SSC CPO Tier- I Previous Year Paper (Held On: 9 December 2019 Shift 2)

The option in which the given figure is embedded is,

Hence, option 4 is the correct answer.

The pattern followed is,

The third letter in the given pair and the last two letters are capital letters.

All follow the same pattern, except ‘deefFF’.

Hence, “deefFF” is the odd one.

The option in which the given figure is embedded is,

Hence, option 2 is the correct answer.

Arranging them according to the given information,

After interchanging places,

Here A, E, I, O, U, H, F, and W are in same sequence, H is facing to north, So that all are facing away from centre.

Thus, O will be facing North – East.

Hence, “north – east” is the correct answer.

Drawing diagram according to the given information,

‘B’ is 10 km East of ‘A’.

Hence, “10 km, East” is the correct answer.

Fox is a wild animal.

Whereas,

Cow is not a wild animal, so it is represented separately.

The correct Venn diagram representation is,

Hence, option 2 is the correct answer.

The mirror image, when mirror is placed to right side of the figure is,

Hence, option 4 is the correct answer.

Weary comes first in the order.

It is followed by Weather.

Weather is followed by Weigh.

Weigh is followed by Whip.

Whip is followed by Wing.

Wing is followed by Wink.

The correct dictionary order is,

Weary → Weather → Weigh → Whip → Wing → Wink

‘Wing’ comes fifth in the order.

Hence, “wing” is the correct answer.

The number of triangles in the given figure are,

Hence, “24” is the correct answer.

171, 209 and 133 are multiples of 19.

While,

195 is not a multiple of 19.

Hence, “195” is the odd one.

According to given information,

Verifying the given options,

Option 1 → (35E15) C (5f5) A (20G4)

( 35 – 15 ) = (5 × 5) > (20 /4)

20 = 25 > 5 is not correct.

Option 2 → (5D6) A (4D3) A (3D3)

(5 + 6 ) > (4 + 3) > (3 + 3)

11 > 7 > 6 is correct.

Option 3 → (27G3) C (75G5) C (6F2)

(27 / 3) = (75 / 5) = (6 × 2)

9 = 15 = 12 is not correct.

Option 4 → (5D6) A (6D12) A (13D6)

(5 + 6) > (6 + 12) > (13 + 6)

11 > 18 > 19 is not correct.

Hence, option 2 is the correct answer.

According to the given diagrams,

‘3’ will be facing opposite ‘5’

‘1’ will be facing opposite ‘2’

And,

‘4’ will be facing opposite ‘6’

‘6’ will appear on the bottom face of the last cube.

Hence, “6” is the correct answer.

The pattern followed is,

The arrow symbol moves anti clockwise increasing its places by one, two and three simultaneously.

And,

The geometric figures move anti clockwise increasing their sides simultaneously.

In the first figure there is a triangle, in the second one there is a square, in the third figure there is a pentagon and in the fourth figure there should be a hexagon.

The figure that completes the given pattern is,

Hence, option 2 is the correct answer.

The pattern followed is,

Option 1 → 42 and 72 are even numbers.

Option 2 → 56 is an even number and 63 is an odd number.

Option 3 → 20 and 42 are even numbers.

Option 4 → 132 and 182 are even numbers.

All are in the same pattern, except ’56, 63’.

Hence, “56, 63” is the odd pair.

The shaded part represents Indian doctors who are also Surgeons.

‘5’ represents Indian doctors who are also Surgeons.

Hence, “5” is the correct answer.

According to the given information:

And,

Similarly,

Hence, “QHZFN” is the correct answer.

Pattern followed here is,

KITE has 4 letters, 4 × 2 + 1 = 8 + 1 = 9

MAGIC has 5 letters, 5 × 2 + 1 = 10 + 1 = 11

Similarly,

FELICITATION has 12 letters, 12 × 2 + 1 = 25

Hence, 25 is the correct answer.

The pattern followed is,

The number of figures keeps on increasing along with the number of sides.

In the first image there is only one circle, in the second image there are two triangles, in the third image there are three squares.

And,

The fourth image should consist of four figures, which are 4 pentagons.

Hence, option 2 is the correct answer.

The pattern followed is,

The image is moving anti – clock wise by 45°.

The figure which will come next is,

Hence, option 3 is the correct answer.

According to given information:

Interchanging the following signs and using BODMAS rule,

76 - 5 × 6 ÷ 3 + 4 = ?

76 – 5 × 2 + 4 = ?

76 – 10 + 4 = ?

80 – 10 = 70

Hence, “70” is the correct answer.

Mile comes first.

Mile is followed by furlong.

Furlong is followed by yard.

Yard is followed by foot.

Foot is followed by inch.

The correct logical order is,

2)Mile → 1) Furlong → 4)Yard → 5)Foot → 3)Inch

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

The pattern followed is,

AEONS, PIOUS and QUAIL have three vowels.

Whereas,

PENAL has only two vowels.

Hence, “PENAL” is the odd one.

The pattern followed is,

The place values of letters in ULTERIOR are,

U → 21, 2 + 1 = 3

L → 12, 1 + 2 = 3

T → 20, 2 + 0 = 2

E → 5

R → 18, 1 + 8 = 9

I → 9

O → 15, 1 + 5 = 6

R → 18, 1 + 8 = 9

So,

ULTERIOR is coded as ‘33259969’.

Similarly,

The place values of letters in NAVIGATION are,

N → 14, 1 + 4 = 5

A → 1

V → 22, 2 + 2 = 4

I → 9

G → 7

A → 1

T → 20, 2 + 0 = 2

I → 9

O → 15, 1 + 5 = 6

N → 14, 1 + 4 = 5

So,

NAVIGATION is coded as ‘5149712965’.

Hence, “5149712965” is the correct answer.

The paper when unfolded looks like,

Hence, option 4 is the correct answer.

According to the given information,

‘Pink’ is coded as ‘dur’.

Hence, ‘dur’ is the correct answer.

7 days form a week.

And,

24 hours form a day.

The correct Venn diagram representation is,

Hence, option 2 is the correct answer.

Tin, Zinc and Aluminium are metals.

Whereas,

Steel is an alloy, a mixture of one or more metals.

Hence, “steel” is the odd one out.

Interchanging operators ‘-‘ and ‘ × ’ and numbers ‘4’ and ‘3’

Option 1 → 4 - 9 × 3 = 4

4 – 27 is not equal to 4

Option 2 → 3 × 4 - 9 = 3

12 – 9 = 3

Option 3 → 4 – 3 × 9 = 9

4 – 27 is not equal to 9

Option 4 → 9 × 3 - 4 = 21

27 – 4 is not equal to 21

Hence, option 2 is the correct answer.

The mirror image when the mirror is placed to right side of the figure is,

Hence, option 4 is the correct answer.

The pattern followed is,

For,

(9, 28, 85)

9 × 3 = 27, 27 + 1 = 28

9 × 9 = 81, 81 + 4 = 85

Similarly,

The pair which follows the same pattern is,

(7, 22, 67)

7 × 3 = 21, 21 + 1 = 22

7 × 9 = 63, 63 + 4 = 67

Hence, “(7, 22, 67)” is the correct answer.

Drawing the Venn diagram,

Conclusion 1: Some petunias are black → False (This is definitely false)

Conclusion 2: No petunia is black → True (This is definitely true)

Hence, “only conclusion 2” follow.

Drawing the Venn diagram,

Conclusion 1: Some stationery are papers → True (This is definitely true)

Conclusion 2: No stationery is paper → False(This is definitely false)

Conclusion 3: No book is stationery → False (This is definitely false)

Conclusion 4: Some books are papers → True (This is definitely true)

Hence, “only conclusions 1 and 4” follow.

The pattern followed is,

The place values of SPORTS are,

S → 19, P → 16, O → 15, R → 18, T → 20, S → 19

SPORTS → 19 + 16 + 15 + 18 + 20 + 19 = 107, 107 × 2 = 214

So,

SPORTS : 214

Similarly,

For SOCIAL,

S → 19, O → 15, C → 3, I → 9, A → 1, L → 12

SOCIAL → 19 + 15 + 3 + 9 + 1 + 12 = 59, 59 × 2 = 118

So,

SOCIAL : 118

Hence, “118” is the correct answer.

The pattern followed is,

The number in the first bracket from the left is incorrect.

37 is the correct number which has to be in the first bracket, not 39.

Hence, option 4 is the correct answer.

Eagle, Ostrich and Kiwi are birds.

Similarly,

Sparrow is a bird.

‘Sparrow’ is similar to the given words and hence belong to the same group.

Hence, “sparrow” is the correct answer.

The pattern followed is,

For first column:

48 – 28 = 20

3 × 20 = 60

And,

For second column:

71 – 65 = 6

18 × 6 = 108

Similarly,

For third column:

35 – 21 = 14

7 × 14 = 98

Hence, “21” is the correct answer.

Howdah is a carriage which is positioned on the back of a camel to carry things.

Similarly,

A saddle is the seat fastened on the back of a horse for riding, which is made of leather.

‘Saddle’ is related to the third term in the same way as the second term is related to the first term.

Hence, “saddle” is the correct answer.

Wall is made of Bricks.

Similarly,

Fabric is made of Yarn.

Hence, “yarn” is the correct answer.

Chef is a trained professional cook, who is proficient in all aspects of food preparation.

Similarly,

A producer is a person who oversees film production, plan and coordinate various aspects of film production.

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

Hence, “film : producer” is the correct answer.

Grill, Roast and Steam are different methods of cooking.

Whereas,

Fire is a process in which substances combine chemically with oxygen from the air and typically give bright light.

Hence, ‘Fire’ is odd one out.

The pattern followed is-

Option 1 → 25 × 2 + 3 = 53

Option 2 → 19 × 2 + 1 = 39

Option 3 → 68 × 2 + 1 = 137

Option 4 → 37 × 2 + 1 = 75

All follow the same pattern, except ’25, 53’.

Hence, “25, 53” is the correct answer.

The pattern followed is,

9 × 7 : 9 × 8

So,

63 : 72

Similarly,

161 : 184

23 × 7 : 23 × 8

So,

161 : 184

Hence, “161 : 184” is the correct answer.

The pattern followed is,

Option 1 → 6 × 12 = 72

Option 2 → 12 × 8 = 96

Option 3 → 24 × 4 = 96

Option 4 → 6 × 16 = 96

All other pairs when multiplied give 96 as a result, except ‘6, 12’.

Hence, “6, 12” is the odd pair.

The pattern followed is,

17² = 289

17 + 1 = 18

18² = 324

So,

289 : 324

Similarly,

21² = 441

21 + 1 = 22

22² = 484

So,

441 : 484                   

Hence, “484” is the correct answer.

The pattern followed is,

For 10 : 142

10 + 2 = 12

12² = 144

144 – 2 = 142

So,

10 : 142

And, For 17 : 359

17 + 2 = 19

19² = 361

361 – 2 = 359

So,

17 : 359

Similarly,

21 + 2 = 23

23² = 529

529 – 2 = 527

So,

21 : 527

Hence, “527” is the correct answer.

The pattern followed is,

Similarly,

Hence, “ZPKYVR” is the correct answer.

The pattern followed here is,

Hence, “77” is the correct answer.

The pattern followed is,

Hence, “REA” is the correct answer.

The pattern followed is,

1 × 1 + 1 = 2

1 × 2 + 1 = 3

2 × 3 + 1 = 7

3 × 7 + 1 = 22

7 × 22 + 1 = 155

Hence, “155” is the correct answer.

The pattern followed is,

Hence, “I” is the correct answer.

• Jaduguda is a village in the Singhbhum district of Jharkhand.
• Jaduguda is known for its uranium mines and uranium deposits.
• The exploitation of Uranium started in 1962.
• Uranium is also found in the mines of Udaipur, Rajasthan.
• Uranium is nuclear fuel with chemical symbol U and atomic number 92

Keratin:-

• Keratin protein protects the epithelial cells from damage.
• Epithelial cells are a type of cell that lines the surfaces of your body.
• They are found on your skin, blood vessels, urinary tract, and organs.
• Keratin is the key structural material making up hair, nails, feathers, horns, claws, hooves, calluses, and the outer layer of skin among vertebrates.
• Keratin proteins comprise the cytoskeletal component of these epithelia.
• Keratin filaments are attached to the plasma membrane via desmosomes, and together these structural components form a three-dimensional array within the cytoplasm of epithelial cells and tissues.

• The Governor-General of India was given the title of Viceroy for the first time in 1858.
• After the mutiny of 1857 the title of Viceroy was created in 1858.
• Lord Canning was the first Viceroy of India.
• Government of India Act, 1858 was passed to end the rule of East India company and and transferred it to the British crown.
• The act also ended the system of double government by abolishing the Board of Control and Court of Directors.
• It also created a new office, Secretary of State for India.

• The term 'Askaryan effect' is associated with the Physics functional area of science.
• It is called the Askaryan effect or Askaryan radiation.
• The Askaryan effect is the phenomenon whereby a particle traveling faster than the phase velocity of light in a dense dielectric medium (such as salt, ice) produces a shower of secondary charged particles which contain a charge anisotropy and thus emits a cone of coherent radiation in the radio or microwave part of the electromagnetic spectrum.
• The Askaryan effect describes coherent electromagnetic radiation from high-energy cascades in dense media with a collective charge.
• This effect is closely related to the Cherenkov effect.
• Cherenkov radiation/effect is light produced by charged particles when they pass through an optically transparent medium at speeds greater than the speed of light in that medium.

• Viceroy Lord Curzon bestowed the Kaiser-i- Hind gold medal to Raja Ravi Varma in 1904.
• Shakuntala, Nair Lady Adorning Her Hair, There Comes Papa were notable works of Raja Ravi Verma.
• Raja Ravi Varma was related to the royal family of Travancore.
• Mahatma Gandhi was also awarded the Kaisar-i-Hind title for raising an Indian Ambulance Core during Boer wars.
• Mahatma Gandhi returned the Kaisar-i-Hind title as a protest against the Jallianwala-Bagh massacre in 1919.

• Aparna Kumar became India’s first woman IPS officer to successfully complete the South Pole expedition.
• Aparna Kumar is also an officer of Indo-Tibetan Border Police (ITBP).
• The first person to reach the south pole was Roald Amundsen.
• Lieutenant Ram Charan of the Indian Navy, was the first Indian to visit the South Pole.
• Colonel J.K. Bajaj became the first Indian to reach the South Pole at a 0-degree latitude in Antarctica, South Pole.

• The Glass bottle constitutes a closed system and when it is filled with water, the water fills the bottle completely.
• But when the water freezes, the ice expands and the volume of the water increases and the bottle breaks because it is made of glass and glass cannot endure tensile stress which the ice exerts on the bottle.
• When ice expands its volume becomes 9-10% more than that of water. Hence, the glass bottle cannot accommodate the increase in the volume of 10% and hence it breaks.
• All inelastic materials will break when tensile stress is acting on them.

• According to Census 2011, Hindi has retained its position as a predominant language spoken by about 43.63% of the population.
• Bengali was the second most spoken language which is spoken by 8.03% of the population.
• Marathi was at 3rd with 6.86% of speakers.
• Out of 22 scheduled languages,13 were reported as the mother tongue by at least 1% of the population.
• Sanskrit is spoken by nearly 25000 people.
• The Eighth Schedule of the Indian Constitution provides a list of all the officially recognized languages in India. It is found in Article 344(1) and 351 of the Constitution
• As of now, there are 22 languages present that are officially recognized by the Indian government
• They are 1) Assamese, (2) Bengali, (3) Gujarati, (4) Hindi, (5) Kannada, (6) Kashmiri, (7) Konkani, (8) Malayalam, (9) Manipuri, (10) Marathi, (11) Nepali, (12) Oriya, (13) Punjabi, (14) Sanskrit, (15) Sindhi, (16) Tamil, (17) Telugu, (18) Urdu (19) Bodo, (20) Santhali, (21) Maithili and (22) Dogri
• Information on the other schedules is given below
• | Schedule | Description | | --- | --- | | Fifth | Administration Of Scheduled Areas and Tribes | | Ninth | Protection of land reform laws from being challenged in courts on the grounds of violation of fundamental rights | | Twelfth | Contains powers, authorities and responsibilities of municipalities |

• Balwant Moreshwar Purandare was awarded the Padma Vibhushan, the second-highest civilian award, for contribution in the field of art-acting-theatre.
• He is popularly known as Babasaheb Purandare.
• He is known for his books like 'Raja Shiv Chhatrapati', 'Purandaryanchi Daulat', 'Purandaryanchi Naubat' and 'Gadsanch'.
• The Maharashtra government had bestowed the ‘Maharashtra Bhushan’, the state’s highest honour, on Purandare in 2015.
• Along with him, 3 other people were awarded Padma Vibhushan in 2019.

• In Multi-brand product retail trading, only 51% FDI is allowed.
• There are two routes in India's FDI they are Automatic Route and Government Route.
• In single-brand retail trading, 100 percent Foreign Direct Investment (FDI) is allowed.
• In the wholesale trading, a 100 % FDI is allowed under the automatic route.
• In India, foreign direct investment policy is governed by the Reserve Bank of India, under the Foreign Exchange Management Act, 2000.

• Arpinder Singh won a Gold Medal for India in Men’s triple jump event after a gap of 48 years in the Asian Games in Jakarta.
• Before Arpinder, the previous champion was Mohinder Singh Gill in 1970.
• Arpinder's last medal was bronze in the 2014 Commonwealth Games in Glasgow.
• Ruslan Kurbanov of Uzbekistan won the silver while Shuo Cao of China was third with a bronze medal.

• Sweating is a process done by the body to regulate its temperature.
• When the body perspires the moisture then evaporates and takes excess heat with it.
• It leads to the lowering of internal temperature.
• Sweat consists of water and salts.
• The perspiration works on the principles of the First and second laws of thermodynamics.
• Hypothalamus is responsible for sending the signal to the sweat-producing skin glands whenever the temperature of the body increases.
• If the temperature decreases, such glands constrict so that the production of sweat also gets reduced.
• Hypothalamus is also responsible for the dilation of blood vessels.

Key Points

• The process of transformation of a substance in a gaseous state into a liquid state due to change in pressure or temperature of the substance is called "condensation".
• Condensation is caused by the loss of heat.
• When moist air is cooled, it may reach a level when its capacity to hold water vapor ceases.
• Then, the excess water vapor condenses into liquid form.
• If it directly condenses into solid form, it is known as sublimation.
• Condensation also takes place when the moist air comes in contact with some colder object and it may also take place when the temperature is close to the dew point.
• Condensation depends upon the amount of cooling and the relative humidity of the air.
• Condensation is influenced by the volume of air, temperature, pressure, and humidity.

Explanation:

Thundering: The continuous sound produced during the process of lightning.

• During the occurrence of thunder and lightning, lightning is seen before thunder is heard as light travels faster than sound.
• The speed of light is 3 x 10⁸ m/s and the speed of sound is 343 m/s.
• When the positive and negative charges grow large enough, a giant spark or lightning occurs between the two charges within the cloud.

Lightning is an electrical discharge caused by imbalances between storm clouds and the ground, or within the clouds themselves.

• Thunder is caused by lightning. When a lightning bolt travels from the cloud to the ground it actually opens up a little hole in the air.

Once the light is gone the air collapses back in and creates a sound wave that we perceive as thunder and so lightning is seen before thunder is heard.

• The sun heats the earth through radiation.
• Radiation is energy traveling through space. The radiation form of energy does not require a medium to travel through.
• Sunlight carries energy, which warms up the Earth, as the ground is heated by sunlight, it begins to radiate.
• When the heat reaches the earth it warms the molecules of the atmosphere, and they warm other molecules and so on and this heat transfer is called conduction.

• The 10 percent reservation in central government jobs under economically weaker sections (EWS) category is available to the persons whose family income is below 8 lakhs.
• The family or person should not possess agricultural land of size 5 acres or above.
• The family or person should not own or possess a residential flat of area 1000 sq.feet or more.
• The person or person's family should not own a residential plot of area 100 sq.yards or more in notified municipalities as per GOI.

• Bhutia tribes are of Tibetan origin, who migrated to Sikkim around the 16th century.
• Bhutia tribes speak Sikkimese Lepcha, Bhutia, Nepali, English and Hindi.
• Losar and Losoong are the main festivals celebrated among the Bhutia tribes. Most of them follow tantric Buddhism.

• Kharavela, the then Emperor of Kalinga,  inscribed the Hathigumpha (Elephant Cave) inscription in Udayagiri Hills, Odisha during 2nd century BCE.
• The Hathigumpha inscription situated near Bhubaneswar gives information about year-wise achievements of Kharavela.
• The inscription starts with a version of the auspicious Jain Namokar Mantra.
• The Inscription consists of seventeen lines in deep-cut Brahmi script.
• The contents of the Hatigumpha Inscriptions are taken as true records of Kharavela’s reign.
• The inscription gives a note on the political, religious, cultural and social condition of Kalinga during that glorious period.

• Rabindranath Tagore returned the knighthood after the Jallianwala massacre.
• Rabindranath Tagore received the Knighthood for his Services to Literature.
• The arrest of Dr. Saifuddin Kitchlu and Dr. Satyapal led to unrest among the masses of Punjab
• The unrest led to a peaceful meeting at Jallianwala Bagh in Amritsar.
• General Reginald Dyer ordered the indiscriminate heavy firing on this masses leading to Jallianwala Bagh Massacre of 13th April 1919.

Key Points

• Ponung dance is a popular art form practiced in Arunachal Pradesh.
• It is traditionally the folk dance of the Adis community.
• It has women dancers and they often hold each other’s hand and dance in formations.
• It is a lively dance accompanied by mesmerizing songs.
• It is exhibited during the festival that is celebrated before the harvesting.
• This dance is performed on all-important and auspicious occasions.
• Costume: mainly comprises of a long skirt and Kurti.
• The purpose of this dance festival is to seek a good harvest and welfare of the village community.

The correct answer is Jyotirao Phule.

• Jyotirao Phule founded the Satyashodhak Samaj in 1873 in present-day Maharashtra.
• The objective of the Samaj - to liberate the Shudras and to prevent their ‘exploitation’ by the upper caste Maratha.
• It campaigned against idolatry, denounced the chaturvarnya system (the caste system) and rejected the need for a Brahman priestly class as educational and religious leaders.
• Satyashodhak Samaj campaigned for the spread of rational thinking and rejected the need for priests.
• Phule was a social activist and thinker, who pioneered women’s education in India, especially in Maharashtra.
• He established this Samaj with the ideals of human well-being, happiness, unity, equality, and easy religious principles and rituals.
• In 1873, he wrote a book named Gulamgiri, meaning slavery.

• The infant mortality rate in India in 2016 was 34 per 1,000 live births.
• The infant mortality rate declined by 8% in 2016.
• The highest decline was reported by Chandigarh which was of 7 points
• The highest increase was reported by Arunachal Pradesh which was 6 points.
• The Infant mortality rate (IMR) is defined as the number of deaths per 1,000 live births of children under one year of age.

• Dattu Bhokanal is associated with Rowing.
• Dattu Baban Bhokanal is an Indian rower who had qualified for the 2016 Rio Summer Olympics.
• He qualified for the Olympics after winning a silver in the men's single sculls event at the FISA Asian and Oceania Olympic Qualification Regatta at Chung-ju in South Korea where he clocked 7 minutes and 07.63 seconds.
• He is the only Indian rower to qualify for the Rio Olympics and is only the ninth rower to represent India in the Olympics.
• He won the gold medal in the 2018 Asian Games in Men's Quadruple sculls.

The correct answer is five.

• Every Panchayat can continue for 5 years from the date of its first meeting. It can be dissolved earlier in accordance with State law.
• A Panchayat reconstituted after premature dissolution, continues only for the remainder of the period. But if the remainder of the period is less than 6 months it is not necessary to hold elections.
• The 73rd Amendment Act of 1992 gave constitutional status to the Panchayati Raj institutions.
• The Panchayati Raj system is for only those states having a population of more than 20 lakhs.
• The first gram panchayat of India was at Nagaur district of Rajasthan.

• Bharat Ratna Awards 2019 was conferred to Bhupen Hazarika, Nanaji Deshmukh, Pranab Mukherjee.
• Bhupen Hazarika is an Assamese singer-composer.
• Nanaji Deshmukh is a social activist from Maharashtra.
• Pranab Mukherjee was Former President of India.
• Shyama Prasad Mukherjee wasn't awarded the Bharat Ratna. He was a politician and a Union Minister in Jawaharlal Nehru cabinet.

• The summer Olympic Games 2024 to be held in Paris.
• Paris will become the second city to host the Olympics three times, after London (1908, 1948, and 2012).
• It was previously the host in the year 1900 and 1924. The year 2024 will mark the centenary of the Paris Games of 1924.
• These will be the sixth Olympic Games hosted by France (three summer and three winter).
• Paris was elected as the host city on September 13, 2017, at the 131st IOC Session in Lima, Peru.
• Paris is the capital of France.
• Currencies: Euro, CFP franc.

The correct answer is Warli.

• Warli is a traditional and tribal painting from Maharashtra.
• The tribes who mostly indulged in Warli paintings are from the north of Sahyadri Range.
• A painting is made using only white pigment made up of a mixture of rice paste and water, and the gum is used as a binder.
• Madhubani Painting is famous in the state of Mithila in Nepal and Bihar in India.
• Madhubani painting is done with tools which include fingers, twigs, brushes and matchsticks and natural dyes.

• India finished with 3rd rank in the 2018 Commonwealth Games with 26 Gold medals.
• India won a total of 66 medals including 26 Gold, 20 Silver and 20 Bronze.
• India's shooters won 16 medals and wrestlers bagged 12 medals at CWG 2018.
• Table Tennis sensation Manika Batra was India's best athlete at the Gold Coast Games, winning 4 medals.

• Professor Chintamani Nagesa Ramachandra Rao, popularly known as CNR Rao, of the Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore was awarded the First Sheikh Saud International Prize for Materials Research given by the Centre for Advanced Materials of the UAE.
• The prize includes a plaque, a medal and a cash prize of $100000.
• Other awards of CNR Rao are Bharat Ratna (2014), Padma Shri (1974), Padma Vibhushan (1985) and Karnataka Ratna (2001), among other honors.
• Jayant Vishnu Narlikar is an Indian astrophysicist who developed the conformal gravity theory with Sir Fred Hoyle, known as Hoyle–Narlikar theory.
• Raghunath Anant Mashelkar, also known as Ramesh Mashelkar, is an Indian Chemical Engineer.
• Ashoke Sen is an Indian theoretical physicist and professor.

• Cinematographer, screenwriter and filmmaker, Govind Nihalani honored with the 'Kalamaharshi Baburao Painter Award' for his contribution to the film industry at 2019 Kolhapur International Film Festival (KIFF).
• The 7th edition of the film festival was held in February 2019.
• The award is named after Baburao, a native of Kolhapur, Maharashtra, who was a painter, sculptor, and filmmaker of the silent film era.
• Baburao was one of the leading stage painters for theatres in Western India during the period of 1910 and 1916.

The correct answer is option 3.

• The function of the retina is to process the information gathered by photoreceptor cells and send them to the brain to decide what the picture is.
• The retina is located near the optic nerve and is a thin layer of tissue that lines the back of the eye on the inside.
• The purpose of the retina is to receive light that the lens has focused, convert the light into neural signals, and send these signals on to the brain for visual recognition.
• The retina is a complex transparent tissue consisting of several layers, only one of which contains light-sensitive photoreceptor cells.
• The light must pass through the overlying layers to reach the photoreceptor cells.

The correct answer is Mohammad Bin Tughlaq.

Key Points

• Ibn Battuta visited India during the rule of Mohammed Bin Tughlaq.
• Ibn Battuta was a Moroccan traveller.
• Rihla was a book written by Ibn Batuta.
• Rihla is a travelogue based upon the experiences of the travellers.

Additional Information

• As per the Constitution of India, Panchayats at the intermediate level may not be constituted in a state having a population not exceeding twenty lakhs.
• PART IX Article 243(B) provides for Panchayati raj institutions in every village, district and state. It provides the conditions to be met for setting up a panchayat
• The 73rd Constitutional Amendment Act(1992) provided a Constitutional status to the Panchayati Raj Institutions in India through the insertion of Article 243 to Part IX of Indian Constitution.
• Part IX focused on organizing the 3 tier Panchayat system, which would be constituted in every state at the village level, intermediate level and district level.

Surkotada is situated in Kutchh district of Gujarat.

• It is the only Indus Valley site where the remains of a horse have actually been found.
• Kalibangan is situated in Hanumangarh, Rajasthan.
• Banawali is situated in Hisar, Haryana.
• Mohenjo Daro is situated in Larkana, Sindh.

• All disputes and doubts regarding the election of the President are adjudicated by the Supreme Court.
• The decision given by the Supreme Court will not be challenged.
• Article 54 of the Indian Constitution deals with Election of President and Article 61 deals with his impeachment.
• The President is elected by members of the Electoral College consisting of the elected members of both the Houses of Parliament.
• The elected members of the Legislative Assemblies of the states and the elected members of the Legislative Assemblies of the Union Territories of Delhi and Puducherry.

• Correct answer is option 2 i.e 40 years.
• Atal Pension Yojana is a pension scheme aimed at the unorganized sector, who join the National Pension System (NPS) and who are not members of any statutory social security scheme.
• This scheme replaced the previous Swavalamban Yojana.
• Benefits under APY: Fixed pension for the subscribers ranging between Rs. 1000 to Rs. 5000, if he joins and contributes between the age of 18 years and 40 years.
• Age to join APY: Minimum - 18 years and maximum - 40 years. Under APY minimum period of contribution by the subscriber would be 20 years or more.
• Eligibility: It is open to all bank account holders who are not members of any statutory social security scheme.
• It is Government of India Scheme, which is administered by the Pension Fund Regulatory and Development Authority.

• The process of clot formation is known as coagulation.
• The process of coagulation is known as Hemostasis.
• Hemostasis involves three steps that are avascular spasm, the formation of a platelet plug, and coagulation.
• Platelets and proteins present in plasma helps in coagulation.
• Vitamin K helps in blood clotting.
• The process of transferring blood is called a Blood transfusion.

• The Kidneys are located on both sides of the human body.
• The kidneys are bean-shaped organs, located against the back muscles in the upper abdominal area.
• They sit opposite each other on both the left and right sides of the body.
• Each kidney is about 4 or 5 inches long and their role is to filter the blood.
• They remove waste, control the body's fluid balance, and keep the right levels of electrolytes.
• The nephron is the structural and functional unit of the kidney.
• Each human adult kidney contains around 1 million nephrons.

The correct answer is LIC of India.

• Pradhan Mantri Vaya Vandana Yojana is a pension scheme for senior citizens aged 60 or above.
• The scheme has a rate of return of 8% annually for 10 years.
• This scheme is being implemented through the Life Insurance Corporation of India (LIC).
• The scheme was launched in July 2017.
• It is exempted from goods and services (GST) tax

The correct answer is Madhya Pradesh

Key Points

• Bagh Print is a traditional Indian handicraft originating in Bagh, Dhar district of Madhya Pradesh.
• Bagh gets its name from the ancient Bagheshwari Devi temple situated there and is famous both for the ancient Bagh Caves.
• The process of printing and fabric treatment is a multi-layered process that includes colour treatment, fabric soaking, boiling, drying, washing, and printing.
• Bagh prints are made by hand applying natural and vegetable-based dyes using carved wood relief blocks.
• Red and black dyes are most common, but indigo, mustard, and khaki dyes are also used.

Additional Information

• Know about Madhya Pradesh:
• Capital: Bhopal.
• Formed in: 1 November 1956.
• Official Language: Hindi.
• Regional Festivals: Kumbha in Ujjain known as Simhastha, Aalami Tableegi Ijtima, fair of Ramlila, fair of Hira Bhumia, fair of Pir Budhan, fair of Nagaji, fair of Tejaji.
• Art Forms:
• Painting - Lok chitrakar, Chitravan, Mandana, Sanjhi, Thapa, Pithora.
• Music - Relo, Gooning, Leja, Chait Parah, Dhankul.
• Dance - Karma, Jawara, Tertali, Lehangi, Ahiri, Baredi, Gaur. Maria, Drum, Matki, Grida, Phulpati.
• Geographical Indications: Chanderi Fabric, Leather Toys of Indore, Bagh Prints, Bell Metal Ware of Datia and Tikamgarh, Maheshwar Sarees & Fabrics, Ratlami Sev.
• Tiger Reserve: Kanha, Pench, Bandhavgarh, Panna, Satpura, Sanjay-Dubri.

• Starred Question is one for which an oral answer is required to be given by the Minister on the floor of the House.
• The maximum number of Starred Questions for oral answers admitted for discussion on a particular day in the Lok Sabha is 20.
• Unstarred Question is one for which the Minister lies on the table written answer.
• Short Notice Question is one for which can be asked by members on matters of the public importance of an urgent nature.
• In India, the first hour of every Parliamentary sitting is allotted for Question Hour.
• In this hour, the Members of the Parliament raise questions related to the activity of the Administration.
• Types Of Questions during Question Hour Method of Answer :
• 1. Starred Oral reply
• 2. Non- starred Written reply

• The National Capital Territory of Delhi shall have Council of Ministers consisting of not more than 10% or 0.1, of the total number of members in the Legislative Assembly, including the Chief Minister.
• 69^th constitutional amendment Act made the Union territory of Delhi into a National capital region and provided for a state legislative assembly and a Lieutenant Governor.
• As per the 91st constitutional amendment act, the strength of the council of ministers should not exceed 15% to that of Lok sabha.
• Article 81 caps the number of Lok Sabha seats at 550 of which 20 members are to be elected from Union Territories.

• The amount of insurance cover available for accidental death under the Pradhan Mantri Suraksha Bima Yojana (PMSBY) is ₹2 lakh.
• PMSBY is a social security scheme announced by the Government of India in the 2015 Budget.
• It is an accident insurance scheme, which offers a one-year accidental death and disability cover, which can be renewed.
• The cover is for a one-year period, starting June 1 to May 31 of the subsequent year.
• Under this scheme, the risk coverage available is Rs 2 lakh for accidental death & permanent total disability, and Rs 1 lakh for permanent partial disability.
• Eligibility: All individual bank account holders in the 18-70 year age group are eligible to join PMSBY.
• The premium payable is Rs 20 per annum per member.

The correct answer is option 2, i.e. Vice President.

• The President may resign from his office by writing a letter of resignation addressed to the Vice President of India.
• The candidate should have completed 35 years of age to be eligible as a candidate for the presidential election.
• Article 61, deals with the impeachment of President.
• If the office falls vacant by resignation, removal, death or otherwise, then election to fill the vacancy should be completed within six months from the date of the occurrence of such a vacancy.
• Vice president gives his resignation to President
• Chief Election commissioner gives his resignation to President.

• Colour of the plants is green due to the presence of Chlorophyll.
• Chlorophyll is the green color pigment which absorbs wavelength from sunlight.
• It helps leaves to capture the energy of the sunlight and this energy is used to synthesis food from carbon dioxide and water.
• Since the synthesis of food occurs in the presence of sunlight, it is called photosynthesis.
• Chlorophyll absorbs certain wavelengths of light within the visible light spectrum.
• Chlorophyll absorbs light in the red and the blue regions of the visible light spectrum.
• Greenlight is not absorbed but reflected, making the plant appear green.
• Chlorophyll is found in the chloroplasts of plants.

• A ‘solar eclipse’ occurs between sun rays and new moon when the moon passes directly in front of the sun so that its shadow lies on the earth.
• The moon lies between the sun and the earth.
• The ‘lunar eclipse’ takes place when the earth comes in between the sun and the moon. A lunar eclipse takes place on a full moon.

The correct answer is Sultan Abdullah.

Key Points

• Sultan Abdullah was elected as Malaysia's new King on 24 January 2019, following the abdication of Sultan Muhammad V in January 2019.
• He is the ruler of the Malaysian state of Pahang.
• He will have a five-year term.
• He is the current President of the Asian Hockey Federation and a council member of FIFA, the world football body.
• Malaysia's King Muhammad V has abdicated after two years on the throne on 6 January 2019.
• It is for the first time a king has resigned before completing their five-year tenure.
• Malaysia is a constitutional monarchy and the king assumes a largely ceremonial role.
• However, the king's assent is needed before the appointment of a Prime minister or senior public officials.

Additional Information

• Capital of Malaysia- Kuala Lumpur
• Currency of Malaysis- Malaysian ringgit

• Himshikha is NOT one of the three parallel ranges of the Himalayas in its longitudinal extent.
• The three parallel ranges of the Himalayas are 1) Himadri (Great or Inner Himalayas) 2) Himachal (Lesser Himalayas) 3) Shiwaliks (Outer Himalayas).
• Himadri is the most continuous range consisting of the loftiest peaks and contains all the prominent Himalayan peaks.  The core of this part of Himalayas is composed of granite.
• Himachal is the range lying to the south of the Himadri and is mainly composed of highly compressed and altered rocks. This region is well known for its hill stations. Pir Panjal range forms the longest and the most important range.
• Shivalik is the outer most range of the Himalayas extends over a width of 10-50 Km . It is composed of unconsolidated sediments brought down by rivers from the main Himalayan ranges located farther north.

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

• Hemis National Park is a high altitude national park in the eastern Ladakh Union Territory of the Republic of India.
• The north of this protected area is enclosed by the banks of the Indus River.
• It is named after the famous monastery, Hemis gompa that is situated 40 km southeast of Leh.
• It is home to an immense population of snow leopards.
• Apart from snow leopards, the flora includes bharal, argali, Asiatic ibex, Eurasian brown bear, Tibetan wolf, red fox, etc.
• The Hemis National Park is the second-largest contiguous protected region of the country after the Nanda Devi Biosphere Reserve.

• Madai Festival is one of the most popular festivals of Chhattisgarh.
• Madai Festival is celebrated by the Gond tribe.
• It is celebrated from the beginning of December to the end of March.
• Kurna and Charama tribes of Chhatisgarh celebrate the Madai festival.
• Konark Festival, International sand art festival are festivals of Odisha.
• Dosmuchey festival, Matho Narang, Gemis festival, Galdan Namchot are festivals of Jammu & Kashmir.

(cosθ + sinθ)/(cosθ – sinθ) = (√3 + 1)/( √3 – 1)

Using dividendo and componendo,

⇒ (cosθ + sinθ + cosθ – sinθ)/(cosθ + sinθ – cosθ + sinθ) = (√3 + 1 + √3 – 1)/( √3 + 1 - √3 + 1)

⇒ 2cosθ/2sinθ = 2√3/2

⇒ cotθ = √3

⇒ cotθ = cot30

⇒ θ = 30

Now,

⇒ sec θ = sec 30 = 2/√3 = 2√3/3

Number of employees in department C = 122.4°

Total number of employees in department D and E = 64.8° + 36° = 100.8°

Required percentage = [(122.4 – 100.8°)/100.8] × 100 = 21.4%

Total surface area of cylinder = 2πr(r + h)

Curved surface area of cylinder = 2πrh

⇒ 2πr(r + h)/2πrh = 3/1

⇒ (r + h)/h = 3

⇒ r + h = 3h

⇒ 2h = r

⇒ h = r/2

⇒ 2πr(r + h) = 1848

⇒ 2 × 22/7 × r × (r + r/2) = 1848

⇒ 2 × 22/7 × r × 3r/2 = 1848

⇒ r² = 7 × 7 × 4

⇒ r = 7 × 2

⇒ r = 14

⇒ h = r/2

⇒ h = 14/2 = 7 cm

⇒ Volume of cylinder = πr²h = 22/7 × 14 × 14 × 7 = 4312 cm³

As we know,

4309 – 2388 = 1921

8151 – 4309 = 3842

8151 – 2388 = 5763

HCF of 1921, 3842 and 5763 is 1921.

As we know, 1921 = 17 × 113

So, the three - digit number is 113.

When we divide 2388, 4309 and 8151 by 113 we find remainder 15 in each case.

Short Trick:

∠BIC = 90 + ∠A/2

108 = 90 + ∠A/2

∠A = 18 × 2 = 36

Detailed Method:

In △ BIC,

∠B/2 + ∠C/2 + ∠BIC = 180°

⇒ ∠BIC = 180° – (∠B + ∠C)/2

⇒ ∠BIC = 180° – (180° – ∠A)/2

⇒ ∠BIC = 180° – 90° – ∠A/2

⇒ 108° = 90° – ∠A/2

⇒ ∠A/2 = 108 – 90 = 18

⇒ ∠A = 18 × 2 = 36°

A can do 2/5 of work in 6 days

A can complete the whole work in 6 × 5/2 = 15

B can do 2/3 of work in 12 days

B can complete the whole work in 12 × 3/2 = 18 days

Total work = 90

Work done by A and B in 6 days = (6 + 5) × 6 = 11 × 6 = 66

Remaining work = 90 – 66 = 24

Let efficiency of C be x.

⇒ 8 × x = 24

⇒ x = 24/8 = 3

So, efficiency of C is = 3

A and C will complete the same work in 90/(6 + 3) = 90/9 = 10 days

The number of workers whose daily wages are Rs. 500 or more but less than Rs. 650 is = 58 + 72 + 60 = 190

Number of workers whose daily wages are Rs. 650 or more but less than Rs. 750 = 55 + 48 = 103

Required percentage = [(190 – 103)/103] × 100 = 84.466 ≈ 84.5%

Let the length of the second train be x cm.

Length of the firsttrain = 270 m

Speed of the first train = 42 km/h

Speed of the second train = 57 km/h

Time taken to cross each other = 18 sec

∵ Speed = Distance/Time

According to the question,

⇒ (57 + 42) × 5/18 = (270 + x)/18

⇒ 99 × 5 = 270 + x

⇒ x = 495 – 270

⇒ x = 225

∴ Length of second train 225 m.

As we know

S = (a + b + c)/2

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

S = (60 + 112 + 164)/2 = 336/2 = 168

Area of triangle = √{168 (168 – 60) (168 – 112) (168 – 164)}

= √(168 × 108 × 56 × 4)

= √[2 × 2 × 2 × 3 × 7 × 2 × 2 × 3 × 3 × 3 × 2 × 2 × 2 × 7 × 2 × 2]

= 2016 m²

Cost of levelling of 1 m² of the park = 8.5

Cost of levelling of 2016 m² of the park = 8.5 × 2016 = Rs. 17136

Let speed of train and bus x km/hr and y km/hr respectively

According to the question,

⇒ 150/x + 90/y = 7/2

Divided by 3

⇒ 50/x + 30/y = 7/6     ----(1)

100/x + 140/y = 11/3

Divided by 2

⇒ 50/x + 70/y = 11/6      ----((2)

Subtract equation (1) from equation (2)

⇒ 40/y = 4/6

⇒ y = 60 km/hr

From equation (1)

⇒ 50/x + 30/60 = 7/6

⇒ 50/x + 1/2 = 7/6

⇒ 50/x = 7/6 – 1/2

⇒ 50/x = (7 – 3)/6 = 4/6

⇒ x = 50 × (6/4)

⇒ x = 75 km/hr

Speed of train 75 km/hr

Total work = 30 unit

Work done by A, B and C in 3 hours = (3 + 2 + 1) × 3 = 6 × 3 = 18

Let the efficiency of Pipe D be x.

⇒ 30 × x = 18

⇒ x = 18/30 = 3/5

Pipe D alone empty the full tank in = 30/(3/5) = 50 hrs

Given:

The average of n numbers is 42.

75% of the numbers are increased by 4 each and the remaining numbers are decreased by 8 each.

Formula used:

Average = sum of observations/Number of observations

Calculation:

Average of n numbers = 42

Sum of n numbers = 42n

New sum of n number = 42n + {n × (75/100) × 4} – {n × (25/100) × 8}

⇒ 42n + 3n – 2n

⇒ 43n

New average of n numbers = 43n/n

⇒ 43

∴ The average of the numbers, so obtained is 43.

x² - √7x + 1 = 0

⇒ x - √7 + 1/x = 0

⇒ x + 1/x = √7

(x + 1/x)³ = x³  + 1/x³ + 3( x + 1/x)

⇒ (√7)³ = x³ + 1/x³ + 3√7

⇒ x³ + x ^{- 3} = 7√7 - 3√7

⇒ x³ + x ^{- 3} = 4√7

Given, OP = 14 cm, PA = 10 cm, PB = 16 cm

Let radius of circle be r cm.

⇒ OQ = OE = r cm

⇒ PE = (14 – r) and PQ = (14 + r)

As we know,

PE × PQ = PA × PB

⇒ (14 – r) (14 + r) = 10 × 16

⇒ 14² – r² = 160

⇒ 196 – r² = 160

⇒ r² = 196 – 160 = 36

⇒ r = √36

⇒ r = 6 cm

⇒ Diameter of the circle = 2 × 6 = 12 cm

The number of workers whose daily wages are Rs. 450 or more but less than Rs. 600

= 50 + 58 + 72 = 180

x + y + z = 10, xy + yz + zx = 25 and xyz = 100

As we know,

x³ + y³ + z³ – 3xyz = (x + y + z) [(x + y + z)² – 3 (xy + yz + zx)]

x³ + y³ + z³ – 3 × 100 = 10 [10² – 3 × 25]

x³ + y³ + z³ – 300 = 10 (100 – 75) = 10 × 25 = 250

x³ + y³ + z³ = 250 + 300 = 550

Number of male employees in department D = 64.8 × 4/9 = 28.8°

Number of male employees in department E = 36 × 9/20 = 16.2°

Total males employees in department D and E = 28.8° + 16.2° = 45°

Total number of employees in department B = 57.6°

Required ratio = 45° : 57.6° = 25 : 32

AQ = AR [Tangents]

BP = BQ [Tangents]

CP = CR [Tangents]

Perimeter of △ABC = AB + BP + PC + AC

26.4 = AB + BQ + CR + AC

26.4 = AQ + AR

26.4 = AQ + AQ

26.4 = 2AQ

AQ = 26.4/2

AQ = 13.2 cm

CP of the article = 648

SP of the article = 648 × (116/100)

MP of the article = 648 × (116/100) × (100/90) = Rs. 835.20

Follow BODMAS rule to solve this question, as per the order given below:

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated. 

$\left( {5\frac{1}{4} \div \frac{3}{7}of\frac{1}{2}} \right) \div \left( {5\frac{1}{9} - 7\frac{7}{8} \div 9\frac{9}{{20}}} \right); \times ;\frac{{11}}{{21}}; + ;\left( {2 \div 2;of\frac{1}{2}} \right)$

$\Rightarrow {\rm{;}}\left( {\frac{{21}}{4} \div \frac{3}{7}{\rm{;}} \times {\rm{;}}\frac{1}{2}} \right) \div \left( {\frac{{46}}{9} - \frac{{63}}{8} \div \frac{{189}}{{20}}} \right){\rm{;}} \times {\rm{;}}\frac{{11}}{{21}}{\rm{;}} + {\rm{;}}\left( {2 \div 2{\rm{;}} \times {\rm{;}}\frac{1}{2}} \right)$

$\Rightarrow {\rm{;}}\left( {\frac{{21}}{4} \div \frac{3}{{14}}} \right) \div \left( {\frac{{46}}{9} - \frac{{63}}{8}{\rm{;}} \times {\rm{;}}\frac{{20}}{{189}}} \right){\rm{;}} \times {\rm{;}}\frac{{11}}{{21}}{\rm{;}} + {\rm{;}}\left( {2 \div 1} \right)$

$\Rightarrow {\rm{;}}\left( {\frac{{21}}{4}{\rm{;}} \times {\rm{;}}\frac{{14}}{3}} \right) \div \left( {\frac{{46}}{9} - \frac{5}{6}} \right){\rm{;}} \times {\rm{;}}\frac{{11}}{{21}}{\rm{;}} + {\rm{;}}2$

⇒ (49/2) ÷ {(92 – 15)/18} × (11/21) + 2

⇒ (49/2) × (18/77) × (11/21) + 2

⇒ 3 + 2 = 5

Shortcut Trick

When a sphere is melted and recast into a cylinder, the Volume remains constant.

Direct Ratio: h = (4/3) × (r_sphere³ / r_cylinder²)

h = (4/3) × (8.4 × 8.4 × 8.4) / (12 × 12)

h = (4 × 0.7 × 0.7 × 2.8) = 5.488 cm

Rounding to one decimal place, h ≈ 5.5 cm.

∴ The correct answer is 5.5 cm.

Alternate Method

Given:

Radius of the metallic sphere (r₁) = 8.4 cm

Radius of the right circular cylinder (r₂) = 12 cm

Formula Used:

Volume of Sphere = (4/3) × π × r³

Volume of Cylinder = π × r² × h

Calculations:

⇒ Volume of Sphere = Volume of Cylinder

⇒ (4/3) × π × (8.4)³ = π × (12)² × h

⇒ (4/3) × 8.4 × 8.4 × 8.4 = 144 × h

⇒ h = (4 × 8.4 × 8.4 × 8.4) ÷ (3 × 144)

⇒ h = (4 × 592.704) ÷ 432

⇒ h = 2370.816 ÷ 432

⇒ h = 5.488 cm

⇒ h ≈ 5.5 cm

∴ The correct answer is 5.5 cm.

Additional Information

Total Surface Area of Sphere

The total surface area of a sphere with radius r is given by 4 × π × r².

Curved Surface Area of Cylinder

The curved surface area (CSA) of a cylinder with radius r and height h is 2 × π × r × h.

Volume Conservation

In melting and recasting problems, the total volume of the material remains constant regardless of the change in shape.

Hemisphere Properties

Volume of a hemisphere is (2/3) × π × r³ and its Total Surface Area is 3 × π × r².

SP of the article = Rs. 1134

CP of the article = 1134 × (100/90) = Rs. 1260

New SP of the article = 1354.50

Profit = 1354.5 – 1260 = 94.5

Profit % = (94.5/1260) × 100 = 7.5%

△DCA ∼ △ACB

CD/AC = AC/BC

CD/10 = 10/16

CD = (10 × 10)/16 = 6.25 cm

Given, AP = 36m

In△PAB

⇒ tan45 = PA/AB

⇒ 1 = 36/AB

⇒ AB = 36

⇒ AB = PR = 36

In △PQR,

⇒ tan60 = QR/PR

⇒ √3 = QR/36

⇒ QR = 36√3 = 36 × 1.7 = 61.2

⇒ QB = QR + RB  [RB = PA]

⇒ QB = 61.2 + 36 = 97.2

⇒ QB ≈ 98

Total production of wheat in states A, B and E = 500 + 375 + 475 = 1350

Total production of rice in states C, D and E = 575 + 400 + 525 = 1500

Required percentage = [(1500 – 1350)/1500] × 100 = 10%

Let ∠ACB = θ

∠ADB = (90 – θ)

DB = 18m and BC = 32m

In △ACB

tanθ = AB/BC

tanθ = AB/32    ----(1)

In △ADB

tan (90 – θ) = AB/BD

cotθ = AB/18    ----(2)

From equation (1) and equation (2)

tanθ cotθ = (AB/32) × (AB/18)

AB² = 32 × 18

AB = √(32 × 18) = √(16 × 2 × 9 × 2) = 4 × 2 × 3

AB = 24m

Short trick :

Height of the tower AB = √(BD × BC)

Height of the tower AB = √(32 × 18) = 24 m

r = 8 cm and h = 15 cm

As we know,

l² = r² + h²

l² = 8² + 15²

l² = 64 + 225

l² = 289

l = √289

l = 17

Total surface area of cone = πr (l + r) = π × 8 × (17 + 8) = π × 8 × 25 = 200 π

Total work = 90

Work done by A, B and C in 3 days = 3A + B + C = 3 × 3 + 2 + 1 = 12

Work done by A, B and C in 21 days = 12 × 7 = 84

Remaining work = 90 – 84 = 6

A will complete 6 unit work in 6/3 = 2 days

Total days = 21 + 2 = 23

Total number of employees in department A and B = 79.2° + 57.6° = 136.8°

Total number of employees in department C = 122.4°

Number of employees in A and B is more than that of C by = 136.8° – 122.4° = 14.4°

Number of employees in A and B is more than C by = 3200 × 14.4/360 = 128

As we know, 128 lies between 120 and 140.

As we know

A = P(1 + r/100)^t

⇒ 35680 = P( 1 + r/100)³

⇒ 35680/P = (1 + r/100)³    ----(1)

⇒ 53520 = 35680 (1 + r/100)³

⇒ 53520/35680 = (1 + r/100)³    ----(2)

From equation (1) and equation (2),

⇒ 35680/P = 53520/35680

⇒ P = (35680 × 35680)/53520

⇒ P = 23786.6

⇒ CI for first 3 years = 35680 – 23786.6 = 11893.3 ≈ Rs. 11893

Short trick:

Let consumption of sugar be x kg.

⇒ x = (112/128) × 18.4 = 16.1 kg

Detailed Solution:

Let the price of sugar be 100x.

Price of sugar after increment = 100x × (128/100) = 128x

Price ratio of sugar = 100x : 128x

Consumption is inversely proportional to price.

Consumption ratio of sugar before to after = 128x : 100x

New price of sugar if family wants to increase in expenditure on sugar 12% only

= 100x × (112/100) = 112x

Now price ratio of sugar = 100x : 112x

Now Consumption ratio of sugar before to after = 112x : 100x

⇒ Consumption ratio of sugar before, at 12% increase in price and at 28% increase in price

= 128x : 112x : 100x

⇒ 128x = 18.4 kg

⇒ x = 18.4/128

⇒ 112x = (18.4/128) × 112 = 16.1 kg

Shortcut Trick Identify 7 − 4√3 as the perfect square (2 − √3)2. The expression becomes 1 / (2 − √3). Rationalizing 1 / (2 − √3) gives its conjugate 2 + √3. Using the approximate value √3 ≈ 1.732. The result is 2 + 1.732 = 3.732, which is closest to 3.7. ∴ The correct answer is 3.7. Alternate Method Given: The expression is 1 / √(7 − 4√3). Method Used: Simplification of Surds and Rationalization. ⇒ First, simplify the denominator: √(7 − 4√3) ⇒ 7 − 4√3 can be written as 4 + 3 − 2 × 2 × √3 ⇒ 22 + (√3)2 − 2 × 2 × √3 = (2 − √3)2 ⇒ √(7 − 4√3) = √(2 − √3)2 = 2 − √3 ⇒ Now the expression is 1 / (2 − √3) ⇒ Rationalize by multiplying numerator and denominator by (2 + √3): ⇒ [1 × (2 + √3)] / [(2 − √3) × (2 + √3)] = (2 + √3) / (22 − (√3)2) ⇒ (2 + √3) / (4 − 3) = 2 + √3 ⇒ Taking √3 ≈ 1.732, value = 2 + 1.732 = 3.732 ∴ The correct answer is 3.7. Additional Information Square Root of a Surd For a surd in the form x − 2√y, if we find two numbers a and b such that a + b = x and ab = y, then √(x − 2√y) = √a − √b (where a > b). Rationalization To rationalize a denominator of the form (a − √b), multiply both numerator and denominator by its conjugate (a + √b) to use the identity (x − y)(x + y) = x2 − y2. Approximate Surd Values Common values for exams: √2 ≈ 1.414, √3 ≈ 1.732, √5 ≈ 2.236, and √10 ≈ 3.162.

The number of workers in the factory whose daily wages are below Rs. 600 = 40 + 50 + 58 + 72

= 220

The number of workers in the factory whose daily wages are more Rs. 650 = 55 + 48 + 37 = 140

Required ratio = 220 : 140 = 11 : 7

According to the question

2πr – 2r = 60

⇒ 2r(22/7 – 1) = 60

⇒ r × 15/7 = 30

⇒ r = 14 cm

Area of the circle = πr² = 22/7 × 14 × 14 = 616 cm²

Let the income of C be 100x

Income of B = 100x × (124/100) = 124x

Income of A = 124x × (40/100) = 49.6x

Income of C is more than that of A by (%) = [(100x – 49.6x)/49.6x] × 100 = 101.6%

Short Trick:

Difference of rate for 1 year = 4%

Difference of rate for 3½ year = 4 × 7/2 = 14%

14% = 4452

100% = 4452 × (100/14) = Rs. 31800

Detailed method:

Let sum be Rs x

t = 3½ year

r = 4%

According to the question

Prt/100 = SI

[x × (y + 4 – y) × (7/2)] /100 = 4452

(x × 4 × 7)/(2 × 100) = 4452

x = (4452 × 2 × 100)/(4 × 7)

x = Rs. 31800

Total production of rice of all five states = 350 + 450 + 575 + 400 + 525 = 2300

20% of the total production of rice of all five states = 2300 × 20/100 = 460

There are three states A, D, and E (500, 560, and 475 respectively)whose production is more than 20% of the total production of wheat.

Total production of rice in states C and E = 575 + 525 = 1100

Total production of wheat in states B and D = 375 + 560 = 935

⇒ Required ratio = 1100 : 935 = 20 : 17

x² + xy + y² = 3    ---(1)

As we know,

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

21 = 3 (x² – xy + y²)

x² – xy + y² = 21/3

x² – xy + y² = 7    ---(2)

From equation (1) and equation (2)

2xy =  -4

4xy = 2 × (-4)

4xy = (-8)

Let total number of students be x

Average weight of x students = 60.5 kg

Sum of weight of x students = 60.5x

Average weight of 8 students = 65

Sum of weight of 8 students = 65 × 8 = 520

According to the question

60.5x + 520 = (x + 8)(60.5 + 0.9)

60.5x + 520 = (x + 8) × 61.4

60.5x + 520 = 61.4x + 491.2

61.4x – 60.5x = 520 – 491.2

0.9x = 28.8

x = 28.8/0.9

x = 32

Short Trick :

0.9 kg weight increase for = 1 students

(65 – 60.5) × 8 kg weight increase for = (1/0.9) × 4.5 × 8 = 40 students

Number of students before = 40 – 8 = 32

Efficiency of (A + B + C) is 1 unit.

Let the total work be 12 units.

Work done by A, B and C together in 1 hr = 1 unit

Work done by A, B and C together in 4 hr = 4 unit

Remaining work = 12 – 4 = 8 unit

Let efficiency of A and B together be x.

⇒ 10 × x = 8

⇒ x = 8/10 = 0.8

⇒ Efficiency of C = 1 – 0.8 = 0.2

⇒ 2/3 of the cistern = 12 × 2/3 = 8

⇒ 2/3 of the cistern filled by C in = 8/(0.2) = 40 hrs

Calculation:

Divisibility law of 11: If the difference of the alternating sum of digits of the number is a multiple of 11 (e.g. 2343 is divisible by 11 because (2 + 4) – (3 + 3) = 0, which is a multiple of 11).

x468Y05 is divided by 11, then

(x + 6 + y + 5) – (4 + 8 + 0) = 11

⇒ (x + y + 11) – 12 = 11

⇒ x + y – 1 = 11

⇒ x + y = 12

1/(cosecθ + 1) + 1/(cosecθ – 1) = 2 secθ

⇒ (cosecθ – 1 + cosecθ + 1)/(cosec²θ – 1) = 2 secθ

⇒ 2cosecθ/cot²θ = 2 secθ

⇒ (2/sinθ) × (sin²θ/cos²θ) = 2/cosθ

⇒ tanθ = 1

⇒ tanθ = tan45°

⇒ θ = 45°

Now,

⇒ (tanθ + 2secθ**)/**cosecθ

⇒ (tan45 + 2 sec45)/cosec45

⇒ {(1 + 2√2)/ √2} × (√2/√2)

⇒ (√2 + 4)/2

Short trick:

1/(cosecθ + 1) + 1/(cosecθ – 1) = 2 secθ

Put θ = 45

⇒ {1/(√2 + 1)} + {1/(√2 – 1)} = 2√2

⇒ (√2 – 1 + √2 + 1)/(2 – 1) = 2√2

⇒ 2√2 = 2√2 (Satisfied)

Now,

⇒ (tanθ + 2 secθ)/cosecθ

⇒ (tan45 + 2 sec45)/cosec45

⇒ {(1 + 2√2)/√2} × (√2/√2)

⇒ (√2 + 4)/2

MP of the article = 530

SP of the article after first discount = 530 × (85/100) = 450.5

Second discount = 450.5 – 396.44 = 54.06

Second discount = (54.06/450.5) × 100 = 12%

Capital of A, B and C = 4 : 2 : 9

⇒ Suppose capital of A = 4

⇒ Suppose capital of B = 2

⇒ Suppose capital of C = 9

⇒ Total capital of A after end of the year = 4 × 3 + (4/2) × 3 + (4/4) × 3 + (4/8) × 3

= 12 + 6 + 3 + (3/2) = 45/2

⇒ Total capital of B after end of the year = 2 × 3 + 4 × 3 + 8 × 3 + 16 × 3 = 6 + 12 + 24 + 48

= 90

⇒ Total capital of C after end of the year = 9 × 12 = 108

⇒ Profit ratio of A, B and C = (45/2) : 90 : 108 = 5 : 20 : 24

⇒ 5 unit = 24000

⇒ 1 unit = 24000/5 = 4800

⇒ (5 + 20 + 24) unit = 49 unit = 4800 × 49 = Rs. 235200

⇒ Total profit = Rs. 235200