SSC GD Constable Previous Year Paper (Held on: 16th November 2021 Shift 1)

Table show alphabet serial number –

The pattern followed is,

All follow the same pattern, except 'NMP’.

Hence, “NMP” is the odd one.

The image obtained when the paper is unfolded is,

Hence, option 3 is the correct answer.

The embedded part of this image is:

Hence, option (1) is the correct answer.

The logic followed here is:

Bhubaneswar : Odisha → Bhubaneswar city is the capital of Odisha state of India.

Similarly,

Aizawl : Mizoram →  Aizawl city is the capital of Mizoram state of India.

Hence, ‘Mizoram’ is the correct answer.

Additional Information

Total eight friends facing north:-  A, B, C, D, E, F, G and H

1. E is third to the left of G. G is sitting at one of the corners.

2. F is sitting between D and G.

3. H is third to the left of C.

4. B is sitting between H and A.

Hence,  'C' is sitting between A and E.

The shaded part represents a set of letters representing root vegetables that grow in summer but NOT in hard soil.

 

The set of letters representing root vegetables that grow in summer but NOT in hard soil  = D

Hence, ‘D’ is the correct answer.

The pattern followed here is,

Let (1st number : 2nd number)

1st number + 59 = 2nd number

Now follow the steps:

31 : 90

=> 31 + 59 = 90 = 2nd number

Similarly,

43 : ?

=> 43 + 59 = 102 = 2nd number

Hence, "102" is correct answer.

Given: C 2 _ X 2 C C _ X X 2 _ C 2 _ X _ C

By checking options and substituting accordingly.

1)  C2X2X → C 2 C X 2 C / C 2 X X 2 X / C 2 2 X X C

2)  X2CX2 → C 2 X X 2 C / C 2 X X 2 C / C 2 X X 2 C

3)  AXX2C → C 2 A X 2 C / C X X X 2 X / C 2 2 X C C

4)  XCX2C → C 2 X X 2 C / C C X X 2 X / C 2 2 X C C

Option (2) gives a cyclic pattern of C 2 X X 2 C / C 2 X X 2 C / C 2 X X 2 C

Hence, ‘X2CX2’ is the correct answer.

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

Hence, "option (4)" is the correct answer.

Additional Information In Mirror image left side and right side changed vice-versa where the top and bottom remain the same.

The reflection of an object into the water is its water image. It appears by inverting an object vertically i.e. upside down.

The water image of the figure looks like the mirror image of the figure in case the mirror is horizontally at the bottom of the figure.

Water image is just a reflection where top and bottom part of the images changed where left and right side of the image remain same.

The pattern followed here is:

 

Hence, '109' is the correct answer.

The pattern followed here is:

 

Hence, '176' is the correct answer.

Total five friends facing south:-  P, Q, R, S and T

1. Q is sitting in the centre position.

2. P is sitting at the west end.

3. Two persons are sitting between P and R.

4. T and R are sitting on one side of Q.

The final sitting arrangement is

Hence, 'S' is sitting between Q and P.

For this question, the relation is given below -

Logic: If two dice have the same two face values in the given image then the third number is opposite to each other.

In first dice and second dice.

Symbols 'Y' and 'Z' are common.

So, the symbol '&' is the opposite of $.

Hence, the correct answer is “&”

Family Chart:

Given:

‘R + S’ means ‘R is the daughter of S’.

‘R − S’ means ‘R is the husband of S’.

‘R × S’ means ‘R is the brother of S’.

Let us first decode the given symbols and then draw a family tree.

Now break the code ‘T × V + Z’

1) T × V

‘T × V’ means ‘T is the brother of V’.

2) V + Z

‘V + Z’ means ‘V is the daughter of Z’.

Now, check all the options

Option (1) T is the uncle of Z → False (T is the son of Z)

Option (2) T is the father of Z → False (T is the son of Z)

Option (3) T is the son of Z → True

Option (4) T is the brother of Z → False (T is the son of Z and brother of V)

Hence, “option (3)” is the correct answer.

The logic followed here is:

 ‘ARROW’ is coded as ‘FOOSE’

‘GERM’ is coded as ‘THOR’

So, by observing the pattern, we can conclude that,

 A = F, R = O, O = S, W = E, G = T, E = H, R = O and M = R.

Now, we have to find the code for MOWER

As the codes of all the letters have been given in the question,

M = R, O = S, W = E, E =H, and R = O

Hence,

‘MOWER’ = ?

Hence, MOWER is coded as ‘RSEHO’.

According to the sequence in the dictionary:

The correct order of the given words is:

Pr is common in all words;

5. Premium
6. Prepaid
7. Prescribe
8. Prestige
9. Pristine

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

Table show alphabet serial number –

The pattern followed is,

Hence, “GSD” is the complete series.

Given:

  

Here the pattern followed in each column is:

1^st number + 3^rd number = 2^nd number

Column 1: 13, 30, 17

1^st number + 3^rd number

= 13 + 17

= 30 = 2^nd number

Column 2: 26, 42, 16

1^st number + 3^rd number

= 26 + 16

= 42 = 2^nd number

Similarly,

Column 3: 39, ?, 15

1^st number + 3^rd number

= 39 + 15

= 54 = 2^nd number

Hence, “54” is correct answer.

The table is alphabets place value:

The pattern followed here is:

First letters are arranged in reverse order.

And then letters are increased or decreased by +1 or -1 alternatively.

Given:

BLOCK : LBPKC

• BLOCK → Reverse order → KCOLB.
• Now letters are increased or decreased by +1 or -1 alternatively.

Similarly,

MARGIN = ?

• MARGIN → Reverse order → NIGRAM.
• Now letters are increased or decreased by +1 or -1 alternatively.

 

<br>

 

Hence, 'MARGIN' is coded as "OHHQBL".

Alternate Method

Let the number is ‘x’

Given:

A number is added to its multiple of 5 and its square, the sum of these three numbers is 91.

=> x + 5x + x² = 91

=> x² + 6x - 91 = 0

=> x² + 13x – 7x - 91 = 0

=> x(x + 13) – 7(x + 13) = 0

=> (x + 13)(x - 7) = 0

So,

x + 13 = 0 and x - 7 = 0

x = - 13 and x = 7

There are two values of x = -13, 7

But we take positive value.

Hence, “7” is the correct answer.

Alternate MethodWe can solve this question by option method,

Option 1.

Let the number be 9,

According to the question,

=> 9 + 5 × 9 + 92 = 91

=> 9 + 45 + 81 = 91

=> 135 = 91, not satisfied.

Option 2.

Let the number be 11,

According to the question,

=> 11 + 5 × 11 + 112 = 91

=> 11 + 55 + 121 = 91

=> 187 = 91, not satisfied.

Option 3.

Let the number be 7,

According to the question,

=> 7 + 5 × 7+ 72 = 91

=> 7 + 35 + 49 = 91

=> 91 = 91, satisfied.

Option 4.

Let the number be 6,

According to the question,

=> 6 + 5 × 6 + 62 = 91

=> 6 + 30 + 36 = 91

=> 72 = 91, not satisfied.

Now, we can see only option 3 satisfied.

∴ The number is 7.

The table is alphabets place value:

The pattern followed here is:

‘CIRCLE’ is written as ‘DLWAHY’

Similarly,

SQUARE = ?

Hence, 'SQUARE' is coded as "TTZYNY".

Statements:

All blues are whites.

Some whites are greys.

The least possible diagram for the given statements is as follows

Conclusions:

I. All greys are whites → False (because statement given some whites are greys)

II. All greys are blues → False (because no direct relationship is given between greys and blues)

Hence, “Neither conclusion I nor conclusion II follows".

BODMAS rule:

Decoding the information, 

 Given:

240 × 72 + 8 ÷ 24 – 6

After replacing the signs from left to right and using the BODMAS rule,

240 - 72 ÷ 8 × 24 + 6

= 240 - 9 × 24 + 6

= 240 - 216 + 6

= 246 - 216

= 30

Hence, “30” is the correct answer.

The logic followed here is:

1. Square rotates in a clockwise direction each corner in a box and one by one square part becomes dark in a clockwise direction

2. Line rotate in a clockwise direction and one by one line increase.

Final series is

Hence, ‘option 3’ is the correct answer.

According to the given information

‘Country’ is coded as 7.

Hence, ‘7’ is the correct answer.

The correct answer is Pattadakal.

Key Points

• Pattadakal:
• Pattadakal represents the high point of eclectic art as designated by UNESCO.
• In the 7th and 8th centuries under the Chalukya dynasty, achieved a harmonious blend of architectural forms from northern and southern India.
• An impressive series of nine Hindu temples and a Jain sanctuary can be seen there.
• It is located on the west bank of the Mallaprabha River in Bagalkot district in Karnataka.
• The Hindu temples are generally dedicated to Shiva, but elements of Vaishnavism and Shaktism theology and legends are also featured.

​

Additional Information

• Three very closely located sites in the State of Karnataka provide a remarkable concentration of religious monuments dating from the great dynasty of the Chalukya (c. 543-757).
• The three capital cities are- Aihole (ancient Aryapura), Badami, and Pattadakal, the 'City of the Crown Rubies' (Pattada Kisuvolal).
• The Pattadakal was, moreover, for a brief time the third capital city of the Chalukya kingdom; at the time the Pallava occupied Badami (642-55).
• While Aihole is traditionally considered the 'laboratory' of Chalukya architecture, with such monuments as the Temple of Ladkhan (c. 450) which antedate the dynasty's political successes during the reign of King Pulakeshin I.

The correct answer is India, Australia, Japan and the US.

Key Points

• Malabar exercise is a naval exercise which is being conducted between
• India
• USA
• Japan
• Australia
• 2020 Malabar exercise was conducted in the Arabian Sea and Bay of Bengal in two phases.
• The 24th edition of the MALABAR maritime exercise, hosted by the Indian Navy (IN) in two phases, concluded in the Arabian Sea on 20 Nov 20.
• Phase 1 of the exercise involving participation by the Indian Navy (IN), United States Navy (USN), Japan Maritime Self Defense Force (JMSDF), and Royal Australian Navy (RAN), was conducted off Visakhapatnam in the Bay of Bengal from 3-6 November 2020.
• The second phase was conducted in the Arabian Sea from 17-20 November 2020.
• Indian Navy’s participation in Phase 2 was led by Rear Admiral Krishna Swaminathan, Flag Officer Commanding Western Fleet, and included
• Aircraft carrier Vikramaditya
• Indigenous destroyers Kolkata and Chennai
• Stealth frigate Talwar
• Fleet Support Ship Deepak
• Indigenously built submarine Khanderi
• P8I and IL-38 maritime reconnaissance aircraft.

Additional Information

• India and the USA conduct Yudh Abhyas (Army)
• Tiger Triumph - Tri-Services  exercise between India and USA
• Indra Dhanush - India and UK (Air Force)
• Ajeya Warrior - India and UK
• Hand in Hand - India, and China (Army)
• Vajra Prahar - Special forces of India and USA

The correct answer is Raja Ram Mohan Roy.

Key Points

• Raja Ram Mohan Roy was the founder and editor of the following two vernacular weekly newspapers-
• Sambad Kaumudi in Bengali.
• Mirat-ul-Akhbar in the Persian language​
• Raja Ram Mohan Roy is known as 'the father of Indian renaissance',
• He was the founder of 'Brahmo Samaj' and the man who tirelessly fought against the social evils prevailing in the Indian society.
• Roy was the one who pioneered western education in India.
• Roy established the Brahmo Samaj on August 20, 1828, which acted against the evil practices that existed in the Hindu society, especially, the practice of ‘Sati’.

Additional Information

The correct answer is Deepika Kumari.

Key Points

• Deepika added more gold medals at the 2018 Salt Lake City World Cup.
• She won the individual event and added another bronze medal in Samsun.
• The year 2021 has been fantastic for the Indian star archer who won individual and gold team medals at the Guatemala City World Cup.
• Deepika Kumari defeated Germany’s Michelle Kroppen by 7-3 in the circuit final of Stage III.
• Deepika Kumari has won four silver medals (2011, 2012, 2013, 2015) and one Bronze in the 2018 World Cup.
• She has also represented India's women team in the World Championships and won two silver medals (2011, 2015).
• Deepika Kumari is from Jharkhand, India.​

Additional Information

The correct answer is 2020-21.

Key Points

• Swachh Bharat Mission:
• The Swachh Bharat Abhiyan is aimed to accelerate the efforts to achieve universal sanitation coverage and to put the focus on sanitation all over India.
• The Prime Minister of India, Narendra Modi launched the Swachh Bharat Mission on 2nd October 2014.
• Under the mission, all villages, Gram Panchayats, Districts, States and Union Territories in India declared themselves "open-defecation free" (ODF) by 2 October 2019, the 150th birth anniversary of Mahatma Gandhi, by constructing over 100 million toilets in rural India.
• Second Phase :
• The government has launched Swachh Bharat Mission Phase 2 with a focus on plastic waste management, biodegradable solid waste management, grey water management, and faecal sludge management.
• The mission is aimed at progressing towards target 6.2 of the Sustainable Development Goals Number 6 established by the United Nations in 2015.

Important Points 

• Prime Minister Narendra Modi nominated the name of Pune industrialist Adar Poonawalla, as an ambassador for the Swachh Bharat mission, who comes in recognition of his major initiative towards a cleaner and greener Pune.

The correct answer is Father of Indian Software (IT) Industry.

Key Points

• Faqir Chand Kohli, known as the father of Indian Software Industry, passed away in November 2020.
• Mr Kohli was the founder-CEO of TCS.
• He joined Tata Electric Co. in 1951 where he helped set up the load dispatching system to manage system operations.
• He became director of Tata Electric in 1970.
• He pioneered India’s IT revolution and helped the country build the $190-billion IT industry.

The correct answer is helium.

Key Points

• Alpha Particle
• α-particles consist of two protons and two neutrons.
• They are doubly-charged helium ions. Since they have a mass of 4 u, the fast-moving α-particles have considerable energy.
• An alpha particle is obtained by removing 2 electrons from a helium atom. So, an alpha particle is a doubly-charged helium ion.
• Helium:
• Helium is a chemical element with the symbol He and atomic number 2.
• It is a colourless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table.
• Its boiling and melting point are the lowest among all the elements.
• It is the second lightest and most abundant element in the observable universe (hydrogen is the lightest and most abundant).

Additional Information

• Lithium
• ​Lithium is a chemical element with the symbol Li and atomic number 3.
• It is a soft, silver-white metal belonging to the alkali metal group of chemical elements.
• ​Beryllium
• Beryllium is very similar to Aluminium.
• Beryllium is soft and has a low density.
• It is used in gears and in alloys with copper or nickel.
• Beryllium is used in Nuclear Reactors.
• Oxides of Beryllium have a high melting point.
• Hydrogen​
• Hydrogen was discovered by Henry Cavendish.
• Hydrogen gas is called as the fuel of the future.
• Most abundant element in the universe: Hydrogen.
• Most abundant element on earth's crust: Oxygen
• Hydrogen is the 'lightest element' in the periodic table.
• Lithium is the 'lightest metal' in the periodic table.

The correct answer is 43 B.

Key Points

• Article 43 B:
• According to Article 43 B of the Constitution of India, the State shall endeavor to promote voluntary formation, autonomous functioning, democratic control and professional management of cooperative societies.
• Article 43 B is included in Part IV of the constitution.

Important Points 

• The 97th Amendment Act of 2011 gave constitutional status and protection to cooperative societies.
• In this amendment following changes in the constitution were made:
• It made the right to form cooperative societies a fundamental right- Article 19.
• It included a new Directive Principle of State Policy on promoting cooperative societies- Article 43B.
• It added a new Part IX-B in the constitution entitled “The Cooperative Societies”- Article 243-ZH to 243-ZT.

Additional Information 

• Article 43A was inserted by the 42nd amendment, directing the state to take steps to ensure workers’ participation in the management of industries.
• Article 43A - Participation of workers in the management of industries, states that the State shall take steps, by suitable legislation or in any other way, to secure the participation of workers in the management of undertakings, establishments, or other organizations engaged in any industry."
• Article 31A saves five categories of laws from being challenged and invalidates on the ground of contravention of fundamental rights conferred by Articles 14 and 19.
• These categories are the acquisition of estates and related rights by states, taking over the management of properties by state, the amalgamation of corporations, extinguishment or modification of rights of directors or shareholders of corporations, and extinguishment or modification of mining leases.
• Article 31A does not immunize a state law from judicial review unless it has been reserved for the President's consideration and has received his assent.
• Article 31A also provides for compensation at market value when the state acquires the land held by a person under his personal cultivation and the land is within the statutory ceiling limit.
• Article 31B saves the acts and regulations included in the Ninth Schedule from being challenged and invalidated on the ground of contravention of any of the fundamental rights.
• Thus, the scope of Article 31B is wider than Article 31A.
• Article 31B immunizes any law included in the Ninth Schedule from all the fundamental rights whether or not the law falls under any of the five categories specified in Article 31A

The correct answer is 1761.

Key Points 

• The Third Battle of Panipat took place on 14 January 1761, at Panipat, about 60 miles (95.5 km) north of Delhi.
• This was fought between a northern expeditionary force of the Maratha Empire and a coalition of the King of Afghanistan, Ahmad Shah Durrani with two Indian Muslim allies, the Rohilla Afghans of the Doab, and Shuja-ud-Daula, the Nawab of Oudh.
• The battle pitted the French-supplied artillery and cavalry of the Marathas against the heavy cavalry and mounted artillery (zamburak and jizail) of the Afghans and Rohillas led by Ahmad Shah Durrani and Najib-ud-Daulah, both ethnic Pashtuns (the former is also known as Ahmad Shah Abdali).
• The battle is considered one of the largest fought in the 18th century and has perhaps the largest number of fatalities in a single day reported in a classic formation battle between two armies.

Additional Information 

• The first battle of Panipat, on 21 April 1526, was fought between rival armies of Babur and the Lodi dynasty. It originated in North India and marked the beginning of the Mughal Empire and the end of the Delhi Sultanate. It was one of the most elementary battles in the Indian subcontinent, starting with gunpowder firearms and wing artillery, which was launched by the Mughals in this battle.
• The second battle of Panipat was fought on 5 November 1556 between the armies of Hemu and the Mughal emperor Akbar, the Hindu emperor of North India. Hemu announced a few weeks ago over the kingdoms of Delhi and Agra by defeating the Mughals led by Tardi Beg Khan in the Battle of Delhi and anointing King Vikramaditya to the Purana Fort in Delhi. Akbar and his patron Bairam Khan, who, after learning about the loss of Agra and Delhi, marched Panipat to reclaim the lost territories. Not far from the site of the First Battle of Panipat in 1526, the two armies clashed at Panipat.

The correct answer is Indus.

Key Points

The Indus River System

• The river Indus rises in Tibet, near Lake Mansarovar.
• Flowing west, it enters India in the Ladakh
• It forms a picturesque gorge in this part.
• Several tributaries, the Zaskar, the Nubra, the Shyok, and the Hunza, join it in the Kashmir region.
• The Indus flows through Baltistan and Gilgit and emerges from the mountains at Attock.
• The Satluj, the Beas, the Ravi, the Chenab, and the Jhelum join together to enter the Indus near Mithankot in Pakistan.
• The major Himalayan rivers are the Indus, the Ganga, and the Brahmaputra.
• These rivers are long and are joined by many large and important tributaries. A river along with its tributaries is called a river system.
• Beyond this, the Indus flows southwards eventually reaching the Arabian Sea, east of Karachi.
• The Indus plain has a very gentle slope. With a total length of 2900 km, the Indus is one of the longest rivers in the world.
• A little over a third of the Indus basin is located in India in the states of Jammu and Kashmir, Himachal Pradesh, and Punjab and the rest is in Pakistan.

The correct answer Switch.

Key Points

• A switch is a simple device that is used to either break the electric circuit or to complete it.
• A resistor is a passive electrical component that resists the flow of electric current.
• A transistor is a semiconductor device that acts as both an amplifier and switch.
• A fuse is an electrical device for safety that removes electrical current from the circuit if the current gets too high.

Additional Information

• Transistors:
• Transistors are semiconductor devices, which are commonly used in amplifiers or electrically controlled switches
• Transistors are the basic building block that regulates the operation of computers, mobile phones, and all the other modern electronic circuits
• The most important transistor function is as a current amplifier and as a switch
• Transistors as current amplifiers are often used in amplifiers while transistors as switches are often found in automatic light circuits
• The functions of a transistor are variable resistors and switching devices.
• Capacitor:
• ​A capacitor is a device that stores electrical energy in an electric field.
• It is a passive electronic component with two terminals.
• The effect of a capacitor is known as capacitance.
• Capacitance: The capacitance is the capacity of the capacitor to store charge in it.
• Two conductors are separated by an insulator (dielectric) and when an electric field is applied, electrical energy is stored in it as a charge.
• The capacitance of a capacitor (C): The capacitance of a conductor is the ratio of charge (Q) to it by a rise in its potential (V), i.e.
• C = Q/V
• ​Resistor:
• A resistor is a passive element.
• It is represented by ‘R’ and is measured in ohms (Ω).
• Resistors are used to reduce current flow, adjust signal levels, to divide voltages.

The correct answer is Football.

Key Points

• Kerala Blasters:
• Kerala Blasters Football Club is an Indian professional football club based in Kochi, Kerala, that competes in the Indian Super League.
• The club was established in May 2014 during the inaugural season of the Indian Super League.
• The Blasters are the three-time runners-up of the Indian Super League.
• The club is also known for its fan base, including the supporters' group called Manjappada, which has gained a reputational for being one of the most vocal and passionate fan clubs in India.
• The club's crest features an elephant holding a football with its trunk, denoting Kerala's deep connection with the football.
• The coach of this team is Ivan Vukomanović.

​

Additional Information

• Indian Super League:
• The Indian Super League (ISL) is the men's professional top-tier football league in the Indian football league system.
• It is organized by the All India Football Federation (AIFF), and their commercial partner Football Sports Development Limited (FSDL).
• Hero MotoCorp is the official sponsor and it is officially called Hero Indian Super League.
• The league currently comprises 11 clubs.
• The competition was founded on 21 October 2013 to grow the sport of football in India.

The correct answer is United Nations.

Key Points

• The United Nations along with “the Vaccine Confidence Project” of the University of London launched an initiative called ‘Team Halo’ to counter misinformation on the Covid-19 vaccine.
• The initiative aims to tackle misinformation by sharing information on the safety and effectiveness of vaccines via social media.
• Over 100 scientists from different countries have joined hands to tackle the issue of misinformation surrounding Covid-19 vaccines.
• Under the initiative, the scientists will create social-media-friendly videos on COVID-19 vaccine science based on their personal experiences.
• In India, over 22 scientists have joined Team Halo from renowned institutes such as the Institute of Medical Sciences and Sum Hospital, Bhubaneswar.
• It will also act as a platform for communication between scientists working on Covid-19 vaccines and citizens of different countries.

The correct answer is Cheraw.

Key Points 

• Cheraw is the traditional bamboo dance of Mizoram.
• The Cheraw or bamboo dance is a traditional dance of Mizoram.
• It is considered to be one of the oldest dances of Mizoram. The dance is believed to have emerged out of a ritual.
• In this dance form, bamboos are kept in horizontal or cross formations on the ground. Pairs of these bamboo staffs are held by six to eight people.
• The male dancers move these bamboos to a rhythmic beat while the female dancers move gracefully while stepping in and out of the bamboo formations.
• The bamboos are clapped together by the male dancers to a specific beat.

Additional Information 

• Thang ta is a martial art from Manipur.
• Maanch is a dance performed in Malwa, Madhya Pradesh.
• Yak Chaam dance is performed in Sikkim by the Bhutia community.

The correct answer is 103.

Key Points

• As of October 2021, there have been 105 amendments to the Constitution of India since it was first enacted in 1950.
• There are three types of amendments to the Constitution of India of which the second and third types of amendments are governed by Article 368.

Additional Information

• The 42nd Amendment of the Constitution is also called the 'Mini Constitution'
• 101st Amendment Act introduces The GST system all over India
• The last or the 105th amendment act states to restore the power of the state governments to identify Other Backward Classes (OBCs) that are socially and economically backward.
• This amendment annulled the Supreme Court judgment of 11 May 2021, which had empowered only the Central government for such identification.

Important Points

• The three methods of amendment of the constitution are as follows:
• By Simple Majority of Parliament, Some changes such as admission, the formation of new states and making changes into territorial boundaries of the states, abolition and creation of legislative councils, etc can be done like any other ordinary law by a simple majority.
• By Special Majority of the Parliament, Most of the provisions of the constitution need to be amended by a special majority i.e. majority of more than 50% of total membership and 2/3rd members present and voting. Some of the amendments included in it are Fundamental Rights, Directive Principles, etc.
• By Special Majority of the Parliament and Ratification by half of the State Legislatures, There are a few provisions in which interest of the states and federal features of the constitution may be involved. Such bills first need to be passed on both the houses of the parliament and then need to secure ratification by half of the state legislatures. Examples include those related to Centre-State Relations, Election of the President etc.

The correct answer is Akbar.

Key Points

• Raja Todar Mal:
• He was one of the Navaratna in Akbar's Darbar.
• Raja Todar Mal introduced standard weights and measures, a land survey and settlement system, revenue districts, and officers.
• He introduced a new system of revenue known as zabt and a system of taxation called Dahshala.
• The Kashi Vishwanath Temple was rebuilt in 1585 by Todar Mal.
• The Navratnas of Akbar were as follows: Raja Birbal, Tansen, Abul Fazal, Faizi, Raja Man Singh, Raja Todar Mal, Mullah Do Piaza, Fakir Aziao-Din, Abdul Rahim Khan-I-Khana.​

Additional Information

• Akbar (1556 to 1605)
• Akbar was the third Mughal emperor (1556 to 1605) and son of  Humayun.
• Akbar succeeds in the throne at just 13 years old due to the death of Humayun.
• The kingdom Akbar inherited was little more than a collection of frail fiefs, under the regency of  Bairam Khan.
• Akbar introduced the Mansabdari system.
• The Navratnas of Akbar were as follows: Raja Birbal, Tansen, Abul Fazal, Faizi, Raja Man Singh, Raja Todar Mal, Mullah Do Piaza, Fakir Aziao-Din, Abdul Rahim Khan-I-Khana.
• Abul Fazl started the writing of Akbarnama in 1589.
• It is the most detailed history of the reign of Akbar.

The correct answer is MPL Sports.

Key Points 

• The Board of Control for Cricket in India (BCCI) announced its partnership with MPL Sports, as the new kit sponsor and official merchandise partner for the Indian Cricket Team.
• Under the newly-inked strategic partnership, MPL Sports has entered into a three-year agreement from November 2020 to December 2023.
• MPL Sports association with the BCCI begins with the upcoming India tour of Australia, 2020-21, which will see Team India sporting the new jerseys.
• The senior men and women and the Under-19 teams are also a part of the deal for the new kits.
• Apart from Team India jerseys, MPL Sports will also sell licensed Team India merchandise. MPL Sports will offer the jerseys and its wide range of Team India merchandise to fans at affordable prices.
• MPL Sports offers a wide range of affordable products, from sports and athleisure wear to Cricket equipment, as well as other accessories such as masks, wrist bands, footwear, and headgear, etc. The brand also plans to launch affordable high-performance clothing and accessories dedicated to esports fans.

The correct answer is Sharda.

Key Points

• Sarayu River:
• The Sarayu is the largest tributary of the Sharda River.
• Sarayu originated from Surmool and joined Mahakali at Pancheshwar which is at the border of Nepal.
• Sarayu flows through the cities of Kapkot, Bageshwar and Seraghat in the state of Uttarakhand.
• The famous city of Ayodhya in Uttar Pradesh is situated on the bank of the Sarayu river.
• Bhuni, Sup, and Khati are some of the famous ghats on this river's bank river.
• The river forms the south-eastern border between the districts of Pithoragarh and Almora.
• Temperate and sub-Tropical forests cover the entire catchment area of the Sarayu River.
• Ramganga meets the left side of the Sarayu at Rameshwar.

Additional Information

• Pindar River:
• Pindar originates from Pindari Glacier which is located in the Bageshwar district of the Kumaon region in Uttarakhand.
• The source of this river, the Pindar glacier is located at an altitude of 3,820 m (12,530 ft).
• The length of the Pindar river is 105 km.
• The mouth of the Pindar river is located at Karnaprayag where it ends by its confluence with the Alaknanda River.
• The river crosses some small villages like Bagholi, Naryanbagar, Nauligaon, Kulsari and Nauti.
• Bhagirathi: 
• Bhagirathi is considered the source stream of the Ganges.
• The source Bhagirathi River is at Gaumukh at the foot of the Gangotri glacier.
• The Bhagirathi and Alaknanda join at Devprayag in Garhwal and are thereafter known as the Ganges.
• Tons:
• The Tons river is a tributary of the Yamuna and flows through the Garhwal region in Uttarakhand, touching Himachal Pradesh.
• The source of this river is Bandarpuch Mountain.
• Its source lies in the 20,722 feet (6,316 m).
• Pabbar and Asan rivers are some of the tributaries of the Tons river.
• Sharda River:
• The Sharda River also called the Kali river and Mahakali River originates at Kalapani in the Himalayas.
• It originates from an elevation of 3,600 m (11,800 ft) in the Pithoragarh district in Uttarakhand.
• It joins the Ghaghra River which is a tributary of the Ganga.
• It takes the name Kali River from the union of the two streams at Gunji as it flows through the hills.
• After crossing Brahmadev Mandi near Tanakpur, it enters the Terai plains, where it is called the Sharda River.

The correct answer is Girish Karnad.

Key Points

• Girish Karnad:
• Girish Karnad was an Indian actor, film director, Kannada writer, playwright, and a Jnanpith awardee, who predominantly worked in South Indian cinema and Bollywood.
• Girish Karnad wrote his first play 'Yayati' in 1961 at the age of 23 when he was still studying at Oxford.
• In the story of King Yayati in Mahabharata, Yayati was cursed to old age for his sexual misconduct and he tries to avert the catastrophe by demanding his son, Pooru's, youth in exchange for the curse on him. 'What makes his version of the tale so resonant, and startlingly original,is that he rejects the traditional glorification of the son's 'self-sacrifice' and, against a backdrop of lust, jealousy, and racial tensions.
• One of Karnad's best-known works, this 1964 play tells the story of 14th-century Delhi ruler Muhammad Bin Tughlaq.
• The 13-scene play closely paralleled 'contemporary' socio-political events in the country at that time. Known in history as the 'wisest fool', Muhammad Bin Tughlaq was a gifted man, but an unlucky one perhaps because all brilliant plans led to catastrophic results.
• He received the 1998 Jnanpith Award, the highest literary honour conferred in India.
• He was conferred Padma Shri and Padma Bhushan by the Government of India and won four Filmfare Awards.
• He continued to work in film, directing such movies as Kanooru Heggadithi (1999) and acting in Iqbal (2005), Life Goes On (2009), and 24 (2016) etc.

The correct answer is Banda Bahadur.

Key Points

• After Guru Gobind Singh's death, the institution of Guruship came to an end and the leadership of the Sikhs passed to his trusted disciple Banda Singh Bahadur.
• Banda Singh Bahadur was a Sikh warrior & a commander of the Khalsa army.
• Since creating his Khalsa rule at Punjab, Banda Singh Bahadur had abolished the zamindari regime & had given "property rights" to the land tiller.
• Banda Singh had rallied together with the lower castes & peasants of Punjab from "Delhi to Lahore"  and had undertaken a vigorous "unequal struggle" against the army of Mughal for almost 8  years.
• However, in the year 1715, he was captured and put to death. There many reasons for his failure. One, the Mughal army was very strong, and second the upper castes & classes of Punjab had joined forces against Banda Singh Bahadur because of his campaign for the rural poor & the lower castes.​

Additional Information

• Guru Nanak Dev was the first Sikh guru.
• Guru Arjan Dev was executed by Mughal Emperor Jahangir.
• Khalsa Panth - a kind of Praetorian Guard was founded by Guru Gobind Singh on April 13, 1699.
• Guru Har Krishan was the youngest Sikh guru, he became guru at the age of 5.

Important Points

• Golden temple:-
• Guru Arjan Sahib got its foundation laid by a muslim saint Hazrat Mian Mir ji of Lahore on 1st of Magh, 1645 Bikrmi Samvat (December,1588).
• The construction work was directly supervised by Guru Arjan Sahib himself.
• The planning to excavate the holy tank (Amritsar or Amrit Sarovar ) was chalked out by Guru Amardas Sahib, the Third Nanak.
• But it was executed by Guru Ramdas Sahib under the supervision of Baba Budha ji.

The correct answer is The US.

Key Points

• The USA remained India's top trading partner for the second consecutive fiscal in 2019-20, which shows increasing economic ties between the two countries.
• In 2019-20, the bilateral trade between the USA and India stood at USD 88.75 billion as against USD 87.96 billion in 2018-19.
• In 2018-19, the USA surpassed China to become India's top trading partner.
• The USA is one of the few countries with which India has a trade surplus.
• The bilateral trade between India and China has dipped to $81.87 billion in 2019-20 from$87.08 billion in 2018-19.
• The Government of India is also considering certain steps like framing technical regulations and quality control orders for a host of items with a view to cut import dependence on China and boost domestic manufacturing.
• India and the US are negotiating a limited trade pact with a view to iron out differences on the trade front and boost commercial ties.
• India is seeking relaxation in the US visa regime, exemption from high duties imposed by the US on certain steel and aluminum products, and greater market access for its products from sectors such as agriculture, automobile, automobile components, and engineering.
• On the other hand, the US wants greater market access for its farm and manufacturing products, dairy items, medical devices, and data localization, apart from a cut on import duties on some information and communication technology products.

The correct answer is Rs.816.

Key Points

• In the year 2011 - 12, the poverty line for a person was fixed at Rs 816 for rural areas.
• For urban areas, it is Rs. 1000 under the Suresh Tendulkar methodology.
• The poverty line in urban is quite high due to the high prices of goods and services in urban areas.
• In 2011-12, the number of poor is 26.92 crore.

Additional Information

• A common method used to estimate poverty in India is based on the income or consumption levels and if the income or consumption falls below a given minimum level, then the household is said to be Below the Poverty Line (BPL).
• NITI Aayog as a policy think tank has replaced Planning Commission, which was earlier responsible for calculating the poverty line in India.
• Poverty Line:
• The conventional approach to measuring poverty is to specify a minimum expenditure (or income) required to purchase a basket of goods and services necessary to satisfy basic human needs and this minimum expenditure is called the poverty line.
• According to the World Bank,  the latest data provides the fact that India’s extreme poverty has declined by 12.3% in 2019 from 2011.

The correct answer is EnglishPro.

Key Points 

• EnglishPro App:​
• Union Minister of Education RameshPokhriyal Nishank launched EnglishPro, a free mobile app, developed by the English and Foreign Languages University, Hyderabad.
• The App has been developed by University Social Responsibility (USR) is the first-of-its-kind initiative by any university in the country and will help learners develop Indian English Pronunciation in the unique “Indian” way.
• It is an educational resource for teachers, students, and people from varied backgrounds.
• This app is a good hand-maid to the “skilling” of youth.
• It tries to achieve the objectives of the interconnected measures by the Government — Skill India and Digital India.

Additional Information

• Other educational apps by Union Government:
• Diksha App: It is a national platform for school education, an initiative of the National Council for Education, Research, and Training. It will help teachers to create training content, profile, in-class resources, and assessment aids and connect with the teacher community.
• Vidyanjali App:

The Union Ministry of Human Resource Development (HRD) on 16 June 2016 launched the Vidyanjali Mobile App that can be used by anyone to register for volunteer work at government schools. Vidyanjali's initiative is in line with the Union HRD Ministry's ongoing efforts under Padhe Bharat Badhe Bharat.

The correct answer is  cultivation of grapes.

Key Points

• Viticulture is the cultivation and harvesting of grapes.
• When the grapes are being used specifically for wine production, the study of grapes can also be called viniculture.
• Both viniculture and viticulture fall under the umbrella of horticulture.
• Viticulture as a science and pursuit, has existed as long as humans have been making and drinking wine.
• The most common grapevine, Vitis vinifera, has been cultivated and fermented by humans since at least the neolithic era.

Additional Information

• The science and art of growing fruit, vegetable, flowers and fruits is known as Horticulture.
• breeding of fish
• Fish farming or raising the fishes in tanks or ponds is called Pisciculture.
• The most important species which are being raised worldwide are Tilapia, Salmon, Carp, and Catfish.
• Pisciculture provides more than 50% of seafood in the world.
• It helps in development by means of generating employment in the fishing community.
• Freshwater Cultivable Fishes: Catla, Rohu, Mrigal, Catfishes, Murrels, and Tilapia
• Marine water cultivable fishes: Sea bass, Grey mullet, and Milk Fish
• Fishery By-products: Fish Oil (comprises of liver and body oil), Fish meal
• rearing of silkworms
• Sericulture is related to the rearing of silkworms.
• Sericulture is an agro-based industry.
• It involves the rearing of silkworms for the production of raw silk.
• India is the second-largest producer of silk within the globe.

The correct answer is 1 : 8.

Key Points Concept:

• Molecular mass is the sum of the atomic masses of the elements present in a molecule.
• The mass of one mole of a substance in grams is called its molar mass.

Explanation:

It is obtained by multiplying the atomic mass of each element by the number of its atoms and adding them together

1 mole of hydrogen = 1gm

1 mole of oxygen = 16gm

Water (H2O) = 2 Hydrogen atoms + 1 Oxygen atom

2 mole of hydrogen = 2gm

1 mole of oxygen = 16 gm

The ratio of the mass of Hydrogen: Ratio of mass of Oxygen =  2/16 = 1/8 

The ratio of the mass of Hydrogen to the mass of Oxygen is always 1:8.

Shortcut Trick

Ratio of Salaries A : B = 6 : 7

B’s salary after 5.5% increase = 105.5% = ₹1,47,700

B’s original salary (7 units) = (1,47,700 ÷ 105.5) × 100 = ₹1,40,000

If 7 units = ₹1,40,000, then 1 unit = ₹20,000

A’s salary = 6 units = 6 × ₹20,000 = ₹1,20,000

∴ The correct answer is ₹1,20,000.

Alternate Method

Given:

Ratio of salaries A : B = 6 : 7

Percentage increase in B’s salary = 5(1/2)% = 5.5%

New salary of B = ₹1,47,700

Calculations:

⇒ Let the initial salaries of A and B be 6x and 7x respectively.

⇒ B’s new salary = 7x + (5.5 ÷ 100) × 7x = 1,47,700

⇒ 7x × (1 + 0.055) = 1,47,700

⇒ 7x × 1.055 = 1,47,700

⇒ 7.385x = 1,47,700

⇒ x = 1,47,700 ÷ 7.385

⇒ x = 20,000

⇒ Salary of A = 6x = 6 × 20,000 = 1,20,000

∴ The correct answer is ₹1,20,000.

Additional Information

Percentage Increase Formula

New Value = Original Value × (100 + Increase%) ÷ 100. This is used to find the final value after a hike.

Ratio and Proportion

If A : B = m : n, then A = m × k and B = n × k, where k is a common multiplication factor.

Base Change in Percentages

To find the original value from an increased value: Original = [New Value ÷ (100 + r)] × 100.

Given:

3 × 7 + 5 - 6 ÷ 3 - 9 + 45 ÷ 5 × 4 - 45

Concept used:

Calculation:

3 × 7 + 5 - 6 ÷ 3 - 9 + 45 ÷ 5 × 4 - 45

⇒ 3 × 7 + 5 - 2 - 9 + 9 × 4 - 45

⇒ 21 + 5 - 2 - 9 + 36 - 45

⇒ 62 - 56

⇒ 6

∴ Required answer is 6.

Shortcut Trick

Identify the Original Price (MP) = Rs. 14,500 and Sale Price (SP) = Rs. 11,890.

Calculate the Discount = 14,500 − 11,890 = Rs. 2,610.

Apply ratio: Discount % = (Discount ÷ MP) × 100.

Discount % = (2,610 ÷ 14,500) × 100 = 2610 ÷ 145 = 18%.

∴ The correct answer is 18%.

Alternate Method

Given: Marked Price (MP) = Rs. 14,500, Selling Price (SP) = Rs. 11,890.

Formulas: Discount = MP − SP | Discount % = (Discount ÷ MP) × 100

⇒ Amount of Discount = Rs. 14,500 − Rs. 11,890 = Rs. 2,610.

⇒ Discount Percentage = (2,610 ÷ 14,500) × 100.

⇒ Discount Percentage = 261,000 ÷ 14,500 = 18%.

∴ The correct answer is 18%.

Additional Information

Marked Price & Discount

The Marked Price is the price printed on an item. The reduction offered on this price is the Discount.

Percentage Calculation

Always calculate the Discount Percentage on the Marked Price (Initial Price), not the Selling Price.

Given:

Amount = Rs. 9982.5

Rate = 12%

Time =  $2\frac{1}{2}$ years

Concept used:

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

Here,

A = amount, P = principal or sum, r = rate, t = time

When interest is calculated on a certain monthly

Then,

r = (r/12) × month

t = total month given in the form of year/no. of months

Calculation:

$2\frac{1}{2}$ years = 30 months   [As 1 year = 12 months]

So, t = 30/10 = 3

r = (12/12) × 10 = 10%

Let the sum be Rs. P

Now,

9982.5 = P(1 + 10/100)³

⇒ 9982.5 = P(1 + 1/10)3

⇒ 9982.5 = P(11/10)3

⇒ 9982.5 = 1331P/1000

⇒ P = 9982.5 × (1000/1331)

⇒ P = 7500

So, sum = Rs. 7500

∴ The sum (in Rs.) is Rs 7500.

Shortcut Trick

Simple Interest (SI) for 4 years = 16400 − 13200 = ₹3200.

Principal (P) = Amount after 4 years − SI for 4 years = 13200 − 3200 = ₹10000.

Required SI = 10000 × 10% × (16/5) = 1000 × 3.2 = ₹3200.

∴ The correct answer is ₹3200.

Alternate Method

Given: Amount (A₁) after 4 years = ₹13,200 | Amount (A₂) after 8 years = ₹16,400.

Formula Used: Simple Interest = (P × R × T) ÷ 100 | Amount = Principal + Simple Interest

⇒ Simple Interest for 4 years = A₂ − A₁ = 16,400 − 13,200 = ₹3,200

⇒ Principal (P) = A₁ − SI for 4 years = 13,200 − 3,200 = ₹10,000

⇒ New Rate (R) = 10% p.a. | New Time (T) = 3 1/5 years = 16/5 years

⇒ New Simple Interest = (10,000 × 10 × 16/5) ÷ 100

⇒ New Simple Interest = (10,000 × 10 × 16) ÷ 500 = 20 × 160 = ₹3,200

∴ The correct answer is ₹3200.

Additional Information

General SI Formula

The simple interest is calculated using the formula: SI = (P × R × T) ÷ 100, where P is the principal, R is the rate of interest per annum, and T is time in years.

Amount in SI

The total amount after time T is given by A = P + SI, which can also be written as A = P(1 + (R × T) ÷ 100).

Rule for SI Difference

If a sum amounts to A₁ in T₁ years and A₂ in T₂ years, then the SI for (T₂ − T₁) years is simply (A₂ − A₁).

Shortcut Trick

Distance = 1600 m = 1.6 km

Time = 4 min = 4/60 h = 1/15 h

Speed = Distance ÷ Time = 1.6 ÷ (1/15) = 1.6 × 15 = 24 km/h

∴ The correct answer is 24 km/h.

Alternate Method

Given:

Distance (D) = 1600 m

Time (T) = 4 min = 4 × 60 = 240 seconds

Formula Used:

Speed = Distance ÷ Time

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

Calculations:

⇒ Speed in m/s = 1600 ÷ 240

⇒ Speed in m/s = 160 ÷ 24 = 20/3 m/s

⇒ Speed in km/h = (20/3) × (18/5)

⇒ Speed in km/h = (20 ÷ 5) × (18 ÷ 3)

⇒ Speed in km/h = 4 × 6 = 24 km/h

∴ The correct answer is 24 km/h.

Additional Information

Unit Conversion for Speed

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

Average Speed

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

Relative Speed

Same direction: Relative Speed = S₁ − S₂. Opposite direction: Relative Speed = S₁ + S₂.

Given:

The average of the two numbers is 13

The square root of their product is 12

Concept used:

(a + b)2 = a2 + b2 + 2ab

(a - b)2 = a2 + b2 - 2ab

Calculation:

Sum of the numbers = 13 × 2 = 26

Let the two numbers be a and b

So, (a + b) = 26      ----(i)

Now,

√ab = 12

⇒ √ab² = 12²

⇒ ab = 144

Now,

(a + b)² = 26²

⇒ a² + b² + 2ab = 676

⇒ a2 + b2 + 2ab - 4ab = 676 - 4 × 144

⇒ a2 + b2 - 2ab = 676 - 576

⇒ (a - b)² = 100

⇒ (a - b) = 10      ----(ii)

From eq (i) and eq (ii) we can say

a = 18 and b = 8

Now,

Difference of the two numbers = 18 - 8

⇒ 10

∴ The difference between the numbers is 10.

Shortcut TrickLet the two numbers be a and b 

Sum of the numbers = 13 × 2 = 26

So, a + b = 26

According to the question, √(a × b) = 12

⇒ ab = 144 (Square on both sides)

(a - b) = $\sqrt{(a + b)^2-4ab}$

⇒ $\sqrt{(26)^2-4\times144}$

⇒ $\sqrt{676-576} = \sqrt{100}$ = 10

∴ (a - b) = 10

∴ The difference between the numbers is 10.

Given:

Length of the train = 725 m

Lenght of the tunnel = 235 m

Time taken to cover the tunnel = 48 sec

Concept used:

Speed = Distance/time

km/h × (5/18) = m/sec

When a train passes a bridge/tunnel/platform, then it will cover its own length + length of that bridge/tunnel/platform

Calculation:

According to the concept,

The train had covered 725 + 235 = 960 m

Speed of the train in m/sec = 960/48

⇒ 20 m/sec

Speed of the train in km/h = 20 × (18/5)

⇒ 72 km/h

∴ The speed of the train is 72 km/h.

Given:

45 - 3 × (4 of 6 + 12 ÷ 3 × 6 - 4 × 5) + 6

Concept used:

Calculation:

45 - 3 × (4 of 6 + 12 ÷ 3 × 6 - 4 × 5) + 6

⇒ 45 - 3 × (24 + 12 ÷ 3 × 6 - 4 × 5) + 6

⇒ 45 - 3 × (24 + 4 × 6 - 4 × 5) + 6

⇒ 45 - 3 × (24 + 24 - 20) + 6

⇒ 45 - 3 × 28 + 6

⇒ 45 - 84 + 6

⇒ 51 - 84

⇒ - 33

∴ Required answer is - 33.

Given:

Selling price of the chair = Rs. 720

Discount % = 10

Cost price of the chair = Rs. 640

Concept used:

Selling price = Marked price - Marked price × discount%

Profit = Selling price - cost price

Profit % = (profit/cost price) × 100

Calculation:

Let the marked price of the article be 10a

According to the question,

10a - 10a × 10% = 720

⇒ 9a = 720

⇒ a = 720/9 = 80

So, the marked price of the chair = 10 × 80

⇒ Rs. 800

Now,

Profit on the chair when it is sold at marked price = 800 - 640

⇒ Rs. 160

Profit % = (160/640) × 100

⇒ 25

∴ The profit percentage will be 25%.

Shortcut Trick Initial Ratio of Ravi and Sumit = 4 : 5 New Ratio = 35 : 40 = 7 : 8 (after simplifying by 5) Change in ratio parts for both = 7 − 4 = 3 units (or 8 − 5 = 3 units) Since each salary increased by Rs. 6,000, then 3 units = Rs. 6,000 1 unit = Rs. 2,000 ⇒ Sumit's increased salary = 8 units = 8 × 2,000 = Rs. 16,000 ∴ The correct answer is Rs. 16,000.

Alternate Method Given: Initial salaries of Ravi and Sumit = 4 : 5 Salary increase for each = Rs. 6,000 New salary ratio = 35 : 40 Formula Used: New Ratio = (Initial Salary + Increase) ÷ (Initial Salary + Increase)

Calculations: ⇒ Let the initial salaries be 4x and 5x. ⇒ (4x + 6000) / (5x + 6000) = 35 / 40 ⇒ (4x + 6000) / (5x + 6000) = 7 / 8 ⇒ 8 × (4x + 6000) = 7 × (5x + 6000) ⇒ 32x + 48,000 = 35x + 42,000 ⇒ 35x − 32x = 48,000 − 42,000 ⇒ 3x = 6,000 ⇒ x = 2,000 ⇒ Sumit's increased salary = 5x + 6,000 ⇒ (5 × 2,000) + 6,000 = 10,000 + 6,000 = 16,000 ∴ The correct answer is Rs. 16,000.

Additional Information Ratio Scaling A ratio remains unchanged if both its terms are multiplied or divided by the same non-zero number. For example, 35 : 40 = (35/5) : (40/5) = 7 : 8. Comparison of Ratios When the same quantity is added to both terms of a ratio a : b, the new ratio behaves differently depending on whether a < b or a > b. If a < b, then (a + k)/(b + k) > a/b. Proportions If two ratios are equal, they are said to be in proportion. If a : b = c : d, then the product of extremes equals the product of means (a × d = b × c).

Given:

A loss of $10\frac{1}{2}\%$ gets converted into a profit of $11\frac{3}{5}\%$ when the selling price is increased by Rs. 132.60

Concept used:

SP = CP + CP × Profit%

SP = CP - CP × Loss%

Calculation:

Let CP of the article be 100a

Now,

SP for 1st case = 100a - 100a × $10\frac{1}{2}\%$

⇒ 89.5a

SP for 2nd case = 100a + 100a × $11\frac{3}{5}\%$

⇒ 111.6a

According to the question,

111.6a - 89.5a = 132.6

⇒ 22.1a = 132.6

⇒ a = 132.6/22.1

⇒ a = 6

So, cost price = 100 × 6

⇒ Rs. 600

∴ The cost price (in Rs.) the article is 600.

Shortcut TrickLoss = 10.5%, Profit = 11.6%

Overall profit increased = 11.6% - (- 10.5%) = 22.1%

22.1% = 132.6

1% = 6

100% = Rs. 600

Given:

89563x87y is divisible by 72

Concept used:

Divisibility rule of 8 = If the last three digits of a number are divisible by 8, then the number is completely divisible by 8.

Divisibility rule of 9 = If the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.

Calculation:

72 = 8 × 9

So, the number should be divisible by both 8 and 9

Now,

87y is divisible by 8

The only possible value of y is 2

Now,

8 + 9 + 5 + 6 + 3 + x + 8 + 7 + 2 = 48 + x is divisible by 9

Clossest value of (48 + x) which is divisible by 9 is 54

So, x = 6

Now,

$\sqrt{7x-3y}$ = $\sqrt{7 \times 6-3 \times 2}$

⇒ $\sqrt{42-6}$

⇒ $\sqrt{36}$

⇒ 6

∴ Required answer is 6.

Given:

A shopkeeper sold an article at a gain of 20%

Concept used:

Selling price = cost price × (1 + profit%)

Calculation:

Let the actual cost price be Rs. 100x

So, actual selling price = 100x × 120%

⇒ Rs. 120x

Now,

If he had bought it at 20% less than the actual then its cost price = 100x × 80%

⇒ Rs. 80x

Now, new selling price = 80x × 125%

⇒ 100x

According to the question,

120x - 100x = 10

⇒ 20x = 10

⇒ x = 1/2

So, actual cost price = 100 × (1/2)

⇒ Rs. 50

∴ The Cost Price of the article is Rs. 50.

Given:

Anu is four times as good as Binni in completing a task.

Together they finish the same task in 7 hours.

Concept used:

Total work = Efficiency of the workers × time taken by them

Calculation:

Let the efficiency of Binni be x

So, the efficiency of Anu = 4x

Effective efficiency of the them = x + 4x = 5x

Total work = 7 × 5x

⇒ 35x units

Now,

Time taken by Anu to complete the work alone = 35x/4x

⇒ 35/4 hours

∴ Anu alone will complete the task in 35/4 hours.

Shortcut Trick

Total Work (LCM of 10, 20, 30) = 60 units.

Efficiencies: P = 6, Q = 3, R = 2.

Day 1 (P+Q) = 6 + 3 = 9 units | Day 2 (P+R) = 6 + 2 = 8 units.

2-day cycle = 9 + 8 = 17 units.

In 3 cycles (6 days), work done = 17 × 3 = 51 units. Remaining = 60 − 51 = 9 units.

Day 7: (P+Q) completes remaining 9 units in 1 day.

∴ The correct answer is 7 days.

Alternate Method

Given: Time taken by P = 10 days, Q = 20 days, R = 30 days.

Formula Used: Total Work = Efficiency × Time

⇒ Work done on Day 1 (P + Q) = 6 + 3 = 9 units

⇒ Work done on Day 2 (P + R) = 6 + 2 = 8 units

⇒ Work done in one cycle (2 days) = 9 + 8 = 17 units

⇒ Work done in 3 cycles (6 days) = 17 × 3 = 51 units

⇒ Remaining work = 60 − 51 = 9 units

⇒ On Day 7, P and Q work together and complete 9 units.

⇒ Total time = 6 + 1 = 7 days.

∴ The correct answer is 7 days.

Additional Information

Alternate Day Work

In alternate day problems, calculate the work done in one complete cycle first, then divide the total work by the cycle's work to find the number of full cycles.

Efficiency and Time

Efficiency is inversely proportional to the time taken to complete the work. Efficiency = Total Work ÷ Time.

Given:

Total score of the batsman = 124 run

He has hitten 6 boundaries and 10 sixes

Calculation:

The batsman scored from boundaries = 6 × 4

⇒ 24 runs

The batsman scored from sixes = 10 × 6

⇒ 60 runs

Total runs scored by running between the wickets = 124 - (24 + 60)

⇒ 124 - 84

⇒ 40 runs

Required % = (40/124) × 100

⇒ $32\frac{8}{31}$

∴ He scored $32\frac{8}{31}\%$ of his total score by running between the wickets.

Shortcut Trick

Subtract the remainders from the numbers: 398 − 7 = 391, 437 − 12 = 425, 5425 − 2 = 5423.

The greatest number is the HCF of 391, 425, and 5423.

Check options: 425 is divisible by 17 (17 × 25) and 391 is divisible by 17 (17 × 23).

∴ The correct answer is 17.

Alternate Method

Given: Numbers 398, 437, 5425 and remainders 7, 12, 2.

Formula: Greatest number = HCF(Number₁ − Remainder₁, Number₂ − Remainder₂, Number₃ − Remainder₃)

⇒ First number = 398 − 7 = 391

⇒ Second number = 437 − 12 = 425

⇒ Third number = 5425 − 2 = 5423

⇒ Using Long Division Method for HCF of 391 and 425:

⇒ 425 = 391 × 1 + 34

⇒ 391 = 34 × 11 + 17

⇒ 34 = 17 × 2 + 0

⇒ HCF(391, 425) = 17

⇒ Now check if 5423 is divisible by 17: 5423 ÷ 17 = 319

∴ The correct answer is 17.

Additional Information

HCF with Remainders

To find the largest number that divides x, y, and z leaving remainders a, b, and c, calculate HCF(x−a, y−b, z−c).

LCM with Remainders

To find the least number which when divided by x, y, and z leaves the same remainder r in each case, calculate LCM(x, y, z) + r.

Difference Method for HCF

The HCF of a set of numbers is always a factor of the difference between any two numbers in the set.

Given:

Profit = SP of 12 m jute

Concept used:

Profit = SP - CP

Profit % = (Profit/CP) × 100

Here,

CP = Cost price

SP = Selling price

Calculation:

According to the question,

SP of 36 m = CP of 36 m + SP of 12 m

⇒ SP of 24 m = CP of 36 m

So,

SP/CP = 36/24 or 3/2

So, if CP of 1 m jute is Rs. 2 then its SP is Rs. 3

So, profit = Rs. 1

Profit % = (1/2) × 100

⇒ 50%

∴ The gain percentage is 50%.

Shortcut Trick

Side of an equilateral triangle = Perimeter ÷ 3

Side = 36√3 ÷ 3 = 12√3 cm

Height = (√3 ÷ 2) × Side

Height = (√3 ÷ 2) × 12√3 = 6 × 3 = 18 cm

∴ The correct answer is 18 cm.

Alternate Method

Given:

Perimeter of the equilateral triangle = 36√3 cm

Formula Used:

Perimeter of an equilateral triangle = 3 × Side

Height of an equilateral triangle = (√3 ÷ 2) × Side

Base = 12√3 cm 12√3 cm 12√3 cm

h = 18

A B C D

Calculations:

⇒ 3 × Side = 36√3

⇒ Side = 36√3 ÷ 3

⇒ Side = 12√3 cm

⇒ Height = (√3 ÷ 2) × Side

⇒ Height = (√3 ÷ 2) × 12√3

⇒ Height = 6 × √3 × √3

⇒ Height = 6 × 3 = 18 cm

∴ The correct answer is 18 cm.

Additional Information

Area of Equilateral Triangle

The area can be calculated directly if the side length (a) is known: Area = (√3 ÷ 4) × a².

Inradius (r)

The radius of the inscribed circle is exactly one-third of the triangle's height: r = a ÷ 2√3.

Circumradius (R)

The radius of the circumscribed circle is exactly two-thirds of the triangle's height: R = a ÷ √3.

Shortcut Trick

Ratio of parts for equal amounts in Simple Interest is 1/(100 + R₁T₁) : 1/(100 + R₂T₂).

Ratio = 1/(100 + 5 × 2) : 1/(100 + 5 × 4) = 1/110 : 1/120 = 12 : 11.

Total units = 12 + 11 = 23 units → ₹2,760.

1 unit = 2,760 ÷ 23 = 120.

Smaller part (11 units) = 11 × 120 = 1,320.

∴ The correct answer is ₹1,320.

Alternate Method

Given:

Total principal (P) = ₹2,760

Rate (R) = 5% p.a.

Time periods: T₁ = 2 years and T₂ = 4 years

Formula Used:

Amount (A) = P + (P × R × T) ÷ 100 = P[1 + (RT ÷ 100)]

Calculations:

⇒ Let the two parts be P₁ and P₂.

⇒ A₁ = P₁[1 + (5 × 2) ÷ 100] = P₁[1 + 0.10] = 1.10 P₁

⇒ A₂ = P₂[1 + (5 × 4) ÷ 100] = P₂[1 + 0.20] = 1.20 P₂

⇒ According to the question: 1.10 P₁ = 1.20 P₂

⇒ P₁ ÷ P₂ = 1.20 ÷ 1.10 = 12 ÷ 11

⇒ Ratio P₁ : P₂ = 12 : 11

⇒ Total principal ratio = 12 + 11 = 23 units

⇒ 23 units = ₹2,760

⇒ 1 unit = 2,760 ÷ 23 = ₹120

⇒ Smaller part (P₂) = 11 × 120 = ₹1,320

∴ The correct answer is ₹1,320.

Additional Information

Simple Interest Amount Relationship

When the amounts are equal, the principals are in the ratio P₁ : P₂ : ... : P_n = 1/(100 + R₁T₁) : 1/(100 + R₂T₂) : ... : 1/(100 + R_nT_n).

Equal Interest Condition

If the interests earned are equal (SI₁ = SI₂), the ratio of principals is P₁ : P₂ = 1/R₁T₁ : 1/R₂T₂.

Effective Rate of Interest

Effective Rate for Amount in Simple Interest = (100 + R × T)%, where 100% represents the Principal.

Given:

The number = 2 × 10⁶

Calculation:

10⁶ = (10²)³

⇒ 100³

According to the question,

Required number = 2 × 1003 × $\frac{12}{100} ×\frac{4}{100} ×\frac{7}{100}$

⇒ 2 × 100 × 100 × 100 × $\frac{12}{100} ×\frac{4}{100} ×\frac{7}{100}$

⇒ 2 × 12 × 4 × 7

⇒ 672

∴ Required answer is 672.

Given:

The number of students in class IX and class X is 42 and 45, respectively

The ratio of the number of boys to girls in classes is IX and X is 9 ∶ 5 and 8 ∶ 7

Calculation:

Number of boys in class IX = 42 × (9/14)

⇒ 27

Number of girls in class IX = 42 × (5/14)

⇒ 15

Again,

Number of boys in class X = 45 × (8/15)

⇒ 24

Number of girls in class X = 45 × (7/15)

⇒ 21

Total of boys in two classes = 27 + 24

⇒ 51

Total of girls in two classes = 15 + 21

⇒ 36

Difference = 51 - 36

⇒ 15

∴ The difference between the total number of boys and the total number of girls in both the classes taken together is 15.

Shortcut Trick

Equate the Volume of Cuboid and Volume of Cylinder: 112 × 44 × 25 = (22/7) × 35 × 35 × h.

Solving for Height (h): 123200 = 3850 × h ⇒ h = 32 cm.

Curved Surface Area (CSA) = 2 × (22/7) × 35 × 32.

CSA = 44 × 5 × 32 = 7040 cm².

∴ The correct answer is 7040 cm².

Alternate Method

Given:

Dimensions of rectangular block: Length (L) = 112 cm, Breadth (B) = 44 cm, Height (H) = 25 cm.

Cylinder Radius (r) = 35 cm, π = 22/7.

Formula Used:

1. Volume of Cuboid = L × B × H
2. Volume of Cylinder = πr²h
3. Curved Surface Area (CSA) of Cylinder = 2πrh

 

 

Calculations:

⇒ Volume of Rectangular Block = 112 × 44 × 25 = 123200 cm³

⇒ When melted, Volume of Cylinder = Volume of Block

⇒ (22/7) × 35 × 35 × h = 123200

⇒ 22 × 5 × 35 × h = 123200

⇒ 3850 × h = 123200

⇒ Height (h) = 123200 ÷ 3850 = 32 cm

⇒ Curved Surface Area = 2 × (22/7) × 35 × 32

⇒ CSA = 2 × 22 × 5 × 32

⇒ CSA = 44 × 160 = 7040 cm²

∴ The correct answer is 7040 cm².

Additional Information

Melting and Recasting Rule

When one solid object is melted and recast into another shape, the total volume remains constant, provided there is no wastage.

Total Surface Area of Cylinder

The Total Surface Area (TSA) includes the curved area and the area of two circular bases: TSA = 2πrh + 2πr² = 2πr(h + r).

Volume of Sphere

For comparison in similar problems, the Volume of a Sphere is given by (4/3)πr³ and its Surface Area is 4πr².

∴ The correct answer is 7040 cm².

Given:

The average of 10 numbers is 46.

Concept used:

Average = Sum of elements/Number of elements

Calculation:

Sum of all numbers = 46 × 10 = 460

Correct sum = 460 - 42 + 142

⇒ 602 - 42

⇒ 560

Correct Average = 560/10

⇒ 56

∴ The correct average is 56.

The correct answer is "Apparent".

Key Points

• Let us understand the meaning of the given and the marked words.
• Visible means something that is capable of being discovered or noticed. (कुछ ऐसा जो खोजा या देखा जा सके)
• Synonyms: Observable or viewable.
• Example: The house is clearly visible from the beach.
• Apparent means something clear, obvious or can be easily observed. (कुछ स्पष्ट, स्पष्ट या आसानी से देखा जा सकता है)
• Synonyms: Evident or noticeable or recognizable.
• Example: Her happiness was apparent to everyone.
• From the above explanation, it is clear that the word "apparent" is the synonym of "visible".
• Hence, the correct answer is option 2) Apparent.

Additional Information

• Let us understand the meaning of the other given words.
• Secret means something that is not or must not be known to other people. (ऐसा कुछ जो अन्य लोगों को ज्ञात नहीं है या नहीं होना चाहिए।)
  
• Vague means something that is not clear or definite. (कुछ ऐसा जो स्पष्ट या निश्चित न हो।)
  
• Hidden means something/someone being out of sight or not readily evident. (कुछ / कोई दृष्टि से बाहर हो रहा है या आसानी से स्पष्ट नहीं है।)
  

The correct answer is "Omniscient".

Key Points 

• One-word substitution is the use of one word in place of a wordy phrase in order to make the sentence structure clearer.
• The meaning, with the replacement of the phrase remains identical while the sentence becomes shorter.
• For example The one who eats human flesh : Cannibal.
• In the same way, to substitute the group of words "A person who knows everything", let us understand the meaning of the given options.
• Naive means someone without enough experience of life and too ready to believe or trust other people.(ऐसा व्यक्ति जिसके पास जीवन का पर्याप्त अनुभव नहीं है और वह अन्य लोगों पर विश्वास करने या भरोसा करने के लिए तैयार है)
• Example: I was young and naive at the time and used to easily believe everyone.
• Omniscient means someone having complete or unlimited knowledge.(पूर्ण या असीमित ज्ञान रखने वाला व्यक्ति)
• Example: They give the impression that the book is omniscient.
• Intelligent means having a good amount of mental ability or being clever.(अच्छी मात्रा में मानसिक क्षमता होना या चतुर होना)
• Example: The professor was very intelligent.
• Omnipresent means something that is present everywhere at the same time.(कुछ ऐसा जो एक ही समय में हर जगह मौजूद हो)
• Example: The actor became an omnipresent icon of style.
• From the above-explained meanings, it can be inferred that "omniscient" is the required word.
• Hence, the correct answer is option 2) Omniscient.

The correct answer is "Auditor".

Key Points 

 

• One word substitution is the use of one word in place of a wordy phrase in order to make the sentence structure clearer.
• The meaning, with the replacement of the phrase remains identical while the sentence becomes shorter.
• For example: One who loves his country: Patriot.
• In the same way, to substitute the group of words "One who examines a company's financial record", let us understand the meaning of the given options.
• Conductor means a person in charge of a public means of transportation (as a train) ;  a person or thing that directs or leads.
• Example: The woman conductor kindly responded to my question.
• Author means a person who writes a book, play, etc..
• Example: My favorite author is Munshi Premchand.
• Auditor means a person authorized to review and verify the accuracy of financial records.
• Example: The accounts were certified by an auditor.
• Instructor means someone whose job is to teach a practical skill or a sport.
• Example: Rahul is a certified fitness instructor.
• From the above-explained meanings, it can be inferred that "Auditor" is the required word.
• Hence, the correct answer is option 3) Auditor.

The correct answer is "advised".

Key Points 

• In the given sentence, The manner in which the doctor informed the object is to be filled in the blank.
• The doctor in the sentence is giving his counsel to the object regarding her eating habits.
• Now, let us explore the meaning of the given options:
• Advised means to tell somebody what you think he/she should do..
• Example: I advised Riya to stop wasting her time on social media.
• Considered means to think about something carefully, often before making a decision.
• Example: I considered all the options before coming to this decision.
• Arranged means to put something in order or in a particular pattern.
• Example: He arranged a meeting between the two rivals.
• Expressed means to show or convey feelings by words or action.
• Example: I expressed my fear regarding the merger of the two companies.
• From the meanings of the words we can infer that "advised" is the word that matches the process of giving counsel by the doctor in the given sentence.
• Hence, the correct answer is option 1) Advised.

The correct answer is "to make excuses or do things to gain time".

Key Points

• An idiom is a group of words in a fixed order that has a particular meaning that is different from the meanings of each word on its own.
• For example: Rain cats and dogs: to rain very heavily.
• The sky suddenly turned gray and it rained cats and dogs for almost an hour.
• The given idiom "play for time" means to make excuses and delay until you are ready.
• Example: My computer crashed just as the meeting began, so I had to play for time while I waited for it to reboot.
• From the given explanation it is clear that the meaning of the given idiom is "To make excuses or do things to gain time".
• Hence, the correct answer is option 2).

Additional Information

• Let us have a look at  some commonly used idioms:

The correct answer is "No substitution required".

Key Points

• In the given sentence, the possibility of the object to grab the opportunity to earn some money is discussed.
• The underlined part "to earn" is correctly used because:
• "to earn" is used as an infinitive verb and the use of 'to' here is not as a preposition instead it is a part of the verb.
• An infinitive verb is essentially the base form of a verb with the word "to" in front of it.
• From the above explanation, it can be inferred that the options 2), 3) and 4) is incorrect as the base form of verb is not used.
• Thus, the correct answer is option 1).

The correct answer is "To die".

Key Points 

• An idiom is a group of words in a fixed order that has a particular meaning that is different from the meanings of each word on its own.
• For example: Pull someone's leg: to joke with someone.
• I panicked when she told me the test is today but then I realized that she was just pulling my leg.
• The given idiom "to breath one's last" means to die.
• Example: This is the room where my grandfather breathed his last.
• Hence, the correct answer is option 4).

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Additional Information

• Let us have a look on some commonly used idioms:

The correct answer is "efficiently".

Key Points

• In the given sentence, the efficacy of microwave ovens is discussed as compared to conventional ovens.
• The qualities of the microwave oven are described before and after the underlined word.
• But the underlined word "anxiously" does not exactly describe a quality.
• Anxiously means a way that shows you are eager to get or do something in an uneasy or worried manner.
• For example - The children were anxiously waiting for their Christmas gifts.
• Thus, we have to substitute 'anxiously' with a word that describes the quality of the oven.
• Let's go through the options to understand their meanings and see whether they describe a characteristic of the oven.
• Angrily means in a way that shows that you are angry with someone.
• Example: She angrily rejected the opinions of the board members.
• Efficiently means working or operating in an organized, quick, and effective way.
• Example: London city's transport system is one of the most efficient in the world.
• Beautifully means in a way that is very attractive.
• Example: Their house is beautifully decorated.
• Accidently means something happening by chance or accident.
• Example: I accidentally deleted the file.
• From the above-explained meanings, it can be inferred that the correct word to substitute will be "efficiently".
• Thus, the correct answer is option 2) Efficiently.

The correct answer is "out of your system".

Key Points

• In the given sentence, the use of the preposition "from" is inaccurate.
• The sentence explains that the subject is required to make the cholesterol get out of her body.
• The double preposition is a proposition that is made by combining two simple prepositions. For example, the phrase "out of" would be a double preposition, since both "out" and "of" are simple prepositions.
• As "out of" is already used as a preposition that talks about movement from within somewhere or something, usually with a verb that expresses movement ("get" in this sentence).
• The use of another preposition i.e. "from" is superfluous.
• Hence, the correct answer is option 1) out of your system.

The correct sentence: You need to get the cholesterol out of your system.