SSC GD Constable Previous Year Paper (Held on: 17th November 2021 Shift 1)

Given: KILOGRAM is written as LZQFNKHJ. 

The logic followed here is: As shown below, 

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Similarly,

Hence, SEZQBQHZ is the correct answer.

Given: ‘Complicated’ is related to ‘Simple’

The logic followed here is:

• Complicated is the antonym of Simple.

Similarly,

• Shrink is the antonym of Expand.

Hence, Expand is the correct answer.

The logic followed here is:

• 27 - positional values of the given letters (positional values of the opposite letter), as shown below,
• 'NOTION' is coded as '13127181213'.

​

Similarly,

• BEAUTIFY = ?

Hence, 2522266718212 is the correct answer.

Eight friends: P, Q, R, S, T, U, V, and W.

(1) T sits third to the left of W.

(2) T sits third to the right of S.

(3) Q is to the immediate left of S. 

(4) V is between U and W. 

(5) P is in between R and S. Thus, the final seating arrangement is as follows,

Hence, Q is sitting between S and W.

The logic followed here is:

The paper when unfolded will look like this:

Hence, option (1) is the correct answer.

Given: 16, 9, 27, 19, 76, 67, 335, ?

The logic followed here is:

It is an alternate series,

• Here a natural number (starting from 7) is subtracted from the first number.
• The second number is multiplied with a natural number (starting from 3), as shown below,

Hence, 325 is the correct answer.

By checking options:

(1) LOPK

(2) EVIR

(3) CXGV

(4) HSLO

Hence, CXGV is different.

Given: 

The logic followed here is:

Detailed Explanation:

• The line PQ is the mirror.
• The given word "sxg5AY" ends with Y. So the mirror image will start with 'Y' ⇒ Option 1 is eliminated.
• The given word "sxg5AY" has third last digit "5", So the third digit of the mirror image should be "

" ⇒ Option 4 is eliminated.

• The given word "sxg5AY" has fourth last digit "g", So the fourth figure of the mirror image should be "

" ⇒ Option 2 is eliminated.

Hence, option (3) is the correct answer.

Given: P_RQPS_ P _Q_SR_P_RQ

By checking options and substituting accordingly:

1) SRQSRPQS → PSRQ - PSRQ - PSRQ - PSRQ - PSRQ

       ♦  Here "PSRQ" is repeated.

2) SRSQRPQS → PSRQ - PSRS - PQRQ - PSRQ - PSRQ

3) QRQSRPQS → PQRQ - PSRQ - PSRQ - PSRQ - PSRQ

4) SQQSRPQS → PSRQ - PSQQ - PSRQ - PSRQ - PSRQ

• Option (1) gives a pattern of PSRQ - PSRQ - PSRQ - PSRQ - PSRQ.

Hence, SRQSRPQS is the correct answer.

The least possible diagram is as follows:

Conclusions:

I. Some comets are planets → True (as some planets are comets)

II. All stars are comets → False (it is possible but not definite as shown in the diagram above)

Hence, only conclusion I follows.

Given: 

The logic followed here is:

        ♦   By interchanging only two letters in the clockwise direction and placing a number (starting from 1) in between them in each step, as shown below,

Hence, option (4) is the correct answer.

From the given information,

(1) Radha and Gyanesh have three daughters - Manuja, Tarini, and Sushma.

(2) Tarini is married to Jai and Sushma is married to Abhay.

(3) Akhil is the third son-in-law of Gyanesh.

(4) Akhil has two children Piyush and Rani.

(5) Jai has two daughters Richa and Neha.

(6) Mridul is the only son of Abhay. Thus, the final family tree is as follows,

Hence, Radha is the maternal grandmother of Rani.

Given: 240, 258, 278, 300, ?

The logic followed here is:

Hence, 324 is the correct answer.

Given: Two years ago, T was twice as old as P. P is thrice as old as R. In five years, P will be 29. 

According to the question,

Two years ago, T was twice as old as P.

• T - 2 = 2 × (P - 2);     _________(i)

At present, P is thrice as old as R.

• P = 3 × R;    ____________(ii)

In five years, P will be 29. 

• P + 5 = 29
• P = 29 - 5 = 24 years

Now, by substituting the age of P, we get,

• T - 2 = 2 × (P - 2)
• T - 2 = 2 × (24 - 2)
• T - 2 = 2 × 22
• T = 44 + 2
• T = 46 years

Hence, the present age of T is 46 years.

Given: 

• Logic: If two dice have same face value in given image than their clockwise or anticlockwise wise number/letter are know as opposite number/letter in dice.
• While moving in clockwise direction from common face (3) of dice (1) and dice (2):

From the both dices:

 

• As it is a dice so it Implies that 3 will be on the opposite face of 6.

Hence, 3 is the correct answer.

Given: 'ABSTRACT’ is written as ‘IIYYVDEU’.

The logic followed here is: 

Similarly,

Hence, QUYYMQEU is the correct answer.

Given: 

The logic followed here is: the given image is embedded in the answer figure as shown below,

Hence, option (3) is the correct answer.

The logic followed here is:

• All fathers are men and no men is a mother, as shown in the diagram below:

<br>

 

Hence, option (2) is the correct answer.

Given: METHOD : OIZPYP :: NORMAL : ?

The logic followed here is:

• Adding the multiples of 2 to the positional values of the given letters, as shown below,
• METHOD : OIZPYP

Similarly,

• NORMAL : ?

Hence, PSXUKX is the correct answer.

Six friends: A, B, C, D, E, and F.

(1) E sits third to the right of C.

(2) D is sitting immediately to the left of E. 

(3) B sits between F and C.

Thus, the final seating arrangement is as follows,

Hence, A is second to the right of B.

The logic followed here is:

• Row wise addition:
• Second number + third number = first number

Row (1) → 28 + 29 = 57

Row (3) → 37 + 35 = 72

Similarly,

Row (2) → ? + 33 = 68

? = 68 - 33

? = 35

Hence, 35 is the correct answer.

Given: UC, AE, GG, MI, SK, ?

The logic followed here is: 

• First letters + 6
• Second letter + 2

Hence, YM is the correct answer.

Arranging all the words as per their order in the dictionary:

• The first three letters are common to each word: C, R, E.
• So, we will compare the words from the fourth letter.

2. Creature
3. Credentials
4. Credible
5. Creditable
6. Creditor

Hence, 2, 5, 3, 4, 1 is the correct order.

By substituting the following symbols,

 

(1) 66 B 2 D 54 C 18 = 135

LHS = 66 - 2 ÷ 54 × 18 

= 66 - 0.037 × 18 

= 66 -  0.666

= 65.334 ≠ 135

LHS ≠ RHS

(2) 45 A 5 C 7 D 14 = 77

LHS = 45 + 5 × 7 ÷ 14

= 45 + 5 × 0.5

= 45 + 2.5

= 47.5 ≠ 77

LHS ≠ RHS

(3) 45 D 5 C 7 A 14 = 77 

LHS = 45 ÷ 5 × 7 + 14 

= 9 × 7 + 14

= 63 + 14

= 77

LHS = RHS

(4) 66 C 2 B 54 D 18 = 135

LHS = 66 × 2 - 54 ÷ 18

= 66 × 2 - 3

= 132 - 3

= 129 ≠ 135

LHS ≠ RHS

Hence, 45 D 5 C 7 A 14 = 77 is the correct equation.

Given: 16 : 256 :: 21 : ? :: 19 : 361

The logic followed here is:

16 : 256 → 16² = 256

And,

19 : 361 → 19² = 361

Similarly,

21 : ? → 21² = 441

Hence, 441 is the correct answer.

The correct answer is 19.**

 Key Points

• Indian National Congress (INC) won 19 seats in the 17th Bihar Legislative Assembly Election.
• INC was founded on 28th December 1885 by A O Humes.
• The former president of INC was Sonia Gandhi.
• the present president of congress is Shri Mallikarjun Kharge.
• Its current headquarters is located at Akbar Road, New Delhi.

Additional Information

• 17th Bihar Legislative Assembly Election was held in three phases in October-November, 2020.
• The term of the previous 16th Bihar Legislative Assembly ended on 29th November 2020.
• Current Chief Minister of Bihar - Nitish Kumar
• Total Seats in Bihar Legislative Assembly - 243 Seats.
• The current government in Bihar is the Coalition Government of RJD and JDU.

The correct answer is Currency Deposit Ratio.

Key Points

• Currency Deposit Ratio is the ratio of money held by public in currency to that they hold in bank deposits.
• The currency deposit ratio shows the amount of currency that people hold as a proportion of aggregate deposits.
• It reflects people's preference for liquidity.
• An increase in the currency deposit ratio leads to an Decrease in the money multiplier effect.
• An increase in deposit rates will induce depositors to deposit more, thereby leading to a increase in the Cash to Aggregate Deposit ratio. This will in turn lead to a fall in Money Multiplier.

Additional Information

• The proportion of the total deposits commercial banks keep as reserves are the Reserve Ratio.
• Cash Reserve Ratio is the fraction of money that banks must deposit with the RBI. Banks do not earn any interest on this amount.
• Statutory Liquidity Ratio is the fraction of the total deposits of a bank that must be kept in a liquid form.
• Banks can use this money to purchase Government Securities (G-Sec).

The correct answer is 9000

Key Points

• Chandrayaan 2 mission launched on July 22, 2019, from GSLV (Geosynchronous Satellite Launch Vehicle) Mark-III Satish Dhawan Space Centre, Sriharikota, Andhra Pradesh.
• Chandrayaan 2 mission was the 2nd lunar exploration mission by the ISRO (Indian Space Research Organisation) after Chandrayaan 1.
• Chandrayaan 2 mission comprised an Orbiter, Lander - Vikram and Rover-Pragyan to explore the unexplored South Pole of the Moon.

Additional Information

• Chandrayaan-2 mission is related to lunar scientific knowledge and detailed study of topography, seismography, mineral identification and distribution, of the Moon to understand the origin and evolution of the moon.
• India has become 4th country after the United States of America, Russia and China to soft-land on the moon.
• ISRO chairman is Sreedhara Panicker Somanath (as of July 2022)

Important Points

About ISRO-

• ISRO is the space agency under the Department of Space of the Government of India, headquartered in the city of Bengaluru, Karnataka.
• ISRO was set up by the Government of India in 1969.​
• ISRO is one of the six largest space agencies in the world.

The correct answer is Tamil Nadu.

Key Points

• According to APEDA report 2020, Tamil Nadu has the highest percentage of commercially cultivated floriculture.
• The Agricultural and Processed Food Products Export Development Authority (APEDA) is an Indian Apex-Export Trade Promotion Active government body, founded on 13 February 1986.

Additional Information

• APEDA actively supported the Government in taking the export of agricultural products to USD 20.67 billion in 2020-21 from USD 0.6 billion in 1986 when it was founded.
• APEDA also helped expand the export basket to 205 countries.
• The share of APEDA exports (USD 20.67 billion) constituted 49% of overall agri- product exports in 2020-21 out of which, Cereals and fresh horticulture comprised 59%, Cereal preparations and miscellaneous processed items 23% and animal products 18%.
• The target given to APEDA in the current financial year (2021-22) is USD 23.7 billion, out of which more than 70% i.e.
• USD 17.20 billion has been achieved till January 2022, and the remaining target is expected to be completed within the stipulated time period.

The correct answer is Ahmedabad.

 Key Points

• Saptak Annual Festival of Music is organized by the Saptak School of Music.
• It is an annual 13-day Indian classical music festival held in Ahmedabad, India.
• This festival was started in 1980 by Nandan Mehta and his wife Manju Mehta.
• Besides pure classical music, it also includes the performance of Folk Music, Classical Dance Forms, and Semi-Classical Dance Forms such as Thumri.

Important Points

• Notable festivals of other cities are as follows:
• Amritsar - Lohri. Celebrated on the 13th of January every year.
• Bhopal - Bhopal Utsav Mela.
• Lucknow - Saifai Mahotsav

The correct answer is Major Dhyan Chand Khel Ratna Award.

Key Points

• In August 2021, Prime Minister Narendra Modi announced that the Rajiv Gandhi Khel Ratna Award would be renamed to Major Dhyan Chand Khel Ratna Award.
• The Major Dhyan Chand Khel Ratna award is the highest sporting honour of the Republic of India.
• It is awarded annually by the Ministry of Youth Affairs and Sports.

Additional Information

• Dhyan Chand himself has been conferred with several honours, including India’s third highest civilian honour of Padma Bhushan in 1956.
• In addition to this, the Government of India also celebrates his birthday on August 29 as National Sports Day.
• The Khel Ratna award is the highest sporting honour in the nation.
• The prestigious award carries prize money of Rs. 25 lakh.

The correct answer is Rukmani Devi Arundale.

Key Points

• Rukmani Devi Arundale -
• ​She was an Indian classical dancer of Bharatnatyam dance form.
• She is best known for catalyzing the renaissance of the Bharatanatyam dance form.
• She founded the Kalakshetra Foundation in Madras (now Chennai).
• Rukmini Devi Arundale was instrumental in setting up the Animal welfare board of India and was its first chair.

Additional Information

• Bharatanatyam, presumably the oldest classical dance of India is regarded as the mother of many other Indian classical dance forms.
• It is indigenous to the Tamil Nadu region and prevalent in southern India.
• Its techniques and terminology have been traced back to ancient texts such as the Natya-shastra.
• Bharatanatyam was originally performed exclusively by female temple dancers and was not brought to the stage for public performance until about 1930.
• Alarippu, Jatiswaram, Shabdam, Padam, Varnam are some of the elements of Bharatanatyam.

The correct answer is Japan.

Key Points

• Sumo is a form of competitive full-contact wrestling where a rikishi attempts to force his opponent out of a circular ring or touch the ground.
• Sumo word refers to the Modern martial art form.
• Sumo is the national sport of Japan.

Additional Information About Japan

• Japan is called the "Land of Rising Sun".
• Japan is a amalgation of four island (Honshu, Hokkaido, Shikoku and Kyushu).
• Japan is surrounded by the Pacific Ring of Fire, which is affected by earthquakes, volcanoes and tsunamis.
• Recently in July 2022 Sakurajima volcano of Kyushu island of Japan erupted.

 Important Points

As of August 2022

The correct answer is Elamite

Key Points

• Amorite, member of an ancient Semitic-speaking people who dominated the history of Mesopotamia, Syria, and Palestine from about 2000 to about 1600 bc.
• Akkadian was an East Semitic language, now extinct.

Important Points 

• Mesopotamian civilizations formed on the banks of the Tigris and Euphrates rivers in what is today Iraq and Kuwait.
• Mesopotamia was believed to have been founded around 5500 BCE.
• Mesopotamians were the first people to understand the concept of zero and to start experimenting with mathematics.
• Their religion did not believe in life after death.
• Babylon was the capital of Mesopotamia.​

The correct answer is Allahabad. 

Key Points

• Chandrashekhar Azad shoot himself on being besieged by the British police in Allahabad.
• On February 27, 1931, betrayed by one of the associates, he was besieged by the British police in Alfred Park, Allahabad.
• He fought valiantly but seeing no other way he shot himself and fulfilled his resolve to die a 'free man'.

Additional Information

• Chandrashekhar Azad was born on 23rd July 1906 in Bhavra village of Madhya Pradesh.
• He joined the non-cooperation movement at the age of 15.
• He joined the Hindustan Republican Association after the suspension of the non-cooperation movement.
• He was associated with the Kakori conspiracy which was the Kakori train Incident conducted by Hindustan Republican Association in 1925.
• The Hindustan Socialist Republic Association was established by Chandrashekhar Azad and his colleagues in 1928 at Feroz Shah Kotla, New Delhi.
• He was involved in 1926 attempt to blow the viceroys train and Saunder's shooting in 1928.

The correct answer is Compressed natural gas.

Key Points

• Compressed natural gas (CNG) is a fuel gas made of petrol which is mainly composed of methane (CH4),
• compressed to less than 1% of the volume it occupies at standard atmospheric pressure.
• It is stored and distributed in hard containers at a pressure of 20–25 MPa (2,900–3,600 psi),
• usually in cylindrical or spherical shapes.
• CNG is known to be an eco-friendly alternative option to gasoline which is harmful to nature​

Additional Information

• The chemical formula of CNG – CH4 – is also the chemical formula for Natural Gas and is also the chemical formula for Methane.
• CNG is odourless, tasteless and non-toxic.
• Is made up of 93.05% methane, nitrogen, carbon dioxide, propane and traces of ethane.
• The primary source of obtaining CNG is from oil wells, bed methane wells, coal wells and even natural gas wells.
• Green Fuel is Commonly referred to as green fuel because of its lead and sulphur-free character.
• CNG reduces harmful emissions.
• The properties of CNG make it a safe fuel.

​

  

CNG Production rank

The correct answer is Alfred Marshall.

Key Points

• Alfred Marshall was an English economist and Father of Microeconomics.
• Alfred Marshall was the founder of neoclassical economics Principles.
• Alfred Marshall brought the idea of supply and demand, marginal utility and cost of production into economics.

Additional Information

• Microeconomics is the study of the behaviour of individual economic agents in the markets for different goods and services and tries to figure out how prices and quantities of goods and services are determined through the interaction of individuals in these markets.
• Microeconomics involves the study of key concepts like Incentives and behaviours, Utility theory, Production theory and Price theory.

The correct answer is Vikram Seth.**

Key Points

• Vikram Seth is an Indian Novelist and Poet.
• He was born on 20th June 1952 in Kolkata, West Bengal.
• He has written several fictional novels, poetry, and Children's fiction books.
• He has been honored with Padma Shri, Sahitya Academy Award, and Pravasi Bhartiya Samman.
• His poems such as Mappings and Beastly Tales are notable contributions to Indian English Language poetry.

Additional Information

1. V S Naipaul was a Trinidadian-born British writer, who is well known for his book named "India, a wounded civilization"
2. Arvind Adiga is an Indian writer whose debut novel "The White Tiger" won him the 2008 Man Booker Prize.
3. Salman Rushdie is an Indian-born British American Novelist.

The correct answer is 1971.

Key Points

• Bangladesh (East -Pakistan) was part of Pakistan from 1947 to 1971.
• India joined the war on 3 December 1971, after Pakistan launched preemptive air strikes on North India.
• The subsequent Indo-Pakistani War witnessed engagements on two war fronts
• The Indian government decided to save the Bangali Muslims and Hindus
• On 16 December 1971, 93,000 Pakistani military and govt officials surrendered before the Indian Army,
• ending the Bangladesh Liberation War that began on 3 December

​ 

Additional Information

• 26 march is the independence day of Bangladesh
• General A A K Niazi signed the Instrument of Surrender on 16 December 1971 in Dhaka, marking the formation of East Pakistan as the new nation of Bangladesh.
• On December 6, she announced in Parliament that India had accorded recognition to the Bangladesh Government
• On July 2, 1972, India and Pakistan signed the Shimla Agreement under which the former agreed to release all the 93,000 Pakistani prisoners of war

​

The correct answer is James Ramsay MacDonald.

Key Points 

• The communal award was announced by Ramsay Macdonald, the British PM.
• This was another expression of the British policy of Divide and Rule.
• It declared the depressed classes to be minorities and entitled them to a separate electorate.
• Congress though opposed to separate electorates was not in favour of changing the Communal Award without the consent of minorities.

Additional Information

• Important features of communal award​:
• The separate electorate for the Muslims, Sikhs, Anglo Indians, Indian Christians, as well as the depressed classes.
• 3 per cent of seats were reserved for women.
• 71 seats in total were reserved for the depressed classes in the provincial legislature.
• Gandhi rejected it and then started fast unto death in Yervada Jail against this award.

The correct answer is Godavari.

Key Points

• The Kadam dam is located at the confluence of the Kadam river into Godavari..
• It is also known as Kadem Adi Narayan Reddy Project.
• It is located on the River Kadem.
• This river is the tributary of godavari in located in the Nirmal district.
• The kadem project is constructed over this river in Nirmal district.
• The project is linked with sriram sagar project.

Additional Information

• Important river projects:

The Correct answer is Lord Dalhousie

Key Points

• On 7th February 1856, Lord Dalhousie ordered to depose of Wajid Ali Shah on the account of alleged internal misrule
• This was in line with Dalhousie's Doctrine of Lapse, in which the British would take over a kingdom if there was misrule also.
• Awadh was the last territory to be annexed by the British government.

Additional Information

• Lord Dalhousie:
• James Andrew Brown-Ramsay also known as Lord Dalhousie.
• He served as governor-general of India from 1848-1856.
• James Outram was made the British Resident of Awadh in place of Sleeman.
• He said that the administration of Awadh is very corrupt and the condition of the people is very contemplative.
• Outram's report was the basis for the annexation of Awadh.
• Lord Dalhousie annexed the Nawab of Awadh, Wajid Ali Shah on February 13, 1856, accusing him of misrule.
• Apart from Awadh, under the principle of Doctrine of Lapse, the merged territories- Satara (1848), Jaitpur and Sambalpur (1849), Udaipur (1852), Jhansi (1853), Nagpur (1854), and Karauli (1855).
• The first attempt towards railway construction in India was made by Lord Dalhousie in 1853 AD.
• It was laid between Bombay to Thane at the time of Dalhousie.
• The last expansion of British Indian territory took place during Dalhousie.
• During his tenure, for the first time, a separate public Works Department was created.

The correct answer is a resolution of the Lok Sabha passed by a majority of all the then members of the Lok Sabha.

Key Points

• Parliament consists of Lok Sabha, Rajya Sabha and President.
• Lok Sabha has a preceding officer called the Speaker who controls the proceeding of the house.
• Lok Sabha also has a Deputy Speaker who chairs as a preceding officer when the Speaker of the house is absent.
• To remove the Speaker and Deputy speaker a resolution of the Lok Sabha was passed by a majority of all the then members of the Lok Sabha.

Additional Information

The correct answer is pupa.

Key Points

• When the caterpillar is ready to enter the next stage of its life cycle called pupa, it first weaves a net to hold itself.
• The life cycle of a silkworm is Egg­ > Caterpillar ­> Pupa­ > Adult.
• The egg is the first and primary stage of the life cycle of Silkworm.
• The egg is laid by a  female moth and the egg is having the size of small dots.
• More than 350 eggs are laid by a female moth at a time.
• The eggs hatch in the springtime due to the warmth in the air.
• This procedure takes place once a year.

Additional Information

• Silkworm arises after the eggs crack and they are hairy.
• They feed on mulberry leaves and consume a large amount of these leaves for around thirty days.
• The Silkworms spin a cocoon around themselves which protects them.
• This cocoon is made up of a single thread of soil.
• Cocoon appears as a small cotton ball.
• The pupa is a motionless stage.
• The last stage is when the Pupa changes into an adult moth.
• The Silk was invented around 3500 BC in China.

Image of Life Cycle of Silkworm:

The correct answer is Candela.

Key Points

• Photometry is the science of the measurement of light in terms of perceived brightness to the human eye.
• In simple terms, the measurement of the intensity of brightness of light that can be perceived by the human eye is called Photometry.
• Candela is the SI's base unit for photometry. 
• There are two types of Photometry:
• ​​Differential Photometry
• Absolute Photometry
• There are two weighting functions:
• Photopic sensitivity function - for light conditions
• Scotopic function - for dark conditions.

The correct answer is 10th.

Key Points

• In the 'Climate Change Performance Index (CCPI) 2021,' published on 7 December 2020, India is ranked 10th. India's total score is 63.98.
• For the second time in a row, from among the 58 economies, India emerged among the top 10 countries with higher climate results.
• India was in ninth position in the index last year.

Additional Information

• The first three positions in the 2021 list, including CCPI 2020, still remain unoccupied, as none of the countries are on the road consistent with the Paris climate goals to adopt policies to minimize global warming below 2 or even 1.5 °C.
• In the table, Sweden (4th), the United Kingdom (5th), Denmark (6th), Morocco (7th), Norway (8th), Chile (9th) were among the top 10.
• It was also noted that only the EU as a whole, along with the UK and India, ranked among the high-performing G20 countries.

The correct answer is Bank of India.

Key Points

• WhatsApp has partnered with five Indian banks to process its payment services. These are
• State Bank of India,
• HDFC Bank,
• ICICI Bank,
• Axis Bank and
• Jio Payments Bank.
• Hence Bank of India is NOT one of the five banks.

Additional Information

• Whatsapp was launched in the year 2009 in California, the USA.
• It was co-founded by Jan Koum and Brian Acton.
• Facebook Inc. acquired the company in February 2014 for $19bn.
• Abhijit Bose is the head of Whatsapp in India.
• India is the biggest market for Whatsapp with 400 million users.

The correct answer is Pavan Sukhdev.

Key Points

• Renowned Indian environmental economist and UN Environment Programme (UNEP) Goodwill Ambassador Pavan Sukhdev has won the 2020 Tyler Prize.
• It is regarded as the "Nobel Prize for the Environment".
• He was awarded for his groundbreaking "green economy" work.
• Sukhdev will receive the award alongside conservation biologist Gretchen Daily on 1 May 2020.

Additional Information

• UNEP is a programme of the United Nations that coordinates the organization's environmental activities and assists developing countries in implementing environmentally sound policies and practices.
• UNEP Headquarters: Nairobi, Kenya

The correct answer is Sikkim.

Key Points

• Yumthang Valley is located in the Sikkim state of India.
• Yumthang is popularly known as 'Valley of Flowers'.
• In the spring season, wildflowers such as primulas and Rhododendrons bathe the landscape in rich colors, making it a tourist hot spot.
• The Shingba Rhododendron Sanctuary over here has 24 species of Rhododendron flowers which bloom from April to May end.

Additional Information

The correct answer is 15 years old.

Key Points

• The International Cricket Council (ICC) Board announced a minimum age policy for International cricket in November 2020.
• As per the policy, a player must be at least 15 years old to play cricket globally.
• To improve the safeguarding of players, the International Cricket Council (ICC) has introduced a 'minimum age policy' in International Cricket. A player should be at least 15 years old to play International Cricket. However, countries still have the option to field a player below the said age limit.
• In case of exceptional circumstances, a Member Board could apply to the ICC to allow a player under the age of 15 to play for their respective country.
• Hasan Raza of Pakistan holds the record of being the youngest cricketer to play International Cricket.
• He made his Test debut when he was 14 years and 227 days old.

Additional Information

• The International Cricket Council (ICC), the international governing body of Cricket founded in 1909 by representatives from England, Australia, and South Africa, was initially known as Imperial Cricket Conference.
• In 1965, it was renamed as International Cricket Conference and in 1965, it was renamed the International Cricket Council (ICC) in 1989.

Shortcut Trick

Ratio of number of students in Class 8 and Class 9 = 20 : 15 = 4 : 3.

Let the assumed average be 152 cm.

Net deviation from assumed average = (168 − 152) × 3 = +48.

Average deviation = +48 ÷ (4 + 3) = 48 ÷ 7 ≈ +6.85 cm.

Combined average = 152 + 6.85 = 158.85 cm ≈ 159 cm.

∴ The correct answer is 159 cm.

Alternate Method

Given:

Number of students in Class 8 = 20

Average height of Class 8 = 152 cm

Number of students in Class 9 = 15

Average height of Class 9 = 168 cm

Formula Used:

Combined Average = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂)

Class 8 (20 students) 152 cm

Class 9 (15 students) 168 cm

Combined Avg ≈ 159 cm

3 parts ratio 4 parts ratio

Calculations:

⇒ Total height of Class 8 students = 20 × 152 = 3040 cm

⇒ Total height of Class 9 students = 15 × 168 = 2520 cm

⇒ Total combined height = 3040 + 2520 = 5560 cm

⇒ Total number of students = 20 + 15 = 35

⇒ Combined Average = 5560 ÷ 35

⇒ Combined Average = 1112 ÷ 7 ≈ 158.85 cm

⇒ Rounding to the nearest cm, we get 159 cm.

∴ The correct answer is 159 cm.

Additional Information

Weighted Average Formula

When two groups of sizes n₁ and n₂ have averages A₁ and A₂, the combined average is given by: A = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Deviation Method for Averages

To simplify calculations, select an assumed average. The true average = Assumed Average + (Sum of Net Deviations ÷ Total Observations).

Alligation & Ratio Method

The distances from the combined average to the individual averages are inversely proportional to the ratio of the quantities in each group. Ratio of distances = n₂ : n₁.

Shortcut Trick

Total Simple Interest = (P₁ × effective rate 1) + (P₂ × effective rate 2)

Effective Rate = Rate × Time

Total Interest = (14000 × 15%) + (19000 × 18%)

Total Interest = 2100 + 3420 = 5520

∴ The correct answer is ₹5,520.

Alternate Method

Given:

Principal 1 (P₁) = ₹14,000, Rate 1 (R₁) = 5%, Time (T) = 3 years

Principal 2 (P₂) = ₹19,000, Rate 2 (R₂) = 6%, Time (T) = 3 years

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ SI₁ = (14000 × 5 × 3) ÷ 100 = 140 × 15 = ₹2100

⇒ SI₂ = (19000 × 6 × 3) ÷ 100 = 190 × 18 = ₹3420

⇒ Total Interest = SI₁ + SI₂

⇒ Total Interest = 2100 + 3420 = ₹5520

∴ The correct answer is ₹5,520.

Additional Information

Total Amount Formula

The total amount (A) after T years is given by A = P + SI = P × [1 + (R × T) ÷ 100].

Simple vs Compound Interest

In Simple Interest, the interest is calculated only on the initial principal. In Compound Interest, interest is calculated on both principal and the accumulated interest of previous periods.

Effective Rate Method

For Simple Interest, the effective rate for T years is simply R × T%. Here, 5% for 3 years becomes a 15% flat interest rate on the principal.

Given:

Marked Price = Rs. 550

Selling price = Rs. 317.90

Successive discount (1) = 15%

Successive discount (2) = x%

Successive discount (3) = 20%

Single discount = 2x%

Formula Used:

Selling price = Marked price × $\frac{100 - Discount\%}{100}$ 

Calculation:

Case:1

317.9 = 550 × $\frac{(100 - 15)}{100} × \frac{(100 - x)}{100} × \frac{(100 - 20)}{100}$

By cross multiplication:

⇒ 5610 = 374x

⇒ x = 15

Case:2

Single discunt = 2x% = 2 × 15 = 30%

Cost price = Rs. 550

⇒ Selling price = 550 - 30% of 550

⇒ Selling price = 385

∴ Its selling price is Rs. 385

Given:

Distance = 1950 m

Speed = 26 km/hr

Formula Used:

Time = Distance/Speed

1 km = 1000 m

1 hr = 60 min

Calculation: 

26 km/hr = $26 × \frac{1000}{60}$ = $\frac{1300}{3}$m/min.

⇒ Time = 1950 ÷  $\frac{1300}{3}$

⇒ Time = 1950 × $\frac{3}{1300}$

⇒ Time = $4\frac{1}{2}$ minutes

∴ In $4\frac{1}{2}$minutes will be taken to cover 1950 m.

Calculation:      

LCM of 3, 4,5 and 6 is 60

2483 ÷ 60

Q = 41

R = 23

Now,

60 - 23 = 37

⇒ 37 must be added to 2483 to make is divisible 60.

3000 ÷ 60 

Q = 50

R = 0

∴ Atleast 37 must be added to 2483 so, that is completely divisible by 3, 4, 5, and 6.

Given:

Amount = 2 × Principal

Time = 6 years

Formula Used:

Simple Interest = Principal × Time × R/100

Amount = Principal + Simple interest

Calculation:

Let the principal be x

So, the amount is 2x

Interest = 2x - x = x

⇒ x = x × 6 × R/100

⇒ R = 100/6 

⇒ R = $\frac{50}{3}$%

Case:2

Amount = 5x

Principal = x

Simple Interest = 5x - x = 4x

⇒ 4x = x × Time × $\frac{50}{3 \times 100}$

⇒ Time = 24 years

∴ In 24 years the amount will be 5 times of principal.

Given:  

h - r = 23 cm

TSA of cylinder = 1628 cm²

Formula Used:

 

TSA of cylinder = 2πr(r + h)

Where, r = radius h = height

Calculation:

TSA of cylinder = 2πr(r + h)

⇒ 1628 = 2 ×$\frac{22}{7}$ × r(r + h)

⇒ 259 = r (r +h)      ----(1)

⇒ h - r = 23 cm     

⇒ h = 23 + r      ----(2)

From equation (1) and (2)

⇒ 259 = r(r + 23 + r)

⇒ 259 = 23r + 2r²

⇒ 2r² + 23r - 259 = 0 

By factorisation method:

⇒ (r - 7)(r + 37/2) = 0

⇒ r - 7 = 0 

⇒ r = 7

⇒ r + 37/2 = 0

⇒ r = -37/2

⇒ Radius is 7 cm

⇒ h = 23 + 7 = 30 cm

∴ r= 7 cm and h = 30 cm

Given:

Principal = Rs. 5,000

Amount = Rs. 5,832

Rate = 16% p.a.

Formula Used:

Amount = Principal × (1 + $\frac{R}{100}$)^Time

Calculation:      

When interest compounded annually

R will be half and Time will be doubled.

So,

R = 16/2 = 8% p.a.

Amount = Principal × (1 + $\frac{R}{100}$)Time

⇒ 5832 = 5000 × (1 + $\frac{8}{100}$)^Time

$⇒ \frac{5832}{5000} = (\frac{108}{100})^T$

$⇒ (\frac{729}{625}) = (\frac{27}{25})^T$

$⇒ (\frac{27}{25})^2 = (\frac{27}{25})^T$

⇒ Time = 2 years

Because interest is compounded semiannually so, time 2/2 = 1 year.

∴ ₹5,000 becomes ₹5,832 at a rate of 16% per annum in 1 year when compounded half-yearly

Shortcut TrickRate = 16% compounded semi-annually, 

R/2 = 16/2 = 8%

Net Rate/Effective Rate,

⇒ 8 + 8 + (8 × 8)/100 = 16.64%

Now,

⇒ 5,000 × 16.64% = 832

Interest = Rs. 832

∴ ₹5,000 becomes ₹5,832 at a rate of 16% per annum in 1 year when compounded half-yearly

Shortcut Trick

Total capacity of tank = LCM(15, 20, 8) = 120 units.

Efficiency of A = −120/15 = −8; B = −120/20 = −6; C = 120/8 = +15.

Combined efficiency = 15 − 8 − 6 = 1 unit/min.

Total time = 120 / 1 = 120 minutes.

Time in hours = 120 / 60 = 2 hours.

∴ The correct option is C.

Alternate Method

Given: Pipe A empties in 15 min, Pipe B empties in 20 min, Pipe C fills in 8 min.

Formula: Efficiency = Total Work ÷ Time

⇒ Total Work (LCM of 15, 20, 8) = 120 units

⇒ Net efficiency of (A + B + C) = −8 − 6 + 15 = 1 unit/min

⇒ Total time taken to fill the tank = Total Work ÷ Net Efficiency

⇒ Time = 120 / 1 = 120 minutes

⇒ Time in hours = 120 / 60 = 2 hours

∴ The correct option is C.

Additional Information

Pipes and Cisterns Convention

Filling pipes (inlets) are assigned positive efficiency, while emptying pipes (outlets) are assigned negative efficiency.

Net Rate of Work

If multiple pipes work together, the net rate of work is the algebraic sum of their individual efficiencies.

Unit Conversion

To convert minutes to hours, divide the total minutes by 60 (1 hour = 60 minutes).

Shortcut Trick

Let the initial profit be P. Then the new profit at the higher selling price is 3P.

Difference in profit = 3P − P = 2P

Difference in Selling Price = 1800 − 1350 = 450

⇒ 2P = 450 ⇒ P = 225

Cost Price = Selling Price − Profit = 1350 − 225 = 1125

∴ The correct answer is ₹1125.

Alternate Method

Given:

Selling price 1 (SP₁) = ₹1800

Selling price 2 (SP₂) = ₹1350

Profit at SP₁ = 3 × Profit at SP₂

Formula Used:

Profit = Selling Price − Cost Price

CP = ?SP₂ = 1350SP₁ = 1800P2P = 450Total Profit = 3PCP = 1350 − 225 = 1125

Calculations:

Let the Cost Price (CP) of the article be ₹x.

⇒ Profit obtained at SP₁ = 1800 − x

⇒ Profit obtained at SP₂ = 1350 − x

According to the given condition:

⇒ 1800 − x = 3 × (1350 − x)

⇒ 1800 − x = 4050 − 3x

⇒ 3x − x = 4050 − 1800

⇒ 2x = 2250

⇒ x = 1125

∴ The correct answer is ₹1125.

Additional Information

Marked Price and Discount

Discount is always calculated on the Marked Price (MP) unless specified otherwise. The basic formula to find the Selling Price after allowing a discount is: SP = MP − Discount.

Successive Discounts

When two successive discounts of a% and b% are offered, the effective single discount percentage can be quickly calculated using the formula: Effective Discount = (a + b − (a × b) ÷ 100)%.

Dishonest Dealer Concept

If a shopkeeper claims to sell his goods at the exact cost price but uses false weights, the actual profit percentage generated is given by: Profit % = (Error ÷ False Weight) × 100.

Given:

Rate 1 = at the rate of 12 for Rs. 100.

Rate 2 = at the rate of 15 for Rs. 135.

Concept Used:

In such questions,

Assume the total number of articles purchased is the LCM of the given rate

Calculation:

Here the number of articles will be,

⇒ Common multiple of 12 & 15 = 180

Case:1

Cost of 12 pens = Rs. 100

⇒ Cost of 180 pens (12 × 15) = 100 × 15 = Rs.1500

Case: 2

Cost of 15 pens = Rs. 135

⇒ Cost of 180 pens (12 ×15) = 135 × 12 = Rs.1620

⇒ Total cost of (180 + 180) of 360 pens = 1500 + 1620 = Rs. 3120

Total cost of 360 pens = Rs. 3120

⇒ The cost of 1 pen = 3120/360

⇒ Total selling price = RS. 260

Total cost price = $260 \times (\frac{100}{100 + 20})$

⇒ Total cost price = $260 \times \frac{100}{120}$

⇒ Pens can be purchased = $260 \times \frac{100}{120} \times \frac{360}{3120}$

⇒ Number of pens = 25

∴ 25 pens can be purchased in Rs. 260

Alternate Method

12 pens for 100

15 pens for 135

LCM of 12, 15 is 60.

So 12 × 5 pen = 100 × 5 = 500, similarly for second rate 60 pens for 540

so, a total of 120 pens for 1040.

so cost of one pen = 1040/120

Now 260 is the price after 20% profit, CP of all the pen = (260 × 100)/120.

Let the number of pens be x.

x × 1040/120 = (260 × 100)/120.

x = 25

Shortcut Trick

Cost Price (CP) for the shopkeeper = 82% of ₹2600 = ₹2132

Selling Price (SP) of the shopkeeper = 85% of ₹2800 = ₹2380

Earnings (Profit) = SP − CP = 2380 − 2132 = ₹248

∴ The correct answer is ₹248.

Alternate Method

Given:

Initial Marked Price (MP₁) = ₹2600

Discount allowed to shopkeeper = 18%

New Marked Price set by shopkeeper (MP₂) = ₹2800

Discount allowed to customer = 15%

Formula Used:

Selling Price (SP) = MP × (100 − D%) ÷ 100

Profit = SP − CP

Calculations:

⇒ Cost Price for shopkeeper (CP) = 2600 × (100 − 18) ÷ 100

⇒ CP = 2600 × 82 ÷ 100 = ₹2132

⇒ Selling Price of shopkeeper (SP) = 2800 × (100 − 15) ÷ 100

⇒ SP = 2800 × 85 ÷ 100 = ₹2380

⇒ Earnings = SP − CP

⇒ Earnings = 2380 − 2132 = ₹248

∴ The correct answer is ₹248.

Additional Information

Marked Price and Discount

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

Profit and Loss

Profit is earned when Selling Price (SP) is greater than Cost Price (CP). Profit = SP − CP, and Profit % = (Profit ÷ CP) × 100.

Successive Discount

When two consecutive discounts x% and y% are given, the equivalent single discount is (x + y − xy ÷ 100)%.

Calculation:      

$\frac{{33}}{{40}} + \frac{1}{5}\left[ {\frac{4}{5} - \frac{1}{5} \times \left( {\frac{7}{8} - \frac{5}{4}} \right)} \right] - \frac{4}{5}$

$⇒ \frac{{33}}{{40}} + \frac{1}{5}\left[ {\frac{4}{5} - \frac{1}{5} \times \left( {\frac{7 - 10}{8}} \right)} \right] - \frac{4}{5}$

$⇒ \frac{{33}}{{40}} + \frac{1}{5}\left[ {\frac{4}{5} - \frac{1}{5} \times \left( {\frac{7 - 10}{8}} \right)} \right] - \frac{4}{5}$

$⇒ \frac{{33}}{{40}} + \frac{1}{5}\left[ {\frac{4}{5} - \frac{1}{5} \times \left( {\frac{-3}{8}} \right)} \right] - \frac{4}{5}$

$⇒ \frac{{33}}{{40}} + \frac{1}{5}\left[ {\frac{4}{5} + \frac{3}{40}} \right] - \frac{4}{5}$

$⇒ \frac{{33}}{{40}} + \frac{1}{5}\left[ {\frac{32 + 3}{40}} \right] - \frac{4}{5}$

$⇒ \frac{{33}}{{40}} + \frac{1}{5}\left[ {\frac{35}{40}} \right] - \frac{4}{5}$

$⇒ \frac{{33}}{{40}} + \frac{7}{40} - \frac{4}{5}$

$⇒ \frac{{40}}{{40}} - \frac{4}{5}$

$⇒ 1 - \frac{4}{5}$

$⇒ \frac{5 - 4}{5}$

$\frac{1}{5}$

Given:

Five years ago,

The average age of A, B and C = 20 years

Six years ago,

The average age of B and C = 9 years

Formula Used:

Average = Sum of all observations/ Number of observations

Calculation:

5 years ago, the total of age of A, B and C = 20 × 3 = 60 years

⇒ Present age of A, B and C = 60 + (5 × 3) 

⇒ Present age of A, B and C =60 + 15 = 75 years

⇒ 6 years ago, the total of age of B and C = 9 × 2 = 18 years

Present age of B and C = 18 + (6 × 2)

⇒ Present age of B and C = 18 + 12 = 30 years

⇒ Present age of A = 75 - 30 = 45 years

⇒ A's age after 3 years = 45 + 3 = 48 years

∴ A's age after 3 years is 48 years.

Given:

Amount = Rs. 73,500

A ∶ B ∶ C ∶ D = 3 : 7 : 9 : 11

Formula Used: 

Share of a person = Total Amount × $\frac{Ratio\space of\space indiviual}{Sum\space of\space ratios}$(\frac{Ratio\space of\space indiviual}{Sum\space of\space ratios}\)

Calculation:

Share of A and D = $73500 \times \frac{(3 + 11)}{30}$

⇒ Share of A and D = $73500 \times \frac{14}{30}$

⇒ Share of A and D = Rs. 34,300

∴ The sum of share A and D is Rs. 34,300

Shortcut Trick

Equation: 0.30(x + 60) − 0.25x = 40

0.30x + 18 − 0.25x = 40 ⇒ 0.05x = 22 ⇒ x = 440

Value A = 35% of (440 − 40) = 0.35 × 400 = 140

Required % = [(140 − 120) / 120] × 100 = (20 / 120) × 100 = 16²/₃%

∴ The correct answer is 16²/₃%.

Alternate Method

Given:

25% of x = (30% of (x + 60)) − 40

Calculations:

⇒ (25/100)x = (30/100)(x + 60) − 40

⇒ 0.25x = 0.3x + 18 − 40

⇒ 0.3x − 0.25x = 40 − 18

⇒ 0.05x = 22

⇒ x = 22 / 0.05 = 440

⇒ Now, calculate 35% of (x − 40) = 0.35 × (440 − 40)

⇒ 0.35 × 400 = 140

⇒ Percentage more than 120 = [(140 − 120) / 120] × 100

⇒ (20 / 120) × 100 = (1 / 6) × 100 = 16.66% = 16²/₃%

∴ The correct answer is 16²/₃%.

Additional Information

Percentage Change

Percentage more/less = [(Difference) / (Base Value)] × 100. Always identify the value after 'than' as the base.

Fraction to Percentage Conversion

Common fractions: 1/6 = 16.66% or 16²/₃%, 1/8 = 12.5% or 12¹/₂%, 1/3 = 33.33% or 33¹/₃%.

Successive Percentage

Net Change = [a + b + (ab/100)]% where a and b are successive percentage changes.

Given:

Cost price (1) + Cost price (2) = Rs. 50,000

Profit% = 15%

Loss% = 20%

Selling Price (1) = Selling Price (2)

Formula Used:

Selling price = Cost price × ($\frac{100 - loss\%}{100}$)

Selling price = Cost price × ($\frac{100 + Profit\%}{100}$)

Calculation: 

Let assume that cost price(1) = x

And, Cost price(2) = y

⇒ x + y = 50,000     ______(1)

Now,

⇒ x × ($\frac{100 + 15}{100}$) = y × $(\frac{100 - 20}{100})$

⇒ x/y = 16/23

x ∶ y = 16 : 23    _______(2)

From equation (1) and  (2) 

x = $50,000 \times \frac{16}{39}$ = 20513 approx

y = $50,000 \times \frac{23}{39}$ = 29,487 approx

∴  Approx 29,487 is the cost price of mobile phone sold on loss.

Calculation:

Let's assume that y = 100

So, x is = 100 + 12.25% of 100 = 112.25

Now,

According to the question:

$\frac{12.25}{112.25} \times 100$

⇒ 10.9%

∴ Y is approximately 10.9% less than X.

Given:

a ∶ b = 9 ∶ 11

HCF = 23

Formula Used: 

Co-prime number: Co-prime numbers or relatively prime numbers are those numbers that have their HCF (Highest Common Factor) as 1.

Calculation:

9 and 11 are co- prime numbers

So,

⇒ First number = 9 × 23 = 207

⇒ Second number = 11 × 23 = 253

⇒ Difference = 253 - 207 = 46

∴ Difference of first number and second number is 46.

Given:

Number of machines = 56

Days = 144

Formula Used:

$\frac{M1 \times D1}{W1} = \frac{M2 \times D2}{W2}$

M = Men/Machines

D = Days 

W = Work

Calculation:

M₁ = 56

D₁ = 144

D₂ = 96

W₁ = W₂

 $\frac{M1 \times D1}{W1} = \frac{M2 \times D2}{W2}$

$⇒ \frac{56 \times 144}{W} = \frac{M2 \times 96}{W}$

⇒ M₂ = 84 

∴ 84 machines to be required

Given:

A can do work in days = 15

The efficiency of B = Efficiency of A - 10%

The efficiency of C = Efficiency of A + 20%

Work done by A, B and C = 3 days 

Remaining work done by D = $9\frac{1}{2}$ days

Formula Used:

Total work = Efficiency × Days

Calculation: 

Let's assume that the efficiency of A is 100 units per day

So, 

Efficiency of B = 100 -10% of 100 = 90 units per day

Efficiency of C = 100 + 20% of 100 = 120 units per day

⇒ Work done by A + B + C in a day = 100 + 90 + 120 = 310 units

⇒ Total work = Work done by A in a day × Days

⇒ Total work = 100 × 15 = 1500 units

⇒ Work done by A+ B + C = 310 × 3 = 930 units

⇒ Remaining work = 1500 - 930 = 570 units

⇒ 570 units of work done by D in days = 19/2

⇒ 1500 units of work will be done by D in days = $1500 \times \frac{19}{2} \times \frac{1}{570}$ = 25 days

∴ D will complete work in 25 days.

Shortcut Trick

Total perimeter = Total cost ÷ Rate = 2880 ÷ 15 = 192 m

Ratio of Length to Breadth = 7 : 5 ⇒ Perimeter in ratio parts = 2 × (7 + 5) = 24 parts

24 parts = 192 m ⇒ 1 part = 8 m

Length = 7 parts = 7 × 8 = 56 m

∴ The correct answer is 56 m.

Alternate Method

Given:

Length and Breadth ratio = 7 : 5

Total cost of fencing = ₹2880

Rate of fencing = ₹15/m

Formula Used:

Perimeter of Rectangle = 2 × (Length + Breadth)

Perimeter = Total Cost ÷ Rate

Calculations:

⇒ Perimeter = 2880 ÷ 15 = 192 m

⇒ Let the length be 7x and the breadth be 5x.

⇒ 2 × (7x + 5x) = 192

⇒ 2 × 12x = 192

⇒ 24x = 192

⇒ x = 192 ÷ 24

⇒ x = 8

⇒ Length = 7x = 7 × 8 = 56 m

∴ The correct answer is 56 m.

Additional Information

Perimeter vs Area

Fencing is always done along the boundary, so it requires calculating the perimeter. Flooring or painting a surface requires calculating the area.

Area of a Rectangle

Area = Length × Breadth. The total cost of flooring is determined by multiplying the total area by the rate per square unit.

Diagonal of a Rectangle

The length of the longest pole that can be placed inside a rectangular area is its diagonal. Formula: Diagonal = √(L² + B²).

Formula Used:

a³ + b³ = (a + b)(a² - ab + b²)

If a^m = aⁿ

Then m = n 

Calculation:

$\frac{{{{\left( {251} \right)}^3} + {{\left( {249} \right)}^3}}}{{25.1 × 25.1 - 624.99 + 24.9 × 24.9}}$ = 5 × 10k

$⇒ \frac{(251 + 249)(251 × 251 - 62499 +249 ×249)}{{25.1 × 25.1 - 624.99 + 24.9 × 24.9}}$ = 5 × 10^k

$⇒ \frac{(251 + 249)(251 ×251 - 62499 + 249× 249)}{\frac{(251 × 251 - 62499 + 249 × 249)}{100}}$ = 5 × 10^k

$⇒ (251 + 249) × 100$ = 5 × 10^k

⇒ 500 × 100 = 5 × 10^k

⇒ 5 × 10000 = 5 × 10^k

⇒ 5 ×  10⁴ = 5 × 10^k

⇒ 10⁴ = 10^k

⇒ k = 4

∴ The value of k is 4.

Given:

Length of tunnel = 600 m

Time = 54 sec.

Length of bridge = 350 m

Time = 36 sec.

Formula Used:

Speed = Distance/ Time

Calculation:

Let's assume that the speed of the train is 'S' m/sec.

And, Length of the train = x m

Case:1

Total distance = (x + 600) m

Time = 54 seconds

Speed = S m/sec.

⇒ S = $\frac{x + 600}{54}$      ____(1)

Case:2

Total distance = (x + 350) m

Time = 36 seconds

Speed = S m/sec.

⇒ S = $\frac{x + 350}{36}$     _____(2)

From equations (1) and (2)

$⇒ \frac{x + 600}{54}$ = $\frac{x + 350}{36}$

⇒ x = 150 m

⇒ S = $\frac{150 + 600}{54}$

⇒ S = 13.88 m/sec. or $13.88 \times \dfrac {18}{5}$ = 49.96 km/hr ≈ 50 km/hr.

∴ Only statement II is true.

The length of the train is 150 m

Given:

The present age of P∶ The present age of Q = 5 ∶ 7

Eight years ago the age of P ∶ Eight years ago the age of Q = 7 ∶ 13

Calculation:

Let assume that present age of P = 5x

The present age of Q = 7x

Eight years ago 

P's age = 5x - 8

Q's age = 7x - 8

According to the question:

$\frac{5x - 8}{7x - 8} = \frac{7}{13}$

By cross multiplication:

⇒ 13(5x - 8) = 7(7x - 8)

⇒ 65x - 104 = 49x - 56

⇒ 16x = 48

⇒ x = 3

P's present age = 5x = 5 × 3 = 15 years

Q's present age = 7x = 7 × 3 = 21 years

∴ P's present age is 15 years and Q's present age is 21 years.

The segment that contains a grammatical error is 'and that helping to him stay fit.'.

Key Points 

• Using the verb 'help' with or without a 'to infinitive'. The meaning remains the same.
• Help is a verb that can be used with or without to and with or without an object before the infinitive.
• When we use it with an infinitive it sometimes sounds more informal.
• Helping to shall be replaced by helps.

 

Therefore, the correct answer is option 4.

Hence, the corrected sentence is: Angad says that he follows his exercise regimen strictly and that helps him stay fit.