SSC GD Constable Previous Year Paper (Held on: 16th November 2021 Shift 2)

The logic followed here is :-

First number² + (First number × 4)

20 : 480 → 20² + (20 × 4) = 400 + 80 = 480

Similarly,

25 : ? → 25² + (25 × 4) = 625 + 100 = 725

Hence, the correct answer is "725".

The logic followed here is :-

Experimenter conducts or do variety of experiments in Lab

Similarly,

Chef do variety of dishes in 'Kitchen'.

Hence, the correct answer is "Kitchen".

The logic followed here is :-

Six friends are sitting in a straight line.

1. E is 4th from the right.

2. E is between B and D.

Case (i) :

Case (ii) :

3. D is between E and C and D is adjacent to C.

Case (i) :

Case (ii) :

4. F is adjacent to C.

So, here case (i) gets eliminated.

5. A is adjacent to B.

∴ Here, 'C' is sitting between F and D.

Hence, the correct answer is "C".

By using BODMAS RULE :

 

‘A’ denotes ‘addition’, ‘B’ denotes ‘multiplication’, ‘C’ denotes ‘subtraction’, and ‘D’ denotes ‘division’,

 

Given equation is : 100 D (1 B 4) A 2 B (13 A 11) C 3 B (17 C 12)

By inserting the given symbols the equation formed is as follows :

100 ÷ (1 × 4) + 2 × (13 + 11) - 3 × (17 - 12)

= 100 ÷ (1 × 4) + 2 × (13 + 11) - 3 × (17 - 12)

= 100 ÷ 4 + 2 × 24 - 3 × 5

= 25 + 2 × 24 - 3 × 5

= 25 + 48 - 15

= 73 - 15

= 58

Hence, the correct answer is "58".

The relation followed from given statements is as follows :

Family chart :

Family diagram :

1) Aditi is the daughter of Sanket.

2) Vritti is the daughter of Ankit.

3) Kriti is the mother of Mahi.

4) Neeta is Sanket's wife.

5) Neeta is the mother-in-law of Vritti's mother Kriti.

By checking the given options :

1. Ankit is the father of Mahi → True (From above diagram) 2. Vritti is the sister of Mahi → True (From above diagram) 3. Aditi is the daughter of Neeta → True (From above diagram) 4. Kriti is the daughter of Sanket → False (Here Kriti is Daughter-in-law of Sanket from above diagram hence, False)

∴ Here, 'Kriti is daughter of Sanket' is not correct from given statements.

Hence, the correct answer is "Kriti is the daughter of Sanket".

The logic followed here is :-

1) (46, 65, 82)

2) (54, 73, 90)

3)  (21, 40, 57)

4)  (39, 48, 75)

∴ Here, '(39, 48, 75)' is different from other three alternatives.

Hence, the correct answer is "(39, 48, 75)".

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

• One sided arrow present in pentagon moves one step clockwise.
• From 1st figure to 2nd figure an one sided arrow line moves one step clockwise and represents with two sided arow line.
• From 2nd to 3rd figure an two sided arrow line moves one step clockwise and represents with one sided arrow line.
• From 3rd to 4th figure an one sided arrow line moves one step clockwise and represents with two sided arow line.

Hence, the correct answer is "Option 4".

Given : A _ _ B _ _ A B _ C A _ B B C

By checking options and substituting accordingly.

1. B, C, A, A, A, B → A B C B A / A A B A C / A B B B C 2. B, A, B, A, C, B → A B A B B / A A B C C / A B B B C 3.  A, B, C, A, B, A → A A B B C / A A B B C / A A B B C 4. B, B, C, C, A, B → A B B B C / C A B A C / A B B B C

Option (3) gives a pattern of : A A B B C - A A B B C - A A B B C

Hence, the correct answer is " A, B, C, A, B, A".

The least possible Venn diagram for the given relations is as follows :-

• Some Employee work in School.
• Some Teacher work in school.
• All Teacher are Employee.

Hence, the correct answer is "Option 4".

Note:

• For this question, a discrepancy was found in the question/answer in the exam. So, this question was ignored for all candidates.
• Because of the discrepancy, we have altered the question and changed the second option.

The logic followed here is :-

'MANGO' is written as 'QERKS'.

and

'APPLE' is written as 'ETTPI'.

Similarly,

'GUAVA' will be written as :

Hence, the correct answer is "KYEZE".

The logic followed here is :-

All letters are arranged in reverse dictionary order (i.e. decreasing order of positional value).

ZYGOTE : ZYTOGE

Similarly,

SEQUENCE : ?

Hence, the correct answer is "USQNEEEC".

Area of Square (A₁) = S² ................... (1)

Length of diagonal (d₁) = $\sqrt{2}$ S .............. (2)

From eq(2) → S = d₁/$\sqrt{2}$

Area of square (A₁) = (d₁/$\sqrt{2}$)²

A₁ = (d₁)²/2 ........... (3)

∴ The diagonal of the square increased by 4cm and its area increased by 56cm².

Increased diagonal of square (d₂) = d₁ + 4 ........... (4)

Increased area of square (A₂) = A₁ + 56 .......... (5)

A₂ = (d₂)²/2

From eq (3) we get, 

A₂ = (d₁ + 4)²/2 .......... (6)

From eq (4) we get,

A₂ - A₁ = 56 .......... (7)

Substitute eq (3) and eq (6) in eq (7)

⇒ (d1 + 4)2/2 - (d1)2/2 = 56

⇒ (d₁ + 4)² - (d1)2 = 56 × 2

⇒ (d1 + 4)2 - (d1)2 = 112

⇒ (d₁)² + 8d₁ + 16 - (d1)2 = 112

⇒  8d1 + 16 = 112

⇒  8d1 = 112 - 16

⇒  8d1 = 96

⇒ d₁ = 12

∴ d₂ = d₁ + 4

d₂ = 12 + 4 = 16

Ratio of the new area of the square to the initial area of the square = A₂ / A₁

A₂ / A₁ = ((d2)2/2) / ((d1)2/2 )

A2 / A₁ = (16² / 2) / (12² / 2)

A2 / A₁ = (256 / 2) / (144 / 2)

A2 / A₁ = 128 / 72

A2 / A₁ = 16 / 9

∴ Here, the Ratio of the new area of the square to the initial area of the square A₂ : A₁ = 16 : 9

Hence, the correct answer is "16 : 9".

The logic followed here is :-

Hence, the correct answer is "59".

The logic followed here is :-

Hence, the correct answer is "125".

The logic followed here is:

Hence, the correct answer is "XDB".

The correct mirror image of the given combination when the mirror is placed at 'PQ' as shown below :

Hence, the correct answer is "Option 1".

The image shown below is as follows :

Hence, the correct answer is "Option 2".

The logic follows here is :-

GAME is written as TUZANOVW.

and

CAR is written as XYZAIJ.

Similarly,

POST will be written as :

Hence, the correct answer is "KLLMHIGH".

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

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

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

Below are the opposite surfaces shown :

 

Note :- Two opposite face are never seen together or adjacent to each other.

Given :

By option elimination method:

• Figures A and C cannot be two positions of the same dice. So, option 4 is eliminated.
• Also, 4 and 6 will be adjacent to 1 if the question figure is folded to form a cube. So, either figure A or figure C has to be a part of the final answer. Thus, only option 2 satisfies this condition.

Hence, the correct answer is "Only B ,C and D".

Mistake Points

The question figure of unfolded dice can be represented as follows

The Figure A is as follows

As seen from above figures, the sequence in the Figure A is opposite to the sequence in the question figure.

Thus, the dice shown in Figure A can't be formed by folding the given sheet along the lines.

The arrangement of the given words in an English dictionary order is as follows :-

DE is common in all the words.

5. Dereliction
6. Dermatitis
7. Derogation
8. Descendant
9. Desistance

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

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

Hence, the correct answer is "Option 4".

The logic followed here is :-

1) FDB

2) OMK

3) JHF

4) USP

∴ Here, 'USP' is different from other three alternatives

Hence, the correct answer is "USP".

The logic followed here is :-

'PHENYL' is coded as ‘9-11-17-8-5-13’.

and

'COLONY' is coded as ‘6-12-13-12-8-5’

Similarly,

'COLONEL' will be coded as :

Hence, the correct answer is "6-12-13-12-8-17-13".

The logic followed here is :-

1. O, P, Q, R, S, T and U are sitting in a row facing north. 2. P, who is on the extreme right, is sitting to the immediate right of O.

3. Q is sitting in between R and O.

4. S is sitting to the immediate left of R.

5. U is sitting to the immediate right of T.

∴ Here, 'R' is sitting in middle of the row.

Hence, the correct answer is "R".

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

Conclusions:

I. All cats are plants → False (As Some cats are animals and All animals are plants so, some cats can be plants but all cats are plants is definitely False)

II. Some plants are cats → True (As All animals are plants and Some cats are animals so, Some plants are cats it is definitely true)

III. Some plants are animals → True (As All animals are plants so, Some plants are animals it is definitely true)

IV. All animals are cats → False (Some cats are animals so, All animals are cats it is definitely false)

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

The correct answer is Red Fort.

Key Points

• Red Fort was the main residence of the emperors in the Mughal dynasty for nearly 200 years.
• The Red Fort of Agra was founded by Akbar.
• Red Fort at Delhi was built by Shah Jahan.

Additional Information

The correct answer is Ranjan Gogoi.

Key Points

• Former Chief Justice of India Justice Ranjan Gogoi released the Assamese version of the book 'Courts of India: Past to Present' in Guwahati on 10 Nov 2019.
• The book has been published by the Publication Division and explains the Indian justice system.
• The book has captured the historical developments which took place in the history of the nation's courts.

Additional Information

• Books written by Shashi Tharoor are Inglorious Empire, Why I am a Hindu, Pax Indica, Bookless in Baghdad.
• Satyarth Nayak is known for his bestselling novel The Emperor's Riddles, for authoring the biography of Sridevi and for scripting Sony's historical television epic Porus.
• I Am HIV Positive, So What? A World Champion’s Fight Against Drugs, Disease and Discrimination book is written by Jayanta Kalita.

The correct answer is Chandragupta - Bindusara - Ashoka - Brihadratha.

Key Points

• The Mauryan Empire was the first pan-India empire formed around 322 BCE and ended in 185 BCE.
• It spanned central and northern India as well as over parts of modern-day Iran.
• The chronological order of the rulers of the Mauryan empire is:
• The empire was founded by Chandragupta Maurya in 322 BCE.
• The second ruler was Bindusara who ruled from 297 Bc to 273 BC.
• Ashoka was the most popular ruler of the dynasty who ruled from 268 to 232 BCE.
• Brihadratha was the last ruler of the Mauryan dynasty ruled from 187–185 BCE

Additional Information

• Mauryan Empire
• The Maurya dynasty (321–185 BC) was a powerful dynasty in ancient India.
• The Maurya dynasty ruled India for 137 years.
• The credit for its establishment is given to Chandragupta Maurya and his minister Chanakya (Kautilya).
• This empire started from the plains of the Ganges river (today's Bihar and Bengal) in the state of Magadha in the east.
• Its capital was Pataliputra (near present-day Patna city).
• Chandragupta Maurya established this empire in 321 BC and rapidly expanded his empire towards the west.
• The Mauryan Empire grew and thrived during the Iron Age.
• He took advantage of the differences between several small regional kingdoms that had arisen after Alexander's invasion.
• By 316 BC, the Maurya dynasty had occupied the whole of North Western India.
• The Maurya dynasty expanded on a large scale in the reign of the Chakravarti emperor Ashoka.
• Due to Emperor Ashoka, the Maurya Empire became the greatest and most powerful and became famous all over the world.

The correct answer is golf.

Key Points

• Tvesa Malik is an Indian golf player.
• She is from Gurugram, Haryana.
• She has won the 4th leg of the Hero Women’s Golf Tour.
• Gursimar Badwal is also an Indian golf player.

Additional Information

The correct answer is Anurag Singh Thakur.

Key Points

• The Minister of Youth Affairs and Sports (MYAS), Shri Anurag Singh Thakur would launch the Fit India Mobile Application on 29th August 2021.
• The app would be available on both the Android and the iOS platforms and would work even on basic smartphones.
• The Fit India Movement was launched on 29th August 2019 with the vision of making India a Fit and Healthy Nation.

Additional Information

• Youth Affairs and Sports Minister Anurag Singh Thakur launched six new and rare Reference Materials (RMs) on 3 April 2022.
• They have been developed by National Dope Testing Laboratory with the National Institute of Pharmaceutical Education and Research-Guwahati.
• These are the purest form of chemicals required for anti-doping analysis in all WADA-accredited laboratories across the world.
• Nisith Pramanik is an Indian politician and a Union Minister of State, Ministry of Home Affairs and Minister of State, Ministry of Youth Affairs and Sports from West Bengal.
• Shri Ravi Mittal took charge as Chairperson of the Insolvency and Bankruptcy Board of India in New Delhi.
• Usha Sharma served as the Director General of the Archaeological Survey of India from 2017 - 2020.

The correct answer is Football.

• La Liga Trophy is associated with Football.

Additional Information 

The correct answer is South Africa.

Key Points

• The ICC U19 Cricket World Cup 2020 held in South Africa.
• Bangladesh won the ICC U19 Cricket World Cup 2020.
• 2018 ICC under-19 cricket world cup was held in New Zealand.
• India won the 2018 ICC Under-19 Cricket World Cup.
• Australia was the Runner up of the 2018 ICC under-19.

Additional Information

• The ICC Under-19 Cricket World Cup is an international cricket tournament organized by the International Cricket Council (ICC).
• It is contested by national under-19 teams.
• The first edition was held in 1988, as the Youth World Cup.
• It was not staged again until 1998. Since then, the World Cup has been held as a biennial event.
• India has won the World Cup on a record 5th times and India is the most successful team.

The correct answer is Kewal Kumar Sharma.

Key Points

• Kewal Kumar Sharma was appointed as the State Election Commissioner of Jammu and Kashmir on October 30, 2020.
• She who was serving as Adviser to Jammu and Kashmir Lt. Governor Manoj Sinha was appointed State Election Commissioner (SEC).
• Mr Sharma, a 1983 batch IAS officer, was appointed as Adviser to the L-G in November 2019.
• He has also served as Chief Secretary of Delhi and Goa.

Additional Information

• Jammu and Kashmir Lieutenant Governor Manoj Sinha has announced a committee to work out modalities for the economic revival of the union territory and extending support to its business community.
• The announcement was made during an interaction with the representatives of the Kashmir Chamber of Commerce and Industry (KCCI) at the Raj Bhavan auditorium on 17 August.
• The interaction was organised to get a first-hand appraisal of the issues and problems of the business community.
• The committee will be headed by the advisor to the Lt Governor, Kewal Kumar Sharma.

The correct answer is Arthur Crawford.

Key Points

• Arthur Crawford was appointed as the first Municipal Commissioner of Bombay in 1865.
• Arthur Travers Crawford was a British government employee.
• Crawford was famous as an able administrator as well as for his allegedly, underhand financial dealings.
• During the legal training of Arthur Crawford, he resolved to rebuild the municipality of Bombay and even put forward his proposal.
• He passed the Municipal Corporation Act of 1872, and since then he is known as the father of the Mumbai Municipal Corporation.
• In 1873, he became the municipal commissioner of the Bombay Municipal Corporation.
• He founded the Bombay Presidency Association in 1885.

Additional Information

• The Hunter Commission of 1882 was presided by Sir William Hunter and was appointed by Lord Ripon, the then Viceroy of India.
• Charles Joseph Atkinson is a British former boxer, fight promoter, manager, agent and trainer/coach.
• Sir Ralph Howard Fowler OBE FRS was a British physicist and astronomer.

The correct answer is Jeevan Pramaan.

Key Points

• Jeevan Pramaan is a biometric-enabled digital service for pensioners launched by the Government of India.
• The Jeevan Pramaan scheme provides the benefit of pension to employees of Central Government, State Government or other Government organizations by providing them with a digital certificate as pension proof.
• The total number of pensioners exceeds 50 lakhs and also includes Army and Defense personnel.

Additional Information

• According to the Pradhan Mantri Mudra Yojna, there are three categories of schemes/ loans which are as follows:
• Shishu- Loan of up to Rs. 50,000
• Kishore-  Rs. 50,000 to 5.0 Lakhs
• Tarun- Rs 5.0 Lakhs to 10.0 Lakhs
• ​MUDRA stands for Micro Units Development & Refinance Agency Ltd., is a financial institution set up by the Government of India for the development and refinancing of micro units enterprises.
• Pradhan Mantri Jan-Dhan Yojana( PMJDY)
• It was launched on 28 August 2014 from New Delhi.
• ​It is the National Mission for Financial Inclusion launched by the Government Of India.
• It is started with the aim to provide universal banking services to every unbanked adult.
• There is no minimum limit to maintaining an account balance(commonly known as a zero balance account) opened under PMJDY.
• The Ministry of Finance is the nodal ministry for PMJDY.

The correct answer is Frog.

Key Points

• The frog breathes through its skin.
• Respiration is the process of exchanging gases in all life forms between an organism and its environment, which can occur in different ways, either independently or in tandem.
• The gills of a newly hatched Tadpole are external. When water passes over these gills, they take in oxygen.
• The gills are absorbed by the body as the tadpole matures, and become an internal part of the anatomy of the tadpole.
• Frogs can live both on land and in freshwater and belong to the class Amphibia of phylum Chordata.
• Frogs respire on land and in the water by two different methods. In water, skin acts as a respiratory organ(i.e cutaneous respiration) by diffusion.

​

Additional Information

Respiration is of 2 types:

The correct answer is Sulphur.

Key Points

• Sulphur is a poly-atomic element.
• It contains more than two atoms of the same element joined together by covalent bonds.
• Eg: Sulphur, Phosphorous, and Selenium

Additional Information

• Atomicity: 
• The present number of atoms in any molecule of an element is called its atomicity.
• For example, oxygen is diatomic & helium is monoatomic.
• Types of Atomicity: 
• Monoatomic – when an element consists of a single atom. Example – all kinds of metals in nature.
• Diatomic – The element which consists of two atoms. Example – all types of gases.
• Triatomic – The element which consists of three atoms.
• Tetra-atomic – The element, consists of four atoms.
• Poly-atomic – The element consists of more than two atoms.

The correct answer is Tamil Nadu.

Key Points

• Hogennekkal falls is located in Dharmapuri district of the state of Tamilnadu.
• It is formed on the Kaveri River.
• Kaveri River flows through the states of Karnataka and Tamilnadu and empties in the Bay of Bengal.

Additional Information

• List of important waterfalls:

The correct answer is Tarun Chaudhri.

Key Points

• Wing commander Tarun Chaudhri became the first pilot of the Indian Armed Forces (IAF ) to do a wingsuit jump.
• The jump was accomplished by Chaudhri from a Mi-17 helicopter at an altitude of 8500 feet.
• This is the first flying wingsuit jump demonstration at an organised gathering.
• The jump was undertaken during the Kargil Diwas celebrations at Air Force Station Jodhpur on 21-22 July 2019.

Additional Information

• Shital Mahajan Rane, is an Indian extreme sportsperson, skydiver and the holder of five world records and 14 National records in the sport.
• The first woman in the world to have executed a sky-dive from the North and South Poles.
• Archana Sardana is India's first female base jumper.
• Rachel Thomas is an American computer scientist and founding Director of the Center for Applied Data Ethics at the University of San Francisco.

The correct answer is Gorakhpur.

Key Points

• Recently, the Uttar Pradesh Cabinet approved a proposal to set up a zoological garden in Gorakhpur on 121 acres.
• A plan to set aside Rs 234 crore for the development of a zoological garden named after Shaheed Ashfaqullah Khan was approved by the Uttar Pradesh state government on 8 January 2020.
• It aims to attract tourists and to increase employment opportunities.

Additional Information 

• Ashfaqulla Khan was a freedom fighter in the Indian independence movement.
• He was born on 22 October 1900 in Shahjahanpur, Uttar Pradesh.
• He participated in Gandhi's non-cooperation movement (NCM), Chauri Chaura incident.
• Ashfaqulla Khan formed the Hindustan Republican Association (HRA) along with Ram Prasad Bismil.
• At present, there are two zoological gardens in Uttar Pradesh namely:
• Nawab Wajid Ali Shah Zoological Garden in Lucknow
• Kanpur Zoological Park in Kanpur

The correct answer is Potassium.

Key Points

• Potassium (K) is a most reactive metal and reacts vigorously with air and water.
• A large amount of heat is produced in their reaction.
• To avoid such accidents this metal is kept immersed in kerosene oil.
• Potassium undergoes a reaction with water similar to that of sodium; the products of the reaction are potassium hydroxide and hydrogen gas.
• This reaction releases a great deal of heat energy, often igniting the hydrogen gas that is produced.
• Sodium (Na) and Lithium (Li) are also very reactive to air and water and need to be stored under oil to prevent them from reacting with gases in the air and water.
• Caesium (Cs) is the most reactive of all metals.

Additional Information

• Metals react with water and oxygen present in the air.
• Metal with higher reactivity has vigorous reactions.
• For example, sodium catches fire in the air, hence it is kept in kerosene oil.
• Due to such reactivity of metals, most of the metals are not available in nature in a free state.
• They are present in form of their compounds (oxides, carbonates, sulphides etc,)
• Few metals which are least reactive are available in a free state.
• Such metals are gold, silver, Platinum

The correct answer is Chhattisgarh.

Important Points 

• Bhoramdeo Temple or the ‘Khajuraho of Chhattisgarh’, carved on the rocky stones in the Nagar style is an ancient Hindu temple dedicated to Lord Shiva.
• It is situated in the Kabirdham district of Chhattisgarh.
• Each year in the last week of March ‘Bhoramdeo Mahotsav’ is celebrated
• The temples are said to be built during the reign of King Ramchandra of the Nag Dynasty.
• It is similar to the Khajuraho temple and the Konarak Sun Temple.

The correct answer is Vardhamana Mahavira.

Key Points

• Vardhamana Mahavira was the son of a Chief of the Jnatrika (or Jhatrika) Kshatriya clan.
• He was the 24th Tirthankara of the Jain tradition.
• He was born at Kundagrama near Vaisali to Kshatriya parents Siddhartha and Trisala.
• Bimbisara was the contemporary of Vardhamana Mahavira.
• At the age of thirty, he became an ascetic and wandered for twelve years.
• In the 13th year of his penance, he attained the highest spiritual knowledge called Kevala Gnana.

Additional Information

The correct answer is Assam. 

Important Points

• Defence Minister Rajnath Singh gave away Best Tableaux awards for Republic Day Parade, 2020 in New Delhi on 28 Jan 2020.
• Assam's tableau which portrayed the unique craftsmanship and culture of the state has been chosen as the best tableau.
• The tableau of National Disaster Relief Force and Jal Shakti Mission were chosen as the best among the Ministries and Departments.

Additional Information

• Odisha and Uttar Pradesh were tied for the second position.
• The tableau of Odisha displayed the famous Rukuna Ratha Yatra of Lord Lingaraja while the tableau of Uttar Pradesh mirrored the cultural and religious tourism of the state with the theme 'Sarva Dharma Sama Bhav'.
• Assam: State Animal - Indian Rhinoceros
• State Bird - White-winged duck

The correct answer is uniform.

Key Points

• The acceleration of an object is said to be uniform when an object travels in a straight line and its velocity increases or decreases by equal amounts in equal intervals of time.
• A body is said to have a uniform acceleration when it travels in a straight line with its velocity increasing at equal intervals of time.
• For uniform acceleration, the displacement- time graph is a parabola of a symmetric displacement axis.
• An object is said to be with nonuniform acceleration if the velocity of the object changes by unequal amounts in equal intervals of time.
• Velocity-time graph for the Non-uniform acceleration is a curved line.

Additional Information

• Acceleration: The rate of change of velocity is called the acceleration of the body. i.e.,

$a = \frac{{{v_2} - {v_1}}}{{{t_2} - {t_1}}}$

• Where v2 = velocity of the object at t2 and v1 = velocity of the object at t1
• It is a vector quantity.
• Its direction is the same as that of change in velocity (Not of the velocity).

The correct answer is It drains into the Arabian Sea.

Key Points

• The Mahanadi river system is the third-largest river system in peninsular India.
• It is about 860 km long.
• It is the largest river in Odisha state.
• The word Mahanadi is made of the Sanskrit words Maha which mean great and Nadi which means river.
• The river is bounded by the Central India hills on the north, by the Eastern Ghats on the south and east, and by the Maikala range on the west.
• The river originates in the northern foothills of Dandakaranya, Raipur District of Chhattisgarh.
• It rises in the highlands of Chhattisgarh.
• The river is one of the major rivers of the peninsular rivers, in water potential and flood-producing capacity.
• Hence, the river is also known as the Sorrow* of Orissa.*
• The Mahanadi River flows through the states of Chhattisgarh and Odisha, Jharkhand, Maharashtra, and Madhya Pradesh.
• So, A part of its river basin lies in Maharashtra.
• It drains into the Bay of Bengal.
• Hence option 2 is an incorrect statement.

Additional Information

• Left bank Tributaries of the Mahanadi river are The Seonath, the Hasdeo, the Mand, and the Ib.
• Right bank Tributaries of the Mahanadi river are The Ong, the Tel, and the Jonk.
• Major projects on the Mahanadi River are The Hirakud Dam, The Gangrel Dam and The Dhudhwa Dam.

The correct answer is 2018.

Key Points

• Prime Minister Narendra Modi had launched the Ayushman Bharat - Pradhan Mantri Jan Aarogya Yojana from Ranchi in Jharkhand on 23rd September 2018.
• Over two crore people have availed treatment under Ayushman Bharat Pradhan Mantri Jan Arogya Yojana.
• The scheme, which is the world's largest health care program, provides a cover of up to Rs. 5 lakh per family per year for secondary and tertiary care hospitalization to over 10.74 crore poor and vulnerable families.
• It helps to reduce hospital expenditure and mitigate financial risk.
• It provides cashless and paperless access to services for the beneficiaries at the point of service.

Additional Information

• The insurance cost is shared by the centre and the state mostly in the ratio of 60:40.
• There are about 1,400 packaged rates for various medical procedures under the scheme.
• These packaged rates also mention the number of average days of hospitalization for a medical procedure and supporting documents that are needed.
• Under no circumstances can hospitals charge the beneficiary.
• The scheme also has prescribed a daily limit for medical management.
• National Health Agency has been constituted as an autonomous entity under the Society Registration Act, 1860 for effective implementation of PMJAY in alliance with state governments.
• This includes the formulation of PMJAY policies, development of operational guidelines, implementation mechanisms, coordination with state governments, and monitoring and oversight of PMJAY amongst others.

The correct answer is gross domestic product.

Key Points

• The money value of all the final goods and services produced within the country during a particular year is called Gross Domestic Product.
• The nominal gross domestic product is the gross domestic product (GDP) evaluated at current market prices.
• Real GDP, on the other hand, is calculated by taking a base year as a determinant.
• Real GDP adjusts for price changes due to inflation/deflation.
• The main difference between nominal GDP and real GDP is the adjustment for inflation.

Additional Information

• The average income received per person in a given area (city, region, world, etc in a given year is determined by per capita income (PCI) or average income.
• Net domestic product (NDP) is an annual measure of the economic output of a nation that is adjusted to account for depreciation.
• The National Income of any country means the complete value of the goods and services produced by any country during its financial year.

The correct answer is Right to property.

Key Points

• The right to property was deleted from the list of Fundamental Rights by the 44th Amendment Act, 1978.
• It is made a legal right under Article 300-A in Part XII of the Constitution. So at present, there are only six Fundamental Rights.
• Article 19 provided to all citizens the right to acquire, hold, and dispose of the property whereas Article 31 provides that "no person shall be deprived of his property save by authority of law."
• Later, in 44thAmendment of 1978 deleted the right to property from the list of fundamental rights.
• The right to property is no longer a fundamental right, however, it is still a constitutional right.

Additional Information

• Part III of the Indian Constitution guarantees six fundamental rights to all citizens:
• ​(a) Right to Equality (Articles 14–18),
• (b) Right to Freedom (Articles 19–22),
• (c) Right against Exploitation (Articles 23–24),
• (d) Right to Freedom of Religion (Articles25–28),
• (e) Cultural and Educational Rights (Articles 29–30), and
• (f) Right to Constitutional Remedies (Article 32)

The correct answer is 1956.

Key Points

• The Life Insurance Corporation of India Act was passed by the Parliament in the year 1956.
• The Life Insurance Corporation of India was founded when the Parliament of India passed the Life Insurance of India Act that nationalized the insurance industry in India.
• Life Insurance Corporation of India is an Indian state-owned insurance group and investment corporation owned by the Government of India.
• The Oriental Life Insurance Company, the first company in India offering life insurance coverage, was established in Kolkata in 1818.
• Surendranath Tagore had founded the Hindusthan Insurance Society, which later became Life Insurance Corporation.
• The LIC's executive board consists of Chairman, currently M R Kumar, and Managing Directors, Vipin Anand, T. C. Suseel Kumar, Mukesh Kumar Gupta, and Raj Kumar.

Shortcut Trick

Assume the Total quantity is 3 units (as denominator is 3).

Part 1 (2/3 of 3) = 2 units at +35% profit.

Part 2 (Remaining 1/3) = 1 unit at −10% loss.

Net Profit = (2 × 35) + (1 × −10) = 70 − 10 = 60.

Overall Profit % = 60 ÷ 3 = 20%.

∴ The correct answer is 20%.

Alternate Method

Given:

Quantity sold at profit = 2/3 | Profit = 35%

Quantity sold at loss = 1/3 | Loss = 10%

Formula Used:

Overall Profit/Loss % = (n₁ × p₁ + n₂ × p₂) ÷ (n₁ + n₂)

Calculations:

⇒ Let the Total Cost Price of all toys be ₹300.

⇒ Cost price of 2/3 toys = 2/3 × 300 = ₹200.

⇒ Cost price of remaining toys = 1/3 × 300 = ₹100.

⇒ Profit on first part = 35% of 200 = 200 × (35/100) = ₹70.

⇒ Loss on second part = 10% of 100 = 100 × (10/100) = ₹10.

⇒ Total Net Profit = Profit − Loss = 70 − 10 = ₹60.

⇒ Overall Profit % = (Total Profit ÷ Total CP) × 100

⇒ Overall Profit % = (60 ÷ 300) × 100 = 20%.

∴ The correct answer is 20%.

Additional Information

Weighted Average Method

When parts of a whole are sold at different profit/loss rates, the overall profit % is the weighted average: (Weight₁ × Rate₁ + Weight₂ × Rate₂) / Total Weight.

Net Profit and Loss

If the net result is positive, it is a Profit; if negative, it represents a Loss. Profit % = (Profit/CP) × 100.

Marked Price and Discount

Relationship between CP and MP: CP/MP = (100 − Discount%) / (100 + Profit%). This is useful when the shopkeeper offers a discount.

Given:

Three numbers are in the ratio 4 : 9 : 13 and their LCM is 2340.

Concept used:

LCM is the smallest common multiple of two or more numbers.

HCF is the largest number or quantity that is a factor of each member of a group of numbers.

Calculation:

Let, the HCF of the numbers = H

So, the three numbers are 4H, 9H, and 13H.

According to the question,

⇒ LCM (4H, 9H, 13H) = 2340

⇒ (4 × 9 × 13) × H = 2340

⇒ 468 × H = 2340

⇒ H = 2340/468

⇒ H = 5

∴ Their HCF is 5.

Shortcut Trick

Effective Compound Interest rate for 2 years = R + R + (R × R) ÷ 100.

Effective rate for 9% = 9 + 9 + (81 ÷ 100) = 18.81%.

Let the principal sum be P.

⇒ 18.81% of P = 3762

⇒ P = 3762 × (100 ÷ 18.81) = 20000

∴ The correct answer is Rs. 20,000.

Alternate Method

Given:

Rate of interest (R) = 9% p.a.

Time (n) = 2 years

Compound Interest (CI) = Rs. 3,762

Formula Used:

CI = P × [(1 + R ÷ 100)ⁿ − 1]

Calculations:

⇒ 3762 = P × [(1 + 9 ÷ 100)² − 1]

⇒ 3762 = P × [(109 ÷ 100)² − 1]

⇒ 3762 = P × [11881 ÷ 10000 − 1]

⇒ 3762 = P × [(11881 − 10000) ÷ 10000]

⇒ 3762 = P × [1881 ÷ 10000]

⇒ P = (3762 × 10000) ÷ 1881

⇒ P = 2 × 10000 = 20000

∴ The correct answer is Rs. 20,000.

Additional Information

Effective Rate of Compound Interest

For 2 years at R% per annum, the effective compound interest rate is calculated using the formula: R + R + (R² ÷ 100)%. This helps in quickly calculating the CI without deriving the total amount first.

Difference Between CI and SI for 2 Years

The difference between Compound Interest and Simple Interest on a principal P at rate R% for exactly 2 years is given directly by the formula: Difference = P × (R ÷ 100)².

Amount in Compound Interest

The total amount A after n years at compound interest is calculated using A = P(1 + R ÷ 100)ⁿ. The interest is then simply found by subtracting the original principal from the final amount.

Given:

SI = Rs. 3,040

Rate of interest = 8% p.a

Duration = 5 years

Concept used:

Simple Interest, SI = (P × R × T)/100

Amount = P + SI

Where, P = Principal amount, R = Rate of interest per year,

T = Time in years

Calculation:

Let, the sum = Rs. P.

According to the question,

⇒ (P × 8 × 5)/100 = 3040

⇒ P × 40 = 304000

⇒ P = 304000/40

⇒ P = 7600

∴ The sum is Rs. 7,600.

Shortcut Trick

Total time: A = 15 days, B = 10 days. Total work = LCM(15, 10) = 30 units.

Efficiencies: A = 2, B = 3. Together they did (2 + 3) × 4 = 20 units in 4 days.

Remaining work = 30 − 20 = 10 units, completed by C in 6 days → C's efficiency = 10 ÷ 6 = 5/3 units/day.

Target work = 70% of 30 = 21 units. Combined efficiency of B and C = 3 + 5/3 = 14/3 units/day.

Time taken by (B + C) = 21 ÷ (14/3) = (21 × 3) ÷ 14 = 4½ days.

∴ The correct answer is 4½ days.

Alternate Method

Given:

A's time for complete work = 6 × (5/2) = 15 days

B's time for complete work = 3 × (100/30) = 10 days

Let Total Work = LCM(15, 10) = 30 units.

Calculations:

⇒ Work done by (A + B) in 4 days = (2 + 3) × 4 = 20 units

⇒ Remaining work = 30 − 20 = 10 units

⇒ C completes 10 units in 6 days → Efficiency of C = 10 ÷ 6 = 5/3 units/day

⇒ Target work = 70% of 30 units = (70 ÷ 100) × 30 = 21 units

⇒ Combined efficiency of (B + C) = 3 + (5/3) = 14/3 units/day

⇒ Time taken by (B + C) = Target work ÷ Combined Efficiency

⇒ Time taken = 21 ÷ (14/3) = (21 × 3) ÷ 14 = 9/2 = 4½ days

∴ The correct answer is 4½ days.

Additional Information

Total Work and Efficiency

Efficiency is inversely proportional to time. Total Work = Efficiency × Time Taken.

Pipes and Cisterns Concept

Works similarly to Time and Work, but involves negative efficiency for emptying pipes which drain the total volume.

Wages and Work

Wages are always distributed in the ratio of the total work done by each individual, not strictly by their time taken or days spent.

Given:

Average of 4, 6, 8, 12, and x = 7

Average of x, 9, 13, 15, and y = 9

Concept used:

Total = Average × Number of entities

Calculation:

There are 5 numbers in the series 4, 6, 8, 12, x.

According to the question,

4 + 6 + 8 + 12 + x = 7 × 5

⇒ 30 + x = 35

⇒ x = 35 - 30

⇒ x = 5     ---(1)

There are 5 numbers in the series x, 9, 13, 15, y.

According to the question,

x + 9 + 13 + 15 + y = 9 × 5

Substituting the value of x from equation (1),

⇒ 5 + 9 + 13 + 15 + y = 45

⇒ 42 + y = 45

⇒ y = 45 - 42

⇒ y = 3

Now, (2x - 3y)

⇒ (2 × 5 - 3 × 3)

⇒ 10 - 9 = 1

∴ The value of (2x - 3y) is 1.

Given:

After giving a discount of 20% on MP, SP = Rs. 120

If the discount has not been given, Profit = 20%.

Concept used:

SP = MP - MP × Discount %

SP = CP + CP × Gain%

Calculation:

Let, MP of the article = Q, and CP of the article = P

According to the question,

⇒ Q - Q × 20% = 120

⇒ Q - 0.2Q = 120

⇒ 0.8Q = 120

⇒ Q = 120/0.8

⇒ Q = 150

Now,

⇒ P + P × 20% = 150

⇒ P + 0.2P = 150

⇒ 1.2P = 150

⇒ P = 150/1.2

⇒ P = 125

∴ The cost price of the article is Rs. 125. 

Shortcut Trick

Let, original MP = X

X  = 100 × 120/80 = 150

Let, original CP = Y

<br>

So, Y = 100 × 150/120 = Rs. 125

∴ The cost price of the article is Rs. 125.

Given:

SP of each article = Rs. 9,180

He gains 8% on one article and loses 15% on the other.

Concept used:

SP = CP - CP × Loss%

SP = CP + CP × Gain%

Loss = CP - SP

Calculation:

Let the cost price of the first and second article be P and Q.

According to the question,

⇒ P + P × 8% = 9180

⇒ P + 0.08P = 9180

⇒ 1.08P = 9180

⇒ P = 9180/1.08

⇒ P = 8500

Now,

⇒ Q - Q × 15% = 9180

⇒ Q - 0.15Q = 9180

⇒ 0.85Q = 9180

⇒ Q = 9180/0.85

⇒ Q = 10,800

Total CP = 10,800 + 8500 = Rs. 19,300

Total SP = 9180 × 2 = Rs. 18,360

Now, the overall loss

⇒ 19,300 - 18,360 = Rs. 940

∴ His overall loss is Rs. 940.

Shortcut Trick

Subtract the remainders from the given numbers: 2675 − 5 = 2670 and 2320 − 6 = 2314.

Find the HCF of 2670 and 2314.

Difference between numbers = 2670 − 2314 = 356.

The HCF must be a factor of 356. Factors of 356 are 1, 2, 4, 89, 178, 356.

From the options, 178 is the only factor that divides both numbers.

∴ The correct answer is 178.

Alternate Method

Given: Numbers are 2675 and 2320 with remainders 5 and 6 respectively.

Formula: Greatest number = HCF of (Number₁ − Remainder₁) and (Number₂ − Remainder₂).

⇒ First number = 2675 − 5 = 2670

⇒ Second number = 2320 − 6 = 2314

⇒ Applying Long Division Method for HCF:

⇒ 2670 = 2314 × 1 + 356

⇒ 2314 = 356 × 6 + 178

⇒ 356 = 178 × 2 + 0

⇒ Since the last divisor is 178, the HCF is 178.

∴ The correct answer is 178.

Additional Information

HCF with Same Remainder

If the question states that the same remainder 'r' is left in each case, the number is the HCF of (x−r) and (y−r).

HCF of Differences

If the remainder is same but not given, the number is the HCF of the absolute differences: HCF(|x−y|, |y−z|, |z−x|).

LCM vs HCF Logic

Use HCF when finding the 'greatest number' that divides others. Use LCM when finding the 'least number' divided by others.

Shortcut Trick

Let the larger number be 9x and the smaller number be 5x.

According to the condition: 9x + 8 = 2 × (5x − 4)

9x + 8 = 10x − 8 ⇒ x = 16.

Larger number = 9 × 16 = 144.

∴ The correct answer is 144.

Alternate Method

Given: Ratio of numbers = 9 : 5. Changes: +8 to larger, −4 from smaller. New ratio = 2 : 1.

⇒ Let numbers be 9x and 5x.

⇒ (9x + 8) = 2(5x − 4)

⇒ 9x + 8 = 10x − 8

⇒ 10x − 9x = 8 + 8

⇒ x = 16

⇒ Larger number = 9 × 16 = 144

∴ The correct answer is 144.

Additional Information

Ratio and Proportion

A ratio compares two quantities by division. If a : b is the ratio, numbers can be assumed as ax and bx where x is the highest common factor.

Cross Multiplication Method

For ratio changes, if (a/b) changes with additions c and d to (p/q), then q(a + c) = p(b + d) can be solved quickly.

Given:

9 and 36 are the first and middle proportions respectively.

Concept used:

If A : B :: C : D then, (A × D) = (B × C)

Calculation:

Let the third proportion be P.

So, the proportion becomes

⇒ 9 : 36 :: 36 : P

According to the concept,

9 × P = 36 × 36

⇒ P = 1296/9

⇒ P = 144

∴ The third proportion is 144.

Given:

The speed of an aircraft is 120 Km /min.

Concept used:

Time × Speed = Distance

1m/s = 18/5 km/h

Calculation:

The aircraft in 1 minute goes = 120 km

So, the aircraft in 60 minutes goes = 120 × 60 = 7200 km

Speed of the aircraft = 7200 km/h.

Now, the speed of the aircraft

⇒ 7200 × (5/18) = 2000 m/s

∴ The speed of the aircraft is 2000 m/s.

Given:

Number of students in section A = 38

Number of students in section B = 42

Average weight of students of section A = 55 Kg

Average weight of students of section B = 32 Kg.

Concept used:

Total = Average × Number of entities

Calculation:

Total weight of all students in section A

⇒ 38 × 55 = 2090 kg

Total weight of all students in section B

⇒ 42 × 32 = 1344 kg

Total number of students in both sections together

⇒ 38 + 42 = 80

Now, the average weight of all the students in the class

⇒ (2090 + 1344)/80

⇒ 3434/80 = 42.925 kg

∴ The average weight of all the students in the class is 42.925 kg.

Given:

The price of a car increased by 5% while its sales decreased by 16%.

Concept used:

Successive increment of A% and B% results into

⇒ (A + B + ${AB \over 100}$)%

Calculation:

Here, we're taking a decrease by 16% as a (-16%) increase.

According to the concept,

Now, the percentage change in the total revenue

⇒ (5 - 16 + ${(5 \times -16) \over 100}$)%

⇒ (5 - 16 - ${(5 \times 16) \over 100}$)%

⇒ (-11 - 0.8)%

⇒ -11.8%

Here, a negative sign means the percentage change in the total revenue is decreased by 11.8%

∴ The change in the total revenue is 11.8% decrease.

Shortcut Trick

Sum of ages of A, B, and C 5 years ago = Present sum − (3 persons × 5 years) = 135 − 15 = 120.

Total ratio parts 5 years ago = 4 + 5 + 7 = 16 parts.

Value of 1 ratio part = 120 ÷ 16 = 7.5 years.

Sum of ages of B and C 5 years ago = (5 + 7) parts = 12 × 7.5 = 90 years.

Sum of B and C 3 years from now = Sum 5 years ago + (5 years + 3 years) × 2 persons = 90 + 16 = 106 years.

∴ The correct answer is 106 years.

Alternate Method

Ages 5 Years Ago (Total = 16x)

A: 4x

B: 5x

C: 7x

Sum 5 years ago = Present Sum − (3 × 5) = 135 − 15 = 120 16x = 120 → x = 7.5 Target: B + C (+3 yrs) = 12x + 16 = 106

Given:

⇒ Ratio of ages of A, B, and C (5 years ago) = 4 : 5 : 7

⇒ Sum of their present ages = 135 years

Formula Used:

⇒ Sum of ages n years ago = Present sum − (n × number of persons)

⇒ Future age = Past age + Total years passed

Calculations:

⇒ Sum of their ages 5 years ago = 135 − (3 × 5) = 120 years.

⇒ Let the ages of A, B, and C 5 years ago be 4x, 5x, and 7x respectively.

⇒ Total sum 5 years ago = 4x + 5x + 7x = 16x

⇒ 16x = 120

⇒ x = 120 ÷ 16 = 7.5

⇒ Sum of ages of B and C 5 years ago = 5x + 7x = 12x

⇒ 12x = 12 × 7.5 = 90 years.

⇒ The time gap between '5 years ago' and '3 years from now' is (5 + 3) = 8 years.

⇒ Since 8 years pass for both B and C individually, their sum increases by 8 × 2 = 16 years.

⇒ Sum of ages of B and C (3 years from now) = 90 + 16 = 106 years.

∴ The correct answer is 106 years.

Additional Information

Constant Age Difference

The age difference between two individuals always remains constant, regardless of how many years pass into the past or the future.

Sum of Ages Over Time

If the sum of present ages of n people is S, their combined sum t years ago was S − (n × t), and t years hence will be S + (n × t).

Cross-Multiplication Method for Ages

When past and future age ratios are given, setting up a fraction (ax + t) ÷ (bx + t) = c ÷ d directly helps find the common multiple, where t represents the time gap.

Given:

The sides of the triangle are 21 cm, 35 cm and 28 cm.

Concept used:

Semi-permieter of a triangle, S = (A + B + C)/2

Area of a triangle

⇒ $\sqrt {S (S - A) (S - B) (S - C)}$

Where, A,B,C are the length of three sides of the triangle.

The measure of the inradius of a triangle

⇒ ${Area\ of\ the\ triangle} \over {Semi\ perimeter\ of\ the\ triangle}$

Calculation:

Semi-permieter of the triangular park

⇒ (21 + 35 + 28)/2

⇒ 84/2 = 42 m

Area of the triangular park

⇒ $\sqrt {42 (42 - 21) (42 - 35) (42- 28)}$

⇒ $\sqrt {42 × 21 × 7 × 14}$

⇒ $\sqrt { 7 × 3 × 2 × 7 × 3 × 7 × 7 × 2}$

⇒ 7 × 7 × 3 × 2

⇒ 294 cm²

Now, the inradius of the triangle

⇒ 294/42 = 7 cm

∴ The measure of the inradius is 7 cm.

Alternate Method

Concept used:

Pythagoras Theorem states that "In a right-angled triangle. the square of the hypotenuse side is equal to the sum of squares of the other two sides."

Area of △ = 1/2 × Base × Height

Calculation:

Here, 352 = 282 + 212

So, the given triangle is a right-angled triangle.

 

 

Area of △

⇒ 1/2 × 21 × 28

⇒ 294 cm² 

Semi-perimeter of the triangular park

⇒ (21 + 35 + 28)/2

⇒ 84/2 = 42 cm

So, the inradius of the triangle

⇒ (Area of △)/Semi-perimeter

⇒ 294/72 = 7 cm

∴ The measure of the inradius is 7 cm.

Shortcut Trick

Difference in speed = 60 − 50 = 10 km/h.

Time taken to meet = Extra distance ÷ Speed difference = 110 ÷ 10 = 11 hours.

Relative speed (opposite direction) = 60 + 50 = 110 km/h.

Total distance = Relative speed × Time = 110 × 11 = 1210 km.

∴ The correct answer is 1210 km.

Alternate Method

Given: Speed of Train 1 (S₁) = 60 km/h, Speed of Train 2 (S₂) = 50 km/h, Difference in distance (ΔD) = 110 km.

Formula Used: Distance = Speed × Time

Since both trains start at the same time and meet, the time (t) is constant.

⇒ Distance covered by Train 1 (D₁) = 60 × t

⇒ Distance covered by Train 2 (D₂) = 50 × t

⇒ Difference D₁ − D₂ = 110

⇒ 60t − 50t = 110

⇒ 10t = 110

⇒ t = 11 hours

⇒ Total Distance (AB) = D₁ + D₂ = 60(11) + 50(11)

⇒ Total Distance = 660 + 550 = 1210 km

∴ The correct answer is 1210 km.

Additional Information

Relative Speed Concept

When two objects move towards each other, their relative speed is the sum of their individual speeds (S₁ + S₂).

Distance-Speed Proportionality

When time is constant, the ratio of distances covered is equal to the ratio of their speeds (D₁/D₂ = S₁/S₂).

Meeting Time Formula

Time to meet = Initial distance between objects ÷ Relative speed.

Given:

The sides of a triangular park are 96 m. 110 m and 146 m.

Area of the park = Area of the rhombus-shaped field

Diagonal of the rhombus-shaped field = 60 m.

Concept used:

Semi-permieter of a triangle, S = (A + B + C)/2

Area of a triangle

⇒ $\sqrt {S (S - A) (S - B) (S - C)}$

Where, A, B, C are the length of three sides of the triangle.

Area of a rhombus = (D₁ × D₂)/2

Where, D1 and D2 are the two diagonals of rhombus.

Calculation:

Let, Length of the other diagonal of the rhombus = Q m

Semi-perimeter of the triangular park

⇒ (96 + 110 + 146)/2

⇒ 352/2 = 176 m

Area of the triangular park

⇒ $\sqrt {176 \space (176 - 96) \space (176 - 110) \space (176 - 146)}$

⇒ $\sqrt {176 × 80 × 66 × 30}$

⇒ $\sqrt {16 × 11 × 8 × 10 × 6 × 11 × 3 × 10}$

⇒ $\sqrt {16 × 11 × 11 × 10 × 10 × 144}$

⇒ 4 × 11 × 10 × 12

⇒ 5280 m²

According to the concept,

⇒ (60 × Q)/2 = 5280

⇒ Q = (5280 × 2)/60

⇒ Q = 176

∴ The length of other diagonal of the rhombus is 176 m.

Alternate Method

Concept used:

Pythagoras Theorem states that "In a right-angled triangle. the square of the hypotenuse side is equal to the sum of squares of the other two sides."

Area of △ = 1/2 × Base × Height

Area of a rhombus = (D1 × D2)/2

Where, D1 and D2 are the two diagonals of rhombus.

Calculation:

Here, 1462 = 1102 + 962

So, the given triangle is a right-angled triangle.

Area of △

⇒ 1/2 × 110 × 96

⇒ 5280 m2 

According to the concept,

⇒ (60 × Q)/2 = 5280

⇒ Q = (5280 × 2)/60

⇒ Q = 176

∴ The length of other diagonal of the rhombus is 176 m.

Shortcut Trick

Let the prices of the two articles be P₁ and P₂.

According to the question: 20% of P₁ = 25% of P₂.

⇒ 20 × P₁ = 25 × P₂

⇒ P₁ ÷ P₂ = 25 ÷ 20 = 5 ÷ 4.

The ratio of prices must be 5 : 4. Checking options, only Rs. 50 and Rs. 40 satisfies this ratio.

∴ The correct answer is Rs. 50 and Rs. 40.

Alternate Method

Given: Discount% on Article 1 = 20%, Discount% on Article 2 = 25%.

Formulas: Discount Value = (Discount% ÷ 100) × Price.

⇒ Let the prices be x and y.

⇒ (20 ÷ 100) × x = (25 ÷ 100) × y

⇒ 0.20x = 0.25y

⇒ x ÷ y = 0.25 ÷ 0.20 = 5 ÷ 4

⇒ If x = 50, then y = (4 ÷ 5) × 50 = 40.

∴ The correct answer is Rs. 50 and Rs. 40.

Additional Information

Inverse Proportion of Prices

When the absolute discount values are equal, the prices are inversely proportional to their discount percentages. Price₁ × D₁% = Price₂ × D₂%.

Marked Price and Discount

Discount is always calculated on the Marked Price (MP) unless stated otherwise. Selling Price (SP) = MP − Discount.

Given:

A sum in 3 years at simple interest at x% p.a is Rs. 5,472.

The same sum in $7\frac{1}{2}$ i.e., 7.5 years at x% p.a. at simple interest is Rs. 6,930.

Concept used:

Simple Interest, SI = (P × R × T)/100

Amount = P + SI

Where, P = Principal amount, R = Rate of interest per year, 

T = Time in years

Calculation:

Let the sum be Rs. p.

According to the question,

p + (p × x × 3)/100 = 5472      ....(1)

According to the question,

p + (p × x × 7.5)/100 = 6930      ....(2)

Subtracting equation (1) from equation (2),

p + (p × x × 7.5)/100 - p - (p × x × 3)/100 = 6930 - 5472

⇒ 7.5xp/100 - 3xp/100 = 1458

⇒ 4.5xp/100 = 1458

⇒ xp = 145800/4.5

⇒ xp = 32400      ....(3)

Putting xp = 32400 in (2),

p + (p × x × 7.5)/100 = 6930

⇒ p + (32400 × 7.5)/100 = 6930

⇒ p = 6930 - (32400 × 7.5)/100

⇒ p = 6930 - 2430

⇒ p = 4500       ....(4)

Putting p = 4500 in (3),

x × 4500 = 32400

⇒ x = 32400/4500

⇒ x = 7.2

∴ The value of x is 7.2.

Shortcut Trick

When 'rate of interest' is uniform and time varies then-

R = $\large{(\frac{A_1 - A_2}{A_2× T_1 - A_1× T_2})× 100}$

Where, A₁ = First amount, A₂ = Second amount

T₁ = first time, T₂ = Second time, R = Rate of interest

∴ According to the question -

R = [(5472 - 6930)/(6930 × 3 - 5472 × 7.5)] × 100

R = [(-1458)/(20790 - 41040)] × 100

R = (1458/20250) × 100

R = 7.2%

∴ Required rate of interest is 7.2%

Shortcut Trick

Difference in percentage = 8% − (−4%) = 12%.

Given 12% of Cost Price = ₹120.

⇒ 1% of Cost Price = ₹10.

To gain 11%, Selling Price should be 111%.

⇒ Required Selling Price = 111 × 10 = ₹1,110.

∴ The correct answer is ₹1,110.

Alternate Method

Given:

Initial Loss = 4% | Final Gain = 8% | Increase in Price = ₹120

Calculations:

⇒ Let the Cost Price (CP) be 100 units.

⇒ First Selling Price (SP₁) = 100 − 4 = 96 units.

⇒ Second Selling Price (SP₂) = 100 + 8 = 108 units.

⇒ Difference = 108 − 96 = 12 units.

⇒ 12 units = ₹120 ⇒ 1 unit = ₹10.

⇒ CP = 100 × 10 = ₹1,000.

⇒ To gain 11%, New SP = 111% of ₹1,000.

⇒ New SP = (111/100) × 1,000 = ₹1,110.

∴ The correct answer is ₹1,110.

Additional Information

Profit and Loss Percentage

Profit % = (Profit/CP) × 100 and Loss % = (Loss/CP) × 100. Both are always calculated on the Cost Price unless specified.

Selling Price Calculation

SP = CP × (100 + Gain%)/100 or SP = CP × (100 − Loss%)/100. This is the base for solving change-in-price problems.

Successive Discounts

Single equivalent discount for two successive discounts a% and b% = (a + b − ab/100)%.

Concept used:

Calculation:

42 ÷ 9 of 6 - [64 ÷ 48 × 3 - 15 ÷ 8 × (11 - 17) ÷ 9 ] ÷ 14

⇒ 42 ÷ 54 - [64 ÷ 48 × 3 - 15 ÷ 8 × (11 - 17) ÷ 9 ] ÷ 14

⇒ 42 ÷ 54 - [64 ÷ 48 × 3 - 15 ÷ 8 × (-6) ÷ 9 ] ÷ 14

⇒ 7/9 - [(4/3) × 3 - 15/8 × (-2/3) ] ÷ 14

⇒ 7/9 - [4 + 5/4] ÷ 14

⇒ 7/9 - [(16 + 5)/4] ÷ 14

⇒ 7/9 - 21/4 ÷ 14

⇒ 7/9 - 3/8

⇒ (56 - 27)/72

⇒ 29/72

∴ The simplified value is $\frac{{29}}{{72}}$.

Given: 

A and B can complete a work in 120 days.

B and C can complete it in 150 days.

A and C can complete it in 200 days.

Concept used:

Total work = Work done per day × Total time taken 

Calculation:

LCM (120, 150, 200) = 600 units

Let, Total work = LCM of the time taken by different workers

The efficiencies of A, B, and C be denoted by a, b, and c.

So, Total work = 600 units

Let the efficiencies of A, B, and C be denoted by A, B, and C.

According to the question,

a + b = 600/120

⇒ a + b = 5     ---(1)

b + c = 600/150

⇒ b + c = 4     ---(2)

a + c = 600/200

⇒ a + c = 3     ---(3)

Equation (1) + Equation (2) + Equation (3),

⇒ a + b + b + c + a + c = 5 + 4 + 3

⇒ 2(a + b + c) = 12

⇒ (a + b + c) = 12/2

⇒ (a + b + c) = 6     ---(4)

Subtracting equation (4) from equation (3),

(a + b + c) - (a + c) = 6 - 3

⇒ a + b + c - a - c = 3

⇒ b = 3

Now, the time taken by B to complete 2/5th of the work

⇒ {(2/5) × 600}/3

⇒ {1200/5}/3

⇒ 240/3 = 80 days

∴ In 80 days B can alone complete two-fifths of the work.

Concept used:

BODMAS Rule:

Calculation:

523 + 523 × 523 ÷ 523

⇒ 523 + 523 × 1

⇒ 523 + 523

⇒ 1046

∴ The simplified value is 1046.

Given:

Spends on food = 42% of monthly salary

Spends on house rent = 16% of monthly salary

Spends on entertainment = 11% of monthly salary

Spends on conveyance = 7% of monthly salary

Borrowed Rs. 12,000 to meet the expenses of Rs. 18,000.

Calculation:

Let, the monthly salary of Vignesh = 100 %

Percentage of salary left after all expenditure

⇒ 100% - (42 + 16 + 11 + 7)%

⇒ 100% - 76% = 24%

Before borrowing, he had left with

⇒ 18,000 - 12,000 = Rs. 6,000

Now,

24% of his salary = Rs. 6000

100% of his salary = 6000/24 × 100 = Rs. 25,000

∴ His salary is Rs. 25,000.

The correct answer is 'monotony'.

Key Points

• Let us look at the meaning of the given options - 
• scrutiny - critical observation or examination.
• symphony - an elaborate musical composition for full orchestra, typically in four movements, at least one of which is traditionally in sonata form.
• monotony - lack of variety and interest; tedious repetition and routine.
• company - the fact or condition of being with another or others, especially in a way that provides friendship and enjoyment.
• The sentence talks about tourism providing a break in daily life which involves repetition and routine.
• Logically, we need a break because things have been boring and we need to shake things up.
• Hence, monotony is the most appropriate option that can substitute the underlined word in the given sentence.
• So, option 3 is the correct answer.

Correct sentence - Besides generating revenue, tourism brings a break from the monotony of daily life.

The erroneous part is 'are to'.

Key Points

• Using the linking verb are in the part 'are to' violates subject-verb agreement.
• The subject of the sentence is singular  - the person wants to learn English which is the most important of his goals.
• Hence, we cannot use the plural linking verb are with a singular subject.
• Hence, option 3 is the correct answer.
• The sentence can be correct by using the singular linking verb is.

Correct sentence - The most important / of all my goals / is to/ learn English.

The erroneous part is 'I am'. 

Key Points

• The given sentence is an example of subjunctive mood.
• The subjunctive mood is the verb form used to explore a hypothetical situation (e.g., "If I were you") or to express a wish, a demand, or a suggestion (e.g., "I demand he be present").
• I am is the normal present tense verb form. It cannot be used for the subjunctive mood.
• Hence, option 3 is the correct answer.
• The sentence can be corrected by using I were.

Correct sentence - I wish / I were / the Principal / of the school!

The correct answer is 'control'.

Key Points 

• Let us look at the meaning of the given options - 
• control - a means of limiting or regulating something.
• convey - communicate (a message or information).
• conduct - the manner in which a person behaves, especially in a particular place or situation.
• consume - eat, drink, or ingest (food or drink).
• The given blank needs a word that would represent the type of action that the government should perform with respect to pollution.
• Hence, control is the most appropriate option to fill in the blank.
• So, option 1 is the correct answer.

Correct sentence - The government should take steps to control pollution.

The correct answer is 'brought about'.

Key Points

• The underlined part of the given sentence bring in has an error in tense form.
• Bring is the infinitive form and produces compounds with the verb "to do".
• Thus, "has bring in" is incorrect.
• 'has' followed by V3 hence we will use 'brought'.
• Brought is the past tense and forms compound forms with the verb "to have".
• Brought about' is a phrasal verb which means to cause to happen : accomplish.
• This phrase is contextually and grammatically correct for the given sentence.
• So, the correct replacement for the underlined part is brought about.
• Hence, option 2 is the correct answer.

Correct sentence - The new President has brought about many reforms.

Additional Information

• brought out: to expose, reveal, or cause to be seen.

The correct answer is 'Shoal'.

Key Points 

• Let us look into the meaning of the words in the options - 
• Shoal - a large number of fish swimming together.
• Bevy - a large group of people or things of a particular kind.
• Brood - a family of birds or other young animals produced at one hatching or birth.
• Flock - a number of birds of one kind feeding, resting, or travelling together.
• From the above meanings it is clear that shoal is the best word to substitute the given group of words.
• Hence, option 1 is the correct answer.

The correct answer is 'To agree on something'.

Key Points

• To be on the same page is an idiom that means agreeing about something (such as how things should be done).
• ​Example - Try to get employees and clients on the same page.
• So, to agree on something is the most appropriate meaning of the given idiom.
• Hence, option 4 is the correct answer.

The correct answer is 'Very pleased'.

Key Points

• Tickled pink is an idiomatic expression that means very happy or amused.
• ​Example - I was tickled pink to see her.
• So, very pleased is the most appropriate meaning of the given idiom.
• Hence, option 3 is the correct answer.

The correct answer is 'Invigilator'.

Key Points 

• Let us look into the meaning of the words in the options - 
• Invigilator - the person in the examination room responsible for conducting a particular examination session in the presence of the candidates.
• Examinee - a person taking an examination or test.
• Principal - the head of a school, college, or other educational institution.
• Administrator - a person responsible for carrying out the administration of a business or organization.
• From the above meanings it is clear that invigilator is the best word to substitute the given group of words.
• Hence, option 1 is the correct answer.

The erroneous spelling is 'Wistle'.

Key Points

• The correct spelling for the word is whistle which means a clear, high-pitched sound made by forcing breath through a small hole between partly closed lips, or between one's teeth.
• The meanings of the other options are as follows - 
• Cereal - a grain used for food, for example wheat, maize, or rye.
• Tunnel - an artificial underground passage, especially one built through a hill or under a building, road, or river.
• Rustle - make a soft, muffled crackling sound like that caused by the movement of dry leaves or paper.
• Hence, option 1 is the correct answer.

The correct answer is 'Sufficient'.

Key Points 

• Ample is an adjective which means enough or more than enough; plentiful.
• The meaning of the given options are as follows - 
• Sparse - thinly dispersed or scattered.
• Sufficient - enough; adequate.
• Limited - restricted in size, amount, or extent; few, small, or short.
• Scarce - (especially of food, money, or some other resource) insufficient for the demand.
• From the above meanings it is evident that sufficient is the correct synonym for the word ample.
• Hence, option 2 is the correct answer.