RRB NTPC CBT-I Official Paper (Held On: 2 Feb 2021 Shift 1) (Previous Year Paper)

Given:

Purchase price of TV = Rs. 4,600

Selling price of TV = Rs. 5,406

Profit percentage = 6%

Formula used:

Profit = Selling Price (SP) - Cost Price (CP)

Profit% = (Profit/CP) × 100

CP = Purchase price + Repair Cost

Calculation:

⇒ Profit = (Profit% × CP) / 100

⇒ 5,406 - CP = (6 × CP) / 100

⇒ 540,600 = 6 × CP + 100 × CP

⇒ 540,600 = 106 × CP

⇒ CP = 540,600 / 106

⇒ CP = 5,100

⇒ CP = Purchase price + Repair Cost

⇒ 5,100 = 4,600 + Repair Cost

⇒ Repair Cost = 5,100 - 4,600

⇒ Repair Cost = Rs. 500

Thus, Rupert spent Rs. 500 on the repairs.

The correct answer is Art. 243.

Key Points

• A Gram Sabha may exercise such powers and perform such functions at the village level as the Legislature of a State may, by law, provide.
• A panchayat at the village level shall be elected. in such manner as the Legislature of a State may, by. law, provide.
• A Panchayat at the intermediate level or district level shall be elected by, and from amongst, the elected members thereof.

Additional Information

• According to the Article, 270 taxes were levied and collected by the Union and distributed between the Union and the States.
• The Right to Protection of Life and personal liberty is the main object of Article 21 and it is a right guaranteed against State Action as distinguished from violation of such right by private individuals.
• According to the Article 51 A: develop the scientific temper, humanism and the spirit of inquiry and reform to safeguard public property and to abjure violence

Given:

Four cows are tethered to the four corners of a square field of length 28 m

Each cow can just touch the two cows in the adjacent corners

The grass in the area inside the square field that was accessible to the cows was enough to fee them for 22 days

Concept used:

Area of square = a² 

Area of sector = π r² (θ/360)

Calculations:

According to the question,

Area of remaining part = Area of square field - Area of 4 sectors

⇒ (28)² - 4 × π × (14)² × (90°/360°)

⇒ 784 - 4 × π × 196 × (1/4)

⇒ 784 - (22/7) × 196

⇒ 784 - 22 × 28

⇒ 784 - 616 =168 m²

Area of the part that is accessible to the cow is 616 m² which is enough to feed for 22 days.

⇒ 22 = 616

⇒ 1 = 28

⇒ 1 × 6 = 28 × 6

⇒ 6 = 168

∴ It is enough to feed for 6 days.

The alphabets and their positions are:

First, we will check all the options:

1. W-A: 

2. T-Y:  

3. M-Q: 

4. B-F: 

Thus, we can say that every option has the same pattern except the letter cluster T-Y.

Hence, the correct answer is 'option 2'.

The correct answer is Jahangir.

Key Points

• Nur-ud-Din Muhammad Salim, known by his imperial name Jahangir.
• He was the fourth Mughal Emperor.
• He ruled from 1605 until his death in 1627.
• He was born on 30 August 1569 in Fatehpur Sikri and died on 28 October 1627 in Rajouri.
• He is famous for his 'golden chain of justice.
• A golden chain having 60 bells and weighing several 'maunds' was fastened between the Shahburj of Agra fort and a stone pillar raised on the banks of river Jamuna.
• He was the Mughal ruler of India who gave permission to the British to establish their first factory in Surat.

Additional Information

• Shah Jahan, Mughal emperor from 1628 to 1658, is perhaps best remembered for the grand monuments constructed during his reign, especially the Taj Mahal and the Motī Masjid (Pearl Mosque) in Agra and the Jāmiʿ Masjid and Red Fort in Delhi.
• Bahadur Shah Zafar was a noted Urdu poet, having written a number of Urdu ghazals. While some part of his opus was lost or destroyed during the Indian Rebellion of 1857, a large collection did survive and was compiled into the Kulliyyat-i-Zafar.
• Aurangzeb is known for being the emperor of India from 1658 to 1707. He was the last of the great Mughal emperors. Under him the Mughal Empire reached its greatest extent, although his policies helped lead to its dissolution.

According to the given information, we have:

Hence, the position of the faulty lamp from the left end is '21st'

The correct answer is 2 years.

Key Points

• The United Nations Security Council is one of the six principal organs of the United Nations.
• It is charged with ensuring international peace and security.
• And recommending the admission of new UN members to the General Assembly, and approving any changes to the UN Charter.
• Its headquarter is in  New York, United States.
• The Security Council is the United Nations' most powerful body, with "primary responsibility for maintaining international peace and security."
• It has two types of members:
• Five powerful countries sit as "permanent members"
• Ten elected members with two-year terms. They are non-permanent members.
• 10 non-permanent members, five of which are elected each year by the General Assembly for a two-year term.
• In 1963, the General Assembly recommended an amendment to the Charter to increase the membership of the Security Council.

Additional Information

• 5 permanent members with veto power:
• China
• France
• Russian Federation
• United Kingdom of Great Britain and Northern Ireland
• United States of America

Given:

The two unequal sides of a rectangle are in the ratio of 3: 4.

The perimeter = 42 cm

Concept used:

Perimeter of Rectangle = 2(l + b)

Diagonal of Rectangle = √(l² + b²)

Calculations:

Let the length of unequal sides of the rectangle be = 3x and 4x.

According to the question,

Perimeter of Rectangle = 42 cm

⇒ 2(3x + 4x) = 42

⇒ 14x = 42

⇒ x = 3

Length of unequal sides = 9 cm and 12 cm

Now Diagonal of Rectangle

⇒ √[(9)² + (12)²]

⇒ √(81 + 144)

⇒ D = √225 = 15 cm

∴ The length of the diagonal will be 15 cm.

The correct answer is Mumbai.

Key Points

• National Stock Exchange of India Limited is the leading stock exchange of India, located in Mumbai, Maharashtra.
• It is the world’s largest derivatives exchange in 2021 by the number of contracts traded based on the statistics maintained by the Futures Industry Association, a derivatives trade body.
• It is under the ownership of some leading financial institutions, banks, and insurance companies.
• NSE was established in 1992 as the first dematerialized electronic exchange in the country.
• NSE was the first exchange in the country to provide a modern, fully automated screen-based electronic trading system that offered easy trading facilities to investors spread across the length and breadth of the country.
• Ashishkumar Chauhan is the Managing Director and Chief Executive Officer of NSE.
• The Indian stock exchange BSE and NSE have been engulfed in a series of corruption scandals such as the 1992 Indian stock market scam and others.

Additional Information

• BSE Limited, also known as the Bombay Stock Exchange, is an Indian stock exchange located on Dalal Street in Mumbai.
• Established in 1875 by cotton merchant Premchand Roychand, a Jain businessman, it is the oldest stock exchange in Asia, and also the tenth oldest in the world.
• Shri Ashishkumar Chauhan is the MD & CEO of BSE (Bombay Stock Exchange), the first stock exchange in Asia.
• He is one of the founders of India's National Stock Exchange ("NSE") where he worked from 1992 to 2000.

The correct answer is Nuclear power generation plants.

Key Points

• Most of the hydrogen in normal water is made by the common hydrogen isotope.
• The water with a heavier hydrogen isotope has different chemical properties.
• Deuterium contains protons and neutrons. As compared to the protium atom, the deuterium atom is very heavy.
• Each hydrogen atom is heavier in heavy water.
• Deuterium oxide is the scientific name for heavy water.
• Nuclear power plants are a type of power plant that uses the process of nuclear fission in order to generate electricity.
• They do this by using nuclear reactors in combination with the Rankine cycle, where the heat generated by the reactor converts water into steam, which spins a turbine and a generator.

Additional Information

• The fertilizer industry is made up of companies who represent the entire supply chain from production to distribution to retail, all working together to deliver fertilizer to farmers in a safe, timely, and sustainable manner.
• The pharmaceutical industry discovers, develops, produces, and markets drugs or pharmaceutical drugs for use as medications to be administered to patients (or self-administered), with the aim to cure them, vaccinate them, or alleviate symptoms.
• At hydropower plants, water flows through a pipe, or penstock then pushes against and turns blades in a turbine to spin a generator to produce electricity.

The correct answer is It is located in low earth orbit.

Key Points

• The International Space Station is the largest modular space station currently in low Earth orbit.
• It is a multinational collaborative project involving five participating space agencies: NASA, Roscosmos, JAXA, ESA, and CSA.
• The space station is jointly run by the space agencies of Russia, the U.S., Europe, Japan and Canada.
• The first piece was put in orbit in 1998, and the outpost has been continuously inhabited for nearly 22 years.
• It is used to conduct scientific research in zero gravity and test out equipment for future space journeys.
• The mission of the International Space Station is to enable long-term exploration of space and provide benefits to people on Earth.
• With six state-of-the-art laboratories, the Space Station will be the premiere research facility in space, four times larger and more capable than any previous space station.

Additional Information

• The International Space Station was taken into space piece-by-piece and gradually built in orbit using spacewalking astronauts and robotics.
• Most missions used NASA's space shuttle to carry up the heavier pieces, although some individual modules were launched on single-use rockets.
• Several systems are currently used on board the ISS to maintain the spacecraft's atmosphere, which is similar to the Earth's.

The correct answer is Bt Cotton.

Key Points

• Bt. Cotton is the only GM crop that can be commercially cultivated in India.
• It was first used in India in the year 2002.
• Genetically modified crops are plants used in agriculture, the DNA of which has been modified using genetic engineering methods.

Additional Information

• The Bt Potato is a genetically engineered potato that has genes added so it will produce the insecticide (Bacillus thuringiensis or Bt toxin) in every cell. Two different types of Bt Potato exist: Potato Tuber Moth Resistant Bt Potato. Colorado Potato Beetle Resistant Bt Potato.
• Bt Brinjal is a transgenic brinjal created by inserting a gene cry1Ac from the soil bacterium Bacillus thuringiensis into Brinjal.
• GM Mustard a genetically modified hybrid variety of the mustard species Brassica juncea. It was developed by Professor Deepak Pental from the University of Delhi,

Given:

Cost Price of article = Rs. 500

Selling Price = Rs. 550

Formula used:

Gain% = [$\frac{(SP - CP)}{CP}$] × 100

Calculation:

According to the question

Gain% = [$\frac{(550 - 500)}{500}$] × 100

⇒ Gain% = ($\frac{50}{500}$) × 100

⇒ Gain% = ($\frac{1}{10}$) × 100 = 10%

∴ The percentage gain is 10%.

By taking the information from the above statements, we get

Thus, for the word FLY, we have:

Hence, the code language is '527' for the given word.

The correct answer is In three years 2,00,000 clusters will be formed.

Key Points

• The Paramparagat Krishi Vikas Yojana (PKVY)– a traditional farming improvement programme.
• It was launched in 2015.
• It is an extended component of Soil Health Management (SHM) under the Centrally Sponsored Scheme (CSS).
• PKVY aims at supporting and promoting organic farming, reducing in dependence on fertilizers and agricultural chemicals.
• Organic food, thus produced will be linked with modern marketing tools and local markets.

Additional Information

• Objectives:
• The objective is to produce agricultural products free from chemicals and pesticidal residues by adopting eco-friendly, low-cost technologies.
• Promote organic farming among rural youth/ farmers/ consumers/ traders.
• Disseminate the latest technologies in organic farming.
• Utilize the services of experts from the public agricultural research system in India.
• Organize a minimum of one cluster demonstration in a village,

The correct answer is Venus.

Key Points

• Venus is the second planet from the Sun and is named after the Roman goddess of love and beauty.
• As the brightest natural object in Earth's night sky after the Moon, Venus can cast shadows and can be visible to the naked eye in broad daylight.
• Venus is a terrestrial planet.
• The terrestrial planets are the 4 inner rocky worlds in the Solar System: Mercury, Venus, Earth, and Mars.
• The atmosphere of Venus is made up mainly of carbon dioxide, and thick clouds of sulfuric acid completely cover the planet.
• It's the hottest planet in our solar system, even though Mercury is closer to the Sun.
• Solar Orbiter found that Venus' magnetic field extends at least 188,000 miles behind the planet — about the distance from Earth to the Moon.
• The planet Venus rotates clockwise. The rotation of Venus on its axis is somewhat unusual.

Additional Information

• Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousandth the mass of the Sun.
• Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth.
• Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, being larger than only Mercury.

The correct answer is Mundaka Upanishads.

Key Points

• The words Satyameva Jayate from Mundaka Upanishad.
• The saying of the Indian National Emblem is 'Satyamev Jayate' or 'Truth Alone Triumphs.
• It is written in the Devanagari script.
• The word alludes to an antiquated Sanskrit Vedic content, which is inserted inside Atharva Veda.
• It had been embraced as the public aphorism of India on the date of 26 January 1950.
• It is engraved in the Devanagari script at the foundation of the Lion Capital of Ashoka and furthermore frames a basic piece of the Indian public seal.
• The image and the words "Satyameva Jayate" have been engraved on more than one side of all Indian money just as the public records.

Additional Information

• The Puranas are religious texts composed in Sanskrit, orally narrated for centuries before being written down from the 2nd century CE onwards. They are part of the sacred literature of the Hindu faith that also comprises the Vedas, Brahmanas, Aranyakas, Upanishads, and the great epics.
• Bhagavadgita is an episode recorded in the great Sanskrit poem of the Hindus, the Mahabharata. It occupies chapters 23 to 40 of Book VI of the Mahabharata and is composed in the form of a dialogue between Prince Arjuna and Krishna, an avatar (incarnation) of the god Vishnu.
• The Jatakas are a voluminous body of literature native to South Asia which mainly concern the previous births of Gautama Buddha in both human and animal form. According to Peter Skilling, this genre is "one of the oldest classes of Buddhist literature."

The correct answer is Bay of Bengal.

Key Points

• Super Cyclonic Storm Amphan was a powerful and catastrophic tropical cyclone that caused widespread damage in Eastern India.
• Specifically in West Bengal and Odisha, and in Bangladesh, in May 2020.
• The cyclone produced sustained winds of 112 km/h (70 mph) and gusts to 190 km/h (120 mph)
• Wind speed along coastal areas was measured up to 150–160 km/h (93–99 mph).
• The causes of the Amphan cyclone included the formation of an area of low pressure over the Bay of Bengal about 1020 km to the southeast of Visakhapatnam.

Additional Information

• The Mediterranean Sea has been the focal point of western civilization. It is an area rich in history and has played critical roles in the development of shipping and trade, as a resource for feeding growing populations.
• The Persian Gulf is located in the Middle East between Iran and the Arabian Peninsula. It is an extension of the Indian Ocean.
• The Arabian Sea is a region of the northern Indian Ocean bounded on the north by Pakistan, Iran and the Gulf of Oman, on the west by the Gulf of Aden.

The correct answer is R. K. Narayan.

Key Points

• Rasipuram Krishnaswami Iyer Narayanaswami was an Indian writer.
• He is known for his work set in the fictional South Indian town of Malgudi.
• He was a leading author of early Indian literature in English along with Mulk Raj Anand and Raja Rao.
• In 1980 he was awarded the A.C. Benson Medal by the Royal Society of Literature.
• In 1981 he was made an Honorary Member of the American Academy and Institute of Arts and Letters.
• He was also nominated for the Nobel Prize for Literature multiple times.
• R**.K. Narayan died in 2001**.

Additional Information

• Girish Karnad was an Indian actor, film director, Kannada writer, playwright and a Jnanpith awardee, who predominantly worked in South Indian cinema and Bollywood.
• Babukodi Venkataramana Karanth was a film and theatre personality from India. Throughout his life he was director, actor and musician of modern Indian theatre both in Kannada as well as Hindi, and one of the pioneers of Kannada and Hindi new wave cinema.
• Udupi Rajagopalacharya Ananthamurthy was an Indian contemporary writer and critic in the Kannada language. He was born in Thirtahalli Taluk and is considered one of the pioneers of the Navya movement.

The correct answer is Madhya Pradesh.

Key Points

• Kanha Tiger Reserve, also called Kanha National Park, is one of the tiger reserves of India.
• It is the largest national park of Madhya Pradesh, a state in the heart of India.
• The present-day Kanha area is divided into two sanctuaries, Hallon and Banjar, of 250 and 300 km2 respectively.
• Kanha National Park was created on 1 June 1955 and in 1973 was made the Kanha Tiger Reserve.
• Today it stretches over an area of 940 km² in the two districts Mandla and Balaghat.

Additional Information

• The park has a significant population of the Royal Bengal tiger, Indian leopards, the sloth bear, barasingha, and Indian wild dog.
• The forest depicted in the famous novel by Rudyard Kipling, The Jungle Book is based on jungles including this reserve.
• It is also the first tiger reserve in India to officially introduce a mascot, “Bhoorsingh the Barasingha”.

BODMAS Rule

According to the given information, 

$\nabla$ = 1^st number + (3 x 2^nd number)    -------- (i)

Given: (4 $\nabla$ 5)$\nabla$ 6

Applying (i), we will get,

= [4 + (3 $\times$ 5)] $\nabla$ 6

Using BODMAS Rule, we get,

= [4 + 15] $\nabla$ 6

Solving the bracket, we will get,

= 19 $\nabla$ 6

Again applying (i), we will get,

= 19 + (3 $\times$ 6)

Using BODMAS Rule, we get,

= 19 + 18

= 37

Hence, the value of the given expression is '37'.

The logic here is:

The first line numbers are all prime numbers.

Thus, the odd term is '16Q12' which does not follow the pattern.

Hence, the correct answer is 'option 2'.

The correct answer is the United Province

 Key Points

• The province with the maximum representation in the Constituent Assembly of India on that date was United Provinces
• Uttar Pradesh, then known as the United Provinces, was one of the most populous and politically active regions in India.
• Its demographic weight translated into a substantial number of representatives.
• The United Provinces had a rich history of political activism, social reform movements, and intellectual discourse.
• Several influential leaders from Uttar Pradesh played pivotal roles in shaping India’s destiny.
• Notable figures like
• Pandit Jawaharlal Nehru, Sardar Patel, and Dr. Rajendra Prasad were actively involved in the Constituent Assembly proceedings.

Additional Information

• Constituent Assembly of India
• The Constituent Assembly was specifically elected to draft the Indian Constitution.
• It was formed after India gained independence from British colonial rule in 1947.
• The assembly consisted of 299 members, representing various regions, communities, and ideologies.

Given:

Values = 1, 2, 3, 4, ..., n

Frequencies = 1, 2, 3, ..., n

Concept used:

Mean = $\frac{(∑f_ix_i)}{(∑f_i)}$

Calculation:

According to the question,

∑fixi =  (1 × 1) + (2 × 2) + (3 × 3) + ....... (n × n)

Where, f_i = Frequency, x_i = Observation

⇒ ∑fixi = 1² + 2² + 3² + ...... n²

⇒ ∑fixi = $\frac{[n(n+1)(2n+1)]}{6}$

Now for Frequencies

∑fi = 1 + 2 + 3 + ...... + n

⇒ ∑fi = $\frac{[n(n + 1)]}{2}$

Accordingly,

Mean = $\frac{\frac{[n(n+1)(2n+1)]}{6}} {\frac{[n(n + 1)]}{2}}$

⇒ Mean = $\frac{\frac{[n(n+1)(2n+1)]}{3}} {n(n + 1)}$

⇒ Mean = $\frac{n(n+1)(2n+1)} {3[n(n + 1)]}$

⇒ Mean = $\frac{(2n+1)}{3}$

∴ The mean of the values will be $\frac{{2n + 1}}{3}$.

Given:

Time = 10 years

Amount = 2(Principle)

Concept used:

Simple interest = $\frac{(P × R × T)}{100}$

Amount = SI + P

Calculations:

According to the question,

Amount = P + [$\frac{(P × R × T)}{100}$]

⇒ 2P = P + [$\frac{(P × R × 10)}{100}$]

⇒ P = $\frac{(P × R × 10)}{100}$

⇒ R = $\frac{100}{10}$ = 10%

∴ The rate is 10%.

The correct answer is PPM.

Key Points

• PPM stands for Paper per minute which is used to measure the printing speed of both inkjet and laser printers.
• The abbreviation is used in marketing to describe printer speed.
• Most printers include a PPM rating for both black and color documents.
• These speed measurements are typically listed in the printer's technical specifications.

Additional Information

• Cost per mille also called cost per thousand, is a commonly-used measurement in advertising. It is the cost an advertiser pays for one thousand views or impressions of an advertisement.
• LPM is an abbreviation of liters per minute (l/min). When used in the context of a particle counter's flow rate, it is a measurement of the velocity at which air flows into the sample probe.

The correct answer is Quicksilver.

Key Points

• Mercury is a chemical element.
• Its symbol is Hg and the atomic number 80.
• It is also known as quicksilver and was formerly named hydrargyrum from the Greek words.
• Mercury is used in many scientific instruments such as thermometers and barometers.
• Due to its electrical conductivity, it is used to make silent switches, while its vapor form makes it useful in streetlights and fluorescent lamps.
• It is a liquid metal.

Additional Information

• Zinc White (PW4) is a cool, semi-transparent white pigment composed of zinc oxide which has been used in artist paints since the 18th century. It is commonly found in paints labeled as Mixing White and Transparent White.
• Potassium carbonate is the primary component of potash and the more refined pearl ash or salts of tartar.
• White lead is, heavy, white substance, poisonous, insoluble in water, and extensively used as a white pigment and base in paints. It is one of the oldest paint pigments used by humans. Chemically, it is basic lead carbonate, a mixture of lead carbonate and lead hydroxide.

Given: Ant, Insect, Fox, Mammal

As, we know that Ant is an Insect and Fox is a Mammal.

Since, both ant and fox are not related to each other so it is represented separately.

Thus, the logical Venn diagram is:

Hence, 'option 2' is the correct answer.

Logic: 1st figure total side x 4 and 2nd figure total sides x 5 

For 1st row:

 Here we have total sides = 6. So, we have  $\Rightarrow$ 6 $\times$ 4 = 24

 Here we have total sides = 3. So, we have  $\Rightarrow$ 3 $\times$ 5 = 15

For 2nd row we have:

 Here we have total sides = 5. So, we have  $\Rightarrow$ 5 $\times$ 4 = 20

 Here we have total sides = 4. So, we have  $\Rightarrow$ 4 $\times$ 5 = 20

Similarly, for the 3rd row, we have:

 Here we have total sides = 4. So, we have  $\Rightarrow$ 4 $\times$ 4 = 16

 Here we have total sides = 3. So, we have  $\Rightarrow$ 3 $\times$ 5 = 15

Thus, the correct answer is:

Hence, the correct answer is 'option 1'.

Given:

Principal = Rs 16,000

Time = 2 years

Difference between CI and SI = Rs 1000

Rate of interest is same for both CI and SI.

Concept Used:

Simple Interest = $\frac{P\times R\times T}{100}$

Compound Interest = $P\left(1+\frac{r}{100}\right)^t-P$

Calculation:

⇒ Putting the values in the formula, we get

⇒ CI – SI = 1000

⇒ $16000\left(1+\frac{r}{100}\right)^2-16000-\frac{16000\times r\times 2}{100}=1000$

⇒ $16000\left[\frac{(100+r)^2}{10000}-1-\frac{2r}{100}\right]=1000$

⇒ $16000\left[\frac{10000+r^2+200r-10000-200r}{10000}\right]=1000$

⇒ $\frac{8}{5}r^2=1000$

⇒ $r^2=\frac{1000\times 5}{8}=125\times 5=625$

⇒ $r=\sqrt{625}=25\%$

Therefore, the rate of interest per annum is 25%.

Given:

Atulit buys an old bicycle for Rs. 4,000

He spends Rs. 400 towards its repairs.

He sells the bicycle for Rs. 5,000

Concept used:

Profit% = [$\frac{(S.P - C.P)}{C.P}$] × 100

Calculations:

Total cost price = 4000 + 400 = Rs. 4400

According to the question,

P% = [$\frac{(5000 - 4400)}{4400}$] × 100

⇒ P% = [$\frac{600}{4400}$] × 100

⇒ P% = 0.13636 × 100 = 13.636 or ​​​$13\frac{7}{{11}}\%$​​

∴ His percentage gain is  ​​​$13\frac{7}{{11}}\%$.

Given:

The angles of a quadrilateral are in the ratio of 1 : 3 : 4 : 7

Concept used:

Sum of all the angles of a quadrilateral is 360° 

Calculation:

Let all the angles be = x, 3x, 4x, and 7x

According to the question,

360 = x + 3x + 4x + 7x

⇒ 360 = 15x

⇒ x = $\frac{360}{15}$ = 24° 

Now the difference between the largest and the smallest angle

⇒ 7x - x

⇒ 7 × (24) - 24

⇒ 168 - 24 = 144° 

∴ The difference between the largest and the smallest angle is 144°.

The correct answer is Article 18.

Key Points

• Article 18 talks about the abolition of titles.
• It says No title, not being a military or academic distinction, shall be conferred by the State.
• No citizen of India shall accept any title from any foreign State.
• Everyone has the right to freedom of thought, conscience, and religion.
• This right includes the freedom to change his religion or belief and freedom.
• Either alone or in community with others and in public or private, to manifest his religion or belief in teaching, practice, worship and observance.

Additional Information

• Article 25 gives Freedom of conscience and free profession, practice, and propagation of religion.
• Article 23 in The Constitution Of India 1949. 23**. Prohibition of traffic in human beings and forced labor**.
• Article 22 is one such Fundamental Right that safeguards the rights of individuals who have been arrested and detained for committing an offense.

Here, we have the state and its winter capital

Logic → State : Winter Capital 

So, for Himachal Pradesh : Dharamshala → Dharamshala is called the winter capital of Himachal Pradesh.

Similarly for Maharashtra : ? → Nagpur is called the winter capital of Maharashtra.

Thus, the missing word is 'Nagpur'.

Hence, the correct answer is 'option 2'.

Given: 

$\frac{{\tan 45^\circ - \tan 30^\circ }}{{1 + \tan 45^\circ \tan 30^\circ }}$

Concept used:

tan 30° = $\frac{1}{√3}$

tan 45° = 1

(a - b)² = a² - 2ab + b² 

(a² - b²) = (a - b)(a + b)

Calculation:

$\frac{{\tan 45^\circ - \tan 30^\circ }}{{1 + \tan 45^\circ \tan 30^\circ }}$

⇒ $\frac{[1 - (\frac{1}{\sqrt 3})]}{[1 + 1(\frac{1}{\sqrt 3})]}$

⇒ $\frac{[\frac{(√ 3 - 1)}{√ 3}]}{[\frac{(√ 3 + 1)}{√ 3}]}$

⇒ $\frac{(\sqrt 3 - 1)}{(\sqrt 3 + 1)}$ ...[multiplying ($\sqrt 3$ - 1) to both numerator and denominator]

⇒ $\frac{[(\sqrt 3 - 1)(\sqrt 3 - 1)]}{[(\sqrt 3 - 1)(\sqrt 3 + 1)]}$

⇒ $\frac{[(\sqrt 3\ -\ 1)^2]}{[(\sqrt 3)^2\ -\ (1)^2] }$

⇒ $\frac{[3 - 2(√3)1 + 1]}{[3 - 1]}$

⇒ $\frac{(4 - 2√3)}{2}$

⇒ $\frac{2(2 - \sqrt 3)}{2} = (2 - \sqrt 3)$

∴ The value of the given equation is ($2 - \sqrt 3$).

The correct answer is Carbon dioxide.

Key Points

• The main ingredient in sweetened soft drinks is water; they are about 90 percent carbonated water.
• Carbonated water is water that has been infused with carbon dioxide gas under pressure.
• This produces a bubbly drink that's also known as sparkling water, club soda, soda water, seltzer water, and fizzy water.
• Apart from seltzer water, carbonated waters usually have salt added to improve their taste.
• Carbonated beverage consumption has been linked with diabetes, hypertension, and kidney stones, all risk factors for chronic kidney disease.

Additional Information

• Nitrogen is important to the chemical industry. It is used to make fertilizers, nitric acid, nylon, dyes, and explosives. To make these products, nitrogen must first be reacted with hydrogen to produce ammonia. This is done by the Haber process.
• Hydrogen can be used in fuel cells to generate electricity, or power and heat. Today, hydrogen is most commonly used in petroleum refining and fertilizer production, while transportation and utilities are emerging markets.
• Freon is a non-combustible gas that is used as a refrigerant in air conditioning applications. This freon undergoes an evaporation process over and over again to help produce cool air that can be circulated throughout your AC system

The correct answer is Winston Churchill.

Key Points

• The Cripps Mission was sent by the British government to India in March 1942 to obtain Indian cooperation for the British war efforts in the 2nd World War.
• It was headed by Sir Richard Stafford Cripps, a labor minister in Winston Churchill's coalition government in Britain.
• Cripps Mission was sent by the British Government in March 1942 to India with the key objective to secure Indian cooperation and support for British War Efforts.

Additional Information

• Clement Richard Attlee, 1st Earl Attlee was a British politician who served as Prime Minister of the United Kingdom from 1945 to 1951 and Leader of the Labour Party from 1935 to 1955.
• James Ramsay MacDonald was a British politician who served as Prime Minister of the United Kingdom, the first who belonged to the Labour Party, leading minority Labour governments for nine months in 1924 and again between 1929 and 1931.
• Stanley Baldwin, 1st Earl Baldwin of Bewdley was a British Conservative Party politician who dominated the government of the United Kingdom between the world wars, serving as Prime.

Given:

$\rm \sqrt {\frac{x}{{1 - x}}} + \sqrt {\frac{{1 - x}}{x}} = \frac{{25}}{{12}}$

Concept Used:

(a + b)² = a² + b² + 2ab

Calculation:

⇒ Let t = $\sqrt{\frac{x}{1-x}}$, so $\frac{1}{t}=\sqrt{\frac{1-x}{x}}$.

⇒ Putting the values in the equation, we get

⇒ $t+\frac{1}{t}=\frac{25}{12}$

⇒ $\frac{t^2+1}{t}=\frac{25}{12}$

⇒ $12t^2-25t+12=0$

⇒ Splitting the middle term, we get

⇒ $12t^2-16t-9t+12=0$

⇒ $4t(3t-4)-3(3t-4)=0$

⇒ $(4t-3)(3t-4)=0$

⇒ $t=\frac{3}{4}$ or $\frac{4}{3}$

⇒ Equating with the value, we get

⇒ $\frac{3}{4}=\sqrt{\frac{x}{1-x}}$

⇒ Squaring both sides, we get

⇒ $\frac{x}{1-x}=\frac{9}{16}$

⇒ $16x=9-9x$

⇒ 16x + 9x = 9

⇒ $x=\frac{9}{25}$

⇒ Equating with the second value of t, we get

⇒ $\frac{4}{3}=\sqrt{\frac{x}{1-x}}$

⇒ $\frac{16}{9}=\frac{x}{1-x}$

⇒ $16-16x=9x$

⇒ 16x + 9x = 16

⇒ $x=\frac{16}{25}$

Therefore, the possible values of x can be $\frac{9}{25}$ or $\frac{16}{25}$.

Here, we are given three words: Swimming, Cycling, Exercises

As we know, Swimming (S) and Cycling (C) are comes under Exercises (E).

So, we will check all the options as:

1) 

Thus, we have S and C in the circle E.

2) 

This is not possible as all are not connected to each other.

3) 

This is not possible, as some E are not some S, and some S are not some C.

4) 

This is impossible, as C and S are not related to each other but are related to E.

Hence, the correct answer is 'option 1'.

The correct answer is 1st January 2015.

Key Points

• The NITI Aayog was formed by a resolution.
• It was passed by the Union Cabinet on 1st January 2015.
• By forming the NITI Aayog the Planning Commission Of India was scraped immediately.
• The full form of NITI is National Institution for Transforming India.
• It is the 'Think Tank' of the Government of India
• The Governing Council of NITI has Prime Minister Narendra Modi as its Chairman and also has the Chief Ministers of all states and Lt. Governors of all union territories.

Additional Information

• NITI AAyog
• NITI Aayog has the twin mandate to oversee the adoption and monitoring of the SDGs in the country and promote competitive and cooperative federalism among States and UTs.
• The task at hand for NITI Aayog is not just to periodically collect data on SDGs but to proactively realise the goals and targets.

BODMAS Rule:

Given: 

Logic = Sides of outer image [(4 + sides of hexagon) + (3 + sides of pentagon) + (2 + sides of rhombus)]

= 6 × [(4 + 6) + (3 + 5) + (2 + 4)]

Applying the BODMAS rule, we will get,

= 6 × [(10) + (8) + (6)]

= 6 × [24]

= 144

Thus, the answer to the given question is 144.

Hence, the correct answer is 'option 2'.

The correct answer is National Payments Corporation of India.

Key Points

• The NPCI was founded on 2008 for the operation of retail payments in India.
• NPCI exercises this role through its wing IDRBT (Institute for Development of Research in Banking Technology).
• IDRBT created a massive network called National Financial Switch in the year 2004 for linking all the ATMs in India.
• The NPCI provides a variety of services are Rupay: A domestic card scheme, BHIM: Unified payment interface, Check truncation system and Aadhar enabled payment system.

Additional Information

• Indian Bank Association (IBA) is formed in 1946.
• It is a representative body of management of banking in India.
• IBA was formed for the development, coordination, and strengthening of Indian banking, and to assist the member banks in various ways.
• National Securities Depository Limited (NSDL) is a financial organization created to hold securities such as bonds, shares etc. in the form of physical or non-physical certificates i.e. in dematerialized format.
• These securities are held in depository accounts such as funds held in bank accounts.
• NSDL is one of the largest Depositories in the World.
• It was established in August 1996.

The alphabets and their corresponding (reverse) are as:

Given: DMO : WNL

First we will check all the options:

1) GHI : TSR

This is true.

2) CFH : XUT

which is not equal to XUT. This is not true.

3) DQG : ELP

which is not equal to ELP. This is not true.

4) ZAT : EGD

which is not equal to EGD. This is not true.

Hence, the correct answer is 'option 1'.

Given:

Speed of A = 3 km/h

Speed of B = 4 km/h

Time = 6h

Concept used:

Distance = Speed × Time

Calculation:

Distance traveled by A = 3 × 6 = 18 km

Distance traveled by B = 4 × 6 = 24 km

According to the question, after 6 hours

Difference between them = 24 - 18 = 6 km

∴ The distance between them after 6 h will be 6 km.

The logic here is:

Hence, the missing number is '336'.

Given:

Numbers less than 10000 are there which are exactly divisible by 21, 35 and 63

Calculations:

LCM (21, 35, 63) = 315

The numbers less than 10,000 which are divisible by 315 i.e. the integral part when 10,000 is divided by 315 is 31.

∴ 31 numbers are divisible by (21, 35 and 63).

Given:

The selling price of an article is 3 times the discount offered

The percentage of the discount is equal to the percentage profit

Concept used:

Discount = MP − SP

D% = [(MP - SP)/MP] × 100

P% = [(SP - CP)/CP] × 100

Calculations:

SP = 3 × discount offered 

⇒ S.P = 3(MP − SP)

⇒ S.P = 3M.P − 3S.P

⇒ 4S.P = 3 M.P

⇒ M.P = 4SP/3

According to the question,

D% = P%

⇒ [(MP - SP)/MP] × 100 = [(SP - CP)/CP] × 100

⇒ [(4SP/3 - SP)/(4SP3)] × 100 = [(SP - CP)/CP] × 100

⇒ [(4SP - 3SP)/3 ÷ (4SP/3)] × 100 = [(SP - CP)/CP] × 100

⇒ 1/4 = (SP/CP) - 1

⇒ SP/CP = 1/4 + 1

⇒ SP = (5/4)CP

MP = 4/3 SP =(4/3)(5/4)CP = 5/3CP 

Now Ratio of discount to C.P

D/CP = (MP - SP)/CP

⇒ D/CP = (5/3CP - 5/4CP)/CP

⇒ D/CP = 5CP(1/3 - 1/4)/CP

⇒ D/CP = 5(4 - 3)/12 = 5/12

⇒ D : CP = 5 : 12

∴ The ratio of the discount offered to the cost price is 5 : 12.

The Corrrect Answer is Russsia.

Key Points

• The 2018 FIFA World Cup is scheduled to take place in Russia from 14 June to 15 July 2018.
• It was awarded the hosting rights in 2010.
• This will be the first World Cup held in Europe since 2006.
• The tournament will involve 32 national teams; 31 teams determined through qualifying competitions and the automatically qualified host team.
• A total of 64 matches will be played across 12 venues located in 11 cities.

The correct answer is Michael Phelps.

Key Points

• Michael Fred Phelps II is an American former competitive swimmer.
• He is the most successful and most decorated Olympian of all time with a total of 28 medals.
• Phelps also holds the all-time records for Olympic gold medals, Olympic gold medals in individual events, and Olympic medals in individual events.
• He was born on 30 June 1985 in Baltimore, Maryland, United States.

Additional Information

• Mark Andrew Spitz is an American former competitive swimmer and nine-time Olympic champion. He was the most successful athlete at the 1972 Summer Olympics in Munich, winning seven gold medals, all in world record time.
• Kathleen Genevieve Ledecky is an American competitive swimmer. She has won six Olympic individual gold medals and 14 world championship individual gold medals, the most in history for a female swimmer.
• Ryan Steven Lochte is an American professional swimmer and 12-time Olympic medalist. Along with Natalie Coughlin, Dara Torres, and Jenny Thompson, he is the second-most decorated swimmer in Olympic history measured by total number of medals, behind only Michael Phelps.

The correct answer is It is a fresh water lake.

Key Points

• The Great Rann of Kutch is a salt marsh in the Thar Desert in the Kutch District of Gujarat, India.
• It is about 7500 km² in the area and is reputed to be one of the largest salt deserts in the world.
• This area has been inhabited by the Kutchi people.
• The Rann of Kachchh is famous for its white salty desert sand and is reputed to be the largest salt desert in the world.
• 'Rann' means desert in Hindi which in turn is derived from the Sanskrit word 'Irina' which also means desert
• Great Rann of Kutch has not a fresh water lake.

Additional Information

• The low-lying mudflats of the White Rann fill with water during the wet season (June-September) and then dry out over the rest of the year.
• By December, once evaporation has done its work, the saline crust hardens to form the signature luminous white color.

Given: A < B < C > D < E > A

So, from this we can say that, A < B < C  and C > D or D < C

Also, we have E > A or A < E

First we will check all the options:

1) A < D < B 

$\Rightarrow$ A < B and D < C.

This is not correct because we can not establish the relation between B and D.

2) C > A < E

$\Rightarrow$ A < B < C , this means A < C or C > A

And, A < E is also true.

This is correct.

3) B > A > E

$\Rightarrow$ A < B this means B > A

Also, E > A and not A > E

This is not correct.

 4) E > C > D

$\Rightarrow$ E > A and C > D

This is not correct because we can not establish the relation between C and E.

Hence, the correct answer is 'option 2'.

Given:

60% of 40% of 32% of an amount is Rs. 432.

Calculations:

Let the amount be 'x'

According to the question,

60% of 40% of 32% of x = Rs. 432

⇒ [($\frac{60}{100}$) × ($\frac{40}{100}$) × ($\frac{32}{100}$)]x = 432

⇒ [0.60 × 0.40 × 0.32] × x = 432

⇒ 0.0768 × x = 432

⇒ x = $\frac{432}{0.0768}$ = Rs. 5625

∴ The amount is Rs. 5625.

The correct answer is Sarnath.

Key Points

• The Lion Capital of Ashoka is the capital, or head, of a column, erected by the Mauryan emperor Ashoka in Sarnath, India, c. 250 BCE.
• Its crowning features are four life-sized lions set back to back on a drum-shaped abacus.
• The national emblem is an adaptation of the Lion Capital, originally found atop the Ashoka Column at Sarnath.
• The capital has four Asiatic lions—symbolizing power, courage, pride, and confidence—seated.
• Ashoka the Great, was an Indian emperor of the Maurya Empire, son of Bindusara.
• He ruled almost the entire Indian subcontinent from c**. 268 to 232 BCE**.
• Ashoka promoted the spread of Buddhism across ancient Asia

Additional Information

• The capital had five components:
• The shaft (now broken into many parts)
• A lotus base bell.
• A drum on the base bell with 4 animals proceeding clockwise (abacus)
• Figures of 4 lions.
• The crowning part, a large wheel (this is also broken and displayed at the museum)

Given:

A, B and C begin together to move around a circular stadium and they completed their revolution in 42 s, 63 s and 84 s respectively

Calculations:

According to the question,

They will meet together at starting point after,

LCM of (42, 63, 84) seconds.

⇒ 84 = 2 × 2 × 3 × 7

⇒ 42 = 2 × 3 × 7

⇒ 63 = 3 × 3 × 7

LCM = 2 × 2 × 3 × 3 × 7 = 252 seconds

∴ They will meet together at starting point after 252 sec.

Given:

x + y + z = 0

Concept Used:

If x + y + z = 0, then x³ + y³ + z³ = 3xyz

Calculation:

⇒ We have to find, $\frac{{{x^2}}}{{yz}} + \frac{{{y^2}}}{{zx}} + \frac{{{z^2}}}{{xy}}$

⇒ Multiplying each of the term by $\frac{x}{x},\frac{y}{y},\frac{z}{z}$ respectively, we get

⇒ $\frac{{{x^3}}}{{xyz}} + \frac{{{y^3}}}{{yzx}} + \frac{{{z^3}}}{{zxy}}$

⇒ $\frac{x^3+y^3+z^3}{xyz}=\frac{3xyz}{xyz}=3$

Therefore, the required value of $\frac{{{x^2}}}{{yz}} + \frac{{{y^2}}}{{zx}} + \frac{{{z^2}}}{{xy}}$ is 3

Logic: Number of corners of outer figure $\times$ Number of figure in inner figure $\times$ number inside the figure = Final Answer

443=48

345=60

334=36

So, we have

⇒ 4 $\times$ 4 $\times$ 3 = 48

And,

⇒ 4 $\times$ 3 $\times$ 5 = 12

Similarly we have, each time the answer has 4 less than the previous one. 

⇒ 3 $\times$ 3 $\times$ 4 = 36

Hence, the correct answer is '36'

The correct option is Rice-wheat-coarse cereals-pulses.

Key Points

• India ranks second worldwide in farm outputs.
• Agriculture sector contributed 17–18% to country's GDP in 2018.
• India is the second-largest producer of wheat and rice in the world.
• West Bengal is the largest producer of rice in India.
• Uttar Pradesh is the state with maximum production of wheat.

Additional Information

• China is the largest producer of Rice in the world.
• Largest producer of Wheat is China with 29% of the total production in the world.
• Cuba is known as the 'Sugar Bowl of the world'.
• Darjeeling tea, Mysore betel leaf, Odisha rasgulla and Kashmir saffron are some of the products which are given GI tags in India.

Given:

$\frac{{\sqrt {225} }}{{14}} \times \frac{{\sqrt {196} }}{{22}} \times \frac{{\sqrt {484} }}{{15}}$

Calculation:

$\frac{{\sqrt {225} }}{{14}} \times \frac{{\sqrt {196} }}{{22}} \times \frac{{\sqrt {484} }}{{15}}$

⇒ ($\frac{15}{14}$) × ($\frac{14}{22}$) × ($\frac{22}{15}$)

⇒  ($\frac{15}{22}$) × ($\frac{22}{15}$) = 1

∴ The value of the given expression is 1.

The correct option is Mark.

Key Points

• OMR stands for Optical Mark Recognition.
• The first mark sense scanner was the IBM 805 Test Scoring Machine.
• The first successful optical mark-sense scanner was developed by Everett Franklin Lindquist.
• Some applications of OMR are:
• Data compilation
• Consumer surveys
• Lotteries and voting
• Geocoding etc.

Additional Information

• OCR is the electronic or mechanical conversion of images of typed, handwritten or printed text into machine-encoded text.
• Facial Recognition system is a technology capable of matching a human face from a digital image or a video frame against a database of faces.
• Gesture recognition is a topic in computer science and language technology with the goal of interpreting human gestures via mathematical algorithms.
• Pattern recognition is the automated recognition of patterns and regularities in data.