SSC CPO Tier- I Previous Year Paper (Held On: 13 December 2019 Shift 1)

Placing the signs and using BODMAS rule,

Option 1 → + ÷ – =

(157 + 13) ÷ 36 – 1 = 5

170 ÷ 36 – 1 = 5

4. 72 – 1 is not equal to 5

Option 2 → – ÷ + =

(157 - 13) ÷ 36 + 1 = 5

144 ÷ 36 + 1 = 5

4 + 1 = 5

5 = 5

Option 3 → + – ÷ =

(157 + 13) – 36 ÷ 1 = 5

170 – 36 ÷ 1 = 5

170 – 36 is not equal to 5

Option 4 → ÷ – + =

(157 ÷ 13) – 36 + 1 = 5

12. 07 – 36 + 1 = 5
13. 07 – 36 is not equal to 5

Hence, option 2 is the correct answer.

Vowels are A, E, I, O and U.

Here they are represented as,

A → 5, E → 4, I → 3, O → 2 and U → 1

The pattern followed is,

Similarly,

Hence, “I4O5G32M” is the correct answer.

According to the given information, codes for different letters are,

HALOGENS is written as,

HALOGENS → LOANSGEH

Hence, “LOANSGEH”is the correct answer.

Hackle comes first.

It is followed by Heart.

Heart is followed by Height.

Height is followed by Heist.

Heist is followed by Higher.

The correct dictionary order is,

Hackle (4) → Heart (3) → Height (2) → Heist (1) → Higher (5)

Hence, option 1 is the correct answer.

The pattern followed is,

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

Similarly,

Option 1 → Barometer is an instrument used to measure pressure, not depth.

Option 2 → Seismograph is an instrument used to detect and record earthquakes.

Option 3 → Scale is an instrument used to measure or compare level of something, not current.

Option 4 → Odometer is an instrument used to measure distance travelled by a wheeled vehicle, not pressure.

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

Hence, “Seismograph : Earthquake” is the correct answer.

According to the given diagram,

Number of MBA’s = 25 + 12 + 11 + 5 + 3 + 7 = 63

The shaded part represents male employees who are computer experts, but not engineers = 11.

Hence, “63, 11” is the correct answer.

The given figure is embedded in,

Hence, option 4 is the correct answer.

According to the given diagram,

‘Square’ will be opposite to ‘hexagon’.

‘Triangle’ will be opposite to ‘rhombus’.

And,

The symbol that will be opposite to ‘☆’ is

Hence, option 1 is the correct answer.

The pattern followed is,

The symbols in the given image are rotating in clock – wise direction.

The image which will come next in the series is,

Hence, option 2 is the correct answer.

 Select the option that can replace the question mark (?) in the following series.

The pattern followed is,

The symbols are rotating in clock – wise direction with an addition of new symbol in every image.

The image which will come next in the series is,

Hence, option 3 is the correct answer.

Table, Stationery and Carpet are three individual things.

The correct Venn diagram representation is,

Hence, option 1 is the correct answer.

The correct mirror image of the given combination when the mirror is held at the right side is,

Hence, option 3 is the correct answer.

Drawing diagram according to the given information, 

Vimla is ’30 m, east’ with reference to her home.

Hence, “30 m, east” is the correct answer.

By decoding given information,

Using BODMAS rule,

25 × 2 - 32 ÷ 8 + 4

= 25 × 2 – 4 + 4

= 50 – 4 + 4

= 50

Hence, “50” is the correct answer.

The pattern followed is,

Similarly,

Hence, “15-23-7-21-23-15” is the correct answer.

The paper when unfolded looks like, 

Hence, option 3 is the correct answer.

The option that is embedded in the given figure is,

Hence, option 2 is the correct answer.

The logic follows here is:

Logic: (Multiplication of digits of 1st number) + 1 = 2nd number.

Now,

For, 78 - 57 

→ (7 × 8) + 1

→ 56 + 1 = 57.

Similarly, for 45 - 21 

→ (4 × 5) + 1

→ 20 + 1 = 21.

Hence, the correct answer is "Option 3".

Alternate Method

The pattern followed is,

78 and 57 are divisible by 3.

Similarly,

Option 1 → 35 and 19 are not divisible by 3

Option 2 → 67 is not divisible by 3, 42 is divisible by 3

Option 3 → 45 and 21 are divisible by 3

Option 4 → 24 is divisible by 3, 19 is not divisible by 3

’45 : 21’ share the same relationship as that shared by the given pair of numbers.

Hence, “45 : 21” is the correct answer.

The pattern followed is,

(1^st term)² + (2^nd term)² + (4^th term)² = 3^rd term

For row 1 :

3² + 2² + 5² = 38

For row 2 :

5² + 3² + 4² = 50

For row 3 :

7² + 1² + 2² = 54

Hence, “50” is the correct answer.

The number of triangles in the given figure are,

Hence, “15” is the correct answer.

Homo Sapiens is the scientific name of humans.

Homo Sapiens can be singers as well as Cricketers.

The correct Venn diagram representation is, 

Hence, option 2 is the correct answer.

The pattern followed is,

Similarly,

Hence, “IBONUCALSR “ is the correct answer.

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

Hence, option 4 is the correct answer.

Trillion comes highest in the order.

It is followed by Billion.

Billion is followed by Million.

Million is followed by Thousand.

Thousand is followed by Hundred.

The correct order is,

Trillion (2) → Billion (1) → Million (4) → Thousand (5) → Hundred (3)

Hence, option 4 is the correct answer.

The pattern followed is,

The symbols ‘×’ and ‘0’ are rotated anti – clockwise.

The symbol ‘>’ is also rotated clock – wise and is replaced with a new symbol in every image.

The image which will come next in the series is,

Hence, option 4 is the correct answer.

1: This follows, because it is given in the statement that students are studying, so that

they could pass in the examination.

Conclusion 2: This does not follow, because there is nothing mentioned about teachers in the

statement.

Hence, “only conclusion 1” follow.

Given:

A = 1, B = 3, C = 5, D = 7, E = 9, F = 11, G = 13, H = 15, I = 17, J = 19, K = 21, L = 23, M = 25, N = 27, O = 29, P =31, Q = 33, R =35, S = 37, T = 39, U = 41, V = 43, W = 45, X = 47, Y = 49, Z = 51

The total value of the letters of the word CARDINAL is,

CARDINAL → 5 + 1 + 35 + 7 + 17 + 27 + 1 + 23 = 116

Hence, “116” is the correct answer.

Drawing the Venn diagram, 

Conclusion 1 : Some éclairs are toffees → True (This is definitely true)

Conclusion 2 : Some éclairs are chocolates → True (This is definitely true)

Hence, “both conclusions 1 and 2” follow.

The pattern followed is,

3rd number + 22 = 2nd number

2nd number + 33 = 1st number

For (143, 110, 88)

2nd number = 88 + 22 = 110,

1st number = 110 + 33 = 143

Similarly,

Option 1 → (69, 36, 14)

2nd number = 14 + 22 = 36,

1st number = 36 + 33 = 69

Option 2 → (61, 28, 6)

2nd number = 6 + 22 = 28,

1st number = 28 + 33 = 61

Option 3 → (114, 82, 60)

2nd number = 60 + 22 = 82,

1st number = 82 + 33 = 115 ≠ 114

Option 4 → (123, 90, 68)

2nd number = 68 + 22 = 90,

1st number = 90 + 33 = 123

All follow the same pattern, except ‘(114, 82, 60)’

Hence, “(114, 82, 60)” is not related in the same way as are the numbers in the given set.

The pattern followed is,

Hence, “149” is the correct answer.

The pattern followed is,

Hence, “22” is the correct answer.

Son is a male.

And,

Daughter is a female.

Similarly,

Reindeer is a male deer found in the tundra regions.

And,

Doe is a female deer.

‘Doe’ has the same relation to the third word as the second word has to the first word.

Hence, “doe” is the correct answer.

90, 165 and 195 are divisible by ‘3’.

Whereas,

170 is not divisible by ‘3’.

Hence, “170” is the correct answer.

Malaria, Typhoid and Flu are physical diseases that occur in the body.

Whereas,

Depression is a mental disease.

Hence, “depression” is the odd word.

 Three of the following four words are alike in a certain way and one is different. Select the odd word.

Quarrel is a heated argument or disagreement.

And,

War is a state of armed conflict between countries or different groups within a country.

Both mean to fight against something.

Similarly,

Error is a mistake.

And,

Blunder is a careless mistake.

‘Error’ is related to ‘blunder’

Hence, “blunder” is the correct answer.

Gladsome, Joyous and Cheerful mean happy and optimistic.

Whereas,

Morose means ill – tempered and gloomy.

Hence, “morose” is the odd word.

Three of the following four words are alike in a certain way and one is different. Select the odd word.

The pattern followed is,

16 × 8 = 128

And,

18 × 9 = 162

Similarly,

22 × 11 = 242

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

Hence, “242” is the correct answer.

The pattern followed is,

184 : 207

23 × 8 : 23 × 9

Similarly,

208 : ?

26 × 8 : 26 × 9

208 : 234

Hence, “234” is the correct answer.

The pattern followed is,

All follow the same pattern, except ‘OPR – JKL’.

Hence, “OPR – JKL” is the odd one.

The pattern followed is,

Option 1 → 5 and 7 are consecutive prime numbers.

Option 2 → 17 and 23 are not consecutive prime numbers, there is 19 in the middle.

Option 3 → 13 and 19 are not consecutive prime numbers, there is 17 in the middle.

Option 4 → 31 and 41 are not consecutive prime numbers, there is 37 in the middle.

Hence, “5 : 7” is different from the rest.

Interchanging signs and using BODMAS rule,

Option 1 → × and +

48 – 8 ÷ 4 × 5 + 6 = 32

48 – 2 × 5 + 6 = 32

48 – 10 + 6 = 32

54 – 10 is not equal to 32

Option 2 → ÷ and –

48 ÷ 8 - 4 + 5 × 6 = 32

6 – 4 + 5 × 6 = 32

6 – 4 + 30 = 32

36 – 4 = 32

32 = 32

Option 3 → × and ÷

48 – 8 × 4 + 5 ÷ 6 = 32

48 – 8 × 4 + 0.83 = 32

48 – 32 + 0. 83 = 32

48. 83 – 32 is not equal to 32

Option 4 → ÷ and +

48 – 8 + 4 ÷ 5 × 6 = 32

48 – 8 + 0. 8 × 6 = 32

48 – 8 + 4. 8 = 32

52. 8 – 8 is not equal to 32

Hence, option 2 is the correct answer.

The pattern followed is,

Option 1 → 8 × 2 : 8²

Option 2 → 17 × 2 : 17²

Option 3 → 12 × 2 : 12² is 144, not 142

Option 4 → 7 × 2 : 7²

All follow the same pattern, except ’24 : 142’

Hence, “24 : 142” is the different number – pair.

 Four number-pairs are given out of which three are alike in a certain way and one is different. Select the number-pair that is different from the rest.

The pattern followed is,

Option 1 → 18 : 306 → 18 : 18² – 18

Option 2 → 23 : 552 → 23 : 23² + 23

Option 3 → 13 : 182 → 13 : 13² + 13

Option 2 → 25 : 650 → 25 : 25² + 25

All follow the same pattern, except ’18 : 306’.

Hence, “18 : 306” is the correct answer.

Four number-pairs are given out of which three are alike in a certain way and one is different. Select the number-pair that is different from the rest.

The pattern followed is,

Hence, “97” is the correct answer.

Track is the passage on which a train runs.

Driver drives a train.

Similarly,

Sea is the place where a ship sails.

A ship captain is in command of water vessels in lakes, oceans, coastal waters, rivers, or bays. 

‘Sea : Ship : Captain’ share the same relationship as that shared by the given set of words.

Hence, “Sea : Ship : Captain” is the correct answer.

The pattern followed is,

Hence, “HNU” is the correct answer.

The pattern followed is,

Similarly,

‘GWJMYOMG’ is related to the third from in the same way as the second term is related to the first

term.

Hence, “GWJMYOMG“ is the correct answer.

The pattern followed is,

Hence, “JUX” is the correct answer.

The pattern followed is,

Hence, “G” is the correct answer.

Arranging them according to the given information,

Jyoti is to the immediate right of Priya and to the immediate left of Trisha. Aditi and Priya have one person between them.

Trisha and Diksha have two persons between them. Aditi is to the immediate right of Akshaya.

‘Anika’ is at the extreme right end.

Hence, “Anika” is the correct answer.

• Vikramaditya(Chandra Gupta-II) was a Gupta ruler.
• He was one of the Gupta Empire's most powerful Emperors in northern India.
• He vanquished the Western Kshatrapas and spread the Gupta empire from the Indus River in the west to the eastern Bengal region, and from the northern Himalayan foothills to the southern Narmada River.
• During the rule of Chandragupta II, the Gupta Empire reached its zenith.
• He was the dynasty's second ruler to bear the name "Chandragupta" , the first being his grandfather Chandragupta I.

In 2000, the first Exchange-traded Index Derivative Contract was traded on the Bombay Stock Exchange (BSE).

• ​The Bombay Stock Exchnage is an Indian stock exchange which located in Mumbai.
• It is Asia's oldest exchange which established in 1875.
• The BSE is the 10th biggest stock exchange in the world with an overall market capitalization of over $2.2 trillion as of April 2018.
• BSE used that index to open its derivatives market in 2000 which trading futures contracts for S&P BSE SENSEX.
• In 2001 and 2002, the introduction of S&P BSE SENSEX options along with equity derivatives followed, widening the trading platform for the BSE.

The noted freedom fighter Saheed Laxman Nayak belonged to the state of Odisha.

• He had been a South Odisha tribal civil rights activist in eastern India.
• He belonged to the Odisha bhuyan tribe.
• He fought single handed with consummate ability and a remarkable zeal and fervor of a warrior against repressive foreign rulers.
• He became an involved member of Congress in registering as an Indian Natinal Congress charanna member.
• He played a key role in popularizing the Koraput congress programme.

Anemophily is the term used for pollination by wind.

• The features of the wind-pollination syndrome include a lack of fragrance development, a lack of showy flower bits, decreased nectar production and the production of huge numbers of pollen grains.
• When the pollination is performed with the help of the wind, this pollination is called anemophilous cross-pollination type.
• Anemophilia pollen grains are small and non-sticky, so that air currents will carry them.
• Angioplasty is a treatment for restoring blood flow through the artery.

The Mughal Sarai Railway Station has been renamed after Deen Dayal Upadhyaya.

• Pt. Deen Dayal Upadhyaya junction located in the state of Uttar Pradesh.
• The station has the biggest Asian railroad marshalling yard.
• The largest Indian Railways wagon repair workshop is located at Mughalsarai.
• In 2017, the Indian government approved a fresh proposal to rename the station, forwarded by the Yogi Adityanath-led government.
• In August 2018, the station was officially renamed to the Pandit Deen Dayal Upadhyaya junction.

Sulphuric acid makes the atmosphere of Venus have thick white and yellowish clouds.

• The Venus atmosphere is the layer of gasses that cover Venus.
• This consists mainly of carbon dioxide and is much denser and hotter than the Earth atmosphere.
• The Venusian atmosphere contains white and yellowish clouds composed of sulfuric acid, rendering Earth-based visual and surface orbital observation difficult.
• ESA scientists announced on January 29, 2013, that planet Venus ionosphere is flowing outward in a manner similar to "the ion tail seen coming out of a comet under similar conditions."

​The queen Ahilyabai Holkar associated with the Maheshwari saree.

• She was the Maratha Malwa Kingdom Holkar Queen, India.
• Rani Ahilyabai was a great founder of Hindu temples and builder.
• She appointed Tukojirao Holkar as army chief.
• Lakshmibai was the Rani of Jhansi, the queen of Jhansi.

• The Kharif season in India largely coincides with the Southwest monsoon.
• These are domesticated plants such as rice which are grown and harvested in India, Pakistan, and Bangladesh during the monsoon season of the Indian subcontinent, which lasts from June to November depending on the area.
• Kharif literally means "autumn" in Arabic and since this time coincides with the beginning of autumn in the Indian subcontinent, the monsoonal sowing season is called the Kharif period.
• Kharif crops contrast with rabi crops which are grown during the dry season.
• Rice is the most important Kharif Crop.

• Article 148 of the Constitution of India provides for an independent office of the Comptroller and Auditor General (CAG) of India.
• CAG audits all receipts and expenditures from the Government of India and the Governments of the State, including those from government-funded agencies and authorities.
• It is also the head of the Department of Indian Audit and Accounts, whose affairs are handled by Indian Audit and Accounts Service officers, and has over 58,000 employees nationally.
• The CAG is ranked 9th in Indian order of precedence and has the same standing as a Supreme Court judge of India.
• G. C. Murmu is the current CAG of India.

• 75-76 years is the periodicity of Halley's comet.
• It is a "periodic" comet, which returns to the vicinity of Earth once every 75 years.
• It was here last time in 1986 and is expected to return in 2061.
• The comet is named after the English astronomer Edmond Halley, who in 1531, 1607 and 1682 investigated evidence about a comet approaching Earth.

Palamu Hills is NOT a part of the Meghalaya Plateau.

• Palamu is a district of Jharkhand state.
• The Khasi and Jaintia Hills are a mountainous region largely part of the Assam and Meghalaya states.
• The Khasi Hills lie east of the Garo Hills.
• East Khasi hills are the wettest part of the world.

Under the provisions of Article 18(1) of the Constitution of India, the Bharat Ratna Award can NOT be used as a prefix or suffix to the recipient’s name.

• As Bharat Ratna Award, Padma Award also can't be used as prefix or suffix to the recipient's name.
• The article is about 'Abolition of Titles' and its section 1 states, "The State shall not grant any designation, not being a military or academic distinction."
• 307 people received the Padma Vibhushan, 1255 Padma Bhushan and 3005 Padma Shri.
• The Bharat Ratna is the Republic of India's highest civilian award which Established on 2 January 1954.

• Coppersmith Barbet is a bird  with crimson coloured forehead.
• It is found in South India and South Asia.
• It has several colours in his body.
• Malabar Barbet of Western Ghat looks similar to Coppersmith Barbet.

The line “Khoob lari mardani woh to Jhansi wali Rani thi”, was written by Subhadra Kumari Chauhan.

• In 1921, Subhadra Kumari Chauhan joined the Non-Cooperation Movement of Mahatma Gandhi.
• She was the first Satyagrahi woman to be convicted in court in Nagpur and was jailed twice in 1923 and 1942 for her participation in demonstrations against British rule.
• Her popular composition, which describes emotionally the life of the Queen of Jhansi(British India) and her participation in the 1857 Revolution.
• ICGS Subhadra Kumari Chauhan which is an Indian Coast Guard ship has been named after the poet.

• The painting of Bharat Mata was originally done by Abanindranath Tagore.
• He was the creator of the "Indian Society of Oriental Art".
• He was also the first major exponent of Swadeshi values in Indian art and thus established the influential art school in Bengal which led to the development of modern Indian painting.
• He also wrote books like Rajkahini, Budo Angla, Nalak, and Khirer Putul are landmarks in Bengali language children's literature.
• In 1942, he became Chancellor of Visva Bharati .

Debayan Saha invented a device called PM 2.5 which when fitted near the silencer pipe in vehicles will curb air pollution.

• Debayan Saha, a graduate of mechanical engineering from IIT Kharagpur, who invented the device, believes that one car fitted with the device can neutralize the emissions generated from 10 cars nearby.
• This technology is the combination of electric energy and waves energy to influence the pollutant like PM 2.5.
• Deepak Gupta is an Indian Supreme Court judge and former Tripura High Court chief justice and Chhattisgarh High Court chief justice.
• Nikesh Arora is an Indian businessman who has worked as an executive for Google.

BP Mandal was the Chairman of the Second Backward Classes Commission.

• He was also the 7th chief minister of Bihar.
• From 1967 to 1970 and from 1977 to 1979, he was a Member of Parliament for Madhepura from the state of Bihar.
• The Indian Government issued a stamp in honour of B.P. Mandal in 2001.
• The mission of Jyotiba Phule spread to many fields including the eradication of untouchability and the caste system and the emancipation of women.
• Babu Jagjivan Ram was the 4th deputy Prime Minister of India.
• Bhim Rao Ambedkar influenced the Dalit Buddhist movement and worked towards the untouchables against social discrimination.

The Third Round Table Conference was held in the year 1932.

• The British Government planned it for constitutional reform in India.
• All three conferences were held in compliance with the Simon Commission report of 1930.
• The Government's "White Paper" was the primary result of the Third Round Table Conference.
• The First Round Table Conference was held from November 1930 through January 1931.
• The Second Round Table Conference took place from September to December 1931.

'Amar Sonar Bangla’, the national anthem of Bangladesh was composed by Rabindranath Tagore.

Key Points

• In 1905, The lyrics were written by Bengali polymath Rabindranath Tagore while the hymn melody was adopted from the song "Ami Kothay Pabo Tare" put to Dadra Tala by the Baul singer Gagan Harkara.
• The song was written during Bengal's first partition in 1905, when an undivided province of Bengal's presidency was split into two sections by the governing British Empire; the decision was announced by India's then-Viceroy Lord Curzon on 19 July, taking effect on 16 October.
• In 1913, He became the first non-European in literature to receive the Nobel Prize.
• He also wrote the Jana Gana Mana which India's National Anthem.

• The Kaveri river rises from The Brahmagiri hills.
• The Kaveri River rises on the Brahmagiri Hill of the Western Ghats in southwestern Karnataka state, flows through the states of Karnataka and Tamil Nadu in a southeasterly direction for 765 km, and descends the Eastern Ghats in a series of great falls.
• The Kaveri river is joined by two tributaries the Hemavati and Lakshmantirtha.
• Brahmagiri hills is a mountain range in the Western Ghats of Maharashtra.
• Trimbakeshwar Shiva Temple is located near the Brahmagiri hills.

• United Nations Development Program (UNDP) publishes the Human Development Report.
• United Nations Development Program (UNDP) is a global development network of the United Nations.
• It offers expert advice, training, and assistance to developing countries, with a growing focus on supporting the least developed countries.
• The headquarters of UNDP is located in New York City.
• The World Trade Organization(WTO) is an intergovernmental organization that is concerned with the regulation of international trade between nations.
• The International Labour Organization(ILO) is an organization of the United Nations whose mission is to advance social justice by setting international labour standards and to facilitate decent work.

Dhoti-Gamosa is the indigenous textile symbol of Assam.

• It is typically a white rectangular piece of cloth with mostly three-sided red border and fourth red woven motifs.
• A 1,455.3 meter long Gamosa exhibited in Delhi created world record as it became the longest hand woven piece of cloth in the world.
• It is representative of Assam's natural life and culture.
• The gamosa is widely used similarly by all regardless of religious or ethnic backgrounds.

Arundhati Roy is the author of the book the 'Ministry of Utmost Happiness'.

• It is the second novel of her after the God of small things.
• The novel weaves tales of people experiencing some of the worst and most brutal moments in modern Indian history together.
• In 1997, The God of small things won the Man Booker Prize for fiction.
• It became by a non-expatriate Indian author the largest-selling book.
• In 2014, She was featured in the list of Time 100 and also the 100 most influential people in the world.

Rahul Dravid is a former cricket player was appointed as the head of National Cricket Academy (NCA) in 2019.

• He was the former Indian team Captain and currently he is monitors the progress of India A and India U19.
• He has scored nearly 25,000 runs in international cricket and is widely considered to be one of the best batsmen in cricket history.
• He also known as the Great wall of Indian cricket team.
• he became the fifth Indian cricketer to be inducted to the ICC Hall of Fame in July 2018.
• He joined the GoSports Foundation in 2014, in Bangalore.

The correct answer is option 1, i.e. Dachigam.

• Dachigam is a National Park located in Srinagar, Jammu and Kashmir.
• There are a total of 18 biosphere reserves in India.
• Dachigam means ten villages.
• Dachigam is famous for Hangul Deers.
• Hangul Deer is an endangered species and is very famous in Jammu and Kashmir

Additional Information

• The first biosphere reserve of the world was established in 1979.
• Globally, there are 686 biosphere reserves in 122 countries, including 20 transboundary sites.
• A biosphere reserve is divided into three zones:
• • Core area:
• It involves an entirely secured and protected ecosystem that contributes to the preservation of ecosystems and species.
• It is kept free from human interference.
• Buffer zone:
• It encompasses the core areas and is regarded as an area in which human use is less intensive than what might be found in the transition zone.
• Research and educational activities are to be encouraged.
• Transition area:
• The large outer area of a reserve where people live and work, using the natural resources of the area in a sustainable manner.
• It is the zone of cooperation where human ventures and conservation are done in harmony.

• Paleontology is a branch of geology that studies dinosaurs.
• The father of Indian Paleontology is Birbal Sahani.
• Birbal Sahini was an Indian palaeontologist and his major contributions were in the study of the fossil plants of Indian subcontinent.
• He established the Birbal Sahni Institute of Palaeobotany at Lucknow in 1946.

With a view to having animal protection world over, several countries have been brought under the cover of CITES with effect from 26th August 2019. Endangered does 'E' stand for in the acronym.

• CITES (the Convention on International Trade in Endangered Species of Wild Fauna and Flora) is an intergovernmental international agreement.
• The goal is to ensure that international trade in wild animal and plant specimens does not endanger survival.
• It was drafted following a resolution adopted at a conference of IUCN (World Conservation Union) representatives in 1963.
• It is an international agreement jointly adhered to by States and regional organizations of economic integration.

Johann Wolfgang Dobereiner made his first observation as a catalyst on Platinum and discovered similar triads of elements which led to the creation of the Periodic Table of Elements.

• He was a German chemist best known for his work, which foreshadowed the periodic rule for chemical elements, and for inventing the Döbereiner's first lighter.
• Döbereiner is also known for his discovery of the furfural, for his work on using platinum as a catalyst.
• Dmitri Mendeleev produces a farsighted interpretation of the periodic element table.
• Hans Christian Oersted discovered that electric currents produce magnetic fields, which was the first relation between magnetism and electricity.
• Michael Faraday contributed to the study of electromagnetism and electrochemistry.

The pH value of Human body is 7.0 to 7.8.

• pH scale used to measure that the water based solution is acidic or basic.
• Pure water is neither acidic nor basic at room temperature (25 ° C or 77 ° F) and has a pH value of 7.
• At 25°C, solutions with a pH below 7 are acidic, and solutions with a pH above 7 are basic.
• pH measurements are essential for chemistry, agronomy, medicine and water treatment.

The Banihal Pass is situated in Pir Panjal Himalayan Range.

Key Points

• The Pir Panjal Range is a range of Inner Himalayan mountains stretching from east-southeast (ESE) to west-northwest (WNW) through Himachal Pradesh, Indian state, and Jammu and Kashmir, Indian Union Territory.
• Pir Panjal is the greatest range of the Lesser Himalayas.
• The Pir Panjal Railway Tunnel, a rail tunnel of 11,215 meters passes through Jammu and Kashmir's Pir Panjal Range.
• The tunnel was opened to regular service on 26 June 2013.
• It is the longest railway tunnel in India and the fourth-longest tunnel in Asia.

The term ‘Peninsula’ means a piece of land surrounded by water on three sides.

• A peninsula is a land type that covers the majority of its boundary with water while being connected to a mainland from which it spreads.
• The surrounding water is generally understood to be constant, although not usually named as a single water body.
• A point is generally considered a tapering piece of land extending into a less prominent body of water than a cape.
• South India is also considered as the Peninsula of Asia.

Galvanometer is an instrument can detect the presence of a current in a circuit.

• It is a similar function to the ammeter.
• It is an analogue electromechanical transducer which, through a limited arc, produces a rotary deflection in response to the electrical current flowing through its coil.
• Johann Schweigger invented the galvanometer.
• The sphygmomanometer is an instrument which is used to measure the Blood Pressure.
• The barometer is an instrument which is used to measure the air pressure.
• The Magnetometer is an instrument which measures the magnetism.

The Dadasaheb Phalke Award was introduced in 1969.

• The Dadasaheb Phalke Award is India's biggest cinematographic award.
• It is presented annually by the Directorate of Film Festivals, an organisation established by the Ministry of Information and Broadcasting, at the National Film Awards ceremony.
• Dada Shahab also known as "the father of Indian cinema".
• The award's first winner was actress Devika Rani, who was presented at the 17th National Film Awards.

• During the 1857 Uprising, Maulvi Ahmadullah took up the leadership at Faizabad.
• He was also recognized as the Lighthouse of Rebellion in the Awadh region.
• He was also an epitome of the Faizabad tradition of religious unity and Ganga-Jamuna.
• Kunwar Singh also led the Indian Rebellion of 1857 from Arrah, Bihar.
• During the Indian Rebellion of 1857, Begum Hazrat Mahal rebelled against the British East India Company from Lucknow.
• In the Indian rebellion against the British in 1857, Khan Bahadur Khan established his own government at Bareilly.

Vote-on-account allows the government to meet the expenses of administration until the new parliament passes the Budget for the whole year.

• Vote on Account is an advance grant that allows the government to move on until grant applications are voted and the Appropriation Bill and Finance Bill is passed.
• It allows the government to finance its expenses for a short time, or until a full budget is passed.
• Voice-voting is a form of voting in deliberative assemblies where a collective vote on a subject or motion is taken by the oral response.
• It is considered by deliberative legislatures to be the easiest and fastest form of voting.

In 1959, The Tibetan Spiritual leader the Dalai Lama seek political asylum in India.

• The Dalai Lama fought his way through the snow on 31 March 1959 to reach Chutangmu, a tiny Assam Rifles outpost near Tawang, to apply for asylum in India.
• Dalai Lamas are important Gelug school monks, Tibetan Buddhism's newest school which was formally led by the Ganden Tripas.
• The Dalai Lama has called on the rights of Tibetans to the United Nations. This appeal resulted in three resolutions adopted by the General Assembly in 1959, 1961 and 1965, all before being allowed to represent the People's Republic at the United Nations.
• The Tibetan Institute of Performing Arts was founded in 1959, and in 1967 the Central Institute of Higher Tibetan Studies became India's primary university for Tibetans.

• Deepa Karmakar is associated with Produnova.
• Produnova is also known as Vault of Death.
• In Produnova, gymnasts first toss himself/herself into the air using the vault as a jumping board then they are required to do two neat somersaults mid-air.
• Pradunova was named after Russia's Elena Produnova, who first performed it.

The Securities and Exchange Board of India is located in Mumbai.

• The Securities and Exchange Board of India (SEBI) is India's government-owned agency for the securities market in India.
• It was formed in 1988 and given legislative powers through the 1992 SEBI Act, on 30 January 1992.
• The headquarters are located in the Bandra Kurla Complex business district in Mumbai and have Northern, Central, Southern and Western Regional Offices in New Delhi, Kolkata, Chennai, and Ahmedabad.
• On 10 February 2017, Ajay Tyagi was named as Chairman.

Virender Sehwag is a former Indian cricketer has scored two test triple centuries.

• The only batsmen to cross 300 more than once are Donald Bradman (Australia), Brian Lara (West Indies), Virender Sehwag (India) and Chris Gayle (West Indies).
• The first triple century test was reached in 1930 by England's Andy Sandham against the West Indies in the first series of tests played in the West Indies.
• Virender Sehwag's 278-ball triple century for India against South Africa is the fastest triple-century test by number of balls faced.
• The highest individual score in test cricket is 400 which is scored by Brian Lara.

Bal Gangadhar Tilak is the author of the book 'Arctic Home of the Vedas'.

• This book is the origin of Aryanic People in 1903.
• This propounded the theory that the North Pole was Aryan's original home during the pre-glacial period that they had to abandon because of the ice deluge around 8000 B.C. And had to move to the northern parts of Europe they Asia to look for new settlement lands.
• The book was written in late 1898, but first published in Pune in March 1903.
• The Indian Independence Movement was lead by the Bal Gangadhar tilak.

In October 2019, Lionel Messi received his 6th Golden Shoe as the top scorer in the European leagues.

• Barcelona Captain Leo Messi has won the trophy for a third straight year after scoring 36 goals, three more than his closest challenger, Paris Saint-Germain's Kylian Mbappe.
• He is an Argentine professional footballer who plays as a forward and is captain of both Barcelona Spanish club and the Argentine national team.
• He also won six times the Ballon d'Or award.
• In 2019, Forbes rated him as the highest-paid athlete in the world.

The correct answer is Article 30.

Article 30 of the Indian Constitution gives the right to minorities to establish and administer educational institutions.

• The protection of religious and ethnic minority rights is the foundation of secular values in India.
• Article 30 of the Indian Constitution is one of many provisions that ensure that minority rights are preserved.
• It is listed under Part III of the Indian Constitution which sheds light on the fundamental rights granted to Indian citizens regardless of caste, religion, and gender.

Additional Information

• Article 28 tells us about the Right to follow religious instruction or religious worship in certain educational establishments.
• Article 17 is about the Abolition of Untouchability.
• Article 32 focuses on the rights of constitutional remedies.

Explanation:

• SI Unit: It is an abbreviation from the French name Le Systeme International d’Unites.
• There are 7 fundamental units and two supplementary units.

• This provides a coherent system of measurement units based on seven base units, the second, meter, kilogram, ampere, kelvin, mole, and candela units.
• It is based on the meter–kilogram–second unit system (MKS) instead of any version of the CGS.

Sanjay Subrahmanyam is an the Indian historian won Israel’s prestigious Dan David Prize.

• He holds the chair of the Irving and Jean Stone Endowed Social Sciences at UCLA that he established in 2004.
• He became chair Navin and Pratima Doshi in Indian History at UCLA in 2004.
• He became the founding Director of the Center for India and South Asia at UCLA in 2005.
• He was named to the Chair of Social Sciences at UCLA in Irving and Jean Stone Endowed in 2014.

The correct answer is option 4 i.e Government Of India Act of 1935,

The abolition of Dyarchy in the provinces was recommended by the Government of India Act of 1935.

• British Parliament adopted it in August 1935.
• This was the longest act enacted so far by the British Parliament and was later split into two parts. Government of India Act of 1935 and the State of Burma Act of 1935.
• It extracted content from four primary sources viz. Report of the Simon Commission, discussions at the Third Round Table Conference, the reports of the Joint select committees and the White Paper of 1933.
• The Indian Government Act of 1919 was passed to increase Indians' involvement in the Indian government.
• Government of India Act of 1858 provided for the winding up of the Former East India Company.
• It is called the Blueprint of the Indian Constitution.

The National Song of India featured in Anandamath novel.

• ​It is a Bengali novel, which was written and published in 1882 by Bankim Chandra Chattopadhyay.
• It is influenced by and set in the context of the late 18th-century Sannyasi Rebellion, and is considered one of the most important novels in Bengali and Indian literary history.
• The history of the plot was based on the catastrophic 1770 Bengal famine under the British Raj and failed revolt against Sannyasi.
• In 1952, the novel was later adapted into a film Anand Math.

• Potassium is a chemical element with the symbol K.
• The Atomic number of potassium is 19.
• It is a silvery-white metal that is smooth enough to be sliced with little force with a knife.
• Potassium reacts rapidly with atmospheric oxygen within seconds of exposure to form flaky, white potassium peroxide.
• Na is the symbol of chemical element Sodium.
• S is the symbol of chemical element Sulphur.
• Ca is the symbol of chemical element Calcium.

Eight times world champion squash player Nicol David belongs to Malaysia.

• Nicol David is a female professional squash player from Malaysia, currently ranked 6th worldwide.
• She was number one in the world for a record-breaking 108 consecutive months, and eventually ceded the ranking to Raneem El Weleily in September 2015.
• She is the first squash player twice to win the World Junior title; in 1999 and in 2001.

• Money is working capital in the farming sector.
• A simple measure of the total amount of liquidity available in the farm sector is working capital.
• Current liabilities are determined by subtracting from current assets.
• This is a good indication of how much cash farmers have at their disposal to make transactions and repay their short-term debt obligations.
• Because the easiest way for farmers to raise liquidity or labour capital is to earn profits, working capital continues to decrease as productivity declines.
• Farmers can not reinvest in their crops without working capital.

• Iron is not a compound.
• Iron is an element, and not a mixture or solution compound or heterogeneous.
• An element is formed by atoms with exactly the same properties, that is, it consists of exactly the same atoms as an element.
• A compound consists of two or more different elements and has different characteristics from the constituent elements.
• A solution consists of a liquid dissolved in it.

Given:

A : B = 8 : 9

B : C = 2 : 3

C : D = 9 : 13

Calculation:

A : B : C : D = 16 : 18 : 27 : 39

(16 + 18 + 27 + 39) unit = 12000

100 unit = 12000

1 unit = 12000/100 = 120

Difference between B and D = (39 - 18) × 120 = 21 × 120 = 2520

Therefore the correct answer is 2520.

Calculation:

Let Pole be AD and tower be BD.

Given,

AD = 7 m

In △BCD

tan45 = BD/BC

1 = BD/BC

BC = BD

In △ABC

tan60 = AB/BC

√3 = AB/BC

AB = √3BC

AD + BD = √3 BD

√3BD – BD = 7

BD(√3 – 1) = 7

BD = {7/(√3 – 1)} × {(√3 + 1)/(3 + 1)}

BD = 7(√3 + 1)/[(√3)² – 1²]

BD = 7(√3 + 1)/(3 – 1)

BD = 7(√3 + 1)/2

Shortcut Trick

(√3 – 1) unit = 7

1 unit = {7/(√3 – 1)} × {(√3 + 1)/(3 + 1)}

= 7(√3 + 1)/[(√3)² – 1²]

= 7(√3 + 1)/(3 – 1)

= 7(√3 + 1)/2

Let CP of the article be Rs. X.

According to the question

(115 – x) = (x – 104) × 120/100

5(115 – x) = 6(x – 104)

575 – 5x = 6x – 624

6x + 5x = 624 + 575

11x = 1199

x = 1199/11

x = 109

CP of the article = Rs. 109

New SP of the article = Rs. 130.80

Profit percentage = (130.80 – 109)/109 × 100 = 20%

Alternate Method Gain/Loss = (100 + 20)/100

⇒ 120/100 = 6/5

In both cases Cost price will be same.

⇒ S.P₁ - Gain = S.P₂ + Loss

⇒ 115 - 6x = 104 + 5x

⇒ 6x + 5x = 115 - 104

⇒ 11x = 11

⇒ x = 1

Putting x = 1 

⇒ 115 - 6 = 109 that is C.P.

New SP of the article = Rs. 130.80

Profit percentage = (130.80 – 109)/109 × 100 = 20%

Total exports of type A cars during 2012 to 2016 = 275 + 250 + 225 + 260 + 340 = 1350

Average exports of type A cars = 1350/5 = 270

In 2012, 2013, 2014 and 2015 the exports of type B cars more than the average exports of type A cars during 2012 to 2016.

Given:-

A = B - 75%B

C = 75%(A - B)

Calculation:-

Let B = 100

∴ A = 100 × (25/100) = 25

C = (100 - 25) × 75/100 = 56.25

∴ C is more than that of A by = (56.25 - 25)/25 × 100 = 125%

Let speed of boat be x km/hr

Speed of current = 9 km/hr

Distance between x and y = 10.5 km

Upstream speed = (x - 9) km/h

Downstream speed = (x + 9) km/h

According to the question

10.5/(x - 9) + 10.5(x + 9) = 4

We can solve this using option

Put x = 12, the

10.5/3 + 10.5/21 = 4

3.5 + 0.5 = 4

4 = 4 (satisfied)

Detailed solution:

10.5[(x + 9 + x - 9)]/(x² - 81) = 4

10.5 × 2x = 4x² - 324

4x² - 10.5 × 2x - 324 = 0

2x² - 10.5x - 162 = 0

After solving quadratic equation we get x = 12

Given, BC = 4.2m

In △ABC

tan60 = AB/BC

√3 = AB/4.2

AB = 4.2 × 1.73 = 7.3 m

Short Trick:

1 unit = 4.2m

√3 unit = 4.2√3 = 4.2 × 1.73 = 7.3 m

Given:-

A class of 54 students

Average of mathematic score of boys = 50% more than of girls

Formula used:-

Average = (Sum of values)/No. of values

Calculation:-

Total number of students = 54

$33\frac{1}{3}$ = (100/3)% = 1/3

Number of boys = 54 × 1/3 = 18

Number of girls = 54 – 18 = 36

Average score of girls = 2x

Average score of boys = 2x × (3/2) = 3x

According to the question,

18 × 3x + 36 × 2x = 54 × 70

54x + 72x = 3780

126x = 3780

x = 3780/126 = 30

Average score of boys = 30 × 3 = 90

Given:-

Side of cube = a

Volume of cube = a³

Radius of cylinder = a/2

Height of cylinder = a

Formula used:-

Volume of cylinder = πr²h

Volume of cube = a³

Calculation:- 

Volume of cylinder = πr²h = π × (a/2)² × a

= 3.14 × a³/4

= 0.785a³

Remaining volume of cube = a³ – 0.785a³

= 0.215a³

Required percentage = [(0.215a³)/a³] × 100

= 21.5%

∴ Required % is 21.5.

Total number of workers in the factory are = 60 + 85 + 95 + 105 + 90 + 80 + 70 + 65 + 50

= 700

Number of workers whose weekly earning are Rs. 6500 or above but less than Rs. 6,500 = 105 + 90 + 80 + 70 = 345

Required percentage = (345/700) × 100 = 49.3%

Given:

A person bought an article at a 30% discount on its marked price.

The person then sold It at a 30% profit for Rs. 427.70.

Concept used:

S.P = [(100 - D%)/100] × M.P

S.P = [(100 ± P/L%)/100] × C.P

Calculation:

Let MP of the article be Rs. x

CP of the article for the man = x × 70/100

According to the question

x × 70/100 × 130/100 = 427.70

x = 42.70 × 100/130 × 100/70

x = 470

Average of 19 numbers = 22.8

Sum of the 19 numbers = 22.8 × 19 = 433.2

Average of next 10 numbers = 18.4

Sum of next 10 numbers = 18.4 × 10 = 184

Average of last 10 number = 28.6

Sum of last 10 number = 28.6 × 10 = 286

10^th number = 286 + 184 – 433.2 = 36.8

Sum of 18 number = 433.2 – 36.8 = 396.4

Average of 18 number = 396.4/18 = 22 

Alternate Method

Average of 19 numbers = 22.8 

Average of next 10 numbers = 18.4

⇒ 18.4 - 22.8 = (-4.4)

Average of last 10 number = 28.6

⇒ 28.6 - 22.8 = 5.8

Net Increase = -4.4 × 10 + 5.8 × 10

⇒ 14

10th Number = 14 + 22.8 = 36.8

Sum of the 19 numbers = 22.8 × 19 = 433.2

When 10th number excluded then,

Sum of 18 number = 433.2 – 36.8 = 396.4

Average of 18 number = 396.4/18 = 22

As we know,

If, (a - b)² + (c - d)² = 0

a = b and c = d

${\left( {{x^3} + \frac{1}{{{x^3}}} - k} \right)^2} + {\left( {x + \frac{1}{x} - p} \right)^2} = 0$

${\left( {{x^3} + \frac{1}{{{x^3}}} - k} \right)^2} = 0$

x³ + 1/x³ = k

And

${\left( {x + \frac{1}{x} - p} \right)^2} = 0$

x + 1/x = p

As we know,

(x + 1/x)³ = x³ + 1/x³ + 3 (x + 1/x)

p³ = k + 3p

k = p³ - 3p

k/p = p² - 3

Short Trick:

${\left( {{x^3} + \frac{1}{{{x^3}}} - k} \right)^2} + {\left( {x + \frac{1}{x} - p} \right)^2} = 0$

Put x = 1, then

(2 - k)² + (2 - p)² = 0

k = 2 and p = 2

k/p = 2/2 = 1

From option 4.

p² - 3

2² - 3

4 - 3

1 (satisfied)

Calculation:-

$\large{\frac{{\left( {2\frac{1}{3} + 2\frac{1}{2} - \frac{1}{6}} \right) \div 2\frac{1}{3}; \times ;5\frac{2}{3} \div 1\frac{2}{3}of;4\frac{1}{4}}}{{3\frac{1}{5} \div 4\frac{1}{2}of;5\frac{1}{3} + 5\frac{1}{3}; \times ;\frac{3}{4} \div 2\frac{2}{3}}}}$

$\large{\frac{{\left( {\frac{7}{3} + \frac{5}{2} - \frac{1}{6}} \right) \div \frac{7}{3}; \times ;\frac{{17}}{3} \div \frac{5}{3}of\frac{{17}}{4}}}{{\frac{{16}}{5} \div \frac{9}{2}of\frac{{16}}{3} + \frac{{16}}{3}; \times ;\frac{3}{4} \div \frac{8}{3}}}}$

$\large{\frac{{\frac{{14}}{3} \div \frac{7}{3}; \times ;\frac{{17}}{3} \div \frac{{85}}{{12}}}}{{\frac{{16}}{5} \div 24 + \frac{{16}}{3}; \times ;\frac{3}{4}{\rm{;}} \times {\rm{;}}\frac{3}{8}}}}$

$\large{\frac{{2; \times ;\frac{{17}}{3}{\rm{;}} \times {\rm{;}}\frac{{12}}{{85}}}}{{\frac{{16}}{5}{\rm{;}} \times {\rm{;}}\frac{1}{{24}} + \frac{3}{2}}}}$

$\large{\frac{{\frac{8}{{5}}}}{{\frac{2}{{15}} + \frac{3}{2}}}}$

[8/5] × [30/49]

48/49

Required difference = 48/49 - 6/7 = 6/49

Note: This question has been asked in the previous year exam and we have changed the option to given answer accordingly.

Given:

A invested $33\frac{1}{3}$ of the total capital, B invested $33\frac{1}{3}$ of the remaining capital and C, the remaining.

Total profit = Rs. 20250

Concept used:

The ratio of investment = Ratio of profit share.

Calculation:

Let total capital be 9x, then

Capital of A = 9x × 1/3 = 3x

Capital of B = (9x – 3x) × 1/3 = 2x

Capital of C = 6x – 2x = 4x

The profit share of A, B, and C at the end of the year = 3x : 2x : 4x

Total profit = 20250

3x + 2x + 4x = 20250

9x = 20250/9

x = 2250

The profit share of C is more than that of B by = (4x – 2x) × 2250 = 4500

Shortcut Trick Let total capital be 9.

${33}{1\over3}$% = $1\over3$

So, (3 + 2 + 4) = Rs. 20,250

⇒ 9 → 20,250

⇒ 1 → 2,250

The profit share of C is more than that of B by

⇒ (4 - 2) × 2,250 = Rs. 4,500

∴ The profit of C exceeds the profit of B is Rs 4,500.

Concept:

Numbers which are divisible by 'a' or 'b' = (Number divisible by 'a') + (Number divisible by 'b') - (Numbers divisible by lcm of 'a' and 'b')

Calculation:

Number which is divisible by 3 or 4 up to 2001 are = 2001/3 + 2001/4 - 2001/12 = 667 + 500 - 166 = 1001

Now,

Numbers which are divisible by 3 or 4 but not by 5 = (Numbers divisible by 3 or 4) - (Numbers divisible by lcm of 3 and 5) - (Numbers divisible by lcm of 4 and 5) + (Number divisible by lcm of 3, 4, and 5)

Numbers which is divisible by 3 or 4 but not by 5 up to 2001 are = 1001 - 2001/15 - 2001/20 + 2001/60 = 1001 - 133 - 100 + 33 = 801

∴ The correct answer is 801.

Given:

MP of the washing machine = Rs. 7200

SP of the washing machine = Rs. 5512.50

Concept used:

S.P = [(100 - D%)/100] × M.P

Discount = M.P - S.P

Calculation:

We know that,

S.P = [(100 - D%)/100] × M.P

⇒ 5512.50 = 7200 × [(100 - x)/100] × [(100 - x)/100]

⇒ [(100 - x)/100]2 = 5512.50/7200

⇒ [(100 - x)/100]2 = 49/64

⇒ [(100 - x)/100] = (49/64)1/2

⇒ [(100 - x)/100] = 7/8

⇒ 800 - 8x = 700

⇒ x = 100/8

⇒ x = 12.5

∴ The Required Percentage is 12.5%.

Shortcut Trick

12.5% = 1/8

64 unit = 7200

1 unit = 112.5

49 unit = 5512.5

Given:-

Tap A fill a tank = 15 min

Tap B will a tank = 10 min

Tap C will empty a tank = x min

Calculation:-

According to the question

8 + 12 – x = 15

x = 20 – 15 = 5

So, the efficiency of C = 5

Total work = 120

3/8 of the total work = 120 × 3/8 = 45

Tap C alone will empty 3/8 part of the tank in 45/5 = 9 min

∴ Required time of C is 9 min.

Given:-

Sides of triangular field = 120 m × 170 m × 250 m

Rate = Rs. 7.40/m²

Formula used:-

Area of triangle = √S(S – a)(S – b)(S – c)

where, S = (a + b + c)/2

Calculation:-

Dimension of triangular field are 120m, 170m and 250m

S = (120 + 170 + 250)/2 = 540/2 = 270

As we know,

Area of triangle = √S(S – a)(S – b)(S – c)

= √{270(270 – 120)(270 – 170)(270 – 250)}

= √{270 × 150 × 100 × 20}

= √(9 × 3 × 10 × 5 × 3 × 10 × 4 × 5 × 100)

= 3 × 3 × 10 × 5 × 2 × 10

= 9000 m²

Cost of levelling 1 m² = Rs. 7.40

Cost of levelling 9000 m² = 7.40 × 9000 = Rs. 66600

∴ Required cost of leveling is 66000.

Given:

The total cost of painting its four walls at the rate of Rs 25/m2 is Rs. 3,600.

Rate 90.50 Rs./m²

Formula used:

The area of four walls, A = 2(l + b)h

Area of floor = l × b

Calculation:

Let length of the room be 6x

Breadth of the room = 6x/2 = 3x

Height of the room = 6x/3 = 2x

Cost of painting Rs. 25/m²

Area of four wall = (1/25) × 3600 = 144m²

Area of four wall = 2(l + b)h

⇒ 2(6x + 3x) × 2x = 144

⇒ 2x × 18x = 144

⇒ 36x² = 144

⇒ x² = 144/36 = 4

⇒ x = √4 = 2

Area of floor = l × b = 6x × 3x = 6 × 2 × 3 × 2 = 72 m²

Cost of laying carpet on 1m² = 90.50

Cost of laying carpet on = 72m² = 90.50 × 72 = RS. 6516

As we know,

If a + b + c = 0

Then, a³ + b³ + c³ = 3abc

$\frac{{{{\left( {0.321} \right)}^3} + {{\left( {0.456} \right)}^3} - {{\left( {0.777} \right)}^3}}}{{0.9; \times ;\left( {0.107} \right)\left( {0.76} \right)\left( {0.777} \right)}}$

0.321 + 0.456 – 0.777 = 0,

Then 0.321³ + 0.456³ – 0.777³ = – 3 × 0.321 × 0.456 × 0.777

$\frac{{ - 3{\rm{;}} \times {\rm{;}}0.321{\rm{;}} \times {\rm{;}}0.456{\rm{;}} \times {\rm{;}}0.777}}{{0.9; \times ;\left( {0.107} \right)\left( {0.76} \right)\left( {0.777} \right)}}$

⇒ -6

Given:-

Numbers 6454, 7306, 8797

Calculation:-

If remainder in each case is same.

7306 - 6454 = 852

8797 - 7306 = 1491

8797 - 6454 = 2343

HCF of 852, 1491 and 2343:

∴ HCF is 213

Greatest number(d) = 213

Remainder (r) = 64

∴ d - r = 213 - 64

⇒ d -r = 149

Shortcut TrickConcept used:-

HCF(d₁ ,d₂ ,d₃) = Greatest number who left equal remainder

where, d₁ = difference between numbers

Calculation:-

∴ HCF = Greatest number(d) = 213

Remainder(r) = 

∴ d - r = 213 - 64 = 149

∴ Required value of d - r is 149.

Shortcut Trick As we know,

∠TPS = (∠TQP - ∠PRQ)/2

24 = (78 - ∠PRQ)/2

78 - ∠PRQ = 24 × 2 = 48

∠PRQ = 78 - 48 = 30

Alternate MethodGiven: 

 In ΔPQR, PT ⊥ QR at T and PS is the bisector of ∠QPR

∠PQR = 78° and ∠TPS = 24° 

Calculation:

In ΔPQT,

∠QPT = 180° - ∠PQR - ∠PTQ = 180° - 78° - 90° = 12°

∠SPQ = ∠QPT + ∠TPS = 12° + 24° = 36°

Since PS is the bisector of ∠QPR.

∠QPR = 2 × ∠SPQ = 2 × 36° = 72°

In ΔPQR,

∠PRQ = 180° - ∠PQR - ∠QPR = 180° - 78° - 72° = 30°

Hence the required answer is 30°

Exports of type A cars in 2014 are = 225

120% of 225 = 225 × 120/100 = 270

In 2016 the exports of type B cars exactly 20% more than the exports of type A cars in 2014.

Given:

3(cot2θ - cos2θ) = 1 - sin2θ

Formula used:

sec²θ - tan²θ = 1

cosec²θ - cot²θ = 1

Calculation:

3(cot²θ - cos²θ) = 1 - sin²θ

⇒ 3cos²θ[1/sin²θ - 1] = cos²θ

⇒ cosec²θ - 1 = 1/3

⇒ cot²θ = 1/3

⇒ cotθ = 1/√3

⇒ cotθ = cot60

∴ θ = 60°

Shortcut Trick3(cot²θ - cos²θ) = 1 - sin²θ

Put θ = 60°

⇒ 3(cot²60 - cos²60) = 1 - sin²60

⇒ 3[1/3 - 1/4] = [1 - 3/4]

⇒ 3[1/12] = 1/4

⇒ 1/4 = 1/4 (Satisfied)

So, θ = 60°

If ABCD is a cyclic quadrilateral in which AC bisects BD.

AD/BC = AB/DC

AD/12 = 15/10

AD = 3/2 × 12 = 18 cm

Given:-

3 men + 5 women = 6 days

4 men + 9 women = 4 days

Calculation:-

Let efficiency of 1 man and 1 woman be x and y respectively

As we know,

Total work = Total work

According to the question

(3x + 5y)6 = (4x + 9y)4

18x + 30y = 16x + 36y

18x – 16x = 36 – 30y

2x = 6y

x/y = 6/2 = 3/1

x : y = 3 : 1

Total work = (3 × 3 + 5 × 1) 6 = 84

Let n women complete the whole work in 7 days, then

n × 1 × 7 = 84

n = 84/7 = 12

∴ Required number of women is 12.

Let remaining question right be x, then

According to the question

60 × (65/100) + x = 120 × 75/100

39 + x = 90

x = 90 - 39 = 51

Required percentage = 51/60 × 100 = 85%

SHORT TRICK:

Using average method

(65 + y)/2 = 75

65 + y = 75 × 2

y = 150 - 65 = 85%

Calculation:-

Total employees = 360°

Number of employees in company E = 64.8°

Number of employees in company D = 57.6°

If 50% employees of company E transferred to company D, then number of employees in company D = 57.6° + 64.8°/2 = 57.6° + 32.4° = 90°

Required percentage = [90°/360°] × 100 = 25%

Given:

x4 + x2y2 + y4 = 133

x2 - xy + y2 =7

Concept used:

(x2 - xy + y2) (x2 + xy + y2) = x4 + x2y2 + y4

Calculation:

x² - xy + y² = 7     ---(1)

As we know,

(x² - xy + y²) (x² + xy + y²) = x⁴ + x²y² + y⁴

7 × (x² + xy + y²) = 133

x² + xy + y² = 19     ---(2)

Subtract equation (1) from equation(2)

2xy = 12

xy = 12/2 = 6

∴ The Required answer is 6.

Given:-

A train length = 342 m

Train speed = 54 km/h

Bridge length = 438 m

Formula used:-

Time = Distance/Speed

Calculation:-

Speed of train = 54 km/h

Length of train = 54 × (5/18) = 15 m/s

Length of bridge = 438 m

∴ Total distance = Train length + Bridge length

Total length = 342 + 438 = 780

∴ Time = 780/15 = 52 sec

∴ The required time to cross a bridge is 52 sec.

Given:-

LCM(165, 176, 385, 495) = k

Calculation:-

LCM of 165, 176, 385 and 495

LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7 × 11 = 55440

∴ k = 55440

HCF(165, 176, 385 and 495) = HCF(d₁, d₂, d₃)

∴ HCF = 11

So, p = 55440/11

∴ p = 5040

∴ the required value of p is 5040.

Given:

The height of a cylinder is 2/3rd of its diameter.

Cylinder volume is equal to the volume of a sphere whose radius is 4 cm.

Formula used:

Volume of cylinder = πr2h

Volume of sphere = 4/3 πR3

Curved surface area of cylinder = 2 πrh

Calculation:

Let radius of cylinder be 3x

Diameter of cylinder = 2 × 3x = 6x

Height of the cylinder = 6x × 2/3 = 4x

Radius of sphere R = 4 cm

As we know,

Volume of cylinder = πr²h

Volume of sphere = 4/3 πR³

Curved surface area of cylinder = 2 πrh

According to the question

πr²h = 4/3 πR³

3x × 3x × 4x = 4/3 × 4 × 4 × 4

x³ = (4 × 4 × 4)/(3 × 3 × 3)

x = ∛(4 × 4 × 4)/(3 × 3 × 3) = 4/3

Curved surface area of cylinder = 2 πrh = 2π × 3x × 4x = 2π × 3 × 4/3 × 4 × 4/3 = 128 π/3

Given:

A can complete 1/3 of a work in 10 days

⇒ A can complete the whole work in 10 × 3 = 30 days

B can complete 3/5 of the work in = 24 days

⇒ B can do the whole work in 24 × 5/3 = 40 days

Formula used:

Total work = Efficiency × Time

Calculation:

Let the total work = LCM of (30, 40) = 120

Work done by A and B in 10 days = (4 + 3) × 10 = 70

Remaining work = 120 - 70 = 50

Now, let efficiency of C be x, then

⇒ 15x = 50

⇒ x = 50/15 = 10/3

2/3 of the total work = 120 × 2/3 = 80

2/3 of the total work C alone can complete in = 80/(10/3) = 24 days

∴ The correct answer is 24 days.