SSC CGL 2020 Tier-I Official Paper (Held On : 24 Aug 2021 Shift 1) (Previous Year Paper)

The logic followed here is:-

Ottawa is the capital of Canada.

Similarly, 

Havana is the capital of Cuba.

Hence, "option 2" is the correct answer.

Additional Information

• Oslo is the capital of Norway.
• Madrid is the capital of Spain.
• Bern is the capital of Switzerland.

Let the age of Sanju at their silver anniversary = x years

18 years of marriage = 7 years before silver anniversary.

Sanju's age 7 years before silver anniversary = x - 7

Sanju's age 25 years after silver anniversary (golden anniversary) = x + 25

Note:- Silver anniversary = 25 years and golden anniversary = 50 years.

(x - 7)/(x + 25) = 5/21

Cross multiplying both sides,

21x - 147 = 5x + 125

16x = 272

x = 17 years.

Sanju's age on silver anniversary = 17 years

Sanju is born 25 - 17 years = 8 years after the marriage.

Hence, "option 1" is the correct answer.

Mistake Points

The question is asking to find the NOT Related numbers, so we need to find the wrong option, so Solve accordingly.

The logic followed here is:-

(64, 91, 118)

The difference between the second and first numbers is 27 and the difference between the third and second numbers is also 27.

91 - 64 = 27

118 - 91 = 27

From option 1:-

(46, 73, 101)

73 - 46 = 27

101 - 73 = 28

It does not follow because both differences are not 27.

From option 2:-

(48, 75, 102)

75 - 48 = 27

102 - 75 = 27

It is follow.

From option 3:-

(72, 99, 126)

99 - 72 = 27

126 - 99 = 27

It is follow.

From option 4:-

(45, 72, 99)

72 - 45 = 27

99 - 72 = 27

It is follow.

Hence, "option 1" is the correct answer.

The logic followed here is:-

Tintometer is used  to measure colours.

Similarly,

Protractor is used to measure angles.

Hence, "option 3" is the correct answer.

Additional Information

• Planimeter is used to measure of  the area of an arbitrary two dimensional shape not pressure.
• Spirometer is used to measure of amount of air you are able to breath not speed.
• Viscometer is used to measure of fluid viscosity not wind.

The sequence of folding a piece of paper and the manner in which the folded paper has been cut is shown and the paper looks when unfolded:-

Hence, "option 3" is the correct answer.

The logic followed here is:-

The A is opposite to C, T is the opposite to J and F is the opposite to L. 

Which is given below:-

In the dice only one side of the letter is present.

In figure A:-

Only A, F, and T are present in which there is no opposite pair present. So, it can be formed**.**

In figure B:

Only C, F, and T are present in which there is no opposite pair present. So, it can be formed.

In figure C:-

Only C, A, and J are present in which A and C are opposite pairs present. So, it can not be formed.

In figure D:-

Only T, L, and F are present in which L and F are opposite pairs present. So, it can not be formed.

Hence, "option 3" is the correct answer.

The logic followed here is:-

Hence, "option 1" is the correct answer.

The mirror image of the given figure is given below:-

Detailed Explanation:

• The line PQ is the mirror.
• The given word "COGNITIVE" has a first letter C. So the mirror image should be 

 ⇒ options 2 and 3 are eliminated.

• The given word "COGNITIVE" has the third letter G. So the mirror image should be 

 ⇒ an option 4 is eliminated.

Hence, "option 1" is the correct answer.

Given that:-

156 - 13 + 9 × 18 ÷ 5 = 169

From option 1:-

÷ and +

• After replacing the symbols with their meanings, we get

156 - 13 ÷ 9 × 18 + 5 = 169,

156 - 1.44 × 18 + 5 = 169

156 - 26 + 5 = 169

156 + 5 - 26 = 169(the positions of 26 and 5 are interchanged with their symbols)

161 - 26 = 169

135 ≠ 169, it is not follow.

From option 2:-

× and ÷

• After replacing the symbols with their meanings, we get

156 - 13 + 9 ÷ 18 × 5 = 169

156 - 13 + 0.5 × 5 = 169

156 - 13 + 2.5 = 169

156 + 2.5 - 13 = 169(the positions of 2.5 and 13 are interchanged with their symbols)

158.5 - 13 = 169

145.5 ≠ 169, it is not follow.

From option 3:-

× and -

• After replacing the symbols with their meanings, we get

156 × 13 + 9 - 18 ÷ 5 = 169

156 × 13 + 9 - 3.6 = 169

2028 + 9 - 3.6 = 169

2037 - 3.6 = 169

2033.4 ≠ 169, it is not follow.

From option 4:-

÷ and -

• After replacing the symbols with their meanings, we get

156 ÷ 13 + 9 × 18 - 5 = 169

12 + 9 × 18 - 5 = 169

12 + 162 - 5 = 169

174 - 5 = 169

169 = 169, it is follow.

Hence, "option 4" is the correct answer.

The logic followed here is:-

Addition of place value and multiply with number of letter of the word.

M(13) I(9) N(14) T(20) = Place Value × Number of letters of the word = (13 + 9 + 14 + 20) × 4 = 56 × 4 = 224,

F(6) A(1) N(14) C(3) Y(25) = (6 + 1 + 14 + 3 + 25) × 5 = 49 × 5 = 245,

Similarly,

C(3) O(15) N(14) T(20) O(15) U(21) R(18) = (3 + 15 + 14 + 20 + 15 + 21 + 18) × 7 = 106 × 7 = 742

Hence, "option 4" is the correct answer.

The Logic here is as follows:

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

In (12, 14, 143)

(1^st Number - 1) × (2^nd number - 1)

= (12 - 1) × (14 - 1)

= (11 × 13)

= 143 = 3^rd Number

Now check the all options,

Option (1): (16, 10, 235)

(1^st Number - 1) × (2^nd number - 1)

= (16 - 1) × (10 - 1)

= (15 × 9)         

= 135 ≠ 3^rd Number

Option (2): (15, 19, 252)

(1^st Number - 1) × (2^nd number - 1)

= (15 - 1) × (19 - 1)

= (14 × 18)       

= 252 = 3^rd Number

Option (3): (12, 18, 246)

(1^st Number - 1) × (2^nd number - 1)

= (12 - 1) × (18 - 1)

= (11 × 17)       

= 187 ≠ 3^rd Number

Option (4): (17, 12, 134)

(1^st Number - 1) × (2^nd number - 1)

= (17 - 1) × (12 - 1)

= (16 × 11)       

= 176 ≠ 3^rd Number

Hence, the correct answer is "(15, 19, 252)".

The logic followed here is:-

Square of the first number and add 2 then we get second number.

23 : 531

23² + 2 = 529 + 2 = 531,

Similarly,

27 : ?

27² + 2 = 729 + 2 = 731

Hence, "option 3" is the correct answer.

The logic followed here is:

1^st number × 6 - 5 = second number

From option 1:-

28 ∶ 163

28 × 6 - 5 = 168 - 5 = 163

From option 2:-

22 ∶ 127

22 × 6 - 5 = 132 - 5 = 127

From option 3:-

27 ∶ 82

27 × 6 - 5 = 162 - 5 = 157 ≠ 82

From option 4:-

16 ∶ 91

16 × 6 - 5 = 96 - 5 = 91

In which option 3 is different from others.

Hence, "option 3" is the correct answer.

The logic followed here is:-

Hence, "option 1" is the correct answer.

The Venn diagram is given below:-

Conclusions:

I. Some sharpeners are erasers. → Ture (All pencils are erasers, some sharpeners are pencils then we can say that some sharpeners are erasers is true.)

II. All pencils are sharpeners. → False (All pencils are erasers, and some sharpeners are pencils so we can say some pencils are sharpeners but all pencils are sharpeners it can be possible but not definite, hence, false)

Hence, "option 1" is the correct answer.

Additional Information

The figure of triangles are given below:-

The total number of triangles = 11.

Hence, "option 2" is the correct answer.

The logic followed here is:-

"E" moves to top left side to the bottom right side, then bottom right side to bottom left side then bottom left side to middle and then middle to top right side.

"A" moves to top right side to the top left side, then top left side to bottom right side then bottom right side to the bottom left side and then bottom left side to the middle.

"U" moves to the middle to the top right side, then top right side to top left side then top left side to the bottom right side and then bottom right side to the bottom left side.

"I" moves to the bottom left side to the middle, then the middle to the top right side then the top right side to the top left side and then the top left side to the bottom right side.

"O" moves to the bottom right side to the bottom left side, then the bottom left side to the middle then the middle to the top right side and then the top right side to the top left side.

Hence, "option 2" is the correct answer.

The option in which the given figure is embedded:-

Hence, "option 2" is the correct answer.

Important Points

• Do not get tensed by the complexity of the figures.
• Carefully understand the structure of the given question figure.
• The embedded figure may not be of exact size. It may be small or big.
• Sometimes the rotation or reflection of the figures may be confusing.
• So think wisely before selecting the answer.

Table show alphabet serial number –

The pattern followed is,

All follow the same pattern, except ‘FHWU’.

Hence, “FHWU” is the odd one.

Alternate Method Logic: The sum of the place value is equal in all options except option 1.

Option 1) FHWU → 6 + 8 + 23 + 21 = 58.

Option 2) RDMI → 18 + 4 + 13 + 9 = 44.

Option 3) JNCQ → 10 + 14 + 3 + 17 = 44.

Option 4) TFKG  → 20 + 6 + 11 + 7 = 44.

Hence, the correct answer is "FHWU".

The logic followed here is:-

Except Ecology, all other words are a part of human body.

Ophthalmology, Myology, and Dermatology are terms related to medical terms but Ecology is related to the study of the field.

Option 1: Ophthalmology is the branch of medicine concerned with the study and treatment of disorders and diseases of the eye.

Option 2: Myology is the study of the structure, arrangement, and action of muscles.

Option 4: Dermatology is the branch of medicine concerned with the diagnosis and treatment of skin disorders.

Option 3: Ecology is the branch of biology that deals with the relations of organisms to one another and to their physical surrounding.

Hence, "option 3" is the correct answer.

The logical Venn diagram is given below:-

The number of rural businessmen, who are not graduates = 8.

Hence, "option 1" is the correct answer.

From option 1:-

r l v q l / m m v q l / r m r q v / r m v q l → don't follow a pattern.

From option 2:-

r m v q l / r m v q l / r m v q l / r m v q l → Follows a pattern and 'rmvql' remains the same.

From option 3:-

r v v q l / v m v q l / r m r q l / r m m q l → don't follow a pattern.

From option 4:-

r q v q l / r m v v l / r m l q v / r m m q l → don't follow a pattern.

Hence, "option 2" is the correct answer.

The words in the order in which they appear in an English dictionary order is:-

4. Together, then come 
5. Tolerance, then come 
6. Tomorrow, then come 
7. Topology, and then come 
8. Topper

So, the sequence is 4, 3, 5, 1, 2.

Hence, "option 2" is the correct answer.

The logic followed here is:-

And,

Similarly,

Hence, "option 4" is the correct answer.

Sripad Said:- 

The family tree is given below:-She is the daughter of my father's mother's only daughter's elder daughter.

Here, My(Sripad) father's mother = Sripad's Paternal Grandmother.

Sripad's Paternal Grandmother's only daughter's = Sripad's paternal Aunt.

Sripad's paternal Aunt's elder daughter = Sripad's cousin sister daughter.

Sripad's cousin sister's daughter(Baby Girl) = Sripad's neice.

So, The mother of Baby Girl is Cousin of Sripad.

In which Sripad's father's mother's only daughter is the only sister of Sripad's father and grandmother of the baby girl. So, the baby girl's mother is the cousin of Sripad.

Hence, "option 2" is the correct answer.

Note: There was an ambiguity in the original question paper in the previous year's paper. We have selected the correct options as per the given statement in question.

The correct answer is Magnesium.

• Magnesium is known as alkaline earth metal.

Key Points

• The alkaline earth metals are named after the alkaline earth whose old-fashioned names were beryllia, magnesia, lime, strontia, and baryta, after their oxides. When mixed with water, these oxides are simple (alkaline).
• The elements of Group 2 of the periodic table are alkaline earth metals.
• Beryllium, magnesium, calcium, strontium, barium, and radium are the elements in Group 2.
• For two reasons, these elements are referred to as Alkaline Earth metals. Their oxides remain in the crust of the earth and are very heat-stable.
• In group 1 of the periodic table, alkali metals are the elements.
• The key distinction between alkaline and alkali is that there is one valence electron in alkali metals, while two valence electrons are in alkaline earth metals.

Additional Information 

The correct answer is Shyama Prasad Mukherjee.

• Shyama Prasad Mukherjee is one of the founder members of Bhartiya Jana Sangh.

Key Points

• The Bharatiya Jana Sangh was an Indian right-wing political party that existed from 1951 to 1977.
• In 1977, Bharatiya Jana Sangh merged with several other left, centre and right parties opposed to the Indian National Congress and formed the Janata Party.
• In 1980, the Jana Sangh faction broke away from Janata Party over the issue of dual membership and formed Bharatiya Janata Party.

Additional Information

The correct answer is Karnataka.

• In the present-day state, you will find the Meguti temple in Karnataka.

Key Points

• The only dated monument in Aihole, the Meguti Temple was built atop a small hill in 634 AD.
• The Aihole Inscription, also known as the Aihole Prashasti, is a nineteen-line Sanskrit inscription in Kannada script at Meguti Jain temple in Aihole, Karnataka, India.
• The Megudi temple is historically important for its Aihole Prashasti inscription. A slab on the outer east side wall of the temple is inscribed in the Sanskrit language and Old Kannada script.
• It is dated to Saka 556 (634 CE) and is a poem by Jain poet Ravikirti. He was in the court of king Pulakeshin II.
• This inscription opens with the equivalent of Jai Jinendra salutation in Sanskrit.

Additional Information

The correct answer is Rajasthan.

• Ghoomar is a folk-dance form from the state of Rajasthan.

Key Points

• Ghoomar is a traditional folk dance of Rajasthan, India, and Sindh, Pakistan.
• The dance is chiefly performed by veiled women who wear flowing dresses called Ghaghara.
• The dance typically involves performers pirouetting while moving in and out of a wide circle.
• The word ghoomna describes the twirling movement of the dancers and is the basis of the word Ghoomar.
• Ghoomar is often performed on special occasions, such as at weddings and during Holi, and sometimes lasts for hours.
• Famous dances of Rajasthan are:
• Kalbeliya
• Bhavai
• Kachchhi Ghodi
• Chari

Additional Information

The correct answer is Muhammad Bin-Qassim.

• Muhammad Bin-Qassim had invaded India in 712 AD.

Key Points

• The foundation of Arab domination in Sind in 712 A.D. was the result of a number of efforts to enter India. In fact, Muhammad-bin-Qasim's exploration of India was actually the third attempt.
• The Sind conquest by Muhammad Bin Qasim in 712 AD gave the Muslims a strong dominance in the Indian sub-continent.
• The conquest of Sind led the Islamic civilization to come in contact with the ancient Vedic civilization of the subcontinent.
• Muhammad bin Qasim:
• Muhammad Bin Qasim was an Arab military commander in the service of the Umayyad Caliphate who led the Muslim conquest of Sindh from the last Hindu king, Raja Dahir in the battle of Aror.
• He was the first Muslim to have successfully captured Hindu territories and initiated early Islamic India in 712 AD.
• Muhammad Bin Qasim's success has been partly ascribed to Dahir being an unpopular Hindu king ruling over a Buddhist majority who saw Chach of Alor and his kin as usurpers of the Rai Dynasty.

Additional Information

The correct answer is 6.

• As of December 2020, there are 6 official languages of the United Nations.
• These are Arabic, Chinese, English, French, Russian and Spanish.

Key Points

• The history of the UN’s official languages, presented by the Dag Hammarskjold Library, gives the history of when each of the six official languages of the United Nations became official, beginning in 1946.
• The United Nations is one of the world’s largest employers of language professionals.
• Several hundred language professionals work for the Department for General Assembly and Conference Management (DGACM) in New York, Geneva, Vienna, and Nairobi.

Additional Information

• Language Days at the UN are:
• Arabic Language Day (18 December)
• Chinese Language Day (20 April)
• English Language Day (23 April)
• French Language Day (20 March)
• Russian Language Day (6 June)
• Spanish Language Day (23 April)

Important Points

• The United Nations is an intergovernmental organization aiming to maintain international peace and security.
• The United Nations was founded on 24 October 1945 in San Francisco, California, United States.
• The United Nations general secretary is Antonio Guterres and its headquarters is located in New York, United States.

The correct answer is Stagflation.

• Stagflation is an economic scenario where a particular combination of low growth and rising inflation leads to high unemployment.

Key Points

• Stagflation:
• The term was coined by lain Macleod, a Conservative Party MP in the United Kingdom, in November 1965.
• Stagflation is a situation in which the inflation rate is high, the economic growth rate slows and unemployment remains steadily high.
• With stalled economic growth, unemployment tends to rise and existing incomes do not rise fast enough, and yet, people have to contend with rising inflation.
• So people find themselves pressurized from both sides as their purchasing power is reduced.

Additional Information

• Causes of looming stagflation situation in India:
• Reduced consumption
• Volatile Oil
• Decreased credit availability
• Unemployment
• Inflation

The correct answer is Mohammed Salim.

• Mohammed Salim was the first player from the Indian sub-continent to play for a European Football club (Celtic FC).

Key Points

• Mohammed Salim was an Indian footballer from Calcutta, West Bengal.
• He was best known for his role in the fabled 1930s Mohammedan SC team which claimed five successive Calcutta Football League titles.
• He was honoured with Dr. Bidhan Chandra Roy State Award in 1976.

Additional Information

The correct answer is Uttar Pradesh.

• Uttar Pradesh became the first one to launch blockchain-enabled solar power trading in December 2020.

Key Points

• Uttar Pradesh has launched India and South-Asia’s first blockchain-enabled peer-to-peer (P2P) trading platform for rooftop solar power.
• The Uttar Pradesh Power Corporation (UPPCL), MVVNL, and UPNEDA are hosting the first-of-its-kind pilot project, involving energy generated from solar rooftop systems installed on buildings in Lucknow.
• Madhyanchal Vidyut Vitran Nigam Limited (MVVNL)​
• Uttar Pradesh New and Renewable Energy Development Agency (UPNEDA)
• India Smart Grid Forum (ISGF), along with blockchain technology partner Power Ledger, Australia, and Abajyon Consulting, will execute the project.
• The P2P trading platform’s first 12 participants would comprise nine customers with rooftop solar (prosumers) and three customers without rooftop solar (net buyers), identified in consultation with MVVNL.

Additional Information

The correct answer is Coral.

• Coral is a sessile animal, that relies upon its relationship with plants like algae to build the largest structures of biological origin on earth.

Key Points

• Corals are sessile, which means that they permanently attach themselves to the ocean floor, essentially taking root as most plants do.
• Corals actually comprise an ancient and unique partnership, called symbiosis, that benefits both animal and plant life in the ocean.
• Corals are animals, though, because they do not make their own food, as plants do.
• Most corals contain algae called zooxanthellae, which are plant-like organisms.

Additional Information 

Important Points 

The correct answer is Asus.

• Asus announced the launch of India’s first virtual academy program Esports Academy.

Key Points

• The Asus Republic of Gamers (ROG) has announced the launch of the Asus ROG Academy in India.
• The competitive Esports training initiative will be India's first virtual academy program for upcoming gamers who are looking to be professionals.
• Asus ROG will identify PC gamers through a screening process and the selected individuals will be provided with the necessary equipment and coaching.

Additional Information

The correct answer is Deepika Padukone.​

Key Points

• Actor Deepika Padukone has joined the list of the Young Global Leaders (YGLs) compiled by the World Economic Forum.
• The list also includes several Indian citizens and India-origin persons.
• Deepika Padukone is an internationally acclaimed actor, fashion and youth icon, and mental health ambassador from India.
• Deepika features in listings of the nation's most popular personalities, and Time named her one of the 100 most influential people in the world in 2018.
• Padukone is the founder of the Live Love Laugh Foundation, which creates awareness on mental health in India.

Additional Information

The correct answer is Hazaribagh.

• Hazaribagh is NOT located on the banks of river Ganga.

Key Points

• Hazaribagh is a city and a municipal corporation in the Hazaribagh district in the Indian state of Jharkhand.
• It is the divisional headquarters of the North Chotanagpur division.
• Hazaribagh is located geographically near the Chotanagpur Plateau.
• Konar river is flowing through the entire Hazaribagh.
• Hazaribagh has the historical significance of Indian forestry. This area was free from external invasion till the British East India Company came to India.
• Hazaribagh has a police training centre for the whole of Jharkhand. The Border Security Force (BSF) also has a large presence.
• East India's largest training centre is here in the forest with hilly terrain.
• Famous tourist places in Hazaribagh are:
• Barso Pani Cave
• Budhwa Mahadev Mandir
• Chadwa Dam

Additional Information

• Ganga River:
• The Ganges is a transboundary river of Asia that flows through India and Bangladesh.
• Total length: 2525 km.
• Source: Gangotri Glacier.
• Mouth: Ganges Delta.

Important Points

• Varanasi:
• Varanasi is famous for its production of silks and brocades with gold and silver threadwork.
• Varanasi is one of the oldest living cities in the world. Varanasi`s Prominence in Hindu mythology is virtually unrevealed.
• Kanpur:
• Kanpur is a city in the state of Uttar Pradesh in India. Founded in 1803, Kanpur became one of the most important commercial and military stations of British India.​
• The city is famous for its leather and textile industries.
• Phaphamau:
• ​Phaphamau is a satellite locality/township of the city of Prayagraj, Uttar Pradesh, India, located on either side of the Prayagraj-Lucknow highway.
• It lies on the banks of the Ganga River.

The correct answer is ampere.

• Coulomb per second is equivalent to ampere.

Key Points

• One coulomb is the charge flowing through a wire in 1 second if the current is 1 Ampere. A coulomb is a unit of electric charge.
• A coulomb is a name given in the memory of French physicist Charles Augustin de Coulomb.
• Coulomb force and gravitational force follow the same inverse square law.
• But gravitational force has only one sign (always attractive), while Coulomb force can be of both signs (attractive and repulsive), allowing the possibility of cancellation of electric force.

Additional Information

The correct answer is Plate Tectonics.

• Due to plate tectonics, the lithosphere move over the asthenosphere.

Key Points

• The lithosphere is the rocky outer part of the Earth.
• It is made up of the brittle crust and the top part of the upper mantle.
• The lithosphere is the coolest and most rigid part of the Earth.
• There are two types of lithosphere:
• Oceanic lithosphere and continental lithosphere. Oceanic lithosphere is associated with oceanic crust and is slightly denser than continental lithosphere.

  

Additional Information

• Plate Tectonics:
• The most well-known feature associated with Earth’s lithosphere is tectonic activity. Tectonic activity describes the interaction of the huge slabs of the lithosphere called tectonic plates.
• The lithosphere is divided into tectonic plates including the North American, Caribbean, South American, Scotia, Antarctic, Eurasian, Arabian, African, Indian, Philippine, Australian, Pacific, Juan de Fuca, Cocos, and Nazca.
• The movement of tectonic plates is made possible by thermal energy (heat**) from the mantle part of the lithosphere. Thermal energy makes the rocks of the lithosphere** more elastic.

Important Points

The correct answer is Muhammad Bin Tughlaq.

• Muhammad Bin Tughlaq established a separate department (Diwan-i-Amir Kohi) to take care of agriculture.

Key Points

• Muhammad Bin Tughlaq created a department of agriculture known as Diwan-i-Kohi.
• The main object of the department was to increase the land under cultivation.
• Under the Diwan-i-Kohi loans were advanced to farmers for the purchase of cattle, seeds, and digging of wells but to no avail.
• Mohammad Bin Tuglaq:
• Muhammad-bin-Tughlaq pushed for India's administrative and political union.
• Muhammad bin Tughlaq ascended the throne of the Tughlaq dynasty of Delhi in February 1325 CE.
• In 1327, Tughluq ordered to move his capital from Delhi to Daulatabad in the Deccan region of India.

Additional Information

The correct answer is Seven.

• The seven brightest stars in the constellation are called the Great Bear.

Key Points

• Ursa Major constellation lies in the northern sky. Its name means the great bear, or the larger bear, in Latin. The smaller bear is represented by Ursa Minor.
• Ursa Major is the largest northern constellation and the third largest constellation in the sky. Its brightest stars form the Big Dipper asterism, one of the most recognizable shapes in the sky, also known as the Plough.
• Ursa Major is well-known in most world cultures and associated with a number of myths. It was one of the constellations catalogued by the Greek astronomer Ptolemy in the 2^nd century.
• Ursa Major contains a number of notable stars and famous deep-sky objects. These include the Pinwheel Galaxy (M101), Bode’s Galaxy, the Cigar Galaxy, and the Owl Nebula.

Additional Information

• Ursa Major constellation map:

Important Points

• The biggest known galaxy is IC 1101, which is 50 times the Milky Way's size and about 2,000 times more massive.
• It is about 5.5 million light-years across.
• Our Sun (a star) and all the planets around it are part of a galaxy known as the Milky Way Galaxy.
• A galaxy is a large group of stars, gas, and dust bound together by gravity. The Milky Way is made up of about 90% dark matter, the matter which cannot be seen, and about 10% luminous matter, or matter that we can see with our eyes.
• The solar system lies about 30,000 light-years from the galactic centre.

The correct answer is cohesive force.

• The force of attraction between the same kind of molecules is called the force of cohesion.
• The force of attraction between different kinds of molecules is called the force of adhesion.

Key Points

• The cohesion force of fine particles is important for the growth and strength of green granules.
• The former affects the size distribution of final granules formed, while the latter has a direct impact on the permeability of a packed granule bed.
• The cohesive forces between molecules down into a liquid are shared with all neighbouring atoms.

Additional Information

• Viscosity:
• Viscosity is the resistance of a fluid (liquid or gas) to a change in shape or movement of neighbouring portions relative to one another.
• ​Viscosity is a measure of a fluid's resistance to flow. The SI unit of viscosity is poiseuille (PI).
• Its other units are newton-second per square meter (N s m-2) or pascal-second (Pa s.). The dimensional formula of viscosity is (ML-1T-1).
• Surface tension:
• Surface tension is the tendency of fluid surfaces to shrink into the minimum surface area possible.​
• Surface tension is typically measured in dynes/cm, the force in dynes is required to break a film of length 1 cm.
• Adhesive force:
• The adhesion forces can be one of the results of electrostatic forces which are exerted on different substances.​
• Adhesion is generally the force of attraction present between the water molecules and the walls of xylem vessels.

The correct answer is Greece.​

Key Points

• The first known Olympics were held in the summer of 776 B.C. at Olympia, a site in southern Greece where people went to worship their gods.
• The ancient Greek Games lasted until 393 CE.
• The Olympics were revived in the late 1800s. The Games that began then are called the modern Olympics.
• Until the early 1990s, the Summer and Winter Games were held in the same year.
• Today they are separated by two years.
• The International Olympic Committee (IOC) governs the modern Games. It was founded in 1894. Its headquarters are in Lausanne, Switzerland.
• The last Olympic games are held in Tokyo, Japan in 2020.

Additional Information

The correct answer is Watershed.

• A/an watershed is a natural geo-hydrological unit of land, which collects water and drains it through a common point by a system of streams.

Key Points

• A Watershed is defined as a geohydrological unit draining to a common point by a system of drains.
• Watershed is thus the land and water area, which contributes runoff to a common point.
• Types of watersheds are:
• Macro watershed (> 50,000 Hect).
• Sub-watershed (10,000 to 50,000 Hect).
• Milli-watershed (1000 to10000 Hect).
• Micro watershed (100 to 1000 Hect).
• Mini watershed (1-100 Hect).

Additional Information

• The different objectives of watershed management programs are:
• To control damaging runoff and degradation and thereby conservation of soil and water.
• To manage and utilize the runoff water for a useful purpose.
• To protect, conserve and improve the land of a watershed for more efficient and sustained production.
• To protect and enhance the water resource originating in the watershed.
• To check soil erosion and to reduce the effect of sediment yield on the watershed.

Important Points

Warabandi System:

• It is also called the Water Distribution System.
• It is a rotational water allocation system that can fulfill the requirement of equality.
• Warabandi is an Urdu word that combines wahr ("turn") and bandi (“fixed)” So “warabandi” means “rotation of water supply according to a fixed schedule".

Aquifer: 

• It is an underground geological formation that contains water and a sufficient amount of water can be extracted economically using water wells. It generally comprises layers of sand and gravel and fractured bedrock.

The correct answer is Seventh.

• Prophet Muhammad founded the faith of Islam in the seventh century.

Key Points

• Prophet Muhammad was born around 570 in the city of Mecca, located on the Arabian Peninsula.
• In 622, the prophet Muhammad completes his Hegira, or “flight,” from Mecca to Medina to escape persecution.
• The four holiest sites in Islam are:
• The Kaaba (inside the Masjid al-Haram) in Mecca
• Al-Masjid an-Nabawi in Medina
• Al-Aqsa Mosque in Jerusalem
• Umayyad Mosque in Damascus

Additional Information

• Central to Islamic beliefs are the Five Pillars of Faith are:
• There is only one universal God: Allah.
• Followers of Islam (Muslims) are expected to pray five times each day while facing Mecca.
• All Muslims are expected to pay a yearly tax that is mostly intended to help the poor and needy.
• For the entire month of Ramadan, Muslims must not eat, smoke, drink, or have sexual relations from sunrise to sunset.
• All able Muslims must make a pilgrimage (hajj) to Mecca at least once in their lifetimes.

The correct answer is G Krishnan.

• G Krishnan is one of the authors of The Hitman.

Key Points

• The Hit Man book is based on one of the cricket players Rohit Sharma.
• Rohit Sharma is an Indian international cricketer who captains the India national cricket team in ODIs and T20Is. He vice-captains the Indian cricket team in Test cricket.
• Sharma made his List A debut for West Zone against Central Zone in the Deodhar Trophy at Gwalior in March 2005.
• In November 2013, during Sachin Tendulkar's farewell series, Sharma made his Test debut at Eden Gardens in Kolkata against the West Indies.
• In November 2020, Sharma was nominated for the ICC Men's ODI and T20I Cricketer of the Decade awards.

Additional Information

The correct answer is Mixed.

• An economy in which both, the private sector and the government are involved is known as a/an mixed economy.

Key Points

• A mixed economic system is a system that combines aspects of both capitalism and socialism.
• A mixed economic system protects private property and allows a level of economic freedom in the use of capital, but also allows for governments to interfere in economic activities in order to achieve social aims.
• Mixed economic systems are not laissez-faire systems, because the government is involved in planning the use of some resources and can exert control over businesses in the private sector.
• The term mixed economy gained prominence in the United Kingdom after World War II, even though many of the policies associated with it at the time were first proposed in the 1930s.
• India, England, France, and Brazil are examples of mixed economies.

Additional Information

  

Important Points

The correct answer is Kerala.

• Thullal is a solo satiric dance form belonging to the state of Kerala.

Key Points

• Ottam Thullal is a dance-drama performing art form of Kerala, created by Kunchan Nambiar, as an alternative to the Chakyar koothu.
• The distinguishing factor of Ottanthullal is the performer himself singing and playing the story, which is a tedious task.
• Most popular Art and Dance forms of Kerala are: 
• ​Theyyam
• Kathakali
• Kutiyattam
• Nangiar Koothu

Additional Information

The correct answer is Bhavya Lal.

• Bhavya Lal, an Indian-American scientist, was appointed as the acting Chief of Staff of the US space agency NASA, in February 2021.

Key Points

• In January 2021, Lal was the senior-most White House appointee and acting chief of staff at NASA for the first 100 days of the Biden Administration.
• Lal is an active member of the space technology and policy community, having chaired, co-chaired, or served on five high-impact National Academy of Science committees.
• She served two consecutive terms on the National Oceanic and Atmospheric Administration Federal Advisory Committee on Commercial Remote Sensing and was an External Council member of NASA’s Innovative Advanced Concepts Program.
• Before joining STPI, Lal was president of C-STPS LLC, a science and technology policy research and consulting firm.

Additional Information

Given:

∠ADE = 80° 

∠AED = 50° 

Concept used:

In a cyclic quadrilateral, the sum of opposite angles are 180° 

Sum of linear pair of angles of is always 180° 

Sum of all 3 interior angles of triangle is 180° 

Calculation:

  

 

∠ADE + ∠ABC = 180° 

⇒ 80° + ∠ABC = 180° 

⇒ ∠ABC = (180° – 80°)

⇒ ∠ABC = 100° 

∠ABC + ∠CBE = 180° [straight line]

⇒ 100° + ∠CBE = 180° 

⇒ ∠CBE = (180° – 100°)

⇒ ∠CBE = 80° 

In ΔAED

⇒ ∠AED + ∠CBE + ∠ECB = 180° 

⇒ 50° + 80° + ∠ECB = 180° 

⇒ 130° + ∠ECB = 180° 

⇒ ∠ECB = (180° – 130°)

⇒ ∠ECB = 50° 

 Now,

⇒ ∠ECB = ∠DCF = 50° (Vertically opposite angles)

and 

∠FDC = 180° - ∠ADC (Linear pair)

∠FDC = 180° - 80° = 100°

∠FDC + ∠DCF + ∠AFB = 180° 

⇒ 100° + 50° +  ∠AFB = 180° 

⇒ 150° +  ∠AFB = 180° 

⇒ ∠AFB = (180° – 150°)

⇒ ∠AFB = 30° 

∴ The required value of ∠AFB is 30° 

Alternate Method 

From the above diagram,

⇒ ∠ADC + ∠CDF = 180°       [ Linear pair of angles]

⇒ 80° + ∠CDF = 180° 

⇒  ∠CDF = 100° 

Now, In  ΔAED

⇒ ∠AED + ∠ADE + ∠EAD = 180° 

⇒ 50° + 80° + ∠EAD = 180° 

⇒ ∠EAD = 180° - 130° = 50° 

Now, ∠EAD = ∠DCF = 50° 

In ΔDCF

⇒ ∠CDF + ∠DFC + ∠DCF = 180° 

⇒ 100° + ∠DFC + 50° = 180° 

⇒ ∠DFC = 180° - 150° = 30° 

⇒ ∠DFC = ∠AFB = 30° 

∴ The required value of ∠AFB is 30°

Calculation:

The trees planted in Chandigarh in 2017 = 2500

The trees planted in Kolkata in 2020 = 1750

The total number of trees planted in Chandigarh in 2017 and in Kolkata in 2020 = (2500 + 1750)

⇒ 4250

∴ The total number of trees planted is 4250

Given:

An item purchased by customer = Rs. 10000

First types of discounts = 25%

Second types of discount = successive discounts of 14% and 12%.

Formula used:

Single discount on two successive discount = (a + b – ab/100)

Calculation:

According to the question

Single discount on two successive discount = (a + b – ab/100)

⇒ (14 + 12 – 14 × 12/100)

⇒ (26 – 1.68)

⇒ 24.32%

The best discount = First types of discount – Second types of discount

⇒ (25 – 24.32)% 

⇒ 0.68%

Now,

The better offer for the customers = Rs. (10000 × 0.68/100)

⇒ Rs. 68

∴ First offer by Rs. 68

Given:

$\rm \sec^2 α\left(1+\frac{1}{cosec\ α}\right)\left(1-\frac{1}{cosec\ α}\right)$

Formula used:

(a² – b²) = (a + b)(a – b)

sec²α = 1/cos²α 

1/cosecα = sinα 

1 – sin²α = cos²α 

Calculation:

$\rm \sec^2 α\left(1+\frac{1}{cosec\ α}\right)\left(1-\frac{1}{cosec\ α}\right)$

⇒ 1/cos²α (1 + sinα)(1 – sinα)

⇒ 1/cos²α (1² – sin²α)

⇒ 1/cos²α (1 – sin²α)

⇒ 1/cos²α × (cos²α)

⇒ 1

So, the required value is 1

Given:

2x + 3y = -1

Formula used:

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculation:

According to the question

2x + 3y + 1 = 0

⇒ 2x + 3y = -1

Now,

(2x + 3y)³ = (2x)³ + (3y)³ + 3 × 2x × 3y (-1) = -1

⇒ 8x³ + 27y³ – 18xy = -1

Now,

The value of (8x3 + 8 + 27y3 – 18xy) = (8 – 1)

⇒ 7

∴ The required value is 7

Given:

Amount = Rs. 11495

Principal = Rs. 9500

Time = 2 years

Formula used:

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

SI = (P × R × T)/100

Calculation:

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

⇒ 11495 = 9500(1 + r/100)²

⇒ (1 + r/100)² = (11495/9500)

⇒ (1 + r/100)2 = (121/100)

⇒ (1 + r/100)² = (11/10)²

⇒ r = 10%

Now,

According to the question

Principal = Rs. 9500

Rate = double the rate = (2 × 10) = 20%

Time = 2 years

SI = (P × R × T)/100

⇒ Rs. (9500 × 20 × 2)/100

⇒ Rs. (95 × 20 × 2)

⇒ Rs. 3800

∴ The required SI is Rs. 3800

Given:

$\frac{ar(Δ ABC)}{ar(Δ PQR)}=\frac{16}{25}$

PQ = 4 cm

QR = 6 cm

PR = 7 cm

Concept used:

The ratio of the two similar triangles is equal to the square of the ratio of their corresponding sides.

Calculation:

$\frac{ar(\Delta ABC)}{ar(\Delta RPQ)}=\frac{16}{25}$

Now,

According to the question

ar(ΔABC)/ar(ΔRPQ) = AC²/QR²

⇒ 16/25 = AC²/6²

⇒ 25AC² = 36 × 16

⇒ AC = (24/5)

⇒ AC = 4.8 cm

∴ The required value of AC is 4.8 cm

Given:

Length of the side AC is 4 cm more than 2 times the length of the side AB

Length of the side BC is 4 cm less than the three times the length of the side AB.

The perimeter of ΔABC = 60 cm

Formula used:

Area of triangle = 1/2 × base × height

Calculation:

Let the side of AB be x cm

Then,

Length of the side AC is 4 cm more than 2 times the length of the side AB = (2x + 4) cm

Length of the side BC is 4 cm less than the three times the length of the side AB. = (3x – 4) cm

Perimeter of ΔABC = 60 cm

⇒ (x + 2x + 4 + 3x – 4) = 60

⇒ 6x = 60

⇒ x = 10 cm

Now,

Side of AB = x = 10 cm

Side of AC = (2x + 4) = (2 × 10 + 4) = 24 cm

Side of BC = (3x – 4) = (3 × 10 – 4) = 26 cm

We know that 10, 24, and 26 is a triplet, 

⇒ We can say that the given triangle is a Right angle triangle.

Now,

⇒ Area of triangle = 1/2 × base × height

Area of triangle = (1/2 × 10 × 24)

⇒ (5 × 24) 

⇒ 120 cm²

∴ The required area is 120 cm2

Given:

The average of 23 numbers = 51

The average of first 12 numbers = 49

The average of last 12 numbers = 54

Formula used:

Average = sum of observations/Number of observations

Calculation:

The sum of 23 numbers = (23 × 51) = 1173

The sum of first 12 numbers = (12 × 49) = 588

The sum of last 12 numbers = (12 × 54) = 648

Now,

The twelfth number = [(588 + 648) – 1173]

⇒ (1236 – 1173)

⇒ 63

The 12^th number = 63

Now, If the twelfth number is removed,

The sum of remaining numbers = (1173 – 63) = 1110

The average of remaining number = (1110/22)

⇒ 50.45

∴ The required average number is 50.45

Given:

Time taken to complete a work by A = $11\frac{1}{2}$ days = 23/2 days

B is 25% more efficient than A = (25/100) = 1/4

Efficiency of A = 4 days

Efficiency of B = (4 + 1) = 5 days

C is 50% efficient than B = (50/100) = 1/2

Efficiency of C = (5/2) = 2.5 days

Formula used:

Work = Efficiency × Time

Calculation:

Total work = (23/2 × 4) = 46 days

Total time taken by A, B and C together = [46/(4 + 5 + 2.5)] days

⇒ (46/11.5) days

⇒ 4 days

∴ The required time is 4 days

Shortcut TrickEfficiency of them

So, total work = 8 × 23/2 = 92 units

Total time taken by A, B and C together = [92/(8 + 10 + 5)] = 4 days

Given:

the selling price of 75 articles is equal to the cost price of 60 articles

Formula used:

Loss = SP – CP

Loss% = Loss/CP × 100

Calculation:

Selling price of 75 articles is equal to the cost price of 60 articles

According to the question

75 SP = 60 CP

SP/CP = 4/5

SP : CP = 4 : 5

Suppose SP = 4 unit and CP = 5 unit

Loss = CP – SP = 5 – 4 = 1

Loss percentage = (1/5) × 100 = 20%

Given:

cot A = 1/2

Formula used:

sinθ = p/h

cosθ = b/h

Calculation:

AC (h) = √{2² + 1²} = √{4 + 1} = √5

Sin A = 2/√5

Cos C = 2/√5

Cos A = 1/√5

Sin C = 1/√5

Now,

The value of $\frac{\sin A(\cos C+ \cos A)}{\cos C(\sin C-\sin A)}$ = [(2/√5)(2/√5 + 1/√5)]/[(2√5)(1/√5 – 2/√5)]

⇒ (3/√5)/(-1/√5)

⇒ -3

∴ The required value is -3

Given:

The area of a table top in the shape of an equilateral triangle is 9√3 cm²

Formula used:

Area of equilateral triangle = √3a²/4 

Calculation:

According to the question

The area of a table top in the shape of an equilateral triangle is 9√3 cm²

⇒ √3a²/4 = 9√3 

⇒ a² = (4 × 9)

⇒ a² = 36

⇒ a = 6 cm

∴ The length of each side of the table is 6 cm

Given:

The total number of students in a school = 1400

Number of girls = 35%

Number of boys who passed an annual examination = 80%

Number of girls who passed an annual examination = 90%

Calculation:

The total number of students in a school = 1400

Number of girls = (1400 × 35/100)

⇒ 490

Number of boys = (1400 – 490) = 910

Number of boys who passed an annual examination = (80% of 910)

⇒ (80/100 × 910)

⇒ 728

Number of boys who failed the annual examination = (910 – 728) = 182

Number of girls who passed an annual examination = (90% of 490)

⇒ (90/100 × 490)

⇒ 441

Number of girls who failed the annual examination = (490 – 441) = 49

Now,

Total number of failed students = (182 + 49) = 231

Required percentage of failed students = (231/1400 × 100)

⇒ (231/14)

⇒ 16.5%

∴ The required percentage of failed students is 16.5

Given:

AD ⊥ BC

∠B = 68° 

∠C = 52° 

Calculation:

Join O to B where point O is the circum centre of the triangle.

⇒ ∠BOA = 2∠BCA

⇒ 2 × 52° 

⇒ 104° 

In ΔBOA

⇒ OB = OA [radius of the circle]

⇒ ∠OBA = ∠OAB

⇒ ∠AOB + ∠OAB + ∠OBA = 180° 

⇒ 2∠OAB = (180° – 104°)

⇒ 2∠OAB = 76° 

⇒ ∠OAB = (76/2)

⇒ ∠OAB = 38° 

In ΔABD

⇒ ∠ABD + ∠BDA + ∠DAB = 180° 

⇒ ∠DAB = (180° – 90° – 68°)

⇒ ∠DAB = 22° 

Now,

∠DAP = ∠BAO – ∠BAD 

⇒ ∠DAP = (38° – 22°)

⇒ ∠DAP = 16° 

So, the required value is 16°

Calculation:

Total number of passed students from school R in 2015 to 2017 = (285 + 288 + 294)

⇒ 867

Average number of passed students from school R in 2015 to 2017 = (867/3)

⇒ 289

The number of students passed from school Q in 2015 = 320

The value of x = (320 – 289) = 31

∴ The value of x lies between 30 and 35

Calculation:

tanθ + 3cotθ – 2√3 = 0

⇒ tan2θ+  3 - 2√3tanθ = 0

⇒ (tanθ - √3)2 = 0

⇒ tanθ = √3

⇒ θ = 60° 

Now,

⇒ cosec2 θ + cos2 θ = cosec260° + cos260°

⇒ (2/√3)2 + (1/2)2 = (4/3) + (1/4) = 19/12

∴ The correct answer is 19/12

Alternate Method Given:

tanθ + 3cotθ – 2√3 = 0

Formula used:

(AC)² = (AB)² + (BC)²

tanθ = sinθ/cosθ 

cotθ = cosθ/sinθ 

tanθ = p/b

cosecθ = h/p

cosθ = b/h

Calculation:

tanθ + 3cotθ – 2√3 = 0

⇒ sinθ/cosθ + 3 cosθ/sinθ – 2√3 = 0

⇒ sinθ/cosθ + 3 cosθ/sinθ = 2√3

⇒ sin²θ + 3cos²θ = 2√3cosθsinθ 

⇒ sin2θ + 3cos2θ – 2√3cosθsinθ 

⇒ (sinθ – √3cosθ)² = 0

⇒ sinθ = √3cosθ 

⇒ tanθ = √3

Now,

(AC)2 = (AB)2 + (BC)²

⇒ (AC)² = (√3)² + (1)²

⇒ (AC)² = (3 + 1)

⇒ (AC)² = 4

⇒ AC = 2 cm

cosecθ = h/p = 2/√3

cosθ = b/h = 1/2

Now,

The value of (cosec²θ + cos²θ) = (2/√3)² + (1/2)²

⇒ (4/3 + 1/4)

⇒ (16 + 3)/12

⇒ 19/12

∴ The required value is 19/12

Given:

p is the third proportional to 3, 9

Calculation:

Let the fourth proportion be x

p is the third proportional to 3, 9

⇒ 3/9 = 9/p

⇒ 3p = 81

⇒ p = 27

Now,

The fourth proportion is

⇒ 6/27 = 4/x

⇒ 6x = (27 × 4)

⇒ 6x = 108

⇒ x = 18

∴ The value of fourth proportion is 18

Concept Used:       

Follow the BODMAS rule according to the table given below:

Calculation:

$3\frac{1}{5}÷4\frac{1}{2}of\ 5\frac{1}{3}-\frac{1}{8}÷\frac{1}{2}\ of\ \frac{1}{4}+\frac{1}{4}\left(\frac{1}{2}÷\frac{1}{8}×\frac{1}{4}\right)$

⇒ 16/5 ÷ 9/2 of 16/3 – 1/8 ÷ 1/2 of 1/4 + 1/4(1/2 ÷ 1/8 × 1/4)

⇒ 16/5 ÷ 9/2 of 16/3 – 1/8 ÷ 1/2 of 1/4 + 1/4(1/2 × 8 × 1/4)

⇒ 16/5 ÷ 9/2 of 16/3 – 1/8 ÷ 1/2 of 1/4 + 1/4 × (1)

⇒ 16/5 ÷ 9/2 of 16/3 – 1/8 ÷ 1/2 of 1/4 + 1/4

⇒ 16/5 ÷ 24 – 1/8 ÷ 1/2 of 1/4 + 1/4

⇒ 16/5 ÷ 24 – 1/8 ÷ 1/8 + 1/4

⇒ 16/5 × 1/24 – 1/8 ÷ 1/8 + 1/4

⇒ 2/15 – 1/8 ÷ 1/8 + 1/4

⇒ 2/15 – 1/8 × 8/1 + 1/4

⇒ 2/15 – 1 + 1/4

⇒ (8 – 60 + 15)/60

⇒ (-52 + 15)/60

⇒ -37/60

∴ The required value is $-\frac{37}{60}$

Given:

The sum of three digit numbers = abc, cab and bca

Calculation:

We have,

⇒ abc + cab + bca = (100a + 10b + c) + (100c + 10a + b) + (100b + 10c + a)

⇒ (100a + 10a + a) + (100b + 10b + b) + (100c + 10c + c)

⇒ (111a + 111b + 111c)

⇒ 111(a + b + c)

⇒ 3 × 37(a + b + c)

∴ The number abc, cab and bca are not divisible by 31.

Given:

a4 + b4 + a2b2 = 273 and a2 + b2 - ab = 21

Formula used:

(a2 + b2 + ab) (a2 + b2 – ab) = a⁴ + b⁴ + a²b²

Calculation:

a4 + b4 + a2b2 = 273

⇒ (a² + b² + ab) (a² + b² – ab) = 273

⇒ (a² + b² + ab) (21) = 273

⇒  (a2 + b2 + ab) = (273/21)

⇒  (a2 + b2 + ab) = 13 ....(1)

a2 + b2 – ab = 21 .....(2)

Adding equation (1) and (2), we get

⇒ (a2 + b2 + ab) = 13 + a2 + b2 – ab = 21

⇒ 2(a² + b²) = (21 + 13)

⇒ 2(a² + b²) = 34

⇒ a² + b² = 17

Putting the value of 17 in equation (2)

⇒ 17 – ab = 21

⇒ -ab = 4

⇒ ab = -4

Now,

(a + b)2 = a2 + b2 + 2ab

⇒ (a + b)² = 17 + 2 × (-4)

⇒ (a + b)² = 17 – 8

⇒ (a + b)² = 9

⇒ (a + b) = 3

Then,

The value of $\left(\frac{1}{a}+\frac{1}{b}\right)$

⇒ [(b + a)/ab] = [3/(-4)]

⇒ -3/4

∴ The required value is -3/4

Calculation:

The total number of students passed from school S in 2014 and 2017 = (273 + 247)

⇒ 520

The total number of students appeared from school T in 2015, 2016 and 2017 = (300 + 320 + 350)

⇒ 970

Now,

According to the question

90% of the total number of students appeared from school T in 2015, 2016 and 2017 = (90% of 970)

⇒ (90/100 × 970)

⇒ 873

The total number of students passed from school S in 2014 and 2017 is what percent of 90% of the total number of students appeared from school T in 2015, 2016 and 2017 = (520/873 × 100)

⇒ 59.564% ~ 59.6%

∴ The required percentage is 59.6

Calculation:

The Salary of Varun = 42000

The other income of Varun other than salary = (7500 + 1240 + 1500)

⇒ 10240

The ratio of salary of Varun to his income other than salary = (42000 : 10240)

⇒ 525 : 128

∴ The required ratio is 525 : 128

Alternate MethodLet the actual speed be x km/h and the actual time taken be t hr.

Distance = (X × Y)/(X - Y) × [Time Difference]

⇒ 450 = {x × (x + 5)}/(x + 5 - x) × [t + 1 - t]

⇒ 450 = [x(x + 5)]/5

⇒ 2250 = x × (x + 5)

⇒ 2250 = 45 × (45 + 5)

On comparing x = 45 km/h

Actual time taken = 315/45 = 7 hr

Traditional method:

Given:

If the speed had been 5 km/h more, the train covered a distance = 450 km

If speed had been 1 hour less, the train covered a same distance

Formula used:

Speed = Distance/Time

Calculation:

Let the speed of train be x km

According to the question

⇒ 450/x – 450/x + 5 = 1

⇒ 450(x + 5) – 450x = x² + 5x

⇒ 450x + 2250 – 450x = x² + 5x

⇒ x² + 5x – 2250 = 0

⇒ x² + 50x – 45x - 2250 = 0

⇒ x(x + 50) – 45(x + 50) = 0

⇒ (x – 45)(x + 50) = 0

⇒ x = – 50, 45

⇒ x = 45 km/h

Now,

Time taken to cover the distance of 315 km = (315/45)

⇒ 7 h

∴ The required time is 7 h