SSC CGL 2020 Tier-I Official Paper (Held On : 23 Aug 2021 Shift 2) (Previous Year Paper)

The Logic here is as follows:

(1^st Number)³ + (2^nd number)² = Third Number

In (3, 6, 63)

(1^st Number)³ + (2^nd number)² = Third Number

= 3³ + 6²

= 27 + 36

= 63 = Third Number

Now check the all options,

Option (1) (8, 5, 64)

(1^st Number)³ + (2^nd number)² = Third Number

= 8³ + 5²

= 512 + 25

= 537 ≠ Third Number

**Option (2) (**4, 5, 89)

(1^st Number)³ + (2^nd number)² = Third Number

**= **4³ + 5²

= 64 + 25

= 89 = Third Number

Option (3) (5, 6, 92)

(1^st Number)³ + (2^nd number)² = Third Number

= 5³ + 6²

= 125 + 36

= 161 ≠ Third Number

Option (4) (7, 3, 58)

(1^st Number)³ + (2^nd number)² = Third Number

= 7³ + 3²

= 343 + 9

= 352 ≠ Third Number

Hence, the correct answer is "(4, 5, 89)".

The image obtained when the paper is unfolded is,

Hence, option 4 is the correct answer

The logic followed here is:

Option 1) Bray → Bray is the sound made by a donkey.

Option 2) Growl → Growl is the sound made by lions, bears and tigers.

Option 3) Squeak → Squeak is the sound made by rats and rabbits.

Option 4) Gallop → the fastest pace of a horse or other quadruped

Hence, “Gallop” is an odd one.

Opposite surface of the open dice can be found by the below method:-

• Alternate surfaces are opposite to each other.
• No two opposite surface are touched by side or by corners

So, by using the above rule we can find the opposite surface of open dice.

Below are the opposite surfaces:-

 

Hence, ‘2’ is the number on the opposite side of the number ‘1'.

According to the sequence in the dictionary:

The correct order of the given words is:

3. Singular
4. Sinuous
5. Solemnity
6. Solvable
7. Sorting

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

The logic is here is:

(1^st number)³ – (1^st number)² = 2^nd number

Option (1): 6 : 180

Now, follow the logic:

= 6³ – 6²

= 216 – 36 = 180 = 2^nd number

This option follows the pattern.

Option (2): 5 : 100

Now, follow the logic:

= 5³ – 5²

= 125 – 25 = 100 = 2^nd number

This option follows the pattern.

Option (3): 4 : 52

Now, follow the logic:

= 4³ – 4²

= 64 – 16 = 48 ≠ 2^nd number

This option do not follow the pattern.

Option (4): 7 : 294

Now, follow the logic:

= 7³ – 7²

= 343 – 49 = 294 = 2^nd number

This option follows the pattern.

Hence, pair “4 : 52” is an odd one.

The number of triangles in the given figure is:

So, there are a total of 11 triangles in the figure.

Hence, ‘11’ is the correct answer.

Statements:

All ministers are politicians.

All pilots are ministers.

No engineer is a politician.

The least possible diagram for the given statements is as follows

Conclusions:

I. Some ministers are pilots → True (Because All pilots are ministers so some ministers are also pilots)

Il. No engineer is a minister → True (Because No engineer is a politician and all ministers are politician so definitely No engineer is a minister)

III. No engineer is a pilot → True (Because No engineer is a politician and all pilots are politician so definitely No engineer is a pilot)

Hence, all the conclusions follow.

Additional Information

We know that

Average age = Total age of all persons ÷ total persons

So,

Total age of all persons = Average age × total persons

Given:

1) Average age of 17 persons is 39 years.

Total age of all persons = Average age × total persons

= 39 × 17

= 663

2) Average age of the first 9 persons is 35 years.

Total age of the first 9 persons = Average age × total persons

= 35 × 9

= 315

3) Average age of the last 9 persons is 44 years.

Total age of the last 9 persons = Average age × total persons

= 44 × 9

= 396

So,

The age of the 9^th person = Total age of the first 9 persons + Total age of the last 9 persons - Total age of all persons  

= 315 + 396 – 663

= 711 – 663

= 48

Hence, the age of the 9^th person is ‘48’.

According to BODMAS rule:

Given equation 252 * 14 * 8 * 100 * 16 * 60

Option 1: Using the combination ÷, ×, +, =, - 

252 ÷ 14 × 8 + 100 = 16 - 60 

By BODMAS rule

252 ÷ 14 × 8 + 100 = 16 - 60 

18 × 8 + 100 = 16 - 60 

144 + 100 = 16 - 60 

244 = - 44 (LHS ≠ RHS)

Option 2: Using combination ÷, -, ×, +, =

252 ÷ 14 - 8 × 100 + 16 = 60

18 - 8 × 100 + 16 = 60

18 - 800 + 16 = 60

18 - 800 + 16 = 60

34 – 800 = 60

• 766 = 60 (LHS ≠ RHS)

Option 3: Using the combination ÷, ×, -, +, =

252 ÷ 14 × 8 - 100 + 16 = 60

18 × 8 - 100 + 16 = 60

144 - 100 + 16 = 60

160 – 100 = 60

60 = 60 (LHS = RHS)

Option 4: Using the combination ÷, ×, +, -, =

252 ÷ 14 × 8 + 100 - 16 = 60

18 × 8 + 100 - 16 = 60

144 + 100 - 16 = 60

244 - 16 = 60

228 = 60 (LHS ≠ RHS)

Hence, the answer is “÷, ×, -, +, =”.

The Logic here is as follows:

[(1^st Number)³ + (3^rd number)³] ÷ 2 = 2^nd Number

In (4, 532, 10)

[(1^st Number)³ + (3^rd number)³] ÷ 2 = 2^nd Number

(4³ + 10³) ÷ 2

= (64 + 1000) ÷ 2

= 1064 ÷ 2

= 532 = 2^nd Number

Now check the all options,

Option (1) (9, 396, 4)

[(1^st Number)³ + (3^rd number)³] ÷ 2 = 2^nd Number

(9³ + 4³) ÷ 2

= (729 + 64) ÷ 2

= 793 ÷ 2

= 396.5 ≠ 2^nd Number

Option (2) (3, 269, 8)

[(1^st Number)³ + (3^rd number)³] ÷ 2 = 2^nd Number

(3³ + 8³) ÷ 2

= (27 + 512) ÷ 2

= 539 ÷ 2

= 269.5 ≠ 2^nd Number

Option (3) (2, 121, 6)

[(1^st Number)³ + (3^rd number)³] ÷ 2 = 2^nd Number

(2³ + 6³) ÷ 2

= (8 + 216) ÷ 2

= 224 ÷ 2

= 112 ≠ 2^nd Number

Option (4) (4, 140, 6)

[(1^st Number)³ + (3^rd number)³] ÷ 2 = 2^nd Number

(4³ + 6³) ÷ 2

= (64 + 216) ÷ 2

= 280 ÷ 2

= 140 = 2^nd Number

Hence, the correct answer is "(4, 140, 6)".

The Venn diagrams best represent the relationship between - Reptiles, Frogs, Animals figures are shown below:

Reptiles and Frogs are animals and but no reptiles are frogs.

Hence, ‘option 2’ is the correct answer.

Additional Information

• Frogs are considered amphibians instead of reptiles because their skin is porous, they need to live in habitats where water is plentiful, and they go through a process called metamorphosis. Amphibians are frogs, toads, newts and salamanders.
• Reptiles are turtles, snakes, lizards, alligators and crocodiles. Unlike amphibians, reptiles breathe only through their lungs and have dry, scaly skin that prevents them from drying out.

The logic followed here is,

350 : 5

350 is divisible by 5

and,

990 : 9

990 is divisible by 9

Similarly,

? : 13

1950 is divisible by 13

Hence, “1950” is correct answer.

The pattern followed here is -

Hence, “5” is the correct answer.

The logic followed here is:

Zakir Hussain : Tabla → Zakir Hussain is one of the greatest tabla player.

Now, check the options

Option (1) Amjad Ali Khan : Shehnai → Amjad Ali Khan is one of the greatest sarod player not shehnai player.

Option (2) Hariprasad Chaurasiya : Flute → Hariprasad Chaurasiya is one of the greatest flute player.

Option (3) Bismillah Khan : Sarod → Bismillah Khan is one of the greatest shehnai player not sarod player.

Option (4) Ravi Shankar : Santoor → Ravi Shankar is one of the greatest sitar player not santoor player.

Hence, ‘Hariprasad Chaurasiya : Flute’ is the correct answer.

The table is alphabets place value:

The pattern followed here is:

Step 1: Arrange letters according to the alphabets series.

Step 2: “Opposite letter place values + 1” are coded as numeric values.

'LOAD' is coded as '27241613'

Step 1: LOAD → Alphabetical order → ADLO.

Step 2: “Opposite letter place values + 1” are coded as numeric values.

'CLEAN' is coded as '2725231614'

Similarly, 

'STRIKE' = ?

Step 1: STRIKE → Alphabetical order → EIKSRT.

Step 2: “Opposite letter place values + 1” are coded as numeric values.

Hence, the correct answer is "2319171098".

Additional InformationThe pattern followed here is:

1) Alphabets are coded as their opposite letter and addition of +1.

2) Then Numbers are arranged in descending order.

• Alphabets are arranged in descending order after reverse coding + 1.

'LOAD' is coded as '27241613'

And, 

'CLEAN' is coded as '2725231614'.

• Alphabets are arranged in descending order after reverse coding + 1.

Similarly, 

'STRIKE' = ?

• Alphabets are arranged in descending order after reverse coding + 1.

Hence, the correct answer is "2319171098".

Table show alphabet serial number –

The logic is shown below –

Hence, “G” is complete in the series.

Preparing the family tree using the following symbols,

We can dram following Family Tree from the information given above:

1. Arya's mother's husband is the brother of Meena's mother.

2. Vansh is the brother of Meena and Kavita.

3. Varun is the father of Arya.

Hence, Varun is “Maternal uncle” of Vansh.

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

Hence, "option (3)" is the correct answer.

Table show alphabet serial number –

The logic is shown below –

Hence, “PBQ” is the term that completes the series.

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

1. The series is rotating in clockwise direction in each step.

2) After rotation north-west direction figure create mirror image.

 makes water image after three step, the remaining three image it shows as 

.

Hence, ‘option 1’ is the correct answer.

Table show alphabet serial number –

The pattern followed is,

All follow the same pattern, except ‘WYBY’.

Hence, “WYBY” is the odd one.

Table show alphabet serial number –

The pattern for the code is as follows,

‘TRAVEL' is written as ‘SUWBMF’

Similarly,

‘FROZEN’ is written as

Hence, ‘FROZEN’ is coded as ‘SGAPOF’.

Bats : Colony :: Lions : ?

The logic followed here is:

Bats : Colony → A group of bats is called Colony,.

Similarly,

Lions : Pride → A group of Lions is called Pride.

Hence, ‘Pride’ is the correct answer.

The embedded part of this image is:

Hence, option (2) is the correct answer.

The correct answer is Minhaj-i-Siraj.

Key Points

• Minhaj al-Siraj was a 13th-century Persian historian.
• He was a prominent historian of the 'Mamluk Sultanate' of Delhi in northern India.
• Minhaj dedicated his work 'Tabkat-e-Nasiri' to the ruler of the Ghulam dynasty, Nasiruddin Mahmud.
• Tabaqat-e-Nasiri -
• It gives information about Muhammad Ghori's conquest of India and the early history of the Turkish Sultanate dates back to about 1260 AD.

Additional Information

• Zia-ud-din Barani:
• He was a historian and political thinker who lived in India during the times of Muhammad bin Tughlaq and Firoz Shah.
• 'Tarikh Forozshahi' is a famous historical book.​
• Amir Khusrau:
• He was born in 1253 AD in a town called Patiali in Etah, Uttar Pradesh.
• He was the first Muslim poet and is credited with the invention of 'Khari Boli'.
• He saw the rule of 7 sultans (Balban, Muhammad, Kaiqubad, Jalaluddin Khilji, Alauddin Khilji, Mubarak Shah Khilji, Ghiyasuddin Tughlaq).​
• Ibn Battuta:
• He was an Arab traveler, scholar, and writer.
• He was a resident of Morocco in North Africa.
• He came to India during the rule of Muhammad bin Tughlaq.

The correct answer is Rabindranath Tagore.

• The novel 'Gora' by Rabindra Nath Tagore is a novel epic of the national consciousness of India under British rule.

Additional Information

• Premchand:
• He was born in a Kayastha family in Lamhi village of Varanasi district (Uttar Pradesh).
• His early education was done in 'Persian'.
• Premchand's compositions -
• His famous novels are 'Seva Sadan', 'Nirmala', 'Rangbhoomi', 'Karmabhoomi', 'Gaban', 'Godan' etc.
• His huge collection of stories is published in eight parts under the name **'Mansarovar'.**​
• Mahatma Gandhi:
• ​He is known as the 'Father of India'.
• His full name is Mohandas Karamchand Gandhi.
• Mahatma Gandhi has made a special contribution in getting freedom from the British.
• Champaran Satyagraha, Non-Cooperation Movement, Dandi Satyagraha, Dalit Movement, Quit India Movement are some of his major movements.
• Abanindranath Tagore:
• He infused the spirit of Swadeshi in his paintings.
• He was the chief painter and founder of the 'Indian Society of Oriental Art'.

The correct answer is Environmental Economics.

Key Points

• Environmental Economics deals with the depletion of natural resources stock and pollution, which are a result of rapid economic development.
• It conducts theoretical or empirical studies of the economic impacts of national or local environmental policies around the world.
• Some specific issues include the costs and benefits of alternative environmental policies to combat air pollution, water quality, solid waste, and global warming.

Additional Information

• Developmental Economics -
• it is a branch of economics that focuses on improving fiscal, economic, and social conditions in developing countries.
• it is mainly focused such as health, education, working conditions, domestic and international policies, and market conditions.
• International Economics -
• It is concerned with all those economic deals which are done **outside the borders of the country.**​
• Public Economics -
• It is based on the principle of welfare economics and is ultimately used as a tool to **improve social welfare.**​
• ​Adam Smith is known as 'Father of economics'.

The correct answer is Mg.

Key Points

• Magnesium (Mg)-
• It is a chemical element, its atomic number is 12.
• In the periodic table, it is denoted by 'Mg'. It is an alkaline element.
• It is one of the five major chemical elements found in the human body.
• 50% of the magnesium present in the human body is found in bones.

Additional Information

• Magnesium -
• It is very strong even though it is a light element.
• For this reason, it is considered useful for alloys and the space industry.
• It is found in green leafy vegetables.
• It is very important for keeping the immune system, nerves and heart, and bones strong.
• It is needed for the heart and kidneys to function properly.
• It was discovered by Humphry Davy in 1808.

The correct answer is Madhya Pradesh.

Key Points

• Madhya Pradesh has become the first state to give electricity subsidies through Direct Benefit Transfer.
• Direct Transfer Benefit is a scheme of the Government of India, under which the subsidy amount of subsidy given by the government to the consumer is directly transferred to his bank account.

Additional Information

• Manipur -
• It is a northeastern state of India and its capital is Imphal.
• The original inhabitants of this place are the people of the Meitei tribe, who live in the valley area here.
• Their language is Meitilon, which is also called the Manipuri language.
• This language was added to the Eighth Schedule of the Constitution of **India in 1992.**​
• Sikkim -
• It is a mountainous state of India.
• Gangtok is its capital and largest city.
• India's West Bengal state is to its south.​
• Uttarakhand -
• It is a state located in North India and its capital is Dehradun.
• It was created on 9 November 2000 as the 27th state of the Republic of India.

The correct answer is RK Narayan.

Key Points

• R. K. Narayan:
• His full name was Rasipuram Krishnaswamy Iyer Narayanaswamy.
• R K Narayan's books: Raj - Swami and Friends (1935), The Bachelor of Arts (1937), The English Teacher (1945), The Painter of Signs (1976), A Tiger for Malgudi (1983), and Talkative Man (1987).
• He was awarded the Sahitya Akademi Award in 1960 for his novel 'Guide'.

Additional Information

• Salman Rushdie -
• He is a famous British Indian novelist and essayist.
• His famous novel is Midnight's Children (1981), for which he received the Booker Prize in 1981.
• Khushwant Singh -
• He was a famous journalist, writer, novelist, and historian of India.
• His major novels are famous - 'Delhi', 'Train to Pakistan', 'The Company of Woman'.
• Vikram Seth -
• He is a famous novelist and poet of Indian literature.
• He is best known for his four major novels -
• The Golden Gate (1986), A Suitable Boy (1993), Sanet, An Equal Music (1999).

The correct answer is ​Plague.

Key Points

• Plague -
• It is an infection caused by a bacteria called "Yersinia pestis".
• This bacteria is mainly found in rats or in fleas that bite rats.
• There are two main forms of plague - bubonic and pneumonic (when the plague spreads rapidly to the lungs).​

Additional Information

• Zika -
• It is a mosquito-borne disease caused by a virus.
• The virus is mainly transmitted to humans through the bite of an infected Aedes mosquito.
• AIDS -
• The full name of AIDS is Acquired Immune Deficiency Syndrome.
• It is a contagious venereal disease. It is caused by the HIV virus.
• The full name of HIV is Human Immune Deficiency Virus (HIV).
• Ebola -
• This is an infectious disease.
• The disease is spread through sweat and saliva.
• It is also spread through direct contact with infected blood and feces.​

The correct answer is Keshav Kranthi.

Key Points

• Keshav Kranthi -
• He was the former director of CICR-Nagpur.
• Global cotton research and advisory body, International Cotton Advisory Committee (ICAC), has elevated Keshav R Kranthi as the chief scientist.

Additional Information

• International Cotton Advisory Committee (ICAC) -
• It was founded in 1939 at the International Cotton Meeting in Washington, DC.
• It advocates for cotton-producing countries and publishes studies and technical information on the cotton industry.
• 'World Cotton Day' is celebrated on 7th October.
• The day is observed by the United Nations, the World Food Organization, the United Nations Conference on Trade and Development, the International Trade Center and the International Cotton Advisory Committee.
• The year (2021) theme of World Cotton Day is "Cotton for Good".
• India is the largest cotton-producing country in the world.

The correct answer is Distillation.

Key Points

• Distillation is a process in which impure water is boiled and the steam is collected and condensed in a separate container, leaving many of the solid contaminants behind.
• By this method, different components of crude oil are separated.

Additional Information

• Decantation -
• It is the process of separation of liquid from solid (non-mixing).
• Water can be separated by the method of disposal of a mixture of sand and water.
• The components of a liquid and its insoluble matter can be separated by the use of filtration.​
• Sedimentation -
• The settling of particles present in a liquid on the ground is called sedimentation.
• It is caused by the force of gravity or centrifugal force acting on the particles suspended in the liquid.
• Filtration -
• In this process, the solid particles are separated from a liquid or gaseous substance with the help of filter paper, it is called filtration.​

The correct answer is Ajmer.

Key Points

• Pushkar Fair-
• It is a famous pilgrimage site of Hindus located 11 km away from Ajmer.
• Pushkar Fair is an annual multi-day livestock fair and cultural festival held in the city of Pushkar (Rajasthan, India).
• The fair begins on the Hindu calendar month of Kartik and ends on Kartik Poornima, which usually occurs in late October and early November in the Gregorian calendar.

Additional Information

• Amravati -
• It is a town in the Amravati District of Maharashtra State.
• The 'Bahiram Fair' of Amravati district is famous.
• Ahmedabad -
• It is a famous big city in Gujarat state.
• It is also known as 'Manchester of India'.
• Prayagraj -
• This place is situated at the confluence of the Ganges, Yamuna and Saraswati rivers. Hence it is called 'Triveni Sangam'.
• Kumbh Mela is held here every twelve years, and Ardh Kumbh Mela is organized every six years.

The correct answer is Kerala.

Key Points 

• Anaimudi is a mountain in the Western Ghats ranges of India.
• It is located in Ernakulam district and the Idukki district of Kerala.

Additional Information

• Tamil Nadu-
• Doddabetta is the highest peak of the Nilgiri Mountains in the Nilgiri district of the state.
• It is the 2nd highest peak after Anai Mudi of all the mountains located in the south of the Himalayas.
• Karnataka-
• Mullayyanagiri is the highest peak in Karnataka.
• There is a temple of Saint Mullapa Swamy on this peak.​
• Andhra Pradesh-
• Jindhagada Peak is the highest mountain peak in Andhra Pradesh.
• It forms a part of the Eastern Ghats range and is situated in the basin of the Godavari River.​

The correct answer is 82°30'E.

Key Points

• Standard Meridian of India (82°30'E) passes through Mirzapur (in Uttar Pradesh).
• It is 5 hours 30 minutes ahead of Greenwich Mean Time.

Additional Information

• ​Indian Standard Time Line passes through 5 states -
• Uttar Pradesh, Madhya Pradesh, Chhattisgarh, Orissa, Andhra Pradesh.
• Standard line -
• The meridian drawn on the earth at 0° longitude is called the prime meridian or Greenwich line.
• The standard time of the world is determined by this line.
• Greenwich, a city in London, is located on this line, hence it is also called 'Greenwich Line'.

The correct answer is Continental crust.

Key Points

• Continental crust is made of light rocks like granite. 
• It is thick and high above sea level. like Eurasian and Antarctic Plate.

Additional Information

• Oceanic plate:
• They have more weight and less thickness.
• It is formed by basalt consisting of the ocean floor. such as the Pacific Ocean Plate.
• ​The inner part of the earth is divided into three parts -​
• ​The Crust
• This is the outside layer of the earth and is made of solid rock, mostly basalt and granite.
• There are two types of a crust; oceanic and continental. Oceanic crust is denser and thinner and mainly composed of basalt. It is also known as Sima (most abundant minerals being silicate and magnesium)
• Continental crust is less dense, thicker, and mainly composed of granite. It is also called Sial (the most abundant minerals being silicate and aluminum).
• The Mantle
• The portion of the interior beyond the crust is called the mantle. The mantle extends from Moho’s discontinuity (the boundary between the crust and mantle) to a depth of 2,900 km.
• The crust and the uppermost part of the mantle are called the lithosphere. Its thickness ranges from 10-200 km.
• The upper portion of the mantle is called the asthenosphere which is the main source of magma that finds its way to the surface during volcanic eruptions.
• The lower mantle extends beyond the asthenosphere. It is in solid-state.
• The Core
• The mantle-core boundary (Gutenberg discontinuity) is located at a depth of 2,900 km.
• The outer core is in a liquid state while the inner core is in a solid-state.
• The core is made up of very heavy material mostly constituted by nickel and iron. Thus, it is sometimes referred to as the nife layer.

The correct answer is ​Tarain.

Key Points

• There were two battles between Muhammad Ghori and Prithviraj Chauhan in the plain of Tarain.
• First War (1191 AD) -
• Prithviraj Chauhan was victorious in this war.
• Second Battle of Tarain (1192 AD) -
• In this war, Prithviraj Chauhan was badly defeated by **Muhammad Ghori.**​

Additional Information

• Battle of Chanderi (29 January 1528 AD) -
• This war was fought between the Mughals and the Rajputs.
• In this war, the Mughal army was led by Babur and the Rajput army was led by Medini Rai.​
• Battle of Talikote (23 January 1565 AD) -
• This war was fought between the Deccan Sultanates and the Vijayanagara Empire.
• The Vijayanagara Empire had to face defeat in this war.
• This war was the fall of the last Hindu kingdom of South India.​
• Battle of Chausa (26 June 1539) -
• It was fought near Chausa village in the Buxar district of the modern Bihar state.
• This war was a war in India between the Mughal Emperor Humayun and Sher Shah Suri, the founder of the Suri Empire.
• Sher Shah Suri was victorious in this and Humayun fled from the battlefield to save his life.

The correct answer is ​Table tennis.

Key Points

• Table tennis -
• It is played between two (singles) or four (doubles) players at a time.
• Each player must have a racket.
• Since 1988, table tennis is an **Olympic sport.**​
• Grips in Table Tennis:
• Shakehand grip
• Penhold grip
• Seemiller grip
• Reverse penhold backhand (rpb) grip​

Additional Information

• Badminton -
• It is a game played with a racket.
• It is played face to face by two opposing players (singles) or two opposing pairs (doubles) on a rectangular court divided by a net.
• Terminology related to badminton game -
• Service court, shuttlecock, love, net, four-hand, hit, drop, backhand, smash, double fault, etc.
• Squash -
• It is a racket sport played by two players (or four players for doubles) on a four-walled court with a small, hollow rubber ball.​
• Cricket -
• It is a team game of bat and ball that originated in southern England.
• It is administered by the International Cricket Council (ICC) based in Dubai.
• The ICC regulates both men's and women's cricket played at the international level.​
• Cricket game terminology -
• Pitch, crease, not out, seam, shooter, slag over, umpire, innings, globs, cap, boundary, over boundary, fielder, leg before wicket, short run etc.

The correct answer is option 4.

Key Points

• Wavelength -
• It is a measure of the distance between two equal peaks of a crest or trough.
• It is denoted by the Greek letter 'lambda' (λ). Its SI unit is a 'Meter'.
• There is a relationship between the wavelength (λ), the velocity (v) of the wave, and the frequency (f) of a wave.
• λ = v / f

Additional Information

• Transverse Waves -
• The mechanical wave which, when transmitted, vibrates perpendicular to the direction of propagation of the particle of the medium, is called a transverse wave.
• Transverse waves can only be produced in solids.
• These waves cannot be produced inside liquids.
• It can be produced only on the surface of the liquid.
• Longitudinal Wave -
• If the particles of the medium oscillate back and forth at their mean position in the direction of propagation of the wave, then such waves produced are called longitudinal waves. Like sound waves.
• Longitudinal waves can be produced in all mediums (solids, liquids, gases).
• Sound waves in the air, earthquake waves, and spring waves are also longitudinal waves.​
• Electromagnetic or mechanical wave -
• Waves that do not require any medium for propagation.
• That is, these waves can also propagate in a vacuum.
• Mechanical Waves -
• The disturbance produced by throwing bricks in the water of a calm river or pond is called a mechanical wave.
• For mechanical waves to propagate through a medium, it is necessary that the medium has the properties of elasticity or inertia.

The correct answer is J Jayalalithaa.

• Sheila Dikshit - 15 years, 25 days (Total term) (Delhi - Union Territory)
• J. Jayalalithaa - 14 years, 124 days (Total term) (Tamil Nadu - State)

Key Points

• J Jayalalithaa -
• She was an Indian politician and the Chief Minister of Tamil Nadu.
• She was the general secretary of the South Indian political party All India Anna Dravida Munnetra Kazhagam (AIADMK). ,
• After her film career, she started her political career in 1982 with MG Ramachandran.​

Additional Information

• Sheila Dixit was an Indian politician who was the Chief Minister of Delhi (Union Territory not a state) from 1998 to 2013.
• She was also the Governor of the Indian state of Kerala.
• She related to the Indian National Congress Party.
• Sucheta Kripalani -
• She was an Indian freedom fighter and politician.
• She became the Chief Minister of Uttar Pradesh and was the first woman Chief Minister of India.
• She was the wife of famous Gandhian leader Acharya Kripalani.​
• Syeda Anwara Taimur -
• She is the leader of the Indian National Congress from Assam.
• She was the Chief Minister of Assam from 6 December 1980 to 30 June 1981.
• She is the first Muslim woman chief minister in the history of Assam and also of independent India.

The correct answer is periods.

Key Points

• ​The horizontal rows of the periodic table are called periods.
• The elements in the periodic table are arranged in rows.
• Elements of the same period have the same number of electron orbitals.
• Group -
• There are 18 vertical columns in the periodic table.
• All elements in a group have similar chemical and physical properties.
• Because they have the same number of outer electrons.

Additional Information

• The current periodic table includes 118 known elements.
• Atomic mass -
• It is the mass of the subatomic particle or nucleus.
• Mass number -
• It is the sum of the number of neutrons and the number of protons present in the nucleus of an atom of an element.
• Atomic number -
• It is the number of protons present in the nucleus of an atom of an element.

The correct answer is The UK.

• The first Hockey Association was formed in the UK in 1876.

Additional Information

• International Hockey Federation -
• It is the international body governing hockey.
• FIH was founded on 7 January 1924 in Paris by Paul Leute.
• Its headquarter is located in Switzerland.
• In 1928, India became the first Asian country to become a member of the FIH.
• Spain is a European country and a member state of the European Union.
• It is located in the southwest of Europe on the Iberian Peninsula.

The correct answer is ​Minhaj-us-Siraj.

Key Points

• **Tabaqat-e-Nasiri -**​
• The author of this book is Minhaj-us-Siraj.
• In this book information about the conquest of India of Mohammad Ghori and the early history of the Turkish Sultanate is found till about 1260 AD.

Additional Information

• Zia-ud-din Barani-
• He lived in the times of Muhammad bin Tughlaq and Firoz Shah.
• His famous book is'Tarikh Forozshahi'.
• Amir Khusrau -
• He was the first Muslim poet and played an important role in the invention of 'Khari Boli'.
• He saw the rule of 7 sultans (Balban, Muhammad, Kaiqubad, Jalaluddin Khilji, Alauddin Khilji, Mubarak Shah Khilji, Ghiyasuddin Tughlaq).​​  ​
• Al Beruni -
• He was a Persian scholar, writer, scientist, theologian, and thinker.
• He was with the Sultan in many campaigns of Mahmud of Ghazni (who attacked India several times).
• Alberuni was said to be the first scholar of Indian history.

The correct answer is James Prinsep.

• James Princep was a European scholar who deciphered the edicts of the Ashoka.

Key Points

• James Prinsep -
• He was an English scholar, orientalist, and antiquarian.
• He was the founding editor of the Journal of the Asiatic Society of Bengal.
• He is best remembered for his understanding of the Kharosthi and Brahmi scripts of ancient India.

Additional Information

• V Gordon Childe -
• He was an Australian archaeologist specializing in the study of European prehistory.
• He became the first exponent of Marxist archeology in the Western world.​
• Alexander Cunningham -
• He became famous as a famous scholar of Indian archaeology, historical geography, and history.
• He is considered the father of the Archaeological Survey of India.

Industry and innovation is NOT correct.

<br>

Key Points

• Aspirational District Program -
• It was launched by the Prime Minister in January 2018.
• Its objective is to improve the socio-economic indicators of 112 less developed districts of the country.
• This is an important initiative for the guiding principle of 'Yeh Sabka Saath, Sabka Vikas, and Sabka Vishwas'.
• NITI Aayog is the nodal agency for running this program.
• ADP is based on 49 indicators from the 5 identified thematic areas, which focus closely on improving people’s Health & Nutrition, Education, Agriculture & Water Resources, Financial Inclusion & Skill Development, and Basic Infrastructure.

Additional Information

• ​Human Development Index (HDI) -
• This index includes indicators of life expectancy, access to education or knowledge, and income or standard of living.
• It presents important data on the level of quality of life and changes in it.
• This index is a contribution of two famous economists 'Mehboob-ul-Haq' (Pakistan) and Amartya Sen (India).

The correct answer is Governor.

Key Points

• The governor can dissolve the cabinet in the following circumstances.
• If the governor is convinced that the majority of the cabinet in the assembly has ended.
• So the Governor can ask the Chief Minister to resign or to prove his majority by calling a session of the Legislative Assembly.
• In such a situation, if the Chief Minister is not ready to call the meeting, then the Governor can remove the cabinet.

Additional Information

• ​​Prime Minister -
• The office of the Prime Minister of the Republic of India is the post of the head of government of the Indian Union.
• The Prime Minister is the head of the Council of Ministers of the Central Government and the Chief Advisor to the President.
• Chief Minister -
• He is the political head of the states in India.
• Governor administers the oath of office to the Chief Minister.
• Speaker of the Assembly -
• It is the head of the Legislative Assembly and the Assembly Secretariat, the Presiding Officer (President).
• His authority is supreme in the premises of the Legislative Assembly.
• It is their responsibility to maintain the order of the assembly.
• The Speaker ensures the observance of the rules from the members of the assembly.
• The Speaker does not participate in the debates of the Assembly, rather he gives his arrangements/decisions during the proceedings of the Legislative Assembly.
• The Speaker presides over the assembly and in his absence, the Deputy Speaker presides over the assembly.​

The correct answer is 63rd.

Key Points

• Ease of Doing Business -
• The World Bank issues this index internationally.
• These include labor regulation, online single window, access to information, transparency, etc.
• In the country, it is prepared by the Department for Promotion of Industry and Internal Trade (DPIIT).
• DPIIT, in collaboration with the World Bank, suggests various reform processes under the Business Reform Action Plan (BRAP) for all states and union territories.
• India is ranked 63rd in the World Bank's Ease of Doing Business. India had jumped 14 places.
• It is an aggregate figure that describes the ease of doing business in a country.

Additional Information

• ​Uttar Pradesh has made a quantum jump in the Ease of Doing Business (EODB) ranking of states and union territories.
• He has jumped 10 places in the ranking to reach the second position.
• In doing so, it has left behind many major states like Maharashtra, Gujarat, Telangana, and Rajasthan.
• In this ranking, UP is now behind only Andhra Pradesh.

The correct answer is Southern.

• Andal was a woman saint of South India.
• She is one of the twelve Alvar saints.
• She is called 'Mira of the South'.
• She was born in Vikram No. 770.

Additional Information

• ​Andal has composed two texts- Tiruppavai, Nachiyar Tirumoli
• She also has a famous name 'Kaude'.

Calculation:

The number of students enrolled for VC in institute F in 2015 = 230

The number of students enrolled for VC in institute F in 2017 = 220

The number of students enrolled for VC in institute F in 2018 = 210

Total number of students enrolled for VC in institute F in 2015, 2017 and 2018 = (230 + 220 + 210)

⇒ 660

The average number of students enrolled for VC in institute F in 2015, 2017 and 2018 = (660/3)

⇒ 220

The number of students enrolled in all the six institutes in 2014 = (110 + 120 + 140 + 125 + 150 + 165)

⇒ 810

The average number of students enrolled in all the six institutes in 2014 = (810/6)

⇒ 135 

The difference between the average number of students enrolled for VC in institute F in 2015, 2017 and 2018 and the average number of students enrolled in all the six institutes in 2014 = (220 – 135)

⇒ 85

∴ The required difference is 85

Given:

$x + \frac{1}{x} = 2√ 5$

Formula used:

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculation:

$x + \frac{1}{x} = 2√ 5$

Cube both sides, we get

⇒ (x + 1/x)³ = (2√5)³ 

⇒ x³ + 1/x³ + 3 × x × 1/x (2√5) = 40√5

⇒ x³ + 1/x³ + 6√5 = 40√5

⇒ x³ + 1/x³ = (40√5 – 6√5)

⇒ x³ + 1/x³ = 34√5

Now,

$\frac{\left( x^4 + \frac{1}{x^2} \right)}{x^2 + 1}$

Dividing the equation by x, we get

⇒ (x³ + 1/x³)/(x + 1/x)

⇒ (34√5/2√5)

⇒ 17

∴ The required value is 17

Concept Used:       

Follow the BODMAS rule according to the table given below:

Calculation:

$423 ÷ \left[ 270 ÷ \frac{3}{7} × 35+ \left( 17 ÷ \frac{1}{3} \right) - \left( 8 \frac{1}{2} - \frac{5}{2} \right) \right]$

⇒ 423 ÷ [270 ÷ 3/7 × 35 + (17 ÷ 1/3) – (17/2 – 5/2)]

⇒ 423 ÷ [270 ÷ 3/7 × 35 + (17 ÷ 1/3) – (12/2)]

⇒ 423 ÷ [270 ÷ 3/7 × 35 + (17 ÷ 1/3) – 6]

⇒  423 ÷ [270 ÷ 3/7 × 35 + (17 × 3) – 6]

⇒ 423 ÷ [270 × 7/3 × 35 + 51 – 6]

⇒ 423 ÷ [22050 + 51 - 6]

⇒ 423 ÷ [22101 - 6]

⇒ 423 ÷ [22095]

⇒ 423/22095

⇒ 47/2455

∴ The required value is 47/2455

Shortcut TrickGiven:The cost price of Fridge and Washing machine together = Rs. 57300

Profit = 15%

Loss = 24%

Both are sold at the same price

Calculation:

The cost price of the Washing machine = 11500 × 3

⇒ Rs. 34500

∴ The required CP of a Washing machine is Rs. 34500.

Alternate MethodGiven:

The cost price of Fridge and Washing machine together = Rs. 57300

Profit = 15%

Loss = 24%

Both are sold at the same price

Calculation:

Let the cost Price of Fridge and washing machine be F and W

SP of Fridge at a profit at 15% = Rs. (100 + 15F) = 115F

SP of the Washing machine at a loss of 24% = Rs. (100 – 24W) = 76W

According to the question

The Selling price of the Fridge and Washing machine is sold at the same price.

So, 115F = 76W

⇒ F/W = 76/115

Then,

The cost price of Fridge F = 76

And, The cost price of Washing machine W = 115

Total CP of Fridge and Washing machine = (76 + 115) = 191

Now,

According to the question

⇒ 191 = Rs. 57300

Then,

The cost price of the Washing machine = Rs. (115/191 × 57300)

⇒ Rs. (300 × 115)

⇒ Rs. 34500

∴ The required CP of a Washing machine is Rs. 34500.

Given:

$\frac{ \sin^2 θ}{\tan^2 θ - \sin^2 θ} = 5$

Formula used:

AB² – BC² = AC²

sinθ = p/h

cosecθ = h/p

secθ = h/b

cotθ = b/p

Calculation:

$\frac{ \sin^2 θ}{\tan^2 θ - \sin^2 θ} = 5$

⇒ sin²θ/(sin²θ/cos²θ – sin²θ) = 5

⇒ sin²θ/(sin²θ/1/sec²θ – sin²θ) = 5

⇒ sin²θ/sin²θ .(sec²θ – sin²θ) = 5

⇒ sin²θ/sin²θ(sec²θ – 1) = 5

⇒ sec²θ – 1 = 1/5

⇒ sec²θ = (1/5 + 1)

⇒ sec²θ = 6/5

⇒ secθ = √6/√5

Now,

sinθ = 1/√6

secθ = √6/√5

cosecθ = √6/1

cotθ = √5/1

The value of $\rm \frac{24 \sin^2 θ - 15 \sec^2 θ}{6 \ cosec^2 θ - 7 \cot^2 θ}$

⇒ [24 × (1√6)² – (15 × √6/√5)²]/[6 × √6/1)² – (7 × √5/1)²]

⇒ (24 × 1/6 – 15 × 6/5)/(6 × 6 – 7 × 5)

⇒ (4 – 18)/(36 – 35)

⇒ (-14/1)

⇒ -14

∴ The required value is -14

Given:

x4 + x2y2 + y4 = 21 and x2 + xy + y2 = 3

Formula used:

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

Calculation:

x4 + x2y2 + y4 = 21 

And, x2 + xy + y2 = 3 ......(1)

Now,

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

⇒ 21 = (x2 – xy + y2) × 3

⇒ (x2 – xy + y2) = 7 ......(2)

Subtracting equation (2) from (1) we get,

(x2 – xy + y² = 7) – (x2 + xy + y2 = 3)

⇒ 2xy = (-4)

⇒ xy = (-4/2)

⇒ xy = -2

Now,

The value of -xy = 2

∴ The required value is 2

Given:

∠BAD = 1/2∠ADC

∠BAC = 77° 

∠C = 45° 

Concept used:

The exterior angle theorem: It states that if a triangle's side is extended, then the resultant exterior angle would be equal to the sum of the two opposite interior angles of the triangle.

Angle sum property: Sum of all the three angles of a triangle is 180°.

Calculation:

In ΔABC,

∠BAC + ∠ABC + ∠ACB = 180° [Angle sum property]

⇒ 77° + ∠ABC + 45° = 180° 

⇒ 122° + ∠ABC = 180° 

⇒ ∠ABC = (180° – 122°)

⇒ ∠ABC = 58° 

In ΔBAD,

⇒ ∠ABC + ∠BAD = ∠ADC  [Exterior angle theorem] 

⇒ 58° + ∠BAD = 2∠ADC

⇒ ∠BAD = 58° 

In ΔBAD,

⇒ ∠ABD + ∠BAD + ∠ADB = 180° [Angle sum property]

⇒ 58° + 58° + ∠ADB = 180° 

⇒ 116° + ∠ADB = 180° 

⇒ ∠ADB = (180° – 116°)

⇒ ∠ADB = 64° 

∴ The required value of ∠ADB is 64°

Given:

x is subtracted from each of 24, 40, 33 and 57

Concept used:

Componendo and Dividendo

Calculation:

According to the question

⇒ (24 – x)/(40 – x) = (33 – x)/(57 – x)

Using Componendo and Dividendo 

(24 – x + 40 – x)/(24 – x – 40 + x) = (33 – x + 57 – x)/(33 – x – 57 + x)

⇒ (64 – 2x)/(-16) = (90 – 2x)/(-24)

⇒ 3(64 – 2x) = 2(90 – 2x)

⇒ 192 – 6x = 180 – 4x

⇒ (180 – 192) = (4x – 6x)

⇒ -12 = -2x

⇒ x = 6

Now,

The ratio of (5x + 12) to (4x + 15) = (5 × 6 + 12) : (4 × 6 + 15)

⇒ (42 : 39)

⇒ 14 : 13

∴ The required ratio is 14 : 13

Given:

In ΔABC, D and E are the midpoints of AB and BC respectively.

area(ΔCED) = 8 cm²

Concept used:

The median of a triangle divides it into two triangles of equal areas

Midpoint theorem: The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.

Calculation:

According to the question

Let the side DE be x and AC be 2x.  [By midpoint theorem]

In ΔBDC,

DE is the median of side BC

We know that, the median of a triangle divides it into two triangles of equal areas

⇒ ΔDEC = ΔBDE = 8 cm

Now,

⇒ DE ∥ AC

So,

⇒ ΔBDE/ΔBAC = (DE/AC)²

⇒ ΔBDE/ΔBAC = (x/2x)²

⇒ ΔBDE/ΔBAC = x²/4x²

Now,

⇒ 8/ΔBAC = 1/4

⇒ ΔBAC = (8 × 4) cm²

⇒ ΔBAC = 32 cm²

Now,

The area(ADEC) = area(ΔBAC – ΔBDE)

⇒ (32 – 8) cm² 

⇒ 24 cm²

∴ The required area(ADEC) is 24.

Shortcut Trick Midpoint theorem: The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.

∴ Ac = 2 × DE

Let Ac = 2x, then DE = x

Area of Triangle ABC = 4x²

Area of Triangle BDE = x²

Value of x² = 8

The area(ADEC) =  4x² - x² = 3x²

Value of 3x² = 3 × 8 = 24

Given:

The cost price of an article = Rs. 250

Gain = 20%

Discount = 36%

Formula used:

MP = [(100 + Gain%)/(100 – Discount%) × CP]

Calculation:

Let the ratio of CP and MP be (100 – D)% : (100 + Gain)%

⇒ (100 – 36) : (100 + 20)

⇒ 64 : 120

Now,

According to the question

⇒ 64% = 250

Then,

⇒ 120% = (250/64 × 120)

⇒ (30,000/64)

⇒ 468.75

∴ The MP of the article is Rs. 468.75

Given:

The six digit number = 5z3x4y

Concept used:

Divisibility rule of  7 - The difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should be equal to 0.

Divisibility rule of 11 - If the difference between the sum of the digits at the odd and even places equals 0 or divisible by 11, then the number is divisible by 11.

Divisibility rule of 13 -  A number is divisible by 13 when the ones place digit of a number is multiplied by 4 and the product is added to the rest of the number either gives 0 or a multiple of 13.

7 × 11 × 13 = 1001, when any three digit number multiplied by 1001 then it repeats itself and always completely divisible by 7, 11 and 13.

Calculation:

Let 3 digit number be pqr

⇒ pqr × 1001 = 5z3x4y

⇒ pqrpqr = 5z3x4y

compare both sides

⇒ p = 5, q = 4 and r = 3

Hence that number is 543543

⇒ 5z3x4y = 543543

By comparing both number, x = 5, y = 3 and z = 4

Now,

The value of (x + y – z) = (5 + 3 – 4)

⇒ (8 – 4)

⇒ 4

∴ The required value is 4

Calculation:

Total income of the family = Rs. 144000

The expenditure of the education in a month = 60° 

According to the question

We know that in a pie chart the total angle at the centre of the circle is 360° 

⇒ 360° = 144000

Then, the expenditure of the education

= 60° = (144000 × 60)/360 = 24000

∴ The required expenditure on education is Rs. 24000

Given:

(x + 6)3 + (2x + 3)3 + (3x + 5)3 = (3x + 18)(2x + 3)(3x + 5)

Formula used:

If (a + b + c) = 0 then, 

a³ + b³ + c³ = 3abc

Calculation:

(x + 6)3 + (2x + 3)3 + (3x + 5)3 = (3x + 18)(2x + 3)(3x + 5)

⇒(x + 6)3 + (2x + 3)3 + (3x + 5)3 = 3(x + 6) (2x + 3) (3x + 5)

Now,

According to the question

If (a + b + c) = 0 then, 

a3 + b3 + c3 = 3abc

⇒ (x + 6) + (2x + 3) + (3x + 5) = 0

⇒ 6x + 14 = 0

⇒ 6x = -14

⇒ x = -14/6

⇒ x = -7/3

∴ The required value is -7/3

Given:

Radius = 7 cm

Formula used:

Perimeter of circle = 2πr

Perimeter of square = 4 × side

Area of circle = πr²

Area of square = side²

Calculation:

Let the side of the square be a.

According to the question,

Perimeter of square = Perimeter of circle

⇒ 4a = 2πr

⇒ 4a = 2 × 22/7 × 7

⇒ 4a = 44

⇒ a = 11 cm

Now,

Area of circle = (22/7 × 7 × 7) cm²

⇒ 154 cm²

Area of square = (11)² = 121

Now,

The ratio of the area of the circle to area of the square

⇒ (154 : 121) = 14 : 11

∴ The required ratio is 14 : 11

Shortcut Trick 

Perimeter of square = Perimeter of circle

⇒ 4a = 2 × 22/7 × 7

⇒ 4a = 44

⇒ a = 11 cm

Area of circle = (22/7 × 7 × 7) cm2 = 154 cm2

Area of square = (11)2 = 121

Now,

The ratio of the area of the circle to area of the square

⇒ (154 : 121) = 14 : 11

Given:

Distance of a car = 144 km

Time = 1.8 hours

Formula used:

Speed = Distance/Time

Calculation:

According to the question

Speed = Distance/Time

⇒ Speed = (144/1.8)

⇒ Speed = 80 km/hr

Now,

Speed is increased by 20% = (80 × 20/100) = 16

New speed = (80 + 16) = 96 km/hr

Now,

Time to cover the double the distance = (2 × 144)/96

⇒ (6/2)

⇒ 3 hour

∴ The required time is 3 hour

Given:

The area of a circular path enclosed by two concentric circles = 3080 m2.

The difference between the radius of the outer edge and that of inner edge of the circular path = 10 m

Formula used:

Area of circle = πr²

Calculation:

The outer edge of the radius of the circle be R

The inner edge of the radius of the circle be r

According to the question

⇒ (R – r) = 10 m .....(1)

Now,

Area of circle = π(R² – r²) = 3080

⇒ 22 / 7(R + r)(R – r) = 3080

⇒ (R + r)(R – r) = 980

Now, putting the value of (R – r), we get

⇒ (R + r)(10) = 980

⇒ (R + r) = (980 / 10) m

⇒ (R + r) = 98 m

∴ The required sum of the two radii is 98 m

Calculation:

The total number of students enrolled for VC in institutes D and F in 2014 = (125 + 165) = 290

The total number of students enrolled in institutes A, B and C in 2018 = (205 + 220 + 225) = 650

The percentage of the total number of students enrolled for VC in institutes D and F in 2014 to the total number of students enrolled in institutes A, B and C in 2018

⇒ (290/650 × 100)

⇒ (29000/650)

⇒ 44.6%

∴ The required percentage is 44.6

Calculation:

Total number of students = 800

The total number of girls in sections B, C and D together = (80 + 104 + 98) = 282

The total number of students in section A = (800 × 20/100) = 160 

Number of boys in section A = (160 – 102) = 58

The total number of students in section B = (800 × 18/100) = 144

Number of boys in section B = (144 – 80) = 64

The total number of students in section D = (800 × 17/100) = 136

Number of boys in section D = (136 – 98) = 38

The total number of boys in sections A, B and D together = (58 + 64 + 38) = 160

The percentage of the total number of girls in sections B, C and D together to the total number of boys in sections A, B and D together = [(282 – 160)160 × 100]

⇒ (122/160 × 100)

⇒ (12200/160)

⇒ 76.25%

∴ The required percentage is 76.25

Given:

PT = 8 cm

PA = 5 cm

Concept used:

Tangent secant theorem

PT² = PA × PB

Calculation:

We know that,

PT2 = PA × PB

⇒ (8)² = 5 × PB

⇒ 64 = 5PB

⇒ PB = (64/5)

⇒ PB = 12.8 cm

Then,

AB = (12.8 – 5) = 7.8 cm

∴ The length of chord AB is 7.8 cm 

Shortcut Trick PT2 = PA × PB

⇒ (8)2 = 5 × PB

⇒ 64 = 5PB

⇒ PB = 12.8 cm

Then,

AB = (12.8 – 5) = 7.8 cm

Given:

Money donate by A = 10%

Money donate by B = 7%

Money donate by C = 9%

Salary of A and B are equal

The difference between the donations of A and B = Rs. 900.

The total donation by A and B = Rs. 600 more than that of C

Calculation:

Let the salary of A and B be 100x and C be 100y respectively.

Money donate by A = (100x × 10/100) = 10x

Money donate by B = (100x × 7/100) = 7x

Money donate by C = (100y × 9/100) = 9y

According to the question

⇒ 10x – 7x = 900

⇒ 3x = 900

⇒ x = 300

Total donation of A and B = (10x + 7x) = 17x

⇒ 17 × 300 = 5100

The total donation by A and B is Rs. 600 more than that of C

⇒ 5100 – 9y = 600

⇒ 9y = 4500

⇒ y = 500

Monthly salary of C = 100y = (100 × 500)

⇒ Rs. 50000

∴ The required salary of C is Rs. 50000

Given:

The ratio of efficiency of A and B = 7 : 5

Time taken to complete a work by A and B together = $17 \frac{1}{2}$days = 35/2 days

Formula used:

Work = Efficiency × Time

Calculation:

Efficiency of A = 7

Efficiency of B = 5

Total work = [35/2 × (7 + 5)] = (35/2 × 12)

⇒ 210 units

According to the question

B alone complete 50% of the same work = [(210/2)/5]

⇒ (105/5) days

⇒ 21 days

∴ The required time taken by B is 21 days

Shortcut Trick

So,

To complete 50% of the total work B will take half of his actual time 

So, time = 42/2 = 21 days

Given:

The average weight of 40 students of A = 45.5 kg

The average weight of 40 students of B = 44.2 kg

Two students of section A having average weight 48.75 kg were shifted to section B 

2 students of section B were shifted to section A

Formula used:

Average = sum of observations/Number of observations

Calculation:

Let the two students of section B be x and y respectively

The average weight of 40 students of A = (40 × 45.5) = 1820

The average weight of 40 students of B = (40 × 44.2) = 1768

Two students of section A having average weight 48.75 kg were shifted to section B = (2 × 48.75) = 97.5

2 students of section B were shifted to section A = 2(x + y)

According to the question

⇒ 1820 – 97.5 + (x + y) = 1768 + 97.5 – (x + y)

⇒ 2(x + y) = 1768 + 97.5 + 97.5 – 1820

⇒ 2(x + y) = (1963 – 1820)

⇒ 2(x + y) = 143

⇒ x + y = 71.5

Now,

The average weight (in kg) of the students who were shifted from section B to section A = (71.5/2)

⇒ 35.75

∴ The required average weight is 35.75

Given:

$√{\frac{\sec^2 θ + cosec^2 θ}{\tan^2 θ - \sin^2 θ} }$

Formula used:

sec²θ = 1/cos²θ 

cosec²θ = 1/sin²θ 

tan²θ = sin²θ/cos²θ 

(1 – cos²θ) = sin²θ 

Calculation:

$√{\frac{\sec^2 θ + cosec^2 θ}{\tan^2 θ - \sin^2 θ} }$

⇒ √(1/cos²θ + 1/sin²θ) / (sin²θ/cos²θ – sin²θ)

⇒ √[(sin²θ + cos²θ) / cos²θ.sin²θ] / [(sin²θ – cos²θ.sin²θ)]

⇒ √(1/cos²θ.sin²θ) / [sin²θ(1 – cos²θ) / cos²θ]

⇒ √(1/cos²θ.sin²θ) / [(sin²θ .sin²θ) / cos²θ]

⇒ √(1/sin²θ).(1/sin⁴θ)

⇒ √1/sin⁶θ 

⇒ √cosec⁶θ 

⇒ cosec³θ 

∴ The required value is cosec³θ

Given:

Amount = Rs. 7938

Principal = Rs. 7200

Time = 1 year

Formula used:

1 year = 12 month

half yearly = 12/2 = 6 month

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

Calculation:

According to the question

⇒ 7938 = 7200(1 + r/100)^t

⇒ (1 + r/100)^t = (7938/7200)

⇒ (1 + r/100)^t = (21/20)²

Then,

Half yearly rate = (1/20 × 100) = 5%

Yearly rate = (5 × 2)% = 10%

∴ The required rate is 10%

Given:

(cosec A –  cot A) (1 + cos A) = ?

Formula used:

cosec A = 1/sin A 

cot A = cos A/sin A

1 – cos²A = sin²A

Calculation:

(cosec A –  cot A) × (1 + cos A) = ?

⇒ (1/sin A – cos A/sin A) ×  (1 + cos A) = ?

⇒ [(1 – cos A)/(sin A)] ×  (1 + cos A) = ?

⇒ (1 – cos²A)/sin A = ?

⇒ sin²A/sin A = ?

⇒ sin A = ?

∴ The required value of ? is sin A

The correct answer is option 4) i.e., 'subscribe'.

Key Points

• Let us look into the meaning of the given words - 
• describe - give a detailed account in words of. ( शब्दों में विस्तृत विवरण दें।)
• offend - cause to feel upset, annoyed, or resentful. (परेशान, नाराज या नाराज महसूस करने का कारण।)
• practice - the actual application or use of an idea, belief, or method, as opposed to theories relating to it. (किसी विचार, विश्वास या पद्धति का वास्तविक अनुप्रयोग या उपयोग, इससे संबंधित सिद्धांतों के विपरीत।)
• subscribe - arrange to receive something, typically a publication, regularly by paying in advance. (अग्रिम भुगतान करके नियमित रूप से कुछ प्राप्त करने की व्यवस्था करें, आमतौर पर एक प्रकाशन।)
• From the above meanings it is clear that subscribe is best fit word for the given blank.

The incorrect spelling is option 4) i.e., 'Vacine'.

Key Points

• Let us explore the meaning of the given options
• Detective - a person, especially a police officer, whose occupation is to investigate and solve crimes. (एक व्यक्ति, विशेष रूप से एक पुलिस अधिकारी, जिसका पेशा अपराधों की जांच और समाधान करना है।)
• Priority - the fact or condition of being regarded or treated as more important than others. (दूसरों की तुलना में अधिक महत्वपूर्ण माने जाने या व्यवहार किए जाने का तथ्य या स्थिति।)
• Evidence - the available body of facts or information indicating whether a belief or proposition is true or valid.(तथ्यों या सूचनाओं का उपलब्ध निकाय यह दर्शाता है कि कोई विश्वास या प्रस्ताव सही है या मान्य है।)
• Vacine - There is no such word in English or we can say that there is a spelling mistake in the word.
• Hence, the correct answer is option 4.

Additional Information

• If we add the letter c in the word vacine, we get the word vaccine.
• Vaccine is a proper English word and it means a substance used to stimulate the production of antibodies and provide immunity against one or several diseases, prepared from the causative agent of a disease, its products, or a synthetic substitute, treated to act as an antigen without inducing the disease. (एक पदार्थ एंटीबॉडी के उत्पादन को प्रोत्साहित करने के लिए इस्तेमाल किया जाता है और एक या कई बीमारियों के खिलाफ प्रतिरक्षा प्रदान करता है, जो रोग के प्रेरक एजेंट, उसके उत्पादों, या सिंथेटिक विकल्प से तैयार किया जाता है, जिसे रोग को प्रेरित किए बिना एंटीजन के रूप में कार्य करने के लिए माना जाता है।)

The correct answer is option 1) i.e., 'No substitution'.

Key Points

• The underlined part of the given sentence is grammatically and conceptually correct.
• The underlined part talks about a future event and hence expected to arrive is the correct phrase to use. Also, the verb of the sentence is absolutely correct because the subject of the sentence is 'The minister' and his team members is a prepositional object for the preposition 'with'
• So, the underlined part does not need a substitution.
• This makes option 1 the correct answer.

The correct answer is option 2) i.e., 'Cipher'.

Key Points

• Let us look into the meaning of the words in the options -  
• Symbol - a mark or character used as a conventional representation of an object, function, or process, e.g. the letter or letters standing for a chemical element or a character in musical notation. (किसी वस्तु, कार्य या प्रक्रिया के पारंपरिक प्रतिनिधित्व के रूप में उपयोग किया जाने वाला चिह्न या चरित्र, उदा। एक रासायनिक तत्व या संगीत संकेतन में एक चरित्र के लिए खड़े होने वाले अक्षर या अक्षर।)
• Cipher - a system of words, letters, figures, or symbols used to represent others, especially for the purposes of secrecy. (विशेष रूप से गोपनीयता के प्रयोजनों के लिए दूसरों का प्रतिनिधित्व करने के लिए उपयोग किए जाने वाले शब्दों, अक्षरों, अंकों या प्रतीकों की एक प्रणाली।)
• Emblem - a heraldic device or symbolic object as a distinctive badge of a nation, organization, or family.(एक राष्ट्र, संगठन या परिवार के विशिष्ट बैज के रूप में एक हेरलडीक उपकरण या प्रतीकात्मक वस्तु।)
• Puzzle - a game, toy, or problem designed to test ingenuity or knowledge. (एक खेल, खिलौना, या समस्या जिसे सरलता या ज्ञान का परीक्षण करने के लिए डिज़ाइन किया गया है।)
• From the above meanings it is clear that cipher is the best word to substitute the given group of words.
• Hence, option 2 is the correct answer.

The correct answer is **option 4) i.e., **'He exclaimed with sorrow that he had broken his brother’s watch.'

Key Points

• The given sentence is an exclamatory sentence.
• While changing the narration of an exclamatory sentence, we need the following steps
• The first person 'I' will be changed into 'he'.
• The reporting verb said is changed to exclaimed with sorrow (The given sentence talks about an unfortunate incident.)
• The conjunction 'that' is used in place of commas and inverted commas.
• The verb (have broken) is in the present perfect tense form in the given sentence. In the indirect speech, it will change to past perfect tense (had broken).
• The first person my brother's will be changed into his brother's.
• Eventually, we will get the final sentence - He exclaimed with sorrow that he had broken his brother’s watch.