RRB NTPC CBT-I Official Paper (Held On: 8 Jan 2021 Shift 2) (Previous Year Paper)

Given:

$\cos x=\frac{-1}{2}$ where $π<x<\frac{3π}{2}$ 

Formula used:

cos(π + x) = - cos x    ∵ [$π<x<\frac{3π}{2}$]

Calculation:

cos x = - 1/2 

⇒ cos x = cos(π + π/3) 

⇒ x = 4π/3 

4 tan2x - 3 cosec2x 

⇒ 4 × (√3)² - 3 × (- 2/√3)²

⇒ 4 × 3 - 3 × 4/3 

⇒ 12 - 4 

⇒ 8 

∴ The required value is 8.

Mistake PointsThe value of tan and cot is positive in the third quadrant.

​The correct answer is Awadh.

Key Points

• Awadh was called the “nursery of the Bengal army".
• Awadh known in British historical texts as Avadh or Oudh is a region and proposed state in the modern Indian state of Uttar Pradesh.
• The changes that the families of the sepoys saw around them and the threats they perceived were quickly transmitted to the sepoy lines.
• The large majority of the sepoys of the Bengal Army were recruited from the villages of Awadh and eastern Uttar Pradesh. Many of them were Brahmins or from the “upper” castes. Awadh was, in fact, called the “nursery of the Bengal Army’’.

Additional Information

• Some following facts, Awadh was called “nursery of the Bengal army":-
• The Bengal Army of the East India Company was mainly recruited from high castes living in Bengal, Bihar, and the Awadh.
• The sepoys were Indian soldiers who were recruited into the Company's army just before the rebellion of 1857.
• The Bengal Army recruited higher castes, such as Brahmins, Rajputs, and Bhumihar, mostly from the Awadh and Bihar regions, and even restricted the enlistment of lower castes in 1855. A practice that continued for the next 75 years.

Given:

6(sec2 59° - cot2 31°] + 2/3 × sin 90° - 3 × tan2 56° × y × tan2 34° = y/3

Formulas used:

cosec(90°- A) = sec A

tan(90° - A) = cot A

cosec2A- cot2 A = 1

Calculation:

6(sec2 59° - cot2 31°] + 2/3 × sin 90° - 3 × tan2 56° × y × tan2 34° = y/3

⇒ 6[sec²(90°- 31°) - cot² 31°] + 2/3 × 1 - 3 × tan²(90°- 34°) × y × tan234° = y/3

⇒ 6[cosec²31°- cot2 31°] + 2/3 - 3 × cot²34°× y × tan234° = y/3

⇒ 6 × 1 + 2/3 - 3 × 1/tan234°× tan234° × y = y/3

⇒ 6 + 2/3 - 3y = y/3

⇒ 20/3 = y/3 + 3y

⇒ 20/3 = 10y/3

⇒ 20 = 10y

∴ y = 2

​The correct answer is Carbon dioxide.

Key Points

• Carbon dioxide gas is needed for photosynthesis.
• The raw materials required for photosynthesis are carbon dioxide, water, and sunlight primarily.
• Plants take in carbon dioxide (CO2) and water (H2O) from the air and soil during photosynthesis.
• During photosynthesis in the plant cell, the water is oxidized, meaning it loses electrons, while the carbon dioxide is reduced, meaning it gains electrons.
• This transforms the water into oxygen and the carbon dioxide into glucose. The plant then releases the oxygen back into the air, and stores energy within the glucose molecules.

Additional Information 

Given:

Time taken by A to do a work = 10 days 

Time taken by B to do the same work = 15 days 

Time taken by A, B and C do the same work = 5 days

Amount of earning = Rs.4800 

Formula used:

Ratio of shares of A, B and C = Ratio of their Efficiency

Calculation:

Let total work be = 1 unit

One day work done by A = 1/10 

One day work done by B = 1/15 

One day work done by A, B and C = 1/5 

⇒ One day work done by C = 1/5 - (1/10 - 1/15) 

⇒ 1/30

Ratio of shares of A, B and C = Ratio of their one-day work efficiency 

⇒ A : B : C = 1/10 : 1/15 : 1: 30 

⇒ A : B : C = 3 : 2 : 1 

∴ C's share in earning = Rs.4800 × 1/6 

⇒ Rs.800

Shortcut Trick

Side (s) = 10 cm and half of longest diagonal = 16 ÷ 2 = 8 cm.

In a rhombus, diagonals bisect at 90°, forming right triangles with the side as hypotenuse.

Using Pythagorean triplet (6, 8, 10), the half of the other diagonal = 6 cm.

Length of second diagonal (d₂) = 6 × 2 = 12 cm.

Area of rhombus = 1/2 × d₁ × d₂ = 1/2 × 16 × 12 = 96 cm².

∴ The correct answer is 96 cm².

Alternate Method

Given:

Side (s) = 10 cm

Diagonal 1 (d₁) = 16 cm

Formula Used:

Area of Rhombus = 1/2 × d₁ × d₂

Relation between side and diagonals: s² = (d₁/2)² + (d₂/2)²

Side = 10 cm 8 cm 6 cm d1 = 16 cm | d2 = 12 cm

Calculations:

⇒ (d₁/2) = 16 ÷ 2 = 8 cm

⇒ s² = (d₁/2)² + (d₂/2)²

⇒ 10² = 8² + (d₂/2)²

⇒ 100 = 64 + (d₂/2)²

⇒ (d₂/2)² = 100 − 64 = 36

⇒ d₂/2 = √36 = 6 cm

⇒ d₂ = 6 × 2 = 12 cm

⇒ Area = 1/2 × 16 × 12

⇒ Area = 8 × 12 = 96 cm²

∴ The correct answer is 96 cm².

Additional Information

Properties of a Rhombus

All sides are equal in length and opposite sides are parallel. Diagonals bisect each other at right angles (90°).

Perimeter of a Rhombus

The perimeter is calculated as 4 × side. For this question, Perimeter = 4 × 10 = 40 cm.

Area using Trigonometry

Area can also be calculated as s² × sin(θ), where θ is any internal angle of the rhombus.

Pythagorean Relation

The sum of squares of the diagonals is equal to four times the square of the side: d₁² + d₂² = 4s².

Given:

Compound Interest on a sum for 2 years at 11% p.a. = Rs.4642

Formulas used:

Compound Interest + Principal = Amount 

⇒ Amount = Principal × (1 + R/100)ⁿ

Simple Interest = Principal × Rate/100 × Time 

Calculation:

4642 + P = P × (1 + 11/100)²

⇒ 4642 = P × 111/100 × 111/100 - P 

⇒ 4642 = P(111/100 × 111/100 - 1)

⇒ 4642 = P(12321 - 10000)/10000

⇒ 4642 = P × 2321/10000 

⇒ P = 4642 × 10000/2321 

⇒ P = Rs.20000

∴ Simple Interest = 20000 × 11/100 × 2 = Rs.4400

Alternate Method Percentage MethodCompound interest and simple interest both are calculated on Principal. Effective rate percent of compound interest for 2 years = R + R + (R × R)/100 

⇒ 11 + 11 + (11 × 11)/100 

⇒ 22 + 1.21 = 23.21% 

Simple interest rate percent for 2 years = Rate % × Time = 11% × 2 = 22% 

23.21% of Principal = Rs.4642 

⇒ 22% of Principal = Rs.4642 × 22%/23.21% = Rs.4400 

∴ The simple interest is Rs.4400.

​The correct answer is F2.

Key Points

• The function key in Excel helps to switch to edit mode, that is F2.
• The function key F2 allows to quickly and easily edit the data of a cell by activating Excel's edit mode and placing the insertion point at the end of the active cell's existing contents.
• Pressing the F2 key puts the cell in Excel's edit mode. If the cell contains a formula, We will see the formula in the cell and be able to edit it.
• Use the mouse to click the formula bar at the top of the window. The cell activates, and it switches to editing mode. We also double-click the cell to activate editing mode, or we can press the "F2" key.

Additional Information

​The correct answer is Jineth Bedoya Lima.

Key Points

• 2020, UNESCO/Guillermo Cano Press Freedom Prize has been awarded to Jineth Bedoya Lima.
• Colombian investigative journalist Jineth Bedoya Lima has been named as the laureate of the 2020 UNESCO/Guillermo Cano World Press Freedom Prize on the recommendation of an independent international jury of media professionals.
• Jineth Bedoya Lima was born in 1974.
• Lima's reporting has focused on the armed conflict and peace process in Colombia and on sexual violence against women. Ms Bedoya Lima was herself a victim of sexual violence in 2000.
• The UNESCO/Guillermo Cano World Press Freedom Prize is awarded annually on the occasion of World Press Freedom Day, celebrated on 3 May.
• The $25,000 Prize recognizes a person, organization, or institution that has made an outstanding contribution to the defence or promotion of press freedom, especially in the face of danger.
• Bedoya’s work, activism, and bravery have seen her receive many awards, including the CJFE International Press Freedom Award in 2000, the Courage in Journalism Award of the International Women’s Media Foundation in 2001, and the International Women of Courage Award in 2012.

Additional Information

​The correct answer is Vinaya Pitaka.

Key Points

• The Buddhist text that comprises rules for monks is Vinaya Pitaka.
• Vinaya Pitaka is the oldest and smallest of the three sections of the Buddhist canonical Tipitaka (“Triple Basket”) and the one that regulates monastic life and the daily affairs of monks and nuns according to rules attributed to the Buddha.
• Vinaya Pitaka is the first of the Tripitaka and it contains all the disciplinary rules of ecclesiastical acts and duties formulated by the Buddha himself for the conduct and guidance of monks and nuns.
• It consists of five books: Parajika, Pachittiya, Mahavagga, Chullavagga, and Parivara.
• Vinaya Pitaka tells that there were separate wings for both men and women in Buddhist Sangha. It tells how to behave with each other and within the society. In Vinaya Pitaka, all the rules for Buddhist Sangha were written down.

Additional Information

​The correct answer is Amphan.

Key Points

• The cyclone that hit Odisha and West Bengal in May 2020 is "Amphan".
• The super cyclonic storm Amphan got this name from Thailand, The word 'Amphan' is pronounced as 'Um-pun' which means sky.
• Amphan originated from a low-pressure area persisting a couple of hundred miles (300 km) east of Colombo, Sri Lanka, on 13 May 2020.
• On 20 May 2020, Cyclone Amphan cut a swathe through the northern part of the Indian state of Odisha, before bearing down on the state of West Bengal, with a wind speed of 185 kilometres per hour.
• Coastal areas in West Bengal comprising East Midnapore, North 24 Parganas, South 24 Parganas, Kolkata, Hooghly, and Howrah as well as Odisha were affected by the cyclone. It also caused significant destruction in Bangladesh.

Additional Information

​The correct answer is Imprisonment without trial.

Key Points

• Imprisonment without trial was one of the measures taken by the British government under the Rowlatt Act.
• This law was passed in March 1919 by the Imperial Legislative Council.
• The Rowlatt Act is also known as the Anarchical and Revolutionary Crimes Act of 1919.
• Rowlatt Satyagraha was started by Mahatma Gandhi in response to the British government enacting the Rowlatt Act.

Important Points

• The Rowlatt Commission was appointed by the British Government in 1918.
• It caused a wave of anger in all sections spreading a country-wide agitation by Gandhiji and marking the foundation of the Non-Cooperation Movement.
• Lord Chelmsford was the Viceroy when the Rowlatt Act was passed.

Given:

Mean of a, b, c, d, e and f = 36

Mean b, d and f = 28

Formula used:

Mean = Sum of observations/No of observations 

Calculation:

Sum of a, b, c, d, e and f = 36 × 6 = 216

Sum of b, d and f = 28 × 3 = 84 

Sum of a, c and e = Sum(a, b, c, d, e, f) - Sum(b, d, f) 

⇒ 216 - 84 = 132

∴ Mean of a, c and e = 132/3 = 44

The correct answer is Apurvi Chandela.

Key Points

• Apurvi Chandela became the world number one in women’s 10m Air Rifle category in the 2019 ISSF World Cup.
• She is an Indian athlete who competes in the event of 10-metre air rifle sport shooting.
• She belongs to Rajasthan state.
• She was awarded the Arjuna awards 2016.
• Her Achievements:
• 2019 ISSF World Cup - Gold
• 2014 Commonwealth Games - Gold
• 2015 World Cup Final - Silver
• She will be representing India again at the 2021 Tokyo Olympics.

Additional Information

• Shooting:
• It is an important Olympic sport in India.
• Some of the most prominent Indian shooters include Abhinav Bindra, Jitu Rai, Rajyavardhan Singh Rathore, Vijay Kumar, Apurvi Chandela, Anjali Bhagwat, and many others.
• Chandro Tomar and Prakashi Tomar are the oldest and second oldest most acclaimed international female veteran shooters from India.

The logic is:

4 × 2 + 8 = 8 + 8 = 16

16 × 2 + 8 = 32 + 8 = 40

40 × 2 + 8 = 80 + 8 = 88

Hence, ‘88’ is the correct answer.

Given:

Ratio of the votes cast for two candidates = 2 : 9 

The successful candidate received 984321 votes

Calculation:

The successful candidate gets more votes than the loser candidates. 

⇒ Let the votes cast for two candidates were 2a and 9a respectively      

9a = 984321     [∵ 2a < 2b]

⇒ a = 984321/9 = 109369

∴ Total votes polled = 2a + 9a = 11a 

⇒ 11a = 11 × 109369 = 1203059

Shortcut Trick9 = 984321 

⇒ 1 = 109369

∴ 2 + 9 = 11 = 1×11 = 109369 × 11 = 1203059

Shortcut Trick

Side of the square = √4900 = 70 m, which is also the radius of the circle.

Length of the rectangle = 3/5 × radius = 3/5 × 70 = 42 m.

Area of the rectangle = Length × Breadth = 42 × 20 = 840 m².

∴ The correct answer is 840 m².

Alternate Method

Given:

Area of the square = 4900 m²

Radius of circle = Side of the square

Length of rectangle (L) = 3/5 × Radius of circle

Breadth of rectangle (B) = 20 m

Formula Used:

Area of square = a² (where a is side length)

Area of rectangle = L × B

Calculations:

⇒ a² = 4900

⇒ a = √4900 = 70 m

⇒ Radius of the circle (r) = 70 m

⇒ Length of the rectangle (L) = 3/5 × 70 = 3 × 14 = 42 m

⇒ Area of the rectangle = L × B

⇒ Area of the rectangle = 42 × 20 = 840 m²

∴ The correct answer is 840 m².

Additional Information

Square Properties

A square has all four equal sides. Its Area = a² and Perimeter = 4a (where a is side length).

Circle Properties

The Area of a circle = πr² and its Circumference = 2πr (where r is the radius).

Rectangle Properties

A rectangle has opposite equal sides. Its Area = Length × Breadth and Perimeter = 2 × (Length + Breadth).

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

Clearly, Rahul is Son of Radha.

Hence, ‘Son’ is the correct answer.

Given:

Length of side of a square increases by 10%

Formula used:

Area of square = (Side)²

Calculation:

Let the side of square be = 10 units 

Area of the old square = 10 × 10 = 100 sq. units 

⇒ Increased side of the square = 10 × 110/100 = 11 units 

Area of the new square = 11 × 11 = 121 sq. units 

Percentage increase of area = (New Area - Old Area)/Old Area × 100 

∴ The required increase in the area = (121 - 100)/100 = 21/100 × 100 = 21% 

Alternate MethodEffective rate of increase = 10% + 10% + (10% × 10%)/100 

⇒ 20% + 1% = 21%

​The correct answer is Sevasadan.

Key Points

• Seva Sadan has been written by Munshi Premchand.
• In 1919, Premchand's first major novel Seva Sadan was published in Hindi.
• The novel was originally written in Urdu under the title Bazaar-e-Husn but was published in Hindi first by the name Sevasadan a Calcutta-based publisher.
• An English translation of this book was released by Oxford University Press, India in New Delhi in 2005.
• Sewasadan deals with poor conditions of women in society, child marriage, and dowry. It tells us about the Indian upper class and the opportunities they got from the British government. The novel was a shift from fantasy to a serious reflection of life.
• Dhanpat Rai was born on 31 July 1880 near Varanasi (Benares), his pen name is Premchand.
• He is one of the most celebrated writers of the Indian subcontinent, His works include more than a dozen novels, around 300 short stories, several essays, and translations of a number of foreign literary works into Hindi.

Additional Information

The logic is:

paper : stapler → A stapler is a mechanical device used for joining papers together.

Similarly,

clothes : ? → Hanger is a shaped piece of wood, plastic, or metal with a hook at the top, from which clothes may be hung in order to keep them in shape.

Hence, ‘Hanger’ is the correct answer.

Given:

Sum of square of two positive numbers = 2437 

Square root of one number = 7 

Formula used:

√a = b 

⇒ a = b²

Calculation:

Let the two numbers be a and b respectively. 

a² + b² = 2437 

√a = 7 

⇒ a = 7² = 49  

49² + b² = 2437 

⇒ b² = 2437 - 2401 = 36

⇒ b = √36 = ± 6 

∴ The other number is + 6.

Given:

Principal of Rs.8000 borrowed for 3 years at 5% p.a. and the same sum was lent at 7% p.a. for the same time. 

Formula used:

Simple Interest = (P × R × T)/100 

Calculation:

Simple Interest paid by Ramesh = 8000 × (5/100) × 3 = Rs.1200 

Simple Interest earned by Ramesh = 8000 × (7/100) × 3 = Rs.1680

∴ Gain earned by Ramesh = Interest earned - Interest paid 

⇒ 1680 - 1200 = Rs.480

Alternate MethodTotal interest percent = R% × T

Total interest percent to be paid = 5% × 3 = 15%

Total interest percent to be earned = 7% × 3 = 21% 

Ramesh's gain = 21% - 15% = 6% 

∴ Gain in Rs. = 8000 × 6/100 = Rs.480

​Given:

Distance covered = 400 km 

Formula used:

Time = Distance/Speed 

Calculation:

Let the speed of the train be = a km/h 

As per the question; 

400/a - 400/(a + 10) = 2 

⇒ 1/a - 1/(a + 10) = 2/400 

⇒ (a + 10 - a)/a(a + 10) = 1/200

⇒ 10/a(a + 10) = 1/200

⇒ a² + 10a = 2000 

⇒ a2 + 10a - 2000 = 0

⇒ a2 + 50a - 40a - 2000 = 0

⇒ a(a + 50) - 40(a + 50) = 0

⇒ (a - 40)(a + 50) = 0

⇒ a = 40, a ≠ - 50

∴ The speed of the train is 40 km/h.

Alternate MethodBy Value Putting Method;

By using the following equation. 

⇒ 400/a - 400/(a + 10) = 2 

Option 1: For a = 40, 400/40 - 400/(40 + 10) = 2 

Option 2: For a = 50, 400/50 - 400/(50 + 10) ≠  2

Option 3: For a = 55, 400/55 - 400/(55 + 10) ≠  2

Option 4: For a = 45, 400/45 - 400/(45 + 10) ≠  2

​The correct answer is Bachpan Bachao Andolan.

Key Points

• Nobel Laureate, Kailash Satyarthi is associated with the "Bachpan Bachao Andolan" organization.
• Kailash Satyarthi was born in the Vidisha district of Madhya Pradesh in India. After completing an electrical engineering degree, he worked as a teacher in the area. In 1980, he left teaching and founded the organization Bachpan Bachao Andolan.
• He has freed thousands of children from slave-like conditions. He has also been active in a wide range of other organizations working against child labor and for children's rights to education.
• He is the founder of multiple social activist organizations, including Bachpan Bachao Andolan, Global March Against Child Labour, Global Campaign for Education, and Kailash Satyarthi Children's Foundation.
• He has also contributed to the development of international conventions on the rights of children.

Additional Information

​The correct answer is Kolkata Metro.

Key Points

• The recently added 17th zone of the Indian Railway is Kolkata Metro.
• The Metro Railway of Kolkata, the country's oldest, Kolkata Metro has given December 29, 2010, became the 17th independent zone of the Indian Railways.
• "The making of Kolkata Metro as an independent zone was notified by the Railway Board on December 29, 2010.
• Railway Minister Mamata Banerjee announced that a Rs 10,000 crore project has been taken up for its expansion and infrastructure development.

Additional Information 

​The correct answer is Poverty.

Key Points

• A cause for the Migration of unskilled workers in poverty.
• The unskilled workers migrate searching for ways to provide for their families and to escape unemployment, war, or poverty in their countries of origin.
• The Indian Census (2011) data calculated the total number of internal migrants accounting for inter and intra-state movement to be 450 million, an increase of 45% since the Census 2001 (De, 2019).
• Uttar Pradesh (UP), Bihar, Madhya Pradesh (MP), Rajasthan are among the major origin states of migration in India.
• Delhi, Kerala, Maharashtra, Gujarat, and Tamil Nadu are among the important destination states for these migrant workers.

Additional Information

• International Labour Organization brings together governments, employers and workers of 187 member States, to set labour standards, develop policies and devise programmes promoting decent work for all women and men.
• ILO was established in 1919 by the Treaty of Versailles as an affiliated agency of the League of Nations.
• Its headquarters are in Geneva, Switzerland.
• The President/ Director-General of ILO as of October 2021 is ‎Mr Guy Ryder.

Given:

The ratio of male and female members = 4 : 5

Increase the percentage of males = 80%

Increase the percentage of females = 60%

Calculation:

Let the number of males and females be 40 and 50 respectively. 

New number of males = 40 × 180/100 = 72

New number of females = 50 × 160/100 = 80

∴ The new ratio of males to females = 72 : 80 = 9 : 10

Shortcut Trick

Efficiency ratio of A : B = 5 : 1 → Time ratio of A : B = 1 : 5.

Time difference = 5 − 1 = 4 units → 4 units = 60 days, so 1 unit = 15 days.

Time taken by A = 15 days, Time taken by B = 75 days.

Total work = LCM(15, 75) = 75 units.

Time taken together = Total Work ÷ Total Efficiency = 75 ÷ 6 = 12.5 days.

∴ The correct answer is 12½ days.

Alternate Method

Given:

A is 5 times as efficient as B.

A takes 60 days less than B to complete the job.

Calculations:

⇒ Efficiency is inversely proportional to the time taken.

⇒ Ratio of efficiencies A : B = 5 : 1

⇒ Ratio of time taken A : B = 1 : 5

⇒ Difference in ratio parts = 5 − 1 = 4 parts

⇒ 4 parts = 60 days ⇒ 1 part = 15 days

⇒ Time taken by A = 1 × 15 = 15 days

⇒ Time taken by B = 5 × 15 = 75 days

⇒ Combined efficiency of A and B = 5 + 1 = 6 units/day

⇒ Time taken working together = Total Work ÷ Combined Efficiency

⇒ Time taken = 75 ÷ 6 = 25/2 = 12.5 days = 12½ days

∴ The correct answer is 12½ days.

Additional Information

Efficiency & Time Relationship

Efficiency and time are strictly inversely proportional to each other. If the efficiency ratio of two workers is x : y, the ratio of the time taken by them to complete the same work will be y : x.

Total Work Formula

Total Work = Efficiency × Time Taken. To find the combined time taken by multiple workers, simply divide the total work by the sum of their individual efficiencies.

Alternate Day Work Concept

When workers work on alternate days, calculate the total work done in one complete cycle (e.g., 2 days for two workers) and scale it near to the total work before manually adding the remaining units.

​The correct answer is 129.

Key Points

• India’s Rank in Human Development Index, 2019 is 129.
• Human Development Index, 2019 report said- India, Bhutan (129), Bangladesh (133), Nepal (142), and Pakistan (154) were ranked among countries with medium human development.
• Norway topped the index, while Niger is ranked last at 189.
• India's HDI value for 2019 is 0.645 which puts it in the medium human development category.
• India's Human Development Index or HDI position has marginally dropped after improving last year (2019). In the latest HDI ranking in 2020, India stands at 131. Last year India's ranking was 129.
• The life expectancy of Indians at birth in 2019 was 69.7 years while Bangladesh has a life expectancy of 72.6 years and Pakistan 67.3 years,

Additional Information

• Human Development Index is the measure of a nation's health, education, and standards of living.
• Countries ranked from 1 to 66 in the year 2019 are considered to be of very high HDI, ranked 67 to 119 are considered to be of high HDI, ranked 120 to 156 are considered to be of medium HDI and ranked 157 to 189 are considered to be of low HDI.
• The Human Development Report also reports the HDI for various groups of countries. These include regional groupings based on the UNDP regional classifications, HDI groups including the countries currently falling into a given HDI bracket, OECD members, and various other UN groupings.
• In 2020, the UNDP introduced another index, the planetary pressures–adjusted HDI (PHDI), which decreases the scores of countries with a higher ecological footprint.

​The correct answer is Millie Bobby Brown.

Key Points

• The youngest-ever UNICEF Goodwill Ambassador is Millie Bobby Brown.
• Emmy Award-nominated actress Millie Bobby Brown has been announced as UNICEF's newest Goodwill Ambassador on 20 November 2018 in New York.
• The appointment marked on World Children’s Day at United Nations Headquarters and the Empire State Building in New York makes the 14-year-old UNICEF’s youngest-ever Goodwill Ambassador.
• The British star will use her global platform to help raise awareness of children’s rights and issues affecting youth, such as lack of education, safe places to play and learn, and the impact of violence, bullying, and poverty.
• Millie Bobby Brown was born in Marbella, Spain, on 19 February 2004, She is a British actress and model.

Additional Information

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘ZBN - EHU’ is the odd one out.

​The correct answer is Hampi.

Key Points

• The Heritage site that has the Dravidian style of architecture is Hampi.
• Hampi also referred to as the Group of Monuments at Hampi, is a UNESCO World Heritage Site located in Karnataka.
• The ruins at Hampi are a collection of heritage sites depicting the fine Dravidian style of art and architecture.
• The Virupaksha Temple is the most important heritage monument on this site, which continues to be a very important religious center for the Hindus.
• The Dravida style of architecture is an architectural idiom that emerged in the southern part of the Indian subcontinent or South India,
• The temples under the Dravida style were constructed in five different shapes such as square-shaped, rectangular-shaped, major circular, circular, and octagonal-shaped.
• Brihadishvara Temple, also called Rajarajesvaram or Peruvudaiyar Koyil, is dedicated to Shiva located in Thanjavur, Tamil Nadu, It is one of the largest South Indian temples and the Chennakesava Temple in Belur, Hoysaleswara temple in Halebidu, and the Kesava Temple in Somanathapura, etc an exemplary example of a fully realized Dravidian architecture.

Additional Information

Given:

Smallest six-digit number which is divisible by 4, 8, 12 and 16.

Concept:

LCM (Lowest Common Multiple)

Dividend = Divisor × Quotient + Remainder 

Calculation:

LCM of 4, 8, 12 & 16 will be calculated by writing them as the product of their prime factors. 

4 = 2²

8 = 2³

12 = 2² × 3 

16 = 2⁴

So, LCM (4, 8, 12, 16) = 2⁴ × 3 = 48 

The smallest six-digit number is 100000.

By dividing 100000 by 48, we get the remainder 16. 

So, we need to add the difference between the Divisor and Remainder to 100000 (Dividend) in order to get the smallest six-digit number divisible by 48.

⇒ 100000 + (48 - 16) = 48 × 2083 + 16 + (48 - 16) 

⇒ 100032 =  48 × 2083 + 16 + 32 

⇒ 100032 =  48 × 2083 + 48 

⇒ 100032 =  48 × 2083 + 48 

∴ The smallest six-digit number which is completely divisible by 4, 8, 12 and 16 is 100032.

Given:

Data related to accidents took place from 2000 to 2015 has been given in city A, B and C. 

Calculation:

Number of accidents took place in city A from the year 2000 to 2015 = 400 + 600 + 500 + 550 = 2050

Number of accidents took place in city B from the year 2000 to 2015 = 600 + 550 + 350 + 300 = 1800

Number of accidents took place in city C from the year 2000 to 2015 = 450 + 550 + 650 + 450 = 2100

City B has the lowest number of accidents from 2000 to 2015. 

∴ City B can be said to have controlled accidents most effectively.

Given:

$\sqrt{2116\times\sqrt{48\div x}}=92$

Formula used:

√a = b 

⇒ a = b²

Calculation:

$\sqrt{2116\times\sqrt{48\div x}}=92$

By squaring both sides; 

⇒ 2116 × √(48 ÷ x) = 92²

⇒ 2116 × √(48 ÷ x) = 8464 

⇒√48 ÷ x  = 8464/2116  

⇒ √(48 ÷ x)  = 4

⇒ 48/x = 4²

⇒ 48/x = 16

⇒ x = 48/16

∴  x = 3

Alternate MethodBy Value Putting Method

Option 1: For x = 12;   √(2116 × √48 ÷ 12) ≠ 92

Option 2: For x = 3; √(2116 × √48 ÷ 3) = 92

Option 3: For x = 2;  √(2116 × √48 ÷ 2) ≠ 92

Option 4: For x = 6; √(2116 × √48 ÷ 6) ≠ 92

​The correct answer is Punjab.

Key Points

• In India, Punjab has the biggest consumption of fertilizer (in Kg Per hectare).
• Punjab state alone consumes about 9 per cent of the total fertilizers in India and the use is the highest on a per unit area basis at 190.1 kg/ha of the gross cropped area against 88.2 kg/ha in all India.
• The per-hectare consumption is more than 100 kg in Punjab (190 kg), Haryana (167 kg), Andhra Pradesh (138 kg), Uttar Pradesh, and Uttaranchal (127 kg), West Bengal (122 kg),  and Tamil Nadu (112 kg).
• In the remaining states, the consumption per hectare is lower than the all-India average.
• The uses of major nutrients (N+P+K) went up from just 65.3 thousand tonnes in triennium ending (TE) 1968 to 1463.7 thousand tonnes in TE 2004. The use of K in Punjab soils is not high because soils are rich in K-illicit minerals.

Additional Information

Given:

The data for 2020 follows the trend similar to that of 2015

Calculation:

No of accidents in city A in 2020 = 550

No of accidents in city B in 2020 = 300

No of accidents in city C in 2020 = 500

No of accidents in city D in 2020 = 400 

∴ City A is most likely to have a higher number of accidents.

Given:

 x4 + x-4 = 1154

Formula used:

(a + b)² = a² + b² + 2ab 

Calculation:

x4 + 1/x4 = 1154        (1) 

By adding 2 on both sides in equation (1)

⇒ x4 + 1/x4 + 2 = 1154 + 2  

⇒ (x² + 1/x²)² = 1156

⇒ (x2 + 1/x2) = √1156 = 34       (2)

By adding 2 on both sides in equation (2) 

⇒ (x2 + 1/x2 + 2) = 34 + 2 

⇒ (x + 1/x)² = 36

⇒ (x + 1/x) = √36 = 6

∴  x + x-1 = 6

The correct answer is Chandrashekhar Azad.

Key Points

• Indian revolutionary Chandrashekhar Azad set up a base near Satar river in Jhansi in the 1920s using the alias, Pandit Harishankar Brahmachari.
• Chandrashekhar Azad was born at Bhabra village in Madhya Pradesh on 23^rd July 1906.
• Bhavra also known as Bhabhra or Chandra Shekhar Azad Nagar is a town and a nagar panchayat in Alirajpur district in the state of Madhya Pradesh, where Azad reportedly lived incognito in the guise of a Sanyasi.
• Azad was involved in the 1925 Kakori Conspiracy wherein a train was robbed by Hindustan Republican Association (HRA).
• On 27 February 1931, Azad was killed in a gun battle with two police officers at Allahabad's Alfred Park.

Additional Information

​The correct answer is Bajirao.

Key Points

• In May 2019, the last captive White tiger of Mumbai died. The name of the tiger is Bajirao.
• The last captive white tiger inside Sanjay Gandhi National Park (SGNP) died of age-related complications. The animal was 18 years old.
• Bajirao was the eldest male in their enclosure.
• Bajirao’s carcass was burnt after the autopsy as per National Tiger Conservation Authority guidelines. There are six remaining Royal Bengal tigers at the park– four female and two male, all above 10 years of age.

Additional Information

• Bajirao was born in SGNP in 2001 to tigress Renuka and tiger Siddharth, both white tigers brought from Aurangabad Zoo in 1999.
• An expert advisory committee, comprising of senior veterinarians, both current and retired from SGNP and the Bombay Veterinary College (BVC), had been monitoring Bajirao’s health over the past four years.
• The tiger’s autopsy carried out by the pathology department of BVC indicated multiple organ failures along with old age as the probable cause of death. “The post mortem findings were suggestive of lesions (rotting or putrefied tissues) in visceral organs such as the kidney, heart, and liver,”

​The correct answer is Lakshwadeep.

Key Points

• CSIR scientists have conducted a genetic study for the first time in Lakshwadeep, India.
• A team of researchers led by K Thangaraj at the Council of Scientific and Industrial Research (CSIR)-Centre for Cellular and Molecular Biology, Hyderabad have performed a genetic study on the Lakshadweep islanders.
• The genetic study on the Lakshadweep islanders for the first time and the results have been published in scientific reports on 6 May 2019.
• Centre for Cellular and Molecular Biology (CCMB), Hyderabad the first time has shown that a majority of human ancestry in Lakshadweep is largely derived from South Asia with minor influences from East and West Eurasia. And, there was no evidence of early human migration through the Lakshadweep islands.
• The authors have studied the major islands of Agatti, Andorth, Bitra, Chetlat, Kadmat, Kalpeni, Kiltan, and Minicoy of Lakshadweep and demonstrated a close genetic link of Lakshadweep islanders with people from the Maldives, Sri Lanka, and India.

Additional Information

• Lakshadweep is an archipelago of 36 islands, scattered over approximately 78,000 square km of the Arabian Sea, 200-440 km off the south-western coast of India, with a population of approximately 65,000.
• ‘Lakshadweep’ in Malayalam language and in Sanskrit means “Hundred Thousand Islands”.
• DNA samples of 557 individuals from eight major islands for mitochondrial DNA and 166 individuals for Y chromosome markers were analyzed.
• The authors found a close genetic link of Lakshadweep islanders with people from the Maldives, Sri Lanka, and India. However, it did not find any evidence of early human migration through the Lakshadweep islands.

​The correct answer is Khilafat Movement.

Key Points

• Another movement that was combined with the non-cooperation movement in 1920 was Khilafat Movement.
• The Khilafat Movement was launched by Muhammad Ali and Shaukat Ali.
• The movement finally collapsed when Ataturk abolished the caliphate altogether in 1924.
• Two mass movements that were organized in 1919-1922 to oppose the British rule in India were the Khilafat movement and Non-Cooperation Movement.
• The movements, despite having different issues, adopted a unified plan of action of non-violence and non-cooperation.
• In September 1920, at a special session in Calcutta, Congress approved a non-cooperation program till the Punjab and Khilafat wrongs were removed and swaraj was established.
• In December 1920, at the Nagpur session of the Indian National Congress, the program of non-cooperation was endorsed.

Additional Information

The logic is:

Figure 1: (8 + 4 + 2 + 12) ÷ 2 = 26 ÷ 2 = 13

Figure 2: (16 + 8 + 4 + 24) = 52 ÷ 2 = 26

Similarly, 

Let the missing number be a.

Figure 3: (14 + a + 2 + 22) ÷ 2 = 22

⇒ 38 + a = 22 × 2

⇒ 38 + a = 44

⇒ a = 44 - 38

⇒ a = 6

Hence, ‘6’ is the correct answer.

Shortcut Trick

Required numbers must be exactly divisible by the LCM of 6, 12, and 16, which is 48.

Multiples of 48 between 400 and 600 are 48 × 9, 48 × 10, 48 × 11, and 48 × 12.

Required Sum = 48 × (9 + 10 + 11 + 12)

Required Sum = 48 × 42 = 2016

∴ The correct answer is 2016.

Alternate Method

Given:

Divisors = 6, 12, and 16

Range = Numbers strictly between 400 and 600

Concept Used:

A number is exactly divisible by a set of given numbers if it is a multiple of their Least Common Multiple (LCM).

Calculations:

⇒ Prime factorization of 6 = 2 × 3

⇒ Prime factorization of 12 = 2² × 3

⇒ Prime factorization of 16 = 2⁴

⇒ LCM(6, 12, 16) = 2⁴ × 3 = 16 × 3 = 48

⇒ We need to find all multiples of 48 that lie between 400 and 600.

⇒ Dividing 400 by 48, we get a quotient of 8.

⇒ The first multiple greater than 400 = 48 × 9 = 432

⇒ The maximum multiple less than 600 = 48 × 12 = 576

⇒ The valid numbers are: 432, 480, 528, 576

⇒ Sum of these numbers = 432 + 480 + 528 + 576 = 2016

∴ The correct answer is 2016.

Additional Information

Least Common Multiple (LCM)

The smallest positive integer that is uniformly divisible by two or more numbers. It is obtained by taking the highest power of each prime factor involved in the numbers.

Sum of Arithmetic Progression (A.P.)

Consecutive multiples of a number always form an Arithmetic Progression. The sum can also be calculated using the formula: S_n = n ÷ 2 × (first term + last term). Here, 4 ÷ 2 × (432 + 576) = 2 × 1008 = 2016.

Divisibility Rule

For a number to leave no remainder when divided by a group of divisors, it must be completely divisible by their LCM. If a remainder 'R' is specified, the general format of the number becomes (LCM × k) + R.

​The correct answer is Govind Bhallabh Pant.

Key Points

• In the Constituent Assembly debate on 27 August 1947, Govind Bhallabh Pant said “I believe separate electorates will be suicidal to the minorities."
• Govind Ballabh Pant opposed the demand for separate electorates in the Constituent Assembly because:-

1. Govind Ballabh Pant was of the view that separate electorates would isolate the minorities permanently.
2. Minorities would become vulnerable.
3. The ruling government will not give them an opportunity to have a voice in the government.
4. It was also against the concept of a unified nation-state.

Additional Information

Given:

The least number of five digits, which is exactly divisible by 472. 

Concept:

Dividend = Divisor × Quotient + Remainder

Calculation:

Least five-digit number = 10000

By dividing 10000 by 472; 

⇒ 10000 = 472 × 21 + 88          (1) 

By adding the difference of divisior and remainder that is, (472 - 88) 384 to both the sides in the above equation (1) 

⇒ 10000 + 384 = 472 × 21 + 88 + 384 

⇒ 10384 =  472 × 21 + 472 

∴ 10384 is the least five-digit number that is exactly divisible by 472.

Given:

Reduction percent in the price of wheat = 25%

Expenses on wheat = Rs.600 

Formula used:

Expense = Price × Quantity

⇒ Quantity = Expense/Price 

Calculation:

Let the original price = Rs.100a per kg 

⇒ The reduced price of wheat = 100a × 75/100 = Rs.75a per kg

600/75a - 600/100a = 5 

⇒ 104/3a - 26/a = 5 

⇒ 8/a - 6/a = 5 

⇒ 2/a = 5 

⇒ a = 2/5

∴ The original price per kg = 100a = 100 × 2/5 = Rs.40 

Alternate MethodBy Ratio Method

25% = 25/100 = 1/4 

Original Quantity = 3 × 5 = 15 kg 

Expense = Rs.600 

∴ Original price of wheat per kg = Rs.600/15 = Rs.40

​The correct answer is Dr. BR Ambedkar.

Key Points

• On being criticized for borrowing features from other countries for the constitution, Dr. BR Ambedkar said the following- “Nobody holds any patent rights in the fundamental ideas of a constitution".
• The Indian Constitution is known as a bag of borrowings and draws its features from the Constitutions of many countries. Dr. BR Ambedkar rightly said that it was created after ransacking the known Constitutions across the world.
• With 448 articles in 25 parts, 12 schedules, 5 appendices, and 98 amendments, the Constitution of India is the longest written constitution of any independent country in the world.
• It was adopted on November 26, 1949, while it came into force on January 26, 1950, when all the members of the Constituent Assembly signed the documents.

Additional Information

​The correct answer is Kerala.

Key Points

• As per Public affair Index 2020 (PAI-2020), Kerala state emerged as the best-governed state in the country.
• The rankings were released by the Public Affairs Centre (PAC) in Bengaluru. Uttar Pradesh ended at the bottom in the large states category in the PAC ranking 2020.
• Four southern states - Kerala, Tamil Nadu, Andhra Pradesh, and Karnataka topped the list of 18 large states with a population of more than two crores. Uttar Pradesh, Odisha and Bihar were at the bottom of the ranking, scoring negative points in the category.
• The governance performance has been analyzed in the context of sustainable development defined by three pillars of equity, growth, and sustainability. The analysis used data from Central government sources.

Additional Information

• Four southern States Kerala 1.388 PAI Index point, Tamil Nadu 0.912 PAI Index point, Andhra Pradesh 0.531 PAI Index point, and Karnataka 0.468 PAI Index point stood in the first four ranks in the large State category in terms of governance.
• At the bottom, Uttar Pradesh (-1.461) PAI Index point, Odisha (-1.201) PAI Index point, and Bihar (-1.158) PAI Index point were at the bottom of the ranking.
• In the small State category, Goa ranked first with 1.745 PAI Index points, followed by Meghalaya (0.797,) and Himachal Pradesh (0.725). The worst performers with negative points were Manipur (-0.363), Delhi (-0.289), and Uttarakhand (-0.277).
• Chandigarh emerged at the top in the category of Union Territories with 1.05 PAI points, followed by Puducherry (0.52) and Lakshadweep (0.003). Dadar and Nagar Haveli (-0.69), Andaman, Jammu, and Kashmir (-0.50), and Nicobar (-0.30) were the worst performers.

​The correct answer is Extreme right.

Key Points

• As per the flag code of India 2002, the position of the Indian flag when it is displayed along with flags of other countries in a straight line is Extreme right.
• According to the flag code of India 2002, the general rule is that the Indian flag should be the starting point of all flags. When flags are placed in a straight line, the rightmost flag is the Indian flag, followed by other national flags in alphabetical order.
• When placed in a circle, the Indian flag is the first point and is followed by other flags alphabetically.
• When placed on crossed poles, the Indian flag should be in front of the other flag, and to the right (observer's left) of the other flag.
• The only exception to the preceding rule is when it is flown along with the flag of the United Nations, which may be placed to the right of the Indian flag.

Additional Information

• The Flag Code of India, 2002, took effect from 26 January 2002 and superseded the "Flag Code-India" as it existed earlier.
• The Flag Code of India has been divided into three parts:-

1. First Part: General Description of the National Flag.
2. Second Part: Display of the National Flag by members of the public, private Organisations & educational institutions, etc.
3. Third Part: Display of National Flag by Union or State Governments and their organisations and agencies.

• As per the flag code of India, 2002 all other flags should be of approximately the same size with no other flag being larger than the Indian flag.

Given:

PA and PB are the tangents to the circle with centre O. 

∠PAB= 55°

Concept:

Tangents drawn from the same external point are equal in length. 

A tangent perpendicular to the radius at the point of tangency.

Calculation:

∵ ∠PAB = 55° 

∴ ∠PBA = 55° (PA = PB) 

In triangle PAB,  

∠APB + ∠PAB + ∠PBA = 180°  (Angle Sum Property)

⇒ ∠P + 55° + 55° = 180° 

⇒ ∠P = 70° 

Also, ∠AOB + ∠APB = 180°   (Sum of all the angles of a quadrilateral is 360° & ∠P = 70° ∠B = 90°)

⇒ ∠AOB = 180° - 70° = 110

∴ The measure of ∠AOB = 110°

​The correct answer is Newton.

Key Points

• The three laws of motion were proposed by Sir Isaac Newton.
• Newton was born on January 4, 1643, in Woolsthorpe, Lincolnshire, England.
• Newton's three laws of motion are Law of Inertia, Law of Mass and Acceleration, and the Third Law of Motion.
• In developing his three laws Newton simplified objects, reducing them to mathematical points without size or rotation to let him ignore factors such as friction, air resistance, temperature, and material properties, and focus on outcomes that can be illustrated wholly with reference to mass, length and time.
• In 1687, Newton published Philosophiae Naturalis Principia Mathematica, most often known as Principia. Principia offers an exact quantitative description of bodies in motion, with three basic but important laws of motion:-

1. First Law A stationary body will stay stationary unless an external force is applied to it.
2. Second Law Force is equal to mass times acceleration, and a change in motion (i.e., change in speed) is proportional to the force applied.
3. Third Law For every action, there is an equal and opposite reaction.

Additional Information

Given:

The average weight of A, B, C, and D = 56 kg

The average weight of A, B, and C = 52 kg

The average weight of C and D = 48 kg

Formula used:

Average weight = Total weight/No of persons 

Calculation:

Total weight of A, B, C, & D = 56 kg × 4 = 224 kg     (1)

Total weight of A, B, & C = 52 kg × 3 = 156 kg         (2)

Total weight of C and D = 48 kg × 2 = 96 kg             (3)

By (2) + (3) - (1) 

⇒ (A + B + C) + (C + D) - (A + B + C + D) = 156 kg + 96 kg - 224 kg

⇒ A + B + 2C + D - A - B - C - D = 28 kg 

⇒ C = 28 kg 

∴ The weight of C is 28 kg.

The correct answer is Kalamsat.

Key Points

• The first student satellite was built by an Indian high school student team and launched by NASA  is Kalamsat.
• The satellite is named after former President and nuclear scientist Dr APJ Abdul Kalam and is called 'KalamSat'. It was flown into space in a NASA rocket.
• US space agency NASA has successfully launched the world's smallest and lightest satellite (Weighing just 64 grams.).
• The satellite was designed by 18-year-old Rifath Sharook along with six other teammates.
• The main role of the satellite is to demonstrate the performance of 3D-printed carbon fibre. It’s a 3D-printed satellite. It is for the first time that 3D printing technology is being used in space.

Additional Information

Given:

Number = 4707 

Concept:

Dividend = Divisor × Quotient + Remainder 

LCM = Lowest Common Multiple 

It is the smallest positive number that is divisible by two or more numbers. 

Calculation:

To find the least number which can be added to 4707 that is exactly divisible by 4, 5, 6 and 8, we need to find the LCM of these 4 numbers. 

LCM of 4, 5, 6 and 8 can be calculated by prime factorization; 

4 = 2²

5 = 5

6 = 2 × 3 

8 = 2³

⇒ LCM (4, 5, 6, 8) = 2³ × 3 × 5 = 120

When divided 4707 by 120, we get

⇒ 4707 = 120 × 39 + 27 

By adding the difference of Divisor and remainder (120 - 27) = 93 

⇒ 4707 + 93 = 120 × 39 + 27 + 93 

⇒ 4800 = 120 × 39 + 120 

⇒ 4800 = 120 (39 + 1) 

⇒ 4800 = 120 × 40 

∴ The least number that should be added to 4707 so that the sum is exactly divisible by 4, 5, 6 and 8 is 93.

​The correct answer is INS Vagir.

Key Points

• The Kalvari class submarine launched in Mumbai in Nov 2020 is INS Vagir.
• Indian Navy’s fifth Kalvari-class Diesel Electric attack submarine INS Vagir was launched at Mazgaon Dock in Mumbai, The ship was launched on 12 November 2020.
• The submarine inherits its name from INS Vagir which served in the Navy from 1973–2001 and was named after a species of sandfish.
• It is the fifth among the six Kalvari-class submarines being constructed by the public sector shipbuilder Mazagon Dock Ltd (MDL) in Mumbai.
• The other vessels in the class are INS Kalvari, INS Khanderi, INS Karanj, INS Vela, and INS Vagsheer.

Additional Information

​The correct answer is Common Business Oriented Language.

Key Points

• The full form of COBOL is Common Business Oriented Language.
• COBOL (Common Business-Oriented Language) is a high-level programming language for business applications.
• COBOL was the first popular language designed to be operating system-agnostic and is still in use in many financial and business applications today.
• COBOL is primarily used in business, finance, and administrative systems for companies and governments.
• Today many federal government agencies local banks, COBOL is still in use. For example, an estimated 43% of banking systems and 95% of ATM swipes utilize COBOL code.

Additional Information

• COBOL was designed in 1959 by CODASYL and was partly based on the programming language FLOW-MATIC designed by Grace Hopper.
• It was standardized in 1968 and has since been revised four times. The current standard is ISO/IEC 1989:2014.
• COBOL is a great candidate because it uses fixed-point decimal calculations as opposed to floating-point. A lot of modern languages like Java use floating-point, which means that their calculations are only accurate out to a certain “point”.
• Corporations use mainframes for applications that depend on scalability and reliability. For example, a banking institution could use a mainframe to host the database of its customer accounts, for which transactions can be submitted from any of thousands of ATM locations worldwide.

The logic is:

Column 1: 9 × 5 × 3 = 135

Column 2: 5 × 7 × 4 = 140 

Similarly,

Let the missing number in column 3 be 'a'.

So, 5 × a × 5 = 150

⇒ 25 × a = 150

⇒ a = 150 ÷ 25

⇒ a = 6

Hence, ‘6’ is the correct answer.

Follow BODMAS rule to solve this question, as per the order given below,

Given:

$\frac{6.25+\frac{5}{7}×28-5}{\frac{3}{4}×(15.8-3.4)+5×2.39}$

Calculation:

$\frac{6.25+\frac{5}{7}×28-5}{\frac{3}{4}×(15.8-3.4)+5×2.39}$

⇒ (6.25 + 5 × 4 - 5)/(3/4 × (12.4) + 11.95)

⇒ (6.25 + 20 - 5)/(3 × 3.1 + 11.95) 

⇒ (6.25 + 20 - 5)/(3 × 3.1 + 11.95) 

⇒ 21.25/21.25

⇒ 1

∴ The required result = 1

​The correct answer is Smiling Buddha.

Key Points

• The code name of India’s first successful Nuclear test was Smiling Buddha.
• India on May 18, 1974, conducted its first nuclear test, codenamed 'Smiling Buddha', in Rajasthan's Pokhran, becoming a nuclear power.
• The bomb was detonated on the army base Pokhran Test Range, in Rajasthan, by the Indian Army under the supervision of several key Indian generals.
• At the time of Indian Prime minister Indira Gandhi. The Indian Ministry of External Affairs (MEA) characterized this test as a "peaceful nuclear explosion".
• In May 1998, India again conducted a series of nuclear tests at the same location, it was called Pokhran-2 tests.

Additional Information

​The correct answer is Gopal Krishna Gokhale.

Key Points

• Mahatma Gandhi considers Gopal Krishna Gokhale his mentor in politics.
• Gopal Krishna Gokhale was the senior leader of the Indian National Congress and the founder of Servants of Indian Society. He is known to be a mentor to Mahatma Gandhi.
• Gopal Krishna Gokhale is known as "The Political Guru of Gandhi". He was the one who guided Mahatma Gandhi to travel around India in order to fight against the British.
• He was one of the social and political leaders during the Indian Independence Movement against the British Empire in India.
• He guided Mahatma Gandhi after he came back from South Africa. Gopal Krishna Gokhale had immense knowledge in the field of Indian politics.

Additional Information

• Gopal Krishna Gokhale was born on May 09, 1866, in Kotluk, in a Brahmin family of Maharashtra. He died on February 19, 1915, at the early age of 49.
• Gopal Krishna Gokhale was a mentor to both Mohammed Jinnah and Mahatma Gandhi.
• Gopal Krishna Gokhale was also a social reformer whose goals were to promote non-violence and reform within existing government institutions.

​The correct answer is Trans-Siberian Railway.

Key Points

• The longest railway line in the world is Trans-Siberian Railway.
• The Trans–Siberian Railway connects Moscow with the Russian far east. Its running distance is 9,259 kilometres or 5,753 miles. The journey takes (167 hours) 6 days to complete.
• The Trans-Siberian railway line has connected Moscow to Vladivostok since 1916, and it is still being expanded. There are also branch lines into Mongolia, China, and North Korea.
• Tsar Alexander III and his son personally appointed ministers to build this railway line from 1891 to 1916.
• Trans- Siberian Railway played an important role in World War II in supplying the powers fighting in Europe. It also transported Soviet troops west from the Far East to take part in the Soviet counteroffensive.

Additional Information

​The correct answer is Lichen.

Key Points

• Litmus solution is derived from Lichen.
• Lichen is used to determine the solution is neutral/acidic/basic. It has a mauve (purple) colour in distilled water.
• When added to an acidic solution, it turns red. When added to a basic solution, it turns blue.
• Lichens are plants that belong to the Thallophyta group. To obtain a litmus solution, the crushing and grinding of lichens are done. The dyes are then added to neutral water to get the required litmus solution.
• Litmus solution is obtained from lichens. A natural dye extracted from lichens is dissolved in distilled water to obtain a litmus solution. For example, It is used as an indicator to distinguish between acids and bases.

Additional Information

• Litmus solution is a purple dye, which is extracted from lichen, a plant belonging to the division Thallophyta, and is commonly used as an indicator.
• There are many other natural materials like red cabbage leaves, turmeric, coloured petals of some flowers such as Hydrangea, Petunia, and Geranium, which indicate the presence of acid or base in a solution. These are called acid-base indicators or sometimes simply indicators.
• Most of the acid-base indicators that are commonly used are synthetic but nature has its own indicators. Hydrangea, petunia, and Geranium have the ability to act as indicators.

​The correct answer is Truck farming.

Key Points

• The farmers specialize in vegetables only, this type of farming is known as Truck farming.
• In the regions where farmers specialize in vegetables only, the farming is known as Truck farming, and the distance of truck farms from the market is governed by the distance that a truck can cover overnight, hence the name truck farming.
• Vegetable farms are in some regions known as truck farms: "truck" is a noun for which its more common meaning overshadows its historically separate use as a term for "vegetables are grown for the market".
• The production of crops of some vegetables on an extensive scale in regions especially suited to their culture primarily for shipment to distant markets known as Truck farming.
• The major truck-farming areas are in California, Texas, Florida, along the Atlantic Coastal Plain, and in the Great Lakes area.
• Centres for specific crops vary with the season. Among the most important truck crops are tomatoes, lettuce, melons, beets, broccoli, celery, radishes, onions, cabbage, and strawberries.

Additional Information

​The correct answer is Tamil Nadu.

Key Points

• The highest wind energy production in India is in Tamil Nadu state.
• The south Indian state of Tamil Nadu tops the list, with an annual wind power output of around 9,000 MW per annum- recording 8,631 megawatts (MW) at the end of 2018 and 9,075 MW in 2019.
• Out of the state’s total installed capacity for electricity generation (which was 30,447 MW by the end of 2018), the wind sector contributed 28.34%.
• The Government of Tamil Nadu realized the importance and need for renewable energy, and set up a separate Agency, as a registered society, called the Tamil Nadu Energy Development Agency (TEDA) as early as 1985.
• Boasting India’s largest installed wind power generation capacity, Tamil Nadu has located in the district of Kanyakumari, it features several wind turbines varying from 200KW to 1,650KW.

Additional Information

​The correct answer is Surat.

Key Points

• The second spot in the Swacch Sarvekshan award for 2020 is Surat city, Gujrat.
• In the fifth edition of the annual cleanliness survey (Swacch Sarvekshan) of the country in 2020, Madhya Pradesh's Indore was placed on the first spot, Gujarat's Surat on the second spot, and Maharashtra's Navi Mumbai on third.
• The title of the second cleanest city in India is held by Surat. This commercial city known for textiles and diamonds has undergone rapid development over the years.
• Municipal Corporation has ensured that the dynamic changes included maintaining cleanliness. Surat now attracts local and international tourists to visit its popular attractions such as Ambaji Temple, Swaminarayan Temple, Sarthana Nature Park, Vansda National Park. Sardar Patel Museum, Dutch Garden, and Dumas Beach.

Additional Information

• Swachh Survekshan is a ranking exercise taken up by the Government of India to assess rural and urban areas for their levels of cleanliness and active implementation of Swachhata mission initiatives in a timely and innovative manner.
• The objective of the survey is to encourage large-scale citizen participation and create awareness amongst all sections of society about the importance of working together towards making towns and cities a better place to live. the survey also intends to foster a spirit of healthy competition among towns and cities to improve their service delivery to citizens, towards creating cleaner cities and towns.
• Swachh Survekshan 2020 is the fifth edition of the annual cleanliness urban survey conducted by the Ministry of Housing and Urban Affairs (MoHUA), Government of India.
• Swachh Survekshan 2020 surveyed a total of 4242 cities, 62 Cantonment Boards, and 97 Ganga Towns and saw unprecedented participation of 1.87 crore citizens.

The Venn diagram that best represents the relationship between Students, Interns and Research scholars is shown below:

Some Research scholars are Students and Interns, some Interns are Research scholars and Students and some Students are Interns and Research scholars as well.

A research scholar is typically a college or graduate student who works under an advisor works on projects in a specific field of study, seeking to analyze and uncover new information that can be presented in academic or trade journals.

Hence, ‘option 3’ is the correct answer.

The logic is:

1st figure: (40 + 12) - 30 = 52 - 30 = 22

2nd figure: (34 + 16) - 40 = 50 - 40 = 10

Similarly,

3rd figure: (28 + 20) - 43 = 48 - 43 = 5

Hence, '5’ is the correct answer.

Given:

371 + 372 + 373 + 374 + 375 

Formula used:

aⁿ + a^{n + 1} = aⁿ(1 + a) 

Calculation:

371 + 372 + 373 + 374 + 375 

⇒ 371(1 + 3 + 3² + 3³ + 3⁴)

⇒ 371(1 + 3 + 9 + 27 + 81)

⇒ 371(1 + 3 + 9 + 27 + 81)

⇒371×121 

⇒371×11×11

∴ The expression 371×11×11 has 11 as its factor.

∴ It is divisible by 11.

The logic is:

Column 1: 4 × 9 + 8 = 36 + 8 = 44

Column 2: 3 × 7 + 6 = 21 + 6 = 27

Similarly,

Column 3: 8 × 2 + 4 = 16 + 4 = 20

Hence, ‘20’ is the correct answer.

​The correct answer is Bharat Heavy Electricals Limited.

Key Points

• The full form of BHEL is Bharat Heavy Electricals Limited.
• BHEL is founded and owned by the Government of India, is a manufacturing and engineering company based in New Delhi, India.
• It was established in 1964 and it is the largest and oldest power generation equipment manufacturer in India. In 1974 Heavy Electricals Limited merged with BHEL.
• BHEL alone generates around 20,000 MW per annum out of the available 35,000 MW power generated in the country.
• BHEL is also one of the largest exporters of engineering products and services. It exports in more than 60 countries globally.

Additional Information

• BHEL is founded and owned by the Government of India. Mr. Atul Sobti is Chairman & Managing Director of Bharat Heavy Electricals Limited (BHEL), and the current CEO of BHEL is Nalin Singhal since 08, July 2019.
• BHEL is involved in engineering, manufacturing, construction, servicing, and transmission in addition to power plant service, and evaluation of various products from key economic sectors such as transportation like Railways, energy, water, oil and gas, defence.
• BHEL also offered thousands of electric locomotives and defence equipment to Indian Railways including the Super Rapid Gun Mount (SRGM) naval guns produced to the Indian Army in collaboration with the Indian Ordnance Factories and Defense Simulators.

Follow BODMAS rule to solve this question, as per the order given below,

Given:

17 × 8 - 6 + [(27 - 3) ÷ 6 - 4]

Calculation:

17 × 8 - 6 + [(27 - 3) ÷ 6 - 4]

⇒136 - 6 + [24 ÷ 6 - 4]

⇒130 + [4 - 4]

⇒ 130 + 0

⇒ 130 

∴ The required result = 130

Given:

Perimeter of a right triangle = 60 cm

Hypotenuse = 26 cm

Formulas used:

(x + y)² = x² + y² + 2xy

Perimeter of the right-angle triangle = Base + Height + Hypotenuse 

Pythagoras Theorem:

Base² + Height² = Hypotenuse²

Area of right-angle triangle = 1/2 × Base × Height 

Calculation:

Let the base and height be x and y respectively 

Sum of base and height (x + y) = 60 - 26 = 34 cm         (1)

Also, x² + y² = 26²

⇒ x2 + y2 = 676        (2)

From (1)

(x + y) = 34 

By squaring both sides;

⇒ x2 + y2 + 2xy = 1156 

⇒ 676 + 2xy = 1156            ∵ [x2 + y2 = 676]                                       

⇒xy = (1156 - 676)/2          

⇒ xy = 240           (3) 

∴ Area of right-angle triangle = 1/2 × 240 = 120 cm²

Given:

a2 + b2 = 82

ab = 9

Formulas used:

(a + b)² = a² + b² + 2ab

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculation:

(a + b)2 = 82 + 2 × 9

⇒(a + b)2 = 100 

⇒ (a + b) = √100 = 10          (1)

(a + b)3 = a3 + b3 + 3ab(a + b)

⇒ 10³ = a3 + b3 + 3 × 9 × 10 

⇒ 1000 = a3 + b3 + 270

⇒ a3 + b3 = 1000 - 270 

∴  a3 + b3 =  730

Alternate MethodBy using formula  a3 + b3 = (a + b)(a² - ab + b²)

⇒ a3 + b3 = 10 × (82 - 9) = 10 × 73 

∴ a3 + b3 = 730

​The correct answer is Digboi.

Key Points

• The first oil well was discovered in Assam in Digboi.
• Crude oil was discovered in Digboi in the late 19th century and the first oil well was dug in 1866.
• Digboi is known as the Oil City of Assam where the first oil well in Asia was drilled. The Assam Oil Company was established in 1899 to oversee production.
• In 1901, Digboi Refinery was commissioned supplanting the earlier refinery at Margharita.
• The Indian Oil Corporation Ltd (IOC) took over the refinery and marketing management of Assam Oil Company Ltd. with effect from 1981 and created a separate division. This division has both refinery and marketing operations.
• The refinery at Digboi had an installed capacity of 0.50 million tonnes per year.
• Assam has 4 refineries- Noonmati Refinery, Namuligarh Refinery, Bongaigaon Refinery, and Digboi Refinery.

Additional Information

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘FNY’ is the correct answer.

​The correct answer is Charles Babbage.

Key Points

• Charles Babbage is considered the father of computers.
• Charles Babbage invented the machine called the Analytical Engine, which is a model of today's computers. Since he was the first person who gave us the basic idea of computers, he is known as the 'father of computers.
• In 1837 the Analytical Engine contained an ALU (arithmetic logic unit), basic flow control, and integrated memory, hailed as the first general-purpose computer concept.
• Because of funding issues, this computer was not built while Charles Babbage was alive. However, in 1910 Henry Babbage, Charles Babbage's youngest son was able to complete a portion of the machine that could perform basic calculations.
• Although Babbage never completed his invention in his lifetime, his radical ideas and concepts of the computer are what make him the father of computing.

Additional Information

The logic followed here is:

The positional value of the letter is given as their code.

As "A" is equal to 1, "M" is equal to 13 and "R" is equal 18.

A = 1 which means A positional value is given

M = 13 which means A positional value is given

R = 18 which means A positional value is given

Similarly,

MISSION → ?

Thus MISSION → 139191991514

Hence, the correct answer is "139191991514".

��The correct answer is **392 kg-m/s.**​

Key Points

• The momentum of a particle is a measure of the time required for a constant force to bring it to rest.
• In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object.
• Momentum = Mass * Velocity
• In physics, the symbol for the quantity momentum is the lower case p. Thus, the above equation can be rewritten as p = m • v.
• Momentum is a vector quantity; i.e., it has both magnitude and direction.

Additional Information

• Isaac Newton's second law of motion states that the time rate of change of momentum is equal to the force acting on the particle.
• Conservation of momentum can be described by P1 (before) + P2 (before) = P1 (after) + P2 (after).
• Some of the examples of momentum include - 
• A train moving at 100 km/h.
• A bullet fired from a gun.
• A baseball flying through the air.

Given:

Cost Price of two articles = Rs.3000 each 

Profit on one article = 10% 

Profit on another article = 5% 

Formulas used:

Selling Price = Cost Price × (100 + Profit)/100%

Profit = Selling Price - Cost Price 

Profit percent = Profit/Cost Price × 100 

Calculation:

Selling Price of one article at 10% profit = 3000 × 110/100 = Rs.3300

Selling Price of another article at 5% profit = 3000 × 105/100 = Rs.3150 

Total Selling Price of both articles =  3300 + 3150 = Rs.6450

Total Cost Price of both articles = Rs.3000 + Rs.3000 = Rs.6000 

Profit on both articles = Rs.6450 - Rs.6000 = 450

∴ Profit Percent on both articles = 450/6000 × 100 

⇒ 7.5% 

Alternate MethodBy Average MethodWhen the Cost Price of both the articles is equal; 

Average or aggregate profit on two articles = (Profit1 + Profit2)/2 

⇒ (10% + 5%)/2 = 15%/2 

⇒ 7.5%