RRB NTPC CBT-I Official Paper (Held On: 20 Jan 2021 Shift 2) (Previous Year Paper)

Given:

Given numbers are 24, 144.

Concept used:

If P is the HCF of A and B then

A = P × m

B = P × n

(Where m, and n are arbitrary positive integers and they are co-prime to each other)

Calculation:

24 = 24 × 1

144 = 24 × 6

HCF (24, 144) = 24

According to the question,

10p + 4 = 24

⇒ p = 2

∴ The value of p is 2.

Five friend: G, H, I, J and K, are standing in a row

1) G is at the left end.

2) The person in the middle is between J and I.

Case (i) :

Case (ii) :

3) K is the neighbour of both J and I.

Case (i) :

Case (ii) :

∴ Here, from both the cases 'H' is standing at right end.

Hence, the correct answer is "H".

Concept used:

A% оf B is equal to B% of A.

Calculation:

Hence, x% of y must be equal to y% of x.

∴ x% оfy is y% of x.

Given: 

The diameter of the circle is equal to the sides of the equilateral tringle

Concept used:

Area of an equilateral triangle =  ${√3 \over 4}$ × (Side)2

Area of a circle = π × Radius2

Diameter = Radius × 2

Calculation:

Let the diameter of the circle be 2R unit.

Hence, the measure of the side of the equilateral triangle = 2R units

Thus,

The ratio of the area of a circle and that of an equilateral triangle

⇒ π × (2R ÷ 2)² : ${√3 \over 4}$ × (2R)²

⇒ π : √3

∴ The ratio of the area of a circle and that of an equilateral triangle is π : √3.

The correct answer is Taj Mahal.

• Taj Mahal is considered a fine example of Mughal architecture (a mixture of Indian, Persian and Islamic styles).
• The Taj Mahal is also one of the most iconic monuments in the world, which is visited by millions of tourists every year.
• The complex was designated a UNESCO World Heritage Site in 1983.

Key Points

• The Taj Mahal is situated on the right bank of the Yamuna River in the sprawling Mughal Gardens spread over 17 hectares in the Agra district of Uttar Pradesh.
• Its construction was started by the Mughal Emperor Shah Jahan in memory of his wife Mumtaz Mahal in 1632 AD and was completed in 1648 AD, adding the mosque, guest house and the main entrance to the south, the outer courtyard and its monasteries.
• Later and completed in 1653 AD.

Additional Information

Some of the UNESCO World Heritage Sites in India:

Given:

A can finish a piece of work in 20 days and B can finish it in 24 days.

They work together for 10 days then A leaves.

Concept used:

Total work = Efficiency (Work done per hour) × Total time taken 

Calculation:

LCM (20, 24) = 120

Let the total work be the LCM of the time taken by A and B.

Hence,

A does each day = 120 ÷ 20 = 6 units

B does each day = 120 ÷ 24 = 5 units

Remaining work after 10 days = 120 - (5 + 6) × 10 = 10 units

B will complete the rest of the work in = 10 ÷ 5 = 2 days

∴ B will finish the remaining work in 2 days.

The logic followed here is :-

• J is coded as N.

• R is coded as V.

• X is coded as B.

Similarly, JOY is coded as :

Hence. the correct answer is "NSC".

The correct answer is Madhya Pradesh.

• In 2013 Madhya Pradesh Government declared 'Malkhamb' as the state sport and also launched 'Mission Olympics 2020' for imparting coaching to the budding talents.
• The name Mallakhamb is derived from the words Malla, meaning wrestler, and Khamb, meaning pole.
• Literally meaning wrestling pole, the term refers to the traditional training implement used by wrestlers.
• In this sport, a gymnast performs aerial yoga or gymnastic poses and wrestling grips in concert with a vertical stable or hanging wooden pole, cane or rope.

Additional Information

• The Sports Authority of India (SAI) is the apex national sports body of India, established by the Ministry of Youth Affairs and Sports, Government of India for the development of sports in India.
• Sports Authority of India (SAI) was set up in 1984 to carry forward the legacy of the IXth Asian Games held in New Delhi in 1982 under the Department of Sports.
• The Major Dhyan Chand Khel Ratna is India's highest award for achievement in sports, while the Dronacharya Award is given for excellence in coaching.

Given:

A tank has two inlets A and B that can fill it in 5 h and 6 h respectively.

An outlet C can empty the full tank in 30 h.

Concept used:

Total work = Efficiency (Work done per hour) × Total time taken 

Calculation:

LCM (5, 6, 30) = 30

Let the capacity of the tank be the LCM of the time taken by all pipes.

Hence, the capacity of the tank = 30 units

Thus,

Inlet A fills the tank each hour by = 30 ÷ 5 = 6 units

Inlet B fills the tank each hour by = 30 ÷ 6 = 5 units

Outlet C empties the tank each hour by = 30 ÷ 30 = 1 unit

Hence, time taken to fill the tank when all pipes are opened = ${30 \over (6\ +\ 5\ -\ 1)}$ = 3 hours

∴ All the three pipes are opened together in the empty tank, 3 hours will the pipes take to fill the tank.

The correct answer is Chandrakanta.

• Chandrakanta Santati Babu is a Hindi novel written by Devaki Nandan Khatri.
• It is considered to be the first work of prose in the Hindi language.
• The book has a love story of two lovers who belong to rival kingdoms. Chandrakanta - A princess of Vijaygarh and Prince Virendra of Naugarh.

Additional Information

The correct answer is .jpeg.

Key Points

• JPEG stands for Joint Photographic Experts Group (JPEG)
• It is a standardized image compression mechanism designed for compressing either full-colour three-band (RGB) or grey-scale one-band images.JPEG stands for Joint Photographic Experts Group (JPEG)
• It is a standardized image compression mechanism designed for compressing either full-colour three-band (RGB) or grey-scale one-band images.
• Hence it is the correct answer.

Additional Information

• There are 8 common video formats data MP4, MOV, WMV, FLV, AVI, AVCHD, WebM, and MKV.
• The video format is the container that stores audio-video subtitles and any other metadata.
• A codec encodes and decodes the multimedia data such as audio or video.
• A QT file is a movie file saved in the QuickTime File Format (QTFF), which is a multimedia container format developed by Apple.

Family chart :

Radha is the sister of the son of Abhinav's son.

Family Tree :

∴ Here, Radha is 'Grand daughter' of Abhinav.

Hence, the correct answer is "Grand daughter".

Given:

14, 14, 15, 17, 16, 17, 17, 22, 13

Concept used:

The median is the middle value in a list ordered from smallest to largest.

Calculation:

Given series in the ascending order,

13, 14, 14, 15, 16, 17, 17, 17, 22

Hence, the median = 16

∴ The median of the given series is 16.

Shortcut Trick

The difference between two distinct irrational numbers (√2 and √3) where neither is a multiple of the other by a rational factor always results in an irrational number.

√2 ≈ 1.4142... and √3 ≈ 1.7320...

√2 − √3 ≈ −0.3178... which is non-terminating and non-repeating.

Such decimals represent irrational numbers.

∴ The correct answer is an irrational number.

Alternate Method

Given: The expression is √2 − √3.

Method: Proof by Contradiction.

⇒ Let us assume that √2 − √3 = r, where r is a rational number.

⇒ Squaring both sides: (√2 − √3)² = r²

⇒ (√2)² + (√3)² − 2(√2 × √3) = r²

⇒ 2 + 3 − 2√6 = r²

⇒ 5 − 2√6 = r²

⇒ 5 − r² = 2√6

⇒ √6 = (5 − r²) / 2

⇒ Since r is rational, r² is rational, and (5 − r²) / 2 is also rational.

⇒ However, √6 is an irrational number (as 6 is not a perfect square).

⇒ An irrational number cannot be equal to a rational number.

⇒ This is a contradiction, so our assumption was wrong.

∴ The correct answer is an irrational number.

Additional Information

Irrational Numbers

These are numbers that cannot be expressed as a ratio of two integers (p/q). Their decimal expansion is non-terminating and non-repeating.

Properties of Irrationals

The sum or difference of a rational and an irrational number is always irrational. The sum or difference of two irrationals may be rational or irrational.

Square Roots of Primes

The square root of any prime number (like 2, 3, 5, 7, etc.) is always an irrational number.

Real Numbers

Real numbers are the union of rational numbers and irrational numbers. Every point on the number line represents a unique real number.

Given: 

sin 3θ  = cos (θ – 6°)

Concept used:

Cos (90° - α) = Sinα 

Calculation:

sin 3θ  = cos (θ – 6°)

⇒ Cos (90° - 3θ) = cos (θ – 6°)

⇒ 4θ = 96° 

⇒ θ = 24°

∴ The value of θ is 24°.

The correct answer is pH scale.

Key Points

• pH means the potential of Hydrogen.
• The strength of acids and bases depends on the number of H+ ions and OH- ions produced, respectively.
• 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 scales is 0 to 14.
• If pH < 7 then solution is acidic.
• If pH > 7 then solution is basic.
• If pH = 7 then solution is neutral.

Additional Information 

• The human body works within the pH range of 7.0 to 7.8.
• When the pH of rainwater is less than 5.6, it is called acid rain.
• Tooth decay starts when the pH of the mouth is lower than 5.5.

Given:

The number exceeds 25% of itself by 60.

Concept used:

Application of Percentage

Calculation:

Let the number be Q

According to the question,

Q = 60 + Q × 25%

⇒ $3Q \over 4$ = 60

⇒ Q = 80

∴ The number is 80.

The correct answer is Rahul Dravid.

Key Points

• "The Nice Guy Who Finished First" is a biography of Rahul Dravid.
• The book was authored by Devendra Prabhudesai.
• Rahul Dravid is an Indian former International cricketer and a batsman.
• His nickname is 'The Great Wall', 'Mr. Dependable'.
• He got Padma Bhsuhan (2013), Padma Sri (2004), Arjuna Award (1998).

Additional Information

• David Beckham is an English former professional footballer, the current president & co-owner of Inter Miami CF and the co-owner of Salford City.
• Michael Phelps belongs to the United States of America.
• He is also known as the "Flying Fish" or "The Baltimore Bullet".
• He is one of the most celebrated Sportsperson in the Olympic games ever with rewards of approximately two dozen Gold medals.
• Tiger Woods is an American golfer.
• He holds the record for being World Number One for the most consecutive weeks as well as for the greatest total number of weeks.

The followed here is :-

• Case (i) :

Position of Rajeshwari from left side of the row = 5^th

Position of Rajeshwari from ight side of the row = 6^th

Total number of girls in the row = Left side position + Right side position - 1

• Total number of girls in the row = 5 + 6 - 1
• Total number of girls in the row = 11 - 1
• Total number of girls in the row = 10.
• Case (ii) :

Position of Rajeshwari from left side of the row = 6^th

Position of Rajeshwari from ight side of the row = 5^th

Total number of girls in the row = Left side position + Right side position - 1

• Total number of girls in the row = 6 + 5 - 1
• Total number of girls in the row = 11 - 1
• Total number of girls in the row = 10.

Hence, the correct answer is "10".

The logic followed here is :-

• 23 A 64 A 13 = 136423

and,

• 9 A 57 A 12 = 12579

Similarly,

• 29 A 4 A 6 = ?

Hence, the correct answer is "6429".

Given:

Length of the train = 200m

Length of the platform = 600m

Speed = 72kmph

Concept used:

Meter per second (mps) = (5 / 18) × Kilometer per hour (kmph)

While a train crosses a bridge, it crosses the sum of its length and the length of the bridge.

Calculation:

72 kmph = 72 × (5 / 18) = 20 m/s

Hence, time taken to cross the bridge = $(600\ +\ 200) \over 20$ = 40 seconds

∴ It will taken 40s to cross a 200m long bridge.

The correct answer is Brahmaputra.

• The Brahmaputra river with a length of 891 km between the Bangladesh border and Sadiya was declared as National Waterway No. 2 (NW-2) on 1 September 1988.

Key Points

• The National Waterways Act came into force in 2016.
• In 1986, the Government of India created the Inland Waterways Authority of India (IWAI) to regulate and develop inland waterways for navigation and shipping.

Additional Information

Given:

In April, the profit of a book store is increased by 25%, and in May, it is decreased by 20%

Concept used:

Incremented/Reduced value = Initial value (1 ± change%)

Calculation:

Let the initial profit at beginning of April be 100Q

In April, the profit = 100Q × 1.25 = 125Q

In May, the profit = 125Q × 0.8 = 100Q

Hence, the profit remains the same at the end of May compared to that at the beginning of April.

∴ The profit remains the same at the end of May compared to that at the beginning of April.

The correct answer is Quick lime.

Key Points

• Quick lime is another name for calcium oxide.
• Calcium oxide, commonly known as lime, is a chemical compound with the formula CaO.
• It is believed that quicklime is one of the oldest chemicals known to the human race.
• It can also be referred to as burnt lime or lime.
• Calcium oxide can be produced by the thermal decomposition of materials like limestone or seashells that contain calcium carbonate (CaCO3 mineral calcite) in a lime kiln.
• Cement is a mixture formed by the heating together of CaCO3 and clay.
• Sodium Bicarbonate is the chemical name is ‘baking soda’.

Given: 

If an article is sold at a gain of 5% instead of being sold at a loss of 5%, a man gets Rs. 5 more. 

Concept used:

Selling Price = Cost Price × (1 + Gain%)

Selling Price = Cost Price × (1 - Loss%)

Calculation:

Let the cost price of the article be Rs. Q.

According to the question,

Q × (1 + 5%) - Q × (1 - 5%) = 5

⇒ Q × 0.1 = 5

⇒ Q = 50

∴ The cost price of the article is Rs. 50.

The correct answer is Johann Wolfgang Dobereiner.

• In 1817, German chemist Johann Wolfgang Dobereiner arranged elements with similar properties into a group.
• The Dobereiner triad is based on a group of three elements.
• He was the first to start grouping the elements on the basis of atomic mass.
• The three elements of the triad were arranged in such a way that the atomic mass of the middle element was approximately the average of the atomic masses of the other two elements.

Additional Information

• Dmitri Mendeleev was a Russian chemist.
• He is considered to be the most important contributor to the development of the periodic table.
• His version of the periodic table organized elements into rows according to their atomic mass and into columns based on chemical and physical properties.
• The British chemist John Newlands was the first to arrange the elements in the periodic table with increasing order of atomic mass.
• He found that each of the eight elements has similar properties and called this the law of octaves.
• He arranged the elements into eight groups but did not leave any gaps for the unseen elements.
• Henry Moseley: In 1913, while working at the University of Manchester, he observed and measured the X-ray spectra of various chemical elements using diffraction in crystals. Through this, he discovered a systematic relationship between wavelength and atomic number. This discovery is now known as Moseley's law.

The correct answer is Andaman Islands.

Important Points

• The cellular jail built by Britishers in the Andaman and Nicobar Island is known as Kala Pani.
• The construction of the Cellular Jail started in 1893 and was completed in 1905-06.
• Prisoners were used as labour.
• It is built in a way that no communication of any kind was possible between prisoners in the same or different wings.
• The remoteness and terror of the facility gave it a name, ‘Kala Pani’ (Blackwaters).

The logic followed here is :-

• METHOD is written as DOHTEM.

Similarly,

• CHOCOLATE will be written as :

Hence, the correct answer is "ETALOCOHC".

The correct answer is Radial.

Key Points

• ​When the rivers originate from a hill and flow in all directions, the drainage pattern is known as ‘radial’.
• Volcanoes usually display excellent radial drainage.
• The rivers originating from the Amarkantak range present a good example of it.

Additional Information

• Centripetal Patterns
• ​When the rivers discharge their waters from all directions in a lake or depression, the pattern is known as ‘centripetal’.
• ​Dendritic patterns
• These are by far the most common, develop in areas where the rock (or unconsolidated material) beneath the stream has no particular fabric or structure and can be eroded equally easily in all directions.
• The drainage pattern resembling the branches of a tree is known as “dendritic” the examples of which are the rivers of the northern plain.
• Trellis drainage
• When the primary tributaries of rivers flow parallel to each other and secondary tributaries join them at right angles, the pattern is known as ‘trellis’.
• These patterns typically develop where sedimentary rocks have been folded or tilted and then eroded to varying degrees depending on their strength.
• The Rocky Mountains of B.C. and Alberta are good examples of this, and many of the drainage systems within the Rockies have trellis patterns.

The correct answer is CR Das.

Important Points

• Swaraj Party was formed on 1 January 1923.
• Chittaranjan Das, Narasimha Chintaman Kelkar and Motilal Nehru formed the Congress-Khilafat Swarajaya Party with Das as the president and Nehru as one of the secretaries.
• The Swaraj Party was established as the Congress-Khilafat Swaraj Party.
• It was a political party formed in India on 1 January 1923 after the Gaya annual conference in December 1922 of the National Congress, that sought greater self-government and political freedom for the Indian people from the British Raj.
• Within the Congress, some leaders were by now tired of mass struggles and wanted to participate in elections to the provincial councils that had been set up by the Government of India Act of 1919.
• They felt that it was important to oppose British policies within the councils, argue for reform and also demonstrate that these councils were not truly democratic.
• C. R. Das and Motilal Nehru formed the Swaraj Party within Congress to argue for a return to council politics.

Let us consider,

Present age of husband = x.

Present age of wife = y.

Present age of son = z.

Given :

20 years ago, the average age of a husband and his wife was 23 years.

Age of husband 20 years ago = x - 20.

Age of wife 20 years ago = y - 20.

average age of a husband and his wife was 23 years.

⇒ (x - 20 + y - 20) / 2 = 23

⇒ (x - 20 + y - 20) = 46

⇒ x + y - 40 = 46

⇒ x + y = 86 ............ (i)

average age of the family consisting of the husband, wife and their son is 34 years.

⇒ (x + y + z) / 3 = 34

⇒ x + y + z = 102 ............ (ii)

Substitute equation (i) in equation (ii) we get,

⇒ 86 + z = 102

⇒ z = 102 - 86

⇒ z = 16

∴ Here, the present age of son is 16 years.

Hence, the correct answer is "16 years".

The correct answer is AYUSH.

• The Ministry of AYUSH, a ministry of the Government of India, is responsible for the development of education, research and dissemination of indigenous and alternative systems of medicine in India.
• AYUSH is an acronym for Ayurveda, Yoga and Naturopathy, Unani, Siddha and Homeopathy and are the six Indian systems of medicine prevalent and practised in India and some of the neighbouring Asian countries with very few exceptions in some of the developed countries.

Key Points

• Presently (National Social Assistance Programme) NSAP comprises five schemes, namely –
• Indira Gandhi National Old Age Pension Scheme (IGNOAPS): The eligible age for IGNOAPS is 60 years.
• The pension is Rs.200 p.m. for persons between 60 years and 79 years. For persons who are 80 years and above the pension is Rs.500/ - per month.
• Indira Gandhi National Widow Pension Scheme (IGNWPS): The eligible age is 40 years and the pension is Rs.300 per month. After attaining the age of 80 years, the beneficiary will get Rs.500/ - per month.
• Indira Gandhi National Disability Pension Scheme (IGNDPS): The eligible age for the pensioner is 18 years and above and the disability level has to be 80%.
• The amount is Rs.300 per month and after attaining the age of 80 years, the beneficiary will get Rs 500/ - per month.
• Dwarfs will also be an eligible category for this pension.
• Annapurna Scheme: 10 kgs of food grains (wheat or rice) is given per month per beneficiary.
• The scheme aims at providing food security to meet the requirements of those eligible old aged persons who have remained uncovered under the IGNOAPS

The correct answer is 1792.

• The establishment of the Calcutta Cricket Club (what we know today as CC & FC) in 1792, was another watershed for the sport in the land.
• It is the second-oldest cricket club in the world, after the MCC (1787).

Key Points

• Calcutta Cricket and Football Club is a sports club founded in 1792 AD, which currently has the resources to practice cricket, field hockey, football, rugby, cycle polo and tennis.
• The club was originally founded as the 'Calcutta Cricket Club Clippers' by the British, who came with the British East India Company.
• The Calcutta Cricket Club and the Calcutta Football Club were respectively the oldest cricket and football clubs outside the United Kingdom, which later merged to form the Calcutta Cricket and Football Club in 1965.

Additional Information

• The Board of Control for Cricket in India is the governing body for cricket in India and is under the jurisdiction of the Ministry of Youth Affairs and Sports, Government of India.
• It is an autonomous organization and does not come under the National Sports Federation of India.
• Headquarters: Mumbai
• Founded: December 1928

The correct answer is Banaras Hindu University.

Key Points

• Gandhiji, the first major public appearance was at the opening of the Banaras Hindu University in February 1916. 
• Banaras Hindu University is an internationally reputed temple of learning, situated in the holy city of Varanasi.
• This creative and innovative university was established in 1916 by the great nationalist leader Pandit Madan Mohan Malaviya in collaboration with great personalities like Dr Annie Besant, who saw it as the University of India.
• Banaras Hindu University was created under the Parliamentary Act - B.H.U. Act 1915.

 Important Points

• Mahatma Gandhi was born October 2, 1869, in Porbandar, India & died January 30, 1948, in Delhi.
• Champaran Satyagraha
• In the Champaran district of Bihar, farmers were forced by Europeans to grow indigo.
• They could not grow the food they needed, nor did they get paid enough for the indigo.
• Gandhi accompanied the prince to Champaran in early 1917 to start the Satyagraha.
• Ahmedabad Mill Strike
• In 1918, it was one of the early movements led by Gandhi.
• In March 1918, under the leadership of Gandhiji, there was a strike in the cotton mills.
• In this strike, Gandhi used the weapon of hunger strike.

The correct answer is It has a high melting point and boiling point.

Important Points

• Properties of ionic compounds:
• Due to the strong attractive force between the positive and negative ions, ionic compounds are solids that are rather rigid.
• These compounds are often brittle and break into fragments when pressure is applied.
• The melting and boiling points of ionic compounds are extremely high. 
• This is due to the significant amount of energy necessary to break the strong inter-ionic affinity.
• ​In general, ionic compounds are soluble in water but insoluble in solvents such as kerosene, petrol, ether, alcohol, carbon tetrachloride, etc.
• In solution, the movement of charged particles is involved in the conduction of electricity.
• In the solid-state ionic compounds do not conduct electricity because ion mobility in a solid is impossible due to its rigid or hard structure, on the other hand, in molten or in aqueous solution it conducts electricity. As heat overcomes the electrostatic forces of attraction between oppositely charged ions.
• Hence Option 3 is the correct answer.

Given: 

The radius of a semicircular compound is 35 m.

Concept used:

The circumference of the semicircle = π × Radius + 2 × Radius

Calculation:

The circumference of the semicircular compound

⇒ π × 35 + 35 × 2

⇒ 180m

∴ Its circumference is 180m

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

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

From the positions 1, 2, 3 of Dice the opposite faces identified as :

∴ Here, the opposite letter of U is 'P'.

Hence, the correct answer is "P".

The correct answer is Satish Dhawan Space Centre.

• The PSLV-C45 was launched from the second launch pad of the Satish Dhawan Space Centre in Sriharikota, Andhra Pradesh, India.

Key Points

• ISRO has many facilities each dedicated to a specialized field of study in space:
• Vikram Sarabhai Space Centre (VSSC), Thiruvananthapuram
• Liquid Propulsion Systems Centre (LPSC), Thiruvananthapuram
• Satish Dhawan Space Centre (SDSC-SHAR), Sriharikota
• Space Applications Centre (SAC), Ahmedabad
• National Remote Sensing Centre (NRSC), Hyderabad

Additional Information

• The Indian National Committee for Space Research (INCOSPAR) was established by Jawaharlal Nehru in 1962 under the Department of Atomic Energy (DAE).
• Eminent scientist Dr Vikram Sarabhai had a big role in this development.
• INCOSPAR established the Thumba Equatorial Rocket Launching Station (TERLS) at Thumba near Thiruvananthapuram on the southern tip of India.
• INCOSPAR became ISRO in 1969.
• Gaganyaan Mission: India's maiden space mission, Gaganyaan, will be launched in 2023.
• Chandrayaan-3 Mission: Chandrayaan-3 is likely to be launched during the third quarter of 2022.
• Three Earth Observation Satellites (EOSs):
• EOS-4 (Risat-1A) and EOS-6 (Oceansat-3) — will be launched using Isro’s workhorse PSLV, the third one, EOS-2 (Microsat), will be launched in the first developmental flight of the Small Satellite Launch Vehicle (SSLV).

The correct answer is Wangari Mathai.

• Wangari Maathai was the founder of the Green Belt Movement and the 2004 Nobel Peace Prize, Laureate.
• She authored four books: The Green Belt Movement; Unbowed: A Memoir; The Challenge for Africa; and Replenishing the Earth.
• Peace on earth depends on our ability to secure our living environment.
• Maathai stands at the front of the fight to promote ecologically viable social, economic and cultural development in Kenya and in Africa.
• She has taken a holistic approach to sustainable development that embraces democracy, human rights and women’s rights in particular.

Additional Information

Nobel Prizes 2021

Given:

Principal amount = Rs. 25000

Rate of interest = 6%

Time = 2 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:

The compound interest incurred

⇒ 25000 (1 + 6/100)² - 25000

⇒ 28090 - 25000

⇒ 3090

∴ The compound interest on Rs. 25,000 at the rate of 6% per annum in 2 years will be 3090.

The correct answer is Meghalaya.

• Rat Hole mining is majorly only practised in Meghalaya.
• Rathole mining involves digging very small tunnels, usually only 3-4 feet high, which workers (often children) enter and extract coal.

Key Points

• Meghalaya is a state in Northeast India.
• Meghalaya was formed by merging two districts from the state of Assam: the United Khasi Hills and Jaintia Hills, and the Garo Hills on 21 January 1972.

Additional Information

Some of the mineral mines are:

Given:

The ratio of the cost price and the selling price of an article is 4 : 5.

Concept used:

Gain percentage = ${(Selling\ Price\ -\ Cost\ Price) \over Cost\ Price} \times 100\%$

Calculation:

Let the common ratio be Q.

Hence,

the selling price of the article = 5Q

the cost price of the article = 4Q

Thus, Gain% = ${(5Q\ -\ 4Q) \over 4Q} \times 100\%$ = 25%

∴ The percentage gain is 25%.

The correct answer is New Delhi.

Key Points

• United Nations Environment Programme office in India is located in New Delhi.
• United Nations Environment Programme is an agency of United Nations that sets the global environmental agenda and promotes the implementation of the environmental dimension of sustainable development within the United Nations system.
• It is headquartered in Nairobi, Kenya.
• It was founded by Maurice Strong, the first director of UNEP, as a result of the United Nations Conference on the Human Environment in June 1972.

Additional Information

The logic followed here is :-

1) $\frac{65}{16}$ → Here Quotient = 4 and Remainder = 1

2) $\frac{62}{15}$ → Here Quotient = 4 and Remainder = 2

3) $\frac{37}{9}$ → Here Quotient = 4 and Remainder = 1

4) $\frac{49}{12}$ → Here Quotient = 4 and Remainder = 1

∴ Here, $\frac{62}{15}$ is different from other three alternatives.

Hence, the correct answer is "$\frac{62}{15}$".

Given:

The photograph of a bacteria enlarged 60000 times attains a length of 6 cm.

Calculation:

Let the actual length of the bacteria be Q cm.

According to the question,

Q × 60000 = 6

⇒ Q = $\frac{1}{10000}$

∴ The actual length of bacteria $\frac{1}{10000}$.

Given:

(0.63 ÷ 1.26) × 4 + 5 × 3

Concept used:

Calculation:

(0.63 ÷ 1.26) × 4 + 5 × 3

⇒ 0.5 × 4 + 5 × 3

⇒ 2 + 15

⇒ 17

∴ The simplified value is 17.

The correct answer is John Dalton.

• John Dalton's atomic theory:
• His theory was based on the laws of chemical combination.
• Dalton's atomic theory provided an explanation of the law of conservation of mass and the law of definite proportions.
• In 1808 he presented his atomic theory which was a turning point in the study of matter.

Key Points

• According to Dalton’s atomic theory, all matter, whether an element, a compound or a mixture is composed of small particles called atoms. The postulates of this theory may be stated as follows:
• (i) All matter is made of very tiny particles called atoms.
• (ii) Atoms are indivisible particles, which cannot be created or destroyed in a chemical reaction.
• (iii) Atoms of a given element are identical in mass and chemical properties.
• (iv) Atoms of different elements have different masses and chemical properties.
• (v) Atoms combine in the ratio of small whole numbers to form compounds.
• (vi) The relative number and kinds of atoms are constant in a given compound.

Additional Information

• Ernest Rutherford is best known for his pioneering studies of radioactivity and the atom.
• He found that there are two types of radiation coming from uranium, alpha and beta particles.
• He found that the atom consists mostly of empty space, with its mass concentrated in a centrally positively charged nucleus.
• Antoine Lavoisier determined that oxygen was a major substance in combustion, and he gave the element its name.
• He developed a modern system of naming chemical substances and has been called "the father of modern chemistry" for his emphasis on careful experimentation.
• In chemistry, the law of definite proportions, sometimes called Proust's law or law of constant structure, states that a given chemical compound always has its constituent elements in a fixed proportion (by mass) and that it does not depend on its source and method of preparation.

The correct answer is United States.

Key Points

• The model for “Fundamental Rights” in India is taken from the US constitution.
• As Indian citizens, We have 6 Fundamental Rights by our constitution.
• They are-
• Right to Equality.
• Right to Freedom.
• Right against Exploitation.
• Right to Freedom of Religion.
• Cultural and Educational Rights.
• Right to Constitutional Remedies.

Additional Information

• Sources of Indian Constitution

Minister of State in the Ministry of Defence is NOT correct.

• The Minister of State in the Ministry of Defence is NOT a Cabinet Minister.

Key Points

• A minister of state is a junior minister in the council of ministers in the central government who may assist a cabinet minister or hold an independent charge of the ministry.
• The Constitution of India restricts the number of Ministers of State in the federal government.
• A minister of state with an independent charge is a minister without a supervising cabinet minister in the state or central government of India.
• He is himself in charge of his ministry, unlike a minister of state who is also a minister but assists a cabinet minister.
• In addition, such ministers can participate in cabinet meetings on important issues unlike ministers of state who do not participate in any cabinet meeting.
• The Ministry of Defense is directly charged with coordinating and supervising all agencies and functions of the government directly related to national security and the Indian Armed Forces.
• The President of India is the formal Commander-in-Chief of the country's armed forces.

Given:

Two boxes, A and B, have the capacity of holding 85 and 68 units of an article respectively.

Concept used:

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

Calculation:

The maximum number of units that should be put into each of these packets such that both boxes A and B are filled to their full capacity should be the HCF the capacity of A and B.

HCF (85, 68) = 17

∴ The maximum number of units that should be put into each of these packets such that both boxes A and B are filled to their full capacity is 17 units per packet.

The correct answer is BR Ambedkar.

Important Points

• Dr B. R. Ambedkar established the Depressed Classes Federation (DCF) in 1930.
• He established the Independent Labour Party (ILP) in 1935.
• The first convention of Depressed Classes changed into convened on November 11, 1917, via way of means of Justice Chandravarkar.
• The convention pleaded the needs of untouchables earlier than the government.
• The first All India Depressed Classes convention was changed into held in Bombay on March 23, 1918, below the Chairmanship of Maharaja Shivajirao of Baroda.
• It changed into attended via way of means of many distinguished leaders.

The logic followed here is :-

Hence, the correct answer is "3157".

The correct answer is Rajarajeshwara temple.

Important Points

• Rajarajeshwara temple is near Taliparamba in Kerala, where women are allowed to enter only after 8 p.m.
• A unique feature of this temple is the absence of a flagstaff.
• Raja Rajeshwara Temple is dedicated to Lord Shiva.
• It is also known as Brihadeshwara Temple.
• It is located in Thanjavur(Tanjore), Tamil Nadu on the bank of the Cauvery River.
• It is one of the best examples of the Dravidian style of temple architecture.
• It was built by Chola emperor Raja Raja Chola I between 1003 AD and 1010 AD.
• The temple comes under the list of UNESCO World Heritage Sites in 1987 and it is also a part of the "Great Living Chola temple".
• It is the largest and tallest of all Indian temples.

Family chart :

Pointing to a photograph of a man, a woman said, “That man is the son of the only brother of my husband." 

Family Tree :

∴ Here, Woman is paternal aunt to the man in photo.

Hence, the correct answer is "Paternal Aunt".

Concept used:

A² -  B² = (A + B) (A - B)

Calculation:

$(\sqrt3 - \sqrt2)$ × $(\sqrt3 + \sqrt2)$

⇒ ${(\sqrt3)^2\ -\ (\sqrt2)^2}$

⇒ 3 - 2

⇒ 1

∴ The simplified value is 1.

Calculation:

$\frac{27}{25}$ = 1.08

∴The decimal expansion of $\frac{27}{25}$ will terminate after two decimal places.

Given:

A dealer lists his goods at 40% above the cost price and allows a discount of 20%.

Concept used:

Successive percentage change of A% and B%, results into =  $(A + B + {(A \times B) \over 100})\%$

Calculation:

Profit percentage = $40 - 20 - {(40 \times 20) \over 100}$ = 12%

(Here discount is considered as a negative percentage change)

∴ His profit is 12%.

The correct answer is Habeas corpus.

Key Points

• Habeas corpus means " to produce the body" or " to have the body".
• This writ is issued for the enforcement of the fundamental right.
• It can be issued by both the supreme court and the high court.
• It is issued against both public and private authorities.
• It is not issued on certain grounds such as detention being outside the jurisdiction of the court or detention being by a competent court.

Additional Information

• Writs are a written order from the Supreme Court or High Court that commands constitutional remedies for Indian Citizens against the violation of their fundamental rights.
• Article 32 in the Indian Constitution deals with constitutional remedies that an Indian citizen can seek from the Supreme Court and High Court against the violation of his/her fundamental rights.
• Five kinds of writs are issued for enforcing the fundamental rights of the citizens.
• Habeas Corpus
• Mandamus - We command.
• Prohibition - To forbid.
• Certiorari - To be certified’ or ‘To be informed.
• Quo-Warranto- By what authority or warrant.

The logic followed here is :-

2 + 2 = 12, 3 + 3 = 24, 4 + 4 = 34 and 5 + 5 = 42 :

∴ Here, the value of 8 + 8 = 54.

Hence, the correct answer is "54".

The correct answer is Malayalam.

Important Points

• Malayalam is the language spoken by a majority of the people in Lakshadweep.
• According to Census 2011, Hindi has retained its position as a predominant language spoken by about 43.63% of the population.
• Bengali was the second most spoken language which is spoken by 8.03% of the population.
• Marathi was at 3^rd with 6.86% of speakers.
• Out of 22 scheduled languages,13 were reported as the mother tongue by at least 1% of the population.
• Sanskrit is spoken by nearly 25000 people.
• The Eighth Schedule of the Indian Constitution provides a list of all the officially recognized languages in India.
• It is found in Articles 344(1) and 351 of the Constitution

The correct answer is Canada.

• The first Pressurised Heavy Water Reactor (PHWR) of India in 1964 was a Collaborative venture between Atomic Energy of Canada Ltd and NPCIL of India.
• Plans for building the first Pressurised Heavy Water Reactor (PHWR) were finalized in 1964, and this prototype Rajasthan 1, which had Canada's Douglas Point reactor as a reference unit, was built as a collaborative venture between Atomic Energy of Canada Ltd (AECL) and NPCIL.

Key Points

• IPHWR-700 (Indian Pressurized Heavy Water Reactor-700) is an Indian pressurized heavy water reactor designed by Bhabha Atomic Research Center.
• It is a Generation III reactor developed from earlier CANDU based 220 MW and 540 MW designs.
• PHWR technology was introduced to India in the late 1960s with the construction of RAPS-1, a CANDU reactor in Rajasthan.
• All the main components for the first unit were supplied by Canada. India did the construction, installation, and commissioning.
• In 1974, after India conducted its first nuclear weapons test by Smiling Buddha, Canada ended its support for the project.

Important Points

• Apsara is the first nuclear reactor in India.
• It was built in the year 1956.
• It is the first nuclear reactor in Asia.
• Kamini (Kalpakkam Mini reactor) is the first fast breeder neutron reactor in India.
• Uranium-233 is used as the fuel in this reactor.
• Kudankulam nuclear power plant is the largest nuclear power station in India.
• It was established with the collaboration of India and Russia.

The correct answer is GSAT-31.

• In February 2019, GSAT-31 was launched by ISRO to help in bulk data transfer for telecommunication applications.

Key Points

• The Indian Space and Research Organization (ISRO) has launched GSAT-31 on an Ariane 5 rocket from French Guiana in South America.
• GSAT-31 is India's 40^th communication satellite
• GSAT will replace 31 satellites INSAT-4CR and INSAT-4A which are going to be phased out soon and will help in maintaining the continuity of the services currently provided by these satellites.
• The satellite will provide connectivity to Very Small Aperture Terminals (VSATs) for ATMs, stock exchanges, e-governance applications and direct-to-home (DTH) services.
• It will also provide telecom applications for bulk data transfer for applications, emergency communication, and disaster management support.

Additional Information

• The Indian National Committee for Space Research (INCOSPAR) was established by Jawaharlal Nehru in 1962 under the Department of Atomic Energy (DAE).
• Eminent scientist Dr Vikram Sarabhai had a big role in this development. He understood the need for space research and was convinced of the role it can play in helping a nation develop.
• INCOSPAR set up the Thumba Equatorial Rocket Launching Station (TERLS) at Thumba, near Thiruvananthapuram at India’s southern tip. TERLS is a spaceport used to launch rockets.
• The INCOSPAR became ISRO in 1969.

Given: 

$\sqrt[3]{40}$

Calculation:

$\sqrt[3]{40}$

⇒ $\sqrt[3]{2× 2 × 2 × 5}$

⇒ 2$\sqrt[3]{5}$

⇒ 2 × $5^{1 \over 3}$

∴ Rationalising factor of $\sqrt[3]{40}$ is $5^{1 \over 3}$.

Given: 

tan 5° tan 25° tan 45° tan 65° tan 85°

Concept used:

tan (90° - θ) = cot θ

tanθ cotθ = 1

Calculation:

tan 5° tan 25° tan 45° tan 65° tan 85°

⇒ tan (90° - 85°) tan (90° - 65°) tan 45° tan 65° tan 85°

⇒ cot 85° cot 65° tan 45° tan 65° tan 85°

⇒ tan 45°

⇒ 1

∴ The simplified value is 1.

The logic followed here is :-

1) Rahul is shorter than Raman.

• Raman > Rahul

2) Ramesh is shorter than Ravi but taller than Raman.

• Ravi > Ramesh > Raman

Thus final arrangement;

• Ravi > Ramesh > Raman > Rahul.

∴ Here, 'Ravi' is tallest among them.

Hence, the correct answer is "Ravi".

Shortcut Trick

In the binomial expansion of (x + a)ⁿ, the term containing x¹ is given by ⁿC_n−1 × x¹ × aⁿ⁻¹.

Here, n = 3 and a = 3.

Coefficient of x = ³C₂ × 3³⁻¹ = 3 × 3²

Coefficient = 3 × 9 = 27.

∴ The correct answer is 27.

Alternate Method

Given: The algebraic expression (x + 3)³.

Formula Used: (a + b)³ = a³ + 3a²b + 3ab² + b³

Calculations:

⇒ Let a = x and b = 3.

⇒ (x + 3)³ = x³ + 3(x²)(3) + 3(x)(3²) + 3³

⇒ (x + 3)³ = x³ + 9x² + 3(x)(9) + 27

⇒ (x + 3)³ = x³ + 9x² + 27x + 27

⇒ The coefficient is the numerical factor of the variable term.

⇒ In the term 27x, the coefficient of x is 27.

∴ The correct answer is 27.

Additional Information

Binomial Theorem

The general expansion of (x + y)ⁿ is Σ ⁿC_k × x^n−k × y^k for k = 0 to n.

Algebraic Identity (a − b)³

The expansion of (a − b)³ is a³ − 3a²b + 3ab² − b³.

Coefficient Definition

A coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number.

The correct answer is Dry deciduous forests.

• Dry deciduous forests are more pronounced in areas that record annual rainfall between 70–100 cm.
• The main species found in moist deciduous forests are teak, shisham, sal, hurra, amla, safflower and sandalwood.
• The main species found in dry deciduous forests are tendu, amaltas, bael, Khair, excelword, palas etc.

Additional Information

• There are five categories of forests in India.
• Tropical Deciduous Forest
• Trees have broadleafs. India also has temperate deciduous forests but they're very less in number.
• These broad leaves are shed within the autumn season but it's within the case of temperate deciduous mode.
• The tropical deciduous forests have trees that shed their leaves within the winter season.
• Tropical Rain Forests
• It is also referred to as equatorial rainforests.
• Rainforests are those forests that are characterized by heavy rainfall between 1750 mm and 2000 mm.
• These forests incur heavy showers of 100-600 cm a year.
• Coffee, bananas, and chocolates come from tropical rainforests.
• Mountain Forests
• It is found in mountain or hilly areas.
• These areas include the hilly area of the Himalayas and Vindhyas or Nilgiri Hills.
• The forests within the northern region are denser than in the South.
• At higher altitudes, fir, juniper, deodar, and chilgoza are often found.
• Tropical Thorn forests
• It is found in a neighbourhood with little or no rainfall (as little as 50cm).
• Arid regions of Rajasthan, Madhya Pradesh, Gujarat, and Uttar Pradesh have these forests.
• Swamp Forests
• It is also referred to as Wetland forests and Littoral forests in Gujarat, Rajasthan, and Rann of Kutch.
• Another name is alpine forests another category of forests.

Given:

One root is 3 + $\sqrt5$ 

Concept used:

(A + B)² = A² + B² + 2AB

Calculation:

Hence,

x = 3 + √5 

⇒ (x - 3)² = 5 (Sqauring both side)

⇒ x² - 6x + 9 = 5

⇒ x² - 6x + 4 = 0

∴ The quadratic equation is x2 - 6x + 4 = 0.

Concept used:

Total = Mean (Average) × number of entities

Calculation:

First ten even natural numbers in the ascending order -

⇒ 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Hence, the mean = Sum (2, 4, 6, 8, 10, 12, 14, 16, 18, 20) ÷ 10 = 11

∴ The mean of the first ten even natural numbers is 11.

The correct answer is Plaster of Paris.

• On heating gypsum at 373 K, it loses water molecules and becomes calcium sulphate hemihydrate.
• This substance is used to make toys, materials for decoration, and smooth surfaces.
• This substance is commonly known as the Plaster of Paris.

Key Points

• Gypsum is the name given to a mineral classified as a calcium sulfate mineral, and its chemical formula is calcium sulfate dihydrate, CaSO₄⋅ 2H₂O.
• Plaster of Paris is prepared by heating calcium sulfate dihydrate or gypsum to 120–180 °C.
• Plaster of Paris has the chemical formula (CaSO₄) 1/2H₂O and is known as calcium sulfate hemihydrate.
• Plaster of Paris generally does not shrink or crack when dry, making it an excellent medium for mould casting.
• It is commonly used to precast and hold parts of decorative plasterwork installed on ceilings and cornices.
• It is also used in medicine to make plaster casts to repair broken bones, although many modern orthopaedic casts are made of fibreglass or thermoplastics.

Given: 

Quantity A is the number of ways to assign a number from 1 to 5 without repetition to each of four people

Quantity B is the number of ways to assign a number from 1 to 5 without repetition to each of 5 people

Concept used:

Permutation and Combination

Calculation:

The number of ways to assign a number from 1 to 5 without repetition to each of four people = 5 × 4 × 3 × 2 = 120

The number of ways to assign a number from 1 to 5 without repetition to each of 5 people = 5! = 5 × 4 × 3 × 2 × 1 = 120

Hence, Quantity A = Quantity B

∴ Both Quantities A and B are equal.

The correct answer is Vinod Khosla.

Important Points

• Vinod Khosla was one of the founders of the American computer company Sun microsystems later acquired by oracle.
• Vinod Khosla is an Indian-American billionaire businessman and venture capitalist.
• Java was originally developed at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform.
• Oracle database is a relational database management system.
• It is also called OracleDB, or simply Oracle.
• It is produced and marketed by Oracle Corporation.
• It was created in 1977 by Lawrence Ellison.

The correct answer is 1962.

Important Points

• The National TB Programme (NTP) was launched by the Government of India in 1962 in the form of the District TB Centre model involved with BCG vaccination and TB treatment.
• In 1978, BCG vaccination was shifted under the Expanded Programme on Immunisation.
• ‘National strategic plan for tuberculosis elimination 2017-2025’
• RNTCP has released a ‘National strategic plan for tuberculosis 2017-2025’ (NSP) for the control and elimination of TB in India by 2025.
• According to the NSP TB elimination has been integrated into the four strategic pillars of “Detect – Treat – Prevent – Build” (DTPB).

Additional Information

• Tuberculosis is caused by Mycobacterium Tuberculosis.
• It is a gram-positive aerobic bacteria.
• It belongs to the family Mycobacteriaceae.
• Tuberculosis is an upper respiratory tract infection.

The correct answer is Deendayal Antyodaya Yojana – National Rural Livelihoods Mission (DAY-NRLM).

• Deendayal Antyodaya Yojana – National Rural Livelihoods Mission (DAY-NRLM) under the Ministry of Rural Development aims to organize rural poor women into their own institutions like Self Help Groups and their associations, producers, collectives etc. and ensure their financial inclusion.
• Deendayal Antyodaya Yojana - National Rural Livelihoods Mission (DAY-NRLM) is a new name given to Livelihoods - NRLM in November 2015.
• An initiative to move towards a demand-driven strategy to enable states to formulate their own livelihood-based poverty reduction action plans is at the core of the mission.

Additional Information

• The National Rural Employment Guarantee Act 2005 or NREGA, later renamed as Mahatma Gandhi National Rural Employment Guarantee Act or MGNREGA in 2009, is Indian labour law and social security measure that aims to guarantee the 'right to work'.
• Beneficial Approach for Transformation of Agriculture and Allied Sector, earlier Rashtriya Krishi Vikas Yojana is a state plan scheme of additional central assistance, which was launched by the Government of India in August 2007 as a part of the 11^th Five Year Plan.
• NSAP stands for National Social Assistance Program.
• NSAP was launched on August 15, 1995.
• The National Social Assistance Program (NSAP) represents an important step toward the fulfilment of the Directive Principles in Articles 41 and 42 of the Constitution, recognizing the concurrent responsibility of the Central and State Governments in this matter.

The correct answer is 15000.

• The government has set an ambitious target of awarding contracts for 20,000 km and building 15,000 km of highways in FY21.

Key Points

• PM GatiShakti
• PM GatiShakti National Master Plan will encompass the seven engines for economic transformation, seamless multimodal connectivity and logistics efficiency.
• The seven engines include roads, railways, airports, ports, mass transport, waterways, and logistics infrastructure.
• To facilitate better movement of people and goods, The National Highways Network will be expanded by 25,000 km in FY23.
• 400 new gen Vande Bharat trains to be manufactured in the next 3 years.
• Railways will develop new products and logistic services for small farmers and MSMEs.
• ‘One Station- One Product’ concept will be promoted to help local businesses and supply chains built on a hub and spoke model.
• 2,000 km of the network to be brought under a new scheme, Kavach – for safety and capacity augmentation.

Additional Information

• Union Budget 2022-23:
• Growth estimates 
• 9.2 per cent expansion in GDP in FY22.
• 8−8.5 per cent projected GDP growth for FY23.
• Deficit 
• The Revised Fiscal Deficit in the current year is estimated at 6.9 per cent of GDP.
• The Fiscal Deficit in 2022-23 is estimated at 6.4 per cent of GDP.
• Infrastructure 
• PM Gati Shakti National Master Plan at a cost of ₹20,000 crores.
• 5G spectrum auctions are to be conducted in 2022.
• The scheme for design-led manufacturing for 5G will be part of the production-linked scheme.
• To award contracts to lay optical fibre in rural areas, completion in 2025.
• To allocate additional 195 billion rupees for production-linked incentives towards solar equipment manufacturing.

The correct answer is Hind Swaraj.

• Hind Swaraj or Indian Home Rule is a book written by Gandhiji in 1909.
• After the Jallianwala Bagh massacre and the death of Bal Gangadhar Tikal, Mahatma Gandhi announced the non-cooperation movement in August 1920.

Additional Information

• Gandhi was an Indian lawyer, anti-colonial nationalist, and political ethicist who employed nonviolent resistance to lead the successful campaign for India's independence from British rule.
• His birthday (2^nd October) is commemorated worldwide as International Day of Nonviolence.
• Books are written by Mahatma Gandhi:
• The Story of My Experiments with Truth (1927).
• Hind Swaraj (1909).
• India of my dreams (1947).
• Satyagraha in South Africa (1928).

Given:

x + $\frac{1}{x}$ = 6

Concept used:

$(A + {1 \over A})^2 = A^2 + {1 \over A}^2 + 2$

Calculation:

x + $\frac{1}{x}$ = 6

⇒ (x + $\frac{1}{x}$)² = 36 (Squaring both side)

⇒ x² + $1 \over x^2$ + 2 = 36

⇒ x2 + $1 \over x^2$ = 34

∴ The value of x2 + $\frac{1}{x^2}$ is 34.

Concept used:

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

Calculation:

Least Prime Natural number = 2

Least Composite Natural number = 4

HCF (2, 4) = 2

∴ The HCF of the least prime number and the least composite natural number is 2.

The correct answer is Karnataka.

Key Points

• Yakshagana is a traditional theatre form of Karnataka.
• It literally means the song of the yaksha.
• It developed in the Udupi district of Karnataka.
• It is believed to have originated between the 10^th and 16^th centuries.
• It is a temple art form that depicts mythological stories, Ramayana, Mahabharata, Bhagavata, and other Hindu epics.

Concept used:

Co-prime numbers are a set of numbers or integers which have only 1 as their common factor i.e. their highest common factor (HCF) will be 1.

Calculation:

Option 1:

14 = 2 × 7

21 = 3 × 7

Hence, 14 and 21 aren't co-prime.

Option 2:

6 = 2 × 3

35 = 5 × 7

Hence, 6 and 35 are co-prime. 

Since Option 2 suffices as the required answer, there is no need to check any further.

∴ 6 and 35 of the following pairs of numbers are co-prime.

According to the given statement :-

Assumption I: This is not implicit, because nothing about staff incompetent is mentioned in the statement.

Assumption II: This is not implicit, because nothing about hiring new staff to expand business is not mentioned in statement.

∴ Here, both the statements are not implicit so, Neither assumption I nor II is implicit.

Hence, the correct answer is "Neither assumption I nor II is implicit".

The correct answer is SAKSHAT.

Important Points

• The Ministry of Human Resource Development has designed an education portal which caters to the needs of students, starting from elementary students to research, scholars, teachers and lifelong learners.
• SAKSHAT is the name of the portal which was launched in the year 2006.
• It was launched by former President of India Dr APJ Abdul Kalam.
• It was developed by eGyanKosh of IGNOU.

The correct answer is Buddhist Circuit Tourist Train.

Key Points

• ​Buddhist circuit tourist train is the train recently started by the Indian Railways.
• It travels to Lumbini, Bodhgaya, Sarnath and Kushinagar.
• It links all the places associated with Budhha and Buddhism.
• The new chairman of the Railway board is Vinay Kumar Tripathi (1 Jan 2022–30 Jun 2022).

Additional Information

• Important Tourist trains:
• Vaishnodevi with Amritsar, Ex Silchar
• Destination: AMRITSAR / VAISHNO DEVI
• 07 Jyotirlinga Yatra
• Destination: BHIMSHANKAR / DWARKADHISH / GRISHNESHWAR / MAHAKALESHWAR / NAGESHWAR / OMKARESHWAR / PARLI VAIJANATH / SABARMATI JN / SOMNATH / STATUE OF UNITY / TRIAMBAKESHWAR
• Banglore Mysore with Dakshin Darshan Yatra
• Destination: BANGALORE / KANYAKUMARI / MADURAI / MYSORE / RAMESHWARAM / TIRUCHIRAPALLI / TIRUPATI / TRIVANDRUM
• Uttar Bharat Darshan With Mata Vaishno Devi
• Destination: AGRA / AMRITSAR / HARIDWAR / Mathura / VAISHNO DEVI
• Dakshin Bharat Tourist Trai
• Destination: Ayodhya / Haridwar / Mathura / Prayagraj / Rishikesh / Varanasi / Vrindavan
• Vaishnodevi with Uttar Bharat Darshan
• Destination: Ayodhya / Haridwar / Shivkhori / Vaishno Devi / Varanasi

The correct answer is ​Vienna.

Key Points

• The International Criminal Police Commission (ICPC), the predecessor to INTERPOL was founded in Vienna in 1923.
• The International Criminal Police Organisation (INTERPOL) is an international organization that facilitates worldwide police cooperation and crime control.
• Interpol uses communication and databases to track criminals across international borders.
• Headquarters of INTERPOL - Lyon, France.
• It was founded in 1923 as the International Criminal Police Commission (ICPC).
• India joined the organization in 1949 and is one of its oldest members.

Concept used:

Total = Mean (Average) × number of entities

Calculation:

The first twelve prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.

Hence, the mean = Sum (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37) ÷ 12

⇒ 197/12

⇒ 16.4166 ≈  16.42

∴ The mean of the first twelve prime numbers is 16.42.

Calculation:

Share of Model C and D = 75% - 45% = 30%

Share of Model F = 100% - 90% = 10%

Total share of Mode C, D and F = 30 + 10 = 40%

Hence, total number of mobile phones produced of models C, D and F in 2008 = 450000 × 40% = 1,80,000

∴ The total number of mobile phones produced of models C, D and F in 2008 is 1,80,000.