RRB NTPC CBT-I Official Paper (Held On: 29 Dec 2020 Shift 1) (Previous Year Paper)

The correct answer is Jim Corbett National Park.

Key Points

• Jim Corbett National Park is a tiger reserve.
• Jim Corbett National Park is the oldest national park in India and was established in 1936 as Hailey National Park to protect the endangered Bengal tiger.
• Jim Corbett National Park is in the Nainital district of Uttarakhand state.

Additional Information

• About Uttrakhand:
• State Animal - Alpine musk deer.
• State Bird - Himalayan monal.
• Total districts - 13
• National Parks - Gangotri National Park, Rajaji National Park, Gangotri National Park, Nanda Devi National Park, etc.

Formula:

cos3A = 4cos³A - 3cosA

cos(A + B) . cos(A - B) = cos2A - sin2B

Calculation:

⇒ ? = cos 20° cos 40° cos 80°

⇒ ? = cos 20° [cos(60° - 20°) cos(60° + 20°)]

⇒ ? = cos 20° [cos² 60° - sin² 20°]

⇒ ? = cos 20° [1/4 - (1 - cos² 20°)]

⇒ ? = 1/4 × cos20° - cos20° + cos³20°

⇒ ? = cos³20° - 3/4 × cos20°

⇒ ? = 1/4(4cos³20° - 3cos20°)

⇒ ? = 1/4 × cos (3 × 20°)

⇒ ? = 1/4 × 1/2

⇒ ? = 1/8

∴ cos 20° cos 40° cos 80° = 1/8

Shortcut Trick If the expression is in the form of cosθ × cos(60 + θ) × cos(60 - θ) = 1/4 cos3θ. 

cos20° cos40° cos80° = 1/4 cos60° 

⇒ 1/4 × 1/2 = 1/8

∴ cos 20° cos 40° cos 80° = 1/8.

Given:

side of equilateral triangle ABC = 28cm

Formula:

Area of an equilateral triangle = √3/4 × side²

Calculation:

Area of equilateral triangle ABC with side 28cm = √3/4 × 28² = 196√3 sq.cm

Area of equilateral triangle PQR = 16 × 196√3 sq.cm

Then,

⇒ 16 × 196√3 = √3/4 × (side of triangle PQR)²

∴ Side of an equilateral triangle PQR = 112 cm

Alternate MethodTwo equilateral triangles are always similar.

Area of ΔABC/Area of ΔPQR = (Side of ABC/Side of PQR)²

⇒ 1/16 = (28/x)²

⇒ 28/x = 1/4

⇒ x = 112 cm

∴ Side of an equilateral triangle PQR = 112 cm

The correct answer is Ajmer.

Key Points

• One of the most important teachers of Chishti Silsila, Shaikh Moinuddin Chishti dargah is located at Ajmer.
• Moinuddin Hasan Chishti was born in Sijistan in Iran in 1141-42 CE.
• After Muizuddin Muhammad bin Sam of Ghor had already defeated Prithviraj Chauhan in the Second Battle of Tarain (1192) and established his rule in Delhi, Khwaja Moinuddin Chishti started living and preaching in Ajmer.

Image:

Additional Information

• The First Battle of Tarain, fought in 1191, was a decisive victory for Prithviraj Chauhan, the Rajput ruler of Delhi and Ajmer, over the invading forces of Muhammad of Ghor (Muhammad Ghori)
• The third Battle of Tarain was fought in 1216 between Iltutmish and Tajuddin.

The correct answer is Google.

Key Points

• Google is not a web browser.
• Google, is a search engine provided by Google.
• It is also the most-visited website in the world.
• The order of search results returned by Google is based, in part, on a priority rank system called "PageRank".

Additional Information

• Safari is a graphical web browser developed by Apple Inc.
• Opera is a multi-platform web browser developed by Opera Software.
• Mozilla Firefox is a free and open-source web browser developed by the Mozilla Foundation and its subsidiary, the Mozilla Corporation.

Given:

x³ + y³ = 35 and x + y = 5

Formula:

x³ + y³ = (x + y)³ - 3xy(x + y)

x² + y² = (x + y)² - 2xy

Calculation:

Solving,

⇒ 35 = 5³ - 3xy(5)

⇒ xy = 6

Then,

⇒ (x² + y²) = 5² - 2 × 6 = 13

Then,

⇒ ? = x⁴ + y⁴

⇒ ? = (x²)² + (y²)²

⇒ ? = (x² + y²)² - 2x²y²

⇒ ? = 13² - 2(6)²

⇒ ? = 97

∴ x⁴ + y⁴ = 97

Given:

Total interest received after 5 years = Rs.1750

Formula:

Let P = Principal, R = rate of interest and N = time period

Simple interest = PNR/100

Calculation:

Let amount lent out at 10% simple interest be Rs.a.

Amount lent out at 5% simple interest = Rs(5000 - a)

⇒ 1750 = (a × 10 × 5)/100 + [(5000 - a) × 5 × 5/100]

⇒ 1750 × 100/5 = 10a + 25000 - 5a

⇒ 5a = 10000

⇒ a = 2000

∴ Amount lent out at 10% simple interest is Rs.2000.

The correct answer is Awadh.

Key Points

• The exile of the ruler of Awadh kingdom was termed as "The life has gone out of the body".
• Awadh, known in British historical texts as Avadh or Oudh.
• Awadh is a region of Uttar Pradesh
• The traditional capital of Awadh was Lucknow, also the station of the British Resident, which now is the capital of Uttar Pradesh.

Important Points Why it was termed as "The life has gone out of the body"?

• Awadh was annexed by the British on the plea that the region was being misgoverned
• The British thought that the Nawab was not popular but on the contrary, he was very popular.
• People considered it as “the life has gone out of the body”.
• The removal led to an emotional upheaval among the people of Awadh.

The correct answer is Indirect Tax.

Key Points

• Goods and Services Tax (GST) is an indirect tax (or consumption tax) used in India on the supply of goods and services.
• It is a comprehensive, multistage, destination-based tax: comprehensive because it has subsumed almost all the indirect taxes except a few state taxes.
• Multi-staged as it is imposed at every step in the production process but is meant to be refunded to all parties in the various stages of production other than the final consumer and as a destination-based tax.
• It is collected from point of consumption.

Important Points

• About GST:
• The tax came into effect on 1 July 2017.
• It is One Hundred and the first Amendment of the Constitution of India.

Given:

Mean : median = 4 : 5

Formula:

mode = 3median - 2mean

Calculation:

Let mean and median be 4a and 5a respectively.

Mode = 3 × 5a - 2 × 4a = 7a

∴ Mean : Mode = 4a : 7a = 4 : 7

Calculation:

From graph,

Total number of web series from 2014 - 2018 = 30 + 35 + 35 + 42 + 48 = 190

Total number of web series with IMBD rating < 5 from 2014 - 2018 = 6 + 9 + 11 + 12 + 12 = 50

Total number of web series with IMBD rating 5 star and above from 2014 - 2018 = 190 - 50 = 140

∴ Required percentage = 140/190 × 100 = 73.68% ≈ 74%

Given:

Range = 100 - 200

Formula:

a = first term, d = common difference and n = number of terms

⇒ Sn = n/2 × [2a + (n - 1)d]

⇒ Tn = a + (n - 1)d

Calculation:

Smaller term between 100 - 200 divisible by 12 = a = 108

⇒ d = 12

Larger term between 100 - 200 divisible by 12 = Tn = 192

⇒ 192 = 108 + (n - 1)12

⇒ n = 8

There are 8 terms between 100 to 200 which are divisible by 12.

Sum of such 8 terms = S8 = 8/2 × [2 × 108 + (8 - 1) × 12] = 1200

∴ The Sum of numbers between 100 to 200 which are divisible by 12 is 1200.

 Hint

Sum of terms = Sn = (a + Tn) × n/2

Here,

a = 108 and Tn = 192, n = 8

Sn = (108 + 192) × 8/2 = 1200

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘ADGJ’ is the correct answer.

Given:

Percentage number of students enrolled in Karate = 25%

Percentage number of students enrolled in Cooking = 8%

Percentage number of students enrolled in creative writing = 14%

Total percentage number of students enrolled in Karate, Cooking and creative writing = 25 + 8 + 14 = 47%

∴ Total number of students enrolled in Karate, Cooking, and Creative writing = 47/100 × 3500 = 1645

The correct answer is Mahatma Gandhi.

Key Points

• Mahatma Gandhi is the inspiration behind Saansad Adarsh Gram Yojana.
• Saansad Adarsh Gram Yojana is a rural development program broadly focusing upon the development in the villages which includes social development, cultural development, and spread motivation among the people on social mobilization of the village community.
• The program was launched by the Prime Minister of India, Narendra Modi on the birth anniversary of Jayaprakash Narayan, on 11 October 2014.

Additional Information

• About Mahatma Gandhi:
• Born - 2 October 1869, Porbandar.
• Full name - Mohandas Karamchand Gandhi.
• Assassinated - 30 January 1948, New Delhi.
• Notable work - The Story of My Experiments with Truth.

The correct answer is HyperText Transfer Protocol.

Key Points

• HTTP stands for HyperText Transfer Protocol.
• The Hypertext Transfer Protocol (HTTP) is an application layer protocol in the Internet protocol suite model for distributed, collaborative, hypermedia information systems.
• HTTP is the foundation of data communication for the World Wide Web, where hypertext documents include hyperlinks to other resources that the user can easily access, for example by a mouse click or by tapping the screen in a web browser.

Important Points

• Some important protocols:
• SMTP - Simple Mail Transfer Protocol.
• FTP - File Transfer Protocol.
• TCP - Transmission Control Protocol
• UDP - User Datagram Protocol
• OSI - Open Systems Interconnection.

The correct answer is Joseph Noel Paton.

Key Points

• Joseph Noel Paton painted ''In Memorium'', a painting dedicated to the British ladies in India during the mutiny of 1857.
• Sir Joseph Noel Paton FRSA was a Scottish artist, illustrator, and sculptor.
• He was also a poet and had an interest in, and knowledge of, Scottish folklore and Celtic legends.

Additional Information

• Some other important works of Joseph Noel Paton:
• Hesperus (1857)
• Home (1855–56)
• How an Angel Rowed Sir Galahad Across the Dern Mere (1888)
• Oberon and the Mermaid (1888)

Given:

? = 24 + 7.2 ÷ 8 - 3 × 2.3 + 5

Concept:

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

⇒ ? = 24 + 7.2 ÷ 8 - 3 × 2.3 + 5

⇒ ? = 24 + 0.9 - 3 × 2.3 + 5

⇒ ? = 24 + 0.9 - 6.9 + 5

⇒ ? = 29.9 - 6.9

⇒ ? = 23

∴ 24 + 7.2 ÷ 8 - 3 × 2.3 + 5 = 23

Given:

Rana got 40% of the votes.

Number of votes Rana defeated = 60000

Calculation:

The total number of votes in the election be n.

Ranvir got number of votes = 60n/100 = 3n/5

Rana got number of votes = 40n/100 = 2n/5

Then,

⇒ 3n/5 - 2n/5 = 60000

⇒ n = 300000

Total number of votes polled in election = 300000

∴ Total number of votes polled in election in favour of Ranvir = 3n/5 = (3/5)× 300000 = 180000

Given:

Length and breadth ratio = 3 : 2

Cost of flooring = 12.50 per sq.m

Formula:

Area of rectangle = length × breadth

Calculation:

Area of flooring = 3675/12.50 = 294 sq.cm

Let length and breadth of flooring 3a and 2a in meters respectively.

⇒ 294 = 3a × 2a

⇒ a = 7

∴ Length of flooring = 7 × 3 = 21m

Given:

CP of 8 tablets = SP of 5 tablets

Formula:

Profit = SP - CP

Profit % = (SP - CP)/CP × 100

Calculation:

Let CP of one tablet be Rs.100.

CP of 8 tablets = Rs.800 = SP of 5 tablets

SP of one tablet = 800/5 = Rs.160

∴ Profit percentage = [(160 - 100)/100]× 100 = 60%

Shortcut TrickCP of 8 tablets = SP of 5 tablets

⇒ CP/SP = 5/8

SP > CP 

Profit % = [(8 - 5)/5]× 100

⇒ 60%

∴ The percentage gain is 60%.

Given:

√4624 = 68

Calculation:

⇒ ? = $√{46.24}+√{0.4624}+√{0.004624}$

⇒ ? = √(4624 × 10^-2) + √(4624 × 10^-4) + √(4624 × 10^-6)

⇒ 68/10 + 68/100 + 68/1000

⇒ ? = 6.8 + 0.68 + 0.068

∴ ? = 7.548

The correct answer is Vinesh Phogat.

Key Points

• Vinesh Phogat was recommended by the Wrestling Federation of India for the prestigious 2020 Rajiv Gandhi Khel Ratna Award.
• Vinesh Phogat is an Indian wrestler.
• She became the first Indian woman wrestler to win gold in both Commonwealth and Asian Games.

Important Points

• About Rajiv Gandhi Khel Ratna Award:
• The award from 1991-2021 was named after Rajiv Gandhi.
• It was renamed as Major Dhyan Chand Khel Ratna Award in 2021.
• Rani Rampal was the first Indian female Hockey to receive the Rajiv Gandhi Khel Ratna award.
• About Wrestling Federation of India:
• Headquarters - New Delhi.
• Affiliated to - United World Wrestling (UWW).
• Secretary - V.N. Prasood.

The correct answer is Kanchanjunga.

Key Points

• Kanchanjunga is the highest peak in India.
• It is the third highest mountain in the world.
• It rises with an elevation of 8,586 m in a section of the Himalayas called Kangchenjunga Himal delimited in the west by the Tamur River, in the north by the Lhonak the Chu and Jongsang La, and in the east by the Teesta River.

Important Points

• Some highest peaks of the Indian mountain range:
• Aravali Hills - Guru Shikhar.
• Satpura Range - Dhupgarh.
• The Western Ghats - Anamudi.
• The Eastern Ghats - Mahendragiri

The correct answer is Deccan Queen.

Key Points

• Deccan Queen was India's first Superfast train.
• The Deccan Queen is a daily Indian passenger train service operated by the Central Railway zone of the Indian Railways connecting the cities of Mumbai and Pune.
• Introduced on June 1, 1930, the Deccan Queen was India's "first superfast train, first long-distance electric-hauled train, first vestibuled train, the first train to have a 'women-only car, and the first train to feature a dining car".

Additional Information

• About Indian Railways:
• Started in 1853.
• Zones - 18
• Headquarters - New Delhi.
• India's Railway network is the fourth largest network in the world.

Given:

Speed of train leaves from Bangalore = 80kmph

Speed of train leaves from Bangalore after 1 hour = 100kmph

Formula:

Speed = distance/time

Calculation:

Both trains meet after n hours after second train leaves.

Distance is same.

⇒ 100n = (n + 1)80

⇒ 100n = 80n + 80

⇒ n = 4

∴ After 4 hours, second train will meet first train.

The correct answer is Germany.

Key Points

• Ruhr region is the most important industrial region of Germany.
• The Ruhr also referred to as Ruhr area, Ruhr district, Ruhr region, or Ruhr valley, is a polycentric urban area in North Rhine-Westphalia, Germany.
• The Ruhr area has no administrative center; each city in the area has its own administration.

Additional Information

• About Germany:
• Capital - Berlin.
• Currency - Euro.
• National Sport - Football.
• National Animal - Federal Eagle.

The correct answer is Further Excavations at Mohenjo-Daro.

Key Points

• 'Further Excavations at Mohenjo-Daro's is the name of the book written by Ernest Mackay about archaeological excavations.
• This book was originally published in 1934.
• Other books are written by Ernest Mackay:
• Chanhu-Daro excavation.
• Indus Civilisation.
• The city of Shepherd Kings and Ancient Gaza V.
• Further Excavations At Mohenjo-Daro.

Additional Information

• Some features of Mohenjo-Daro:
• Mohenjo-Daro was the largest site of the Indus Valley Civilization.
• Mohenjo-Daro was the world's earliest major urban settlement.
• Evidence of 'The great bath'.

Given:

186 - 7 × (63 - 39) + 25 ÷ 5

Concept:

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

Calculation:

⇒ 186 - 7 × (63 - 39) + 25 ÷ 5

⇒ 186 - 7 × 24 + 25 ÷ 5

⇒ 186 - 7 × 24 + 5

⇒ 186 - 168 + 5

⇒ 23

∴ 186 - 7 × (63 - 39) + 25 ÷ 5 = 23

The correct answer is 26^th November.

Key Points

• The Consitution Day of India is celebrated on 26^th November.
• Constitution Day (or Samvidhan Divas), also known as National Law Day, is celebrated in India on 26 November every year to commemorate the adoption of the Constitution of India.
• On 26 November 1949, the Constituent Assembly of India adopted the Constitution of India, and it came into effect on 26 January 1950.
• The Government of India declared 26 November as Constitution Day on 19 November 2015 by a gazette notification.

Additional Information

• Republic Day of India is celebrated on 26th January every year.
• Independence Day of India is celebrated on 15th August.
• Ambedkar Jayanti or Bhim Jayanti is celebrated on 14th April.

The correct answer is Myopia.

Key Points

• Excessive curvature of the eye lens leads to myopia.
• Myopia or Nearsightedness is caused when the image forms right in front of the retina rather than on its surface.
• It happens when the cornea or the lens is too curved for the length of the eyeball.
• There are mainly three common refractive defects of vision.
• (i) myopia or near-sightedness,
• (ii) Hypermetropia or farsightedness, and
• (iii) Presbyopia

Important Points

• The myopia vision defect can be corrected by using a concave lens.
• Convex lenses are used to treat presbyopia, hypermetropia, and aphakia.

Given:

 'a*b' means 'a is the brother of b'

 'a#b' means 'a is the father of b'

 'a$b' means 'a is the wife of b'

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

1.  p$q#r → p is wife of q, q is father of r

r is child of p.

2.  p#q$r → p is father of q, q is wife of r

r is son-in-law of p.

3.  pqr → p is brother of q, q is brother of r

r is either brother or sister of p.

4.  p*q#r → p is brother of q, q is father of r

r is either niece or nephew of p.

Clearly, r is child of p, is possible from option 1 only.

Hence, ‘p$q#r’ is the correct answer.

1 × 2 = 2 and 1 + 2 = 3

Here minimum value obtained is 2 when we replace @ by × sign.

Again, we know that if we add the numbers, the value obtained will be minimum, and if we multiply the numbers, the value obtained will be maximum.

So, replacing first @ by × and remaining @ by +, we get:

1 × 2 + 3 + 4 + 5

= 2 + 3 + 4 + 5

= 14

Therefore, the minimum value of '1@2@3@4@5' is 14.

Hence, ‘14’ is the correct answer.

The correct answer is liver.

Key Points

• Bile is secreted by the liver.
• Bile is a fluid that is made and released by the liver and stored in the gallbladder.
• Bile helps with digestion.
• It breaks down fats into fatty acids, which can be taken into the body by the digestive tract.

Additional Information

• The pancreas is an organ located in the abdomen.
• It plays an essential role in converting the food we eat into fuel for the body's cells.
• Gall bladder stores the bile fluid.
• The Stomach is a muscular sac located on the left side of the upper abdomen.
• The stomach receives food from the esophagus.
• As food reaches the end of the esophagus, it enters the stomach through a muscular valve called the lower esophageal sphincter.
• The stomach secretes acids and enzymes that digest food.

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘SIJT’ is the correct answer.

Given:

Dimension of river = 2m deep and 21m wide.

Speed of river = 5kmph

Formula:

Area of river = depth × width

Calculation:

Area of river = 2 × 21 = 42 sq.m

Flow rate = 5kmph = 5000/60 = 250/3 m/min

Amount of water that falls into the sea in 10 minute = area of river × flow rate × 10

= 42 × 250/3 × 10

= 35000 m³

= 35000 kl

∴ Amount of water that falls into the sea in 10 minute is 35000kl.

The logic is:

Sun : Earth → Earth revolves around the sun.

Similarly,

_______ : Moon → The moon orbits the Earth.

Hence, ‘Earth’ is the correct answer.

The least possible Venn diagram is:          

Conclusions:

1. All chocolates are toffees. → True (As, All chocolates are candies and All candies are toffees → So, All chocolates are toffees)
2. All toffees are chocolates. → False (As, All chocolates are candies and All candies are toffees → So, Some toffees are chocolates)

Hence, only conclusion 1 follows.

The correct answer is France.

Key Points

• In the Indian Constitution, the concepts of liberty, equality, and fraternity were adopted from France.
• Article 21 of the Constitution of India, 1950 provides, “No person shall be deprived of his life or personal liberty except according to procedure established by law.”
• Article 14 - Equality before law. -The State shall not deny to any person equality before the law or the equal protection of the laws within the territory of India.
• Fraternity refers to a feeling of brotherhood and sisterhood and a sense of belonging with the country among its people.

Additional Information

• Some important borrowing in Indian Constitution:
• Fundamental Rights - USA
• Citizenship - Britain
• Amendment - South Africa
• Preamble - USA
• Joint Sitting - Australia

The correct answer is Tamilisai Soundararajan.

Key Points

• Dr. Tamilisai Soundararajan took charge as Governor of Telangana on 8th September 2019 and happens to be the 1st woman to hold this office.
• Dr. Tamilisai Soundararajan (born 2 June 1961) is an Indian politician serving as the 2nd and current Governor of Telangana, also current Lieutenant Governor of Puducherry (Additional charge) as of 18 February 2021.
• She was the National Secretary and Tamil Nadu State Unit President of the BJP prior to this appointment.

Additional Information

• About Telangana:
• Capital - Hyderabad.
• State Animal - Jinka (Deer).
• State Bird - Palapitta (Indian Roller or Blue Jay).
• State Tree - Jand.

The correct answer is Equatorial electrojets.

Key Points

• Thumba was chosen as the ideal site for rocket launch due to the presence of equatorial electrojets.
• Thumba is very close to the earth's magnetic equator.
• Thumba's location at 8°32'34" N and 76°51'32" E is ideal for low-altitude, upper atmosphere, and ionosphere studies.

Image: 

Additional Information

• Thumba is in Thiruvananthapuram.
• The launch site was named the Thumba Equatorial Rocket Launching Station (TERLS), or India’s first spaceport.
• TERLS became an international launch station and the sounding rockets launched from here proved instrumental in studying the equatorial electrojet.

**Source: The Hindu (**MARCH 01, 2018)

The correct answer is Malawi.

Key Points 

• Malawi launched the first Malaria vaccine to immunize children on the occasion of World Malaria Day (observed on 25 April).
• It was launched as part of a pilot program aimed at immunizing children aged 2 years and below in three African countries Malawi, Ghana, and Kenya.
• The name of the Malaria vaccine was launched in Malawi as Mosquirix.
• About Vaccine:
• It is a recombinant protein-based malaria vaccine.
• It is the world’s first and only malaria vaccine.
• Its trade name is Mosquirix.

Additional Information

• About Malawi:
• Capital - Lilongwe.
• Currency - Malawian kwacha.
• National Sports - Football.

The logic is as follows:

(Second number × 10) + 4 = First number

1. 3 × 10 + 4 = 34

2. 5 × 10 + 4 = 54

3. 2 × 10 + 4 = 24

4) 6 × 10 + 4 = 64 ≠ 66

Hence, 66 is the odd one out.

The correct answer is Denmark.

Key Points

• A group of farmers forms a cooperative society by pooling in their resources voluntarily for more efficient and profitable farming.
• Individual farms remain intact and farming is a matter of cooperative initiative.
• Co-operative societies help farmers, to procure all important inputs of farming, sell the products at the most favourable terms and help in the processing of quality products at cheaper rates.
• The co-operative movement originated over a century ago and has been successful in many western European countries like Denmark, Netherlands, Belgium, Sweden, Italy etc.
• In Denmark, the movement has been so successful that practically every farmer is a member of a co-operative.

Given:

? = $62÷ 5 - \left(\frac{8}{9}× \frac{18}{7}\right)× \frac{7}{5}+\frac{5}{4}× \frac{16}{25}$

Concept:

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

Calculation:

⇒ ? = $62÷ 5 - \left(\frac{8}{9}× \frac{18}{7}\right)× \frac{7}{5}+\frac{5}{4}× \frac{16}{25}$

⇒ ? = 62 ÷ 5 - (16/7) × 7/5 + 5/4 × 16/25

⇒ ? = 62/5 - 16/7 × 7/5 + 5/4 × 16/25

⇒ ? = 62/5 - 16/5 + 4/5

⇒ ? = 62/5 + 4/5 - 16/5

⇒ ? = 66/5 - 16/5

⇒ ? = 50/5

∴ ? = 10

Given:

⇒ 1² + 2² + 3² + ....... + 14² = 1015

Calculation:

⇒ 1² + 2² + 3² + ....... + 14² = 1015

Multiply by 9 to both sides,

⇒ 9 × (1² + 2² + 3² + ....... + 14² ) = 9 × 1015

⇒ 9 × 1² + 9 × 2² + 9 × 3² + ....... + 9 × 14² = 9 × 1015

⇒ 3² × 12 + 32 × 22 + 32 × 32 + ....... + 32 × 142 = 9 × 1015

∴ 3² + 6² + 9² + ...... + 42² = 9135

The correct answer is GSLV MK-III-M1.

Key Points

• GSLV MK-III-M1 launch vehicle was used to launch Chandrayaan-2.
• The Geosynchronous Satellite Launch Vehicle Mark III(GSLV MK-III) also referred to as the Launch Vehicle Mark 3, is a three-stage medium-lift launch vehicle developed by the Indian Space Research Organisation.
• Chandrayaan-2 is the second lunar exploration mission developed by the Indian Space Research Organisation, after Chandrayaan-1.

What is PSLV?

• Polar Satellite Launch Vehicle (PSLV) is the third generation launch vehicle of India.
• It is the first Indian launch vehicle to be equipped with liquid stages.
• After its first successful launch in October 1994, PSLV emerged as the reliable and versatile workhorse launch vehicle of India with 39 consecutively successful missions by June 2017.
• PSLV successfully launched two spacecraft – Chandrayaan-1 in 2008 and Mars Orbiter Spacecraft in 2013 – that later travelled to Moon and Mars respectively

What is ASLV?

• The Augmented Satellite Launch Vehicle (ASLV) Programme was designed to augment the payload capacity to 150 kg, thrice that of SLV-3, for Low Earth Orbits (LEO).

Additional Information

• About ISRO:
• Headquarters - Banglore
• Founder - Vikram Sarabhai
• Founded - 15 August 1969
• Subsidiary - Vikram Sarabhai Space Centre

Seven Chocolates: A, B, C, D, E, F and G.

Cost of Chocolates: Between Rs. 40 and Rs. 50 

(1) The cost of the chocolate A is a prime number, implies A can be 41, 43, or 47.

(2) The cost of chocolate F is two more than that of chocolate A, (means F = A + 2), implies F can be 43, 45, or 49.

(3) The cost of chocolate F is more than that of chocolate E, (means F > E), implies E can be 48 or 46.

(4) The cost of chocolate C is five less than that of chocolate E, (means C = E - 5), implies C can be 43 or 41.

(5) The cost of chocolate D is an odd number, implies D can be 41, 43, or 45.

(6) The cost of chocolate G is three more than the cost of chocolate D, (means G = D + 3),  implies G can be 44, 46, or 48. 

(7) None of the chocolates costs Rs. 44. Therefore, G can be 46 or 48 and therefore D can be 43 or 45.

(8) The cost of chocolate B is an even number, implies B can only be 42. Thus the final arrangement is as follows:

We can see that among the options, G(48) is costlier than E (46).

Hence, G  is the correct answer.

The correct answer is A. O. Hume.

Key Points

• A. O. Hume founded the Indian National Congress.
• The Indian National Congress is a political party in India with widespread roots.
• It was founded in 1885.

Important PointsSome important facts:

• First Muslim President of Indian National Congress - Badruddin Tyabji.
• First Female President of Indian National Congress - Annie Besant.
• First Indian woman President of Indian National Congress - Sarojini Naidu.

Additional Information

• Sir Pherozeshah Merwanjee Mehta KCIE was an Indian Parsi politician and lawyer from Bombay.
• He was knighted by the British Government in India for his service to the law.'''
• Dadabhai Naoroji, also known as the "Grand Old Man of India" and "Unofficial Ambassador of India".

Given:

Mean of 150 items = 45

Formula:

Average = (Sum of elements)/(Number of terms)

Calculation:

Sum of 150 items = 45 × 150 = 6750

Corrected sum of 150 items = 6750 - (83 + 76) + (38 + 46) = 6675

∴ Correct mean = 6675/150 = 44.5

Alternate MethodInterest = 13310 - 12100 = Rs. 1210

Rate of interest = (1210/12100) × 100 = 10%

Traditional method:

Given:

Amount in 2 years = Rs.12100

Amount in 3 years =Rs. 13,310

Formula:

Let P = Principal, R = Rate of interest and N = time

Amount = P(1 + R/100)ⁿ

Calculation:

⇒ 12100 = P(1 + R/100)² ----(1)

⇒ 13310 = P(1 + R/100)³  ----(2)

Dividing equation (2) by (1),

⇒ 1.1 = (1 + R/100)

⇒ 0.1 = R/100

⇒ R = 10

∴ Rate of interest is 10% per annum.

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

Clearly, Mahesh is grandfather of Jagat.

Hence, ‘Grandfather’ is the correct answer.

Given:

Number of candidates failed in both subjects = 1200

% candidates passed in English = 55%

% candidates passed in Mathematics = 35%

% candidates passed in both English and Mathematics = 20%

Calculation:

% candidates passed in only English = 55 - 20 = 35%

% candidates passed in only Mathematics = 35 - 20 = 15%

% candidates passed in at least one subject = 35 + 15 + 20 = 70%

% candidates failed in both subject = 100 - 70 = 30%

Let number of candidates took the exam be N.

⇒ 30/100 × N = 1200

⇒ N = 4000

∴ There are 4000 candidates who took the exam.

The correct answer is Norway.

Key Points

• Norway topped in the Human Development Index report, 2019.
• The United Nations Development Programme (UNDP) compiles the Human Development Index (HDI) of 189 countries in the annual Human Development Report.
• The index considers the health, education, and income in a given country to provide a measure of human development that is comparable between countries and over time.
• The HDI was first published in 1990.

Additional Information

• About United Nations Development Programme:
• Headquarters - New York, New York, United States
• Founded - 22 November 1965, United States

The correct answer is Param 8000.

Key Points

• Param 8000 was India's first supercomputer.
• PARAM is a series of supercomputers designed and assembled by the Centre for Development of Advanced Computing in Pune, India.
• PARAM means "supreme" in the Sanskrit language, whilst also creating an acronym for "PARAllel Machine".

Additional Information

• India's present largest HPC AI supercomputer is PARAM SIDDHI AI.
• Since June 2022, USA's Frontier is the world's most powerful supercomputer, reaching 1102 petaFlops (1.102 exaFlops) on the LINPACK benchmarks. Hence Frontier is the fastest supercomputer.
• China has the maximum number of supercomputers.

The correct answer is 1989.

Key Points

• The Sanchi Stupa was declared a world heritage site by UNESCO in 1989.
• Sanchi is a Buddhist complex, famous for its Great Stupa, on a hilltop at Sanchi Town in Raisen District of the State of Madhya Pradesh, India.
• It was originally commissioned by the Mauryan emperor Ashoka the Great.

What was the Sanchi Stupa used for?

• The stupa is a ceremonial burial mound used for the veneration of Buddhist saints and relics, as well as the Buddha himself.

Additional Information

• About UNESCO:
• Headquarters - Paris, France.
• Founded - 16 November 1945

The correct answer is Antonio Guterres.

Key Points

• As of Nov 2020, Antonio Guterres was the Secretary-General of the United Nations.
• Antonio Guterres served as the ninth Secretary-General of the United Nations.
• María Fernanda Espinosa Garcés is an Ecuadorian politician and diplomat.
• She was the President of the United Nations General Assembly for the 73rd session.
• Kofi Atta Annan served as the seventh Secretary-General of the United Nations.
• Ban Ki-moon is a South Korean politician and diplomat who served as the eighth Secretary-General of the United Nations.

Additional Information

• About United Nations:
• Headquarters - New York
• Founded in 1945.
• 24th October is celebrated as United Nations Day.

The correct answer is Lord Rippon.

Key Points

• Lord Rippon was the Viceroy of India who took the initiative to create elected local government bodies.
• Local government is government at the village and district level.
• It was the 74th amendment to the Constitution of India in 1992 that brought constitutional validity to municipal or local governments.

Important Points  Some important governors and viceroys and their important events:

Five people - A, B, C, D and E

Profession - teacher, a doctor, a lawyer, an accountant and an engineer

1. The engineer is married to the teacher
2. C is the unmarried lawyer.
3. D is an accountant.   4. Teacher B is a female whose female friend is the accountant.

1. D is a male → False (As, D is female) 2. E is a teacher. → False (As, B is a Teacher) 3. B is a doctor. → False (As, B is a Teacher) 4. A is an engineer. → It can be possible as the profession of A is not known.

Hence, ‘A is an engineer’ is the correct answer.

The correct answer is Cell.

Key Points

• Robert Hooke discovered the cell.
• Robert Hooke also discovered the law of elasticity.
• Robert Hooke was an English polymath active as a scientist and architect, who, using a microscope, was the first to visualize a micro-organism.
• He illustrated that all organisms are made of cells, which are the basic structural units of life.

Important Points

• Protoplasm was discovered by the Dujardin.
• Nucleus was discovered by Rutherford.
• Atom was discovered by John Dalton.

The logic is:

Cat : Feline → Cat belongs to the family Feline.

Similarly,

Dog : ? → Dog belongs to the family Canine.

Hence, ‘Canine’ is the correct answer.

The correct answer is Soma Mondal.

Key Points

• In Aug 2020, Soma Mondal was selected as the next Chairman of Steel Authority of India Limited.
• Mondal's appointment was approved by the Appointments Committee of the Cabinet (ACC).
• Soma Mondal replaced Anil Chaudhary as the chairman of SAIL.

Additional Information

• About SAIL:
• Headquarters: New Delhi
• Founded: 24 January 1973
• Subsidiaries: Bhilai Steel Plant, Rourkela Steel Plant, etc.

Given:

The ratio of train, bus, airfares = 5 : 8 : 12

The ratio of passengers traveling by train, bus, air = 3 : 4 : 5

Total fair collected for single trip = Rs.107000

Calculation:

Compound ratio of fares and number of travelers of train, bus and air =

= 5 × 3 : 8 × 4 : 12 × 5

= 15 : 32 : 60

Fare collected from air passengers = 60/(15 + 32 + 60) × 107000 = 60000

∴ Fare collected from air passengers is Rs.60000.

Hint

Compound ratio: When two or more ratios are multiplied term-wise, the ratio thus obtained is called compound ratio.

Two ratios = m : n and a : b

compound ratio = ma : nb

The correct answer Atal Tinkering Lab.

Key Points

• The full form of ATL is Atal Tinkering Lab.
• With a vision to Cultivate one Million children in India as Neoteric Innovators.
• Atal Innovation Mission is establishing Atal Tinkering Laboratories (ATLs) in schools across India.
• The objective of this scheme is to foster curiosity, creativity, and imagination in young minds.
• It inculcates skills such as design mindset, computational thinking, adaptive learning, physical computing, etc.

Additional Information

• About Atal Innovation Mission:
• It is a flagship initiative set up by the NITI Aayog to promote innovation and entrepreneurship across the length and breadth of the country.
• It was launched in 2016.

Given:

⇒ ? = $√{150}-√{54}-√{24}$

Calculation:

⇒ ? = √(25 × 6) - √(9 × 6) - √(4 × 6)

⇒ ? = √(5 × 5 × 6) - √(3 × 3 × 6) - √(2 × 2 × 6)

⇒ ? = 5√6 - 3√6 - 2√6

⇒ ? = √6(5 - 3 - 2)

∴ ? = 0

The logic is:

1. Melancholy: Gloomy → Melancholy means a feeling of sadness that lasts for a long time. Both the words are synonyms of each other. 2. Negligent: Attentive → Negligent means not being careful**.** Attentive means watching, listening to or thinking about somebody/something carefully. Both the words are antonyms of each other. 3. Dynamic: Robust → Dynamic means full of energy and ideas. Robust is the synonym of Dynamic. 4. Lethargic: Laidback → Lethargic means having little energy; feeling unwilling and unable to do anything. Laidback is the synonym of Lethargic.

Hence, ‘Negligent: Attentive’ is the odd one out.

The correct answer is Reiwa.

Key Points

• With the abdication of the throne by the Japanese Emperor, Akihito, the new Imperial era in Japan is known as 'Reiwa'.
• The country's current era, Heisei, will end in a month with Emperor Akihito's historic abdication.
• The term for the new era is made up of the two characters Rei and Wa.
• Rei can mean "commands" or "order", as well as "auspicious" or "good".

Additional Information

• About Japan:
• Capital - Tokyo.
• Currency - Japanese Yen
• Highest Peak - Mount Fuji
• National Sports - Sumo.

Given:

PQ = RS = 25m

Calculation:

In right angled triangle PSR,

⇒ tan a = RS/PS = 25/PS

In right angled triangle PST,

⇒ tan a = TS/PS

Then,

⇒ 25/PS = TS/PS

⇒ TS = 25

Height of tower = RS + TS = 25 + 25 = 50m

∴ Height of tower is 50m.

The correct answer is Computer Chip.

Key Points

• Diamonds, computer chips, and mobile manufacturing are some examples of footloose industries.
• These are generally non-polluting industries.

Footloose Industries:

• Footloose industries can be located in a wide variety of places. They are not dependent on any specific raw material, weight loss or otherwise.
• They largely depend on component parts which can be obtained anywhere.
• They produce in small quantities and also employ a small labour force.
• The important factor in their location is accessibility by road network.

Given:

A's 1 day's work = 1/40

B's 1 day's work = 1/60

C's 1 day's work = 1/80

Calculation:

Let number of days in which work will be complete be n.

A worked for = (n - 11) days

⇒ A's (n - 11) days work = (n - 11)/40

B worked for = (n - 8) days

⇒ B's (n - 8) days work = (n - 8)/60

Then,

⇒ (n - 11)/40 + (n - 8)/60 + n/80 = 1

⇒ 6n - 66 + 4n - 32 + 3n = 240

⇒ n = 26

∴ In 26 days work will be completed.

The correct answer is AB+.

Key Points

• Type AB-positive blood is called the "universal recipient" type because a person who has it can receive blood of any type.
• Individuals with type O Rh D negative blood are often called universal donors.
• However, these terms are only generally true with respect to possible reactions of the recipient's anti-A and anti-B antibodies to transfused red blood cells, and also possible sensitization to Rh D antigens.

Important Points 

• The blood group was discovered by Karl Landsteiner in 1901.
• About Rh factor:
• The Rh factor is a protein that can be found on the surface of red blood cells.
• If your blood cells have this protein, you are Rh-positive.
• If your blood cells do not have this protein, you are Rh-negative

The correct answer is Ca(OH)2.

Key Points

• The chemical formula for Lime water is Ca(OH)₂.
• The chemical name for lime water is calcium hydroxide.
• It is a colourless crystal or white powder and is obtained when calcium oxide (called lime or quicklime) is mixed, or "slaked" with water.

Important Points 

• Some important chemical names and common names:

Given:

Total number of students in auditorium = 6889

Calculation:

Let the number of students and number of rows be n.

⇒ n × n = 6889

⇒ n = √6889 

⇒ n = 83

∴ There are 83 rows in the auditorium.

Given:

A + B + C = 1/5

B + C + D = 1/10

C + D + A = 1/15

D + A + B = 1/30

Calculation:

Adding all above equations,

3(A + B + C + D) = 1/5 + 1/10 + 1/15 + 1/30

3(A + B + C + D) = 12/30

(A + B + C + D) = 2/15 \()

∴In 15/2 = $7\frac{1}{2}$days work will be completed when all four worked together.

Given:

⇒ 2x + 5y = 12

⇒ xy = 2

Formula:

⇒ (a³ + b³) = (a + b)(a² - ab + b²)

⇒ (a + b)² = a² + 2ab + b²

Calculation:

⇒ (2x + 5y)² = (2x)² + 2 × 2x × 5y + (5y)²

⇒ 144 = 4x² + 25y² + 20 × 2

⇒ 4x² + 25y² = 104

Then,

⇒ (2x)³ + (5y)³ = (2x + 5y)(4x² - 10xy + 25y²)

⇒ 8x³ + 125y³ = 12 × (104 - 20)

∴ 8x³ + 125y³ = 1008

Given:

One number = 72

Formula:

LCM × HCF = product of two numbers

Calculation:

LCM + HCF = 369

⇒ LCM = 369 - HCF  ---(1)

LCM - HCF = 351

⇒ 369 - HCF - HCF = 351

⇒ 369 - 2HCF = 351

⇒ 2HCF = 369 - 351 = 18 

⇒ HCF = 18/2 = 9

So, LCM = 369 - 9 = 360

Then, Other number × 72 = 360 × 9

⇒ Other number = 360 × 9/72 = 45

∴ Other number is 45

Given:

X is midpoint of AB.

BY = BC/3

Calculation:

⇒ AB = BC = CD = AD

⇒ AX = XB = AB/2

⇒ Area of ΔBXY = 1/2 × BX × BY

⇒ 300 = 1/2 × AB/2 × BC/3

⇒ 300 = 1/12 × AB × AB

⇒ AB = 60 cm

⇒ AB = BC = CD = AD = 60cm

⇒ Diagonal AC = √(AB² + BC²) = √(60² + 60²) = 60√2 cm

∴ Length of diagonal AC is 60√2 cm.

Calculation:

Greatest 3 digit number divisible by 24 = 984

Smallest 4 digit number divisible by 24 = 1008

∴ Required sum = 984 + 1008 = 1992

The correct answer is Kamala Das.

Key Points

• Kamala Das popularly known by her one-time pen name Madhavikutty and married name Kamala Das was an Indian poet in English as well as an author in Malayalam from Kerala**, India.**
• Her popularity in Kerala is based chiefly on her short stories and autobiography, while her oeuvre in English, written under the name Kamala Das, is noted for the poems and explicit autobiography.
• Some awards of Kamala Das:
• 2002: Ezhuthachan Award
• 2006: Muttathu Varkey Award

Additional Information

• Books written by Kamala Das:
• 1976: Alphabet of Lust
• 2005: Vandikkalakal (novel)
• 1996: Aattukattil (short novel)

1. Bella is taller than Shubham.

Bella > Shubham

2. Umesh is taller than Shubham but shorter than Bella.

Bella > Umesh > Shubham

3. Salman is shorter than Rahul and Shubham.

Rahul / Shubham > Salman

4. Shubham is taller than Rahul.

Shubham > Rahul

From all the statements, we get:

Bella > Umesh > Shubham > Rahul > Salman

So, Salman is the shortest in the group.

Hence, ‘Salman’ is the correct answer.

The correct answer is Green Good Deeds.

Key Points

• Green Good Deeds is the name of the Societal movement launched by the Union Minister of Environment, forest, and climate change.
• Green Good Deeds movement was launched to protect the environment and promote good living in the country, has found acceptance by the global community.
• The 'Green Good Deeds' initiative is about simple, practical steps that students/teachers/citizens can perform in their day-to-day life towards the protection of the environment.
• The BRICS Ministerial on Environment was also agreed to include this movement in its official agenda.

Additional Information

• About BRICS:
• Founded: June 2006
• Countries - Brazil, Russia, India, China, South Africa.
• Headquarters - Shanghai, China.

Given:

⇒ A : B = 15 : 16

⇒ B : C = 8 : 25

⇒ C : D = 20 : 9

Calculation:

⇒ A : B = 15 : 16

⇒ B : C = 8 : 25 = 16 : 50

⇒ A : B : C = 15 : 16 : 50

⇒ A : B : C = 30 : 32 : 100

⇒ C : D = 20 : 9 = 100 : 45

⇒ A : B : C : D = 30 : 32 : 100 : 45

⇒ A : D = 30 : 45

∴ A : D = 2 : 3

The correct answer is Pradhan Mantri Kaushal Vikas Yojana.

Key Points

• Pradhan Mantri Kaushal Vikas Yojana is the name of the skill development program of the Government of India.
• The aim of the PMKVY scheme is to encourage aptitude towards employable skills and to increase the working efficiency of probable and existing daily wage earners, by giving monetary awards and rewards and by providing quality training to them.
• The average award amount per person has been kept as ₹8,000 (US$110).
• Those wage earners already possessing a standard level of skill will be given recognition as per the scheme and the average award amount for them is ₹2000 to ₹2500.

Additional Information ​

• About Pradhan Mantri Kaushal Vikas Yojana:
• Launched - 15 July 2015
• Ministry - Skill Development and Entrepreneurship

The correct answer is 1906.

Key Points

• The Calcutta session in 1906 call for the attainment of 'Swaraj'.
• The resolution of Swadeshi was adopted in the 1906 Calcutta session of the Indian National Congress.
• In the Calcutta Session of Congress in 1906, Dadabhai Naoroji had placed Swaraj as a national demand.
• The Calcutta session 1906 was presided by Dadabhai Naoroji.

Additional Information

• Some important facts:
• First Muslim President - Badruddin Tyabji.
• First Female President - Annie Besant.
• First Indian woman President - Sarojini Naidu.
• The Surat Split was the splitting of the Indian National Congress into two groups - the Extremists and the Moderates - at the Surat session in 1907.

The correct answer is Plastic Pollution.

Key Points

• The focus of World Environment Day, 2018 was on Plastic Pollution.
• The theme for 2018 is beating plastic pollution.
• Every World Environment Day has a different global host country, where the official celebrations take place.
• The focus on the host country helps highlight the environmental challenges it faces and supports the effort to address them.

Important Points

• World Environment Day is celebrated on 5 June every year.
• This day was first observed in 1974.
• The theme for 2021 World Environment Day is Ecosystem Restoration.

The least possible Venn diagram is:  

Conclusions:

1. Some dolls are books. → False (As, there is no definite relation between dolls and books. Hence, false)
2. No book is a plant. → False (As, some plants are books)

Hence, neither conclusion 1 nor conclusion 2 follows.

Given expression: 25 + 48 × 6 ÷ 12 – 2

After replacing the symbols by their meaning, we get:

25 - 48 ÷ 6 + 12 × 2

= 25 – 8 + 24

= 49 – 8

= 41

Hence, ‘41’ is the correct answer.

The logic is:

Hence, ‘0’ is the correct answer.

Main Statement:

Whenever Sakshi hears it's someone's birthday, she orders a cake.

Options:

1. DB

D. Sakshi did not ordered a cake.

B. Sakshi did not hear of someone's birthday.

The ordered pair of statements is logically consistent with the main statement.

Sakshi did not ordered a cake because Sakshi did not hear of someone's birthday. (As, whenever Sakshi hears it's someone's birthday, she orders a cake)

2. BD

B. Sakshi did not hear of someone's birthday.

D. Sakshi did not ordered a cake.​

The ordered pair of statements is logically not consistent with the main statement.

Whenever Sakshi hears it's someone's birthday, she orders a cake. So, Sakshi did not hear of someone's birthday, the later is known from the main statement. The statement D is unnecessary.

3. AB

A. Sakshi heard of someone's birthday.

B. Sakshi did not hear of someone's birthday.

The ordered pair of statements is logically not consistent with the main statement.

The pair of statements have absurd meaning.

4. CA

C. Sakshi ordered a cake.

A. Sakshi heard of someone's birthday.

The ordered pair of statements is logically not consistent with the main statement.

Whenever Sakshi hears it's someone's birthday, she orders a cake. So, Sakshi ordered a cake because of the fact we know from the main statement. The statement A is unnecessary.

Hence, ‘DB’ is the correct answer.

Confusion Points

• The options "AB" and "DB" are not the same. This is because in the direction of the question it is mentioned that the options are ordered pairs.

The logic is:

(3 + 0)¹ = 3

(3 + 1)² = 4² = 16

(3 + 2)³ = 5³ = 125

(3 + 3)⁴ = 6⁴ = 1296

Hence, ‘1296’ is the correct answer.

1. Only statement 1 is sufficient but statement 2 is not sufficient. → False

Statement 1: On the 7th day of a month.

From statement 1, we cannot find when is Yuvi's wedding anniversary.

2. Both statement 1 and statement 2 are sufficient independently. → False

As statement 1 is not sufficient independently.

3. ​Only statement 2 is sufficient but statement 1 is not sufficient. → False

Statement 2: The month has 29 days only in a leap year.

Only February has 29 days in a leap year. So, from this statement, it is clear that Yuvi's wedding anniversary is in the month of February, but the date of Yuvi's wedding anniversary cannot be stated from this statement.

So, only statement 2 is not sufficient.

4. Both statement 1 and statement 2 are sufficient together.

Statements:

1: On the 7th day of a month.

2. The month has 29 days only in a leap year.

From 1 we know the date and from 2, we know the month. So, Yuvi's wedding anniversary is on the 7th of February.

Hence, ‘Both statement 1 and statement 2 are sufficient together’ is the correct answer.