RRB NTPC CBT-I Official Paper (Held On: 4 Jan 2021 Shift 1) (Previous Year Paper)

Shortcut Trick

Remaining days of work for Harish + Bimal = 20 − 15 = 5 days.

Work done by Harish alone in 10 days = Work done by (Harish + Bimal) in 5 days.

Efficiency Ratio (Harish + Bimal) : Harish = 10 : 5 = 2 : 1.

Since Harish's efficiency is half of their combined efficiency, he takes double the time.

Time taken by Harish alone = 20 × 2 = 40 days.

∴ The correct answer is 40 days.

Alternate Method

Given: Harish and Bimal work together for 15 days.

⇒ Work completed in 15 days = 15 × 1 = 15 units.

⇒ Remaining work = 20 − 15 = 5 units.

⇒ Harish completes 5 units in 10 days.

⇒ Harish's efficiency = 5 ÷ 10 = 0.5 units/day.

⇒ Time for Harish alone = Total Work ÷ Efficiency

⇒ Time = 20 ÷ 0.5 = 40 days.

∴ The correct answer is 40 days.

Additional Information

Work and Efficiency Relation

Total Work = Efficiency × Time. Efficiency is inversely proportional to the time taken to complete a task.

Combined Efficiency

If person A takes x days and B takes y days, combined efficiency = (1/x + 1/y). Combined time = (x × y) ÷ (x + y).

Remaining Work Concept

Remaining work = 1 − (Work done). This is often used when a person leaves a task mid-way.

The correct answer is Alt + D.

Key Points

• A ledger is the actual account head to identify your transactions and are used in all accounting vouchers.
• Alt + D is the keyboard command used to delete the ledger created in tally.
• Go to Gateway of Tally > Accounts Info. > Ledgers > Alter > Press Alt+D .
• Users can delete any ledger in Tally if the balance does not exist in that particular ledger.

Additional Information

• Alt+C is the short key to access Auto Value Calculator in the amount field during voucher entry.
• Ctrl+C is the short key to create Cost Center from the Ledger creation screen.
• Ctrl+B is the short key to create a Budget from the Ledger creation screen.
• Ctrl+G is the short key to create an account Group from the Ledger creation screen.

The correct answer is agricultural sector.

Key Points

• The First Five Year Plan in India was active between 1951 and 1956.
• The plan was based on the Harrod-Domar model.
• This plan gave priority to the agricultural sector of the country.
• The First Five Year Plan was presented before the parliament by Jawaharlal Nehru.
• Gulzarilal Nanda was the first Deputy Chairman of the Planning Commission of India.
• Economist K N Raj is known as the architect of this plan.
• It was quasi-successful for the government.
• The target growth rate of the First Five Year Plan was 2.1% annual gross domestic product (GDP) growth.

Additional Information

• The second Five Year Plan gave priority to the Industrial development of the country.
• The fifth Five Year Plan gave priority to agriculture, industry, and mines.
• The eighth Five Year Plan gave priority to the development of human resources(Human Model).

Given:

√3n = 729

Formulas used:

(x^a)^b = x^ab

If x^a = x^b then a = b 

Calculation:

√3n = 729

⇒ √3n = (3²)³

⇒ (3n)^1/2 = (32)3

⇒ (3n)1/2 = 3⁶

⇒ n/2 = 6 

∴  n = 12

The correct answer is 1900.

Key Points

• India first participated in the Olympic Games in 1900.
• The International Olympic Committee is a governing body of the Olympics.
• The first modern Olympics were held in 1896 in Athens, Greece.
• Norman Pritchard represented India at the 1900 Olympics, making it the nation’s first Olympic appearance. India sent its first contingent at the 1920 Olympics.
• India first sent a team to the Summer Olympic Games in 1920.
• India won its first gold medal in Hockey at Amsterdam Olympics 1928 and until 1956 Indian men's Hockey team remained unbeaten in Olympics.
• India’s last gold medal in Hockey was in the year 1980 Moscow Olympics.
• In the 1952 Summer Olympics wrestler K.D. Jadhav won the first individual medal for independent India.
• Milkha Singh is the first Indian athlete to reach the Olympic finals in Athletics.

The correct answer is Odisha.

Key Points

• Nabakalebara is a festival celebrated in Odisha state.
• It is a symbolic recreation of the wooden forms of three Hindu deities at Jagannath Temple, Puri.
• Nabakalebara festival was first observed in 1575 A.D.
• It was first organised by Yaduvanshi Bhoi King Ramachandra Deva.
• The meaning of 'Naba' is 'new' and 'Kalebara' is 'body'.
• Nabakalebara celebrating in 8 years or 16 years or 19 years depending on the auspicious day.
• In the 20^th century, the Nabakalebara function was celebrated in the Temple in 1912, 1931, 1950, 1969, 1977 and 1996.
• The last Nabakalebara festival was celebrated in 2015.

Additional Information

• Bihu is the most important festival of Assam.
• Saga Dawa is the most important festival of Sikkim.
• Durga Puja is the most important festival of West Bengal.

The correct answer is Hydrostatics.

Key Points

• Hydrostatics is the branch of physics that deals with the properties of fluids at rest.
• It particularly deals with the pressure in a fluid or exerted by a fluid (gas or liquid) on an immersed body.
• It also deals with Archimedes’ principle and the equilibrium of floating bodies.
• Liquids and gases are sometimes grouped together as fluids.
• The hydrostatic pressure for incompressible fluids that are not subject to gravity is calculated according to Pascal’s law.

Additional Information

• Astrophysics is a branch of science that deals with the laws of physics and chemistry to explain the birth, life and death of stars, planets, galaxies, nebulae and other objects in the universe.
• Thermodynamics is the branch of science that deals with the relationship between heat, work, temperature, and energy.
• Optics is a branch of science that deals with the determination of behaviour and the properties of light.

Given:

HCF of two numbers = 6 

LCM of two numbers = 84 

Formula used:

Product of two numbers = HCF × LCM 

Calculation:

First No × Second No = 6 × 84 

⇒ 42 × Second no = 6 × 84

⇒ Second No = (6 × 84)/42 = 12

∴ The second No = 12

The correct answer is 1951.

Key Points

• The First Amendment to the constitution of India was made in 1951.
• The first Amendment added the ninth schedule to the Indian constitution.
• It restricted the freedom of speech and expression.
• It was introduced to remove certain practical difficulties created by the court's decision in several cases such as Kameshwar Singh Case, Romesh Thapar Case, etc.
• The First Amendment protects us against government limits on our freedom of expression, but it doesn’t prevent a private employer from setting its own rules.
• It prevents the government from requiring you to say something you don't want to or keeping you from hearing or reading the words of others.
• It inserted articles 31A and 31B into the Indian constitution.

The correct answer is 7.35 - 7.45.

Key Points

• The pH range of a human body is 7.35 - 7.45.
• pH means the potential of Hydrogen.
• The pH scale is the scale used to express the acidity or alkalinity of a substance based on the concentration of hydrogen ions in its solution.
• pH scale was discovered by Soren Sorensen.
• The range of pH scale 0 to 14.
• If pH < 7 then solution is acidic.
• If pH > 7 then solution is basic.
• If pH = 7 then solution is neutral
• The strength of acids and bases depends on the number of H+ ions and OH- ions produced, respectively.
• When the pH of rainwater is less than 5.6, it is called acid rain.
• The pH value of the Milk of Magnesia is 10.5.

The correct answer is 1924.

Key Points

• Hindustan Republican Association was a revolutionary organization formed in 1924.
• It was formed by Ram Prasad Bismil and Sachindra Nath Sanyal.
• The main leaders of the Hindustan Republican Association are Chandra Shekar Azad, Ram Prasad Bismil, Ashfaq Ullah Khan, Thakur Roshan Singh, Roshan Singh, and Rajendra Lahiri.
• The constitution for the Hindustan Republican Association was drafted in 1923 at Allahabad.
• It was the first revolutionary movement at the national level against the British.
• Kakori conspiracy is associated with the Hindustan Republican Association.
• The British captured the leaders of the Hindustan Republican Association for involvement in the Kakori Conspiracy.
• Ram Prasad Bismil, Ashfaq Ullah Khan, Roshan Singh, and Rajendra Lahiri were hanged in 1927.
• Chandra Shekar Azad shot himself on 27^th February 1931.
• Hindustan Republican Association was later renamed as Hindustan Socialist Republican Association.

Given:

$\rm x^2y^2+\frac{1}{x^2y^2}=83$

Formula used:

(a - b)² = a² + b² - 2ab

Calculation:

x²y² + 1/x2y2 = 83 

By subtracting 2 from both sides

⇒ x2y2 + 1/x2y2 - 2 = 83 - 2

⇒ (xy - 1/xy)² = 81 

⇒ (xy - 1/xy) = √81 

∴ (xy - 1/xy) = 9

The correct answer is 164.

Key Points

• World Trade Organization (WTO) is an international organization dealing with the rules of trade between nations.
• it operates a global system of trade rules and as a forum for negotiating trade agreements.
• As of Nov 2020, WTO has 164 members representing 98% of world trade. (Note: This data is historical and reflects the membership status as of November 2020.)
• Afghanistan is the last country to join in WTO, joining effective 29 July 2016.
• More than 20 countries are seeking to join the WTO.
• A government has to bring its economic and trade policies in line with WTO rules and negotiate its terms of entry with the WTO membership.
• World Trade Organisation was formed on 1 January 1995.
• The Headquarters of the WTO is located in Geneva in Switzerland.
• Ngozi Okonjo-Iweala is the current director-general of the World Trade Organisation.

The correct answer is Tarapur.

Key Points

• Tarapur power plant was the first commercial nuclear power station built in India.
• It is located in Tarapur, Maharashtra.
• It was owned and operated by the state-run Nuclear Power Corporation of India.
• It was constructed initially with two boiling water reactor (BWR) units.
• It was constructed with the help of the United States.
• A contract between the governments of India and the United States was signed for the construction of the Tarapur nuclear power plant on 8 May 1964.
• France, China, and Russia are supplied uranium fuel to the Tarapur nuclear power plant.

Additional Information

• Madras Atomic Power Station (MAPS) located at Kalpakkam is India's first fully indigenously constructed nuclear power station.
• Kakrapar Atomic Power Station is a nuclear power station that lies in the proximity of Surat and Tapi river in the state of Gujarat.
• Kaiga Generating Station is a nuclear power generating station situated at Kaiga in Karnataka.

The correct answer is Bhisham Sahni.

Key Points

• Bhisham Sahni was an Indian writer in the Hindi language.
• He is best known for his famous Hindi novel 'Tamas'.
• Tamas is a novel based on the riots of the 1947 Partition of India which he witnessed at Rawalpindi.
• Tamas won the 1975 Sahitya Akademi Award for literature.
• Tamas was later made into a television film in 1987 by Govind Nihalani.
• Bhisham Sahni was honoured with the Padma Bhushan for literature in 1998.
• India Post released a commemorative postage stamp to honour Sahni in 2017.

Important Points

• Notable works of Bhisham Sahni are:
• Jharokhe.
• Kadian.
• Basanti.
• Kunto.

Additional Information

• Notable works of Yashpal are:
• Jhutha Sach.
• Meri Teri Uski Baat.
• Pinjre ki Uran.
• Notable works of Nagendra are:
• Vichaar Aur Vivechan.
• Vichaar Aur Vishleshan.
• Arastoo Ka kaavyashaastr.
• Anusandhaan Aur Aalochana.
• Notable works of Trilochan are:
• Earth.
• Gulab and Bulbul.
• Digant.
• Warm Days.

The correct answer is 1928.

Key Points

• The British government appointed the Simon Commission to review the Government of India Act 1919 in the year 1927.
• The Simon commission arrived in India in 1928.
• It was formed to study constitutional reforms and make recommendations to the government in India.
• Simon commission was an all-white commission without any Indian members.
• The commission consisted of seven Englishman and sir John Simon was its chairman.
• It was formed on 26^th November 1927.
• Simon commission arrived in India on 3^rd February 1928.
• The Madras session of the congress passed a resolution to boycott the Simon Commission.
• Simon commission submitted its reports on 27^th May 1930.

Given:

The ratio of number of females to males = 2 : 3

No of male employees = 90

Calculation:

Let the number of females and males be 2y and 3y

⇒ Total no of employees = 2y + 3y = 5y

3y = 90

⇒ y = 30

5y = 5 × 30 = 150

∴ Total no of employees = 150

Shortcut Trick F : M = 2 : 3

⇒ M = 3 = 90

⇒ 5 = 90/3 × 5 = 150

∴ Total no of employees = 150

Given:

Area of a circle = 154 cm2

Formula used:

Area of a circle = πr²

Circumference of a circle = 2πr 

Calculation:

πr2 = 154

⇒ 22/7 × r2 = 154 

⇒ r2 = 154 × 7/22 = 7²

⇒ r = 7

∴ Circumference of a circle = 2 × 22/7 × 7 = 44 cm

The correct answer is Cement.

Key Points

• Limestone is a form of calcium carbonate which is used extensively for the manufacture of cement.
• Cement is manufactured through a closely controlled chemical combination of calcium, silicon, aluminium, iron and other ingredients.
• Crushed limestone is often the main raw ingredient in the manufacture of portland cement.
• CaCO₃ is the chemical formula of Calcium carbonate.
• Limestone is a carbonate sedimentary rock composed primarily of calcium carbonate (CaCO3).
• Limestone released carbon dioxide gas while heating.

Important Points

• Limestone is used as:
• Building material.
• Essential component cement industry.
• Aggregate for the base of roads.
• Filler in products such as toothpaste or paints.

Given:

Cost price of 20 articles = Selling price of 15 articles 

Formula used:

Profit = Selling Price - Cost Price 

Profit percent = Profit/CP × 100

Calculation:

CP × 20 = SP × 15 

⇒ 20/15 = SP/CP 

Here, CP < SP 

Profit = 20 - 15 = 5

Profit percent = 5/15 × 100 = 33.33%

∴ Profit percent = 33.33%

The correct answer is James Gosling.

Key Points

• Java is a high-level object-oriented programming language.
• Java was developed by James Gosling.
• James Gosling is known as the father of Java.
• Java was formerly known as Oak.
• Since Oak was already a registered company the name later changed to Java.
• Java was originally developed at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform.
• Java code can run on all platforms that support Java without the need for recompilation.
• Java is used to develop mobile apps, web apps, desktop apps, games etc.
• Java is a high level, robust and secure programming language.

Additional Information

• Paul Allen is the co-founder of Microsoft.
• Jaap Haartsen is best known for his role in producing the specification for Bluetooth.
• Charles Simonyi is best known for developing the first versions of Microsoft Office software suite.

Given:

A mango kept in a basket doubles every one minute. 

The basket gets filled in 30 minutes. 

Calculation:

The basket is full (1) in 30 minutes. 

The Time required to fill the basket with mango is 30 minutes.

So, half the basket is filled in 29 minutes.

As in every minute, the basket gets doubled. So, in 29 minutes, it is half-filled and in the next minutes, it will be completely filled.

∴ Obviously, the basket will be half-filled (1/2) filled in 29 minutes. 

Alternate MethodAccording to the question,

1^st min = 2¹ = 2

2^nd min = 2² = 4

We have observed every min double the quantity

then in 29 min = 2²⁹ = 536870912

Last 30 min = 2³⁰ = 1073741824

We have observed the 29^th min is half of the 30^th min quantity.

The correct answer is Ashoka.

Key Points

• Sanchi Stupa is a Buddhist complex built by Ashoka.
• It is situated in the Raisen District of Madhya Pradesh.
• It is considered the oldest stone structure in India.
• It was designed by the Mauryan emperor Ashoka within the 3^rd century BCE.
• It is also the UNESCO World Heritage site.
• Sanchi Stupa motif is a feature that can be seen in the new Rs. 200 note.

Important Points

• Ashoka was an Indian emperor of the Maurya Dynasty.
• Ashoka was also known as Devanam Priyadasi.
• Ashoka invaded Kalinga in 261 B.C, In Kalinga War.
• Ashoka was the first king in Indian history who has left his records engraved on stones.

Additional Information

• Chanakya was a royal advisor who assisted the first Mauryan emperor Chandragupta in his rise to power.
• Chandragupta Maurya was the founder of the Maurya Empire in ancient India.
• Bindusara was the second Mauryan emperor of India and the father of its most famous ruler Ashoka.

The correct answer is Kolkata.

Key Points

• The first national flag in India is said to have been hoisted on 7^th August 1906.
• It was hoisted in the Parsee Bagan Square (Green Park) in Kolkata.
• The flag was composed of three horizontal strips of red, yellow and green.
• The second flag was hoisted by Madame Bhikaji Cama in 1907 at Stuttgart, Germany.
• The third flag was hoisted in 1917.

Important Points

• A resolution was passed adopting a tricolour flag as our national flag in 1931.
• The constituent assembly adopted the national flag on 22^nd July 1947.
• The shape of the National Flag of India shall be rectangular.
• The ratio of length to width(height) of the flag shall be 3:2.

Additional Information

• India's national flag is a tricolour panel made up of three rectangular panels or sub-panels of equal widths
• The top panel of the national flag is India saffron (Kesaria) and that of the bottom is India green.
• The middle panel is white.
• The centre of the white panel consists of an Ashoka Chakra in navy blue colour with 24 equally spaced spokes.

The correct answer is a female reproductive part.

Key Points

• Pistil is the female reproductive part of a flower with a stigma at its top.
• Pistil is the ovule producing part of a flower.
• The function of a pistil is to receive pollen and produce seeds.
• The ovary often supports a long style, topped by a stigma.
• The mature ovary is a fruit, and the mature ovule is a seed.
• Pollens are produced by the male part of a flower called the stamen.
• A flower is actually made of specialized stems and leaves.

The correct answer is rich countries.

• According to the World Development Report, countries having per capita income of more than US$12,000 per annum as on 2016 are called rich countries.

Key Points

• World Bank published the 2020 Atlas of the Sustainable Development Goals.
• Sustainable Development Goals seek to guide global action to address many of the world’s greatest challenges such as eradicating poverty, eliminating hunger, expanding access to education, achieving gender equality, and addressing the climate crisis.​

Important Points

The 17 sustainable development goals (SDGs) to transform our world:

• GOAL 1: No Poverty
• GOAL 2: Zero Hunger
• GOAL 3: Good Health and Well-being
• GOAL 4: Quality Education
• GOAL 5: Gender Equality

GOAL 6: Clean Water and Sanitation

• GOAL 7: Affordable and Clean Energy
• GOAL 8: Decent Work and Economic Growth
• GOAL 9: Industry, Innovation, and Infrastructure
• GOAL 10: Reduced Inequality
• GOAL 11: Sustainable Cities and Communities
• GOAL 12: Responsible Consumption and Production
• GOAL 13: Climate Action
• GOAL 14: Life Below Water
• GOAL 15: Life on Land
• GOAL 16: Peace and Justice Strong Institutions
• GOAL 17: Partnerships to Achieve the Goal​$

Given:

[(3√2 + 2) × (3√2 - 2)] of 13 + 15

Formula used:

(a - b)(a + b) = a²- b²

Calculation:

[(3√2 + 2) × (3√2 - 2)] of 13 + 15

⇒ [(3√2)² - (2)²] × 13 + 15 

⇒ [18 - 4] × 13 + 15

⇒ 14 × 13 + 15 

⇒ 197

∴ The required result = 197

Given:

Percentage of students passed = 60%

No of failed students = 240

Calculation:

Total percentage of students = 100%

Percentage of students failed = 100% - 60% = 40%

⇒ 40% = 240 

⇒ 1% = 240/40 = 6

∴ No of students passed = 60% 

⇒ 60 × 6 = 360

Shortcut Trick 40% (Failed students) = 240

∴ 60% (Passed students) = 240 × 60%/40% = 360

The correct answer is 1983.

Key Points

• INSAT-1B was an Indian communications satellite.
• INSAT-1B is the second satellite in the INSAT-1 series.
• It was the first operational satellite in the Indian National Satellite System (INSAT) series.
• It was successfully launched by Space Shuttle of the USA in 1983.
• It was manufactured by Ford Aerospace.
• INSAT-1B was launched on 30 August 1983.
• It was operational till July 1990.

Given:

Length of carpet = $\rm 20 \frac{5}{2}$ m = 45/2 m 

Length of small pieces of carpet = $\rm 4 \frac{1}{2}$ m = 9/2 m 

Formula used:

No of small pieces of carpet = Length of carpet/Length of 1 small piece of carpet

Calculation:

∴ No of small pieces of carpet that can be cut out = 45/2 ÷ 9/2 

⇒ 45/2 × 2/9 

⇒ 5

Given:

Statement 1: Banana price is more than that of lychee. 

Banana > Lychee

Statement 2: Banana price is less than that of kiwi.

Kiwi > Banana 

Statement 3. Kiwi Price is more than that of banana and lychee.

Kiwi > Banana  and Kiwi > Lychee

From 1 and 2: 

Kiwi > Banana > Lychee

∵ Kiwi Price is more than that of banana and lychee is true.

∴ The third statement is true.

Hence, the correct answer is "True".

The correct answer is Operation Shakti.

Key Points

• The Pokhran nuclear test 2 was a series of five nuclear bomb test explosions conducted by India at the Indian Army.
• It was conducted at the Pokhran test range in Rajasthan.
• Pokhran Nuclear Test 2 was conducted in May 1998.
• Pokhran 2 was code-named Operation Shakti.
• It was the second instance of nuclear testing conducted by India.
• The first test, code-named Smiling Buddha was conducted in May 1974.
• The five nuclear bombs were designated Shakti-I through to Shakti-V.

The correct answer is Binary.

Key Points

• Data stored in a compute in the form of binary.
• A binary number is a number expressed only two symbols: typically "0" (zero) and "1" (one).
• Each digit is referred to as a bit or binary digit.
• Bit is the smallest unit of memory.
• Bit is the short form of Binary digit.
• Half byte is known as a nibble.

Additional Information

• The memory of a computer is usually measured in bytes.
• Tera-represents the fourth power of 1000.
• A Terabyte is more precisely defined as 1,024 gigabytes.
• 1 TB equals 1,024 gigabytes (GB).
• The storage capacity of a hard disc is measured in Megabytes, Gigabytes, and Terabytes.

Given:

The ratio between two numbers = 3 : 5 

LCM of the two numbers = 120

Formula used:

Product of two numbers = LCM × HCF 

Calculation:

Let the HCF of two numbers = y 

Let the two numbers be 3y and 5y.

3y × 5y = 120 × y 

⇒ 15y² = 120y 

⇒ 15y = 120 

⇒ y = 8

3y = 3 × 8 = 24 

5y = 5 × 8 = 40

∴ The two numbers are 24, 40.

The correct answer is 2016.

Key Points

• NITI Aayog started the Women Transforming India Awards in 2016.
• The contest was launched to mark the celebration of International Women’s Day, 2016.
• It is an annual contest supported by the United Nations in India.
• It was launched in partnership with MyGov and the United Nations in India.
• Women Transforming India was launched with the aim to celebrate the indomitable spirit of women working tirelessly to empower communities and transform India.

Additional Information

• The NITI Aayog is a policy think tank of the Government of India.
• It was formed on 1^st January 2015.
• Its headquarters is in New Delhi.
• It was established to replace the Planning Commission which followed a top-down model.
• The prime minister of India is the chairman of the NITI Aayog.
• The CEO and Vice-Chairperson of the NITI Aayog are appointed by the Prime Minister.

The correct answer is 10.

Key Points

• The United Nations Security Council is one of the principal organs of the United Nations.
• United Nations Security Council has 15 Members, and each Member has one vote.
• Among these 15 members, 5 are permanent members and 10 are non-permanent members.
• The General Assembly elects non-permanent members for two-year terms
• More than 50 United Nations Member States have never been members of the Security Council.

Important Points

• Non-permanent members:

1. Algeria (2025)
2. Denmark (2026)
3. Greece (2026)
4. Guyana (2025)
5. Pakistan (2026)
6. Panama (2026)
7. Republic of Korea (2025)
8. Sierra Leone (2025)
9. Slovenia (2025)
10. Somalia (2026)

• Permanent members:

1. China.
2. France.
3. Russia.
4. The United Kingdom.
5. The United States.

Additional Information

• The Security Council held its first session on 17 January 1946 at Church House, Westminster, London.
• Since its first meeting, the Security Council has taken permanent residence at the United Nations Headquarters in New York City.
• Originally, there were 11 members of the Security Council: 5 permanent and 6 non-permanent members.
• The General Assembly recommended an amendment to the Charter to increase the membership of the Security Council In 1963.

Important Points

• India will be eligible to run for a non-permanent seat again in 2028–2029

Given:

Difference between two numbers = 1540 

Concept: 

Dividend = Divisor × Quotient + Remainder 

Calculation:

Let the smaller number be = a 

⇒ Larger number = a + 1540 

As per the question: 

 a + 1540 = a × 6 + 5

⇒ 5a = 1535 

⇒ a = 307 

∴ The smaller number = 307

Alternate Method By Hit & Trial Method

Option 1: 580 × 6 + 5 ≠ 580 + 1540

Option 2: 620 × 6 + 5 ≠ 620 + 1540

Option 3: 735 × 6 + 5 ≠ 735 + 1540 

Option 4: 307 × 6 + 5 = 307 + 1540

Given:

$\rm \frac{sin\space23°}{cos\space67°}+\frac{cos\space71°}{sin\space19°}$

Formula used:

sin (90°- x) = cos x 

cos (90°- x) = sin x 

Calculation:

$\rm \frac{sin\space23°}{cos\space67°}+\frac{cos\space71°}{sin\space19°}$

⇒ sin(90° - 67°)/cos 67° + cos (90° - 19°)/sin 19°

⇒ cos 67°/ cos 67° + sin 19°/sin 19°

⇒ 1 + 1 = 2 

∴ The required result = 2

The correct answer is ductility.

Key Points

• Ductility is the ability of a material to be drawn or plastically deformed without fracture.
• It is the ability of metals to be drawn into thin wires.
• Gold is the most ductile metal.
• Ductility is a permanent strain that accompanied fracture in a tension test.
• The ductility of the metals increases as the temperature increases.

Additional Information

• The property of metals by which they can be beaten into thin sheets is called malleability.
• Solubility is the maximum amount of a substance that will dissolve in a given amount of solvent at a specified temperature.
• Reactivity is the ability of matter to combine chemically with other substances.

1. Rajesh ranks 15^th from the top and Prakash ranks 25^th from the bottom.
2. Gyan is on the 10^th place ahead of Prakash.
3. If there are 10 students, exactly in between Rajesh and Gyan. 

Total number of students in the class = 15 + 10 + 1 + 9 + 25 = 60

Hence, ‘60’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

1. MNKL → M + 1 = N; N – 3 = K; K + 1 = L
2. IJGH → I + 1 = J; J – 3 = G; G + 1 = H
3. EFCD → E + 1 = F; F – 3 = C; C + 1 = D

4. OPQR → O + 1 = P; P + 1 = Q; Q + 1 = R

Hence, ‘OPQR’ is the odd one out.

The correct answer is painter.

Key Points

• Raja Ravi Varma was an Indian painting artist.
• was closely related to the royal family of Travancore (present-day Kerala).
• He was honoured with the Kaiser-i-Hind gold medal in 1904.
• The title Raja was conferred as a personal title by the Viceroy and Governor-General of India during the British period.
• He has the ability to reconcile Western aesthetics with Indian iconography.
• Notable works of Raja Ravi Varma are:
• Shakuntala.
• Nair Lady Adorning Her Hair.
• There Comes Papa.
• Galaxy of Musicians.

Given:

Principal = Rs.5000

Rate of interest = 10% per annum 

Time = 3 years 

Formulas used:

Compound Interest = Amount - Principal 

⇒ Amount = P (1 + r/100)^t

Simple Interest = Principal × Rate/100 × Time 

Calculation:

Compound Interest = 5000(1 + 10/100)³ - 5000 

⇒ 5000(110/100)³ - 5000 

⇒ 5000[11/10 × 11/10 × 11/10 - 1]

⇒ 5000[(1331 - 1000)/1000]

⇒ 5 × 331 = Rs.1655

Simple Interest = 5000 × 10/100 × 3 

⇒ Rs.1500 

Difference between compound interest & simple interest = Rs.1655 - Rs.1500

⇒ Rs.155

∴ The required result = Rs.155

Alternate Method

Calculation of effective rate for compound interest:

Effective rate = x + x + x²/100 

Interest rate for 1 year = 10%

Effective rate for 2 years = 10 + 10 + (10 × 10)/100 = 10 + 10 + 1

⇒ 21%

Effective rate for 3 years = 21 + 10 + (21 × 10)/100 

⇒ 31 + 2.1 = 33.1% 

or 

Calculation of effective rate of interest for simple interest:

At 10% per annum for 3 years 

Rate = 10% × 3 = 30%

Difference between the CI and SI rate  = 33.1% - 30% = 3.1%

∴ Difference between the CI and SI for 3 years = 5000 × 3.1/100 

⇒ Rs.155

The logic is:

Similarly,

Hence, ‘A hill is place shimla’ is the correct answer.

Given:

Perimeters of two similar triangles ΔPQR and ΔXYZ are 48 cm and 24 cm respectively. 

XY = 12 cm

Concept:

When two triangles are similar to each other, the ratio of their corresponding sides is equal to the ratio of their respective other sides, medians, and perimeters. 

⇒ Perimeter of ΔPQR/Perimeter of ΔXYZ = PQ/XY

Calculation:

48/24 = PQ/12 

⇒ PQ/12 = 2

⇒ PQ = 24 m 

∴ The length of side PQ = 24 cm

The pattern followed here is:

According to the alphabetical positions of the letters,

Similarly,

Hence, ‘CLVE’ is the correct answer.

Given:

Speed of train A = 80 km/h 

Speed of train B = 70 km/h 

Time taken in crossing = 30 seconds 

Length of train A = 300 m 

Formulas used:

Relative speed of trains (opposite direction) = S_A + S_B

Distance covered while crossing =  Length (Train A + Train B)

Time = Distance/Relative Speed 

Calculation:

Let the length of train B = b m 

30 seconds = (300 + b)/(70 + 80) km/h 

⇒ 30 seconds = (300 + b)/150 km/h 

⇒ 30 secs × 150 km/h × 1000m/3600 secs = 300 + b

⇒ 1250 = 300 + b 

⇒ b = 1250 - 300 = 950

∴ The length of train B = 950 m

Given:

The capacity of a cylindrical tank = 2376 m3

Radius = 21 m

Formula used:

Volume of cylinder = πr²h

Calculation:

πr2h = 2376 m3

⇒ 22/7 × 21 × 21 × h = 2376 

h = 1.714 

∴ The depth of the tank = 1.71 m

The correct answer is Kolkata.

Key Points

• The first high court of India was established in Kolkata.
• It was formerly called the High Court of Judicature at Fort William.
• It was issued under the Indian High Courts Act 1861.
• It was formally opened on 1 July 1862.
• Sir Barnes Peacock as its first Chief Justice of the Calcutta High Court.
• Justice Sumboo Nath Pandit was the first Indian to assume office as a Judge of the Calcutta High Court.

Additional Information

• The Chief Justice of the High Court is appointed by the President.
• Every high court shall consist of a Chief Justice and such other Judges as the President may decide.
• Judges of the High Courts are removed by the President on the same grounds and manner as the judges of the Supreme Court are removed.
• The oath and affirmation to the judges of the High Court are administered by the Governor of the State.
• A judge of the High Court can resign his office by writing to the President.

The correct answer is October 2005.

Key Points

• The Right to Information is a tool, which every person in India can use to find out information that can make their lives better.
• India initiated the enactment of the Right to Information Act in the year 2005.
• ​Right to Information Act 2005 mandates timely response to citizen requests for Government information.
• The Act was passed by the Indian Parliament on 12^th May 2005.
• The Act received Presidential assent on 15^th June 2005.
• The RTI Act came into force on 12^th October 2005.

Important Points

• Mazdoor Kisan Shakti Sangathan is the organization that was instrumental in the passage of the RTI Act.
• Central and State Information commissions consist of a chief information commissioner and not more than 10 information commissioners.
• The first RTI application in India was submitted by Shahid Raza Burney.
• There are only 2 schedules in RTI Act 2005.
• The modified form of the RTI Act was passed in February 2011.
• The main object of the Right to Information Act is to empower the citizens, promote transparency and accountability in the working of the Government, contain corruption, and make our democracy work for the people in a real sense.
• Sweden is the first country to pass the Right to Information Act.

The correct answer is 2003.

Key Points

• The Pradhan Mantri Swasthya Suraksha Yojana (PMSSY) is a national government scheme that attempts to address inequities in the availability of affordable healthcare facilities across the country.
• The scheme was first launched in the year 2003.
• The scheme was approved in March 2006.
• The first phase in the PMSSY consists of two components:

1. Setting up of six institutions in the line of AIIMS.

• Bihar (Patna).
• Chattisgarh (Raipur).
• Madhya Pradesh (Bhopal).
• Orissa (Bhubaneswar).
• Rajasthan (Jodhpur).
• Uttaranchal (Rishikesh)

2. Upgradation of 13 existing Government medical college institutions.

• Ministry of Health and Family Welfare is the nodal agency of Pradhan Mantri Swasthya Suraksha Yojana.

The correct answer is 1556 AD.

Key Points

• Akbar was the third Mughal emperor.
• He became the emperor of the Mughal dynasty in 1556 AD.
• He ruled the Indian subcontinent between 1556 and 1605.
• Din-i-Ilahi was a religion introduced by Akbar in 1582.
• During Akbar's rule, the second battle of Panipat took place in 1556.
• It was fought between Samrat Hem Chandra Vikramaditya(Hemu) and Akbar's army.
• Under the leadership of Bairam Khan, the Mughals won the fight decisively.
• The conflict put an end to the Mughal-Afghan dispute for Delhi's monarchy.
• In 1560, Akbar ended Bairam Khan's regency and, at the age of 18, took over the throne of India.

Additional Information

• The historical structures built during the reign of Akbar are:
• Agra Fort.
• Lahore Fort.
• Fathepur Sikri.
• Allahabad Fort.
• Buland Darwaza.

The correct answer is Malala Yousafzai.

Key Points

• Malala Yousafzai is a Pakistani activist for female education.
• In 2014, she was awarded the Nobel Peace Prize.
• She is the youngest Nobel Prize laureate.
• She was honored with the Nobel Prize at the age of 17.
• Kailash Satyarthi and Malala Yousafzai shared the Nobel Peace Prize in 2014.

Important Points

• Notable work of Malala Yousafzai:
• We are displaced: True Stories of Refugee Lives.
• Malala's Magic Pencil.
• My Story of Standing Up for Girls' Rights.
• Pakistan's first National Youth Peace Prize was given to her.
• 'Gul Makai' is a Malala Yousafzai biographical drama.
• Between 1901 and 2021, 947 laureates and 28 organizations received the Nobel Prize.

Additional Information

• Lawrence Bragg was the second youngest Nobel Laureate.
• He was honored with the Nobel Prize for Physics in 1915 at the age of 25.
• Nadia Murad is the third youngest Nobel Laureate.
• She was honored with the Nobel Prize for Peace in 2018 at the age of 25.
• Tsung-Dao Lee is the fifth youngest Nobel Laureate.
• He was honored with the Nobel Prize for Physics in 1957 at the age of 31.

The correct answer is Brahmagiri hills.

Key Points

• The Godavari is India's largest peninsular river.
• It is the second-longest river in India after the Ganga.
• It rises from Maharashtra's Thriambak hill.
• Its length is about 1500 km.
• Due to its length and the area it covers, it is also known as the ‘Dakshin Ganga’.
• Flows through the states of Maharashtra, Chhattisgarh, Telangana, and Andhra Pradesh.

Important Points

• Purna, Pranhita, Indravati, and Sabari rivers are major left-bank tributaries.
• Pravara, Manjira, and Manair rivers are major right bank tributaries.
• The Pranhita river is Godavari's greatest tributary.
• Important dams built across the Godavari river:
• Jayakwadi dam.
• Gangapur Dam.
• Babli project.
• Sriram Sagar Dam.
• The Coringa mangrove forest is situated in the Godavari delta.
• The Godavari drains into the Bay of Bengal.

Five students are sitting in a circle facing the center.

1. Sumit is between Sunil and Sushmit.

2. Sushma is on the left side of Shweta, Sushmit and Sushma are not sitting next to each other. 

Here case II will be eliminated.

Final arrangement:

Clearly, Sunil is sitting next to Sumit on his right side.

Hence, ‘Sunil’ is the correct answer.

Given:

Sum of two numbers = 25 

Difference of two numbers = 15 

Calculation:

Let the two no be = a & b 

a + b = 25 

a - b = 15 

(1) + (2)

⇒ 2a = 40 

⇒ a = 20 

By putting the value of a in equation (1)

⇒ b = 5

∴ a : b = 20 : 5 = 4 : 1

The correct answer is 1121.

Key Points

• A World Heritage Site is an area with legal protection by an international convention administered by the United Nations Educational, Scientific, and Cultural Organization (UNESCO).
• The sites are designated as having “outstanding universal value” under the Convention Concerning the Protection of the World Cultural and Natural Heritage.
• As of June 2020, there are 1121 world heritage sites that have been protected by UNESCO.
• UNESCO classified these sites as cultural, natural, and mixed.
• UNESCO published its first list of protected places in 1978.
• There were just 12 World Heritage Sites while releasing UNESCO's first list of protected places.
• The first World Heritage Site on the list is the Galápagos Islands.

Mistake Points

• As of February 2025, UNESCO's World Heritage List comprises 1,223 sites across 168 countries.

For more:-https://whc.unesco.org/en/list/

Given :- a_bc_a_bcda_ccd_bcd_

By checking options and substituting accordingly.

1. a, a, b, c, c, d → a a b c a - a b b c d - a c c c d - c b c d d
2. a, c, b, d, b, d → a a b c c - a b b c d - a d c c d - b b c d d

3. a, d, b, b, a, d → a a b c d - a b b c d - a b c c d - a b c d d

4. a, d, b, b, d, d → a a b c d - a b b c d - a b c c d - d b c d d

    ♦  Option (3) gives a cyclic pattern of aabcd - abbcd - abccd - abcdd.

Hence, ‘a, d, b, b, a, d’ is the correct answer.

Shortcut Trick

Apply the direct algebraic identity for expressions of the form x + 1/x = k.

The shortcut formula to find x² + 1/x² is k² − 2.

Given: k = 9

Calculation: 9² − 2 ⇒ 81 − 2 = 79.

∴ The correct answer is 79.

Alternate Method

Given: x + 1/x = 9

Formula Used: (a + b)² = a² + b² + 2ab

To find the value of x² + 1/x², we perform squaring on both sides of the given equation:

⇒ (x + 1/x)² = 9²

⇒ x² + (1/x)² + 2 × x × (1/x) = 81

⇒ x² + 1/x² + 2 = 81

⇒ x² + 1/x² = 81 − 2

⇒ x² + 1/x² = 79

∴ The correct answer is 79.

Additional Information

Square of Difference Identity

If x − 1/x = k, then squaring both sides gives x² + 1/x² = k² + 2.

Cubic Identity (Sum)

If x + 1/x = k, then cubing both sides gives x³ + 1/x³ = k³ − 3k.

Cubic Identity (Difference)

If x − 1/x = k, then cubing both sides gives x³ − 1/x³ = k³ + 3k.

Power 4 Transformation

If x² + 1/x² = m, then x⁴ + 1/x⁴ = m² − 2.

Assumptions:

I. Most of causes of death among wealthy persons are due to diabetes. → The assumption is not implicit in the statement.

The statement only suggests that a wealthy person has a higher chance of having diabetes but it does not implies that most of causes of death among wealthy persons are due to diabetes.

II. Poor persons do not have diabetes. → The assumption is not implicit in the statement.

The statement mentions nothing about poor people.

Hence, neither assumption (I) nor (II) is implicit.

Additional Information

1. Read the statement with an approach that the assumptions would be true with regard to the statement.
2. Do not go too logical with the statements. Analyze the given information and the assumption must only be made based on the information in the statement. Do not over-complicate it.
3. Common assumptions can always be followed but other than that do not align the statement with General Knowledge or other facts
4. Use the elimination method if you are unable to apprehend the answer. Read the statement and then the assumptions given in the options, you shall notice that a few of them will most definitely not follow. Eliminate them and then choosing from lesser options may prove to be more convenient
5. One thing to make a note of is that the assumption is something that the author believes to be true so while choosing the correct option, keep this thought in mind as well. If any option contradicts the statement, then that assumption will not follow.

The logic followed here is:

Hence, the correct answer is "24".

Shortcut Trick

Apply the algebraic identity: a² − b² = (a + b)(a − b).

The given expression is in the form (a² − b²) ÷ (a + b), which simplifies to (a − b).

Here, a = 0.27 and b = 0.13.

Result = 0.27 − 0.13 = 0.14.

∴ The correct answer is 0.14.

Alternate Method

Given:

Expression = ((0.27)² − (0.13)²) ÷ (0.27 + 0.13)

Formula used:

Algebraic Identity: a² − b² = (a + b)(a − b)

Calculations:

⇒ Let a = 0.27 and b = 0.13.

⇒ The numerator is (0.27)² − (0.13)².

⇒ Using the identity, Numerator = (0.27 + 0.13) × (0.27 − 0.13)

⇒ Numerator = (0.40) × (0.14)

⇒ The denominator is (0.27 + 0.13) = 0.40.

⇒ Value = [(0.40) × (0.14)] ÷ 0.40

⇒ Value = 0.14

∴ The correct answer is 0.14.

Additional Information

Difference of Squares

The identity a² − b² = (a − b)(a + b) is one of the most common algebraic factorization tools used to simplify complex fraction expressions.

BODMAS Rule

Always follow the BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) priority while solving multi-step calculations to ensure accuracy.

Sum and Difference Identities

Other related identities include (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b², which are useful for simplifying square terms.

The correct answer is 6.

Important Points

• The Goldman Environmental Prize is the world's foremost award honoring grassroots environmental activists.
• It is given for the six inhabited continental regions: Africa, Asia, Europe, Islands & Island Nations, North America, and South & Central America.
• An international panel chooses the winners from submissions submitted anonymously by a global community of environmental groups and individuals.
• It was created in 1989 by civic leaders and philanthropists Richard N. Goldman and Rhoda H. Goldman.

Key Points

• Six environmental activists received the prestigious Goldman Environmental Prize 2019.
• The winners of the Goldman Environmental Prize 2019 are:

1. Linda Garcia of US.
2. Ana Colovic Lesoska of North Macedonia.
3. Bayarjargal Agvaantseren of Mongolia.
4. Alfred Brownell of Liberi.
5. Jacqueline Evans of the Cook Islands.
6. Alberto Curamil of Chile.

The correct answer is Madhya Pradesh.

Key Points

• The Gandhi Sagar Dam is a dam located in the Mandsaur districts of Madhya Pradesh.
• It is built on the Chambal River.
• Gandhi Sagar Dam is a masonry gravity dam.
• The foundation stone was laid by Prime Minister of India Pandit Jawaharlal Nehru on 7 March 1954.
• The reservoir created by the Gandhi Sagar Dam is the third-largest in India after the Indiranagar Reservoir and Hirakud Reservoir.
• The electricity from the dam's powerhouse is supplied to such far-off places in Madhya Pradesh and in Rajasthan state.

Important Points

• Major dams in Madhya Pradesh are:
• Barna Dam.
• Bargi Dam.
• Bansagar Dam.
• Omkareshwar Dam.
• Kolar Dam.

Additional Information

• Major dams in Maharashtra are:
• Mulshi Dam.
• Koyna Dam.
• Jayakwadi Dam.
• Panshet Dam.
• Kolkewadi Dam.
• Vaitarna Dam
• Major dams in Himachal Pradesh are:
• Nathpa Jhakri Dam.
• Chamera Dam.
• Pong Dam.
• Bhakra Nangal Dam.
• Pandoh Dam.
• Major dams in Rajasthan are:
• Jawahar Sagar Dam.
• Kota Barrage.
• Rana Pratap Sagar dam.
• Chavli Dam.

The correct answer is 1859.

Key Points

• The Revolt of 1857 is a major landmark in the history of India against British rule in India.
• The Revolt of 1857 was started on 10^th May 1857 at Meerut.
• The introduction of greased cartridges was the immediate cause of the 1857 revolt.
• Heavy taxation was one of the major reasons for the outbreak of the 1857 revolt.
• The peasants had to pay heavy taxes in the form of Land tax during 1857.

Additional Information 

• Mangal Pandey was the first martyr of the 1857 revolt.
• Lord Canning was the governor-general of India during the 1857 revolt.
• The English called the revolt the 'devil's wind'.
• Finally, the revolt of 1857 was suppressed by the British in 1859.
• The control of the Indian administration was passed on to the British crown by the Government of India Act 1858.
• All Indian prisoners except those who committed serious offences were released.

Given:

tan θ + cot θ = 5

Formula used:

(a + b)² = a² + b² + 2ab

Calculation:

tan θ + cot θ = 5

Squaring both sides

⇒ tan²θ + cot2θ + 2 tanθ cotθ = 25

⇒ tan2θ + cot2θ = 25 - 2

⇒ tan2θ + cot2θ = 23

tan2 θ + cot2 θ + 2 tan2 60°

⇒ 23 + 2 × (√3)²

⇒ 23 + 2 × 3

⇒ 29

∴ The required result = 29

Given:

No of students in a class = 48 

Fraction of students present = 3/8

Calculation:

Fraction of students absent = 1 - 3/8 = 5/8 

∴ No of absentees on the same day = 48 × 5/8 

⇒ 30

Given:

15 × 14 - 30 + (32 + 17)

Calculation:

⇒ 15 × 14 - 30 + (32 + 17)

⇒ 210 - 30 + (9 + 17)

⇒ 210 - 30 + 26 

⇒ 206 

∴ The required result = 206

The correct answer is Uniform Resource Locator.

Key Points

• Uniform Resource Locator is an address used to identify the name of a web resource.
• Uniform Resource Locator is a web address that indicated a webpage.
• URL is also known as 'internet address' or 'web address'.
• Every valid URL refers to a distinct resource.

Additional Information

• Part of a URL that indicated a particular webpage is known as a domain name.
• Every domain name has a suffix that indicates the top-level domain it belongs to.
• Uniform Resource Locators are also used for file transfer (ftp), email, database access (JDBC), and many other applications.
• The URL allows a computer to find and open a web page on another computer connected to the Internet.

Given:

Angle of elevation = 45° 

Distance of the bottom of the pole from a point = 20m 

Calculation:

In triangle ABC, AB/BC = tan45° 

⇒ h/20 = 1 

∴ The height of the pole = h = 20 m

Shortcut Trick

the total number of triangles in the figure is shown below:

Hence, ‘18’ is the correct answer.

The correct answer is Narmada.

Key Points

• The Sardar Sarovar Dam is a concrete gravity dam located at Narmada District in Gujarat.
• On the Narmada river, the Sardar Sarovar dam is being constructed.
• The Sardar Sarovar dam provides water and energy to Gujarat, Madhya Pradesh, Maharashtra, and Rajasthan.
• The foundation stone of the project was laid out by Prime Minister Jawaharlal Nehru on 5 April 1961.
• Prime Minister Narendra Modi dedicated the dam to the nation in 2017.

Important Points

• Narmada is the largest west-flowing peninsular river in India.
• Narmada is also known as the 'lifeline of Madhya Pradesh'.
• Between the Vindhya and Satpura ranges, it flows through a rift valley.
• Kanha National Park is located on the banks of the Narmada River.

Additional Information

• The Ganges is the national river of India.
• The river Ganga is known as the Padma in Bangladesh.
• The Brahmaputra originates from the Chemayundung glacier near Manasarover lake in Tibet.
• The Brahmaputra is known as Dihang in Arunachal Pradesh.
• The Brahmaputra River enters India west of Sadiya, Arunachal Pradesh.
• The Brahmaputra is the Indian River with the greatest volume of water.
• Lakhwar-Vyasi Dam is built on Yamuna River.

Shortcut Trick

Mode is the observation that occurs most frequently in a data set.

Given marks: 43, 44, 65, 41, 53, 65, 62.

By inspection, the number 65 appears 2 times, while all other numbers appear only 1 time.

Since 65 has the highest frequency, it is the mode.

∴ The correct answer is 65.

Alternate Method

Given: Marks obtained by 7 students = 43, 44, 65, 41, 53, 65, 62

Formula: Mode = Value with the maximum frequency.

⇒ Arrange the data in ascending order: 41, 43, 44, 53, 62, 65

Given:

15 males or 20 females can complete a project in 26 days.

Formula used:

(M1 × D1)/W1 = (M2 × D2)/W2

Calculation:

15 males × 26 days = 20 females × 26 days 

∵ 15 males = 20 females 

∴  30 males = 40 females 

Total work in terms of females  = 20 females × 26 days = 520 units 

No of days taken by 30 males and 12 females:

⇒ (40 females + 12 females) = 52 females 

∴ No of days taken = 520 units /52 females = 10

Given:

Sum of two numbers = 16 

Product of two numbers = 63 

Calculation:

Let the numbers be = a, b 

a + b = 16 

ab = 63 

∴ Sum of the reciprocal of a and b = 1/a + 1/b 

⇒ (b + a)/ab

⇒ 16/63

The correct answer is Odisha.

Key Points

• Odisha is the largest bauxite-producing state in India.
• More than half of India's bauxite deposits are found in Odisha.
• Bauxite is an important mineral used in the production of aluminium.
• Kalahandi in Odisha is famous for the production of bauxite.
• Bauxite deposits are formed by the decomposition of a wide variety of rocks that consists of aluminium silicates.

Important Points

• Odisha, Jharkhand, Chhattisgarh, Madhya Pradesh, Gujarat, Maharashtra, and Tamil Nadu are the major bauxite-producing states.
• Bauxite is primarily utilized in the Bayer process to generate alumina.
• Important bauxite mines in India are:
• Bilaspur & Maikal Hills.
• Singhbhum.
• Jamnagar.
• Balangir.
• Bargarh.
• Koraput.
• Kalahandi.
• Sambalpur.
• Sundergarh.

Additional Information

• Jharkhand is the No. 1 producer in Iron ore, Copper ores, Micca, Kainite, Uranium, Asbestos, etc. and No. 3 in coal production after Odisha and Chattisgarh.
• West Bengal is India's leading rice producer.
• Gujarat is the largest producer of cash crops like cotton, groundnut, cumin, sesame, etc. in India.

1. Aman is older than Sahu.

Aman > Sahu

2. Sahu is younger than Komal but older than Millan.

Komal > Sahu > Millan

3. Komal is older than Aman but younger than Uday.

Uday > Komal > Aman

Combining all the three statements, we get:

Uday > Komal > Aman > Sahu > Millan

Clearly, Aman is the third oldest among them.

Hence, ‘Aman’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Similarly,

Hence, ‘OPK’ is the correct answer.

The least possible Venn diagram is:      

   

Conclusions:

I. Some women are engineers. → True (As, Some women are wise and All wise are engineers → some women are engineers)

II. All engineers are wise. → False (As, All wise are engineers → some engineers are wise)

Hence, only conclusion (I) follows.

 

1. 9 + 5 - 16 × 4 ÷ 2 = 41

After replacing the symbols by their meaning, we get:

L.H.S = 9 × 5 + 16 ÷ 4 – 2

= 45 + 4 – 2

= 49 – 2

= 47 ≠ 41

2. 15 + 15 × 3 - 4 ÷ 5 = 26 

After replacing the symbols by their meaning, we get:

L.H.S = 15 × 15 ÷ 3 + 4 – 5

= 75 + 4 – 5

= 79 – 5

= 74 ≠ 26

3. 10 - 12 ÷ 18 × 6 + 2 = 16

After replacing the symbols by their meaning, we get:

L.H.S = 10 + 12 - 18 ÷ 6 × 2

= 10 + 12 – 3 × 2

= 10 + 12 – 6

= 22 – 6

⇒ 16 = 16

4. 11 ÷ 8 × 2 - 4 + 1 = 41

After replacing the symbols by their meaning, we get:

L.H.S = 11 - 8 ÷ 2 + 4 × 1

= 11 – 4 + 4

= 11 ≠ 41

Hence, ‘10 - 12 ÷ 18 × 6 + 2 = 16’ is the correct answer.

Given:

27% of 250 - 0.02% of 1000

Calculation:

27% of 250 - 0.02% of 1000

⇒ 27/100 × 250 - 2/10000 × 1000

⇒ 6750/100 - 2/10 

⇒ 67.5 - 0.2 

⇒ 67.3 

∴ The required result = 67.3

Given:

Principal = Rs.12,50,000

Rate = 5% per annum

Time = 5 years

Formula used:

Simple Interest = Principal × Rate/100 × Time 

Calculation:

Simple Interest = 12,50,000 × 5/100 × 5 = 312500

∴ The simple interest is Rs.312500

The correct answer is Virus.

Key Points

• Hepatitis A is a disease caused by the virus.
• The hepatitis A virus (HAV) is spread through ingesting tainted food or drinking tainted water, or by coming into close contact with an infected person.
• Hepatitis A does not cause chronic liver disease.
• Chronic liver disease is caused by hepatitis B and C.
• Hepatitis A is very contagious.
• Hepatitis A vaccine is a vaccine that prevents hepatitis A.

Additional Information

• Diseases that are spread to people through mosquito bites:
• Zika virus.
• West Nile virus.
• Chikungunya virus.
• Dengue.
• Important diseases caused by bacteria are:
• Tuberculosis.
• Anthrax.
• Tetanus.
• Leptospirosis.
• Pneumonia.
• Cholera.
• Important diseases caused by protozoa are:
• Leishmaniasis.
• Amoebiasis.
• Diarrhoea.
• Trypanosomiasis.
• Toxoplasmosis.

The correct answer is Liver.

Key Points

• The liver secretes bile juice, which is a digesting juice.
• Bile is stored in the gallbladder.
• Bilirubin and biliverdin, as well as bile salts and cholesterol, make up bile juice.
• Bile juice helps in the emulsification of fat.
• Large fat globules are broken down into smaller globules by bile juice, making it easier for pancreatic enzymes to act on them.
• The human liver is the largest gland in the body.
• The liver is situated on the right side of the stomach.
• The main function of the liver is to produce bile pigment.
• Ammonia and urea are produced in the liver.

Additional Information

• Insulin and Glucagon are the hormones secreted by the pancreas.
• The nutrients in digested food are absorbed from the small intestine.
• The stomach is a hollow organ that holds food while it is being mixed with stomach enzymes.

Given:

PQRS is a cyclic trapezium where PQ is parallel to RS.

PQ is the diameter & ∠QPR = 40° 

Concept:

Angle made in a semicircle is a right angle. 

The sum of the opposite angles of a cyclic trapezium is 180°.

Calculation:

In triangle PQR, 

∠RPQ + ∠RQP + ∠QRP = 180°  [Angle sum property] 

⇒ 40° + ∠RQP + 90° = 180° 

⇒ ∠RQP = 180° - 130° = 50° 

∠RQP + ∠PSR = 180° [Supplementary Angles]

∴ ∠PSR = 180° - 50° = 130°

By using the symbols in the table given below, we can draw the following family tree:

P × Q - S → P is son of Q and Q is wife of S

Clearly, S is the father of P.

Hence, ‘S is the father of P’ is the correct answer.

Conclusions:

I. All irregular students pass in exams. → The conclusion does not follows. (As Some irregular students pass in the examinations)

II. Some irregular students fail in the exam. → The conclusion does follows. (As Some irregular students pass in the examinations → Some irregular students fail in the exam)

Hence, only conclusion (II) follows.

Additional Information

• If there are two or more sentences that are used to frame a statement, then, the sentences must be interrelated, and mutual contradiction should be there.
• Do not look for truthful notions. The information provided in the statement is the only requirement for a student to answer the question. No assumptions must be made.
• Read the statement carefully and look for keywords that are common between the statement and the conclusions
• If there is more than one conclusion that is applicable to the statement, students must ensure that the conclusions they opt for have some relation with each other.