SSC CGL 2021 Tier-I (Held On : 18 April 2022 Shift 1) (Previous Year Paper)

The arrangement of the given words in a logical and meaningful order is as shown below :

The increasing order of universe from core of a planet is shown.

1. Core
2. Surface
3. Atmosphere
4. Galaxy
5. Universe

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

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some rats are birds → True (As Some rats are bats and All bats are birds. so, Some rats are bats is true)

II. Some birds are bats → True (As All bats are birds so, Some birds are bats is true)

III. All rats are bats → False (As Some rats are bats so, All rats are bats is possible but not definite true.)

∴ Here, Conclusions I and II are true.

Hence, the correct answer is "Only conclusions I and II follow".

The figure embedded in the given options is as shown below :

Hence, the correct answer is "Option 1".

The logic followed here is :-

HARMONY : BMLGUDK

Similarly,

RESOLVE : ? 

Hence, the correct answer is "VEOIVHU".

After unfolding the given paper the figure formed is as shown below :

Hence, the correct answer is "Option 4".

The logic followed here is :-

Row (1): (First number × Second number) + 4 = Third number

Row (2): (First number × Second number) + 3 = Third number

Row (3): (First number × Second number) + 2 = Third number

Hence, the correct answer is "62".

Alternate MethodIn a row: First number × Second number + Second number ÷ 2 = Third number.

Row 1) ⇒ (12 × 8) + 8 ÷ 2 ⇒ 96 + 4 = 100

Row 2) ⇒ (18 × 6) + 6 ÷ 2 ⇒ 108 + 3 = 111

Row 3) ⇒ (15 × 4) + 4 ÷ 2 ⇒ 60 + 2 = 62

Let us consider Male = M, Female = F.

The average salary of the entire teaching staff in a college is ₹2,000 per day → (M + F) × 2000

The average salary of the male teachers is ₹2,500 → 2500M

The average salary of the Female teachers is ₹1,200 → 1200F

If the number of male teachers = 16

∴ The total salary of the male teachers = 16 × 2500

The total salary of the male teachers = 40000

⇒ The total salary of the entire teaching staff in a college = The total salary of the male teachers + The total salary of the Female teachers

⇒ (M + F) × 2000 = 40000 + 1200F

As male teachers (M) = 16

⇒ (16 + F) × 2000 = 40000 + 1200F

⇒  (16 + F) × 20 = 400 + 12F

⇒ 320 + 20F = 400 + 12F

⇒ 8F = 80

⇒ F = 10

∴ Here, the number of female teachers in college is 10.

Hence, the correct answer is "10".

Alternate Method 

∴ Here, the number of female teachers in college is 10.

Hence, the correct answer is "10".

The logic followed here is :-

Sum of positional value of opposite alphabet - Number of letters in given word.

‘ROUBST’ is coded as 61.

Number of letter of word ROUBST = 6

= (9 + 12 + 25 + 6 + 8 + 7) - 6

= 67 - 6

= 61

Similarly,

‘FORTUNATE’ will be coded as :

Number of letters of word FORTUNATE = 9

= (21 + 12 + 9 + 7 + 6 + 13 + 26 + 7 + 22) - 9

= 123 - 9

= 114

Hence, the correct answer is "114".

The logic followed here is :-

Positional value of letters of given word + 3. 

ESTEEM is written as HVWHHP.

Similarly,

DOCTOR will be written as :

Hence, the correct answer is "GRFWRU".

Preparing the family tree using the following symbols:

According to the given information,

The given expression is :

'W @ S % K $ G & U & T @ R + C’, → W is the brother of S, S is the son of K, K is husband of G, G is mother of U, U is Mother of T, T is the brother of R, R is the daughter of C.

1) G is the maternal grandmother of R → True (As G is mother of U and U is Mother of T and T is the brother of R so, G is the maternal grandmother of R is true)

2) G is the father of W → False (As W is the brother of S and S is the son of K and K is husband of G and G is mother of U so, G is the father of W is false)

3) C is the wife of U → False (As U is Mother of T and T is the brother of R and R is the daughter of C so, C is the wife of U is false)

4) C is the father-in-law of K → False (As W is the brother of S, S is the son of K, K is husband of G, G is mother of U, U is Mother of T, T is the brother of R, R is the daughter of C. so, C is the father-in-law of K is false)

Hence, the correct answer is "G is the maternal grandmother of R".

Given :- g _ o _ d k _ m _ f _ o _ k k _ g f o _ d _ k m

By checking options and substituting accordingly.

1) f o k g o d m o k → g f o o d k k m - g f o o d k k m - g f o o d k k m

• Here "gfoodkkm" is repeated

2) f o k g o d f o k → g f o o d k k m - g f o o d k k f - g f o o d k k m

3) f o k d o d m o k → g f o o d k k m - d f o o d k k m - g f o o d k k m

4) f o k g o d m o m → g f o o d k k m - g f o o d k k m - g f o o d m k m

• Option (1) gives the pattern of :- g f o o d k k m - g f o o d k k m - g f o o d k k m

Hence, the correct answer is "f o k g o d m o k".

The logic followed here is :-

• 21 : 112

and

• 51 : 272

Similarly,

• 36 : ?

Hence, the correct answer is "192".

The logic followed here is :-

Hence, the correct answer is "BKT".

The least possible Venn diagram for the given relations is as shown below :

A woman can  be an entrepreneur and philanthropist. And an entrepreneur can be a woman and philanthropist.

Hence, the correct answer is "Entrepreneurs, Women, Philanthropists".

Given: 

• Logic: If two dice have same face value in given image than their clockwise or anticlockwise wise number/letter are know as opposite number/letter in dice.
• While moving in clockwise direction from common face (A) of dice (1) and dice (2):

From the both dices:

∴ Here, the opposite side of letter 'C' is side 'E'.

Hence, the correct answer is "E".

The logic followed here is :-

By using BODMAS RULE :

The given expression is : 66 A (132 D 12) C (4 A 3) B (15 D 5) A 16 B (-3)

After inserting the given symbols in the given expression is as follows : 66 + (132 ÷ 12) - (4 + 3) × (15 ÷ 5) + 16 × (-3)

= 66 + (132 ÷ 12) - (4 + 3) × (15 ÷ 5) + 16 × (-3)

= 66 + 11 - 7 × 3 + 16 × (-3)

= 66 + 11 - 21 - 48

= 77 - (21 + 48)

= 77 - 69

= 8

Hence, the correct answer is "8".

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

• Darken polygon present on left top corner is moved to middle from figure to figure.
• Darken polygon on top right corner moves three steps anti-clockwise from figure to figure.
• Darken polygon present on below middle moves three steps anti-clockwise from figure to figure.
• Darken polygon in middle moves to top right corner from figure to figure.

Hence, the correct answer is "Option 1".

The logic followed here is :-

1) BEG

2) GJM

3) TWY

4) LOQ

∴ Here, 'GJM' is different from other three alternatives.

Hence, the correct answer is "GJM".

The logic followed here is:-

Hence, the correct answer is "223".

Alternate Method The Given series is 3, 11, 31, 69, 131, ?

The pattern that can be used is 

1³ + 2 =3

2³ + 3 = 11

3³+ 4 = 31

4³ + 5 = 69

5³ + 6 =131

6³ + 7 = 223

Hence, the correct answer is "223".

The logic followed here is :-

By using BODMAS RULE :

The given expression is : 23 @ 105 $ 15 % 6 # 29

After inserting the mathematical symbols in given expression is as follows : 23 + 105 ÷ 15 × 6 - 29

= 23 + 105 ÷ 15 × 6 - 29

= 23 + 7 × 6 - 29

= 23 + 42 - 29

= 65 - 29

= 36

Hence, the correct answer is "36".

Nine employees, K, L, M, N, O, P, Q, R and S, are sitting in the office in a straight line, all facing the east.

1) O is third to the right of M.

2) N is fourth to the right of M and R is fourth to the left of O.

3) P is to the immediate right of N and Q is immediate between P and S.

4) K is third to the left of P. 

Option 1) L is sitting third to the left of O → False (As from the given information L is Second to the left of O)

Option 2) Q is sitting fourth to the right of K → True (As from the fourth step of given information Q is sitting fourth to the right of K is true)

Option 3) R and S are sitting at the corners → True (As from the fourth step of given information R and S are sitting at the corners is true)

Option 4) O is sitting between K and N → True (As from the fourth step of given information O is sitting between K and N is true)

Hence, the correct answer is "L is sitting third to the left of O".

The logic followed here is :-

Hence, the correct answer is "144".

The logic followed here is :-

Code : Number of letters present in words of a sentence.

In "Laptop is a computer":

laptop = 6 letters is present.

is = 2 letters is present.

a = 1 letters is present.

computer = 8  letters is present.

6218 → Laptop is a computer

and

In "Computer is a machine":

Computer = 8  letters is present.

is = 2  letters is present.

a = 1  letters is present.

machine = 7  letters is present.

8217 → Computer is a machine

Similarly,

In "Machine makes our life easy":

Machine = 7  letters is present.

makes = 5  letters is present.

our = 3  letters is present.

life = 4  letters is present.

easy = 4  letters is present.

Machine makes our life easy → 75344

Hence, the correct answer is "75344".

Given: 

• Logic: If two dice have same face value in given image than their clockwise or anticlockwise wise number/letter are know as opposite number/letter in dice.
• While moving in clockwise direction from common face (e) of dice (1) and dice (2):

From the both dices:

∴ Here, the opposite side of 'D' is side 'f'.

Hence, the correct answer is "f".

The mirror image of the given figure is as shown below :

Hence, the correct answer is "Option 4".

The correct answer is Sakewa.

Key Points

• Sakewa festival is also known as the Bhoomi puja or Chandi puja (worship of mother earth).
• It is a religious festival celebrated by the Kirat Khambu Rai community of Sikkim.
• The nine-day long festival begins on the full moon day of the Hindu month of Baisakh which mostly falls between April and May.
• The celebrations mark the beginning of the new farming year and start off on a big ground or a hilltop.
• The Mangpa (male priest) or Mangma (female priest) performs puja of the soil, followed by various other religious rituals and community feasts.
• The entire state comes alive during the colourful festivities of Sakewa with the sounds of drums and cymbals reverberating in the air.

Additional Information

• Losar
• Losar also known as Tibetan New Year, is a festival in Tibetan Buddhism.
• The festival is celebrated on various dates depending on the location (Tibet, Bhutan, Nepal, India) tradition.
• The festival is a new year's festival, celebrated on the first day of the lunisolar Tibetan calendar.
• It is a significant festival in the North East Indian state of Sikkim and is celebrated with great enthusiasm every year.
• Barahimizong
• ​Barahimizong is a festival observed by the Mangar Community in Sikkim.
• It is celebrated as a day when the Mangar people come together to pay homage to their forefathers and kuldevtaas by performing various religious rituals and rites.
• The first Barahimizong Festival was held in 1998 with the prime objective of keeping alive, the cultural and traditional heritage of the community.
• Indra Jatra
• ​This is an important harvest festival in Kathmandu Valley, also known as Yenya (meaning "Kathmandu celebration").
• Indra Jatra is a regional holiday in the Kathmandu Valley in Nepal.
• The holiday takes place on the 15^th day of Yanla, the 11^th month in the Nepalese calendar.

The correct answer is BR Ambedkar.

Key Points

• On 24 September 1932, the Poona Pact was sealed between Mahatma Gandhi and Dr. B R Ambedkar in the Yerwada Central Jail, Pune.
• Gandhiji was undertaking a fast against the British government’s decision to grant separate electorates for the ‘Depressed classes’.
• The separate electorate for Dalits was a topic upon which Gandhi and Ambedkar could not agree.
• In the First Round Table Conference held in 1930, Dr. Ambedkar had demanded a separate electorate for the ‘Depressed classes’ whom he was representing.
• Gandhi and the Congress Party were against the idea of separate electorates for any class as it was seen as a means to weaken and divide Indian society.
• The then British Prime Minister Ramsay MacDonald granted the ‘Communal Award’ to minority communities including the ‘Depressed classes’.
• Gandhi protested against this award (also known as the MacDonald Award) by undertaking a fast unto death whilst in jail in Poona.
• **When Gandhi started his fast, there was public pressure on Ambedkar to step in and stop the fast. This resulted in the Poona Pact.**​

Additional Information

• Provisions of the Poona Pact
• Seats would be reserved for the ‘Depressed classes’ in the Provincial Councils.
• The number of seats reserved for the provinces depended on the strength of the provinces:
• Madras: 30; Punjab: 8; Bombay and Sindh: 15; Central Provinces: 20; Bihar and Orissa: 18; Bengal: 30; United Provinces: 20; and Assam: 7 (Total reserved: 148)
• In the Central Legislature, 19% of the seats would be reserved for the Depressed Classes.
• The members of the depressed classes who were eligible to vote would form an electoral college. This College would elect four candidates among the depressed classes on the basis of a single vote.
• This principle of ‘Joint electorate and reserved seats’ was to be followed in the Central Assembly too.
• It was agreed that this system would continue for ten years unless it was ended by mutual consent sooner.
• It was also agreed upon to allocate a certain portion of money from the educational grant for the education of the depressed classes in all the provinces.
• Nobody would be discriminated against because they belonged to the depressed classes in the matter of election to the local bodies or appointment to government service.

The correct answer is Men's Basketball.

Key Points

• Los Angeles Clippers and Portland Trail Blazers are Men's Basketball teams.
• The Portland Trail Blazers (colloquially known as the Blazers) is an American professional basketball team based in Portland, Oregon. 
• ​The franchise entered the league as an expansion team in 1970, and has enjoyed a strong following: from 1977 through 1995,
• The team sold out 814 consecutive home games, the longest such streak in American major professional sports at the time, and only since surpassed by the Boston Red Sox.
• ​The Los Angeles Clippers are an American professional basketball team based in Los Angeles.
• The Clippers compete in the National Basketball Association as a member of the Pacific Division in the league's Western Conference.

The correct answer is Turbidity.

Key Points

• Turbidity is the measure of the relative clarity of a liquid.
• It is an optical characteristic of water and is a measurement of the amount of light that is scattered by material in the water when a light is shined through the water sample.
• The higher the intensity of scattered light, the higher the turbidity.
• **The distance at which the disk disappears is the water clarity reading, which is recorded in centimetres.**​

Additional Information

• Turbidity is commonly measured in Nephelometric Turbidity Units (NTU).
• The nephelometric method compares how light is scattered in a water sample against the amount of light scattered in a reference solution.
• An electronic hand-held meter is often used to measure turbidity.
• The WHO (World Health Organization), establishes that the turbidity of drinking water shouldn't be more than 5 NTU, and should ideally be below 1 NTU.

The correct answer is 50%.

Key Points

• **The ownership structure of Regional Rural Bank is different from other government-owned banks 50 percent is held by the central government, 35 percent by sponsor banks, and 15 percent by state governments.**​

Important Points

• Regional Rural Banks were established under the provisions of an ordinance passed on 26 September 1975 and the RRB Act 1976 to provide sufficient banking and credit facility for agriculture and other rural sectors.
• As a result, five RRBs were set up on 2 October 1975 on the recommendations of the Narsimha Committee on Rural Credit, during the tenure of Indira Gandhi's government.
• The purpose was to include rural areas into the economic mainstream since around 70% of the Indian population was rural.
• Prathama Bank, with head office in Moradabad, Uttar Pradesh was the first RRB.
• The other four RRBs were Gaur Gramin Bank (sponsored by UCO Bank), Gorakhpur Kshetriya Gramin Bank (sponsored by State Bank of India), Haryana Kshetriya Gramin Bank (sponsored by Punjab National Bank), and Jaipur-Nagpur Anchalik Gramin Bank (sponsored by UCO Bank).

The correct answer is Peak XV.

Key Points

• Before being renamed, Mount Everest was simply known as Peak XV.
• At first, Mount Everest was simply labelled as “H”; that had been changed to Peak XV by 1850.
• In 1865 Peak XV was renamed for Sir George Everest, surveyor-general of India from 1830 to 1843.
• The Royal Geographic Society subsequently pronounced the official name “Mount Everest” in 1865 based on the recommendation of Andrew Waugh, the British Surveyor General of India.
• Sir George Everest was Waugh’s predecessor in the post of Surveyor-General.

Additional Information

• In 1852, stationed at the survey headquarters in Dehradun, Radhanath Sikdar, an Indian mathematician and surveyor from Bengal was the first to identify Everest as the world’s highest peak, using trigonometric calculations based on Nicolson’s measurements.
• The name of Mount Everest on the border of Nepal and Tibet is Chomo Lungma in the Tibetan language.
• The people of Nepal know it as Sagar-Matha. But in the whole world, it is famous as Mount Everest.

The correct answer is Malappuram.

Key Points

• Malappuram, which recorded a 44 percent rise in its population from 2015 to 2020, topped the ranking as the world's fastest-growing city as per a list compiled by the United Nations Population Division.

​

• These cities are seeing rapid urbanization, and the main reason is the inclusion of new areas within the UA’s limits.
• In Kerala, urbanization is driven by a move away from agriculture, which leads to a change in a village’s Census classification status.
• While the pace of urbanization has been slower in the North, some unnaturally high increases in the population can be expected after the 2021 Census because in some cases, villages on the peripheries were brought within the administrative boundaries of the cities.

The correct answer is 2014.

Key Points

• The Swachh Bharat Mission (SBM)  campaign was officially launched on 2 October 2014 at Rajghat, New Delhi by Prime Minister Narendra Modi.
• It is India's largest cleanliness drive to date with three million government employees and students from all parts of India participating in 4,043 cities, towns, and rural communities.
• The campaign aims to achieve the vision of a ‘Clean India’ by 2^nd October 2019.
• The best tribute India could pay to Mahatma Gandhi on his 150 birth anniversary in 2019.
• Prime Minister said people should neither litter nor let others litter. He gave the mantra of ‘Na gandagi karenge, Na karne denge.’

The correct answer is Haryanka .

Key Points

• Ajatashatru was one of the most important kings of the Haryanka dynasty of Magadha in East India.
• He was the son of King Bimbisara and was a contemporary of both Mahavira and Gautama Buddha.
• He forcefully took over the kingdom of Magadha from his father and imprisoned him.
• Pataliputra was founded by Udayin, the son of the Haryanka king Ajatashatru in 490 BCE.
• Ajatashatru followed policies of conquest and expansion.

Additional Information

• Mauryan Dynasty
• ​The Maurya Empire was founded by Chandragupta Maurya in 322 BCE.
• The three great rulers of the Mauryan Empire were Chandragupta Maurya, Bindusara and Ashoka.
• ​Shishunaga Dynasty​
• ​Shishunaga (413 – 395 BCE) was the founder of the Shishunaga dynasty of the Magadha Empire in present-day northern India.
• Initially, he was an amatya (official) of the Magadha Empire under the Haryanka dynasty.
• Important rulers were Shishunaga, Kalashoka, and Nandivardhana.
• Nanda Dynasty
• The most powerful ruler of the Nanda Dynasty is Mahapadma Nanda.
• He was also the founder of the Nanda Dynasty.
• At the time of Alexander's invasion, Dhana Nand was the ruler of Magadha.
• Nanda Dynasty ruled in Magadha at the time of Alexander's invasion.
• The ruler was Dhana Nand, the last ruler of the Nanda dynasty.

The correct answer is Union Budget 2021-22.

Key Points

• On 1 February 2021, Finance Minister Nirmala Sitharaman presented the first paperless budget. This was done due to the ongoing COVID-19 pandemic in India.
• The Union Budget 2021 was presented in a digital format for the first time to promote the Government of India's (GoI) Digital India flagship programme.

Additional Information

• The Union Budget of India also referred to as the Annual Financial Statement in Article 112 of the Constitution of India, is the annual budget of the Republic of India.
• The Government presents it on the first day of February so that it could be materialized before the beginning of the new financial year in April.
• Until 2016 it was presented on the last working day of February by the Finance Minister in Parliament.
• The budget division of the department of economic affairs (DEA) in the finance ministry is the nodal body responsible for producing the budget.
• It is presented by means of the Finance Bill and the Appropriation bill has to be passed by Lok Sabha before it can come into effect on 1 April, the start of India's financial year.
• Since 1947, there have been a total of 73 annual budgets, 14 interim budgets, and four special budgets, or mini-budgets.

The correct answer is F Scott Fitzgerald.

Key Points

• The Great Gatsby is a 1925 novel by American writer F. Scott Fitzgerald.
• The novel was inspired by a youthful romance Fitzgerald had with socialite Ginevra King, and the riotous parties he attended on Long Island's North Shore in 1922.
• During World War II, the novel experienced an abrupt surge in popularity when the Council on Books in Wartime distributed free copies to American soldiers serving overseas.
• The Great Gatsby is widely **considered to be a literary masterwork and a contender for the title of the Great American Novel.**​

Additional Information

• Harper Lee
• ​Nelle Harper Lee was an American novelist best known for her 1960 novel To Kill a Mockingbird.
• It won the 1961 Pulitzer Prize and has become a classic of modern American literature.
• ​Chinua Achebe
• ​Chinua Achebe was a Nigerian novelist, poet, and critic who is regarded as the dominant figure of modern African literature.
• His first novel and magnum opus, Things Fall Apart, occupies a pivotal place in African literature and remains the most widely studied, translated, and read African novel.
• ​Alice Walker
• ​Alice Malsenior Tallulah-Kate Walker is an American novelist, short story writer, poet, and social activist.
• In 1982, she became the first African-American woman to win the Pulitzer Prize for Fiction, which she was awarded for her novel The Color Purple.

The correct answer is -2.

Key Points

• The SI unit of acceleration is meters/second² (m/s²).
• Hence, the power of the second is -2 as it is in the denominator.
• Acceleration (a) is defined as the rate of change in velocity.
• Velocity is a vector quantity, and therefore acceleration is also a vector quantity.

Additional Information

• Types of acceleration
• Uniform acceleration
• When an object is travelling in a straight line with an increase in velocity at equal intervals of time, then the object is said to be in uniform acceleration. The free-falling of an object is an example of uniform acceleration.
• Non-uniform acceleration
• When an object is travelling with an increase in velocity but not at equal intervals of time is known as non-uniform acceleration. Bus moving or leaving from the bus stop is an example of non-uniform acceleration.
• Instantaneous acceleration
• The acceleration of an object at any instant of time is known as instantaneous acceleration.

The correct answer is Narmada.

Key Points

• Narmada is a peninsular river.
• The Narmada River is the 5^th longest river and overall longest west-flowing river in India, and the largest flowing river in the state of Madhya Pradesh.
• This river flows through Madhya Pradesh and Gujarat states of India.
• It is also known as the "Life Line of Madhya Pradesh and Gujarat".
• Narmada rises from Amarkantak Plateau in Anuppur district Madhya Pradesh.
• It is one of only two major rivers in peninsular India that run from east to west (the longest west flowing river), along with the Tapti River.
• It is one of the rivers in India that flows in a rift valley, bordered by the Satpura and Vindhya ranges.

Additional Information 

• The Indian rivers are divided into two major groups:
• The Himalayan rivers
• The Peninsular rivers
• ​Himalayan Rivers
• The main Himalayan river systems are the Ganga, the Indus, and the Brahmaputra river systems.
• Peninsular Rivers
• The main peninsular river systems include the Narmada, the Tapi, the Godavari, the Krishna, the Kaveri, and the Mahanadi river systems.​

Important Points   Himalayan Rivers Vs Peninsular Rivers

The correct answer is Hockey.

Key Points

• International hockey player Karishma Yadav has received the Vikram Award from the Madhya Pradesh government for excellence in sports.
• Chief Minister Shri Chouhan felicitated players and coaches with Vikram, Eklavya, Vishwamitra, and Lifetime Achievement Award at Madhya Pradesh Shikhar Khel Alankaran Samaroh 2019 in Minto Hall.
• Olympian hockey player Shri Inam-ur-Rehman of Bhopal was honoured with the Life Time Achievement Award of 2019.

Additional Information

• For the year 2020, 13 Eklavya, 10 Vikram, 3 Vishwamitra, 1 Late Prabhash Joshi, and 1 Lifetime Achievement Award have been announced by the Madhya Pradesh government.
• The Lifetime Achievement Award for the year 2020 will be given to Padma Shri Abhay Chhajlani, while Olympic hockey player of the state Vivek Sagar will be awarded the state's best Vikram Award.
• The list of persons announced for the year 2020 state-level sports awards is as follows-
• Eklavya Award:
• Individual Category - Sushma Verma, Kayaking-Canoeing (Sehore), Tushita Singh, Soft Tennis (Bhopal), Sparsh Khare, Wushu (Jabalpur), Arjun Singh, Horse Riding (Bhopal), Sunil Davar, Athletics (Barwani), Gauranshi Sharma, Badminton (Divyang) (Bhopal), Rammilan Yadav, Sailing (Tikamgarh), Ankit Sharma, Fencing (Gwalior), Anuradha Ahirwar, Archery (Bhopal), Preeti Rajak, Shooting (Hoshangabad), Shashank Patel, Taekwondo (Bhopal).
• Group Category – Sadhna Sengar, Hockey (Hoshangabad) and Dhruvraj Kurre, Powerlifting (Bhopal).
• Vikram Award:
• Individual Category - Vishwajit Singh, Canoe-Slalom (Hoshangabad), Sunidhi Chauhan, Shooting (Bhopal), Nidhi Nanhet, Karate (Balaghat), Paridhi Joshi, Horse Riding (Indore), Manju Bamboria, Boxing (Ujjain), Ekta Yadav, Sailing (Bhopal). Party Sports - Vivek Sagar Prasad, Hockey (Hoshangabad), Harshvardhan Tomar, Basketball (Gwalior), Pooja Malviya, Mallakhamb (Ujjain).
• Divyang Category - Prachi Yadav, Para Canoe (Gwalior).
• Vishwamitra Award:
• Individual Category – Virendra Dabas, Para Swimming and Para Athletics (Gwalior) and Richpal Singh Salaria, Archery (Jabalpur).
• Group Category - Dr. Habib Hassan is involved.
• Lifetime Achievement Award: Abhay Chhajlani, Padma Shri, and former President Indore Table Tennis Association.
• Late Prabhas Joshi Sports Award: Vaishnavi Kahar, Mallakhamb (Ujjain).

The correct answer is People belonging to the same gotra were regarded as descendants of the person after whom the gotra was named.

Key Points

• Gotra refers to a lineage segment within an Indian caste that prohibits intermarriage by virtue of the members’ descent from a common mythical ancestor after whom the gotra was named.
• It is an important factor in determining possible Hindu marriage alliances.
• Gotra originally referred to the seven lineage segments of the Brahmans (priests), who trace their derivation from seven ancient seers: Atri, Bharadvaja, Bhrigu, Gotama, Kashyapa, Vasishtha, and Vishvamitra.
• An eighth gotra was added early on, the Agastya, named after the seer intimately linked up with the spread of Vedic Hinduism in southern India.
• In later times the number of gotras proliferated when a need was felt to justify Brahman descent by claiming for one’s line a Vedic seer.
• Marriages within the gotra ('sagotra' marriages) are not permitted under the rule of exogamy in the traditional matrimonial system.
• Women do not retain their father’s gotra after marriage.

The correct answer is iron.

Key Points

• Ferrum is the Latin term for iron and the source of its chemical symbol Fe.
• Iron is a chemical element with the symbol Fe and atomic number 26.
• It is a metal that belongs to the first transition series and group 8 of the periodic table.
• It is, by mass, the most common element on Earth, right in front of oxygen, forming much of Earth's outer and inner core.
• Atomic mass: 55.845 u.
• **Electron configuration: [Ar] 3d64s2.**​

Additional Information

• The Latin name for zinc is Zincum, which means "white thin layer" or "white sediments".
• The symbol 'Cu' denotes the Latin name of copper, which is Cuprum.
• Niccolum is the Latin name for a Nickel.

The correct answer is Jaishankar Prasad.

Key Points

• Kamayani (1936) is a Hindi epic poem by Jaishankar Prasad (1889–1937).
• It is considered one of the greatest literary works written in modern times in Hindi literature.
• Kamayani depicts the interplay of human emotions, thoughts, and actions by taking mythological metaphors.
• A musical play adaptation of "Kamayani" has been directed by Dr. Shakuntala Shukla and Vyomkesh Shukla.
• This play is produced by the banner of **"Roopvani, Varanasi".**​

Additional Information

• Mahadevi Varma
• ​Mahadevi Varma (26 March 1907 – 11 September 1987) was an Indian Hindi-language poet, essayist, sketch story writer and an eminent personality of Hindi literature.
• She is considered one of the four major pillars of the Chhayawadi era in Hindi literature.
• In 1930, Nihar, in 1932, Rashmi, in 1933, and Neerja were composed by her.
• In 1935, her collection of poems called Sandhyageet was published.
• In 1939, four poetic collections were published with their artworks under the title Yama.
• She is also considered the pioneer of feminism in India.
• Mahavir Prasad Dwivedi
• ​Mahavir Prasad Dwivedi (15 May 1864 – 21 December 1938) was an Indian Hindi writer and editor.
• Kavya manjusha, Kavitakalap, Sugandh, Mere Jeevan ki Yatra, Sahitya Sandarbh are some of his literary works.
• Gopala Sarana Sinha
• ​Gopala Sarana Sinha (1891-1960) is an important writer of the modern period of Hindi literature commences with the second half of the 19^th century.

The correct answer is President.

Key Points

• A bill becomes an Act of the Parliament after being passed by both the Houses of Parliament and assented to by the President.
• The basic function of Parliament is to make laws. All legislative proposals have to be brought in the form of Bills before Parliament.
• A Bill is a statute in the draft and cannot become law unless it has received the approval of both the Houses of Parliament and the assent of the President of India.

Important Points

• The process of law-making begins with the introduction of a Bill in either House of Parliament.
• A Bill can be introduced either by a Minister or a member other than a Minister.
• In the former case, it is called a Government Bill and in the latter case, it is known as a Private Member's Bill.
• A Bill undergoes three readings in each House, i.e., the Lok Sabha and the Rajya Sabha before it is submitted to the President for assent.
• First Reading
• The First Reading refers to
• (i) motion for leave to introduce a Bill in the House on the adoption of which the Bill is introduced.
• (ii) in the case of a Bill originated in and passed by the other House, the laying on the Table of the House of the Bill, as passed by the other House.
• Second Reading
• Third Reading
• The Third Reading refers to the discussion on the motion that the Bill or the Bill, as amended, be passed.
• An almost similar procedure is followed in Rajya Sabha in respect of Bills introduced in that House.
• After a Bill has been finally passed by the Houses of Parliament, it is submitted to the President for his assent.
• After a Bill has received the assent of the President, it becomes the law of the land.

The correct answer is Glacier.

Key Points

• A glacier is not a water pollutant but it is a source of fresh water.
• The main water pollutants include bacteria, viruses, parasites, fertilizers, pesticides, pharmaceutical products, nitrates, phosphates, plastics, faecal waste, and even radioactive substances.
• These substances do not always change the colour of the water, meaning that they are often invisible pollutants.
• While some metals are essential for human health at trace concentrations due to their role as coenzymes (eg, Fe and Cu), others are toxic at any concentration level (eg, Pb and Cd) Chromium (Cr VI), cadmium (Cd), lead (Pb), and arsenic (As) have been recognized as water, pollutants.
• Metals can cause severe toxicity in humans, depending on the concentration, the exposure pathway, and the duration of exposure.

Additional Information

• The high concentrations of arsenic (As) in drinking water in inorganic form cause skin, liver, lungs and other organs damage.
• Cr (VI) is the most toxic form of pollutant present in water, producing liver and kidney damage, internal haemorrhage and respiratory disorders.
• Silt in water can cause kidney stones and digestive disorders.

The correct answer is 11.3%.

Key Points

• According to the Economic Survey, 2020-21 exports are expected to decline by 5.8 percent and imports by 11.3 percent in the second half of the year.
• The Economic Survey of India is an annual document of the Ministry of Finance, Government of India.
• The Department of Economic Affairs, Ministry of Finance presents the Survey in the Parliament every year, just before the Union Budget.
• It is prepared under the guidance of the Chief Economic Adviser of India.

Important Points 

• Summary of Economic Survey-2020-21
• India’s real GDP to record an 11.0% growth in FY2021-22 and nominal GDP to grow by 15.4% – the highest since independence.
• The recovery in the second half of FY2020-21 is expected to be powered by government consumption, estimated to grow at 17% YoY.
• Exports are expected to decline by 5.8% and imports by 11.3% in the second half of FY21.
• India expected to have a Current Account Surplus of 2% of GDP in FY21, a historic high after 17 years.
• On the supply side, Gross Value Added (GVA) growth was pegged at -7.2% in FY21 as against 3.9% in FY20.
• Agriculture is set to cushion the shock of the COVID-19 pandemic on the Indian economy in FY21 with a growth of 3.4%.
• Industry and services are estimated to contract by 9.6% and 8.8% respectively during FY21.
• Agriculture remained the silver lining while contact-based services, manufacturing, and construction were hit hardest, and recovering steadily.
• India remained a preferred investment destination in FY 2020-21 with FDI pouring in amidst global asset shifts towards equities and prospects of quicker recovery in emerging economies.
• Net FPI inflows recorded an all-time monthly high of US$ 9.8 billion in November 2020, as investors’ risk appetite returned.
• India was the only country among emerging markets to receive equity FII inflows in 2020.$

The correct answer is It can be rejected or amended by the Rajya Sabha.

Key Points

• Rajya Sabha has no power to reject a money bill.
• It can approve the bill or suggest changes that may or may not be eventually accepted by the Lok Sabha.
• Money Bill is defined in Article 110 of the Indian Constitution.
• Money bills are concerned with financial matters like taxation, public expenditure, etc.

Important Points

• Provisions Related to a Money Bill:
• The Speaker of Lok Sabha decides whether a bill is a Money Bill or not.
• The Lok Sabha can either accept or reject all or any of the recommendations of the Rajya Sabha.
• It can be introduced only in the Lok Sabha.
• It can only be introduced by a minister and not by a private member.
• Rajya Sabha has no power to reject a money bill, it can approve the bill or suggest changes that may or may not be eventually accepted by the Lok Sabha.
• Also, the bill must be returned to the Lok Sabha within 14 days, or the bill is deemed to have passed both houses in the form it was originally passed by the Lok Sabha.

The correct answer is Article 368.

Key Points

• The procedure of amendment in the constitution is laid down in Part XX (Article 368) of the Constitution of India.
• Article 368 of Part XX of the Constitution of India provides for three types of amendments.
• Amendment by a simple majority of the Parliament.
• By a special majority of Parliament.
• By a special majority of the Parliament with the ratification by half of the total states.

Additional Information

• Article 351​
• “It shall be the duty of the Union to promote the spread of the Hindi language to develop it so that it may serve as a medium of expression for all the elements of the composite culture of India and to secure its enrichment by assimilating without interfering with its genius, the forms, style, and expressions used in Hindustani and in the other languages of India specified in the 8^th Schedule, and by drawing, wherever necessary or desirable, for its vocabulary, primarily, on Sanskrit and secondarily on other languages.”
• ​Article 342
• ​Scheduled Tribes: The President may with respect to any State or Union territory, and where it is a State, after consultation with the Governor thereof, by public notification, specify the tribes or tribal communities or parts of or groups within tribes or tribal communities which shall for the purposes of this Constitution be deemed to be Scheduled Tribes in relation to that State or Union territory, as the case may be.
• Article 374
• ​Provisions as to Judges of the Federal Court and proceedings pending in the Federal Court or before His Majesty in Council.

The correct answer is Vikram Seth.

Key Points

• Two Lives was authored by Vikram Seth.
• 'Two Lives' is both a history of a violent century seen through the eyes of two survivors and an intimate portrait of their friendship, marriage, and abiding yet complex love.
• Vikram Seth is an Indian novelist, poet, and travel writer, best known for his epic novel ‘A Suitable Boy'.
• Vikram Seth is an Indian novelist and poet. He has written several novels and poetry books.
• He has received **several awards such as Padma Shri, Sahitya Academy Award, Pravasi Bharatiya Samman, WH Smith Literary Award, and Crossword Book Award.**​

Additional Information

• Arundhati Roy
• Arundhati Roy is an Indian author best known for her novel The God of Small Things, which won the Man Booker Prize for Fiction in 1997.
• She is also a political activist involved in human rights and environmental causes.
• Sudha Murty
• ​Sudha Murty is an educator, author, and philanthropist who is the chairperson of the Infosys Foundation.
• She is married to the co-founder of Infosys, N. R. Narayana Murthy.
• Murty was awarded the Padma Shri, the fourth highest civilian award in India, for social work by the Government of India in 2006.
• Chetan Bhagat​
• ​Chetan Bhagat is an Indian author, columnist, and YouTuber.
• He was included in Time magazine's list of World's 100 Most Influential People in 2010.

The correct answer is Arunachal Pradesh.

Key Points

• Ponung folk dance is a popular dance in Arunachal Pradesh. It belongs to the Adi tribe.
• Tapu is a war dance of the Adi tribe of Arunachal Pradesh.
• The only males perform tapu war dance during the festival of Aran.
• It is performed to drive away evil spirits from villages.
• It is celebrated on 7^th March to herald the season of shifting cultivation.
• Ponung is the harvest dance performed by the Adi tribal community of Arunachal Pradesh.
• It is danced at the festival held just before the harvesting operations.
• **It is believed that the dance will bring about a good harvest and prosperity to the community.**​

Additional Information

The correct answer is the Plane angle.

Key Points

• The physical quantity for the expression of arc/radius is the Plane angle.
• A plane angle is well known: one full revolution is 360° or 2π radians.
• Plane angle- usually refers to an angle in a 2-dimensional figure like a square, triangle, circle, etc.
• Solid angle usually refers to an angle in a 3-dimensional figure like a cube, cuboid, sphere, etc.

Additional Information

• Linear momentum
• ​Linear momentum is the vector quantity and is defined as the product of the mass of an object, m, and its velocity, v.
• The linear momentum formula is given by, P = m v, where m=mass, v= velocity.
• The units of linear momentum are kg m/s.
• Surface tension​
• ​Surface tension can be defined as the property of the surface of a liquid that allows it to resist an external force, due to the cohesive nature of the water molecules.
• Surface tension, represented by the symbol γ (alternatively σ or T), is measured in force per unit length.
• Its SI unit is newton per meter and the cgs unit of dyne per centimetre.
• ​Velocity
• ​Velocity (v) is a vector quantity that measures displacement (or change in position, Δs) over the change in time (Δt).
• Velocity is represented by the equation v = Δs/Δt.

Calculation:

The number of TV sets sold by company A = 64 × 75%

⇒ 48

The number of TV sets sold by company B = 90 × 64%

⇒ 57.6

Ratio = 48 : 57.6

⇒ 5 : 6

∴ Required answer is 5 : 6.

Given:

a + b - c = 5 and ab - bc - ac = 10

Concept used:

(a + b - c)2 = a2 + b2 + c2 + 2ab - 2bc - 2ac

Calculation:

(a + b - c)2 = a2 + b2 + c2 + 2ab - 2bc - 2ac

⇒ (5)² = a2 + b2 + c2 + 2(ab - bc - ac)

⇒ 25 = a2 + b2 + c2 + 2 × 10

⇒ a2 + b2 + c2 = 25 - 20

⇒ a2 + b2 + c2 = 5

∴ The value of a2 + b2 + c2 is 5.

Given:

The angles of elevation of the tops of P and Q are 45° and 60°

Concept used:

Calculation:

Let the height of tower P and tower Q be AB and CE and D is the midpoint of BE.

BD = DE

In ΔABD

tan 45° = AB/BD

⇒ 1 = AB/BD

⇒ BD = AB

In ΔCDE

tan 60° = CE/DE

⇒ √3 = CE/DE

⇒ CE = √3BD 

Ratio of height of tower P and Q = AB : CE = BD : √3BD

⇒ 1 : √3

∴ The ratio of the heights of P and Q is 1 : √3

Given:

$\left(x^{2}+\frac{1}{x^{2}}\right)=23$

Concept used:

$(x + \frac{1}{x})^2 = x^2 + \frac{1}{x^2} + 2$

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

Calculation:

$\left(x^{2}+\frac{1}{x^{2}}\right)=23$

⇒ $x^2 + \frac{1}{x^2}+2=23 + 2$

⇒ $x^2 + \frac{1}{x^2}+2=25$

⇒ $(x + \frac{1}{x})^2=25$

⇒ $(x + \frac{1}{x})=5$

Now,

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

⇒ $\left(x^{3}+\frac{1}{x^{3}}\right)$ = 5³ - 3 × 5

⇒ $\left(x^{3}+\frac{1}{x^{3}}\right)$ = 125 - 15

⇒ $\left(x^{3}+\frac{1}{x^{3}}\right)$ = 110

∴ The required answer is 110.

Shortcut Trick⇒$\left(x^{2}+\frac{1}{x^{2}}\right)=k^2 -2$

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

⇒ k² - 2 = 23

⇒ k2 = 25 

⇒  k = 5 

then,

k³ - 3k = 5³  - 3 × 5 = 110

Given:

A = 60°

Concept used:

Calculation:

$\frac{\left[8 \cos \mathrm{A}+7 \sec \mathrm{A}-\tan ^{2} \mathrm{~A}\right]}{10 \sin \frac{A}{2}}$

⇒ $\frac{\left[8 \times\frac{1}{2}+7 \times2- (\sqrt{3})^2\mathrm{}\right]}{10 \times \frac{1}{2}}$

⇒ $\frac{\left[4+14- 3\mathrm{}\right]}{5}$

⇒ $\frac{\left[15\mathrm{}\right]}{5}$

⇒ 3

∴ Required answer is 3.

Given:

A boat can cover a distance of 56 km downstream in 3.5 hours

The ratio of the boat in still water and the speed of the stream is 3 : 1

Concept used:

Speed = D/T

D = distance

T = time

Calculation:

Speed of the boat downstream = 56/3.5

⇒ 16 km/h

Now,

To cover 41.6 downstream it will take = 41.6/16 hours

⇒ 2.6 hours

∴ The boat will take 2.6 hours to cover a distance of 41.6 km downstream.

Additional InformationHere we do not need to calculate the speed of the boat in still water and the speed of the stream individually, as in the question the operations were asked downstream.

Given:

AB - BC = 4 cm

AB - AC = 2 cm

ΔABC = 32 cm

Concept used:

Perimeter of a triangle = Sum of three sides of the triangle

Calculation:

AB - BC = 4 cm

⇒ BC = AB - 4

AB - AC = 2 cm

⇒ AC = AB - 2

Perimeter of ΔABC = 32 cm

So, AB + BC + AC = 32

⇒ AB + AB - 4 + AB - 2 = 32

⇒ 3AB = 38

⇒ AB = 38/3

Now,

AC = AB - 2 

⇒ AC = [(38/3) - 2]

⇒ AC = 32/3 cm

∴  AC (in cm) is $\frac{32}{3}$.

Given:

Sum of three numbers = 98.

Ratio of First number to Second number is 2 : 3.

Ratio of Second number to Third number is 5 : 8.

Calculation:

Let the three numbers be A, B and C.

Then,

A : B = 2 : 3      ----(i)

B : C = 5 : 8      ----(ii)

Multiplying eq (i) by 5 and eq (ii) by 3 we get

A : B : C = 10 : 15 : 24

Now C = 98 × 24/49

⇒ C = 48 

∴ The third number is 48.

Given:

AB = 9.6 cm

AC = 11.2 cm

BD = 4.8 cm

Concept used:

Angle bisector theorem = The angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.

Calculation:

According to the concept,

BD/CD = AB/AC

⇒ 4.8/CD = 9.6/11.2

⇒ 1/CD = 2/11.2

⇒ CD = 5.6

So, BC = 4.8 + 5.6

⇒ BC = 10.4

Now,

Perimeter of ΔABC = 9.6 + 10.4 + 11.2

⇒ 31.2 cm

∴ The perimeter (in cm) of ΔABC is 31.2.

Given:

234a5b is divisible by 22, but not divisible by 5.

Concept used:

If a number is even or a number whose last digit is an even number i.e. 2,4,6,8 including 0, it is always completely divisible by 2

If the last number is either 0 or 5, the entire number is divisible by 5

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

Calculation:

22 = 11 × 2

So, b can be 0, 2, 4, 6, 8

But the number is divisible by 5 so 0 cannot be the possible value of b

To get the greatest number a > b

Now,

(2 + 4 + 5) - (3 + a + b) = 0 or multiple of 11

⇒ 11 - 3 - a - b = 0 or multiple of 11

⇒ 8 - a - b = 0 or multiple of 11

⇒ a + b = 8

Possible value of a and b are (8, 0), (7, 1), (6, 2), (5, 3), (4, 4), (3, 5), (2, 6), (1, 7), (0, 8)

For b = 2

a = 6

For b = 4

a = 4

So, only possible values of a and b = 6,2

So, the number is 234652

∴ Required number is 234652.

Given:

26, 224, and 608 are three numbers leaving the remainder 2, 7, and 19 on dividing with the greatest number

Concept Used:

The greatest common Divisor of numbers 'a', 'b', and 'c' leaving remainder 'R₁', 'R₂', and 'R₃' will be H.C.F. of (a - R₁), (b - R₂), and (c - R₃)

Calculation:

HCF of (126 - 2), (224 - 7), and (608 - 19)

⇒ 124, 217, and 589

124 = 31 × 4

217 = 31 × 7

589 = 31 × 19

So, HCF = 31

So, the number is 31

∴ Required answer is 31.

Given:

The price of an item is reduced by 20%. As a result, customers can get 2 kg more of it for ₹360

Calculation:

20% = 1/5

Let the actual price be 5x

So, after reduction it will be 4x

According to the question,

(360/4x) - (360/5x) = 2

⇒ (90/x) - (72/x) = 2

⇒ [(90 - 72)/x] = 2

⇒ 18 = 2x

⇒ x = 9

So, actual price = 5 × 9 = 45

∴ The original price (in ₹) per kg of the item is 45.

Given:

∠CPB = 100°

Concept used:

Two angles are said to be supplementary angles if they add up to 180 degrees. Supplementary angles form a straight angle (180 degrees) when they are put together.

The angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle's circumference.

The opposite angles of a cyclic quadrilateral are supplementary which means that the sum of either pair of opposite angles is equal to 180 degrees.

Calculation:

In the given figure,

∠CPB = 100°

So, ∠APB = 80° [∵ ∠APB = Supplementary Angle of ∠CPB]

Now, in ΔAPB,

AP = PB = radius of the smaller circle

So, ∠PAB = ∠PBA

∠PAB = [180° - 80°)/2]

⇒ ∠PAB = 50°

Now,

∠DAB = 180° - 50°

⇒ ∠DAB = 130° [∵ ∠DAB = Supplementary Angle of ∠PAB]

As ABRD is a cyclic quadrilateral 

So, ∠BRD = 180° - 130° = 50°

Now,

According to the concept,

∠BQD = 50 × 2 = 100° i.e x

∴ Required value of x is 100°

Calculation:

Total students in Camp A in 2014, 2016, and 2017 = 160 + 140 + 220

⇒ 520

Total students in Camp B in 2015, 2018, and 2019 = 240 + 200 + 280

⇒ 720

Ratio = 520 : 720

⇒ 13 : 18

∴ Required ratio is 13 : 18.

Given:

Sum = Rs. 32000

Rate = 20%

Time = 9 month

Concept used:

The formula for quarterly compound interest

$\rm A = P(1 + \frac{\frac{r}{4}}{100})^\frac{4t}{12}$

A = amount

P = principal or sum

r = rate of interest

t = time

Calculation:

Interest rate for quarterly = 20/4 = 5%

Time = 4 × 9/12 = 3

So,

A = 32000(1 + 5/100)³

⇒ A = 32000(1 + 1/20)3

⇒ A = 32000(21/20)3

⇒ A = 32000 × (9261/8000)

⇒ A = 37044

So, amount = Rs. 37044

∴ Required amount is Rs. 37044.

Shortcut Trick

Here rate of interest = 20/4 = 5%

So, interest = 1600 × 3 + 80 + 160 + 4

⇒ 4800 + 240 + 4

⇒ 5044

Amount = 32000 + 5044 = 37044.

Shortcut Trick

Total Distance = 30 + (51 × 4/3) = 30 + 68 = 98 km.

Total Time = (30/45) + (4/3) = 2/3 + 4/3 = 6/3 = 2 hours.

Average Speed = 98 / 2 = 49 km/h.

∴ The correct answer is 49 km/h.

Alternate Method

Given:

Case 1: Distance₁ = 30 km, Speed₁ = 45 km/h

Case 2: Time₂ = 1 h 20 min = 1 + 20/60 = 4/3 hours, Speed₂ = 51 km/h

Formula Used:

Average Speed = Total Distance ÷ Total Time

Distance = Speed × Time

Time = Distance ÷ Speed

Calculations:

⇒ Time₁ = Distance₁ ÷ Speed₁ = 30 ÷ 45 = 2/3 h

⇒ Distance₂ = Speed₂ × Time₂ = 51 × (4/3) = 17 × 4 = 68 km

⇒ Total Distance = 30 + 68 = 98 km

⇒ Total Time = 2/3 + 4/3 = 6/3 = 2 h

⇒ Average Speed = 98 ÷ 2 = 49 km/h

∴ The correct answer is 49 km/h.

Additional Information

Average Speed (Equal Distances)

If a certain distance is covered at speed 'a' and the same distance is covered at speed 'b', the average speed is (2 × a × b) ÷ (a + b).

Average Speed (Equal Time Intervals)

If an object travels at speed 'a' for time 't' and speed 'b' for the same time 't', the average speed is simply the arithmetic mean: (a + b) ÷ 2.

Unit Conversion

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

Given:

sec2θ + tan2θ =  $3 \frac{1}{2}$

Concept used:

sec2θ - tan2θ =  1

Hypotenuse²  =  Perpendicular² + Base² 

secθ = H/B

cosθ = (B/H)

sinθ = (P/H)

Calculation:

sec2θ + tan2θ =  $3 \frac{1}{2}$      ----(i)

sec2θ - tan2θ =  1      ----(ii)

By adding eq (i) and eq (ii) we get,

2sec2θ = 9/2

⇒ sec2θ = 9/4

⇒ secθ = 3/2 = H/B

So,

H² = P² + B²

⇒ 9 = P2 + 4

⇒ 9 - 4 = P2

⇒ 5 = P2

⇒ √5 = P

Now,

cosθ + sinθ = (B/H) + (P/H)

⇒ cosθ + sinθ = (2/3) + (√5/3)

⇒ cosθ + sinθ = $\frac{2+\sqrt{5}}{3}$

∴ (cosθ + sinθ) is equal to $\frac{2+\sqrt{5}}{3}$

Given:

Discount % = 28

Profit% = 30

Gain = Rs. 39.90

Concept used:

Selling price = Cost price + cost price × profit%

Selling price = Marked price - marked price × discount%

Calculation:

Gain amount = 39.90

According to the question, 30% of the CP of the article = 39.90

⇒ 10% of the CP of the article = 13.30

⇒ 100% of the CP of the article = 133 i.e cost price

⇒ 130% of the CP of the article = 172.9 i.e selling price

Now,

172.9 = Marked price - Marked price × 28%

⇒ 172.9 = Marked price - 0.28.Marked price

⇒ 172.9 = 0.72.Marked price

⇒ 172.9/0.72 = Marked price

⇒ Marked price = 240.133 ≈ 240

∴ The marked price (to the nearest ₹) of the article is 240.

Calculation:

Let the total number of students be 100

So, students in school C = 100 × 24% = 24

Students in school E = 100 × 15% = 15

Now,

Ratio of boys of school C and girls of school E = 24 × 3/8 : 15 × 4/5

⇒ 9 : 12 = 3 : 4

∴ Required ratio is 3 : 4

Given:

Diameter of the hemispherical depression = 4 cm

Each face of the cube = 10 cm

Concept used:

TSA of the cube = 6a²

CSA of the hemisphere = 2πr²

Area of a circle = πr2

a = side or edge of a cube

r = radius of circle or hemisphere

Calculation:

The figure below of the solid is created as per the given information along with the top view of the solid,

This hemispherical shape will be formed on each face of the cube

Radius of the hemisphere = 4/2 = 2 cm

According to the question,

Required surface area = TSA of the cube - 6 × areas of circle form on the top of each face of the cube + 6 × CSA of hemisphere formed on each face of a cube

⇒ Required surface area = 6 × 10² - 6 × π2² + 6 × 2π2²

⇒ Required surface area = 600 + 6π22

⇒ Required surface area = 600 + 24 × 22/7

⇒ Required surface area = 600 + 528/7

⇒ Required surface area = 600 + $75\frac{3}{7}$ = $675\frac{3}{7}$

∴ The surface area of the remaining solid (in cm2) is $675\frac{3}{7}$.

Shortcut Trick

Let Total Work be LCM(3, 4, 12) = 12 units.

Efficiency of 1 Man = 4, 1 Woman = 3, 1 Boy = 1.

Target time = 1 day, so total efficiency needed = 12 units/day.

Efficiency of (1 Man + 1 Woman) = 4 + 3 = 7 units.

Efficiency required from boys = 12 − 7 = 5 units.

Number of boys required = 5 ÷ 1 = 5 boys.

∴ The correct answer is 5 boys.

Alternate Method

Given: Time taken by 1 Man = 3 days, 1 Woman = 4 days, 1 Boy = 12 days.

Formula Used: Total Work = Efficiency × Time

⇒ Efficiency of 1 Man + 1 Woman + x Boys = 12 (to complete in 1 day)

⇒ (4 × 1) + (3 × 1) + (1 × x) = 12

⇒ 7 + x = 12

⇒ x = 12 − 7

⇒ x = 5

∴ The correct answer is 5 boys.

Additional Information

Work Equivalence Formula

M₁D₁H₁ = M₂D₂H₂ where M is number of workers, D is days, and H is hours.

Efficiency Concept

Efficiency is inversely proportional to time. If a person completes work in 'n' days, their 1-day work (efficiency) is 1/n.

Combined Work

When multiple people work together, their individual efficiencies are added to find the total work rate.

Given:

Two poles of heights 10 m and 17 m are fixed to level ground.

The distance between the bottom of the poles is 24 m

Concept used:

Hypotenuse² = Perpendicular² + Base² 

Calculation:

Let AB be 10 m and CD be 17 m 

AP = BD = 24 m

AB = PD = 10 m

So, CP = 7 m

Applying pythagoras theorem in ΔACP

AC² = AP² + CP²

⇒ AC2 = 242 + 72

⇒ AC2 = 576 + 49

⇒ AC2 = 625

⇒ AC = 25

∴ The distance (in m) between their tops is 25.

Given:

The cost price of the table = Rs. 4600

The cost price of the chair = Rs. 1800

Gain on table = 10%

Gain on chair = 6%

Concept used:

Selling price = Cost price + cost price × gain%

Calculation:

Selling price of table = 4600 + 4600 × 10/100

⇒ 5060

Selling price of chair = 1800 + 1800 × 6/100

⇒ 1908

Total selling price = 5060 + 1908

⇒ 6968

Total cost price of table and chair = 4600 + 1800

⇒ 6400

So, gain = 6968 - 6400

⇒ 568

gain % = (568/6400) × 100

⇒ 71/8 = $8\frac{7}{8}$

∴ The overall gain percentage is $8\frac{7}{8}$.

Given:

$\frac{46+\frac{3}{4} \ \text{of}\ 32-6}{37-\frac{3}{4} \ \text{of}\ (34+6)}$

Concept used:

Calculation:

$\frac{46+\frac{3}{4} \ \text{of}\ 32-6}{37-\frac{3}{4} \ \text{of}\ (34+6)}$

⇒ $\frac{46+\frac{3}{4} \ \text{of}\ 32-6}{37-\frac{3}{4} \ \text{of}\ 40}$

⇒ $\frac{46+\frac{3}{4} \ \times\ 32-6}{37-\frac{3}{4} \ \times\ 40}$

⇒ $\frac{46+24-6}{37-30}$

⇒ $\frac{64}{7}$

∴ Required answer is $\frac{64}{7}$.

Calculation:

Total number of workers whose daily wages less than Rs. 450 = 30

Total number of workers whose daily wages are less than Rs. 650 and above = 35

Difference = 35 - 30 = 5

∴ Required difference is 5.

The correct answer is 'were you watching'.

Key Points

• The underlined part in the given sentence is grammatically incorrect.
• Here, 'were you watching' should be used instead of 'have you watched'.
• The former part of the given sentence must be in the past continuous tense so the verb must be used in its past continuous form(was/were + V-ing) and not in the present perfect form(have + V₃).
• The 'past continuous' describes actions or events in a time before now, which began in the past and were still going on when another event occurred.
• Thus, the correct answer is Option 3.

Correct Sentence: Which movie were you watching on television when I called you?

The correct answer is 'Literate'.

Key Points

• The most appropriate word for the given group of words is 'Literate'.
• It means 'able to read and write'. (पढ़ने व लिखने में सक्षम)
• Example: Kids on the edge of adolescence are increasingly computer literate.

Correct Answer: Literate.

Additional Information

• Let's look at the meaning of other words:
• Eligible: having the right to do or have something. (कुछ करने या कुछ पाने का अधिकार रखने वाला; उपयुक्त)
• Illiterate: not able to read or write. (लिखने या पढ़ने में असमर्थ; निरक्षर, अनपढ़)
• Illegible: difficult or impossible to read. (जिसे पढ़ना कठिन या असंभव हो; अपाठ्‌य, दुर्वाच्य)