RRB NTPC CBT 2 (Level-6) Official paper (Held On: 9 May 2022 Shift 1) (Previous Year Paper)

• Code: letters written in reverse alphabetical order
• RELATIONS

Alphabetical order: A < E < I < L < N < O < R < S < T 

Reverse order: T > S > R > O > N > L > I > E > A

Thus, code is TSRONLIEA

• NUMBER

​Alphabetical order: B < E < M < N < R < U

Reverse order: U > R > N > M > E > B

• Similarly, SPECULATION

Alphabetical order: A < C < E < I < L < N < O < P < S < T < U 

Reverse order: U > T > S > P > O > N > L > I > E > C > A

Hence, "option 1" is the correct answer.

Given series:-

• (Left) K L % Y & 4 E 2 * 3 M & 7 S W # 8 2 H * L (Right)
• If all the numbers are dropped from the series then series given below:-
• (Left) K L % Y & E * M & S W # H * L (Right)
• M is the eighth from the right end.

Hence, "option 1" is the correct answer.

The correct answer is Intergovernmental Panel on Climate Change.

Key Points

• IPCC's full form is Intergovernmental Panel on Climate Change
• It is an international organization that assesses the reasons behind climate change.
• It is a part of the United Nations.
• It was established by the World Meteorological Organization (WMO) and the United Nations Environment Programme (UNEP).
• Its objective is to provide input to all governments regarding the scientific information and Technical Guidance that may be used to design climate policies.
• It releases annual assessment reports that guide the governmental decision-making process and and plays an important role in UNFCCC-COP meetings.

Additional Information

• IPCC
• Established: 1988
• Headquarters: Geneva, Switzerland
• It was awarded the Nobel peace prize in 2007 for its role in assessing man-made climate change.
• Rajendra Pachauri served as chairman of IPCC.

Given:

Speed of the train = 54 kmph

Length of the train = 450m

Concept used:

Time × Speed = Distance

While a train crosses a person, it crosses its own length.

Kilometer per hour (kmph) = 3.6 × Meter per second (mps)

Calculation:

54 km/h = 54 ÷ 3.6 = 15 mps

Time taken by the train to cross the man =  450 ÷ 15 = 30 seconds

∴ A 450m long train running at 54 km/h will take 30 seconds to cross a man standing on a platform.

Given:

A certain sum on compound interest becomes ₹56,180 when compounded annually after 2 years and ₹59,550.80 after 3 years.

Concept used:

Compound interest, CI = P(1 + R/100) n - P

where

P = Principal amount

R = Rate of interest per year

N = Time in years

Calculation:

Amount at the end of the second year, A 2  = ₹56,180

Amount at the end of the third year, A3 = ₹59,550.80

Hence, interest incurred during the second year to the third year = 59,550.80 - 56,180 = ₹3370.8

Let the principal sum be Rs. P and the rate of interest be R%.

CI of the first year = SI of the first year

⇒ ₹3370.8 =  (∵ for the second year, the principal amount should be Rs. 56,180)

⇒ R = 6%

According to the question,

P(1 + 6/100)2 = 56,180

⇒ P = 50000

∴ The principal amount is ₹50000.

Shortcut Trick

In Simple Interest, the percentage increase is directly proportional to the time period.

Percentage increase in 10 years = 75%

Percentage increase in 1 year = 75% ÷ 10 = 7.5%

Percentage increase in 6 years = 7.5% × 6 = 45%

∴ The correct answer is 45%.

Alternate Method

Given:

A sum increases by 75% in 10 years at simple interest.

Time (T₁) = 10 years, Time (T₂) = 6 years.

Formula Used:

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

6 Years (SI = ?) Remaining 4 Years

Total 10 Years: SI = 75% increase

6 Years: SI = 45% increase

Calculation:

Let the principal (P) be 100.

⇒ Since the sum increases by 75%, Simple Interest for 10 years = 75.

⇒ 75 = (100 × R × 10) ÷ 100

⇒ 75 = 10R

⇒ R = 7.5% per annum

Now, calculate the SI for 6 years at the same rate of interest:

⇒ New SI = (100 × 7.5 × 6) ÷ 100

⇒ New SI = 7.5 × 6

⇒ New SI = 45

⇒ Since the principal is 100, an SI of 45 means the sum increases by 45%.

∴ The correct answer is 45%.

Additional Information

Direct Proportion in Simple Interest

For a fixed principal and constant rate, the interest earned is directly proportional to the time period (SI ∝ T). You can directly use the ratio: SI₁ ÷ T₁ = SI₂ ÷ T₂.

Percentage Increase

When a problem states that a sum increases by a certain percentage, that percentage increase is exactly equal to the Simple Interest accumulated. Amount = Principal + SI.

Rate of Interest

Rate per annum (R) can be determined efficiently by isolating it from the SI formula: R = (SI × 100) ÷ (P × T).

The correct answer is Egypt.

Key Points

• The Nile is the longest river in the world.
• It flows across the eastern African region from South to North.
• The major portion of the river flows in Egypt.
• It is the source for agriculture, fishing and facilitates transportation in the country.

Additional Information

• Its basin covers countries like Uganda, Sudan, South Sudan,Ethiopia and Egypt.
• It starts near Lake Victoria(near Uganda) and empties into the Mediterranean Sea(Egypt).
• The main tributaries are White Nile (from Lake Victoria) and Blue Nile (from Ethiopia).
• It is a major lifeline for the countries in the eastern Sahara region.
• It provides transportation and supports agriculture and fishing in the region.
• Alexandria, Cairo(Egypt) and Khartoum(Sudan) are the important cities on the bank of the river.

Given:

$\frac{1}{{1, + ,\tan ,{\rm{θ }}}}, + ,\frac{1}{{1, - ,\tan ,{\rm{θ }}}}, = ,4,,0^\circ < ,{\rm{θ }},{\rm{ < }},{\rm{90}}^\circ$

Concept used:

sec²θ - tan²θ = 1

sin2θ + cos2θ = 1

cosec θ = 1/sin θ 

sec θ = 1/cos θ 

Calculation:

$\frac{1}{{1, + ,\tan ,{\rm{θ }}}}, + ,\frac{1}{{1, - ,\tan ,{\rm{θ }}}}$ = 4

⇒ ${1\ -\ tanθ\ +\ 1\ +\ tanθ} \over {1\ -\ tan^2θ}$ = 4

⇒ ${1\ +\ 1} \over {1\ -\ tan^2θ}$ = 4

⇒ ${2} \over {1\ -\ tan^2θ}$ = 4

⇒ 1 -  tan² θ = 1/2

⇒ tan2 θ = 1/2

Adding both side by 1, as we know 1 + tan²θ = sec²θ

⇒ 1 + tan2 θ = 1/2 + 1

⇒ sec²θ = 3/2      ....(1)

⇒ cos²θ = 2/3

⇒ 1 - cos²θ = 1/3 We know (sin2θ + cos2θ = 1)

⇒ sin²θ = 1/3

⇒ cosec²θ = 3      ....(2)

Hence (1) + (2),

(cosec2 θ + sec2 θ)

⇒ 3 + 3/2

⇒ 9/2

∴ The required value is 9/2.

The correct answer is Tabla.

Key Points

• Alla Rakha Qureshi is an Indian Tabla player.
• He specialised in Hindustani Classical music and belongs to Punjab Gharana.
• He is often seen accompanying Sitar specialist Pandit Ravi Shankar.
• Zakir Hussain, a Tabla expert is the son of Qureshi.
• He played an important role in introducing the Tabla to the West.
• He received Padma Shri in 1977 and Sangeet Natak Akademi  Award in 1982.

Additional Information 

The correct answer is rate of change of consumption as income changes​.

Key Points

• Marginal propensity to consume refers to the change in consumption with respect to the change in income.
• When there is an increase in income it reflects in better purchasing power of a consumer.
• The change in income not only affects consumption but also induces changes in savings.
• The proportion of consumption depends upon the income levels and corresponding necessities of the consumer.
• It is used widely in economics to calculate the required additional production for the increased demand(consumption).

Additional Information

• The complement of the MPC( Marginal propensity to Consume) is Marginal Propensity to Save(MPS).
• They both reflect the increase in income.
• Marginal Propensity To Consume (MPC)- 

In economics, the marginal propensity to consume (MPC) is defined as the proportion of an aggregate raise in pay that a consumer spends on the consumption of goods and services, as opposed to saving it. The marginal propensity to consume is a component of Keynesian macroeconomic theory and is calculated as the change in consumption divided by the change in income. 

The marginal propensity to consume is equal to ΔC / ΔY, where ΔC is the change in consumption, and ΔY is the change in income. If consumption increases by 80 cents for each additional dollar of income, then MPC is equal to 0.8 / 1 = 0.8.

The logic followed here is:-

Hence, "option 3" is the correct answer.

The logic followed here is:-

And,

Similarly,

Hence, "option 3" is the correct answer.

The correct answer is Brahmaputra.

Key Points

• Majuli is the largest river island in the world to be inhabited by people.
• It is located in the state of Assam and is a district by itself.
• It is formed due to course changes to the river Brahmaputra and its tributaries.
• It is located on the National Waterway 2, which is a part of Brahmaputra river.
• It is surrounded by River Brahmaputra and River Subansiri.

The correct answer is option 4.

Key Points

• Article 75 deals with the appointment of the Council of Ministers by the President of India.
• Council of ministers aid and advise the President in the exercise of his/her functions.
• It represents the highest executive body in the Indian polity.
• It is also called the Cabinet, where most executive decisions are made.

Additional Information

• Article 74 tells about constitution of Council of Ministers.
• Article 75 talks about other provisions(like appointment, collective responsibility to Lok Sabha, six months time for becoming MP etc.) related to the Council of Ministers.

Given that:-

Only one person is younger than Y.

• Y > _ .

X is older than E but younger than D.

• D > X > E

E is older than Y.

• E > Y

Neither D nor C is the eldest.

• Z > D > X > E > Y > C
• Thus, no one is older than Z.

Hence, "option 2" is the correct answer.

Given:

72 - 4(40 + 24 ÷ 8 × 6 - 4 × 4) + 20

Concept used:

Calculation:

72 - 4(40 + 24 ÷ 8 × 6 - 4 × 4) + 20

⇒ 72 - 4(40 + 3 × 6 - 4 × 4) + 20

⇒ 72 - 4(40 + 18 - 16) + 20

⇒ 72 - 4 × 42 + 20

⇒ 72 - 168 + 20

⇒ (-76)

∴ The simplified value is (-76).

The correct answer is January 2021.

Key Points

• The initiative of Jail Tourism has been launched by the Maharashtra government in January 2021.
• It is aimed at increasing awareness about the historical prisons and their role in the freedom struggle.
• As a part of the initiative, some parts of Yerwada Prison of Pune are opened for visitors.
• The prison has the historical significance of signing the Poona Pact(between Ambedkar and Gandhi) and accommodating many freedom fighters during the independence movement.

Additional Information

• Maharashtra
• CM: Eknath Shinde
• Governor: Ramesh Bais.
• Parliamentary seats: 48 (LS) and 19(RS).
• Capital: Mumbai , Nagpur(Winter capital
• Recent News : A loan scheme named Jivhala has been launched by the Maharashtra Department of Prisons for the inmates who are serving sentences in various jails across Maharashtra

The logic followed here is:-

Hence, "option 3" is the correct answer.

Shortcut Trick

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

Step 1: Find the smallest difference between the given numbers: 245 − 175 = 70.

Step 2: List the factors of 70 in descending order: 70, 35, 14, 10, 7, 5, 2, 1.

Step 3: Check divisibility. 70 does not divide 175. However, 35 divides 175 (35 × 5), 245 (35 × 7), and 385 (35 × 11).

∴ The correct answer is 35.

Alternate Method

Given: The numbers are 175, 245, and 385.

Formula Used: HCF = Product of the lowest power of all common prime factors.

Calculations:

⇒ Prime factorization of 175 = 5 × 5 × 7 = 5² × 7¹

⇒ Prime factorization of 245 = 5 × 7 × 7 = 5¹ × 7²

⇒ Prime factorization of 385 = 5 × 7 × 11 = 5¹ × 7¹ × 11¹

⇒ Common prime factors are 5 and 7.

⇒ HCF = 5¹ × 7¹ = 35.

∴ The correct answer is 35.

Additional Information

HCF (Highest Common Factor)

Also known as GCF (Greatest Common Factor), it is the largest integer that divides two or more numbers without leaving a remainder.

Successive Division Method

A systematic way to find the HCF of large numbers by dividing the larger number by the smaller one until the remainder is zero.

HCF of Co-prime Numbers

If two numbers have no common factors other than 1, they are called co-prime, and their HCF is always 1.

Relation with LCM

For any two numbers a and b: HCF(a, b) × LCM(a, b) = a × b.

The correct answer is Lost Children Archive.

Key Points

• Valeria Luiselli is a Mexican author, who won the International Dublin Literary Award 2021 for her work Lost Children Archive
• It is a novel based on the theme of the separation of children from their parents near the Mexico-America border.

Additional Information

• International Dublin Literary Prize
• The prize is among the richest literary awards given to the works in English literature
• Akhil Sharma, an Indian-American is the recipient of the Prize in 2016, for his novel Family Life.
• Established in 1994, the International Dublin Literary Award is considered one of the world’s wealthiest awards for literature with prize money of €100,000 (approximately INR 89,27,300).
• The award is given to a novel written or translated into English.

The correct answer is 29 August, 1947.

Key Points

• On 29 August 1947, the Constituent Assembly set up a Drafting Committee under the Chairmanship of Dr. B.R. Ambedkar to prepare a Draft Constitution for India.
• While deliberating upon the draft Constitution, the Assembly moved, discussed, and disposed of as many as 2,473 amendments out of a total of 7,635 tabled.
• The Constitution of India was adopted on 26 November 1949 and the hon'ble members appended their signatures to it on 24 January 1950.
• In all, 284 members actually signed the Constitution.
• On that day when the Constitution was being signed, it was drizzling outside and it was interpreted as a sign of a good omen.
• The Constitution of India came into force on 26 January 1950.
• On that day, the Assembly ceased to exist, transforming itself into the Provisional Parliament of India until a new Parliament was constituted in1952.

Additional Information

Drafting Committee:

• Chairman - Dr B. R. Ambedkar
• Other 6 members -
• K.M.Munshi
• Muhammed Saadulah
• Alladi Krishnaswamy Iyer
• Gopala Swami Ayyangar
• N. Madhava Rao (He replaced B.L. Mitter )
• T. T. Krishnamachari (He replaced D.P. Khaitan)

The logic followed here is:-

• Code for the first 2 letters out of 5 = Positional value - 1
• Code for the remaining letters =  Positional value + 1

And,

• Code for the first 3 letters out of 7 = Positional value - 1
• Code for the remaining letters =  Positional value + 1

Similarly,

• Code for the first 3 letters out of 7 = Positional value - 1
• Code for the remaining letters =  Positional value + 1

Hence, "option 1" is the correct answer.

The correct answer is Andhra Pradesh.

Key Points

• The Chief Minister of Andhra Pradesh Jagan Mohan Reddy inaugurated the ‘Aqua Bazaar’ and ‘Aqua Hub’ project.
• The project was launched in Vishakhapatnam. It aims to raise fish consumption in Andhra Pradesh.
• Over 150 state-of-the-art fish markets are to be set up in rural areas named ‘Aqua-bazaar’, and a hub and spoke model will be formed in urban areas.
• Aqua hubs will come up in big cities from where produce will be distributed to retail outlets.
• Aqua bazaars and outlets will have: a live fish section, ice fish and prawn section, frozen section and a dressing section to clean, cut and pack.

Additional Information

• November 21 is also celebrated as World Fisheries Day.
• The theme of the day was "Mixture of the fishing industry, nature and environment, and a greater focus on biodiversity".

The correct answer is Peacock.

Key Points

• Peacock has a four-chambered heart.
• Peacock is the national bird of India and its scientific name is Pavo cristatus.
• Taxonomy of Peacock:
• Kingdom: Animalia
• Phylum: Chordata
• Subphylum: Vertebrata
• Superclass: Tetrapoda
• Class: Aves
• Order: Galliformes
• Family: Phasianidae
• Genus: Pavo
• Species: cristatus

Additional Information

• The frog belongs to the class Amphibia and has a characteristic three-chambered heart with 2 auricles and 1 ventricle.
• Fishes have a two-chambered heart.
• Sea horses have a two-chambered heart

The correct answer is 1948.

Key Points

• The first industrial policy statement of India is known as Industrial Policy Resolution.
• It was announced in the year 1948.
• It defined the role of the State in industrial development both as an entrepreneur and authority.
• Industrial Policy Resolution,1948 states that India is going to have a Mixed Economic Model.
• The Industries (Development and Regula­tion) Act was passed in 1951.
• It was passed to implement the Industrial Policy Resolution, 1948.

Additional Information

• India’s Industrial Policy classified industries into four broad areas:​
• Strategic Industries (Public Sector) -  It included in its ambit the manufacture of arms and ammunition, production and control of atomic energy and the ownership and management of railway transport. These industries became the exclusive monopoly of the Central government of India.
• Basic/Key Industries (Public-cum-Private Sector) - This included coal, iron and steel, aircraft manufacture, shipbuilding, manufacture of telephone, telegraphs and wireless apparatus, and mineral oils. New undertakings in this category could be started only by the state government.
• Important Industries (Controlled Private Sector) - This included industries of basic importance like machine tools, chemicals, fertilizers, non-ferrous metals, rubber manufacturers, cement, paper, newsprint, automobiles, electric engineering, etc. for which the Central Government would feel necessary to plan and regulate.
• Other Industries (Private and Cooperative Sector) - It included those industries which were left open to the private sector, individual as well as cooperative.

The correct answer is Mandamus.

Key Points

• 'Mandamus' means - We Command.
• It is an order from the Supreme Court or High Court to a lower court or tribunal or public authority to perform a public or statutory duty if it is not discharging its duty.
• There are five writs that can be issued by the Supreme Court of India and the High Court of India - Habeas Corpus, Mandamus, Prohibition, Quo Warranto, and Certiorari.
• Supreme Court has the power to issue writs under Article 32.
• High Courts have the power to issue writs under Article 226.

Additional Information

• Habeas Corpus
• A Latin term which literally means ‘to have the body of’.
• It is an order which is issued by the court to a person who has detained another person to produce the body of the latter before it.
• The court then examines the cause and the legality of the detention.
• It is the only writ that can be issued both against public authorities as well as private individuals.
• Prohibition
• It means ‘to forbid’
• It is issued by the higher court to the lower court or the tribunal to prevent the latter from exceeding its jurisdiction or usurping a jurisdiction that it does not possess.
• Certiorari
• It means ‘to be certified’ or sometimes ‘to be informed’.
• It is issued by a higher court to the lower court or the tribunal either to transfer a case pending with the latter to itself or to squash the order of the latter is the case.
• Quo-Warranto
• It means ‘by what authority or warrants’.
• It is issued by the court to inquire into the legality of the claim of the person to the public office.
• It prevents an illegal usurpation of the public office by the person.

The logic followed here is:-

Hence, "option 3" is the correct answer.

The logic followed here is:-

And,

Similarly,

Hence, "option 3" is the correct answer.

The logic followed here is:-

• "party dresses" would be coded as "ti fs".

Hence, "option 3" is the correct answer.

The correct answer is Disinvestment.

Key Points

• Disinvestment can be defined as the process in which the government sells a majority stake to one or more companies, while the government still owns it and the minority stakeholder persists.
• It is the process of selling subsidiary assets, investments, or divisions of a company in order to maximize the value of the parent company.

Additional Information

• In finance and economics, Disinvestment is the reduction of some kind of asset for financial, ethical, or political objectives or the sale of an existing business by a firm.
• A Disinvestment is the opposite of an investment.
• Divestiture is an adaptive change and adjustment of a company's ownership and business portfolio made to confront with internal and external changes.

Shortcut Trick

Speed Ratio (Original : New) = 100 : 130 = 10 : 13

Since Distance is constant, Time Ratio = 13 : 10

Difference in time = 13 − 10 = 3 units

According to the question, 3 units = 15 min ⇒ 1 unit = 5 min

Original Time = 13 units = 13 × 5 = 65 min = 1 hr 05 min

∴ The correct answer is 1 hr 05 min.

Alternate Method

Given:

Speed increase = 30%

Time reduction = 15 min

Formula Used:

Distance = Speed × Time (D = S × T)

Calculations:

⇒ Let original speed be S and original time be T.

⇒ New speed = S + 30% of S = 1.3S

⇒ New time = T − 15 min

⇒ Since distance is the same: S × T = 1.3S × (T − 15)

⇒ T = 1.3T − 19.5

⇒ 1.3T − T = 19.5

⇒ 0.3T = 19.5

⇒ T = 19.5 ÷ 0.3 = 65 min

⇒ 65 min = 1 hr 05 min

∴ The correct answer is 1 hr 05 min.

Additional Information

Inverse Proportion Rule

When Distance is constant, Speed and Time are inversely proportional (S₁/S₂ = T₂/T₁).

Average Speed

If a person covers the same distance at speed x and speed y, the Average Speed is (2 × x × y) ÷ (x + y).

Unit Conversion

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

Shortcut Trick

Assume the 2-digit number is 14 units (LCM of 2 and 7).

One-seventh of the number = 14 ÷ 7 = 2 units.

Half of the number = 14 ÷ 2 = 7 units.

The difference is 7 units − 2 units = 5 units.

Given, 5 units = 15 ⇒ 1 unit = 3.

The number = 14 × 3 = 42. Sum of digits = 4 + 2 = 6.

∴ The correct answer is 6.

Alternate Method

Given:

Let the 2-digit number be x.

One-seventh of the number = x/7

Half of the number = x/2

Formula Used:

Fractional relation: x/7 = x/2 − 15

Total Number (x)

1/7 of x

1/2 of x

Difference = 15

Calculations:

⇒ x/2 − x/7 = 15

⇒ (7x − 2x) / 14 = 15

⇒ 5x / 14 = 15

⇒ 5x = 15 × 14

⇒ x = 3 × 14 = 42

⇒ Sum of digits = 4 + 2 = 6.

∴ The correct answer is 6.

Additional Information

2-Digit Number Representation

Any 2-digit number with tens digit a and units digit b can be written as 10a + b.

Sum of Digits Property

The sum of digits for the number 10a + b is simply a + b.

LCM in Fraction Problems

Using the LCM of denominators as a base value helps avoid complex fractions and simplifies calculations.

The correct answer is indifference curve.

Key Points

• The optimum bundle of the consumer is located at the point where the budget line is tangent to one of the indifference curves.

• The indifference curve is a geometrical device developed by J.R. Hicks and R.G.D. Allen in the article “A Reconsideration of the Theory of Value”.

• An indifference curve shows a combination of two goods that give a consumer equal satisfaction and utility thereby making the consumer indifferent.

• An indifference schedule is a table which represents various combinations of two goods, which yield equal satisfaction to the consumer.

• The graphical presentation of the Indifference schedule is known as the Indifference curve.

• Along the curve, the consumer has an equal preference for the combinations of goods shown—i.e. is indifferent about any combination of goods on the curve.

• Typically, indifference curves are shown convex to the origin, and no two indifference curves ever intersect.

• A diagram showing different indifference curves corresponding to different indifference schedules of the consumer is an indifference map. In other words, a set or family of indifference curves is an indifference map.

• Law of Demand

• According to the law of demand

• ​​​​when the price of a commodity increase, the quantity demanded decreases

• when the price of a commodity decreases, it’s the quantity demanded increases

• keeping other factors remains the same.

• The consumer’s demand for goods must be inversely related to the price of the good.

• There is an inverse relationship between price and demand and due to this the demand curve always has a downward slope.

• The demand curve is the relation between the quantity of the good chosen by a consumer and the price of the good.

• ​Assumptions for the Law of Demand

• ​​No change in the income of consumers

• No change is the taste and preference of the consumers

• No change in price related to other goods.

The correct answer is Zn.

Key Points

• Zinc is a chemical element with the symbol Zn and atomic number 30.
• Atomic Number is defined as the number of protons in the nucleus of an element.
• It is used to determine the characteristics of an element and it is also referred to for placing an element in the Periodic Table.
• The Atomic Number of Zinc (Zn) is 30 whereas the Mass Number is 65 i.e. it has 35 neutrons.
• It is the first element in group 12 (IIB) of the periodic table.
• Zinc is chemically similar to magnesium: both elements exhibit only one normal oxidation state (+2), and the Zn²⁺ and Mg²⁺ ions are of similar size.

Additional Information

The correct answer is 10.

Key Points

• In Vaishnavism, 10 avatars or incarnations of deity were recognized.
• Matsya (Fish)
• Tortoise
• Boar
• Man-lion
• Dwarf
• Rama-with-the-Ax
• King Rama
• Krishna
• Buddha
• Kalkin
• ​Vaishnavism is the worship and acceptance of Vishnu (Sanskrit: “The Pervader” or “The Immanent”) or one of his various incarnations (avatars) as the supreme manifestation of the divine.
• During a long and complex development, many Vaishnava groups emerged with differing beliefs and aims.
• Some of the major Vaishnava groups include the Shrivaishnavas (also known as Vishishtadvaitins) and Madhvas (also known as Dvaitins) of South India.
• Most Vaishnava believers, however, draw from various traditions and blend the worship of Vishnu with local practices.

The correct answer is 1976.

Key Points

• The fundamental duties of citizens were added to the Constitution by the 42^nd Constitutional Amendment Act (1976).
• The 42^nd Constitutional Amendment Act (1976) included ten Fundamental Duties.
• This amendment added a new part, namely, Part IVA to the Constitution.
• This new part consists of only one Article, that is, Article 51A which for the first time specified a code of ten fundamental duties of the citizens.
• Later there was an addition of one more Fundamental Duty in 2002 by the 86^th Amendment Act.
• The Fundamental Duties in the Indian Constitution are inspired by the Constitution of the erstwhile USSR.
• 42^nd Amendment Act, 1976 is one of the most important amendments to the Indian Constitution. It was enacted by the Indian National Congress headed by Indira Gandhi then. Due to the large number of amendments this act has brought to the Indian Constitution, it is also known as 'Mini-Constitution.

The correct answer is Lipase.

Key Points

• Lipase enzymes are used in the stabilization of rice bran oil.
• Rice bran oil is known as wonder oil and it is the most important vegetable oil in Asia.
• Rice bran oil is extracted from bran which is the outer hard layer of rice.
• It is an emerging category in edible oil with a lot of nutritional properties and health benefits.
• Rice bran oil is heart-friendly, immunity, and prevents other diseases.
• The current study aimed to stabilize rice bran oil through different probiotic isolates and to assess the nutritional content of rice bran oil after stabilization.
• The study was aimed to inactivate naturally occurring lipases that can hydrolyze oil into glycerol and free fatty acid which is a serious problem that gives it a rancid taste and smell.

Additional Information

• Hydrolases are the group of enzymes that catalyze bond cleavages by reaction with water. The natural function of most hydrolases is digestion to break down nutrients into smaller units for digestion.
• Catalase is a key enzyme that uses hydrogen peroxide, a non-radical ROS, as its substrate. This enzyme is responsible for neutralization through the decomposition of hydrogen peroxide, thereby maintaining an optimum level of the molecule in the cell which is also essential for cellular signaling processes.
• Cellulase is any of several enzymes produced chiefly by fungi, bacteria, and protozoans that catalyze cellulolysis, the decomposition of cellulose and of some related polysaccharides. The name is also used for any naturally occurring mixture or complex of various such enzymes, that act serially or synergistically to decompose cellulosic material.

Given that:-

• No of days from 2 January 2017 to 31 March 2017  = 30 + 28 + 31 = 89 as 2017 is a non-leap year.
• Since, it was Thursday on 1 January 2017, every 7^th day from 1 January will be a Thursday.
• Thus, no. of odd days = 89/7 = 5
• Now, 1 January 2017 (Thursday) + 5 odd days = 31 March 2017 (Tuesday)
• 31^st March 2017 will be Tuesday.

Hence, "option 2" is the correct answer.

Given:

56 ÷ 14 × 22 - 12 × 6 ÷ 3 + 10 = z

Concept used:

Calculation:

56 ÷ 14 × 22 - 12 × 6 ÷ 3 + 10

⇒ 4 × 22 - 12 × 2 + 10

⇒ 4 × 4 - 12 × 2 + 10

⇒ 16 - 24 + 10

⇒ 2

∴ The value of z is 2.

The logic followed here is:-

From option 1:-

• (22, 34)
• 22 × 2 = 44 - 10 = 34

From option 2:-

• (11, 12)
• 11 × 2 = 22 - 10 = 12

From option 3:-

• (25, 42)
• 25 × 2 = 50 - 10 = 40  ≠  42,
• It is different from others.

From option 4:-

• (17, 24)
• 17 × 2 = 34 - 10 = 24

Hence, "option 3" is the correct answer.

The logical Venn diagram is given below:-

Conclusions:

I. All dolphins are donkeys. → False → (it is possible but not definite.)

II. Some dolphins are donkeys. → False → (it is possible but not definite.)

III. Some donkeys are cats. → True → (All camels are donkeys, Some cats are camels. So some donkeys are cats is correct.)

IV. All cats are donkeys. → False → (it is possible but not definite.)

Hence, "option 2" is the correct answer.

The correct answer is 72.

Key Points

• In contemporary Carnatic music, 72 Melakarta ragas are there.
• In Carnatic music, Melakarta is a collection of fundamental music scales.
• In this ragas contai all seven swaras.
• Ascending and descending notes have the same notes sometimes.
• 72 Melakarta is divided into two parts "Sudha Madhyama" and "Prati Madhyama".
• This 72 Melakarta rag has 12 groups that are called chakras.
• The chakras are Indu chakra, Netra chakra, Agni chakra, Veda chakra, Bana chakra, Rutu chakra, Rishi chakra, Vasu chakra, Bramha chakra, Disi chakra, Rudra chakra, Aditiya chakra.
• Hanumatodi is one of the ragas from Netra Chakra.

The correct answer is Sasmita Lenka.

Key Points

• Sasmita Lenka became the first official in India to be felicitated with United Nations Asia Environmental Enforcement Award in February 2021 under the Gender Leadership and impact category.
• Sasmita Lenka, who is a divisional forest officer in Athgarh, Cuttack, received the award under the 'Gender Leadership and Impact' category for her work in helping in busting pangolin smuggling rackets in the state.

Additional Information

• Namita Gokhale is the author of twenty books and the Sahitya Akademi (National Academy of Letters) awardee for 2021. She is co-founder and co-director (with William Dalrymple) of the Jaipur Literature Festival. Her acclaimed debut novel, ‘Paro: Dreams of Passion’, was published in 1984.
• Inspector Sudarshan Panthee received the Asia Environmental Enforcement Award from the United Nations for their role in arresting notorious wildlife smuggler Kunjok Chhiring Lama in June 2020.

Shortcut Trick

Efficiency of 1 Man = 1/20 and 1 Woman = 1/30.

Required Efficiency for 2 Men and 3 Women = (2 × 1/20) + (3 × 1/30).

⇒ 1/10 + 1/10 = 2/10 = 1/5.

Total Time taken = Reciprocal of combined efficiency = 5 days.

∴ The correct answer is 5 days.

Alternate Method

Given:

Time taken by one man = 20 days

Time taken by one woman = 30 days

Formula Used:

Total Work = Efficiency × Time

Calculations:

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

⇒ Efficiency of 1 man = 60 ÷ 20 = 3 units/day.

⇒ Efficiency of 1 woman = 60 ÷ 30 = 2 units/day.

⇒ Efficiency of 2 men = 2 × 3 = 6 units/day.

⇒ Efficiency of 3 women = 3 × 2 = 6 units/day.

⇒ Combined Efficiency (2 men + 3 women) = 6 + 6 = 12 units/day.

⇒ Time required = Total Work ÷ Total Efficiency

⇒ Time = 60 ÷ 12 = 5 days.

∴ The correct answer is 5 days.

Additional Information

Work and Efficiency Relationship

Efficiency is inversely proportional to the time taken to complete a task. Efficiency = 1 ÷ Time.

Combined Work Formula

If A takes 'x' days and B takes 'y' days, together they take (x × y) ÷ (x + y) days to finish the work.

Wages and Efficiency

In Time and Work, wages are always distributed in the ratio of the work done or the ratio of efficiencies of the workers.

Given:

0.17y = 10.2

Calculation:

0.17y = 10.2

⇒ y = 10.2 ÷ 0.17

⇒ y = 60

∴ The value of y is 60.

The correct answer is 1974.

Key Points

• The Central Pollution Control Board was set up by the government in the year 1974.
• The Central Pollution Control Board (CPCB) of India is a statutory organization under the Ministry of Environment, Forest and Climate Change (Mo.E.F.C.C.).
• It was established in 1974 under the Water (Prevention and Control of Pollution) Act, 1974.
• The CPCB is also entrusted with the powers and functions under the Air (Prevention and Control of Pollution) Act, 1981.
• The board has approximately 500 full-time employees.
• It Coordinates the activities of the State Pollution Control Boards by providing technical assistance and guidance and also resolves disputes among them.
• It is the apex organization in the country in the field of pollution control, as a technical wing of MoEFCC.

The correct answer is Rana Kumbha.

Key Points

• Rana Kumbha defeated Mahmud Khilji and erected the tower of victory (Vijay Stambha) in Chittorgarh.
• Situated in Chittor Fort of Chittorgarh or Vijay Stambh (1440-48) was built by Maharana Kumbha (King of Mewar).
• It is representative of victory because Maharana Kumbha defeated Mahmood Khilji in 1437.
• Its architect was Rao Jaita.
• It is also called Kriti Stambha/Kiriti Stambha or Vishnu Stambha.
• Mahmood Khilji had a combined army of Gujarat & Malwa which he had used in the Sarangpur war.
• The statue is the symbol of the Rajasthan Police & Secondary Education Board.

Additional Information

• Rana Kumbha achievements
• Rana Kumbha defeated Sultan Mehmood Khilji​ of Malwa.
• According to inscriptions, he brought Mehmood Khilji as a prisoner.
• He kept him in prison for six months and sent him back to his Kingdom.
• Later After making military preparations, Mehmood Khilji invaded Mewar.
• He destroyed the temple at Kumbhalgarh but failed to conquer Mewar.

Given that:-

• H is shorter than E only.

E > H > - > - > -

• F is not as tall as P. P is shorter than G.

F < P < G

• H is taller than G

H>G

• Then final arrangement is:-

F < P < G < H < E

• Thus, F is the shortest person.

Hence, "option 3" is the correct answer.

Given: 

4, 5, 6, 7, 8, 12, 9, 12, 5, 12

Concept used:

The mode is the most frequently occurring value on the list.

Total = Mean (Average) × number of entities

Calculation:

Given series is

4, 5, 6, 7, 8, 12, 9, 12, 5, 12

Mean of the series = 80 ÷ 10 = 8

Mode of the series = 12

Difference in the mode and the mean of the observations = 12 - 8 = 4

∴ 4 is the difference in the mode and the mean of the observations.

Given that:-

• D is taller than A and E.
• A is taller than F.
• E is taller than F.

Case 1: D > A > E > F

Case 2: D > E > A > F

• F is taller than B and C.

Case 1: D > A > E > F > B/C > C/B

Case 2: D > E > A > F > B/C > C/B

• Either B or C is the shortest person.

Hence, "option 2" is the correct answer.

The correct answer is Chittaranjan Locomotive Works.

Key Points

• Chittaranjan Locomotive Works is located in Chittaranjan, West Bengal (32 km from Asansol).
• Production began on January 26, 1950, and the first steam locomotive rolled out of the Chittaranjan Locomotive Works (CLW) factory on November 1.
• Known as Loco Manufacturing Works earlier, it was renamed on November 1 as a tribute to the famous freedom fighter from Bengal, Deshbandhu Chittaranjan Das.
• LW is the first production unit of its kind in the developing world, second in Asia and fifth in the world, to manufacture the three-phase state-of-the-art GTO thyristor-controlled electric loco, and the 6,000 hp freight electric loco WAG-9, called Navyug.
• It is to CLW's credit that today, India is among the select band of five nations with the capability to manufacture the three-phase electric locomotives.

Additional Information 

• Rail Wheel Factory formerly known as Wheel and Axle Plant is situated in Bangalore, Karnataka.
• Integral Coach Factory is located in Perambur (Chennai). India's fastest train, Train 18 which is also known as the "Vande Bharat" express was developed in ICF, Chennai.
• The Diesel Locomotive Works (DLW) in Varanasi, India, is a production unit owned by Indian Railways, that manufactures diesel-electric locomotives and their spare parts.

Given:

The circumference of a circle is given as 308 m.

Concept used:

The circumference of a circle = 2πR

The area of a circle = πR2

Where R is the radius.

Calculation:

Let the radius of the circle be R meter.

According to the question,

2πR = 308

⇒ 2 × 22/7 × R = 308

⇒ R = 49

⇒ πR² = 22/7 × 49²

⇒ πR2 = 7546

∴ The area of the circle is 7546m².

Shortcut Trick

Let the Cost Price (CP) be 100.

Selling Price (SP) with 12.5% gain = 100 + 12.5 = 112.5.

This SP is after a 10% discount on Marked Price (MP), so 90% of MP = 112.5.

MP = 112.5 ÷ 0.9 = 125.

If sold at MP, Profit = 125 − 100 = 25.

Profit% = (25 ÷ 100) × 100 = 25%.

∴ The correct answer is 25%.

Alternate Method

Given: Discount = 10%, Profit = 12.5%.

Formula: CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%)

⇒ CP ÷ MP = (100 − 10) ÷ (100 + 12.5)

⇒ CP ÷ MP = 90 ÷ 112.5

⇒ CP ÷ MP = 900 ÷ 1125 = 4 ÷ 5

⇒ If sold at MP, Profit = MP − CP = 5 − 4 = 1 unit

⇒ Profit% = (1 ÷ 4) × 100 = 25%

∴ The correct answer is 25%.

Additional Information

Relation between CP and MP

The ratio of Cost Price to Marked Price is always (100 − D%) : (100 + P%).

Profit at Marked Price

When no discount is offered, the Marked Price becomes the Selling Price.

The correct answer is the administration of union territories by the President.

Key Points 

• Article 239
• Administration of union territories.
• The president may appoint the governor of the state as the administrator, where he exercises his functions as such administrative independently of his council of ministers

Confusion Points 

• Article 239AA. Special provisions concerning Delhi
• From the date of commencement of the Constitution (Sixty-ninth Amendment) Act, 1991.
• The Union Territory of Delhi shall be called the National Capital Territory of Delhi.

Additional Information

• Part-8 of the Indian Constitution deals with the Union Territory.
• The Union Territory of India is described between articles 239 to 242 in our constitution.
• There were 9 union territories in India but from 26^th January 2020, Dadra and Nager Haveli and Daman and Diu are to be combined into a single territory, thus resulting in 8 Union Territories in India now.

Given:

The average of 30 numbers is 55. The average of the first 15 numbers is 51 and the average of the last 12 numbers is 56.

Concept used:

Total = Average × Number of Entities

Calculation:

Sum of all 30 terms = 30 × 55 = 1650

Sum of first 15 terms = 15× 51 = 765

Sum of last 12 terms = 12 × 56 = 672

After removing first 15 and last 12 terms out of, there will be 3 terms remaining

⇒ Sum of remaining 3 terms = 1650 - (765 + 672) = 213

According to the question, 68 and 74 are added to the sum of 3 terms

Thus, the number of total terms becomes 5

Average of 5 terms = (213 + 68 + 74)/5 = 71

∴ 71 is the average of 68, 74 and the remaining 3 numbers.

The correct answer is The United States of America.

Key Points

• According to Renewable Fuel Association (RFA) data 2020, The United States is the world's largest producer of ethanol, having produced over 13.94 billion gallons followed by Brazil at 8.08 billion gallons in 2020.
• Together, the United States and Brazil produce 82% of the world's ethanol.

Additional Information

• Ethanol can be produced from sugarcane, maize, wheat, etc which are having high starch content.
• In India, ethanol is mainly produced from sugarcane molasses by the fermentation process.
• Ethanol can be mixed with the gasoline to form different blends.
• As the ethanol molecule contains oxygen, it allows the engine to completely combust the fuel, resulting in fewer emissions and thereby reducing the occurrence of environmental pollution.
• Since ethanol is produced from plants that harness the power of the sun, ethanol is also considered a renewable fuel.

Important Points

• The government of India has been promoting the use of ethanol as a blendstock with main automotive fuels like petrol in line with the National Policy on Biofuels (NBP) -2018 under the Ethanol Blended Petrol (EBP) Program.
• This policy envisages an indicative target of blending 20 per cent ethanol in petrol by 5 years to 2025-26.

The correct answer is the USA.

Key Points

• The USA is the highest per capita total spending on health worldwide.
• The total health expenditure in the U.S. exceeded four trillion dollars.

Additional Information 

• Organization for Economic Co-operation and Development (OECD)
• It is an intergovernmental economic organization with 38 member countries, founded in 1961 to stimulate economic progress and world trade.
• India is not a member of OECD but has been a key economic partner.
• OECD Headquarters: Paris, France
• OECD Founded: 30 September 1961

Given: 

The ratio between the marked price and the cost price of an article is 5 : 3.

Selling price = Rs. 3024

Concept used:

Final discount percentage after two successive discounts of A% and B% = $(A + B - {AB \over 100})\%$

Selling Price = Marked Price × (1 - Discount%)

Profit = Selling Price - Cost Price

Calculation:

Let the common ratio be Q.

Hence, the marked and cost price of the article is 5Q and 3Q respectively.

Final discount percentage after two successive discounts of A% and B% = $(16 + 20 - {(16\ ×\ 20)\over 100})\%$ = 32.8%

According to the question,

5Q × (1 - 0.328) = 3024

⇒ 5Q = 4500

⇒ Q = 900

⇒ 3Q = 2700

Hence, profit made = 3024 - 2700 = Rs. 324

∴ The profit is Rs. 324.

Shortcut Trick

The circle touches the parallel sides AB and CD of the rectangle.

Diameter of the circle = Distance between AB and CD = BC = 8 cm.

Radius (r) of the circle = 8 ÷ 2 = 4 cm.

In ΔOBC, the base is BC = 8 cm and the height (altitude from O) is the radius = 4 cm.

Area of ΔOBC = 1/2 × base × height = 1/2 × 8 × 4 = 16 cm².

∴ The correct answer is 16 cm².

Alternate Method

Given: AB = 10 cm, BC = 8 cm. Circle touches AB, BC, and CD.

Formula: Area of Triangle = 1/2 × base × height.

⇒ In rectangle ABCD, side AB is parallel to CD.

⇒ The distance between AB and CD is BC = 8 cm.

⇒ Since the circle touches AB and CD, its diameter = 8 cm.

⇒ Radius of the circle (r) = 8 ÷ 2 = 4 cm.

⇒ The circle also touches side BC, so the distance from the center O to BC is the radius.

⇒ In ΔOBC, let base = BC = 8 cm.

⇒ Height of ΔOBC = Distance from O to BC = radius = 4 cm.

⇒ Area of ΔOBC = 1/2 × 8 × 4

⇒ Area of ΔOBC = 4 × 4 = 16 cm².

∴ The correct answer is 16 cm².

Additional Information

Properties of Inscribed Circles

When a circle touches two parallel lines, its diameter is equal to the perpendicular distance between those lines.

Area of Triangle

The area of any triangle is calculated as 1/2 × base × height, where the height is the perpendicular distance from the opposite vertex to the base line.

Rectangle Geometry

In a rectangle ABCD, opposite sides are equal and parallel (AB = CD and BC = AD), and all interior angles are 90°.

The correct answer is Tauktae.

Key Points

• Cyclone Tauktae
• It was the first cyclonic storm of 2021 that emerged from the Arabian Sea.
• It hit southern Gujarat on 17 May 2021 and was classified as a Very Severe Cyclonic Storm (VSCS).
• It is a tropical cyclone, It has been named by Myanmar.
• It means 'gecko', a highly vocal lizard, in the Burmese language.

Additional Information 

• Tropical Cyclones
• Tropical cyclones are violent storms that originate over oceans in tropical areas and move over to the coastal areas bringing about large-scale destruction due to violent winds (squalls), very heavy rainfall (torrential rainfall) and storm surge.
• They are irregular wind movements involving the closed circulation of air around a low-pressure centre.
• Conditions Favourable for Tropical Cyclone Formation
• Large sea surface with a temperature higher than 27° C,
• The presence of the Coriolis force is enough to create a cyclonic vortex,
• Small variations in the vertical wind speed,
• A pre-existing weak low-pressure area or low-level-cyclonic circulation,
• Upper divergence above the sea level system.
• The depth of warm water (26-27°C) should extend for 60-70 m from the surface of the ocean/sea, so that deep convection currents within the water do not churn and mix the cooler water below with the warmer water near the surface.
• The above condition occurs only in western tropical oceans because of warm ocean currents (easterly trade winds push ocean waters towards the west) that flow from the east towards the west forming a thick layer of water with temperatures greater than 27°C. This supplies enough moisture to the storm.
• The cold currents lower the surface temperatures of the eastern parts of the tropical oceans making them unfit for the breeding of cyclonic storms.

Given:

The outer radius of a spherical shell is 9 cm and the thickness of the shell is 1 cm. 

Concept used:

Volume of a sphere = ${4 \over 3} \times \pi \times (Radius^3)$

Calculation:

Hence, the radius of the inner part = 9 - 1 = 8 cm

The volume of the metal used for the shell should equal the difference between the volume of the outer and inner parts.

Thus, The volume of the metal used for the shell

⇒ ${4 \over 3} \times \pi \times (9^3 - 8^3)$

⇒ ​​$909\frac{1}{3}$ cm³

∴ The volume of the metal used for the shell is $909\frac{1}{3}$ cm3.

Given: 

Five years ago, ages of father and his son were in the ratio 7 : 2.

Five years hence, ages of the father and his son will be in the ratio 9 : 4. 

Concept used:

Ratio Proportion

Calculation:

Let the common ratio be Q.

Hence, five years ago, the ages of the father and his son were 7Q and 2Q years

According to the question,

(7Q + 5 + 5) : (2Q + 5 + 5) = 9 : 4

⇒ 28Q + 40 = 18Q + 90

⇒ Q = 5

Present age

Father = 7Q + 5 = 7 × 5 + 5 = 40

Son = 2Q + 5 = 2 × 5 + 5 = 15

Let after P years the father's age will be twice the age of his son.

According to the question,

40 + P = 2 × (15 + P)

⇒ P = 10

∴ After 10 years the father's age will be twice the age of his son.

Given that:-

• Giridhar was at a temple and was facing west.
• He turns 45° in the clockwise direction to collect a token, then another 180° in the clockwise direction.
• He then turned 45° in the anti-clockwise direction.

The diagram is given below:-

• The east direction he is facing now.

Hence, "option 4" is the correct answer.

Given that:-

B sits second to the right of E.

C sits to the immediate left of E.

F sits second to the right of D.

D sits third to the right of A.

Concept used:

Calculation:

$\frac{{12, - ,6, \div ,2, + ,4}}{{{3^2}, \times ,3 - 7 + 6}}$

⇒ ${12\ -\ 3\ +\ 4} \over {27\ -\ 7\ +\ 6}$

⇒ ${13 \over 26}$

⇒ ${1 \over 2}$

∴ The simplified value is ${1 \over 2}$.

Given:

y = $\sqrt[3]{6}, - ,4$

Concept used:

(A + B)³ = A³ + 3A²B + 3AB² + B³

Calculation:

y = $\sqrt[3]{6}, - ,4$

⇒ y + 4 = $\sqrt[3]{6}$

⇒ (y + 4)³ = 6

⇒ y³ + 12y² + 48y + 64 = 6

⇒ y3 + 12y2 + 48y + 64 + 36 = 6 + 36

⇒ y3 + 12y2 + 48y + 64 + 36 = 42

∴ The value of y3 + 12y2 + 48y + 64 + 36 is 42.

Given:

k is average of 16, 25, 13, 26 and 15

Concept used:

Total = Mean (Average) × number of entities

Calculation:

Average of 16, 25, 13, 26 and 15 = Sum (16, 25, 13, 26, 15) ÷ 5 = 19

Hence,

$\sqrt {{\rm{2k}},{\rm{ + }},{\rm{11}}}$

⇒ $\sqrt {{\rm{2 \times 19}},{\rm{ + }},{\rm{11}}}$

⇒ ${\sqrt49}$

⇒ 7

∴ The value of $\sqrt {{\rm{2k}},{\rm{ + }},{\rm{11}}}$ is 7.

Given:

K is the product of the greatest and the smallest of the numbers $\frac{1}{4},,\frac{2}{3},,\frac{4}{5},,\frac{5}{8},,\frac{3}{4}$ . 

Concept used:

Concept of comparing fractions

Calculation:

Given numbers,

${1 \over 4}$ = ${1 \over 4}$ × 120 = 30

${2 \over 3}$ = ${2 \over 3}$ × 120 = 80

${4 \over 5}$ = ${4 \over 5}$ × 120 = 96

${5 \over 8}$ = ${5 \over 8}$ × 120 = 75

${3 \over 4}$ = ${3 \over 4}$ × 120 = 90

Hence, 

Greatest number = ${4 \over 5}$

Smallest number = ${1 \over 4}$

thus,

k = ${4 \over 5}$ × ${1 \over 4}$ = ${1 \over 5}$ and 1/k = 5

Now,

$\left( {\frac{{\rm{1}}}{{\rm{k}}},{\rm{ + }},{\rm{4}}} \right)\left( {\frac{{\rm{1}}}{{\rm{k}}},{\rm{ - }},{\rm{2}}} \right)$

⇒ (5 + 4) (5 - 2)

⇒ 9 × 3

⇒ 27

∴ The value of$\left( {\frac{{\rm{1}}}{{\rm{k}}},{\rm{ + }},{\rm{4}}} \right)\left( {\frac{{\rm{1}}}{{\rm{k}}},{\rm{ - }},{\rm{2}}} \right)$  is 27.

Shortcut Trick

Equate the coefficients: (2/3) × y = (8/15) × z

Cross-multiply to find the ratio y : z directly.

y : z = (8/15) ÷ (2/3) = (8/15) × (3/2) = 4/5

∴ The correct answer is 4 : 5.

Alternate Method

Given:

(2/3) × y = (8/15) × z

Calculations:

⇒ y / z = (8 / 15) / (2 / 3)

⇒ y / z = (8 / 15) × (3 / 2)

⇒ y / z = (8 × 3) / (15 × 2)

⇒ y / z = 24 / 30

⇒ y / z = 4 / 5

⇒ y : z = 4 : 5

∴ The correct answer is 4 : 5.

Additional Information

Ratio of Fractions

To find the ratio a : b when ma = nb, the ratio is always a/b = n/m.

Inverse Proportion

If two quantities are equated with different coefficients, their individual values are in the inverse ratio of those coefficients.

The correct answer is the direct change of a substance from a solid to a gas state.

Key Points

• Sublimation is a process in which a solid transforms directly into vapours without changing into liquid.
• This phenomenon can be seen in camphor or naphthalene balls.
• In the process snow or ice transforms directly into water vapour without becoming water.

Additional Information 

• Deposition - It is the process of conversion of a gas to a solid.
• Evaporation - It is the process of conversion of a liquid into gas.
• Fusion/Melting - It is the process of conversion of a solid into a liquid.
• Condensation - It is the process of conversion of a gas into a liquid.

The correct answer is KK Shailaja.

Key Points 

• Former Kerala Health Minister KK Shailaja has been awarded the prestigious Central European University (CEU) Open Society Prize in recognition of her commitment to public health services.
• The Open Society Prize was announced during the 30^th graduation ceremony which was held online.
• The prize is awarded annually to persons of exceptional distinction who serve the ideals of an open society.

Additional Information

• Central European University (CEU)
• It is an undergraduate- and graduate-level “crossroads” university.
• It was founded in 1991.
• It was located in Budapest, Hungary.

Shortcut Trick

If the entire ₹5,000 was invested at 10%, the interest for 2 years would be = (5000 × 10 × 2) ÷ 100 = ₹1,000.

Actual interest accrued is ₹1,072, which is an extra 1072 − 1000 = ₹72.

This extra ₹72 is generated because the first part was invested at an extra 2% (12% − 10%) for 2 years.

∴ 2% of Sum₁ × 2 = ₹72 ⇒ 4% of Sum₁ = ₹72

⇒ Sum₁ = 72 × (100 ÷ 4) = ₹1,800

∴ The correct answer is ₹1,800.

Alternate Method

Given:

Total Principal = ₹5,000

Rate₁ = 12% p.a., Rate₂ = 10% p.a.

Total Time = 2 years

Total Simple Interest = ₹1,072

Formula Used:

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

Total Sum = ₹5000

Part 1: ₹x Rate: 12% | Time: 2 yr

Part 2: ₹(5000 − x) Rate: 10% | Time: 2 yr

Interest 1

Interest 2

Total SI = ₹1072

Calculation:

Let the sum invested at 12% p.a. be ₹x.

Then, the sum invested at 10% p.a. will be ₹(5000 − x).

⇒ SI₁ + SI₂ = 1072

⇒ (x × 12 × 2) ÷ 100 + ((5000 − x) × 10 × 2) ÷ 100 = 1072

⇒ 24x ÷ 100 + (100000 − 20x) ÷ 100 = 1072

⇒ 24x + 100000 − 20x = 107200

⇒ 4x = 107200 − 100000

⇒ 4x = 7200

⇒ x = 1800

∴ The correct answer is ₹1,800.

Additional Information

Simple Interest (SI)

Calculated strictly on the original principal. The interest accumulated does not earn further interest. Formula: SI = (P × R × T) ÷ 100

Compound Interest (CI)

Calculated on the initial principal and also on the accumulated interest of previous periods. Formula: Amount = P(1 + R ÷ 100)^T

Alligation Method for Interest

When a total sum is split and invested at two different rates, the ratio of the split principals can be found directly using the net average interest rate through the alligation cross.

The family tree is given below:-

• Z is the brother of P.

Hence, "option 3" is the correct answer.

Given that: 4 ÷ 8 + 5 - 6 × 2 = 34

• From option 1:-

Interchange +, -

4 ÷ 8 - 5 + 6 × 2 = 34

Applying BODMAS rule:-

0.5 - 5 + 6 × 2 = 34

0.5 - 5 + 12 = 34

0.5 - 17 = 34

-16.5 ≠ 34

• From option 2:

Interchange ÷, ×

4 × 8 + 5 - 6 ÷ 2 = 34

Applying BODMAS rule:-

4 × 8 + 5 - 3 = 34

32 + 5 - 3 = 34

37 - 3 = 34

34 = 34

• From option 3:

Interchange ÷, +

4 + 8 ÷ 5 - 6 × 2 = 34

Applying BODMAS rule:-

4 + 1.6 - 6 × 2 = 34

4 + 1.6 - 12 = 34

5.6 - 12 = 34

-6.4 ≠ 34, 

• From option 4:-

Interchange ×, +

4 ÷ 8 × 5 - 6 + 2 = 34

Applying BODMAS rule:-

0.5 × 5 - 6 + 2 = 34

2.5 - 6 + 2 = 34

4.5 - 6 = 34

-1.5 ≠ 34

Hence, "option 2" is the correct answer.

Given:

$1, - ,\frac{{\left( {4, \div ,5, - ,1, \times ,3, + ,2} \right) \times ,8}}{{{3^2}, \times ,8, - ,4, \times ,2}}$

Concept used:

Calculation:

$1, - ,\frac{{\left( {4, \div ,5, - ,1, \times ,3, + ,2} \right) \times ,8}}{{{3^2}, \times ,8, - ,4, \times ,2}}$

⇒ $1, - ,\frac{{\left( {0.8, - ,1, \times ,3, + ,2} \right) \times ,8}}{{{3^2}, \times ,8, - ,4, \times ,2}}$

⇒ $1, - ,\frac{{\left( {0.8, - ,3\ + ,2} \right) \times ,8}}{{9, \times ,8, - ,4, \times ,2}}$

⇒ $1, - ,\frac{{\left( {-0.2} \right) \times ,8}}{{72\ -\ 8}}$

⇒ $1 - {{-1.6} \over 64}$

⇒ $1 + {{1.6} \over 64}$

⇒ 1 + 0.025

⇒ 1.025

⇒ $\frac{{41}}{{40}}$

∴ The simplified value of $1, - ,\frac{{\left( {4, \div ,5, - ,1, \times ,3, + ,2} \right) \times ,8}}{{{3^2}, \times ,8, - ,4, \times ,2}}$ is $\frac{{41}}{{40}}$.