SSC CGL 2021 Tier-I (Held On : 13 April 2022 Shift 2) (Previous Year Paper)

Sahasra started running from her house towards the north.

After 40 meters she turned left and ran for 75 meters. She then turned right and ran for 30 meters, and again turned right to run 75 meters.

∴ Here, Sahasra is facing towards 'East'.

Hence, the correct answer is "East".

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

Conclusions:

I. All colours are pens → False (As All pencils are colours and Some pencils are pens so, All colours are pens is false)

II. Some colours are pencils → True (As All pencils are colours so, Some colours are pencils is true)

III. Some papers are pens → True (As All pens are papers so, Some papers are pens is true)

∴ Here, Only conclusion II and III are true.

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

The logic followed here is :-

(First number + Second number) × (First number - Second number) = Third number

Row 1) :

= (15 + 9) × (15 - 9)

= 24 × 6

= 144

Row 3) :

= (22 + 17) × (22 - 17)

= 39 × 5

= 195

Similarly,

Row 2) :

= (18 + 12) × (18 - 12)

= 30 × 6

= 180

Hence, the correct answer is "180".

The logic followed here is :-

By using BODMAS RULE :

Option 1) : 7 and 2

Given equation : 7 + 56 ÷ 8 × 2 – 13 = 11

After interchanging the numbers in given equation the equation formed is as follows : 2 + 56 ÷ 8 × 7 - 13 = 11

⇒ 2 + 56 ÷ 8 × 7 - 13 = 11

⇒ 2 + 7 × 7 - 13 = 11

⇒ 2 + 49 - 13 = 11

⇒ 51 - 13 = 11

⇒ 38 ≠ 11

LHS ≠ RHS

Option 2) : 8 and 2

Given equation : 7 + 56 ÷ 8 × 2 – 13 = 11

After interchanging the numbers in given equation the equation formed is as follows : 7 + 56 ÷ 2 × 8 - 13 = 11

⇒ 7 + 56 ÷ 2 × 8 - 13 = 11

⇒ 7 + 28 × 8 - 13 = 11

⇒ 7 + 224 - 13 = 11

⇒ 231 - 13 = 11

⇒ 218 ≠ 11

LHS ≠ RHS

Option 3) : 7 and 13

Given equation : 7 + 56 ÷ 8 × 2 – 13 = 11

After interchanging the numbers in given equation the equation formed is as follows : 13 + 56 ÷ 8 × 2 - 7 = 11

⇒ 13 + 56 ÷ 8 × 2 - 7 = 11

⇒ 13 + 7 × 2 - 7 = 11

⇒ 13 + 14 - 7 = 11

⇒ 27 - 7 = 11

⇒ 20 ≠ 11

LHS ≠ RHS

Option 4) : 7 and 8

Given equation : 7 + 56 ÷ 8 × 2 – 13 = 11

After interchanging the numbers in given equation the equation formed is as follows : 8 + 56 ÷ 7 × 2 - 13 = 11

⇒ 8 + 56 ÷ 7 × 2 - 13 = 11

⇒ 8 + 8 × 2 - 13 = 11

⇒ 8 + 16 - 13 = 11

⇒ 24 - 13 = 11

⇒ 11 = 11

LHS = RHS

Hence, the correct answer is "7 and 8".

Given :- r _ k n _c _ _ h _ _ b c b t _ k _ b c b

By checking options and substituting accordingly.

1) h b c q k n h n → r h k n b c c - q h k n b c b - t h k n b c b

2) h b b s k n h c → r h k n b c b - s h k n b c b - t h k c b c b

3) h c b s k n b n → r h k n c c b - s h k n b c b - t b k n b c b

4) h b b s k n h n → r h k n b c b - s h k n b c b - t h k n b c b

• Option (4) give the pattern of :- r h k n b c b - s h k n b c b - t h k n b c b

Hence, the correct answer is "h b b s k n h n".

The logic followed here is :-

Hence, the correct answer is "134".

Preparing the family tree using the following symbol:

Family Tree :-

1) Aakash is the brother of Riva and father of Vansh and Ritu.

2) Ritu is the only daughter of Aakash and Maya.

• This means Ritu is female as she is the only daughter of Maya and Aakash. Thus Vansh will be male.

3) Mahesh is the father of Riva and paternal grandfather of Vansh.

∴ Here, Maya is the 'Daughter-in-law' of Mahesh.

Hence, the correct answer is "Daughter-in-law".

Given, 

Five years ago, the ratio of the ages of Tarun and Saurabh was 4 ∶ 1.

⇒ (Tarun - 5)/(Saurabh - 5) = 4/1

⇒ Tarun - 5 = 4(Saurabh - 5)

⇒ Tarun - 5 = 4Saurabh - 20

⇒ 4Saurabh - Tarun = 15 ............. (i)

After five years, the ratio of their ages will be 2 ∶ 1.

⇒ (Tarun + 5)/(Saurabh + 5) = 2/1

⇒ Tarun + 5 = 2(Saurabh + 5)

⇒ Tarun + 5 = 2Saurabh + 10

⇒ 2Saurabh - Tarun = - 5 .............. (ii)

By solving equation (i) and (ii) we get,

4Saurabh - Tarun = 15

2Saurabh - Tarun = - 5

⇒ 2Saurabh = 20

⇒ Saurabh = 10 years

∴ Here, the present age of Saurabh is 10 years.

Hence, the correct answer is "10".

Shortcut Trick According to the question

we have multiplied by 1 and 3 to make the age difference equal.

since there is a difference of 10 years in the past and future age

2→ 10, 1→ 5

so Saurabh 5 years later age = 5 × 3 = 15 years

so present age of Saurabh age is = 15 - 5 = 10 year

The logic followed here is :-

(First number + 8) ÷ 4

• 68 ∶ 19 → (68 + 8) ÷ 4 = 76 ÷ 4 = 19

Similarly,

• 164 : ? → (164 + 8) ÷ 4 = 172 ÷ 4 = 43

Hence, the correct answer is "43".

Alternate Method (Second number - 2) × 4 = first number

• (19 - 2 ) × 4 = 68

Similarly,

• (fourth number - 2) × 4 = 164

The fourth number is 43.

The logic followed here is :-

∴ Here, 'who' is coded as 'zan'.

Hence, the correct answer is "zan".

The logic followed here is :-

1) BFJNR

2) KOSWA

3) QUYCG

4) VZDHN

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

Hence, the correct answer is "VZDHN".

The logic followed here is :-

'FLASK' is written as 'IPFYR'.

Similarly,

'TOURS' will be written as :

Hence, the correct answer is "WSZXZ".

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

Hence, the correct answer is "Option 1".

The image not embedded in given figure is as shown below :

Hence, the correct answer is "Option 4".

Seven friends E, F, G, H, I, J and K, are sitting along a circular table facing towards the centre.

1) H is sitting third to the left of G.

2) F and I are sitting to the immediate left and right of G, respectively.

3) E and I are the neighbours of J.

∴ Here, 'K' is sitting immediate right of H.

Hence, the correct answer is "K".

The figure that replace the ? by following a certain pattern is as shown below :

• The Ballon shaped image present in middle is rotated 45⁰ clockwise from figure to figure.

Hence, the correct answer is "Option 1".

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

• Noncommunicable diseases are diabetes and cataract.
• Measles disease is a communicable disease.

Hence, the correct answer is "Option 2".

Additional InformationMeasles 

• It is an airborne disease that occurs especially in children.
• Symptoms: Fever, Vomiting, Rashes on the skin.
• Prevention: 
• Complete Rest
• Drinking boiled, filtered water
• Good light intake
• Inoculation of gamma globulin

Diabetes

• Diabetes is a disease that occurs when your blood glucose, also called blood sugar, is too high.
• Blood glucose is your main source of energy and comes from the food you eat. Insulin, a hormone made by the pancreas, helps glucose from food get into your cells to be used for energy.
• Diabetes mellitus, commonly known as diabetes, is a metabolic disease that causes high blood sugar. The hormone insulin moves sugar from the blood into your cells to be stored or used for energy.

Key Points

• There are a few different types of diabetes:
• Type 1 diabetes: Is an autoimmune disease. The immune system attacks and destroys cells in the pancreas, where insulin is made.
• Type 2 diabetes: It occurs when your body becomes resistant to insulin, and sugar builds up in your blood.
• Prediabetes: It occurs when your blood sugar is higher than normal, but it’s not high enough for a diagnosis of type 2 diabetes.
• Gestational diabetes: Is high blood sugar during pregnancy. Insulin-blocking hormones produced by the placenta cause this type of diabetes.

Here cube of n × n formulae is:

• Cube of no side painted = (n - 2)³
• Cube of one side painted = 6 × (n - 2)²
• Cube of two side painted = 12 × (n - 2)
• Cube of three sides painted = Always 8

A cube of side 49 cm is painted purple on all the faces and then cut into smaller cubes of sides of 7 cm each.

⇒ n = 7

∴ Number of smaller cubes having only one face painted = 6 × (n - 2)2

⇒ Number of smaller cubes having only one face painted = 6 × (7 - 2)²

⇒ Number of smaller cubes having only one face painted = 6 × 5²

⇒ Number of smaller cubes having only one face painted = 6 × 25

⇒ Number of smaller cubes having only one face painted = 150

Hence, the correct answer is "150".

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

Hence, the correct answer is "Option 1".

The logic followed here is :-

 

Hence, the correct answer is "HUJ".

The logic followed here is :-

By using BODMAS RULE :

Option 1) : +, ÷ , – , = , × 

Given equation : 88 * 120 * 42 * 240 * 48 * 2

After inserting the symbols in given equation the equation is as follows : 88 + 120 ÷ 42 - 240 = 48 × 2

⇒ 88 + 120 ÷ 42 - 240 = 48 × 2

⇒ 88 + 2.8571 - 240 = 48 × 2

⇒ 88 + 2.8571 - 240 = 96

⇒ 90.8571 - 240 = 96

⇒ - 149.1428 ≠ 96

LHS ≠ RHS

Option 2) : =, × , +, ÷, –

Given equation : 88 * 120 * 42 * 240 * 48 * 2

After inserting the symbols in given equation the equation is as follows : 88 = 120 × 42 + 240 ÷ 48 - 2

⇒ 88 = 120 × 42 + 240 ÷ 48 - 2

⇒ 88 = 120 × 42 + 5 - 2

⇒ 88 = 5040 + 5 - 2

⇒ 88 = 5045 - 2

⇒ 88 ≠ 5043

LHS ≠ RHS

Option 3) : ×, ÷, =, –, +

Given equation : 88 * 120 * 42 * 240 * 48 * 2

After inserting the symbols in given equation the equation is as follows : 88 × 120 ÷ 42 = 240 - 48 + 2

⇒ 88 × 120 ÷ 42 = 240 - 48 + 2

⇒ 88 × 2.8571 = 240 - 48 + 2

⇒ 251.4285 = 240 - 48 + 2

⇒ 251.4285 = 242 - 48

⇒ 251.4285 ≠ 194

LHS ≠ RHS

Option 4) : =, –, +, ÷, × 

Given equation : 88 * 120 * 42 * 240 * 48 * 2

After inserting the symbols in given equation the equation is as follows : 88 = 120 - 42 + 240 ÷ 48 × 2

⇒ 88 = 120 - 42 + 240 ÷ 48 × 2

⇒ 88 = 120 - 42 + 5 × 2

⇒ 88 = 120 - 42 + 10

⇒ 88 = 130 - 42

⇒ 88 = 88

LHS = RHS

Hence, the correct answer is "=, –, +, ÷, × ".

The pattern followed here is :

The process of virus infected to a person and finally getting recovery is as shown.

3. Virus
4. Infection
5. Symptoms
6. Treatment
7. Recovery

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

The logic followed here is :-

Hence, the correct answer is "426".

The logic followed here is :-

Sum of alphabet positional value × 3

'ONION' is coded as 201.

= (15 + 14 + 9 + 15 + 14) × 3

= 67 × 3

= 201

and

'POTATO' is coded as 261.

= (16 + 15 + 20 + 1 + 20 + 15) × 3

= 87 × 3

= 261

Similarly,

'MANGO' will be coded as :

= (13 + 1 + 14 + 7 + 15) × 3

= 50 × 3

= 150

Hence, the correct answer is "150".

The logic followed here is :-

RJB : TGF

Similarly,

QPG : ?

 

Hence, the correct answer is "SMK".

The correct answer is Coorg.

Important Points

• 'Ummatt-aat' is a folk dance form performed in Coorg.
• This dance is performed by the Kodava women wearing the traditional Kodava dress with jewellery and the conventional kumkuma on their foreheads.
• The dance is performed in a circular motion with a swinging rhythm.
• The dancers hold brass cymbals in their hands.

Additional Information

• Other Folk Dances of Karnataka are:-
• Krishna Parijatha,
• Bhootha Aradhane,
• Nagamandala,
• Karaga,
• Gaarudi Gombe,
• Joodu Haligi,
• Kamsale Nritya.

The correct answer is 12.5%.

Key Points

• 12.5% of Gross Domestic Product (GDP) for India in 2021 was given by the International Monetary Fund (IMF) in April 2021.
• The IMF expected world output to grow 6% in 2021 and 4.4% in 2022.
• Advanced economies are projected to grow 5.1% in 2021, with the US and Spain expected to rebound the fastest at 6.4% each.
• According to India’s statistics office, the economy contracted 8% in FY21 while the Economic Survey 2020-21 sees 11% growth in FY22.

Additional Information

• IMF was established in 1944.
• The International Monetary Fund (IMF) is an organization of 190 countries, working to foster global monetary cooperation, secure financial stability, facilitate international trade, promote high employment and sustainable economic growth, and reduce poverty around the world.
• World Economic Outlook, Global financial stability reports, and Regional Economic Reports are published by IMF.
• Managing Director of IMF: Kristalina Georgieva (Apr 2022)
• Headquarters: Washington DC

Important Points

• Economic survey 2021-22:
• As per IMF’s latest World Economic Outlook projections, India’s real GDP is projected to grow at 9 per cent in 2021-22 and 2022-23 and at 7.1 per cent in 2023-2024.
• Which would make India the fastest-growing major economy in the world for all 3years.

The correct answer is Sulabh International.

Key Points

• Sulabh International is an Indian 'not for profit' organisation, working on sustainable solutions to make sanitation and water accessible to all.
• Ministry of Culture, Ministry of Jal Shakti, Ministry of Housing and Urban Affairs in collaboration with Sulabh International is organizing an event “Swacchagraha” on 5 March 2022 in New Delhi.
• The event will be conducted in two sessions.
• It will also feature a performance by Dhruva –The Sanskrit Band, the world’s only music band based on India’s oldest own tradition of Vedic–gaan and Stotra–gaan.

Additional Information

• Sulabh International non-government organizations have constructed and maintained “pay and use” toilets for temporary populations or places such as bus stands, markets, and parks.
• In Darbhanga, Bihar,​ Sulabh International launched the cheapest drinking water project 'Sulabh Jal'.
• The price of the one-liter bottle will be 50 paise as per the 'Sulabh Jal' project.
• The project converts contaminated pond and river water into safe drinking water.
• Sulabh International introduced the concept of 'Sulabh Sauchalya' in India.

The correct answer is Dew point temperature.

Key Points

• Dew point temperature (DPT):
• It is a temperature at which moisture present in the atmosphere starts condensing or it is the temperature at which the first droplet of moisture is formed.
• As we know that for each pressure, the air has a specific saturation temperature, therefore for fully saturated air DBT, WBT and DPT are equal.
• When the relative humidity of the air is 100%, i.e the air is saturated, the dew point temperature (DPT) equals the wet-bulb temperature (WBT), which is also equal to the dry-bulb temperature.
• So DBT = WBT = DPT

Additional Information

• Relative humidity:
• It is defined as the ratio of the mass of vapour to the mass of vapour under saturation conditions.
• Relative humidity represents vapour absorption capacity.

The correct answer is Chris Gayle.

Important Points

• Chris Gayle became the first player to hit 350 sixes during IPL 2021.
• Gayle achieved the iconic milestone in the IPL 2021 match between Punjab Kings and Rajasthan Royals at the Wankhede Stadium in Mumbai.

Additional Information

• A total of eight teams participated in IPL 2021.
• IPL 2021 was the 14th edition of the Indian Premier League (IPL).
• IPL 2021 was hosted in 2 countries:
• 9 April – 2 May 2021: United Arab Emirates.
• 19 September – 15 October 2021: India.
• All the eight existing teams participated in this tournament while the tournament was totally unchanged from the previous editions.
• In this tournament, the opening match was played between defending champions Mumbai Indians and Royal Challengers Bangalore at MA Chidambaram Stadium, Chennai on April 9, 2021.

The correct answer is Burnt Sugar.

Key Points

• Avni Doshi is an author of the novel 'Burnt Sugar' which has been longlisted for the Booker Prize 2020.
• It is her debut book which is a feminist novel set in modern-day India that ponders motherhood and the change of roles from being a daughter to becoming a caregiver for an elderly mother.
• Avni Doshi is an American novelist.
• Her debut novel, "Girl in White Cotton" was published in India in 2019.
• In 2020, it was published in the United Kingdom under the title Burnt Sugar.
• The novel was shortlisted for the 2020 Booker Prize.

Additional Information

• Unaccustomed Earth is a collection of short stories from American author Jhumpa Lahiri.
• Interpreter of Maladies is a book collection of nine short stories by American author of Indian origin Jhumpa Lahiri published in 1999.
• In Other Words, an autobiographical work written in Italian, by Jhumpa Lahiri.

The correct answer is 2019.

Important Points

• India banned unregulated deposit schemes through an Act passed in the year 2019.
• Unregulated Deposit Schemes were banned in India by the 'Banning of Unregulated Deposit Schemes Act, 2019'.
• Parliament has passed the Banning of Unregulated Deposit Schemes Bill, 2019, which seeks to put in place a mechanism by which poor depositors will get back their hard-earned money.
• The Banning of Unregulated Deposit Schemes Bill, 2019 was introduced in Lok Sabha by the Minister of Finance, Ms. Nirmala Sitharaman, on July 19, 2019.
• It also seeks to amend three laws, i.e., the Reserve Bank of India Act, 1934, the Securities and Exchange Board of India Act, 1992, and the Multi-State Co-operative Societies Act, 2002.
• The Bill bans unregulated deposit schemes. A deposit-taking scheme is defined as unregulated if it is taken for a business purpose and is not registered with the regulators.

The correct answer is 2020.

Key Points

• India has been ranked as the 48th most innovative nation in the world in 2020; entering the top 50 nations for the first time.​
• ​India has climbed 2 spots and has been ranked 46th by the World Intellectual Property Organization in the Global Innovation Index 2021 rankings.
• India has been on a rising trajectory, over the past several years in the Global Innovation Index (GII), from a rank of 81 in 2015 to 46 in 2021.

Additional Information

• The Global Innovation Index (GII) is an annual ranking of countries by their capacity for, and success in, innovation.
• It is published by Cornell University, INSEAD, and the World Intellectual Property Organization, in partnership with other organizations and institutions.

The correct answer is 1000.

Key Points

• Salinity is the term used to define the total content of dissolved salts in seawater.
• It is calculated as the amount of salt (in gm) dissolved in 1,000 gm (1 kg) of seawater.
• The average salinity of the oceans is 35 parts per thousand.
• The salinity of the dead sea is around 340 grams per litre of water.
• The Dead Sea is a sea that is the saltiest of all oceans and seas.

Additional Information

• Factors affecting ocean salinity are mentioned below:
• The salinity of water in the surface layer of oceans depends mainly on evaporation and precipitation.
• Surface salinity is greatly influenced in coastal regions by the freshwater flow from rivers, and in polar regions by the processes of freezing and thawing of ice.
• Wind also influences the salinity of an area by transferring water to other areas.
• The ocean currents contribute to the salinity variations.
• Salinity, temperature, and density of water are interrelated. Hence, any change in the temperature or density influences the salinity of water in an area.

The correct answer is 1931.

Key Points

• In 1931, the Karachi Session of the Indian National Congress dwell on how Independent India's Constitution should look.
• Karachi Resolution,1931 on Fundamental Rights guaranteed:
• Free speech and expression.
• Right to form associations.
• Right to assemble.
• Universal adult franchise. (Right to vote)
• Equal legal rights irrespective of caste, creed, and sex.
• The neutrality of the state in religious matters.
• Free and compulsory primary education.
• Protection of culture, language, and the script of minorities and linguistic groups.

Additional Information

• The Karachi Congress Session which was held from March 26 to 31,1931 was chaired by Sardar Vallabhbhai Patel.
• ​Pandit Jawahar Lal Nehru drafted the resolution of the Fundamental Rights and National Economic programme.
• It was a very special session of the Indian National Congress in which Mahatma Gandhi was selected to represent the Indian National Congress in the Second Round Table Conference to be held in London.
• The session also discussed the approval of the Gandhi-Irwin Pact or the Delhi Pact.
• Six days before this session, Bhagat Singh, Rajguru, and Sukhdev were hanged.

The correct answer is Virat Kohli.

Key Points

• The Indian Cricketer, Virat Kohli has been named Wisden Almanack’s ODI player of the 2010s.
• In a ten-year period, he hit over 11,000 runs, averaging over 60 and scoring 42 centuries.
• In 2011, he won the ICC Cricket World Cup, and two years later, he won the Champions Trophy, scoring the most runs in the final.
• Kohli and India have never lost before the semi-final stage of an ICC 50-over tournament in the last decade.

Additional Information

• The Wisden Almanack's 2021 edition includes five ODI cricketers of the decade to commemorate the 50th anniversary of the first One-Day International.
• Between 1971 and 2021, one cricketer from each decade was chosen, with the Indian captain receiving the award for the decade of the 2010s.

The correct answer is Pulakesin II.

Key Points

• Pulakesin II defeated Harshavardhana when he invaded the Chalukya kingdom in the Deccan.
• Pulakeshin II, the King of the Chalukya dynasty defeated Harshavardhana when he sought to enlarge his Empire into the southern peninsula of India.
• He defeated Harshavardhana on the banks of the Narmada river in 618-619 AD.
• The Aihole inscription was written by the Ravikirti, court poet of Chalukya King, Pulakesin II who reigned from 610 to 642 CE.

Additional Information

• Chalukya dynasty:  
• It lasted from 543 A.D. to 755 A.D.
• Pulakesin I was the founder of the Chalukya dynasty. He established a small kingdom with Vatapi or Badami as its capital.
• The Western Chalukyas ruled over an extensive area in the Deccan for about two centuries after which the Rashtrakutas became powerful.
• The family of Western Chalukyas had its offshoots like the Eastern Chalukyas of Vengi and the Chalukyas of Kalyani.
• Kirtivarman II was the last of the rulers of the Chalukyas.
• He was defeated by Dantidurga, the founder of the Rashtrakuta dynasty.

The correct answer is Bajrang Punia.

Key Points

• Bajrang Punia became World No. 1 in 65-kg freestyle wrestling in March 2021.
• Bajrang Punia won gold in the Men’s freestyle wrestling 65 kg category at the Dan Kolov 2019 wrestling event.
• Bajrang Punia is related to Wrestling.
• Bajrang Punia belongs to Haryana.
• He won the bronze medal at Tokyo Olympics.

Additional Information

• Yogeshwar Dutt is an Indian freestyle wrestler.
• He was awarded the Padma Shri by the Government of India in 2013.
• He won gold medals at the 2010 and the 2014 Commonwealth Games.
• Sushil Kumar Solanki is a former Indian wrestler.
• His 2008 Olympic medal was second for India in wrestling, and the first since Khashaba Dadasaheb Jadhav's bronze medal at the 1952 Summer Olympics.

The correct answer is 2024.

Important Points

• Jal Jeevan Mission (Har Ghar Nal Se Jal)
• Launched in 2019.
• To provide every single rural household with functional household tap connections (FHTC)- ‘Har Ghar Nal Se Jal’ by 2024.
• It has a decentralized approach as it is implemented at national, state, and district levels for specific needs and purposes (Targeted Area approach).
• The major role is played by Paani Samitis and women in mobilizing the population.
• The Jal Jeevan Mission will be based on a community approach to water and will include extensive information, education, and communication as a key component of the mission.

Additional Information

• Goa has become the first 'Har Ghar Jal' State in the country as it successfully provided 100% Functional Household Tap Connections (FHTCs) in the rural areas covering 2.30 lakh rural households.
• ​Jal Jeevan Mission (JJM) envisages the supply of 55 liters of water per person per day to every rural household through Functional Household Tap Connections (FHTC) by 2024.
• The fund sharing pattern between the Centre and states is 90:10 for Himalayan and North-Eastern States, 50:50 for other states, and 100% for Union Territories.

The correct answer is Dimapur.

Key Points

• Kachari Ruins or The Dimasa Kachari Ruins is located in the town of Dimapur in Nagaland.
• The ruins are a series of mushroom domed pillars that were created by the Dimasa Kachari Kingdoms that ruled before the Ahom invasion during the 13th century.
• The purpose and origin of the pillars are mysterious; few of the pillars stand in full glory while others are crumbled down.
• It is also believed that a game similar to that of chess was played here with the mushroom shaped dooms.

The correct answer is Octopus.

Important Points

• Octopuses have three hearts, a systemic heart that circulates blood around the body and two branchial hearts that pump it through each of the two gills.
• The systemic heart is inactive when the animal is swimming and thus it tires quickly and prefers to crawl.
• Octopus blood contains the copper-rich protein hemocyanin to transport oxygen.
• This makes the blood very viscous and it requires considerable pressure to pump it around the body.
• Octopus's blood pressures can exceed 75 mmHg.
• All octopuses are venomous, evidence shows that the animal does not make the venom by itself, but are produced by symbiotic bacteria instead.
• The blue-ringed octopus is the most venomous to humans and they are fatal.
• These sea or marine creatures lack the skeletal system and are grouped into:
• Kingdom: Animalia
• Phylum: Mollusca
• Class: Cephalopoda
• Genus: Octopus

The correct answer is Possess only pitted thickenings.

Key Points

• Plant fibres are elongated, most commonly sclerenchyma supportive plant cells with thick cellulose walls with a well-organized structure.
• Cellulose natural fibres are characterised by a fibrillar structure in which the crystalline arranged parts of cellulose I form a periodic array with amorphous cellulose molecules.

The correct answer is Uday Shankar.

Important Points

• Uday Shankar was the President of the Federation of Indian Chambers of Commerce and Industries (FICCI) as of April 2021.
• The Federation of Indian Chambers of Commerce & Industry is a non-governmental trade association and advocacy group based in India.
• It was established in 1927, on the advice of Mahatma Gandhi by GD Birla and Purshottamdas Thakurdas.
• It is the largest, oldest, and apex business organization in India.
• Sanjiv Mehta is the current president of FICCI. (May 2022)

The correct answer is Rs. 2,500.

<br>

Key Points

• The 60th Amendment to the Constitution of India increased the ceiling of profession tax from Rs. 250 p.a. to 2500 p.a.
• The Sixtieth Amendment of the Constitution of India, officially known as The Constitution (Sixtieth Amendment) Act, 1988.
• It amended Article 276 of the Constitution relating to taxes on professions, trades, callings, and employments.

Additional Information

• Article 368 in Part XX of the Constitution deals with the powers of Parliament to amend the Constitution and its procedure.
• It states that the Parliament may, in the exercise of its constituent power, amend by way of addition, variation, or repeal any provision of the Constitution in accordance with the procedure laid down for the purpose.

The correct answer is continental shelf.

Important Points

• The continental shelf is the extended margin of each continent occupied by relatively shallow seas and gulfs.
• The Continental Shelf of all oceans together covers 7.5% of the total area of the oceans.
• The gradient of continental is 1° or even less.
• The continental shelves are covered with variable thicknesses of sediments brought down by rivers, glaciers, etc.
• Massive sedimentary deposits received over a long time by the continental shelves become the source of fossil fuels [Petroleum].
• Seaward extension of the continent from the shoreline to the continental edge approx. 200 m deep.
• In some places, where the coasts are extremely mountainous, such as in the Rocky Mountains, the continental shelf may be entirely absent.

 Additional Information

• Continental slope:
• When seaward slope immediately becomes steep & gradient to about 1 in 20 with average depth 200 – 3000m.
• Most of the canyons & trenches are observed in this region.
• The continental slope connects the continental shelf and the ocean basins. ​
• ​Abyssal Plains:
• The average depth is 3000 – 6000 m.
• These plains are covered with fine-grained sediments like clay and silt.
• ​Oceanic Trench:
• They are some 3-5 km deeper than the surrounding ocean floor.
• The trenches lie along the fringes of the deep-sea plain at the bases of continental slopes and along island arcs.
• The trenches run parallel to the bordering fold mountains or the island chains.
• Deepest trench in the world → Marina trench (11 km) of Guam Islands (Pacific Ocean)

The correct answer is Nepali. 

Important Points

• Nepali is one of the languages in which the denomination is printed on the reverse of a contemporary Indian currency note.
• The currency of Nepal is Nepalese rupee.
• There are 17 languages written on the Currency Note.
• 2 languages (Hindi and English) are written on the front side and 15 on the backside (Assamese, Bengali, Gujarati, Kannada, Kashmiri, Konkani, Malayalam, Marathi, Nepali, Odia, Punjabi, Sanskrit, Tamil, Telugu, Urdu).
• Contemporary Indian currency notes have 15 languages on the panel which appears on the reverse of the note.

The correct answer is Jharkhand.

• Netarhat mountains are found in a town in Latehar district, Jharkhand.
• Referred to as the "Queen of Chotanagpur", it is a hill station.

Additional Information

• Important hills in Jharkhand:
• Parasnath Hill is also recognized as Sri Sammed Sikharji.
• Parasnath Hill is situated in the Giridih district of Jharkhand. Hence, option 1 is correct.
• It is a chief Jain pilgrimage site and the holy place for Jains.
• It is believed in the Jain culture that 20 of the 24 Tirthankaras attained Moksha from this place.
• Rajmahal Hills are located in the Sahibganj and Godda districts of the Eastern part of Jharkhand.
• The Rajmahal hills belong to the Jurassic era.
• These hills like others also have many waterfalls, lakes, and greenery.
• Trikut Hill is located ten kilometers away from Deoghar and lies on the way to Dumka in Jharkhand.
• Tagore Hill is also recognized as Morabadi Hill.
• The Tagore hill is located in Morabadi, Ranchi.

The correct answer is llbert Bill, 1884.

Important Points

• llbert Bill, 1884 ought to allow senior Indian magistrates to preside over cases involving British subjects in India.
• The Ilbert Bill was introduced on 9 February 1883 during the Viceroyship of the Lord Ripon, which was drafted by Sir Courtenay Peregrine Ilbert, the legal member of the Council of the Governor-General of India.
• It was concerned about the jurisdiction of Magistrates or Sessions Judges to try charges against European British subjects if they were themselves not European.
• The bill led to intense opposition in Britain and from British settlers in India that ultimately played on racial tension before it was enacted in 1884 in a severely compromised state.
• After this controversial bill, the formation of the Indian National Congress took place.

Additional Information

• Age of Consent Act,1891:
• It forbade the marriage of girls having aged less than 12 years.
• It was a reward for the efforts of Parsi reformer B.M.Malabari.
• He wrote in his notes that infant marriages and enforced widowhood were social evils that needed to be eliminated.
• The Ingress into India Ordinance, 1914, a law passed in British India in September 1914, at the outset of World War I, allowed the Government of India to screen, detain, and restrict the movement of people returning to India.
• The Government of India Act 1919 was an Act of the Parliament of the United Kingdom.
• Government of India Act, 1919 also known as Montagu-Chelmsford Reforms came into force in 1921.
• It was instituted in the British Indian polity to introduce the Dyarchy.

The correct answer is Aruna Asaf Ali.

• Aruna Asaf Ali was an Indian educator, political activist, and publisher. An active participant in the Indian independence movement, she is widely remembered for hoisting the Indian National flag at the Gowalia Tank Maidan, Bombay during the Quit India Movement in 1942.
• The Quit India Movement was started on 8th August 1942.
• Every year 8 August is celebrated in India as August Kranti Din.
• The failure of the Cripps Mission acted as the immediate cause of the Quit Indian Movement.
• Hindu Mahasabha officially boycotted the movement at an open front.

Additional Information

• Sarojini Naidu was the first Indian woman president of the Indian National Congress.
• She became the president of the Indian National Congress in the Kanpur session in 1925.
• She was given the title of "Nightingale of India" for her contributions in the field of poetry writing.
• She was called 'Bharat Kokila'.
• Matangini Hazra used to lead huge processions and actively participated in the Quit India and Non-cooperation movements.
• During the Salt Satyagrah, she stealthily got into the premises of Tamluk Court without arousing suspicion of the police guarding the building and hoisted the national flag.
• Matangini Hazra was known as Gandhi Buri.
• Tara Rani Srivastava was an Indian freedom fighter, and part of Mahatma Gandhi's Quit India Movement.

The correct answer is Telangana.

Key Points

• Telangana became the second state in the country to achieve 100% functional household tap connections (FHTCs).
• ​Jal Jeevan Mission (JJM) envisages the supply of 55 liters of water per person per day to every rural household through Functional Household Tap Connections (FHTC) by 2024.
• Goa has earned itself the unique distinction of becoming first 'Har Ghar Jal' State in the country as it successfully provides 100% Functional Household Tap Connections (FHTCs) in the rural areas covering 2.30 lakh rural households.

Additional Information

• The fund sharing pattern between the Centre and states is 90:10 for Himalayan and North-Eastern States, 50:50 for other states, and 100% for Union Territories.
• JJM focuses on integrated demand and supply-side management of water at the local level.
• The creation of local infrastructure for source sustainability measures as mandatory elements, like rainwater harvesting, groundwater recharge and management of household wastewater for reuse, would be undertaken in convergence with other government programmes/schemes.

Given:

2√2x3 - 3√3y3 = (√2x - √3y)(Ax2 - Bxy + Cy2)

Formula used:

a³ - b³ = (a - b) (a² + ab + b²)

Calculation:

2√2x3 - 3√3y3 = (√2x - √3y) (Ax2 - Bxy + Cy2)

⇒ (√2x)3 - (√3y)3 = (√2x - √3y) (Ax2 - Bxy + Cy2)

⇒ (√2x - √3y) (2x2 + √6xy + 3y2) = (√2x - √3y) (Ax2 - Bxy + Cy2)

So, A = 2; B = -√6; and C = 3

Then, (A2 + B2 + C2) = 22 + (√6)2 + 32

= 4 + 6 + 9

= 19

∴ The value of (A2 + B2 + C2) is 19

Shortcut Trick

Since speed is constant, distance is directly proportional to time (D₁/T₁ = D₂/T₂).

Initial Distance (D₁) = 225 km, Initial Time (T₁) = 2.5 hours.

New Distance (D₂) = 630 km, New Time (T₂) = ?

225 / 2.5 = 630 / T₂ ⇒ 90 = 630 / T₂ ⇒ T₂ = 630 ÷ 90 = 7.

∴ The correct answer is 7 hours.

Alternate Method

Given:

Distance₁ = 225 km, Time₁ = 2.5 hours, Distance₂ = 630 km.

Formula Used:

Speed = Distance ÷ Time

Calculations:

⇒ Speed = 225 ÷ 2.5

⇒ Speed = 2250 ÷ 25 = 90 kmph

⇒ Time for 630 km = Distance₂ ÷ Speed

⇒ Time = 630 ÷ 90

⇒ Time = 7 hours

∴ The correct answer is 7 hours.

Additional Information

Direct Proportion in Speed

When speed is constant, the ratio of distances is equal to the ratio of times (D₁/D₂ = T₁/T₂).

Unit Conversion

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

Average Speed

Average Speed = Total Distance ÷ Total Time. For two equal distances with speeds x and y, it is 2xy/(x+y).

Given:

The angle of elevation of the top of the tower = 30°

Calculation:

The height of the tower = QR

The distance from the tower to the point P (QP) = 510 m

tan 30° = QR/QP

⇒ 1/√3 = QR/510

⇒ QR = 510/√3

Multiply by √3 in numerator and denominator 

⇒ 510√3/(√3 × √3)

⇒ 510√3/3     

⇒ 170√3 m

Also, 50% of QR = (50/100) × (170√3) = 85√3 m

∴ The 50% of the height of the tower (in m) is 85√3 m

Given:

Chords AB and CD of a circle intersect externally at P.

AB = 7 cm, CD = 1 cm and PD = 5 cm

Concept used:

If two chords of a circle intersect externally, then the product of the lengths of the segments are equal

Calculation:

Let, PB = x cm

PB × PA = PD × PC

⇒ x (x + 7) = 5 (5 + 1)

⇒ x² + 7x = 30

⇒ x2 + 7x - 30 = 0

⇒ x2 + 10x - 3x - 30 = 0

⇒ x (x + 10) - 3 (x + 10) = 0

⇒ (x + 10) (x - 3) = 0

⇒ x + 10 = 0 ⇒ x = - 10 [Not possible]

⇒ x - 3 = 0 ⇒ x = 3

∴ The length of PB (in cm) is 3 cm

Given:

P invested = Rs. 150000

Q invested = Rs. 450000

Total profit = Rs. 160000

Calculation:

P's share : Q's share = 150000 : 450000 = 1 : 3

P get from the profit = (1/4) × 160000 = Rs. 40000

P gets total amount = Rs. 70000

Total salary of P = 70000 - 40000 = Rs. 30000

∴ The salary (in Rs.) P received is Rs. 30000

Given:

5 sin θ – 4 cos θ = 0, 0° < θ < 90°

Calculation:

5 sin θ – 4 cos θ = 0

5 sin θ = 4 cos θ

sin θ/cos θ = 4/5

tan θ = 4/5   .....(1)

So, (5 sin θ - cos θ)/(5 sin θ + 3 cos θ)

= (5 tan θ - 1)/(5 tan θ + 3)  [Divided by cos θ]

= [5 × (4/5) - 1]/[5 × (4/5) + 3]

= (4 - 1)/(4 + 3)

= 3/7

∴ The value of 5 sin θ - cos θ)/(5 sin θ + 3 cos θ) is 3/7

Given:

The given expression = $\frac{48.3×[(4.95)^2+4.95×13.25]}{[(12.55)^2-(5.65)^2]×19.8}$

Calculation:

$\frac{48.3×[(4.95)^2+4.95×13.25]}{[(12.55)^2-(5.65)^2]×19.8}$

= $\frac{48.3×4.95(4.95+13.25)}{[(12.55+5.65)(12.55-5.65)]×19.8}$

= $\frac{48.3×4.95×18.20}{18.20×6.9×19.8}$

= $\frac{48.3×4.95×18.20}{18.20×6.9×19.8}$ = $\frac{48.3×4.95}{6.9×19.8}$

= (7 × 4.95)/19.8

= 35/20

= 1.75

∴ The value of the given expression is 1.75

Hintsince all the options are distinct, we can approximate the values

⇒ (49 × 5)/(7 × 20) = 7/4 = 1.75

Given:

In ΔABC, AB = 7 cm, BC = 10 cm, and AC = 8 cm

Concept used:

An angle bisector of an angle of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Calculation:

AD is the angle bisector of ∠BAC

So, AB/AC = BD/DC

⇒ 7/8 = BD/DC

⇒ 8BD = 7DC

⇒ BD = 7DC/8   .....(1)

Here, BD + DC = BC

⇒ 7DC/8 + DC = BC = 10  [∵ BD = 7DC/8]

⇒ 15DC/8 = 10

⇒ DC = 10 × (8/15) = 80/15 = 16/3

∴ The value of DC (in cm) is 16/3

Given:

The following bar graph shows the total number of youth (in lakhs) and the number of employed youth (in lakhs) in 5 states A, B, C, D, and E.

Calculation:

Unemployed youth = Total youth - Employed youth.

Hope the doubt is now clear.

The youths (in lakhs) are unemployed in states A = 12 - 10.5 = 1.5

The youths (in lakhs) are unemployed in states C = 11.5 - 10 = 1.5

Total youths (in lakhs) are unemployed = 1.5 + 1.5 = 3

∴ The total number of youths (in lakhs) are unemployed in states A and C taken together is 3

Given:

LCM of A and B = 209

Calculation:

Prime factors of 209 = 11 × 19

So, A = 19 and B = 11 [∵ A > B]

Then, B2 - A = 112 - 19 = 121 - 19 = 102

∴ The value of B2 - A is 102

Given:

The diameter of a wooden cylinder = 70 cm

The height of the wooden cylinder = 6 m

The cost of polishing = Rs. 50 per m2

Formula used:

The curved surface area of a cylinder = 2 × π × (radius) × (height)

Calculation:

The radius of the wooden cylinder = 70/2 = 35 cm = 0.35 m

The total cost = 2 × (22/7) × 0.35 × 6 × 50

⇒ 2 × (22/7) × (35/100) × 6 × 50

⇒ 660

∴ The total cost (in Rs.) of polishing the curved surface of a wooden cylinder is Rs. 660

Given:

∠POQ = 54°

Concept used:

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

The sum of the opposite angles of a cyclic quadrilateral = 180°

Calculation:

Take a point on a circle at the point A and connect PA and QA

So, ∠PAQ = ∠POQ/2 = 54°/2 = 27°

APRS is a cyclic quadrilateral

So, ∠PRQ = 180° - 27° = 153°

∴ The measure (in degree) of ∠PRQ is 153°

Shortcut Trick

Rate of interest = 10% (per annum)

Fraction value = 10% = 1/10

∴ Principal = 10; Interest = 1

So, total installment = 10 + 1 = 11

 

So, 210 → Rs. 4620

∴ 121 → (4620/210) × 121 = Rs. 2662

∴ The each instalment (in Rs.) is Rs. 2662

Alternate Method

Given:

Total amount = Rs. 4620

Rate of interest = 10%

Total number of installment = 2

Formula used:

Installment = $\frac{P}{\left(\frac{100}{100+R} \right)+\left(\frac{100}{100+R} \right)^n}$

Where, P = Total amount; R = Rate of interest; n = Number of installment

Calculation:

Installment = $\frac{4620}{\left(\frac{100}{100+10} \right)+\left(\frac{100}{100+10} \right)^2}$

= 4620/[(10/11) + (10/11)²]

= 4620/[(10/11) + (100/121)]

= 4620/(210/121)

= 4620 × (121/210)

= 2662

∴ The each instalment (in Rs.) is Rs. 2662

Given:

The number of students of 160 - 165 cm = 20

The number of students of 165 - 170 cm = 12

Calculation:

 

Total number of students $\left(\displaystyle\sum_{f_i} \right)$= 32

Also, $\displaystyle\sum_{f_ix_i}$ = 3250 + 2010 = 5260

The average height $\left(\displaystyle\sum_{f_ix_i}/\displaystyle\sum_{f_i} \right)$ = 5260/32 = 164.375 cm ≈ 164.4 cm (correct up to one place of decimal)

∴ The average height (in cm) of 32 tallest students of the athletic club is 164.4 cm

Given:

The number of youth (in lakhs) and the number of employed youth (in lakhs) in five states A, B, C, D, and E are shown in the bar graph.

Calculation:

The number of employed youth (in lakhs) in state B = 7

The number of employed youth (in lakhs) in state E = 8

The percentage = (7/8) × 100 = 87.5%

The number of employed youth in state B is 87.5% of the number of employed youth in state E

Given:

The price of one vanilla cake = Rs. 8

The price of one chocolate cake = Rs. 15

Total number of cakes sold in the week = 10500

Calculation:

The total number of cakes sold on Saturday = (16/100) × 10500 = 1680

The ratio of vanilla cakes sold to chocolate cakes sold on Saturday = 4 ∶ 3

The number of vanilla cake sold = (4/7) × 1680 = 960

The number of chocolate cake sold = 1680 - 960 = 720

The total sale = (960 × 8) + (720 × 15) = 7680 + 10800 = 18480

∴ The total amount earned (in Rs.) by selling all vanilla cakes and chocolate cakes on Saturday is Rs. 18480

Given:

Marked price = 20% higher than the cost price

Discount = 10%

Formula used:

S.P. = [(100 - Discount%)/100] × C.P.

Gain% = [(S.P. - C.P.)/C.P.] × 100

Where, C.P. = Cost price; S.P. = Selling price

Calculation:

Let, the cost price = Rs. 100

So, the marked price = 100 + (20% of 100) = Rs. 120

Then, the selling price = 120 × (90/100) = 108

Gain percentage = [(108 - 100)/100] × 100 = 8%

∴ The gain percentage is 8%

Shortcut Trick

A shopkeeper allows a discount of m% on a article and mp of the article is r% more than the cp then

Profit%=$[\frac{r \times (100-m)}{100}-m]$

here r = 20,m = 10

⇒ $[\frac{20 \times (100-10)}{100}-10]$

⇒ 8%

∴ The gain percentage is 8%

Given:

The given number = 8A5146B

Concept used:

Divisibility rule of 8: If the last three digits of a number is divisible by 8, the number will be divisible by 8

Divisibility rule of 11: The provided integer is divisible if the difference between the sum of the digits at odd places and the sum of the digits at even places is 0 or divisible by 11.

Calculation:

8A5146B is divisible by 88

So, 8A5146B is divisible by 8 and 11

⇒ 46B should be divisible by 8

Put B = 4, 464 is divisible by 8

Hence, B = 4

Now, 8A51464 should be divisible by 11

⇒ (8 + 5 + 4 + 4) - (A + 1 + 6) should be divisible by 11

⇒ 21 - (A + 7) should be divisible by 11

⇒ 14 - A should be divisible by 11

Put A = 3 then, 14 - 3 = 11 which is divisible by 11

So, A = 3

∴ AB = 3 × 4 = 12

∴ The value of AB is 12

Given:

∠ADC = ∠BAC

CA = 15 cm and CD = 9 cm

Concept used:

If Two triangles are similar then, their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion)

Calculation:

In ΔCAB and ΔCDA,

∠BAC = ∠ADC (Given)

∠ACB = ∠ACD (Common)

So, ΔCAB ∼ ΔCDA   (by AA similarity)

Then, CA/CB = CD/CA

⇒ 15/CB = 9/15

⇒ CB = (15 × 15)/9 = 25

∴ The value of CB (in cm) is 25 cm

Given:

x + y + z = 18, xyz = 81 and xy + yz + zx = 90

Formula used:

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

Calculation:

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

⇒ x3 + y3 + z3 - (3 × 81) = 18 [18² - (3 × 90)]

⇒ x3 + y3 + z3 - 243 = 18 (324 - 270)

⇒ x3 + y3 + z3 - 243 = 18 × 54

⇒ x3 + y3 + z3 = 972 + 243 = 1215

⇒ x3 + y3 + z3 + xyz = 1215 + 81 = 1296

⇒ x3 + y3 + z3 + xyz = 6⁴

⇒ $\sqrt[4]{x^3+y^3+z^3+xyz}$ = 6

∴ The value of $\sqrt[4]{x^3+y^3+z^3+xyz}$ is 6

Shortcut Trick

Total efficiency = 2 + 1 + 3 = 6

The time required = 18/6 = 3 minutes

∴ All punctures can make the tyre flat in 3 minutes

Alternate Method

Given:

The first puncture alone would have made the tyre flat in 9 minutes

The second puncture alone would have made the tyre flat in 18 minutes

The third puncture alone would have made the tyre flat in 6 minutes

Calculation:

In 1 minute, the first puncture can make (1/9)th of the tyre flat

In 1 minute, the second puncture can make (1/18)th of the tyre flat

In 1 minute, the third puncture can make (1/6)th of the tyre flat

In 1 minute, the all tyres can make (1/9) + (1/18) + (1/6) = (1/3)th of the tyre flat

Total required time to flat = 3 minutes

∴ All punctures can make the tyre flat in 3 minutes

Given:

The average of sixteen numbers = 48

The average of the first six numbers = 45

The average of the last seven numbers = 53

Concept used:

Sum of the terms = Average × Number of the terms

Calculation:

Let, the ninth number = x

So, seventh number = x + 3; eighth number = x + 7

Then, x + (x + 3) + (x + 7) = (16 × 48) - [(6 × 45) + (7 × 53)]

3x + 10 = 768 - (270 + 371)

3x + 10 = 768 - 641

3x = 768 - 641 - 10 = 117

x = 117/3 = 39

∴ The ninth number = 39

∴ The seventh number = 39 + 3 = 42

The average = (39 + 42)/2 = 81/2 = 40.5

∴ The average of the ninth and seventh numbers is 40.5

Given:

A spends 65% of his income

His income is increased by 20.1% and his expenditure is increased by 20%

Concept used:

The gain percentage of savings = [(New savings - Old savings)/Old savings] × 100

Formula used:

Let, the income = Rs. 100

So, the expenditure = Rs. 65; Savings = (100 - 65)% = 35%

His new income = 100 + (20.1% of 100) = Rs. 120.1

His new expenditure = 65 + (20% of 65) = Rs. 78

The new savings = 120.1 - 78 = Rs. 42.1

The gain percentage of savings = [(42.1 - 35)/35] × 100 = 20.28...% ≈ 20.3% (correct to one decimal place)

∴ His saving increases by 20.3%

Given:

A man bought toffees at 3 for a rupee

Formula used:

S.P. = [(100 + Profit%)/100] × C.P.

Where, C.P. = Cost price; S.P. = Selling price

Calculation:

The cost price of 1 toffee = Rs. 1/3

The required selling price of 1 toffee = (1/3) × (150/100) = Rs. 1/2

At the price of Rs. 1/2 we get 1 toffee, then at the price of Rs. 1 we can get $\frac{1}{\frac{1}{2}}$ = 2 toffee

∴ The total 2 toffees for a rupee must be sold to gain 50%

Given:

(cos6 θ + sin6 θ – 1) (tan2 θ + cot2 θ + 2) + 3

Calculation:

(cos6 θ + sin6 θ – 1) (tan2 θ + cot2 θ + 2) + 3

Put θ = 45°

(cos6 45° + sin6 45° – 1) (tan2 45° + cot2 45° + 2) + 3

⇒ [($1\over{\sqrt2}$)⁶ + ($1\over{\sqrt2}$)6 - 1] (1² + 1² + 2) + 3

⇒ [$1\over8$ + $1\over8$ - 1] (1 + 1 + 2) + 3

⇒ [${1+1-8}\over8$] × 4 + 3

⇒ -$3\over4$ × 4 + 3 = - 3 + 3 = 0

∴ The expression (cos6 θ + sin6 θ – 1)(tan2 θ + cot2 θ + 2) + 3 is equal to 0.

Alternate Method(cos6 θ + sin6 θ – 1)(tan2 θ + cot2 θ + 2) + 3

⇒ [(cos2 θ)³ + (sin2θ)3 – 1)](sin2 θ/ cos2 θ+ cos2θ/sin2 θ + 2) + 3

⇒ [{(cos2 θ +sin2θ)(cos4 θ +sin4θ -  sin2θ . cos2 θ) – 1)}(sin4 θ + cos4θ + 2 sin2θ . cos2 θ)/sin2θ . cos2 θ] + 3

⇒ [{(1)(cos4 θ +sin4θ -  sin2θ.cos2 θ) – 1)}(sin4 θ + cos4θ + 2 sin2θ . cos2 θ)/ sin2θ.cos2 θ] + 3

⇒ [{(1)((cos2 θ)² +(sin2θ)² - sin2θ.cos2 θ) – 1)}((sin4θ)2  + cos2 θ)2 + 2 sin2θ . cos2 θ)/ sin2θ.cos2 θ] + 3

⇒ [{((cos2 θ + sin2θ )2 -  2 sin2θ.cos2 θ -  sin2θ.cos2 θ) – 1)}(cos2 θ + sin2θ )2 -  2 sin2θ.cos2 θ + 2 sin2θ.cos2 θ)/ sin2θ.cos2 θ] + 3

⇒ [{((1)2 -  3 sin2θ.cos2 θ – 1)}(1)2 /sin2θ.cos2 θ] + 3

⇒ [(1 -  3 sin2θ.cos2 θ – 1)(1 /sin2θ.cos2 θ)] + 3

⇒ [(- 3sin2θ.cos2 θ)/(sin2θ.cos2 θ)] + 3 = -3 + 3 = 0

∴ (cos6 θ + sin6 θ – 1)(tan2 θ + cot2 θ + 2) + 3 =  0

The correct answer is 'No improvement required'.

Key Points

• The given sentence is grammatically correct.
• Here, 'Many a' makes the sentence singular.
• Hence, a singular auxiliary verb is used after it.
• In the given sentence 'has' is a singular helping verb.
• Thus, the correct answer is Option 1.
  

Correct Sentence: Many a man has succumbed to his temptations.

The correct answer is 'have respond'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'have responded' should be used instead of 'have respond'.
• In the given sentence 'respond' must be changed into 'responded' because we use 'should have + past participle' to talk about things we regret. 
• Example: I got really wet walking home last night, I should have taken an umbrella.
• 'Should + have' is followed by 'past participle'.
• Thus, the correct answer is Option 3.
  

Correct Sentence: You should have responded to my query sooner.

The correct answer is 'Karan pushed Rohan into the pool.'

Key Points

• The given sentence is in Passive Voice. As per the given question, we have to change it into Active Voice.
• The structure of the given sentence is as follows:
• Subject + V2 + Object. (Active Voice)
• Subject (objective case) + was/were + V3 + Object (subjective case). (Passive Voice)
• Example:
• Their cousin showed them some rare photographs. (Active Voice)
• They were shown some rare photographs by their cousin. (Passive Voice)
• The subject of the given sentence is 'Rohan'.​​
• The object of the given sentence is 'Karan'.
• The subject will be put in place of the object and the object will be put in place of the subject.
• And 'was pushed' will be changed into 'pushed'.
• Lastly, the preposition 'by' will be removed. 
  

Correct Sentence: Karan pushed Rohan into the pool.

The correct answer is 'A beautiful beaded curtain is being made by her.'

Key Points

• The given sentence is in the Active Voice. As per the given question we have to change the sentence into Passive Form.
• The given sentence is an example of 'present continuous'.
• The structure of these kinds of sentences is:
• Subject + is/am/are + V1 + ing + Object. (Active Voice)
• Subject(Objective Case) + is/am/are + being+ V3 + by + Object (subjective case). (Passive Voice)
• Example:
• He is riding a bike. (Active Voice)
• A bike is being ridden by him. (Passive Voice)
• The subject of the given sentence is 'She' and the object of the given sentence is 'A beautiful beaded curtain'.
• The subject will be put in place of the object and the object will be put in place of the subject.
• Here, 'is making' will be changed into 'is being made'.
• The preposition 'by' will be used in the end.
  

Correct Sentence: A beautiful beaded curtain is being made by her.

The erroneous part is 'were not perturbed'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'was not perturbed' should be used instead of 'were not perturbed'.
• In the given sentence 'the crew of sailors' is a collective noun.
• If the collective noun refers to the group as a unit, then it takes a singular verb. If it refers to the individuals in the group or the parts that make up the group, then the verb should be plural.
• In the given sentence the collective noun is referring to a single group.
• Exaple: A huge swarm of locusts has destroyed the crops.
• Thus, the correct answer is Option 3.
  

Correct Sentence: The crew of sailors was not perturbed by the strong gale.

The correct answer is 'Acumen'.

Key Points

• The most appropriate word for the given group of words is 'Acumen'.
• It means 'the ability to understand and judge things quickly and clearly'. (स्थिति को तुरंत और स्‍पष्‍टता से समझ लेने की योग्‍यता; विदग्‍धता, कुशाग्रबुद्धि)
• Example: business/financial acumen...
  

Correct Answer: Acumen

Key Points

Let's look at the meaning of other words:

• Experience: the things that you have done in your life; the knowledge or skill that you get from seeing or doing something. (जीवन में किए गए काम; किसी काम कों देखने अथवा करने से प्राप्त ज्ञान अथवा कौशल, अनुभव, तजुरबा)
• Estimation: opinion or judgment. (मत, विचार या परख)
• Knowledge: knowledge (of about something) information, understanding, and skills that you have gained through learning or experience. (शिक्षा या अनुभव से प्राप्‍त जानकारी, समझ और कौशल)

The erroneous word is "Exclaimation".

Key Points

• Among the given Options the incorrectly spelled word is 'Exclaimation'.
• Its correct spelling is 'Exclamation'.
• Exclamation! is a short sound, word, or phrase that you say suddenly because of strong emotion, pain, etc
• Example: ‘Ouch!’ is an exclamation.
• ​Thus, the correct answer is option 2.
  

Additional Information

• Let's understand the meaning of the other options :
• Correspondence: the action of writing, receiving, and reading letters, especially between two people.
• Disciplinarian: a person who believes in or practices firm discipline.
• Miscellaneous: consisting of many different types of things.

The correct answer is 'The teacher advised her students to work hard for their exams.'

Key Points

• The given sentence is in Direct Speech. As per the question we have to change it into Indirect Speech.
• The process of transformation is as follows:
• The given sentence is an example of an imperative sentence.
• Let's look at the rules of transformation:
• While changing the narration of an imperative sentence, we need to follow the given steps:
• The notion of the given sentence is 'advise'.
• The conjunction 'to' should be used in place of a comma (,) and inverted commas (“ ”). 'said' will be changed into 'advised'.
• 'to' is followed by 'V1'.
• 'you' will be changed into 'her' and 'your' will be changed into 'their' because second-person pronouns are changed according to the object of the reporting verb.
• Example:
• The queen said to her servant, "Cook me some delicious food today." (Direct Speech)
• The queen ordered her servant to cook her some delicious food that day. (Indirect Speech)

Correct Sentence: The teacher advised her students to work hard for their exams.

The erroneous part is 'confirm me whether you'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'confirm whether you' should be used instead of 'confirm me whether you'.
• The pronoun 'me' cannot be the direct object of the verb 'confirm' and hence, it must be removed.
• Thus, the correct answer is Option 3.
  

Correct Sentence: The manager said, "Could you please confirm whether you have received all the items that you had ordered?"

The correct answer is 'Careful'.

Key Points

• The most appropriate antonym of the given word 'Negligent' is 'Careful'.
• Negligent: failing to take proper care over something. (किसी चीज की उचित देखभाल करने में असफल होना)
• Example: She was negligent in her work.
• Careful: thinking about what you are doing so that you do not have an accident or make mistakes, etc. (सावधान, ख़बरदार, सतर्क)
• Example: Be careful! There's a car coming.
  

Correct Answer: Careful.

Additional Information

• Let's look at the meaning of other words:
• Faithful: always staying with and supporting a person, organization or belief. [(व्‍यक्ति, संस्‍था, मत आदि के प्रति) सच्‍चा और निष्‍ठावान]
• Indifferent: not interested in or caring about somebody/something. (व्‍यक्ति या वस्‍तु में रुचि या सोच-विचार से रहित; उदासीन)
• Strange: unusual or unexpected. (असामान्‍य या अप्रत्‍याशित; विचित्र; अजीब)

The correct answer is 'DBAC'.

Key Points

• The given question is an example of a Para Jumble.
• We know that the first statement of a para jumbled question is usually an independent general statement, a noun, a universal fact, starting of an incident, or it starts with 'most' or 'once'.
• Sentence D will be the first sentence because it is an introductory sentence that tells us about child-rearing which actually varies from culture to culture.
• Sentence B will be the following sentence because it is connected with the previous sentence and it tells us how a child is cared for in rural communities.
• Sentence A will be the following sentence because it tells us how rural and developed societies vary.
• Lastly, Sentence C will be used.
• Thus, the correct sequence is:
• D: The practices of child rearing vary from culture to culture.
• B: In rural communities, the customs are more uniform.
• A: But, in developed societies, the childhood and adolescence is extended.
• C: This provides more opportunities for education and character development.
  

Correct Sequence: The practices of child rearing vary from culture to culture. In rural communities, the customs are more uniform. But, in developed societies, the childhood and adolescence is extended. This provides more opportunities for education and character development.

The erroneous part is 'five month old'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'five months old' should be used instead of 'five month old'.
• When 'five months' is used as an adjective it is in the singular, because English adjectives are almost never plural.
• If you were to use it as a predicate, then the plural would apply.
• 'five' refers to the plural numeral. Hence, 'months' should be used.
• Example:
• A five-month internship.
• The internship lasts five months.
• Thus, the correct answer is Option 1.
  

Correct Sentence: My neighbour's grandson is only five months old.