SSC CGL 2022 Tier-I Official Paper (Held On : 03 Dec 2022 Shift 1) (Previous Year Paper)

The logic followed here is :-

From the given three different cubes, figure 1 and figure 3 ,the adjacent sides are as shown below :

As 4 is common on both figure 1 and figure 3, it is clear that 2, 3, 5 and 6 are adjacent to it and remaining number i.e., 1 will be opposite to it.

Opposite pairs:

1 → 4

2 → 5

3 → 6

So, the opposite side of "1" will be side "4".

Hence, the correct answer is "4".

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 "ECONOMIST" the second letter is "C". So, the mirror image should be "

" ⇒ Option 2 is eliminated.

• The word "sdw973qa" the second letter is "C". So, the mirror image should be "

" ⇒ Option 3 is eliminated..

• The word "sdw973qa" the second letter is "C". So, the mirror image should be "

" ⇒ Option 4 is eliminated.

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

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

1) For '

' element : Alternately the element is filled then blank subsequently.

​

2) For digit/number element : 

• Consecutive odd number series is written i.e '1, 3, 5, 7, 9, 11, 13, 15'
• The consecutive odd number is written opposite to new odd number
• For example, in 4^th box 11 is a larger one between 11 and 9. so., 11 is shifted anti clock wise direction and replaced by 13, and the consecutive odd number is written opposite of 13.

Final series is :

Hence, ‘option - (3)’ is the correct answer.

Logic : ​(3) is added to the position value according to the English alphabetic series.

​So,

• 'MOBILE' is written as 'PRELOH'​

​And,

• 'SILENT' is written as 'VLOHQW'​

​Similarly,

• 'PAINTING' is written as :

​

Hence, "SDLQWLQJ" is the correct answer.

The logic followed here is : (1^st number - 3^rd number) × 5 = 2^nd number

Given :

• (36, 90, 18)​

​**(36 - 18)** × 5 = 90

18 × 5 = 90

90 = 90 (LHS = RHS)

• (15, 35, 8)

(15 - 8) × 5 = 35

7 × 5 = 35

35 = 35 (LHS = RHS)

So,

• Option - (1) : (14, 45, 5)​

(14 - 5) × 5 = 45

9 × 5 = 45

45 = 45 (LHS = RHS)

• Option - (2) : (14, 42, 7)​

(14 - 7) × 5 = 42

7 × 5 = 42

35 ≠ 42 (LHS ≠ RHS)

• Option - (3) : (13, 78, 6)​

(13 - 6) × 5 = 78

7 × 5 = 78

35 ≠ 78 (LHS ≠ RHS)

• Option - (4) : (12, 60, 8)​

(12 - 8) × 5 = 60

4 × 5 = 60

20 ≠ 60 (LHS ≠ RHS)

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

Given :

So,

• Option - (1) : B ÷ A + C → B is the father of A who is the mother of C.

​

Here, A is the mother of C.

• Option - (2) : A - B ÷ C → A is the sister of B who is the father of C.

​

Here, A is the paternal aunt of C.

• Option - (3) : A + B ÷ C → A is the mother of B who is the father of C.

​

Here, A is the paternal grandmother of C.

• Option - (4) : A ÷ B + C → A is the father of B who is the mother of C.

​

Here, A is the maternal grandfather of C.

Hence, "Option - (4)" is the correct answer.

The logic followed here is :- (1) is subtracted from the position value according to English alphabetic series diagonally.

​So,

• ROAR : QZNQ​

And,

• HEAR : QZDG​

Similarly,

• DAMP :

Hence, the correct answer is "OLZC".

According to the question, after interchanging the given two numbers '5 and 9' :

So,

• Option - (1) : 9 × 4 + 5 - 8 ÷ 2 = 25

5 × 4 + 9 - 8 ÷ 2 = 25

5 × 4 + 9 - 4 = 25

20 + 9 - 4 = 25

29 - 4 = 25

25 = 25 (LHS = RHS)

• Option - (2) : 9 - 5 × 4 + 6 ÷ 3 = -30

5 - 9 × 4 + 6 ÷ 3 = -30

5 - 9 × 4 + 2 = -30

5 + 2 -36 = -30

7 - 36 = -30

-29 ≠ -30 (LHS ≠ RHS)

• Option - (3) : 9 + 7 × 8 ÷ 4 - 5 = 10

5 + 7 × 8 ÷ 4 - 9 = 10

5 + 7 × 2 - 9 = 10

5 + 14 - 9 = 10

19 - 9 = 10

10 = 10 (LHS = RHS)

• Option - (4) : 9 - 4 × 5 + 6 ÷ 2 = -28

5 - 4 × 9 + 6 ÷ 2 = -28

5 - 4 × 9 + 3 = -28

5 + 3 - 36 = -28

8 - 36 = -28

-28 = -28 (LHS = RHS)

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

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

1) For '

' element : Rotating 45° and flipping in the clockwise direction.

​​

2) For '

' element : 

• Number of lines are increasing around the square subsequently starting with 3 lines then 4 and so on till 8.
• Number of lines are increasing alternately from one end and then from another end subsequently.

 

​

Final series is :

Hence, ‘option - (4)’ is the correct answer.

The logic followed here is : (2^nd number + 3^rd number) × 4 = 1^st number

Given :

• (452, 50, 63)

​**(50 + 63)** × 4 = 452

113 × 4 = 452

452 = 452 (LHS = RHS)

• (260, 35, 30)​

​**(35** + 30) × 4 = 260

65 × 4 = 260

260 = 260 (LHS = RHS)

So,

• Option - (1) : (330, 30, 45)​

​(30 + 45) × 4 = 330

75 × 4 = 330

300 ≠ 330 (LHS ≠ RHS)

• Option - (2) : (260, 30, 25)​

​(30 + 25) × 4 = 260

55 × 4 = 260

220 ≠ 260 (LHS ≠ RHS)

• Option - (3) : (260, 50, 15)​

​(50 + 15) × 4 = 260

65 × 4 = 260

260 = 260 (LHS = RHS)

• Option - (4) : (230, 15, 45)

​(15 + 45) × 4 = 230

60 × 4 = 230

240 ≠ 230 (LHS ≠ RHS)

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

The logic followed here is :- The difference between first two and last two letter's position value is 7 and 10 respectively according to English alphabetic series.

​So,

• Option - (1) : CGB

​

• Option - (2) : FYI

​

• Option - (3) : RKU

​

• Option - (4) : KDN​

​

Here, Only 'CGB' difference between first two and last two letter's position value is 4 and 5 respectively according to English alphabetic series.

Hence, the correct answer is "CGB".

The logic followed here is : (1^st number × 3^rd number) = (2^nd number × 2)

Given :

• (12, 42, 7)

​12 × 7 = 42 × 2

84 = 84 (LHS = RHS)

• (13, 52, 8)

​13 × 8 = 52 × 2

104 = 104 (LHS = RHS)

So,

• Option - (1) : (8, 7, 43)

​8 × 43 = 7 × 2

344 ≠ 14 (LHS ≠ RHS)

• Option - (2) : (7, 12, 6)

​7 × 6 = 12 × 2

42 ≠ 24 (LHS ≠ RHS)

• Option - (3) : (9, 26, 8)

​9 × 8 = 26 × 2

72 ≠ 52 (LHS ≠ RHS)

• Option - (4) : (9, 18, 4)

​9 × 4 = 18 × 2

36 = 36 (LHS = RHS)

Hence, "Option - (4)" is the correct answer.

The logic followed here is :-

Consonants + 1,

Vowels - 3.

​​So,

• WINDOW : XFOELX​

And,

• TICKET : UFDLBU​

Similarly,

• REGION :

Hence, the correct answer is "SBHFLO".

The logic followed here is :-

1. First letter ⇒ (3) is added to the position value according to English alphabetic series.
2. Second letter ⇒ (4) is added to the position value according to English alphabetic series.
3. Third letter ⇒ (2) is added to the position value according to English alphabetic series.

​​So,​

 

Hence, the correct answer is "PQR".

Given statement : 14 × 6 ÷ 12 + 15 - 9 = 203

According to the question, after interchanging the given two signs and two numbers :

So,

• Option - (1) : 15, 6, +, ÷

14 × 15 + 12 ÷ 6 - 9 = 203

14 × 15 + 2 - 9 = 203

210 + 2 - 9 = 203

212 - 9 = 203

203 = 203 (LHS = RHS)

• Option - (2) : 12, 15, -, ×

14 - 6 ÷ 15 + 12 × 9 = 203

14 - 0.4 + 12 × 9 = 203

14 + 108 - 0.4 =203

112 - 0.4 = 203

111.6  ≠ 203 (LHS ≠ RHS)

• Option - (3) : 12, 9, ÷, -

14 × 6 - 9 + 15 ÷ 12 = 203

14 × 6 - 9 + 1.25 = 203

84 + 1.25 - 9 = 203

85.25 - 9 = 203

76.25  ≠ 203 (LHS ≠ RHS)

• Option - (4) : 14, 6, ÷, ×

6 ÷ 14 × 12 + 15 - 9 = 203

0.43 × 12 + 15 - 9 = 203

5 + 15 - 9 = 203

20 - 9  ≠ 203 (LHS ≠ RHS)

11 ≠ 203 (LHS ≠ RHS)

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

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

Conclusions:

I. Some bulbs being fans is a possibility → Follow (As some bulbs are switches and all fans are switches. So, as there is no direct negative or cross relation between bulbs and fans therefore some bulbs can be fans is definitely true)

II. No fan is a vase → Follow (As no switch is a vase and all fans are switches. So, as whole fans comes in switches therefore whole fans too have negative or cross relation with vase therefore it is definitely true)

III. All switches are fans → Does not follow (As all fans are switches. So, it is possible but not definitely true)

IV. No bulb is a vase → Does not follow (As some bulbs are switches and no switch is a vase. So, as there is no direct negative or cross relation between bulbs and fans therefore it is definitely false)

∴ Here, Only conclusions I and II follow.

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

Given :

Statement given : W # Q @ T & Y @ M % K

So,

• W # Q → W is the mother of Q.

• Q @ T → Q is the son of T.

• T & Y → T is the brother of Y.

• Y @ M → Y is the son of M.

• M % K → M is the wife of K.

​

Thus, according to the final family tree K is the father-in-law of W.

Hence, "Father-in-law" is the correct answer.

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

Conclusions:

I. Some R are not W → Does not follow (As some W are F and some R are F. So, as there is no direct negative or cross relation between W and R therefore it is definitely false)

II. No W is R → Does not follow (As some W are F and some R are F. So, as there is no direct negative or cross relation between W and R therefore it is definitely false)

∴ Here, Neither conclusion follows.

Hence, the correct answer is "Neither conclusion follows".

Logic : 

1. Consonants - Position value to the English alphabetic series is written.
2. Vowels - Coded in a serial order according to the English alphabetic series i.e :

• A → 1
• E → 2
• I → 3
• O → 4
• U → 5

​So,

• 'BREAK' is written as '2182111'​

​And,

• 'COLOUR' is written as '34124518'​

​Similarly,

• 'TRING' is written as :​

Hence, "20183147" is the correct answer.

Given statement : 20 * 2 * 50 * 5 * 115

According to the question**, after replacing the * signs** :

So,

• Option - (1) : -, ×, =, +

20 - 2 × 50 = 5 + 115

20 - 100 = 120

-80 ≠ 120 (LHS ≠ RHS)

• Option - (2) : +, ×, =, -

20 + 2 × 50 = 5 - 115

20 + 100 = -110

120 ≠ -110 (LHS ≠ RHS)

• Option - (3) : +, ×, -, =

20 + 2 × 50 - 5 = 115

20 + 100 - 5 = 115

120 - 5 = 115

115 = 115 (LHS = RHS)

• Option - (4) : -, ×, +, =

20 - 2 × 50 + 5 = 115

20 + 5 - 100 = 115

25 - 100 = 115

-75 ≠ 115 (LHS ≠ RHS)

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

According to the sequence in the dictionary:

2. Expedition
3. Expel
4. Expenditure 1. Expensive
5. Experience

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

Logic :

1. First letter →  (5) is added to the position value according to the English alphabetic series.
2. Second letter → (6) is added to the position value according to the English alphabetic series.
3. Third letter → (7) is added to the position value according to the English alphabetic series.
4. Fourth letter → (8) is subtracted from the position value according to the English alphabetic series.

​So,

​

Hence, "LOVM" is the correct answer.

Given:

• The image must not to be rotated

 

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

The logic followed here is : Consecutive number series is added starting with 21.

Hence, "116" is the correct answer.

The logic followed here is :

First number × 10 + 1 = Second number

• Option - (1) : 7 - 71

7 × 10 + 1 = 71

• Option - (2) : 11 - 111

11 × 10 + 1 = 111

• Option - (3) : 8 - 81

8 × 10 + 1 = 81

• Option - (4) : 12 - 167

12 × 10 + 1 = 121 ≠ 167

Hence, "Option - (4)" is the correct answer.

Alternate MethodThe logic followed here is : Inserting (1) at the unit place of 1^st number = 2^nd number

S o,

• Option - (1) : 7 - 71

​Inserting (1) at the unit place of 7 → 71

71 = 71 (LHS = RHS)

• Option - (2) : 11 - 111​

​Inserting (1) at the unit place of 11 → 111

111 = 111 (LHS = RHS)

• Option - (3) : 8 - 81​

​Inserting (1) at the unit place of 8 → 81

81 = 81 (LHS = RHS)

• Option - (4) : 12 - 167

​Inserting (1) at the unit place of 12 → 121

121 ≠ 167 (LHS ≠ RHS)

Hence, "Option - (4)" is the correct answer.

The correct answer is Rock.

Key Points

• Earth's crust 
• Each fragment of the Earth's crust is known as a Plate.
• Earth consists of three parts. 
• The crust
• The mantle
• The core
• The Crust is the outer layer of the Earth and it is very thin compared to the core and mantle. It is made up of igneous, sedimentary, and metamorphic rocks.
• There are two types of crust viz oceanic and continental.
• The mantle lies below the crust and it is up to 2900 km thick.
• The core is the center of the earth.

The correct answer is Sangeet Natak Academy Award.

Key Points

• The Diploma in Kathak and Bharatanatyam is offered by the Lasya Centre of Dance Education and Research, whose principal is Rajashree.
• She is a well-known theorist and esteemed scholar.
• One of her research projects is "Madan Samhara," a study of the Avadhi language found in Tulsidas' "Ramcharitra Manas."
• Every year, Lasya holds a festival called Yatra.
• Rajashree Shirke has been given the Sangeet Natak Academy awards of 2013 for her excellence in Kathak.
• Sangeet Natak Academy Award:
• The Sangeet Natak Akademi bestows the Sangeet Natak Academy Award.
• It is the highest honor in India bestowed upon those who work in the performing arts.
• Prior to 2003, the prize came with a citation, a tamrapatra, an angavastram (a shawl), and Rs. 50,000.
• The monetary award has grown to ₹1,000,000 since 2009.
• The distinctions are presented in the performing arts categories of **music, dance, theater, other traditional arts, puppetry, and contribution/scholarship.**​
• ​Sangeet Natak Akademi:
• The Government of India established the Sangeet Natak Akademi as its national performing arts academy.
• The Indian Ministry of Education established it on May 31, 1952, and it started operating in 1953.
• Dr. P. V. Rajamannar was chosen as the organization's first chairman.
• On January 28, 1953, Dr. Rajendra Prasad inaugurated it during a special event held in the Parliament Building.

Additional Information

• Padma Shri:
• The Padma Shri is India's fourth-highest civilian honor, behind the Bharat Ratna, Padma Vibhushan, and Padma Bhushan.
• Kalidas Samman:
• The Indian state of Madhya Pradesh annually bestows the Kalidas Samman, a prize for the arts.
• National Film Award:
• The most prestigious film awards show in India is the National Film Awards.
• It was started in 1954.

The correct answer is Manpreet Singh.

Key Points

• Manpreet Singh:-
• He plays field hockey for India.
• At the 2020 Summer Olympics in Tokyo, he led the Indian field hockey team to the bronze medal.
• He is a halfback for the team.
• He played for India at the Olympics in 2012, and in 2014, he was voted Asia's Junior Player of the Year.

Additional Information

• Amit Rohidas:
• Indian field hockey player Amit Rohidas hails from Odisha.
• He is the vice-captain of the Indian national team and a defender for the group.
• Sreejesh Ravindran:
• ​Sreejesh is a former captain of the Indian national team and a goalkeeper for the professional field hockey squad in India.
• Krishan B Pathak:
• ​Indian field hockey player Krishan Bahadur Pathak serves as the team's goalie for the national squad.

The correct answer is Kirana.

 Key Points

• Indian vocalist Gangubai Hangal specialized in the khayal style of Hindustani classical music.
• She hails from Karnataka and was renowned for her resonant voice.
• Hangal was a member of the Kirana gharana.

Additional Information

• Patiala: 
• Mian Kallu, a sarangi player for the Jaipur durbar, founded the gharana somewhere between the middle and end of the 19^th century.
• Agra:
• The Nauhar Bani is the ancestor of the Agra gharana, a school of Hindustani classical vocal music.
• Gwalior:
• One of the oldest Khyal Gharanas in Indian classical music is the Gwalior Gharana.
• The Mughal emperor Akbar's rule marked the beginning of the Gwalior Gharana's ascent.

The correct answer is Net National Product.

Key Points

• Net National Product (NNP):
• NNP is obtained by subtracting depreciation value (i.e. capital stock consumption) from GNP.
• Net National Product (NNP) = Gross National Product − Depreciation.​

Additional Information

• Gross Domestic Product (GDP):
• It is the total money value of all final goods and services produced within the geographical boundaries of the country during a given period of time.
• GDP = C + G + I
• C = Consumption expenditure
• G = Government expenditure
• I = Investment expenditure
• Gross domestic product at market prices
• Gross domestic product at market prices aims to measure the wealth created by all private and public agents in a national territory during a given period.
• The way of measuring GDP at market prices is the production approach as the sum of added values of all activities which produce goods and services, plus taxes and minus subsidies on products.
• Personal Income: 
• Income is obtained by nationals by subtracting corporate taxes and payments made for social securities provisions from national income and adding to it government transfer payments, business transfer payments and net interest paid by the government.
• Personal Income = National income – undistributed profits of a corporation – payments for social security provisions – corporate tax + government transfer payments + Business transfer payments + Net interest paid by the government.

The correct answer is Na2B4O7.10H2​O.

Key Points

• Borax is the sodium salt of boric acid.
• Chemical formula:- Na2B4O7.10H2O
• Borax occurs naturally as Tincal (suhaga) in certain dried-up lakes of India, Tibet, Srilanka and the USA. It contains about 55% borax.
• Tincal is the crude form of borax, and it contains many impurities. Borax is also found as tincal in Ceylon, Tibet and California.
• In Tibet, tincal is used as a cleaning product by the native tribes.

Important Points

• Preparation Methods of Borax:-

Preparation of Borax from Colemanite (Ca2B6O11)

• In this method, the colemanite mineral is finely powdered and boiled with a solution of sodium carbonate solution. As a result, borax and sodium metaborate is formed.
• The white precipitate of calcium carbonate obtained during the reaction is removed by the process of filtration, and the solution upon concentration and then cooling gives the pure crystals of borax. By passing carbon dioxide gas through the sodium metaborate, which is present in the mother liquor, it can be converted to borax.

Preparation of Borax from Tincal

• Tincal can be transformed into borax by being dissolved in boiling water. The resulting solution is filtered to get rid of any insoluble contaminants like sand, clay, etc.
• The resulting solution can be concentrated to get the pure crystals of borax.

Preparation of Borax from Boric acid

• Boric acid and sodium carbonate can be combined to create borax in modest quantities.

The correct answer is Crown of Incredible India.

Key Points

• ​The Jammu and Kashmir government and the hospitality technology company OYO collaborated to introduce the "Crown of Incredible India" rural tourism project throughout the Union Territory.
• It intends to revive the struggling tourism sector and encourage young people in J&K to launch their own businesses.
• In accordance with this, OYO will collaborate with the Center's "Mission Youth" initiative.
• In order to encourage entrepreneurship and generate prospects for self-employment, it plans to open homestays in 75 communities.

Additional Information

• The first floating financial literacy camp in India was held as part of the "Niveshak Didi" initiative's inauguration in Srinagar, Jammu & Kashmir.
• Around Srinagar's renowned Dal Lake, it was conducted among local locals.
• From a Shikara, Niveshak Didi conducted the financial literacy class in the indigenous Kashmiri language.

The correct answer is Tripura.

Key Points

• For the benefit of those who labor in tea gardens, the Tripura government has launched the Chaa Srami Kalyan Prakalpa Yojana.
• 75 of the 7,000 tea garden employees that labor in Tripura who are benefited by this program are women.
• Through 54 estates and 21 tea processing factories, tea is produced in Tripura.
• The government has introduced this program under which it will give tea workers shelter, rations, and essential financial support in order to maintain their social security.

Additional Information

• Benefits of Mukhyamantri Chaa Srami Kalyan Prakalpa.
• Instead of receiving rupees 130 per day, tea workers would now receive rupees 176.
• Social pension to all eligible families.
• Social allowance for helpers in maternity and pediatric healthcare.
• Health insurance is their ability.
• supporting devices for people with disabilities.
• The government will supervise and coordinate the management to create an environment that is environmentally favorable.

The correct answer is 3 second.

Key Points

• ​A player commits a "walking" offence if they take more than three steps without dribbling, passing, or shooting the ball.
• Additionally, if the player has the ball for more than three seconds, this may occur.
• This guideline is sometimes referred to as the "three-step rule."
• A player that is dribbling has three steps to halt before they are penalized for walking, which causes a turnover.
• After that, each player has three seconds to pass or shot.

Additional Information

• In the team sport of handball, two teams of seven players each pass a ball with their hands in an effort to toss it towards the opposite team's goal.
• Two 30-minute quarters make up a typical game, and the team with the most goals wins.
• A goal is located in the centre of each end of the 40 by the 20-meter court on which modern handball is played.

The correct answer is Rajput dynasties, Khalji dynasty, Tughluq dynasty.

Key Points

• The Delhi Sultanate was an Islamic empire based in Delhi that stretched over 320 years.
• The ruling dynasties of Delhi included:
• Rajput dynasties
• Early Turkish rulers (1206-1290)
• Khalji dynasty (1290-1320)
• Tughlaq dynasty (1320-1414)
• Sayyid dynasty (1414-1451)
• Lodi dynasty (1451-1526)

Additional Information

• Rajput Dynasties
• ​Tomaras Early 12^th C-1165
• Ananga Pala 1130-1145
• Chauhans 1165-1192
• Prithviraj Chauhan 1175-1192
• Khalji Dynasty:
• Founder: Jalal-ud-din Firoz Khilji
• The Khilji dynasty started from 1290 to 1320 AD.
• Famous ruler: Ala-ud-din Khilji
• Last ruler: Quṭb al-Din Mubarak Shah.
• Tughluq Dynasty (1320 to 1413):
• Ghiyas-ud-din Tughluq or Ghazi Malik was the founder of the Tughluq dynasty.
• Ghiyas-ud-din reinstated order in his empire.
• He brought Bengal, Utkala or Orissa, and Warangal under his control
• The Mongol leaders who invaded North India were seized and confined by him.
• In 1325 A.D. Ghiyas-ud-din was crushed to death while attending an event for his victories in Bengal.
• Junakhan, the crown prince succeeded him.

The correct answer is D2D (Distributor-to-Distributor).

Key Points

• B2C (Business-to-Consumer):
• Business-to-consumer marketing describes the practice of companies selling goods and services directly to customers without the use of a middleman.
• B2C mainly refers to online merchants who use the internet to sell goods and services to customers.
• C2C (Consumer-to-Consumer):
• A business model known as "consumer to consumer" (C2C) allows for private customers to deal for goods or services without the involvement of a business on either end of the transaction.
• Today, online businesses handle the majority of C2C transactions.
• B2B (Business-to-Business):
• Business-to-business (B2B) refers to a deal or transaction made between two companies, like a wholesaler and a retailer.
• B2B transactions typically take place in the supply chain, where one business buys raw materials from another in order to utilise them in the production process.
• Companies in the auto business, as well as those in property management, housekeeping, and industrial cleanup, frequently engage in B2B transactions.

Additional Information

• E-commerce is the electronic purchase or sale of goods through online stores or the Internet.
• E-commerce makes use of technology like supply chain management, mobile commerce, electronic payments transfer, Internet marketing, etc.
• Online retail, electronic markets, and online auctions are the three subfields of e-commerce.
• Electronic business provides a foundation for e-commerce.
• There are five essential categories of E-commerce:
• Business to Business
• Business to Consumer
• Business to Government
• Consumer to Business
• Consumer to Consumer

The correct answer is B D Mishra.

Key Points 

• Arunachal Pradesh Governor B D Mishra has been given additional charge of Meghalaya as incumbent Satya Pal Malik completes his term on 4^th Oct 2022.
• Mr Malik was first appointed as the Governor of Bihar in 2017.
• He was appointed as the Governor of J&K when the Centre revoked the special status to J&K under Article 370 on August 5, 2019.
• He was appointed as the Governor of Meghalaya in 2020.

Additional Information 

• Governor is a nominal executive head of the state.
• The primary function of the governor is to preserve, protect and defend the constitution and the law as incorporated in their oath of office under Article 159 of the Indian constitution in the administration of state affairs.
• By the 7^th Constitutional Amendment Act of 1956, the same person can be appointed as a governor for two or more states.
• The State Governor shall have the power to grant pardons, reprieves, respites, or remissions of punishment or to suspend, remit or commute the sentence of any person convicted of any offense against any law relating to a matter to which the executive power of the State extends.

The correct answer is 2.

Key Points

• Cell division is the process by which a parent cell divides into two or more daughter cells.
• Cell division usually occurs as part of a larger cell cycle.
• In unicellular organisms, cell division is the means of reproduction; in multicellular organisms, it is the means of tissue growth and maintenance.
• There are 2 main types of cell division.
• Mitosis: 
• Most of the time when people refer to cell division, they mean mitosis, the process of making new body cells.
• Meiosis: 
• It is the type of cell division that creates egg and sperm cells.

Additional Information

The correct answer is Bombay.

Key Points

• The Indian National Congress (INC) was founded by Allan Octavian Hume on 28^th December 1885.
• The first session of INC was held in Bombay at Gokuldas Tejpal Sanskrit Collegeram.
• The first President of the INC session held in Bombay was Womesh Chandra Banerjee.
• 72 delegates attended the session.
• The important leaders during the foundation of INC were Dadabhai Naoroji, Badruddin Tyyabji, Anand Mohan Bose, R.C Dutt, Pherozshah Mehta, G.K Gokhale, G. Subramaniyam Aiyyar, Dinshaw Vacha, Bal Gangadhar Tilak, Mahadev Govind Ranade, Madan Mohan Malviya, etc.
• Formerly Indian National Congress was known as Indian National Union.
• The INC was formed during the tenure of Lord Dufferin (Viceroy of India from 1884-1888).

Additional Information

The correct answer is ampere.

Key Points

• Electric current is expressed by a unit called the ampere (A), named after the French scientist Andre-Marie Ampere.
• ​Ampere can be defined as one unit of charge flown through a given circuit in one second.

Additional Information

The correct answer is 10 to 200 kilometres.

Key Points

• The crust and the uppermost part of the mantle are called the lithosphere. Its thickness ranges from 10-200 km.
• The lithosphere is the solid, outer part of the Earth.
• The lithosphere includes the brittle upper portion of the mantle and the crust, the outermost layers of Earth’s structure.
• It is bounded by the atmosphere above and the asthenosphere (another part of the upper mantle) below.
• The portion of the interior beyond the crust is called the mantle.
• The mantle extends from Mohorovicic discontinuity to a depth of 2,900 km.
• The upper portion of the mantle is called Asthenosphere.
• It is considered to be extending up to 400 km and it is the main source of magma that finds its way to the surface during volcanic eruptions.

Additional Information There are two types of lithosphere: 

• Oceanic lithosphere, which is associated with oceanic crust and exists in the ocean basins (mean density of about 2.9 grams per cubic centimeter)
• Continental lithosph ere, which is associated with continental crust (mean density of about 2.7 grams per cubic centimeter)
• The thickness of the lithosphere is considered to be the depth of the isotherm associated with the transition between brittle and viscous behavior.
• The temperature at which olivine begins to deform viscously (~1000 °C) is often used to set this isotherm because olivine is generally the weakest mineral in the upper mantle.
• Oceanic lithosphere is typically about 50–140 km thick (but beneath the mid-ocean ridges is no thicker than the crust), while continental lithosphere has a range in thickness from about 40 km to perhaps 280 km; the upper ~30 to ~50 km of the typical continental lithosphere is the crust.

The correct answer is Pandit Shivkumar Sharma.

Key Points

• Pandit Shivkumar Sharma was an Indian famous classical musician, who attained international fame by playing the musical instrument, the santoor.
• The Santoor is a trapezoid-shaped hammered dulcimer often made of walnut wood and has 72 strings, which are struck with two delicate carved wooden mallets.
• The santoor is essentially a folk instrument that originated in the Kashmir Valley, and it achieved the status of a classical instrument due to the persistent efforts and genius of Pandit Shivkumar Sharma.
• With his hard work, determination and talent, Pandit Shivkumar Sharma made the santoor a global name.

Additional Information

The correct answer is MgO.

Key Points

• Magnesium oxide also called magnesia, is an alkaline earth metal oxide.
• It is typically produced by calcining certain minerals that are found in nature.
• It is solid and can withstand high temperatures both physically and chemically.
• Magnesium oxide is composed of the ions Mg2+ and O2-, which are joined together by an ionic bond.
• MgO is used as the magnesium oxide chemical formula.
• Magnesium is a metal and metals react with oxygen to form metallic oxides.

Additional Information 

The correct answer is 14.

Key Points

• Article 24 of the Indian Constitution,
• Prohibition of child labour in Factories and Hazardous Industries.
• It is a Special Provision made for the Protection of Children.
• Under this Article, no child below the age of  14 years can be Employed to Work in any Factory or Mine Or Engaged in any other Hazardous Employment.
• Punishment is 6 months to 2 years Or 5000 rupees Or Both.​

Additional Information

• Nothing in Act shall apply where the child:
• Helps his family or family enterprise, which is other than any hazardous occupations or processes set forth in the Schedule, after his school hours or during vacations.
• Works as an artist in the audio-visual entertainment industry, including the advertisement, films, television serials or any such other entertainment or sports activities except the circus.

The correct answer is Rayon.

Key Points

• Natural Fibres are obtained from plants, insects and worms.
• Cotton, wool, linen and silk are examples of natural fibres.
• Hence Rayon is not a natural fibre.
• All fibres are stretched and twisted to form long threads called yarns.
• This is called spinning.

Important Points

• The yarn is woven on a machine called a loom to produce fabric. 
• Cotton fibres come from the fruit of a cotton plant called a cotton boll.
• Woollen fibres come from the fleece of sheep, rabbits and goats.
• Silk fibres are obtained from the cocoon of silkworms.

Additional Information

• Synthetic fibres
• Fibres which are man-made are called synthetic fibres. Synthetic fibres are made in factories.
• Rayon, terrycloth, terylene, and nylon are some popular synthetic fibres.

The correct answer is All doubts and disputes in connection with the President's election can be inquired into and decided by both the Supreme Court and High Courts.

Key Points

• Election of President of India:
• Article 54 of the Indian Constitution specifies the criteria for electing the president.
• The elected members of both Houses of Parliament, the Legislative Assemblies of every State, the National Capital Territory of Delhi, and the Union Territory of Puducherry make up the Electoral College that chooses the President.
• The President's tenure in office begins on the day he assumes office and lasts for five years.
• A petition challenging the results of the presidential election can be filed with the Supreme Court after the vote has been counted. One voter may only cast one vote in the presidential election.
• The votes of the MLAs may differ from state to state, but never those of the MPs.
• To maintain the balance between the State and the Union, the number of votes from MPs must match the number of votes from MLAs.
• All MLAs do not cast equal numbers of votes.
• Any MP may cast a ballot in the state capital thanks to facilities supplied by the Election Commission.
• Therefore, it follows from the aforementioned considerations that all MLAs' votes have equal weight.

Additional Information

• President of India:
• Current President: Droupadi Murmu(since 25 July 2022)
• Formation: 26 January 1950; 73 years ago
• First holder: Rajendra Prasad
• Vice President of India: Jagdeep Dhankhar

The correct answer is Puthandu.

Key Points

• The Tamil calendar's first day of the year, Puthandu is traditionally observed as a festival by Tamil Hindus.
• The event begins on the first day of the Tamil month of Chittirai, according to the lunisolar Hindu calendar's solar cycle.
• According to the Gregorian calendar, it occurs every year on or around April 14.
• The traditional new year is held on the same day in other parts of South and South East Asia but is referred to by different names there, such as Vishu in Kerala and Vaisakhi or Baisakhi in central and northern India.
• The Tamil New Year usually occurs on April 14 of each Gregorian year, immediately after the spring equinox.

Important Points

• Tamils in India and Sri Lanka celebrate Pongal, a multi-day Hindu harvest celebration. According to the Tamil solar calendar, it is observed at the beginning of the month, and depending on the sun's orbit that particular year, the festival is typically held on January 14 or January 15.
• According to the Hindu calendar, Ugadi is New Year's Day, and it is observed in the Indian states of Andhra Pradesh, Telangana, and Karnataka.
• Onam is an annual harvest festival in India that is mostly observed by Keralan Hindus. It is the official festival of the state and a significant annual event for people in Kerala, featuring a variety of cultural activities.

The correct answer is Chalukyas.

Key Points

• In the early eleventh century, the Chola king Rajendra I built a Shiva temple and filled it with a Sun-pedestal seized from the Chalukyas.
• Rajendra-I of the Cholas erected a Shiva temple in the center of his kingdom and filled it with priceless statues he had taken from defeated kings, including a Sun-pedestal from the Chalukyas, a Ganesha statue, several Durga statues, a Nandi statue, an image of Bhairava and Bhairavi from the Kalingas of Orissa, and a Kali statue from the Palas of Bengal.
• The Chola Empire was ruled by Rajendra Chola I from 1014 until 1044 CE.
• For his role in promoting the arts, fostering trade, and greatly extending the Chola Empire, he is regarded as the most important monarch in early eleventh-century South Asia.
• The settlement of Mahatittha, which was later given the name Rajaraja-pura, was home to a Shiva temple built by Chola official Tali Kumaran.
• The island's Chola-occupied regions were given the name Mummudicholamandalam after Mummudi Chola, also known as Rajaraja I, Rajendra's father.

Important Points

• The Palas Empire, which arose in the Bengal region and ruled the Indian subcontinent from 750 to 1161 CE, was a major imperial force during this time.
• In the middle of the third century CE, the Deccan region of India gave rise to the Vakataka dynasty. Their territory is thought to have spanned from the northern and southern borders of Malwa and Gujarat to the Tungabhadra River, as well as from the western and eastern borders of Chhattisgarh to the Arabian Sea.
• The eastern coastal region known as Kalinga is typically referred to as being between the Mahanadi and the Godavari rivers, while its exact boundaries have changed over time as its rulers' territories have changed.

The correct answer is Nagara-shreshthi.

Key Points

• Nagara-shreshthi office was NOT held by the poet Harishena.
• prathama-kulika, or the chief craftsman, the nagara- shreshthi, or main banker or merchant of the city, the sarthavaha, or the head of the merchant caravans, and the head of the kayasthas, or scribes.
• Harishena held several positions. He was a sandhi-vigrahika, or minister of war and peace, in addition to being a maha-danda-nayaka, or chief judicial officer, and a Kumar-amatya, which denoted a prominent minister.

Important Points

• Samudragupta, the Gupta Emperor, appointed Harishena as his court poet.
• The 33 lines of the Allahabad Pillar inscription, also called Prayag Prashasti, were written by Harishena.
• One of the key epigraphic sources to learn about the political history of the Gupta dynasty is Prayag Prashasti.
• Harishena was one of the many poets and academics who Samudragupta supported.

The correct answer is Limestone.

Key Points

• Rocks made of calcium carbonates or calcium and magnesium carbonates are frequently found next to limestone. Most geological formation's sedimentary rocks include it.
• The primary raw ingredient for the cement industry, limestone is also necessary for the blast furnace to process iron ore.
• The majority of the carbonate rock in sedimentary rock, which makes up 20% to 25% of it, is limestone.
• The majority of the remaining carbonate rock is the closely related dolomite, which has a high concentration of the mineral dolomite, CaMg(CO₃)₂.
• Dolomite, limestone that has a considerable amount of dolomite (dolomitic limestone), and any other type of limestone that contains a significant amount of magnesium are all referred to as magnesia limestone, a defunct and poorly defined word.
• Approximately 30% of the world's petroleum reservoirs are found in limestone rocks.

Important Points

• The chemical element gold has the atomic number 79 and the symbol Au. This places it among the naturally occurring elements with higher atomic numbers.
• The chemical element iron has the atomic number 26 and the symbol Fe. It is a metal that is found in group 8 of the periodic table and the first transition series.
• The atoms of diamonds are grouped in a crystal structure known as diamond cubic, and it is a solid form of the element carbon.

Shortcut Trick

Ratio of speeds = 20 : 30 = 2 : 3

Ratio of time taken = 3 : 2 (since distance is constant)

Difference in time ratio = 3 − 2 = 1 unit

Total time difference = 1.5 hours (late start) + 2.5 hours (early arrival) = 4 hours

⇒ 1 unit = 4 hours, so time taken by Car 1 = 3 × 4 = 12 hours

Distance = Speed × Time = 20 × 12 = 240 km

∴ The correct answer is 240 km.

Alternate Method

Given:

Speed of Car 1 (S₁) = 20 km/h

Speed of Car 2 (S₂) = 30 km/h

Car 2 starts 1.5 hours later and reaches 2.5 hours earlier.

Point A Point B

Total Distance = D km

Car 1: 20 km/h Time = t hrs

Car 2: 30 km/h Time = t − 4 hrs

Formula Used:

Time = Distance ÷ Speed

Difference in time = Late start time + Early arrival time

Calculations:

⇒ Let the total distance between A and B be D km.

⇒ Time difference = 1.5 hours + 2.5 hours = 4 hours.

⇒ Time taken by Car 1 − Time taken by Car 2 = 4 hours

⇒ (D ÷ 20) − (D ÷ 30) = 4

⇒ (3D − 2D) ÷ 60 = 4

⇒ D ÷ 60 = 4

⇒ D = 60 × 4 = 240 km.

∴ The correct answer is 240 km.

Additional Information

Direct Distance Formula

When travelling the same distance at two different speeds S₁ and S₂ with a known total time difference Δt, Distance = (S₁ × S₂ ÷ |S₁ − S₂|) × Δt.

Average Speed

If a vehicle covers equal distance segments at two different speeds S₁ and S₂, the Average Speed over the entire journey = (2 × S₁ × S₂) ÷ (S₁ + S₂).

Relative Speed

When two bodies move in the same direction, their Relative Speed is the difference of their speeds (S₁ − S₂). If they move in opposite directions, it is the sum of their speeds (S₁ + S₂).

Given:

Single Discount = 25%

Successive Discount = 15% and 10%

Difference = Rs. 25

Calculation:

Let the bill amount be Rs. 100x.

Case 1:

25% discount to the 100x = 25x discount

Price after discount = 100x - 25x

⇒ 75x

Case 2:

Discount of 15% to the 100x = 15x

Price after discount = 100x - 15x

⇒ 85x

Second Discount of 10% to the 85x = 8.5x

Price after the second discount = 85x - 8.5x

⇒ 76.5x

According to the question,

76.5x - 75x = 25

⇒ 1.5x = 25

⇒ x = 25/1.5

⇒ x = 16.6667 

⇒ 100x = Rs.1666.67

∴ The bill amount is of Rs.1,666.67.

Shortcut Trick

Two successive discounts of 15% and 10% are equivalent to 15 + 10 - (15 × 10)/100 = 23.5%

So, the difference between the two discounts (25 - 23.5) = 1.5%

Now, 1.5% → 25

Then, 100% → 25/1.5 × 100 = 1666.67

Given:

A trader has a weighing balance that shows 1300 g for a kg.

He further marks up his cost price by 15%.

Calculation:

Let the cost price per gm be Rs. 1

So, cost price of 1300 gm = Rs. 1300

Marked price of 1300 gm = 1300 × 115% = Rs. 1495

Now, the trader gives 1000 g instead of 1300 gm

So, his profit = 1495 - 1000    [As cost price of 1000 g is Rs. 1000]

⇒ 495

Profit% = (495/1000) × 100 = 49.5

∴ The net profit percentage is 49.5%.

 Shortcut Trick

So, profit% = 99/200 × 100 = 49.5%

Shortcut Trick

Find the remainder of 87501 when divided by 765.

Remainder = 87501 (mod 765) = 291.

To find the next greater divisible number, add (Divisor − Remainder) to the number.

Required Number = 87501 + (765 − 291) = 87501 + 474 = 87975.

∴ The correct answer is 87975.

Alternate Method

Given:

Original Number = 87501

Divisor = 765

Formula Used:

Smallest number greater than N divisible by D = N + (D − (N mod D))

Calculations:

⇒ Divide 87501 by 765 to find the remainder:

⇒ 87501 ÷ 765 = 114 with a remainder of 291

⇒ 765 × 114 = 87210 (largest divisible number less than 87501)

⇒ The next divisible number = 87210 + 765

⇒ Required number = 87975

⇒ Verification: 87975 ÷ 765 = 115 (exactly divisible)

∴ The correct answer is 87975.

Additional Information

Divisibility and Remainders

When a number N is divided by D, the remainder R always satisfies 0 ≤ R < D. To make N divisible by D, one can either subtract R from N or add (D − R) to N.

Divisibility Rule for Composite Numbers

For a number to be divisible by 765, it must be divisible by its prime factors. Since 765 = 3² × 5 × 17, the number must be divisible by 5 (ends in 0 or 5) and 9 (sum of digits is a multiple of 9).

Given:

$\rm \frac{\cos A}{1+\tan A}-\frac{\sin A}{1+\cot A}$

Concept used:

a² - b² = (a + b)(a - b)

Calculation:

$\rm \frac{\cos A}{1+\tan A}-\frac{\sin A}{1+\cot A}$

⇒ $\rm \frac{\cos A}{1+\frac{\sin A}{\cos A}}-\frac{\sin A}{1+\frac{\cos A}{\sin A}}$

⇒ $\rm \frac{\cos A}{\frac{\cos A+ \sin A}{\cos A}}-\frac{\sin A}{\frac{\sin A+\cos A}{\sin A}}$

⇒ $\rm \frac{\cos ^2A}{{\cos A+ \sin A}}-\frac{\sin^2 A}{{\sin A+\cos A}}$

⇒ $\rm \frac{\cos ^2A -\sin ^2A }{{\cos A+ \sin A}}$

⇒ $\rm \frac{{(\cos A+ \sin A})({\cos A- \sin A})}{{\cos A+ \sin A}}$

⇒ cos A - sin A

∴ The required answer is cos A - sin A.

Shortcut Trick

According to the Angle Bisector Theorem, the ratio of the two segments BD and DC is equal to the ratio of the corresponding sides AB and AC.

Ratio BD : DC = AB : AC

⇒ Ratio = 10 : 14

⇒ Ratio = 5 : 7

∴ The correct answer is 5 : 7.

Alternate Method

Given:

Side AB = 10 cm

Side AC = 14 cm

AD is the internal angle bisector of ∠BAC.

Formula Used:

Internal Angle Bisector Theorem: BD/DC = AB/AC

Calculations:

⇒ BD/DC = 10/14

⇒ BD/DC = (2 × 5) / (2 × 7)

⇒ BD/DC = 5/7

⇒ BD : DC = 5 : 7

∴ The correct answer is 5 : 7.

Additional Information

Internal Angle Bisector Theorem

In a triangle, the angle bisector of an angle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

External Angle Bisector Theorem

For an external angle bisector at A meeting BC produced at D, the ratio is still BD/CD = AB/AC.

Length of Angle Bisector

The length of the bisector AD can be calculated using the formula: AD² = AB × AC − BD × DC.

Calculation:

Number of people in state C = 144

Number of people in state E = 280

Ratio = 144 : 280

⇒ 18 : 35

∴ The required answer is 18 : 35.

Given:

Rs. 5,000 is divided into two parts such that if one part is invested 4% and the other at 5%

The whole annual interest from both sums is Rs. 223

Calculation:

Let the 1^st investment be Rs x

So, the 2^nd investment = Rs. (5000 - x)

According to the question,

x × 4/100 + (5000 - x) × 5/100 = 223

⇒ 4x/100 + 250 - 5x/100 = 223

⇒ 250 - 223 = 5x/100 - 4x/100

⇒ 27 = x/100

⇒ x = 2700

So, 1^st investment was Rs. 2700

∴ The required answer is Rs. 2700.

Calculation:

Number of trucks sold by L = 80

Number of trucks sold by J = 40

Required % = (80/40) × 100

⇒ 200

∴ Ther required answer is 200%.

Shortcut Trick

Relation between Volume (V) and Surface Area (S) of a sphere: V = (r ÷ 3) × S

First, find radius r: r³ = (3 × 24416.64) ÷ (4 × 3.14) = 5832 ⇒ r = 18 cm

Directly calculate S = (3 × V) ÷ r

S = (3 × 24416.64) ÷ 18 = 24416.64 ÷ 6 = 4069.44 cm²

∴ The correct answer is 4069.44 cm².

Alternate Method

Given:

Volume of the Sphere (V) = 24,416.64 cm³

Value of π = 3.14

Formula used:

Volume (V) = (4 ÷ 3) × π × r³

Surface Area (A) = 4 × π × r²

Calculations:

⇒ 24416.64 = (4 ÷ 3) × 3.14 × r³

⇒ r³ = (24416.64 × 3) ÷ (4 × 3.14)

⇒ r³ = 73249.92 ÷ 12.56

⇒ r³ = 5832

⇒ r = ³√5832 = 18 cm

⇒ Surface Area = 4 × 3.14 × 18²

⇒ Surface Area = 12.56 × 324

⇒ Surface Area = 4069.44 cm²

∴ The correct answer is 4069.44 cm².

Additional Information

Sphere Properties

A sphere is a perfectly round 3D geometrical object. Its Volume is (4/3)πr³ and Surface Area is 4πr².

Hemisphere Formulas

For a hemisphere of radius r: Volume = (2/3)πr³, Curved Surface Area = 2πr², and Total Surface Area = 3πr².

Volume and Surface Area Relationship

The ratio of the Volume of a sphere to its Surface Area is always r ÷ 3.

Given:

$\rm \frac{1}{{1 + \cos (90°-θ )}} + \frac{1}{{1 - \cos (90°- θ )}}$

Concept used:

sin²θ + cos²θ = 1

Calculation:

$\rm \frac{1}{{1 + \cos (90°-θ )}} + \frac{1}{{1 - \cos (90°- θ )}}$

⇒ $\rm \frac{1}{{1 + \sin θ}} + \frac{1}{{1 - \sin θ}}$

⇒ $\rm \frac{1 + \sin θ+1 - \sin θ}{{(1 + \sin θ)(1 - \sin θ)}}$

⇒ $\rm \frac{2}{{1^2 - \sin^2 θ}}$

⇒ $\rm \frac{2}{{cos^2 θ}}$

⇒ 2sec2 θ

∴ The required answer is 2sec2 θ.

Given:

$\left( {4a + \frac{5}{a} + 5} \right)$ = 14

Concept used:

(a + b)² = a² + b² + 2ab

Calculation:

$\left( {4a + \frac{5}{a} + 5} \right)$ = 14

⇒ ${4a + \frac{5}{a}}$ = 9

⇒ $({4a + \frac{5}{a}})^2$ = 9²

⇒ ${16{a^2} + \frac{{25}}{{{a^2}}}+2.4a.\frac{5}{a}}$ = 81

⇒ ${16{a^2} + \frac{{25}}{{{a^2}}}+40}$ = 81

⇒ ${16{a^2} + \frac{{25}}{{{a^2}}}}$ = 41

∴ The required answer is 41.

Calculation:

Number of students from C who passed in science but failed in Mathematics = 8

Total number of students in C = 18 + 10 + 8 + 56

⇒ 92

Required % = (8/92) × 100

⇒ 8.695 ≈ 8.7%

∴ The required answer is 8.70%.

Given:

Ruchi can do the work in 30 days

Khushi can do the work in 40 days

Teju can do the work in 60 days

Formula used:

Work done = Time taken × Efficiency

Calculation:

Let the total work be 120 units  [As LCM of 30, 40, 60 is 120]

So, efficiency of Ruchi, Khushi, Teju = 4, 3, 2

Now,

In 3 days total work completed = 4 + 4 + 9

⇒ 17 units of the work

In 21 days total work completed = 17 × 7

⇒ 119 units

Now remaining 1 unit will complete Ruchi in 1/4 days

So, total time = 21 + 1/4

⇒ $\frac{85}{4}$ days

∴ In $\frac{85}{4}$ days the work will be completed.

Given:

The diameter of a sphere is 3.5 cm

Concept used:

Total surface area = 4πr2

Here r = radius

Calculation:

Total surface area = 4 × 22/7 × (3.5/2)²

⇒ 4 × 22/7 × 12.25/4

⇒ 22/7 × 12.25

⇒ 38.5

∴ The total surface area of the sphere is 38.5 cm2.

Given: 

Ram loses 12$\frac{1}{2}$% and after spending 75% of the remaining, he is left with Rs. 630

Calculation:

Let Ram initially have to be Rs. 100a

100a × 12$\frac{1}{2}$%

⇒ 12$\frac{1}{2}$a

So,

Remaining money = 100a - 12.5a

⇒ Rs. 87.5a

87.5a × 25/100 = Rs. 630

⇒ 87.5a = 630 × 4

⇒ 87.5a = 2520

⇒ a = 2520/87.5

⇒ a = 28.8

So, 100a = 2880

∴ The correct answer is Rs. 2880.

Shortcut Trick

We know, 12$\frac{1}{2}$% = 1/8 and 75% = 3/4, 

So, 7 unit → 630, 

Then, 32 unit → 630/7 × 32 = Rs.2880

Shortcut Trick

If x − 1/x = k, then x² + 1/x² = k² + 2.

Here, k = 13, so x² + 1/x² = 13² + 2 = 171.

To find x⁴ + 1/x⁴, use (x² + 1/x²)² − 2.

Target value = 171² − 2 = 29241 − 2 = 29239.

∴ The correct answer is 29239.

Alternate Method

Given: x − 1/x = 13

Formula Used: (a − b)² = a² + b² − 2ab and (a + b)² = a² + b² + 2ab

Squaring both sides of the given equation:

⇒ (x − 1/x)² = 13²

⇒ x² + 1/x² − 2(x)(1/x) = 169

⇒ x² + 1/x² − 2 = 169

⇒ x² + 1/x² = 171

Now, squaring both sides of the new equation to reach the power of 4:

⇒ (x² + 1/x²)² = 171²

⇒ (x²)² + (1/x²)² + 2(x²)(1/x²) = 29241

⇒ x⁴ + 1/x⁴ + 2 = 29241

⇒ x⁴ + 1/x⁴ = 29241 − 2

⇒ x⁴ + 1/x⁴ = 29239

∴ The correct answer is 29239.

Additional Information

Algebraic Identity (Plus to Plus)

If x + 1/x = k, then x² + 1/x² = k² − 2 and x⁴ + 1/x⁴ = (k² − 2)² − 2.

Algebraic Identity (Cubic)

If x − 1/x = k, then the value of the difference of cubes is x³ − 1/x³ = k³ + 3k.

Nature of Power Expansion

For any even power 2n, we always square the term with power n and adjust the constant term based on the sign in the identity.

Calculation:

Total M2 in 4 stores = 14 + 8 + 8 + 12

⇒ 42

Average M2 in 4 stores = 42/4

⇒ 10.5

So, in S1 and S4 has more than average of M2 per store

∴ The correct answer is Option 4.

Given:

a ∶ b = c ∶ d

Calculation:

a ∶ b = c ∶ d

⇒ a/b = c/d

⇒ a/b + 1 = c/d + 1

⇒ (a + b)/b = (c + d)/d

b/d = (a + b)/(c + d)

So, b : d = a + b : c + d

Again

a ∶ b = c ∶ d

⇒ a/b = c/d

⇒ a/c = b/d

So, a : c = b : d = a + b : c + d

∴ The required answer is a + b : c + d

Formula used:

(a + b)² = a² + b² + 2ab

(a + b)(a - b) = a² - b²

Calculation:

x⁴ + x² + 25

It can be written as (x²)² + 2 × x² × 5 + (5)² - (3x)²

⇒ x4 + 10x2 + 25 - 9x2

⇒ (x² + 5)² - (3x)²

⇒ (x² + 5 + 3x)(x² + 5 - 3x)

∴ The factors of x⁴ + x² + 25 are (x2 + 3x + 5) (x2 - 3x + 5).

Shortcut Trick

Total Area of Circle = Area of Sector × (360° / θ)

πr² = 66 × (360 / 60) = 66 × 6 = 396 cm²

r² = 396 ÷ (22/7) = 396 × (7 / 22) = 18 × 7 = 126

r = √126 = √(9 × 14) = 3√14 cm

∴ The correct option is D.

Alternate Method

Given:

Area of sector = 66 cm²

Angle of sector (θ) = 60°

Value of π ≈ 22/7

Formula Used:

Area of sector = (θ / 360°) × πr²

60° Area = 66 cm²

r = ? Sector of a Circle

Calculations:

⇒ 66 = (60 / 360) × (22 / 7) × r²

⇒ 66 = (1 / 6) × (22 / 7) × r²

⇒ 66 = (22 / 42) × r²

⇒ r² = (66 × 42) / 22

⇒ r² = 3 × 42

⇒ r² = 126

⇒ r = √126

⇒ r = √(9 × 14)

⇒ r = 3√14 cm

∴ The correct option is D.

Additional Information

Length of Arc

The length of the arc of a sector is given by l = (θ / 360°) × 2πr.

Perimeter of a Sector

The perimeter includes the arc length plus two radii: P = l + 2r = [(θ / 360°) × 2πr] + 2r.

Area of Circle

The total area of a circle with radius r is A = πr².

Area in terms of Arc Length

If the arc length l is known, the area of the sector can be calculated as A = (1/2) × l × r.

Shortcut Trick

For finding the HCF of fractions, use the direct formula:

HCF = [HCF of Numerators] ÷ [LCM of Denominators]

Numerators are 12, 14, 16 ⇒ HCF(12, 14, 16) = 2

Denominators are 5, 15, 17 ⇒ LCM(5, 15, 17) = 15 × 17 = 255

∴ The correct answer is 2/255.

Alternate Method

Given Fractions: 12/5, 14/15, and 16/17

Formula Used: HCF of fractions = HCF(a, c, e) / LCM(b, d, f)

Calculations:

⇒ Numerators: 12, 14, 16

⇒ Factors of 12 = 2 × 2 × 3

⇒ Factors of 14 = 2 × 7

⇒ Factors of 16 = 2 × 2 × 2 × 2

⇒ Common Factor (HCF): 2

⇒ Denominators: 5, 15, 17

⇒ LCM of 5 and 15 is 15 (since 15 is a multiple of 5).

⇒ LCM of 15 and 17 = 15 × 17 = 255 (since 17 is a prime number).

⇒ Required HCF: 2 / 255

∴ The correct answer is 2/255.

Additional Information

LCM of Fractions

LCM of fractions = [LCM of Numerators] ÷ [HCF of Denominators].

HCF and LCM Relation

For two numbers A and B: A × B = HCF(A, B) × LCM(A, B).

Co-prime Numbers

The HCF of any two co-prime numbers is always 1, and their LCM is their product.

Given: 

(cos q + sin q) = 31/25

Concept used:

Sin²θ + Cos²θ = 1

Calculation:

(cos q + sin q) = 31/25      -----(i)

⇒ (cos q + sin q)² = (31/25)²

⇒ cos² q + sin² q + 2cosqsinq = 961/625

⇒ 1 + 2cosqsinq = 961/625

⇒ 2cosqsinq = 961/625 - 1

⇒ 2cosqsinq = 336/625

Now,

(cos q - sin q)2 = cos2 q + sin2 q - 2cosqsinq

⇒ (cos q - sin q)2 = 1 - 336/625

⇒ (cos q - sin q)2 = 289/625

⇒ (cos q - sin q) = 17/25      ----(ii)

From eq (i) and eq (ii) we get,

2cos q = 48/25

⇒ cos q = 24/25

So, cos2 q = (24/25)²

⇒ 576/625

∴ The required answer is 576/625.

Shortcut Trick

Concept Used:

Sinθ = Opposite/ Hypotenuse(O/H)

Cosθ = Adjacent/ Hypotenuse(A/H)

Calculation:

According to the question, 

⇒ cos q + sin q = 31/25

⇒ A/H + O/H = 31/25

⇒ (A + O)/H = 31/25

So we get, H as 25 and (A + O) = 31

Now we know a triplet as 7, 24, and 25

This satisfies the given condition,

Using the values, we get,  

Cos q = A/H = 24/25

So, cos2 q = (24/25)2

⇒ 576/625

∴ The required answer is 576/625.

Shortcut Trick

By using the Alligation method, we can directly find the ratio of boys to girls.

Ratio of Boys to Girls = (Girls Average − Overall Average) : (Overall Average − Boys Average)

Ratio = (65 − 62) : (62 − 60) = 3 : 2

Total parts = 3 + 2 = 5 parts = 60 students ⇒ 1 part = 12 students.

Number of boys = 3 parts = 3 × 12 = 36.

∴ The correct answer is 36.

Alternate Method

Given:

Total number of students in the class = 60

Overall average marks of the class = 62

Average marks of boys = 60

Average marks of girls = 65

Formula Used:

Total marks = Average marks × Number of students

Boys

60

Girls

65

Average

62

3 65 - 62

2 62 - 60

Ratio = 3 : 2

Calculations:

Let the number of boys be B and the number of girls be G.

⇒ B + G = 60

⇒ G = 60 − B

Total marks of all students = Total marks of boys + Total marks of girls

⇒ 62 × 60 = (60 × B) + (65 × G)

⇒ 3720 = 60B + 65(60 − B)

⇒ 3720 = 60B + 3900 − 65B

⇒ 65B − 60B = 3900 − 3720

⇒ 5B = 180

⇒ B = 180 ÷ 5 = 36

∴ The correct answer is 36.

Additional Information

Alligation Rule

Alligation is a quick technique to find the ratio in which two components are mixed. The ratio is determined by taking the cross-difference of individual averages from the overall mixture's average.

Weighted Average Formula

When two groups of sizes n₁ and n₂ have averages A₁ and A₂ respectively, the combined average is given by: A = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Net Deviation Method

In any valid dataset, the total sum of deviations of all group items from their true combined average must equal zero. This property allows solving without multiplying large values.