SSC CGL Previous Paper (Held On: 3 March 2020 Shift 1) (Previous Year Paper)

According to the given diagram,

The shaded part represents number of female executives.

Number of female executives in the organisation are ‘5’

Hence, “5” is the correct answer.

The pattern followed is,

Similarly,

Hence, “CZGPXTBV” is the correct answer.

The pattern followed is,

Hence, “WLD” is the correct answer.

The number of rectangles in the given given figure are,

Hence, “35” is the correct answer.

Drawing the family tree,

Kavinder is the Maternal Grandfather of Satish

Hence, “Maternal Grandfather” is the correct answer.

Interchanging the numbers and using BODMAS rule,

Option 1 → 2 and 5

9 + 7 × 2 – 18 ÷ 5 = 3 × 4 – 10 + 45 ÷ 2

9 + 7 × 2 – 3. 6 = 3 × 4 – 10 + 22. 5

9 + 14 – 3. 6 = 12 – 10 + 22. 5

23 – 3. 6 = 34. 5 – 10

19. 4 is not equal to 24. 5

Option 2 → 18 and 45

9 + 7 × 5 – 45 ÷ 2 = 3 × 4 – 10 + 18 ÷ 5

9 + 7 × 5 – 22. 5 = 3 × 4 – 10 + 3. 6

9 + 35 – 22. 5 = 12 – 10 + 3. 6

44 – 22. 5 = 15. 6 – 10

21. 5 is not equal to 5. 6

Option 3 → 9 and 3

3 + 7 × 5 – 18 ÷ 2 = 9 × 4 – 10 + 45 ÷ 5

3 + 7 × 5 – 9 = 9 × 4 – 10 + 9

3 + 35 – 9 = 36 – 10 + 9

38 – 9 = 45 – 10

29 is not equal to 35

Option 4 → 7 and 4

9 + 4 × 5 – 18 ÷ 2 = 3 × 7 – 10 + 45 ÷ 5

9 + 4 × 5 – 9 = 3 × 7 – 10 + 9

9 + 20 – 9 = 21 – 10 + 9

29 – 9 = 30 – 10

20 = 20

Hence, option 4 is the correct answer.

The paper when unfolded looks like,

Hence, option 3 is the correct answer.

The exact mirror image of the given figure when the mirror is held at the right side is,

Hence, option 2 is the correct answer.

Clock is a mechanical or electrical device for measuring time, indicating hours, minutes, and sometimes seconds by hands on a round dial or by displayed figures.

Similarly,

Option 1 → Anemometer is a device used for measuring wind speed and direction.

Option 2 → Taseometer is an instrument used to measure strains.

Option 3 → Balance is an even distribution of weight enabling someone or something to remain upright and steady.

Option 4 → Ammeter is an instrument used to measure current in a circuit.

‘Ammeter: Current’ share the same relationship as that shared by the given pair of words.

Hence, “Ammeter: Current” is the correct answer.

The pattern followed is,

All follow the same pattern, except ‘FVKO’.

Hence, “FVKO” is the odd – cluster.

Given series: k_lmml_mk_mmk_lkkl_m

Option1) k, l, k, l, m

kklmm llmkk mmkll kklmm

Here, Each group has 5 letters of kklmm / llmkk / mmkll / kklmm are being repeated.

In the above series, K change to L then L turns into M again then M turns into K.

Option2) k, l, m, k, k

kklmm llmkm mmkkl kklkm

Option3) k, m, m, k, l

kklmm lmmkm mmkkl kkllm

Option4) l, k, m, k, k

kllmm lkmkm mmkkl kklkm

Hence option 1 is correct answer.

Righteous comes first in the order.

It is followed by Rightly.

Rightly is followed by Rights.

Rights is followed by Rigidly.

Rigidly is followed by Rigour.

The correct dictionary order is,

3. Righteous 

4. Rightly 

5. Rights

6. Rigidly 

7. Rigour

Hence, option 4 is the correct answer.

Option 1 → A submarine is a watercraft capable of independent operation underwater.

Option 2 → A yacht is a watercraft used for pleasure or sports.

Option 3 → A ferry is a merchant vessel used to carry passengers, and sometimes vehicles and cargo, across a body of water. 

Option 4 → A ship is a large watercraft that travels the world's oceans and other sufficiently deep waterways, carrying goods or passengers, or in support of specialized missions, such as defence, research and fishing.

‘Submarine’ is different as it operates under water.

Hence, “submarine” is the odd one.

The given figure is embedded in,

Hence, option 2 is the correct answer.

The pattern followed is,

Similarly,

Hence, “20-7-15-20-3-8” is the correct answer.

The pattern followed is,

12² = 144, 144/ 2 = 72

And,

22² = 484, 484/ 2 = 242

Similarly,

18² = 324, 324/ 2 = 162

‘162’ is related to the third number in the same way as the second number is related to the first number and the sixth number is related to the fifth number.

Hence, “162” is the correct answer.

According to the given information,

The ratio of present ages of Asha and Lata = 5 : 6

Let the ages of Asha and Lata be 5x and 6x respectively. 

Difference between their ages is 6 years

6x – 5x = 6

x = 6

Then,

Asha’s age, 5x = 5 × 6 = 30

Lata’s age, 6x = 6 × 6 = 36

Lata’s age after 5 years = 36 + 5 = 41

Lata’s age after 5 years is ‘41’

Hence, “41” is the correct answer.

The pattern followed is,

(269, 278, 296) → 269 + 9 = 278, 278 + 18 = 296

Similarly,

Option 1 → (109, 118, 128) → 109 + 9 = 118, 118 + 10 = 128

Option 2 → (419, 430, 448) → 419 + 11 = 430, 430 + 18 = 448

Option 3 → (577, 586, 598) → 577 + 9 = 586, 586 + 12 = 598

Option 4 → (313, 322, 340) → 313 + 9 = 322, 322 + 18 = 340

‘(313, 322, 340)’ is related in the same way as the numbers in the given set.

Hence, “(313, 322, 340)” is the correct answer.

Concept:

When two faces are common in two positions of the same given dices then the remaining third face of the first dice will become the opposite pair of the remaining third face of the second dice.

Explanation:

Here the face 3 and 5 is common in both the dice.

so the remaining face in the first dice is 1 and the remaining face in the second dice is 6.

They will become the opposite pair, which means 1 will be opposite to 6.

‘1’ will be on the face opposite to the one showing ‘6’.

Conclusion:

Hence, “1” is the correct answer.

Interchanging ‘ + ’ and ‘-‘ and ‘6’ and ‘7’,

Option 1 :

72 + 76 – 67 = 83

148 – 67 = 83

81 is not equal to 83

Option 2 :

68 + 78 - 77 = 59

146 – 77 = 59

69 is not equal to 59

Option 3:

67 + 65 - 66 = 57

132 – 66 = 57

66 is not equal to 57

Option 4:

76 + 67 - 43 = 100

143 – 43 = 100

100 = 100

Hence, option 4 is the correct answer.

Medicine is a drug or other preparation for the treatment or prevention of disease.

Similarly,

Hunger is feeling or showing the need for food.

‘Hunger’ is related to the third word in the same way as the second word is related to the first word.

Hence, “hunger” is the correct answer.

The pattern followed is,

The symbols in the given image are rotating by 90⁰ and the symbols circle and diamond when facing north and south direction are painted.

In the first image, the circle symbol is facing north, then it is rotated anti – clockwise by 90⁰ in the second image and in the third image it is facing south, in the next image it is facing east.

In the first image, the diamond symbol is facing west, then it is rotated clockwise by 90⁰ in the second image and in the third image it is facing east, in the next image it is facing south.

In the first image, the ‘ + ’ symbol is facing south, then it is rotated anti - clockwise by 90⁰ in the second image and in the third image it is facing north, in the next image it is facing west.

The image which will come next in the series is,

Hence, option 3 is the correct answer.

The pattern followed is,

(1^st Number × 3^rd Number) – (3^rd Number) = 2^nd Number

For Column 1:

(6 × 8) – 8

48 – 8 = 40

For Column 2:

(21 × 25) – 25

525 – 25 = 500

Similarly,

For Column 3:

(14 × 7) – 7

98 – 7 = 91

Hence, “91” is the correct answer.

Concept:

1. We have to check the conclusions are 100% match with the statement. If the conclusion is 100% match with the given statement then the conclusion is true. If there is a 1% chance of not following the statement then the conclusion is considered to be false.

2. The possibility case can be considered to be "false" in "definite case".

3. In Possibility case, either "can" or "possible" word must be present.

Drawing the Venn diagram for the given statements,

Conclusion 1: Some animals are tigers → False (Possible but not definite)

Conclusion 2: No tiger is an animal → False (Possible but not definite)

But,

The given conclusions form a complementary pair.

Hence, “either conclusion 1 or conclusion 2” follow.

Note: 

Conditions of Either-or case:

1. The elements should be the same in both the statements.
2. Individually both the conclusions should be false.
3. One conclusion should be positive and one conclusion should be negative (Complementary pair)

The two complementary pairs are:

1. All + Some not

2. No + Some

Additional Information

The pattern followed is,

Hence, “107” is the correct answer.

Option 2 is the correct answer: 

• Gizzard helps Red worms in grinding their food.
• Red worms are more commonly known as red wrigglers.
• These are the earthworms employed in vermicomposting.
• Eisenia fetida is the scientific name of Redworms.
• The species is hermaphroditic (can produce gametes related to both males and females).
• The Cerebral Ganglion helps them sense moisture, Heat, Light, and Vibrations.
• These creatures have 5 hearts that regulate the flow of nutrients and oxygen.
• Their Pharynx sucks in the food that travels down to the esophagus, crop, and then to gizzard where even the hard soil particles are crushed.
• Thereafter intestines digest the food. Nutrients are absorbed and waste is excreted.
• Their excreta is used as fertilizer.

Option 4 is the correct answer: Sultan Qaboos Bin Said was the ruler of Oman.

• He ascended the throne in July 1970 after a coup and was assisted by the British.
• He succeeded his father, Said bin Taimur.
• He established a council of ministers and granted universal suffrage to the citizens of Oman.
• Under his reign, Oman joined the UN, Arab League and became a founding member of the Gulf Cooperation Council (GCC).
• He passed away on January 10, 2020, and his cousin Haitham Bin Tariq succeeded him.
• He is the longest-serving ruler of the Arab world.

OMAN:

• It is an Arab country and occupies the southeastern coast of the Arabian Peninsula.
• Capital: Muscat.
• Mount Shams is the highest Peak of Oman.
• It occupies a strategic position in strait of Hormuz that connects the Gulf of Oman and the Persian Gulf.
• Currency: Oman Rial.

The correct answer is Cynology.

Key Points

• The scientific study of domestic dogs is called Cynology.
• The Scientific name of Dog is Canis lupus.

Option 4 is the correct answer:

• Virat Kohli set this record in India v/s Bangladesh test series by scoring 204 runs.
• He made double centuries in test series against West Indies, New Zealand, England and Bangladesh consecutively.
• He broke the record of Sir Don Bradman and Rahul Dravid of double hundreds in three consecutive test series.
• Virat Kohli was honoured with Arjun Award, Padma Shri and Rajiv Gandhi Khel Ratna Award in 2013, 2017 and 2018 respectively.
• A.B. de Villiers holds the record for fastest hundred in ODI (in 31 balls against West Indies).
• Rohit Sharma holds the record for three double centuries in ODI.

Option 1 is the correct answer: Solid carbon dioxide is also known as Dry Ice.

The correct answer is option 2: 'An Area of Darkness' is written by VS Naipaul.

The correct answer is option 4: James Chadwick is accredited with the discovery of Neutron.

Key Points

• James Chadwick had discovered some new neutral particles in 1930 which were emitted out by the Beryllium nucleus after it was bombarded by alpha particles.
• Research was carried on and finally, the new neutral particle was confirmed in 1932.

Neutron:

• It is a constituent particle of the nucleus.
• It is a neutral particle i.e. it carries no charge.
• Symbol: 'n' or ₀n¹.

The correct answer is Visakhapatnam.

Key Points

• Araku Valley is a hill station in the Vishakhapatnam district of Andhra Pradesh.
• This tourist spot is present in the Ananthagiri Hills of Eastern Ghats.
• It is also inscribed as 'Ooty of Andhra'.
• The area is also exploited for Bauxite mining.
• Jindanghada peak, the highest peak of Andhra Pradesh and the Eastern Ghats also rises here.
• It is also famous for the well-known Borra caves.

Option 4 is the correct answer: Savithribai Phule belongs to Maharashtra.

• She was born on January 3, 1831, and was married to Jyotirao Phule.
• Her husband decided to educate her in order to elevate the status of women.
• She is a social reformer and worked a lot for women empowerment.
• After the completion of her education, she opened a girl's school at Vishrambag, Pune.
• She started teaching there and is known as the first female teacher of India.
• She died in 1897 off Plague while helping the people effected with Bubonic Plague epidemic.
• Her writings:

1. Kavya Phule.
2. Bavan Kashi Subodh Ratnakar.
3. Go, Get Education.

The correct answer is option 3: 

• Disney purchased the legendary studio of 21st Century Fox in March 2019 for $71.3 bn.
• Disney had purchased many studios and media companies earlier also. Following are some of those:
• Capital cities/ABC in 1996.
• Fox Family in 2001.
• Pixar in 2006.
• Marvel Entertainment in 2009.
• Lucasfilm in 2012.
• Bam tech in 2017.
• 21^st Century Fox in 2019.

Disney:

• It is a media company that was founded by Walt and Roy O. Disney in 1923.
• It is headquartered in California, USA.

The correct answer is option 4:

• Reserve Bank of India (RBI) is responsible for fixing Repo or Reverse Repo Rate.
• RBI regulates these rates as a part of its monetary policy.
• Monetary policy refers to the steps undertaken by the central bank to control the liquidity and supply of money in the market.
• Repo Rate: It is an Acronym for the Repurchasing Agreement Rate. It is the rate at which RBI lends money to other banks in the country for the short term.
• Reverse Repo Rate: When banks deposit their surplus funds with RBI for a short term, the rate then offered by RBI is called Reverse Repo Rate.

Reserve Bank of India (RBI):

• It was established on April 1, 1935, under the RBI Act 1934, but as a private bank.
• RBI was nationalized in 1949.
• It is the apex banking institute of India.

Option 4 is the correct answer: Vidya Balan played the leading lady in the film 'Mission Mangal'.

• Mission Mangal is a movie based on ISRO's mission to Mars.
• Akshay Kumar played the role of Rakesh Dhawan, the Mission Director.
• Vidya Balan played the role of Tara Shinde, the Project Director.

Mars Orbiter Mission (MOM):

• It is India's first and successful space mission to the planet Mars.
• Its success placed India in the elite club of countries that have reached Mars.
• India became the first country to do so in the very first step.
• MOM was launched from Satish Dhawan Space Centre, Shri Harikota using PSLV C-25.
• Its objectives were to map and explore the surface of Mars to study its atmosphere and effects of solar winds on it.

The correct answer is 40%.

• On February 24, 2020, through a notification of the Central Board of Indirect Taxes, all the lotteries were brought under the tax slab of 40%.
• All the lotteries whether State-run or with private ownership will now fall under this uniform tax rate.

Goods and Services Tax:

• It is an indirect tax that was introduced on 1^st July 2017.
• It subsumed many central and state indirect taxes.
• It is a destination-based tax.
• There are four tax slabs under GST viz. 0%, 5%, 18% and 40%.
• Some basic goods and services are exempted from GST.
• GST council is responsible for increasing and decreasing tax slabs and transferring subjects from one slab to another.

Trivia:

• Assam was the first state to ratify the GST bill (12^th August 2016).
• Kerala started the first state-run lottery in India (1967).

Option 4 is the correct answer:

• The femur is not a part of the human ear.

Image of Ear Diagram:

Important Points

The correct answer is option 2: MF Husain has portrayed a number of paintings depicting horses.

Maqbool Fida Husain (1915 - 2011):

• Popularly known as MF Husain, he is one of the greatest artists of the 20th century.
• He started his painting career in Zurich in 1952 through exhibitions.
• He was also entitled to 'Picasso of India' by Forbes magazine.
• In 1973 he was honoured with Padma Bhushan and with Padma Vibhushan in 1991.
• He had directed two National Award-winning movies, 'Through the Eyes of a Painter' and 'Meenakshi: A tale of three cities'. 'Gaj Gamini' was also directed by him.
• The Progressive Artist's Group was founded by him and his friends in 1947 at Bombay.
• In the last phase of his life, he accepted citizenship of Qatar amidst the controversies related to his paintings.

Option 3 is the correct answer:

• Sanchi was rediscovered after 600 years by Bengal Cavalry of Britishers in 1818.
• The discovery is attributed to General Henry Taylor.
• The town of Sanchi, the abode of one of the principal Buddhist sites is located in the state of Madhya Pradesh.
• The Buddhist monuments there were awarded the status of UNESCO World Heritage site in 1989.
• The Sanchi Stupa is the centre of attraction in the town.
• Its foundation was laid by King Ashoka.
• He builds a hemispherical mound over the relics of Buddha.
• Later expansion of Stupa took place during the time of the Shunga, the Satvahnas and the Gupta period.
• The victory of Chandragupta II has been carved on the railing of the Stupa as an inscription.

The correct answer is Karnataka

Key Points

• ​The ruins of the ancient city of Hampi is a historical site located in Karnataka.
• It is a UNESCO world heritage site and was granted that status in the year 1986.
• It was established as Vidyanagar by Harihara and Buka, the founders of the Sangama dynasty, in the memory of their guru Vidyaranya.
• Ancient temples, ruins of forts, and aquatic structures are the major attractions.
• Temples related to Hinduism as well as Buddhism are found here.
• Virupaksha temple, Hemakuta Hill temple, Vijay Vittal temple are the major Hindu temples.

Vijayanagar Empire (1336 - 1580):

• This empire flourished on the banks of River Tungabhadra.
• The Sangam, the Suluvas, the Tuluvas, and the Arivadu were the ruling dynasties of this empire.

Additional Information

​

The correct answer is option 2:

• Sir Thomas Roe visited the court of Emperor Jahangir in 1615 as an ambassador of King James I.
• He was able to get permission for trade and establish factories at Agra, Ahmedabad and Broach.

Option 1 is the correct answer: Shri Bhupesh Baghel is the current CM of Chhattisgarh.

Key Points

• He assumed office on 17 December 2018 and succeeded Raman Singh.
• He belongs to Indian National Congress and Patan Assembly constituency.

Important Points

Chhattisgarh:

• The state came into existence on November 1, 2000, after separation from Madhya Pradesh.
• The capital of Chhattisgarh is Raipur.
• The state ranks 9^th in terms of area and 16^th terms of population.
• State animal: Wild Water Buffalo.
• State bird: Common Hill Myna.

The correct answer is chess.

Key Points

• She has won three bronze medals at the Women's World Chess Championship of 2012, 2015, and 2017.
• She was honored with the Arjuna award in the year 2007 - 08.
• She also won the FIDE Women's Grand Prix in 2016.
• In 2019 she was conferred with Padma Shri.

Additional Information

Padma Shri:

• It is the fourth highest civilian award in India.
• It is one of the three Padma Awards that were constituted in the year 1954.
• This award is given to recognize the distinguished contribution of individuals in various fields like Art, Literature, Science, Social service, etc.
• The awardees are honored with a Sanad and a medallion.
• The President of India presents these awards.

The correct answer is Gotabaya Rajapaksa.

Key Points

• Gotabaya Rajapaksa is the 7^th President of Srilanka.
• He assumed the office on November 18, 2019.
• Former Defence Chief of Sri Lanka Gotabaya Rajapaksa contested elections as a candidate of the Sinhalese Buddhist Nationalist Party.
• He succeeded Maithiripala Srisena as President.

Additional Information

• Sri Lanka:
• It is an island country located in the Indian Ocean.
• President: Ranil Wickremesinghe.
• Capital: Shri Jayawardenepura Kotte.
• Currency: Sri Lankan Rupee.
• Major Religion: Buddhism.
• Highest Peak: Mount Pedro.

The correct answer is Option 4: Prime Minister Narendra Modi inaugurated the Kartarpur Corridor from India and from Pakistan by his counterpart, Imran khan.

• It is a 4.5 km long highway that connects Dera Baba Nanak shrine in India with Shri Darbar Sahib Kartarpur in Pakistan.
• Sikh devotees can access the Holy shrine in Pakistan without a visa through this corridor.
• Kartarpur Sahib was founded by the first Sikh guru in 1504.
• Sikhs could informally access the site till 1965 only.
• In the aftermath of the Indo-Pak war of 1965, the border regulations were made strict.
• The idea of establishing such a corridor was mooted during the tenure of Prime Minister Atal Bihari Vajpayee.
• It was finally inaugurated on the 550^th birth anniversary of Guru Nanak Dev in November 2019.
• Mr. Modi also compared this inauguration with the Fall of Berlin Wall.

Important Points

• Shehbaz Sharif is the current Prime Minister of Pakistan.

Option 3 is the correct answer:

• World Food Programme is a branch of the United Nations and is based in Rome, Italy.
• It was established in 1961 and aims at eradicating world hunger aiding people with food assistance during a humanitarian crisis.
• It is a member of the United Nations Development Programme.
• Structure:  
• It is governed by representatives from 36 member states of the UN or FAO.
• David Beasley is the current executive director of WFP and heads it.
• In addition, there is one deputy executive and three assistant executive directors.
• It works in partnership with various Governments, NGOs and private entities.
  

The correct answer is option 3:

• 2019 Sahitya Akademi Award was accorded to 'An Era of Darkness: The British Empire in India' authored by Shashi Tharoor.
• This book was also published in the UK by the name of 'Inglorious Empire: What British did to India'.
• He is a Member of Parliament from the Indian National Congress and represents Thiruvananthpuram constituency.
• Other bestsellers:

1. Why I am a Hindu.
2. Paradoxical Prime Minister.

Option 2 is the correct answer: ​Kolathunadu, Valluvanad, and Thekkumkoor were the feudal kingdoms of Kerela.

Shortcut Trick

Difference in profit/loss percentages = 20% − (−10%) = 30%.

Given that 30% of Cost Price (CP) = Rs. 332.

Multiplier for Original Selling Price (SP) at 10% loss = 90%.

Since 30% → 332, then 90% → 332 × 3 = 996.

∴ The correct answer is Rs. 996.

Alternate Method

Given: Initial loss = 10%, New profit = 20%, Price increase = Rs. 332.

Formulas: SP = CP × (100 ± P/L%)/100 | Profit = SP − CP.

⇒ Let the Cost Price (CP) be 100 units.

⇒ Original Selling Price (SP₁) = 100 − 10 = 90 units.

⇒ New Selling Price (SP₂) = 100 ± 20 = 120 units.

⇒ Difference (SP₂ − SP₁) = 120 − 90 = 30 units.

⇒ According to question, 30 units = Rs. 332.

⇒ 1 unit = 332 ÷ 30.

⇒ Original SP (90 units) = (332 ÷ 30) × 90 = 332 × 3 = Rs. 996.

∴ The correct answer is Rs. 996.

Additional Information

Base for Profit/Loss

Unless stated otherwise, Profit and Loss percentages are always calculated on the Cost Price of the article.

Percentage Gap Method

If an article is sold at x% loss and then at y% profit, the total difference in SP is represented by (x + y)% of the CP.

Calculation:

Decreasing percentage of type car D in 2017 with reference to 2016 = [(38 - 22)/38] × 100 = (16/38) × 100 = 42.1%

Decreasing percentage of type car C in 2017 with reference to 2016 = (44 - 40)/44 × 100 = (4/44) × 100 = 9.09%

Decreasing percentage of type car A in 2017 with reference to 2016 = (36 - 12)/36 × 100 = (24/36) × 100 = 66.67%

Decreasing percentage of type car E in 2017 with reference to 2016 = (50 - 28)/50 × 100 = (22/50) × 100 = 44%

∴ The percentage decrease in the production of type A car in 2017, with reference to 2016, was the maximum

Shortcut Trick

Interest for 2 years = 4644 − 4300 = ₹344

Interest rate per year = (344 ÷ 2) ÷ 4300 × 100 = 4%

Total interest for 5 years = 4% × 5 = 20%

Amount = 100% + 20% = 120% of Principal

Principal = (10104 ÷ 120) × 100 = ₹8,420

∴ The correct answer is ₹8,420.

Alternate Method

Given:

First case: Principal (P₁) = ₹4,300, Amount (A₁) = ₹4,644, Time (T₁) = 2 years.

Second case: Amount (A₂) = ₹10,104, Time (T₂) = 5 years, Rate (R) is same.

Formula Used:

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

Amount (A) = P + SI = P × [1 + (R × T) ÷ 100]

Calculations:

⇒ Interest (SI₁) = A₁ − P₁ = 4644 − 4300 = ₹344

⇒ R = (SI₁ × 100) ÷ (P₁ × T₁)

⇒ R = (344 × 100) ÷ (4300 × 2) = 344 ÷ 86 = 4%

⇒ Now for the second case, let the Principal be P₂.

⇒ 10104 = P₂ × [1 + (4 × 5) ÷ 100]

⇒ 10104 = P₂ × [1 + 20 ÷ 100] = P₂ × 1.2

⇒ P₂ = 10104 ÷ 1.2 = 101040 ÷ 12

⇒ P₂ = ₹8,420

∴ The correct answer is ₹8,420.

Additional Information

Simple Interest Property

In Simple Interest, the interest remains constant for every year as it is always calculated on the original Principal amount.

Effective Rate of Interest

The total interest percentage for 'T' years at 'R%' rate is simply (R × T)%. This is a very useful shortcut for solving Amount-related problems.

Relationship between A and P

Amount = Principal × [(100 + RT) ÷ 100]. This direct relation helps in finding the Principal when the Amount and Rate-Time product are known.

Total students = 640

Ratio of boys to girls = 5 : 3

Number of boys = [5/8] × 640 = 400

Number of girls = 640 - 400 = 240

Let x boys admitted in the school.

According to the question

(400 + x)/(240 + 30) = 14/9

⇒ 400 + x = [14/9] × 270

⇒ x = 420 - 400

⇒ x = 20

∴ 20 students admitted in the school.

Formula used:

• (a + b)² = a² + 2ab + b²
• (a - b)2 = a2 - 2ab + b2
• sin2 θ  + cos2 θ = 1

Calculation:

Given, x = 4 cos A + 5 sin A and y = 4 sin A - 5 cos A

Hence, x² + y² = (4 cos A + 5 sin A)² + (4 sin A - 5 cos A)²

⇒ 16 cos² A + 25 sin² A + 40 cos A sinA + 16 sin² A + 25 cos²A - 40 sin A cos A

⇒ 16 (sin² A + cos² A) + 25 (sin² A + cos² A)

⇒ 16 + 25

⇒ 41

Radius of the circular garden r = 42 m

Circumference of circular garden = 2 πr = 2 × (22/7) × 42 = 264 m

1 round cover the distance = circumference of the circular garden = 264 m

8 round cover the distance = 8 × 264 = 2112 m

Short trick:

Answer divisible by 11 and 8 also. Only option is divisible by 11 and 8 is 2112.

Given:

Area of ΔABC = 44 cm²

BD = CD

AE = BE

Concept used:

The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it.

If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are similar.

The ratio of areas of two similar triangles is proportional to the squares of the corresponding sides of both triangles.

Calculation:

According to the concept,

DE ∥ AC, and AC = 1/2 × DE

Let BC = 2 unit, and BD = 1 unit

Area of ΔBDE/Area of ΔBCA = (BD/BC)²

⇒ Area of ΔBDE/44 = (1/2)²

⇒ Area of ΔBDE = (1/4) × 44 = 11 cm2

∴ The area of ΔBDE is 11 cm²

x^2a = y^2b = z^2c ≠ 0

Let x^2a = y^2b = z^2c = k, then

x = k^1/2a, y = k^1/2b, z = k^1/2c

Now,

x² = yz

x × x = y × z

k^1/2a × k^1/2a = k^1/2b × k^1/2c

k^{(1/2a + 1/2a)} = k^{(1/2b + 1/2c)}

Comparing on power

1/2a + 1/2a = 1/2b + 1/2c

⇒ 2/2a = (c + b)/2bc

⇒ 1/a = (c + b)/2bc

⇒ 2bc = ac + ab

Now,

$\frac{{ab + bc + ca}}{{bc}}$

⇒ (2bc + bc)/bc

⇒ 3bc/bc

⇒ 3

If we take x = y = z and a = b = c but not equal to zero, take any natural number, but not zero.

x² = yz is satisfied with this condition.

Then we get 

(ab + bc + ca)/bc

⇒ 3bc/bc

⇒ 3

Let, total work = LCM of (24, 15 and 12) = 120

Hence, efficiency of A = 5

Efficiency of B = 8

Efficiency of C = 10

Work done by B and C in 3 days = (8 + 10) × 3 = 54

Remaining work = 120 - 54 = 66

∴ Remaining work done by A in = 66/5 = $13\frac{1}{5}$ days.

As we know,

Volume of cylinder = πr²h

Ratio of radius of 2 cylinder, r₁ : r₂ = 3 : 4

Ratio of heights of 2 cylinder, h₁ : h₂ = 4 : 9

Ratio of volume of two cylinder, V1 : V2 = π(r₁)² h₁ : π(r₂)² h₂ = 3² × 4 : 4² × 9 = 1 : 4

Shortcut Trick

Speed of train = (Difference in distance) ÷ (Difference in time)

Difference in distance = Bridge length = 170 m

Difference in time = 36 − 12 = 24 s

Speed = 170 ÷ 24 m/s = (170 ÷ 24) × (18 ÷ 5) km/h

Speed = 25.5 km/h

∴ The correct answer is 25.5 km/h.

Alternate Method

Given: Time to cross pole = 12 s, Time to cross bridge = 36 s, Length of bridge = 170 m.

Formula Used: Speed = Distance ÷ Time; Conversion: m/s × 18/5 = km/h

Train (L)

Pole Case 1: Dist = L | Time = 12 s

Train (L) Bridge (170m) Case 2: Dist = L + 170 | Time = 36 s

⇒ Let the length of the train be L meters and speed be S m/s.

⇒ For the pole: S = L ÷ 12 → (i)

⇒ For the bridge: S = (L + 170) ÷ 36 → (ii)

⇒ Equating (i) and (ii): L ÷ 12 = (L + 170) ÷ 36

⇒ 3L = L + 170

⇒ 2L = 170 ⇒ L = 85 m

⇒ Now, S = 85 ÷ 12 m/s

⇒ Speed in km/h = (85 ÷ 12) × (18 ÷ 5)

⇒ Speed = 17 × (3 ÷ 2) = 17 × 1.5 = 25.5 km/h

∴ The correct answer is 25.5 km/h.

Additional Information

Unit Conversion

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

Crossing stationary objects

When a train crosses a pole or man, distance = length of train. When it crosses a bridge, platform, or another stationary train, distance = (length of train + length of object).

Relative Speed

If two objects move in the same direction, relative speed = S₁ − S₂. If they move in opposite directions, relative speed = S₁ + S₂.

Total production of car in 2012 = 120

Total production of car in 2016 = 180

∴ The percentage increase of total car in 2016 over 2012 = [(180 - 120)/120] × 100 = 50%

Total production of total car in 2015 = 100

Hence, 20% of 100 = 20

In the year 2015, E type of car constitutes exactly 20% of the total number of cars produced that year.

Short trick:

Area increased by = 40 - 20 - [(40 × 20)/100] = 20 - 8 = 12%

Detailed method:

Let the length and breadth of the rectangle be 10 unit each.

Area of the rectangle = lb = 10 × 10 = 100 sq. unit

New increased length = 10 × (40/100) = 14 unit

New decreased length = 10 × (80/100) = 8 unit

New area of the rectangle = 14 × 8 = 112

Area increased by = 112 - 100 = 12

∴ Area increased by (in %) = (12/100) × 100 = 12%

Shortcut Trick

Ratio of Sum of first 5 numbers to the 6^th number = 7 : 1

Total ratio parts = 7 + 1 = 8 parts

Total sum of 6 numbers = Average × 6 = 136 × 6

Value of 1 part (6^th number) = (136 × 6) ÷ 8 = 17 × 6 = 102

∴ The correct answer is 102.

Alternate Method

Given: Average of 6 numbers = 136, Sum of first 5 = 7 × 6^th number.

Formula Used: Total Sum = Average × Number of items

⇒ Let the 6^th number be x.

⇒ Sum of the first 5 numbers = 7x.

⇒ Total sum of all 6 numbers = 7x + x = 8x.

⇒ According to the average formula, 8x = 136 × 6.

⇒ 8x = 816

⇒ x = 816 ÷ 8

⇒ x = 102

∴ The correct answer is 102.

Additional Information

Basic Average Formula

The average of n numbers is calculated as (Sum of all n numbers) ÷ n. Conversely, Sum = Average × n.

Weighted Average

If two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the combined average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Effect of Change

If every number in a set is increased, decreased, multiplied, or divided by a constant k, the new average will also be increased, decreased, multiplied, or divided by k respectively.

2(1 + tan A) (1 + tan B)

If A + B = 45°

Put A = 45° and B = 0°

2 (1 + tan 45°) (1 + tan 0°)

⇒ 2 (1 + 1) (1 + 0)

⇒ 2 × 2 × 1

⇒ 4

Detailed solution:

Taking tan both sides:

tan(A + B) = tan 45°  

(tan A + tan B)/(1 – tan A tan B) = 1

tan A + tan B = 1 – tan A tan B

tan A + tan B + tan A tan B = 1

adding "1" on both sides

1+ tan A + tan B + tan A tan B = 1 + 1

(1 + tan A) + tan B(1 + tan A) = 2

(1 + tan A)(1 + tan B) = 2 

∴ 2 × (1 + tan A)(1 + tan B) = 2 × 2 = 4

Total production of cars in 2013 and 2014 = 130 + 170 = 300

Hence, 25% of 300 = 300 × 25/100 = 75

Production of car D in 2013 and 2014 are = 40 + 35 = 75

from the following figure.

∠AOB = 110° and ∠AOC = 130°

As we know,

∠AOB + ∠AOC + ∠BOC = 360°

∠BOC = 360° - 110° - 130° = 120°

∠BAC = ∠BOC/2

∴ ∠BAC = 120°/2 = 60°

Shortcut Trick

Given 6 tan A = 5 ⇒ tan A = 5/6.

The expression (8 sin A − 4 cos A) / (cos A + 2 sin A) can be converted to tan A by dividing both numerator and denominator by cos A.

Converted expression = (8 tan A − 4) / (1 + 2 tan A).

Substitute tan A = 5/6: (8 × 5/6 − 4) / (1 + 2 × 5/6) = (20/3 − 4) / (1 + 5/3) = (8/3) / (8/3) = 1.

∴ The correct answer is 1.

Alternate Method

Given: 6 tan A = 5 in First Quadrant (all ratios positive).

⇒ tan A = 5/6 = Perpendicular / Base.

⇒ sin A = 5 / √(5² + 6²) = 5 / √61

⇒ cos A = 6 / √(5² + 6²) = 6 / √61

Calculation:

⇒ Value = [8(5/√61) − 4(6/√61)] / [6/√61 + 2(5/√61)]

⇒ Value = [(40 − 24) / √61] / [(6 + 10) / √61]

⇒ Value = 16 / 16

⇒ Value = 1

∴ The correct answer is 1.

Additional Information

Trigonometric Ratios

tan A = sin A / cos A. This identity is extremely useful for simplifying expressions involving both sine and cosine into a single variable.

Quadrant Rules (ASTC)

In the First Quadrant (0° to 90°), all trigonometric ratios (sin, cos, tan, etc.) are positive.

Pythagorean Triplets

For any right-angled triangle, h² = p² + b². Common triplets include (3,4,5), (5,12,13), and (8,15,17).

Shortcut Trick

Use the direct relationship formula: CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%).

Ratio CP : MP = (100 − 28) : (100 + 12) = 72 : 112.

Simplify the ratio: 72 : 112 = 9 : 14.

Given MP = Rs. 224, so 14 units = 224 ⇒ 1 unit = 16.

Therefore, CP = 9 × 16 = Rs. 144.

∴ The correct answer is Rs. 144.

Alternate Method

Given: Marked Price (MP) = Rs. 224, Discount = 28%, Profit = 12%.

Formulas: SP = MP × (100 − D%) ÷ 100 | CP = SP × 100 ÷ (100 + P%).

⇒ Selling Price (SP) = 224 × (100 − 28) ÷ 100

⇒ SP = 224 × 0.72 = Rs. 161.28

⇒ Cost Price (CP) = 161.28 × 100 ÷ (100 + 12)

⇒ CP = 161.28 ÷ 1.12 = Rs. 144

∴ The correct answer is Rs. 144.

Additional Information

Marked Price & Discount

Marked price is the price displayed on the tag, and the discount is always calculated on this price to find the Selling Price.

Relation between CP and MP

CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%). This is the most efficient formula for problems involving both discount and gain.

Given:

$\frac{{42 - 12 \times 3 + 8 \div 2 + 15}}{{8 \times 2 - 4 + 9 \div 3}}$

Concept used:

Calculation:

According to the question

$\frac{{42 + 12 \div 3 - 8 \times 2 - 15}}{{8 \div 2 + 4 - 9 \times 3}}$

$\Rightarrow {\rm{;}}\frac{{42 + 4 - 16 - 15}}{{4 + 4 - 27}}$

⇒ -(15/19)

Shortcut Trick

x - y = 4 and xy = 45

Put x = 9 and y = 5

x³ - y³

⇒ 9³ - 5³

⇒ 729 - 125

⇒ 604

Detailed solution:

x - y = 4 and xy = 45

(x³ - y³) = (x - y) [(x - y)² + 3xy]

x³ - y³ = 4 [4² + 3 × 45] [Hint: Answer will be divisible by 4, only 1 option 604 divisible by 4.]

x³ - y³ = 4 [16 + 135]

x³ - y³ = 4 × 151 = 604

Shortcut Trick

Ratio of sides AN : AC = 4 : (4 + 5) = 4 : 9.

Ratio of areas ΔMAN : ΔABC = 4² : 9² = 16 : 81.

Ratio of Area(ΔMAN) : Area(quadrilateral MBCN) = 16 : (81 − 16) = 16 : 65.

Given 65 units = 130 cm² ⇒ 1 unit = 2 cm².

Area of ΔMAN = 16 × 2 = 32 cm².

∴ The correct answer is 32 cm².

Alternate Method

Given: MN ∥ BC, Area(MBCN) = 130 cm², and AN : NC = 4 : 5.

Formula Used: If two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides.

⇒ In ΔABC, MN ∥ BC, so ΔMAN ∼ ΔABC (by AA similarity).

⇒ Corresponding sides ratio AN / AC = AN / (AN + NC) = 4 / (4 + 5) = 4 / 9.

⇒ Area(ΔMAN) / Area(ΔABC) = (AN / AC)² = (4 / 9)² = 16 / 81.

⇒ Let Area(ΔMAN) = 16k and Area(ΔABC) = 81k.

⇒ Area(quadrilateral MBCN) = Area(ΔABC) − Area(ΔMAN) = 81k − 16k = 65k.

⇒ Given 65k = 130 ⇒ k = 130 / 65 = 2.

⇒ Area of ΔMAN = 16k = 16 × 2 = 32 cm².

∴ The correct answer is 32 cm².

Additional Information

Area of Similar Triangles

If two triangles are similar, the ratio of their areas is equal to the square of the ratio of any two corresponding sides, altitudes, or medians.

Thales Theorem (Basic Proportionality Theorem)

If a line is drawn parallel to one side of a triangle to intersect the other two sides, then the other two sides are divided in the same ratio.

Similarity via Parallel Lines

Any line segment drawn parallel to the base of a triangle creates a smaller triangle that is similar to the original larger triangle.

Divisibility rule of 8 = A number divisible by 8 if its last three digits are divisible by 8

If the number 1005x4 is divisible by 8, then its last digit 5x4 also divisible by 8

504 is divisible by 8 so the number 100504 is also divisible by 8.

Hence, 0 will be the correct answer.

x + y = 8       ---(1)

y + z = 13       ---(2)

z + x = 17       ---(3)

from equation (1)

y = 8 - x

Put y = 8 - x in equation (2)

8 - x + z = 13

z - x = 13 - 8

z - x = 5       ---(4)

From equation (3) and equation (4)

z = 11 and x = 6

Put z = 11 in equation (2)

y + 11 = 13

y = 2

Now,

x²/yz

⇒ (6 × 6)/(2 × 11)

⇒ 18/11

The correct answer is option 1

Key Points

• Communication is something that can be achieved by willful and aware decisions and thus 'conscious' is the answer.
• Efforts cannot be deemed as important or unimportant.
• 'Unclear' and 'contradictory' efforts cannot achieve anything and thus option 3 and 4 cannot be the answer.
• Thus, the correct answer is option 1.

The correct answer is option 4 i.e. arrival

Exodus: Refers to a mass departure of people.

Arrival: Refers to the coming of someone somewhere.

For e.g., My daughter promptly awaited the arrival of her father

Thus, it is clear that exodus and arrival are opposite words.

Let's look at the meaning of other words:

• Exit: Refers to the act of leaving from somewhere
• Departure: Refers to the act of leaving from somewhere, especially in order to reach somewhere else
• Refund: Refers to a certain amount being paid back to someone who has been wronged

Thus, options 1, 2 and 3 are incorrect

The correct answer is render

Key Points

• One cannot 'exert' an action onto homeless and physically disabled people (बेघर और शारीरिक रूप से अक्षम लोगों पर कोई कार्रवाई नहीं कर सकता)
• One cannot 'donate' an action to homeless and disabled people (बेघर और विकलांग लोगों को कोई कार्रवाई 'दान' नहीं कर सकता)
• One cannot 'contribute' an action to homeless and physically disabled people (बेघर और शारीरिक रूप से अक्षम लोगों की कार्रवाई में कोई 'योगदान' नहीं दे सकता)
• Render: Refers to the act of providing something (कुछ प्रदान करने के कार्य को संदर्भित करता है)
• The sentence refers to doing something for homeless and physically disabled people.
• Thus, the correct answer is option 3.
• Thus, the complete sentence is: We must render help to the homeless and physically disabled people.

The correct answer is option 1 i.e. active

Quiescent: Refers to a period of inactivity or being dormant. (निष्क्रियता या निष्क्रिय होने की अवधि को संदर्भित करता है)

Active: Refers to someone who is willing to engage in physical pursuits. (किसी ऐसे व्यक्ति को संदर्भित करता है जो शारीरिक गतिविधियों में संलग्न होने को तैयार है)

For e.g. The health scare left Sania very active.

Thus, it is clear that quiescent and active are opposite words

Let's look at the meaning of other words:

• Peaceful: Refers to something that is free from disturbance. (किसी ऐसी चीज को संदर्भित करता है जो अशांति से मुक्त हो)
• Dejected: Refers to someone who is sad and depressed. (किसी ऐसे व्यक्ति को संदर्भित करता है जो उदास है)
• Indifferent: Refers to someone who has no particular interest or concern. (किसी ऐसे व्यक्ति को संदर्भित करता है जिसकी कोई विशेष रुचि या चिंता नहीं है)

Thus, options 2, 3 and 4 are incorrect

The correct answer is have been selected

Key Points

• 'has been selected' should be there in place of 'have been selected'
• The 'one of' is a singular term and generally used to talk about a noun or a pronoun.
• The noun or a pronoun used after the phrase “one of” is always in the plural form.
• The helping verb will always be in the singular form, as the helping verb agrees with “one of” and not with the plural noun in the sentence.
  

Example: One of the students was selected to visit NASA.

• Thus, the correct sentence is: One of the boys from our school has been selected for National Badminton Championship

The correct answer is option 4 i.e. a difficult problem

'A hard nut to crack' refers to a problem that is hard to solve. 

Thus, the correct answer is option 4.

The correct answer is No improvement

Key Points

• ​When subjects are connected with as well as, together with, along with, including, excluding, like, unlike, etc., the verb must agree with the first subject.
  

Example: 

• Maya as well as her friends is studying for the test.
• As well as means ‘in addition to’.
• We can combine two sentences using as well as.

Study the example given below.

• Trees give us fruits. They also give us shade.
• We can combine these two sentences using as well as.
• Trees give us fruits as well as shade.
• In the given sentence, the first subject is 'the captain' which is singular, so a singular verb should be used.

The correct answer is option 4 i.e. exhibit

Key Points

• Exhibit-  publicly display (a work of art or item of interest) in an art gallery or museum or at a trade fair. (किसी आर्ट गैलरी या संग्रहालय या व्यापार मेले में सार्वजनिक रूप से प्रदर्शित (कला का एक काम या रुचि की वस्तु)।)
• For e.g.- The gallery is exhibiting his paintings and watercolors.

Additional Information

• Exhale- to breathe out; emit (साँस छोड़ना)
• Exhaust-  fatigue greatly  (अत्यधिक थकान होना)
• Extract-  to remove or take out something (किसी चीज़ को निकालना)

The correct answer is option 4 i.e. fragile

• The sentence refers to a glass table, meaning it is made of glass.
• Option 1 cannot be correct because 'ductile' refers to something that can be made into a thin wire which is not possible for glass
• Option 2 cannot be the answer as 'volatile' refers to the quality of evaporating easily at lower temperatures, a quality that glass tables do not have
• Option 3 cannot be the answer because 'frugal' refers to the human quality of being economical, something glass cannot do.
• Thus, the correct answer is option 4.

The correct answer is option 1 i.e. BDCA

The sentence begins with an introduction to the passage - B which talks about the general human tendency one has to find faults in government policies. Then comes sentence D which talks about how people who find fault condemn the policymakers. Then comes option C which talks about how the people find faults - blaming the government for their slow progress and how they expect miracles. The final sentence A talks about these people ignore the truth and the progress.

Thus, the correct answer is option 1.

Here the correct answer is Leave without any intimation.

Key Points:-

• Let's look at the meaning of the given idiom:-
• To take French leave - absence from work or duty without permission.
• For Example - The caretaker had taken French leave.
• Thus, the correct answer is option 1.

Additional Information

• 'To take French leave' refers to an 18th Century custom where guests at a party would leave without saying goodbye to the host/hostess, thus leaving without any intimation.

The correct answer is option 1 

Key Points

• If you say that something is vital, you mean that it is necessary or very important.
• The sentence refers to communication playing a role in the development of a man, it is not a living thing thus cannot be 'lifeless', it is not something that can have the 'total' responsibility of developing a man and there is no mention of any other variable, so the comparative word 'better' cannot be used.
• Thus, the correct answer is option 1.

The correct answer is option 4 

Key Points

• The sentence refers to skills - reading, writing, and speaking and these skills are represented by the noun 'ability'
• The 'incapacity' to do read, write and speak cannot be the means to effective communication
• 'Variety' refers to different choices and there are no choices in reading, writing, and speaking
• 'Agility' refers to the speed and cannot be used to refer to 'speaking'
• Thus, the correct answer is option 4.

The correct answer is option 3 

Key Points

• A barrier is something such as a rule, law, or policy that makes it difficult or impossible for something to happen or be achieved.
  

Example: Duties and taxes are the most obvious barrier to free trade

• You use to to indicate who or what an action or a feeling is directed towards.
• If something comes from a particular person or thing, or if you get something from them, they give it to you or they are the source of it.
• If you are against something such as a plan, policy, or system, you think it is wrong, bad, or stupid.
• Barriers cannot be against something and thus the correct answer is option 3.

The correct answer is I can swim

Key Points

• 'I could swim' should be there in place of 'I can swim'
• We use can and can't to talk about the ability to do something at a specific time in the present or future.
  

Example: I can see you.

                Help! I can't breathe.

• We use could and couldn't to talk about the past:
  

Examples: She could speak several languages.

                   They couldn't dance very well.

• Since we are talking about past ability, we will use 'could'.

Thus, the correct sentence is: I could swim very fast when I was only five.