RRB NTPC CBT-I Official Paper (Held On: 10 Jan 2021 Shift 2) (Previous Year Paper)

Shortcut Trick

Triangles sharing a common vertex have their areas in the direct ratio of their bases.

Given, BD = (1/2) × DC ⇒ DC = 2 × BD

Total base BC = BD + DC = BD + 2 × BD = 3 × BD

Therefore, the ratio of the area of triangle ABC to triangle ADC is:

Area(ABC) ÷ Area(ADC) = BC ÷ DC = (3 × BD) ÷ (2 × BD) = 3/2

∴ The correct answer is (3)/(2) times.

Alternate Method

Given:

In triangle ABC, the base BC is divided at D such that BD = (1/2) × DC.

Formula Used:

Area of a triangle = (1/2) × Base × Height

Calculations:

Let the length of BD be x.

⇒ DC = 2x

⇒ BC = BD + DC = x + 2x = 3x

Let h be the perpendicular height from vertex A to the base BC.

⇒ Area of triangle ABC = (1/2) × BC × h = (1/2) × 3x × h

⇒ Area of triangle ADC = (1/2) × DC × h = (1/2) × 2x × h

Now, let us find the ratio of the area of triangle ABC to the area of triangle ADC:

⇒ Area(ABC) ÷ Area(ADC) = ((1/2) × 3x × h) ÷ ((1/2) × 2x × h)

⇒ Area(ABC) ÷ Area(ADC) = 3x ÷ 2x = 3/2

⇒ Area(ABC) = (3/2) × Area(ADC)

Thus, the area of triangle ABC is (3/2) times the area of triangle ADC.

Let us analyze why the other options are incorrect:

Option (1) is incorrect because a ratio of 3 would require the base BC to be 3 times DC, which is false since BC is 1.5 times DC.

Option (2) is incorrect because a ratio of 4 would require the base BC to be 4 times DC.

Option (3) is incorrect because a ratio of 2 would require the base BC to be 2 times DC.

∴ The correct answer is (3)/(2) times.

Additional Information

Triangles with a Common Vertex

When two or more triangles share a common vertex and have their bases on the same straight line, their perpendicular heights are equal. Consequently, the ratio of their areas is equal to the ratio of their bases.

Median of a Triangle

A median divides a triangle into two triangles of equal area because it bisects the base, making the ratio of the bases 1:1.

Area Ratio Theorem

For any triangle ABC with a point D on BC, the ratio of the areas of the two sub-triangles is given by Area(ABD) ÷ Area(ADC) = BD ÷ DC.

Given :- bb_cc_bb_bcccc_b

By checking options and substituting accordingly.

Option (1) b; b; c; c → b b b c / c b b b / c b c c / c c c b

Option (2) c; b; c; b → b b c c / c b b b / c b c c / c c b b

Option (3) b; c; c; b → b b b c / c c b b / c b c c / c c b b

Option (4) c; c; b; b → b b c c / c c b b / b b c c / c c b b

    ♦  Option (4) gives a pattern of b b c c - c c b b - b b c c - c c b b.

Hence, ‘c; c; b; b’ is the correct answer

The pattern for the code is as follows,

Similarly,

Hence, ‘APRIL’ is coded as ‘LAIPR’.

The Venn diagrams best represent the relationship between - Mother, sister, female figure is shown below:

Both Mother and Sister are Female and some Sister is also a mother.

Hence, ‘option 2’ is the correct answer.

The correct answer is Palk Strait.

Important Points

• Palk Strait:
• It is a strait between the Tamil Nadu state of India and the Jaffna District of the Northern Province of the island nation of Sri Lanka.
• The strait is 40 to 85 miles (64 to 137 km) wide, 85 miles long, and less than 330 feet (100 meters) deep.
• It receives several rivers, including the Vaigai (India), and it contains many islands on the Sri Lankan side.
• The Sethusamudram Ship Canal Project (SSCP) is a 167 km long shipping canal and envisages the creation of a navigable canal from the Gulf of Mannar to the Bay of Bengal to facilitate the movement of ships.
• The Adam’s Bridge is a series of sand shoals created by sedimentation over a period of time.

Additional Information

• The Durand Line is the 2640-kilometre (1,640-mile) border between Afghanistan and Pakistan.
• It's the result of an agreement between Sir Mortimer Durand, a secretary of the British Indian government, and Abdur Rahman Khan, the emir, or ruler, of Afghanistan.
• Lombok Strait is a strait between the Indonesian islands of Java and Sumatra.
• It connects the Java sea to the Indian ocean.
• Malacca Strait is a narrow stretch of water between the Sumatra island of Indonesia and the Malay Peninsula.
• It is the main shipping channel between the Pacific and Indian oceans.

Given:

a = 17, b = 15, c = $\frac{1}{4}$ of -128

Formula used:

if (a + b + c) = 0 then a3 + b3 + c3  - 3abc = 0

Calculation:

Here,

a = 17

b = 15

c = $\frac{1}{4}$ × -128 = - 32

So (a + b +c) = 17 + 15 - 32

⇒ 0

So a3 + b3 + c3  - 3abc = 0

∴ Required answer of the question is 0

Given:

3 men + 3 boys = 10 day

2 men + 4 boys = 12 day

Concept used:

Total work = total person × total time taken

Calculation:

Let efficiency of men be m and boys be b

(3m + 3b)10 = (2m + 4b)12

⇒ 30m + 30b = 24m + 48b

⇒ 6m = 18b

⇒ m = 3b

Efficiency of men = 3 and boys = 1

Total work = 30 × 3 + 30 × 1

⇒ 90 + 30 = 120

Work will complete in 120/(2 × 3 + 2 × 1)

⇒ 15 days

∴ In 15 days 2 men and 2 boys complete the work

Given:

Mean of class A = 23

Mean of class B = 22

Concept used:

Mean = Sum of the terms/No. of terms

Calculation:

Total score of class A = 40 × 23

⇒ 920

Total score of class B = 45 × 22

⇒ 990

Total score both the classes = 1910

Mean score of two classes together = 1910/85

Ratio = 1910/85 : 23

⇒ 382/17 : 23

⇒ 382 : 391

∴ The ratio of the mean score of both the classes to that of class A is 382 : 391

Given:

No. of toys in good condition = 4800

Concept used:

Percentage of distribution

Calculation:

Let the number of toys originally was x

According to the question,

x × 4/5 × 3/4 = 4800

⇒ 3x/5 = 4800

⇒ x = 4800 × 5/3

⇒ x = 8000

∴ The original number of toys produced was 8000

The correct answer is Protochordata.

Key Points

• Plants are divided into five groups- Thallophytes, Bryophytes, Pteridophytes, Gymnosperms and Angiosperms.

Additional Information

• Bryophytes are the amphibian of the plant kingdom.
• They have a unique feature as compared to other green plant groups that are their sporophyte is attached to the gametophyte.
• Bryophytes are the first land inhabitant plants.
• The ciliated sperms and archegonia are present in bryophytes.
• Thallophytes is a polyphyletic group of non-motile organisms traditionally described as thalloid plants.
• They are simple or lower plants.
• Archegonium is absent in thallophyta.
• Thallophtes are an abandoned division of kingdom Plantae which includes fungi, algae, lichens, and some kinds of bacteria, bryophytes, and slime molds.​
• Gymnosperms are also known as acrogymnosperms.
• It is a group of seed-producing plants.
• It includes conifers, cycads, ginkgo, and gnetophytes.
• The word gymnosperms in greek means naked seeds because they do not have an outer covering or shell around their seeds.
• They do not produce flowers i.e they are non-flowering plants and neither do they produce fruits. Its pollination is done by the wind (Anemophilous).
• Angiosperms are also known as Angiospermae or Magnoliophyta.
• They are flowering and seed-producing plants.
• It consists of 64 orders, 416 families, approximately 13,000 known genera, and 3,00,000 known species.
• Their seeds develop in the ovaries of flowers and are surrounded by a protective fruit.
• Examples of angiosperms are fruits, vegetables, grains, and flowers.
• Angiosperms are classified as Monocotyledons (monocots) and Dicotyledons (dicots) where monocots are flowering plants whose seeds contain only one embryonic leaf or cotyledon and dicots are flowering plants whose seeds contain two embryonic leaves or cotyledons.
• Pteridophytes are known as the Vascular cryptogams because they are the first non-seeded plants to have a vascular system present.
• They are also called vascular crypto games.
• They are used for medicinal purposes.
• They are not completely differentiated into root, stem, and leaves.
• Hence Protochordata is not included in 5 group.

The correct answer is Andhra Pradesh.

Important Points

• Satish Dhawan Space Centre is located at Sriharikota in Andhra Pradesh.
• Satish Dhawan Space Centre is an agency responsible for providing launch base infrastructure for the Indian space programme.
• It was established in 1971.
• Satish Dhawan Space Centre (SDSC) or Sriharikota High Altitude Range (SHAR) is a rocket launch centre operated by Indian Space Research Organisation (ISRO).

Additional Information

• ISRO stands for Indian Space Research Organisation.
• The headquarters of ISRO is in Bengaluru.
• The present chairman of ISRO is Dr. S. Somanath.
• ISRO was the world's first space agency to find water on the moon and insert a probe in orbit of Mars in its maiden attempt.
• Vikram Sarabhai is known as the Father of the Indian Space Program.

The correct answer is Tulabhara.

• Tulabhara is an ancient Hindu practice in which a person is weighed against a commodity (such as gold, grain, fruits or other objects), and the equivalent weight of that commodity is offered as a donation.

Additional Information

• Jallikattu is a traditional event in which a bull, such as the Pulikulam or kangyam breeds, is released into a crowd of people, and multiple human participants attempt to grab the large hump on the bull's back with both arms and hang on to it while the bull attempts to escape.
• The Thimithi is a Hindu festival originating in South India that is celebrated during the month of Aipasi of the Tamil calendar.
• The festival is celebrated to commemorate this event and worship Draupadi.
• Pulikali (Tiger Dance) is one of the folk art forms of Kerala.
• On the fourth day of the Onam festival, artists paint their bodies like tigers with stripes of yellow, red, and black and dance to the rhythm of traditional percussion instruments such as Thakil, Udukku, and Chenda.

Given:

Total quantity of oranges = 20 kg

Rate of per kg = Rs. 45

SP per kg = Rs. 54

Concept used:

Profit % = [(SP - CP)/100] × 100

Calculation:

Total CP = 20 × 45

⇒ Rs. 900

SP of 18.5 kg oranges = 18.5 × 54

⇒ Rs. 999

SP of 1.5 kg spoiled oranges = 1.5 × 10

⇒ Rs. 15

Total SP = 1014

Profit = 1014 - 900

⇒ 114

Profit % = (114/900) × 100

⇒ $12\frac{2}{3}$

∴ His net gain is $12\frac{2}{3}\%$

The correct answer is Karachi.

Important Points

• The Indus Waters Treaty is a water-distribution treaty between India and Pakistan which was signed  in Karachi in 1960.
• According to the treaty, control over the water flowing from Beas, Ravi and Sutlej were given to India while Pakistan was given the control over Indus, Chenab and Jhelum.
• The treaty was signed in Karachi by then Prime Minister of India Jawaharlal Nehru and then President of Pakistan Ayub Khan.

The correct answer is Pune.

• Pune Metro is a metro rail based rapid transit system under construction to serve the city of Pune, India.
• ​Hence Pune metro is still not operational.
• Uttar Pradesh Metro Rail Corporation Limited is a state-owned company that operates the Lucknow Metro in Lucknow, Uttar Pradesh.
• The Kochi Metro is a rapid transit system serving the city of Kochi in Kerala, India.
• Jaipur Metro is a rapid transit system in the city of Jaipur, Rajasthan, India.

Additional Information

• Delhi Metro Rail Corporation Limited (DMRC), a company with equal equity participation from the Government of India and the Government of Delhi, built and operates the Delhi Metro.
• Bengaluru Metro Rail Corporation Limited (BMRCL), a joint venture of the Government of India and the State Government of Karnataka, is the agency for building, operating, and expanding the Namma Metro (Bangalore metro) network.

The correct answer is solution.

Key Points

• A homogeneous mixture of two or more substances is known as the Solution.
• Mixtures are constituted by more than one kind of pure form of matter.
• A solution has a solvent and a solute as its components.
• The component of the solution that dissolves the other component in it (usually the component present in larger amounts) is called the solvent.
• The component of the solution that is dissolved in the solvent (usually present in lesser quantity) is called the solute.

Additional Information

• Mixtures are classified into two categories:-
• A heterogeneous mixture is a mixture of two or more chemical substances where the various components can be visually distinguished.
• A homogeneous mixture is a type of mixture in which the composition is uniform and every part of the solution has the same properties.
• Pure substances are classified into two categories:-
• Elements- A pure substance with only one kind of atom and cannot be broken into two or simpler substances by physical or chemical means is an element.
• Compounds- A pure substance composed of two or more elements and chemically combined in a fixed proportion is called a compound.

Given:

Total distance = 200 km

Concept used:

Relative Speed of 2 bodies

Sum of their individual speeds if they are moving in the opposite direction

Difference of their individual speeds if they are moving in the same direction.

Calculation:

We know the total distance is 200 Km

If both trains crossed each other at a distance of 110 km then one train covered 110 km and the other 90 km [110+90=200km]

So ratio of their speed = 110 : 90 = 11 : 9

∴ The ratio of their speed is 11 : 9

Given:

Rate of interest of A = 8%

Rate of interest of B = 5%

Concept used:

For half year interest in CI = Interest rate/2

Successive increase concept = a + a + a²/100

a = rate %

Calculation:

5% half-yearly = 5 + 5 + (5 × 5)/100

⇒ 10 + 1/4

⇒ 41/4

So ratio of interest = 

41/4 : 8

⇒ 41 : 32

∴ ​At the end of one year the ratio of B's interest to that of A's interest is 41 : 32

Traditional method:

Let the sum be Rs. P.

Simple interest = (P × 8 × 1)/100 = 2P/25

Compound interest = P[(1 + 5/100)² - 1]

⇒ P[(21/20² - 1]

⇒ P(441 - 400)/400

⇒ 41P/400

Required ratio = (41P/400)/(2P/25)

⇒ 41 ∶ 32

∴ ​At the end of one year the ratio of B's interest to that of A's interest is 41 : 32

Mistake PointsHere 5% of CI is for each half-year i.e 6 months

The correct answer is Interface Manager.

• If Bill Gates had his way, by Interface Manager name was Windows OS planned to be released.
• ​The interface manager role varies, depending on the size of the project, the number of engineering resources involved, and also on other roles in the project.
• An Interface Manager / Technical Manager / Technical Interface Manager may be responsible for ensuring that the interface management process functions effectively within the project area.

Key Points

• Bill Gates, was born October 28, 1955, in Seattle, Washington, U.S.
• Bill Gates is an American computer programmer and entrepreneur who cofounded Microsoft Corporation, the world’s largest personal computer software company.
• Since 1987, Gates has been included in the Forbes list of the world's wealthiest people. From 1995 to 2017, he held the Forbes title of the richest person in the world every year except from 2010 to 2013.
• Microsoft and Gates launched their first retail version of Microsoft Windows on November 20, 1985.
• As of 2021, the latest release of the OS is known as Windows 11.

Additional Information

Given:

cot A = $\frac{1}{\sqrt{3}}$ 

Concept used:

Cos(90° + θ) = - Sinθ

Calculation:

cot A = $\frac{1}{\sqrt{3}}$ 

⇒ cot A = cot60°

⇒ A = 60°

$\frac{1 - \cos 2A}{1 + \cos 2A}$

⇒ $\frac{1 - \cos120^o}{1 + \cos 120^o}$

⇒ [1 - cos(90 + 30)°]/[1 + cos(90 + 30)°]

⇒ 1 + sin30°/1 - sin30°

⇒ (1 + 1/2)/(1 - 1/2)

⇒ 3

∴ Required answer is 3

The correct answer is The Civil Disobedience Movement would be called off.

Important Points

• Gandhi–Irwin Pact was signed on 5 March 1931.
• The Gandhi-Irwin Pact was a political agreement signed by Mahatma Gandhi and Lord Irwin.
• The important pacts signed in this agreement were:
• The government will release most of the civil disobedience volunteers.
• Indian National Congress will discontinue Civil disobedience movement.
• The congress will participate in the second Round Table Conference.
• Tax on salt will be removed.

Additional Information

• Lord Irwin (1926 AD-1931 AD):
• Simon Commission visited India in 1928.
• Nehru Report, 1928.
• Lahore Session of the Congress, (1929) and Poorna Swaraj, declaration.
• Civil Disobedience Movement, 1930 started.
• Dandi March (12 March 1930).
• Gandhi-Irwin Pact, 5 March 1931.
• Sharda Act, 1929, under which the marriageable age of girls (14 years) and boys (18 years) was raised.

Given:

Thickness = 3 cm

height 0.83 m

Dimensions are 1.36 m, 1.06 m

Formula used:

L.S.A = 2h(l + b)

Area of a rectangle = (l × b)

Calculation:

Inner length = 136 - 6 = 130 cm

Inner breadth = 106 - 6 = 100 cm

Inner height = 83 - 3 = 80 cm

Surface area which has be to be painted = base area + area of 4 walls

So,

(130 × 100) + 2 × 80(130 + 100)

⇒ 13000 + 36800

⇒ 49800 cm²

Cost = 49800/100 × 50p

⇒ Rs. 249

∴ The cost of painting the inner surface of the tank is Rs. 249

Note:

There was some discrepancy found in this question, In the actual question, height was given as 8.3 m but we have changed it to 0.83 m

From the given information,

Breaking the statement –

His only brother is the father of Vivek's daughter's father so his brother is the father of Vivek.

We can draw the following tree from the information given above:

Hence, the man is ‘Uncle’ of Vivek**.**

The correct answer is Dr. Homi Bhabha.

• Homi Jehangir Bhabha is known as the 'Father of the Indian Nuclear Programme'.
• He was an Indian nuclear physicist who founded Bhabha Atomic Research Centre and Tata Institute of Fundamental Research.
• Ajit Kumar Mohanty was appointed as the director of Bhabha Atomic Research Centre (BARC) for a period of three years in march 2019.
• He is a well-known nuclear physicist. He obtained a PhD degree from Bombay University.
• Dr Homi Bhabha established the Atomic Energy Establishment, Trombay (AEET) in January 1954.
• In 1966, at Atomic Energy Establishment, Trombay was renamed Bhabha Atomic Research Centre (BARC).

Additional Information

Given:

$\frac{1}{1.2.3} + \frac{1}{2.3.4} + \frac{1}{3.4.5} + \frac{1}{4.5.6}$

Concept used:

Simple concept of multiplication and summation

Calculation:

$\frac{1}{1.2.3} + \frac{1}{2.3.4} + \frac{1}{3.4.5} + \frac{1}{4.5.6}$

⇒ 1/6 + 1/24 + 1/60 + 1/120

⇒ (20 + 5 + 2 + 1)/120

⇒ 28/120 = 7/30

∴ Required answer is 7/30

The correct answer is Huawei.

Key Points

• US agencies are banned from doing business with Huawei and other Chinese tech companies, as the Trump administration cites security concerns.

• Huawei is 5G equipment from the Chinese telecom company.

• Sweden has banned on security grounds the use of telecom equipment from China's Huawei and ZTE in its 5G network.

• The UK has banned its companies from sourcing 5G equipment from Chinese telecom company Huawei.

Given:

The window is at a height of 10 meters

Concept used:

tanθ = P/b

P = perpendicular or height

b = base

Calculation:

Let the window be Q.

Height of the building be AB

Let the point P at a distance of x meter.

In ΔQPB

tan30° = QB/BP​

⇒ 10​/x

x =​ 10/tan30°

⇒ 10√3

In Δ ABP

tan60° = h/x

⇒ h = x.tan60°

⇒ h = x.√3

⇒ h = 10√3 × √3

⇒ 30m

So, the height of building = 30 m

∴ The height of the building is 30 m

The correct answer is www.symbolics.com.

Key Points

• The first domain name registered was Symbolics.com.
• It was registered March 15, 1985.

Additional Information

• A domain name is a label that identifies a network domain: a distinct group of computers under a central administration or authority.
• The company managing the reservation of domain names is the domain name registrar.
• A domain name registry is a database of all domain names and the associated registrant information in the top-level domains of the Domain Name System (DNS)

The correct answer is M Venkaiah Naidu.

• Muppavarapu Venkaiah Naidu is an Indian politician serving as the 13th vice president of India since 2017.
• Jagdeep Dhankar is the 14th and current Vice President of India.

Additional Information

• Article 63 of the Constitution of India provides that there shall be a Vice-President of India.
• Articles 64 and 89 provide that the Vice-President of India shall be the ex-officio Chairman of the Rajya Sabha and shall not hold any other office of profit.
• The Vice-President of India will preside over the Upper House and will act as the President in certain contingent situations.
• Thus, the Vice President of India has been assigned a dual role, as the second Chief of the Executive and as the Presiding Officer of the Upper House of Parliament.
• The Vice-President is elected by a single transferable vote according to the proportional representation method by the electorate consisting of members of both houses of Parliament.

The correct answer is Manpreet Singh.

• Manpreet Singh Pawar is an Indian hockey player and is also the captain of the India men’s national field hockey team since May 2017.
• The first Indian to win the FIH (Fédération Internationale de Hockey) Player of the Year award 2019.
• Under Manpreet’s captaincy, the Indian team won the Asia Cup in 2017, the Asian Champions Trophy in 2018.

Additional Information

• Manpreet Singh were the country’s flag bearer at the opening ceremony of the Tokyo Olympics.
• Rani Rampal is the captain of Indian Hockey Team (Women).

The correct answer is Safdarjung Tomb.

• Safdarjung's Tomb is a late Mughal Empire style tomb built for Nawab Safdarjung in the year 1754.
• It is made of sandstone and marble has the domed structure of arched red-brown and white colour located near the Safdarjung airport in Delhi.
• Safdarjung was the Nawab of Oudh, and also he was a prime minister of the Mughal Empire (Wazir ul-Mamlak-i-Hindustan) when Ahmed Shah Bahadur ascended the throne in 1748.

Additional Information

• Other important monuments of UP:
• Taj Mahal
• Agra Fort in Agra.
• Fatehpur Sikri Fort, Agra
• Bara Imambara in Lucknow
• Kans Qila or Kans Fort in Mathura
• Dhamek Stupa Varanasi

Given:

$0.3 ÷ (0.6 × \frac{2}{3}) × 0.2 (0.2 × 2 ÷ \frac{1}{2} + 0.2)$

Concept used:

Calculation:

$0.3 ÷ (0.6 × \frac{2}{3}) × 0.2 (0.2 × 2 ÷ \frac{1}{2} + 0.2)$

⇒ 0.3 ÷ (0.2 × 2) × 0.2 (0.2 × 2 × 2 + 0.2)

⇒ 0.3 ÷ 0.4 × 0.2 (0.2 × 4 + 0.2)

⇒ 0.3 ÷ 0.4 × 0.2 (0.8 + 0.2)

⇒ 0.3 ÷ 0.4 × 0.2 × 1

⇒ 0.3 ÷ 0.4 × 0.2

⇒ 0.3 × 1/0.4 × 0.2

⇒ 0.75 × 0.2 = 0.15

∴ The correct answer is option (2).

The correct answer is Narendra Modi.

Important Points

• Pradhan Mantri Jan Dhan Yojana was announced by PM Narendra Modi on 15 August 2014 from the ramparts of the Red Fort and was launched on 28 August 2014.

Additional Information

• Pradhan Mantri Jan-Dhan Yojana
• Date of launch 28th August 2014
• Government Ministry Ministry of Finance
• The scheme covers both the urban as well as rural areas and provides an indigenous Debit Card (RuPay card) to each of its account holders.
• No minimum balance is required for opening an account under this scheme.
• The beneficiary can open his/her account in any bank branch or Business Correspondent outlet at zero balance.
• It ensures to provide on Core Banking System (CBS) along with mobile banking using USSD facilities.
• A facility of call centre and a toll-free number is available nationwide.
• Pradhan Mantri Jan Dhan Yojana provides each beneficiary with basic banking accounts with a debit card with inbuilt accident insurance.
• Rs. 5,000 overdraft facility for Aadhar-linked accounts as well as a RuPay debit card with inbuilt Rs. 1 lakh accident insurance cover is one of the main features provided by this scheme.
• For accounts that are opened between 15th August 2014 and 26th January 2015, a Life Insurance cover of Rupees 30,000 is provided to the eligible beneficiaries. Also after remaining active for 6 months, the beneficiary will be eligible for an overdraft of up to Rs 5,000.

The pattern followed here is,

Let (M : N)

Step 1 → M³ = A (A any number)

Step 2 → A - 1= N

Now follow the steps:

7 : 342

Step 1 → 7³ = 343

Step 2 → 343 – 1 = 342

And,

9 : 728

Step 1 → 9³ = 729

Step 2 → 729 – 1 = 728

Similarly,

? : 2196

Step 1 → 13³ = 2197

Step 2 → 2197 – 1 = 2196

Hence, ‘13 : 2196’ is correct answer.

Given:

PQ = 30 cm

Diameter = 32 cm

Concept used:

Tangent is perpendicular to the radius at the point of contact

Calculation:

OQ is the radius of a circle

OQ = 16 cm 

∠OQP = 90°

now apply Pythagoras theorem to 

OP² = PQ² + OQ²

⇒ OP² = 30² + 16²

⇒ OP = 1156​

⇒ OP = 34 cm

∴ The length of OP is 34 cm

Given:

Total amount = Rs. 9000

Calculation:

According to the question,

${9000\over a ;+; 20} = {9000\over a} - 160$

⇒ 9000a = (9000 – 160a)(a + 20)

⇒ 9000a = 9000a + 180000 – 160a² – 3200a

⇒ a² + 20a – 1125 = 0

⇒ a² + 45a – 25a – 1125 = 0

⇒ a(a + 45) – 25(a + 45) = 0

⇒ (a – 25)(a + 45) = 0

⇒ a = 25 or a = -45

(- 45 Neglected as the number of people can never be negative)

∴ The original number of people is 25

The correct option is China.

Important Points

• Manushi Chhillar is an Indian actress and model.
• She won the Miss World 2017 pageant.
• She is from Haryana, India.
• Miss World 2017 was held in China.

Additional Information

• Miss World 2020 is Toni-Ann Singh of Jamaica.
• Miss Universe 2020 is Andrea Meza of Mexico.
• Mr. World 2020 won by Dhruba Tamuly from Assam.

The correct answer is India.

• The Constitution of India is the longest written constitution of any sovereign country in the world, containing 448 articles grouped in 22 parts with 12 schedules.

Additional Information

• There were 395 articles originally in the Constitution of India.
• Presently 470 articles are there in Constitution.
• The Indian Constitution was originally written in English.
• Prem Behari Narain Raizada wrote the Indian constitution by hand.
• Dr. BR Ambedkar is known as the father of the Indian Constitution.
• Indian Constitution was adopted by the Constituent Assembly of India on 26 November 1949 and became effective on 26 January 1950.

The Venn diagrams best represent the relationship between - 

Boy, student, farm figure are shown below:

Some boys are students it is possible but any boy and student are farm it is not possible.

Hence, ‘option 2’ is the correct answer.

100’s place - (301, 302, 303,..........399) = 99 times

10’s place (30, 31, 32,..........39) = 10 times

1’s place (03, 13, 23…....93) = 10 times

Total = 99 + 20 = 119 times

∴ Answer is 119 times

The correct answer is found in a particular area.

Important Points

• Endemic species are those species of plants and animals which are found in a particular area.
• In ecology, an endemic species is one that is unique to the area in which it is found.
• A species might be endemic to a limited geographic area, such as a single island, or a larger geographical area, such as a continent.
• The lion-tailed macaque is endemic to India.

Additional Information

Some of the tags of IUCN are

The correct answer is Gopal Krishna Gokhale.

• Gopal Krishna Gokhale did NOT advocate militant opposition to colonial rule through the Swadeshi movement.
• Gopal Krishna Gokhale was born on 9 May 1866 in the Bombay Presidency.
• From 1899 and 1902, he was a member of the Bombay Legislative Council, followed by a stint in the Imperial Legislative Council from 1902 until his death.
• In the Imperial legislature, Gokhale was instrumental in formulating the Morley-Minto Reforms of 1909 and advocated for the expansion of legislative councils both at the center and in the provinces.
• In the Banaras session of 1905, Gokhale became the President of the Congress.​

Key Points

• Swadeshi Movement:
• On August 7, 1905, a boycott resolution was passed at the Calcutta City Hall, where it was decided to boycott Manchester's use of cloth and salt from Liverpool.
• In Western India (Maharashtra), Shivaji and Ganpati festivals were organized by Lokmanya Tilak to spread the Swadeshi message and boycott movements among the masses.
• The Swadeshi and Boycott movements were India's first movements of the 20th century that encouraged collective participation in modern nationalist politics by a large section of society.​

Additional Information

Given:

(a + b) : (b + c) : (c + a) = 6 : 7 : 8

a + b + c = 14

Concept used:

If (a + b) : (b + c) : (c + a) is x : y : z

(a + b + c) = (x + y + z)/2

Calculation:

Let (a + b) : (b + c) : (c + a) be 6x : 7x : 8x

a + b + b + c + c + a = 6x + 7x + 8x

2(a + b + c) = 21x

(a + b + c) = 21x/2

⇒ 21x/2 = 14

⇒ x = 28/21

⇒ 4/3

(a + b) = 6 × 4/3 = 8

So c = 14 - 8

⇒ 6

∴ The value of c is 6

The correct answer is Shandur National Park.

• Shandur National Park is located in District Ghizer, Pakistan.
• It is often called 'Roof of the World'.
• Hence it is the correct answer.

Additional Information

• Important facts about the National Parks in India
• The number of National Park - 104.
• Maximum National Park state-  Madhya Pradesh (10).
• First National Park Jim Corbett National Park.
• Largest National Park Hemis National Park.
• Smallest National Park South Button National Park.

The correct answer is SEBI.

Important Points

• Securities and Exchange Board of India (SEBI) is a statutory body and a market regulator, which controls the securities market in India.
• The basic functions of SEBI are to protect the interests of investors in securities and to promote and regulate the securities market.
• SEBI is run by its board of members, the board consists of a Chairman and several other whole time and part-time members.
• The chairman is nominated by the union government.
• Founded: 12 April 1992
• Headquarters: Mumbai
• Agency executive: Shri Tuhin Kanta Pandey (Chairperson)

Additional Information

• RBI:
• Governor - Sanjay Malhotra.
• Headquarters - Mumbai.
• Founded: 1 April 1935, Kolkata.
• IRDAI:
• Founded: 1999
• Headquarters: Hyderabad
• NABARD:
• Founded: 12 July 1982
• Headquarters: Mumbai
• Chairperson:Shaji K V

The correct answer is Alexander Fleming.

• Alexander Fleming discovered penicillin.
• This discovery led to the introduction of antibiotics that greatly reduced the number of deaths from infection.
• Penicillin prevents the bacteria from synthesizing peptidoglycan, a molecule in the cell wall that provides the wall with the strength it needs to survive in the human body.

Additional Information

• Charles Darwin is regarded as the "Father of Evolution."
• Louis Pasteur developed the Rabies Vaccine.
• Gregor Mendel is called the father of genetics.

Given:

Speed of the student = 8 km/h

Time taken = 3/2 hours

Concept used:

Speed = Distance/time

Calculation:

Distance cover = 8 × 3/2 = 12 km

Now at the time of return, he will cover 11 km as given in the question

He has taken a rest for 30 minutes

So he will cover 11 km in 1 hour

So his new speed = 11 km/h

Speed increased =  3 km/h

% change = 3/8 × 100

⇒ 37.5%

∴ The required increase in speed is 37.5%

The correct answer is Madhubani painting.

Important Points

• Mithila painting, popularly known as Madhubani art.
• It is from the district of the same name in Bihar and Nepal.
• The colours used in Madhubani paintings are usually derived from plants and other natural sources.
• Most commonly, a coloured paste of powdered rice is used for Madhubani painting.
• Women usually paint their homes to celebrate festivals and the theme of the painting can be varied from nature to myths.
• Women decorate the nuptial chamber and the inner walls of their homes to celebrate festivals.

Additional Information

Other states and their traditional artforms:

The correct answer is Gurugram.

Important Points

• Gurugram topped the list of the most polluted cities in the world in a recent study conducted by NGO Greenpeace India.
• It was ranked first among 62 polluted cities in the report, Global Air Pollution 2018.
• The report measures the air quality in terms of PM 2.5 data as aggregated through the IQAir AirVisual platform in 2018.

Additional Information

• According to the 'World Air Quality Report, 2020', prepared by a Swiss organization.
• The world's 30 most polluted cities are in India.
• Delhi is ranked as the most polluted capital city globally.

Given:

Price at which the machine was purchased = Rs.70000

Overhead expenditure = Rs.5000

Formulas used:

Profit or Loss is calculated on the Cost Price of the machine, which is 100% of itself.

Selling Price = Cost Price + Profit 

                        or 

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

Calculation:

Total cost of the machine = Purchasing Price + Overhead Expenses 

⇒ 70000 + 5000 = Rs.75000

As per the question, 

Cost of machine at 15% less = 70000 × (100 - 15)% + 5000 

⇒ Rs.64500 

Selling Price = 64500 × (100 + 15)/100 

⇒ Rs.74175

∴ The selling price of the machine is Rs.74175.

Shortcut Trick

When a solid is melted to form identical smaller objects, the number of objects is equal to the ratio of their volumes.

Number of cones (N) = Volume of Cylinder ÷ Volume of 1 Cone

⇒ N = (π × R² × H) ÷ (1/3 × π × r² × h)

Convert everything to cm (R = 3 cm, H = 5 cm, r = 0.1 cm, h = 1 cm):

⇒ N = 3 × (3² × 5) ÷ (0.1² × 1) = (3 × 45) ÷ 0.01 = 135 ÷ 0.01 = 13,500

∴ The correct answer is 13,500 cones.

Alternate Method

Given:

For the cylinder:

⇒ Radius (R) = 3 cm = 30 mm

⇒ Height (H) = 5 cm = 50 mm

For each cone:

⇒ Radius (r) = 1 mm

⇒ Height (h) = 1 cm = 10 mm

Formula Used:

Volume of Cylinder = πR²H

Volume of Cone = 1/3 × πr²h

Calculations:

⇒ Volume of the given cylinder = π × (30)² × 50 = 45,000π mm³

⇒ Volume of one cone = 1/3 × π × (1)² × 10 = 10π/3 mm³

⇒ Number of cones formed = Total Volume of Cylinder ÷ Volume of One Cone

⇒ Number of cones = 45,000π ÷ (10π/3)

⇒ Number of cones = 45,000 × (3 / 10)

⇒ Number of cones = 4500 × 3 = 13,500

∴ The correct answer is 13,500 cones.

Additional Information

Melting and Recasting of Solids

When a solid object is melted and recast into a different shape, the overall volume of the material remains constant. Total Initial Volume = Total Final Volume.

Volume of a Cylinder

The volume of a right circular cylinder is given by V = πr²h, where r is the base radius and h is the height.

Volume of a Cone

The volume of a right circular cone is exactly one-third of the volume of a cylinder with the same base radius and height: V = 1/3 × πr²h.

Calculation:

Let the number be = a 

So, 1/5 × a × 2/3 × a = 480 

⇒ 2a²/15 = 480 

⇒ a² = 2⁴ × 3² × 5²

⇒ a = √24 × 32 × 52

⇒ a = 4 × 3 × 5 = 60 

∴ The required number is 60.

Alternate MethodBy Hit and Trial Method

We will check the condition as, 1/5 × a × 2/3 × a = 480

Option 1: For a = 80, 1/5 × 80 × 80 × 2/3 ≠ 480 

Option 2: For a = 70, 1/5 × 70 × 70 × 2/3 ≠ 480 

Option 3: For a = 60, 1/5 × 60 × 60 × 2/3 = 480 

Option 4: For a = 100, 1/5 × 100 × 100 × 2/3 ≠ 480

Given:

Percentage of students passed = 82% 

Percentage of students placed in reappear category = 2% 

Number of students failed = 592

Calculation:

Let the total number of students be 100% 

Percentage of students failed = 100% - Passed Percent - Reappear Category Percent 

⇒ 100% - 82% - 2% 

⇒ 16% 

∵ 16% = 592 

⇒ 100% = 592 × 100%/16% 

⇒ 100% = 3700 

∴ Total number of students in the class are 3700.

The correct answer is an American.

• Gertrude Ederle of the United States at the young age of 19 years, became the first woman to swim across the English channel.
• She swam 21 miles in her second attempt from Dover, England.

Additional Information

• Arati Saha was the first Indian swimmer to cross the  English Channel in 1959.
• In 1960, she became the first Indian sportswoman to be awarded the Padma Shri, the fourth highest civilian honour in India.
• She was inspired by the ace Indian swimmer Mihir Sen.
• Mihir Sen was the first Asian to swim across the English Channel.
• English channel connects the North Sea to the Strait of Dover.
• Mihir sen is also the first swimmer to swim across Palk strait.

Given:

Number of question attempted = 120 

Marks received by Ambika = 90 

Marks awarded for correct answer = 1

Marks deducted for wrong answer = 0.5 

Calculation:

Let the number of correct answer be = a 

⇒ Number of wrong answers = 120 - a

Marks for 'a' right answers = a × 1 = a 

Marks deducted for (120 - a) wrong answers = (120 - a) × 0.5 = 60 - 0.5a 

As per the question;

Total marks scored = Marks received for right answers - Marks deducted for wrong answers 

⇒ 90 = a - (60 - 0.5a)

⇒ 1.5a = 150 

⇒ a = 100 

∴ The number of correct answers is 100.

Given:

3 traffic signals change after every 48, 72 and 108 respectively. 

Time when 3 lights started changing simultaneously = 8:20 

Concept Used:

Lowest Common Multiple

Calculation:

The time of changing the 3 traffic lights simultaneously will be the LCM of 48, 72, and 108 as the first common multiple of the numbers. 

By Prime Factorisation we will take LCM of 48, 72 and 108 seconds. 

48 = 2⁴ × 3

72 = 2³ × 3²

108 = 2² × 3³

LCM ( 48, 72, 108) = 2⁴ × 3³ = 432 

Hence after 432 seconds, they will change simultancously. 

⇒ 432/60 minutes 

⇒ 7 minutes 12 seconds 

∴ Lights will change at 8:20:00 + 7 minutes + 12 seconds = 8:27:12 hours

The logic followed here is:

Lion : Cat → Lion and Cat both are 'Felidae' family.

Similarly,

Wolf : Dog → Wolf and Dog both are 'Canidae' family.

Hence, ‘Dog’ is the correct answer. 

Additional Information

• Felidae is a family of mammals in the order Carnivora, colloquially referred to as cats, and constitutes a clade. A member of this family is also called a felid. The term "cat" refers both to felids in general and specifically to the domestic cat.
• Canidae is a biological family of dog-like carnivorans, colloquially referred to as dogs, and constitutes a clade. A member of this family is also called a canid. There are three subfamilies found within the canid family, which are the extinct Borophaginae and Hesperocyoninae, and the extant Caninae.

Given:

A's investment = 3 times as much as B's investment

B's investment = 2/3 times of C's investment 

Total profit of the year = Rs.6600

Concept used:

Ratio of investment = Ratio of Profit to be shared

Calculation:

Let the sum invested by C = a 

⇒ Sum invested by B = 2/3 × a 

⇒ Sum invested by A = 2a/3 × 3 = 2a 

Ratio of profit to be shared between A, B, and C:

A : B : C = a : 2a/3 : 2a 

⇒ A : B : C = 3 : 2 : 6 

B's profit share will be = Rs.6600 × 2/11 

⇒ Rs.1200 

∴ B's share in the profit for the year is Rs.1200.

The correct answer is The Uprising of 1857.

Important Points

• The First War of Indian Independence was fought in the year 1857.
• It is also known as the Indian Sepoy Mutiny of 1857.
• It was called The First War of Indian Independence by V.D Savarkar.
• He authored a book called ‘The History of the War of Indian Independence’ in which he stated his views and announced the mutiny as the First War of Indian Independence.
• Lord Canning (1856-1862) was the Governor-General of India/ Viceroy of India during this revolt.

Additional Information

• Rowlatt Satyagraha was a nationwide satyagraha against the proposed Rowlatt Act (1919).
• It was launched by Mahatma Gandhi in 1919.
• Rowlatt satyagraha made Gandhiji a truly national leader.
• The Santhal Revolt took place in 1855-56.
• This was the first peasant revolt that occurred in India.
• The revolt can be attributed to the introduction of the Permanent Land Settlement of 1793.

The correct answer is Eating food spoilt by microorganisms.

Key Points

• Food poisoning is mostly caused by the consumption of food that is contaminated with bacteria/microorganisms like Salmonella, Listeria or E.coli.
• Although rarely but parasites like Toxoplasma and virus-like the Norwalk virus can also cause food poisoning.
• Symptoms of food poisoning include- nausea, bloody stool, fever, fatigue, and abdominal pain.
• Chemical food preservatives are substances that help either delay the growth of microorganisms/destroy them, thus preventing quality deterioration during manufacture and distribution.

The correct answer is 13th.

• ​IPL 2020 was the 13th edition of India's premier T20 league.
• Indian Premier League was conceptualized after India's landmark victory in the maiden ICC WT20 in 2007.
• IPL has been a great platform for young talent to showcase their skills and rub shoulders with the best players in the world.

Additional Information

• Mumbai Indians won the Indian Premier League (IPL), 2020.
• The final match was played between Mumbai Indians and Delhi Capitals.
• Mumbai Indians won this match by 5 wickets.
• Mumbai Indians also won Paytm Fairplay Award this year.
• This is the consecutive second time Mumbai Indians won the IPL title & and overall 5th time.

The correct answer is ​Amethi and Wayanad.

• Congress leader Rahul Gandhi contest the Lok Sabha Elections of 2019 from Amethi, Uttar Pradesh and Kerala's Wayanad.

Additional Information

• The seventeenth General Elections were held from 11 April to 19 May 2019.
• The Bharatiya Janata Party having 303 Members is the largest party in the Seventeenth Lok Sabha followed by the Indian National Congress having 52 Members.
• There are 541 MPs at present in the 17th Lok Sabha.
• Shri Om Birla is the Speaker of the Lok Sabha.

The correct answer is planting new trees in the destroyed forests.

• Reforestation means planting new trees in the destroyed forests.
• It is the re-growing of forests that have previously been cut down using tree species that are native to the geographic area.

Additional Information

• Afforestation
• It is the process of introducing trees and tree seedlings to an area that has previously not been forested.
• It can be done through tree planting and seeding, naturally or artificially.
• Deforestation
• It refers to the decrease in forest areas across the world that are lost for other uses such as agricultural croplands, urbanization, or mining activities.
• It is a particular concern in tropical rainforests because these forests are home to much of the world's biodiversity.

The Venn diagrams best represent the relationship between - eyes, ears, sensory organs figure are shown below:

Eyes and ears both are sensory organs.

Hence, ‘option 4’ is the correct answer.

Important Points

• The sensory nervous system is a part of the nervous system responsible for processing sensory information. A sensory system consists of sensory neurons, neural pathways, and parts of the brain involved in sensory perception.
• The sense organs are the body organs by which humans are able to see, smell, hear, taste, and touch or feel. The five sense organs are the eyes (for seeing), nose (for smelling), ears (for hearing), tongue (for tasting), and skin (for touching or feeling).

The correct answer is The working class went on strike in many towns and cities.

• Non-cooperation Movement was conducted from September 1920 to February 1922. It was initiated by Gandhi after the Jallianwala Bagh Massacre.
• People started protesting with Non-Ahimsa and at the same time boycotted British goods.
• After the Chauri-Chaura incident, Gandhi withdrew the movement.
• The Khilafat Movement was essentially a movement to express Muslim support for the Caliph of Turkey against the allied powers particularly Britain.
• The Muslims were especially upset about the future of the Islamic places of worship after the allied powers had partitioned the Turkish Empire.
• Maulana Abul Kalam Azad, Dr. M.A. Ansari and the Ali brothers were the prominent leaders of the movement.
• Gandhiji supported the Khilafat movement to unite Hindu and the Muslims.
• By the mid-1920s, the Khilafat leaders joined hands with Gandhi's Non-Cooperation Movement.
• In both the movements the working class went on strike in many towns and cities.

Given:

a, b and c are the sides of a right triangle with c as the hypotenuse. 

An incircle with radius 'r'. 

Formula used:

Inradius = (Base + Height - Hypotenuse)/2 

Calculation:

∴ Inradius of the circle with radius 'r' = (a + b - c)/2

The pattern followed here is,

Option 1 → 2548 → Not a perfect cube of any number

Option 2 → 1728 → Perfect cube of ‘12’

Option 3 → 2197→ Perfect cube of ‘13’

Option 4 → 1331 → Perfect cube of ‘11’

All options follow the same pattern, except ‘Option 1’

Hence, "2548" is the correct answer.

(Note: In original paper this question has discrepancy. We have corrected as per the given statements.)

Given:

Statements:

I. All Doctors are social workers.

II. All social workers need money.

The least possible diagram for the given statements is as follows

Conclusions:

I. All social workers are doctors → False ( it is possible but not definite)

II. Doctors need money → True (because all social workers need money and all doctors are social workers so all doctors need money.)

Hence, “Only conclusions II follow”.

Additional Information

The correct answer is Trade of the British East India Company expanded.

Battle of Plassey - 

• It took place on June 23, 1757.
• It was fought between the forces of East India Company headed by Robert Clive and Siraj-Ud-Daulah (Nawab of Bengal).
• It resulted in the decisive victory of the East India Company over a much larger force of Siraj-Ud-Daulah.
• After the Battle of Plassey, the Britishers virtually monopolized the trade and commerce of Bengal.

Additional Information

• Shuja-Ud-Daula -
• He was Nawab of Avadh (Oudh) and took the title Nawab Wazir.
• He was son of Nawab Safdarjang.
• He is associated with the Battle of Buxar.

The logic is here,

In given series 23, 29, 31, 37, 43, 47 all are prime number except 42.

41 is prime number not 42.

Hence, “42” is correct answer.

The logic followed here is:

Running : Track → Running on the track.

Similarly,

Boxing : Ring → Boxing is played in the ring.

Hence, ‘Ring’ is the correct answer. 

 

Additional Information

The correct answer is Common Business Oriented Language. 

• COBOL stands for Common Business Oriented Language.
• It is first developed in 1960 by the CODASYL Committee (Conference on Data Systems Languages).
• It is primarily designed for use in business-oriented applications.

Additional Information

• Some important Abbreviations

The correct answer is Mercury.

• Minamata Convention is an international treaty that is designed to protect human health and the environment from the harmful effect of Mercury and its compounds.
• The convention is named after the Japanese city, Minamata, which was severely affected by the devastation of Mercury poisoning.
• The agreement is aimed at reducing mercury pollution and spreading awareness of its harmful effects.

Additional Information

The correct answer is US, Russia, China.

• ‘Mission Shakti’ was the country’s first-ever Anti-Satellite (ASAT) Missile Test successfully conducted on 27th March 2019 from Dr AP J Abdul Kalam Island in Odisha, where a fast-moving Indian orbiting target satellite in Low Earth Orbit (LEO) was neutralised with pinpoint accuracy.
• This was a highly complex mission, conducted at extremely high speed with remarkable precision.
• The successful conduct of Mission Shakti was made India the fourth nation in the world after US, Russia, China​ with the capability to defend its assets in outer space.

Additional Information

• Countries that have launched Anti-satellite missions:
• Russia PL-19
• China SC-19
• The United States of America USA-193

Left 2 6 6 3 4 5 2 4 9 8 6 4 3 4 8 2 Right

Odd numbers are preceded by the number 4 in the following series is: 

4 → Odd number.

2 6 6 3 4 5 2 4 9 8 6 4 3 4 8 2.

There are 3 odd numbers are preceded by the number 4.

Hence, "3" is the correct answer.

Mistake PointsImmediately preceded by means immediately before or to come just before.

Immediately followed by means immediately after or to come just after.

Important Points

In this approach, we analyze the number at “ones” place in an integer to check if the number is even or odd. 

• All the numbers ending with 1, 3, 5, 7 and 9 are odd numbers. For example, numbers such as 11, 23, 35, 47 etc. are odd numbers.
• All the numbers ending with 0, 2, 4, 6 and 8 are even numbers. For example, numbers such as 14, 26, 32, 40 and 88 are even numbers.
• Odd numbers are not evenly divisible by 2 and end in 1, 3, 5, 7, or 9.

Shortcut Trick

The series consists of n terms, where each term is of the form (1 − k/n).

Separate the integer parts and the fractional parts: (1 + 1 + ... n times) − (1/n + 2/n + ... + n/n).

Sum of n ones = n. Sum of fractions = (1/n) × [n(n + 1)/2] = (n + 1)/2.

Net result = n − (n + 1)/2 = (2n − n − 1)/2 = (n − 1)/2.

∴ The correct answer is (n − 1)/2.

Alternate Method

Given: The series is (1 − 1/n) + (1 − 2/n) + (1 − 3/n) + ... up to n terms.

Formula Used: Sum of the first n natural numbers (Σn) = n(n + 1)/2.

Calculations:

⇒ Let S = (1 − 1/n) + (1 − 2/n) + (1 − 3/n) + ... + (1 − n/n)

⇒ S = (1 + 1 + 1 + ... up to n terms) − (1/n + 2/n + 3/n + ... + n/n)

⇒ S = n − (1/n) × (1 + 2 + 3 + ... + n)

⇒ S = n − (1/n) × [n(n + 1)/2]

⇒ S = n − (n + 1)/2

⇒ S = (2n − (n + 1))/2

⇒ S = (2n − n − 1)/2

⇒ S = (n − 1)/2

∴ The correct answer is (n − 1)/2.

Additional Information

Sum of First n Natural Numbers

The sum of the first n positive integers is given by the formula S = n(n + 1)/2.

Arithmetic Progression (AP)

A sequence where the difference between consecutive terms is constant. The sum of n terms is S_n = (n/2)[first term + last term].

General Term of the Series

The k-th term of the given series is T_k = (1 − k/n). For k = n, the term becomes (1 − n/n) = 0.

The logic followed here is:

Except Actor, all are intangible whereas Actor is tangible.

 

Hence, the correct answer is "Actor".

Key PointsThe primary difference between tangible and intangible is that tangible is something which a person can see, feel or touch and thus they have the physical existence, whereas, the intangible is something which a person cannot see, feel or touch and thus do not have any of the physical existence.

• Tangible assets are physical; they include cash, inventory, vehicles, equipment, buildings and investments.
• Intangible assets do not exist in physical form and include things like accounts receivable, pre-paid expenses, and patents and goodwill.

Additional InformationScript is defined as the written words of a play, movie or show, or a standard message to deliver on the phone or in person.

• For example of a script is the screenplay for the movie Chinatown. An example of a script is the greeting which is spoken when making phone calls for a call center.

Dialogue is the exchange of spoken words between two or more characters in a book, play, or other written work.

• Conversation between people in a book, play, etc.

Plot → In a literary work, film, or other narrative, the plot is the sequence of events where each affects the next one through the principle of cause-and-effect.

• The series of events which form the story of a novel, film, etc.

The correct answer is ​Adam Smith.

• Adam Smith was a Scottish economist and also known as the Father of economics or the Father of Capitalism.
• Adam Smith work includes 
• The Theory of Moral Sentiments(1759)
• An Inquiry into Nature and Causes of the Wealth of Nations. (1776)
• Economics is a social science concerned with the production, distribution, and consumption of goods and services. It studies how individuals, businesses, governments, and nations make choices about how to allocate resources.

Additional Information

• Amartya Sen is a world-renowned economist awarded the 1998 Nobel Prize.
• He has propounded "the concept of public welfare economics".
• He was also awarded the "Bharat Ratna", India's highest civilian honor in 1999.
• Dr. Manmohan Singh
• Indian economist.
• Served as the 13th Prime Minister of India.
• Served as the Deputy Chairman of the Planning Commission.
• Former Governor of the Reserve Bank of India.
• Notable works: Changing India, The Quest for Equity in Development.
• John Maynard Keynes was an economist who advocated for increased government expenditures and lower taxes to stimulate demand.

Given:

$\frac{x}{2y} = \frac{6}{7}$

Calculation:

$\frac{x}{2y} = \frac{6}{7}$

By cross multiplication, we get 

⇒ 7x = 12y 

⇒ x/y = 12/7 

Now,$\frac{x - y}{x + y} + \frac{14}{19}$

⇒ (12 - 7)/(12 + 7) + 14/19 

⇒ 5/19 + 14/19 

⇒ 19/19 or 1 

∴ The required value is 19/19.

The correct answer is Amazon.

Key Points

• Amazon river is the largest river in the world in terms of discharge volume of water and also the longest river in South America.
• It flows through the continent South America and countries Brazil, Colombia, Peru, Venezuela, Bolivia, Ecuador, and Guyana.
• Hence it is the correct option.

 Important Points

• Orange River primarily flows in South Africa.
• The Orange river extends into Namibia and Botswana to the north.
• It is the longest river in South Africa
• Niger river
• It flows in West Africa and it is the third-longest river in Africa.
• Nile River
• It is a north-flowing river in northeastern Africa and is the longest river in the world.

Given:

A's height = 25% less than that of B

Calculation:

Let the height of B = 100 

⇒ A's height = 100 - 100 × 25/100 

⇒ A's height = 75 

Difference between the height of B and A = 100 - 75 = 25 

∴ The required percentage = 25/75 × 100 

⇒ 33.33%

Shortcut Trick 25% = 25/100 = 1/4 

⇒ A/B = 3/4 

∴ The required percentage = (4 - 3)/3 × 100 

⇒ 33.33%

Given:

Dimensions of rectangular field = 16 m × 12 m 

Cost of fencing = 25 paise per cm 

Formula used:

Length of rectangular field with one side open = 2 × Length + Breadth 

Calculation:

Length of field = 2 × 16 m + 12 m 

⇒ 44 m = 4400 cm 

∴ Cost of fencing at 25 paise per cm = 4400 cm × 25/100 

⇒ Rs.1100

The correct answer is Rashtriya Ispat Nigam Limited.

• Rashtriya Ispat Nigam Limited Company is called Vizag Steel.

Key Points 

• Rashtriya Ispat Nigam Limited, the corporate arm of Visakhapatnam Steel Plant, is a Navratna PSU under the Ministry of Steel.
• It was established in 1982, RINL was wholly owned by the Government of India. In November 2010, the company was accorded Navratna status by the government.
• It is the first coast-based integrated steel plant in the country.
• It is the first steel plant to be certified to ISO 9001:2008 (currently 2015), ISO 14001:2004 (currently 2015), OHSAS 18001:2007 and ISO/IEC 27001:2013 standards.
• It is also the first PSU to be certified ISO 50001:2011 Energy Management System and has received CMMI Level 3 certification for development.

Additional Information

Given:

$X = 2 - √ 3$

Formula Used: 

a2 - b2 = (a + b)(a - b)

Calculation:

$X = 2 - √ 3$

1/X = 1/(2 - √3)

By Rationalization

⇒1/X = 1/(2 - √3) × (2 + √3)/(2 + √3)

⇒ (2 + √3)/(2² - √3²)               ∵ [ a² - b² = (a + b)(a - b)]

⇒ (2 + √3)/(4 - 3) 

⇒ (2 + √3)/1 

∴ X - 1/X = 2 - √3 - (2 + √3)

⇒ 2 - √3 - 2 - √3

⇒ -2√3