and still beats him by 10 sec.

Concept used:

Distance = Time × Speed

Calculation:

Time taken by A to finish the race = 400/16 = 25 seconds

Since B is given a start of 15 metres, B has to cover = 400 - 15 = 385 metres

Time taken by B to finish the race = 25 + 10 = 35 seconds

Now, speed of B = 385/35 = 11 m/s

∴ The speed of B is 11 m/s.

Given:

sin θ + cos θ = $\sqrt5$ sin(90 - θ)

Concept used:

1. cot θ = cos θ ÷ sin θ
2. a² - b² = (a + b)(a - b)

Calculation:

sin θ + cos θ = $\sqrt5$ sin(90 - θ)

⇒ sin θ + cos θ = $\sqrt5$ cosθ

⇒ cos θ($\sqrt5$ - 1) = sinθ

⇒ cot θ = $\frac {1}{\sqrt5 - 1}$

⇒ cot θ = $\frac {\sqrt5 + 1}{(\sqrt5 - 1)(\sqrt5 + 1)}$

⇒ cot θ = $\frac {\sqrt5 + 1}{5 - 1}$

⇒ cot θ = $\frac {\sqrt5 + 1}{4}$

∴ The value of cot θ is $\frac {\sqrt5 + 1}{4}$.

Calculation:

Total production of Company A in 2016 and 2019 together = (40 + 60) = 100 lakh tonnes

Total production of Company C in 2017 and 2018 together = 60 + 60 = 120 lakh tonnes

Now, % = $\frac {100}{120}\times 100\%$ ≈ 83.33%

∴ The total production of Company A in 2016 and 2019 together is 83.33% of the total production of Company C in 2017 and 2018 together.

Calculation:

Total number of workers in all factories = 25 + 30 + 70 + 80 + 15 = 220

∴ The total number of workers working in all factories is 220.

Given:

A, B, C, and D share a property worth Rs. 93,100.

A ∶ B = 1 ∶ 2, B ∶ C = 3 ∶ 4 and C ∶ D = 5 ∶ 6.

Calculation:

A ∶ B = 1 ∶ 2 = 3 : 6

B ∶ C = 3 ∶ 4 = 6 : 8

C ∶ D = 5 ∶ 6 = 5 × 8/5 ∶ 6 × 8/5 = 8 : 9.6

So, A : B : C

⇒ 3 : 6 : 8 : 9.6

⇒ 30 : 60 : 80 : 96

Now, the share of C = $93100 × \frac {80}{30 + 60 + 80 + 96}$ = Rs. 28000

∴ C's share is Rs. 28000.

Given:

cosec A - cot A = $\frac{1}{4}$

Concept used:

1. cosec2 A - cot2 A = 1 2. cot A = 1 ÷ tan A

Calculation:

cosec A - cot A = $\frac{1}{4}$      ....(1)

​According to the concept,

cosec² A - cot² A = 1

⇒ (cosec A + cot A)(cosec A - cot A) = 1

⇒ (cosec A + cot A) × $\frac{1}{4}$ = 1

⇒ (cosec A + cot A) = 4      ....(2)

Now, (2) - (1),

2cot A = 4 - 1/4

⇒ cot A = 15/8

⇒ tan A = 8/15

∴ The required value of tan A is $\frac{8}{15}$.