RRB NTPC CBT-I Official Paper (Held On: 7 Mar 2021 Shift 2) (Previous Year Paper)

Given:

Raj is 60% more efficient than Sundar.

Sundar can finish a certain job in 16 days.

Formula Used:

Time taken by Raj = Time taken by Sundar / Efficiency Ratio

Calculation:

Efficiency of Sundar = 100%

Efficiency of Raj = 160% = 1.6 × Efficiency of Sundar

Time taken by Raj = Time taken by Sundar / 1.6

⇒ Time taken by Raj = 16 / 1.6

⇒ Time taken by Raj = 10 days

Raj alone takes 10 days to complete the same job.

Given:

LCM of two numbers = 126

HCF of two numbers = 2

One number = 18

Formula Used:

LCM × HCF = Product of the numbers

Calculation:

Let the other number be x.

According to the formula:

LCM × HCF = 18 × x

126 × 2 = 18 × x

⇒ 252 = 18 × x

⇒ x = 252 / 18

⇒ x = 14

The other number is 14.

The correct answer is Lumbini

Key Points

• The Lord Buddha was born in 563 BC in the sacred area of Lumbini located in the Terai plains of southern Nepal.
• A World Heritage Site since 1997, Lumbini has attracted travelers and worshippers for centuries.
• The Mahabodhi Temple Complex in Bodh Gaya is located in the central part of the state of Bihar.
• The first temple was built by Emperor Asoka in the 3rd century B.C.
• Mahabodhi temple is a UNESCO world heritage site.

Additional Information

• Mahayana Buddhism:
• After the death of Buddha, a group evolved who believed that compassion for all humanity was an important part of the path, and that teaching is fully available to all.
• Those who followed the newly expanded ideals called themselves Mahayana meaning the big raft.
• In Mahayana Buddhism, all practicing Buddhists are apprentice Bodhisattvas.
• In Mahayana countries, images of the Buddha are set up in the temples and homes as an object of worship.
• Hinayana Buddhism:
• From about 100 years after the death of the Buddha, there had been a movement towards embracing the style of Buddhism.
• The early monks concentrated on personal enlightenment, seeking spiritual answers for themselves, and teaching others the way of enlightenment.
• But the information was severely limited to the lay community as it was assumed only minks could achieve Buddhahood.
• This section came to be known as Hinayana or also known as Theravada.
• Theravada means the way of elders.
• Milindapanha:
• The Milindapanha, or "Milinda's Questions," is an important early Buddhist text that usually is not included in the Pali Canon.
• Even so, the Milindapanha is cherished because it addresses many of Buddhism's most difficult doctrines with wit and clarity.
• The Milindapanha presents a dialogue between King Menander I (Milinda in Pali) and an enlightened Buddhist monk named Nagasena.
• Menander- I was an Indo-Greek king thought to have ruled from about 160 to 130 BCE.
• He was a king of Bactria, an ancient kingdom that took in what is now Turkmenistan, Afghanistan, Uzbekistan, and Tajikistan, plus a small part of Pakistan.

Given,

Statement:

It is appropriate to marry a girl who is 18 years of age and above.

Conclusions:

I. At this age, a girl reaches an appropriate level of physical, biological and psychological maturity to become a mother - True (Because, the statement mentions that it is appropriate to marry a girl who is 18 years of age and above, and the given data we can say it is biologically proven that's why the age of a girl for marry is 18).

II. People do not marry girls less than 18 years of age because of fear - False (Because, the statement does not mention anything about the reason why people do not marry girls less than 18 years of age. It only states that it is appropriate to marry a girl who is 18 years of age and above).

So, Only conclusion 1 follows..

Hence, the correct answer is "Option 4".

The correct answer is Memorandum expelling grants.

Key Points

• The budget is related to the government's fiscal policy.
• The budget is a statement of the receipts and expenditure of the government for each financial year.
• It is mentioned in Article 112 of the Indian Constitution as the Annual Financial Statement.
• It contains different heads like
• Revenue and Receipt Expenditure
• Capital Receipt and Expenditure
• Corporation Tax
• Direct Tax
• Indirect Tax
• Fiscal Policy
• Revenue and Fiscal Deficit
• Non-tax revenue

Additional Information

• Appropriation bill​
• An appropriation bill is a bill that authorizes the Indian government to withdraw funds from the Consolidated Fund of India for use during the financial year.
• Appropriation acts are not included in any official list of Central govt. laws, they technically remain on the books.
• No amendment can be proposed to the Appropriation Bill in either house of the Parliament.​
• Finance bill
• A Bill that contains some provisions related to taxation and expenditure, and additionally contains provisions related to any other matter is called a Financial Bill.
• Therefore, if a Bill merely involves expenditure by the government, and addresses other issues, it will be a financial bill.
• Financial Bills are of two types:
• Financial Bills(1) Articles 117(1)
• Financial Bills(2) Articles 117(3)
• Receipts budget
• It refers to the estimated receipts of the government from all the sources during a fiscal year.
• It is of two types: Capital Receipts, and Revenue Receipts.

The correct answer is Candy.

Key Points

• Android
• Android OS developed by Google is the most widely used mobile operating system.
• The first version bears the name Cupcake.
• Thereafter the version names are on the alphabetical basis.​

Additional Information​

• Marshmallow:
• Android The sixth major edition of the Android operating system and the 13th version of Android is Marshmallow (codenamed Android M during development).
• It was publicly released on October 5, 2015, and was first released as a beta build on May 28, 2015, with the Nexus devices being the first to receive the update.
• Marshmallow mainly focuses on enhancing its predecessor's overall user experience, Lollipop.
• Gingerbread
• Gingerbread is the nickname for Android version 2.3, which was released in December 2010.
• It brought several new features and improvements, including a more refined user interface, support for larger screen sizes, enhanced gaming performance, and improved battery management.
• Gingerbread also introduced features like NFC (Near Field Communication) support and improved copy-and-paste functionality.
• Oreo​
• Oreo is the nickname for Android version 8.0, which was released in August 2017.
• This version introduced several new features and enhancements.

The correct answer is Mumbai and Ahmedabad.

Key Points

• In September 2017, Prime Minister Narendra Modi and Shinzo Abe laid the foundation stone of the bullet train project.
• Due to their appearance and speedJapan's Shinkansen high-speed trains are referred to as bullet trains.  Any train of speed above 250 km/h is termed as the Bullet train.
• The Mumbai-Ahmedabad bullet train route is a 508-kilometer stretch.
• • It is a term generally used to describe a high-speed train of speeds above 250 Kmph.
• India’s first bullet train will run in the Mumbai and Ahmedabad high-speed rail corridor, whose construction began in September 2017.
• It is a 508 km long high-speed rail corridor building with the help of Japan.
• The train will run at a speed of 320kmph and is expected to be completed by 2022.​

Additional Information

• Shinkansen Technology:
• Shinkansen means new trunk lines in literal terms, which refers to the high-speed rail network in Japan.
• The train attains a high speed without having to compromise on comfort and safety, through the use of this technology.
• Unlike conventional rail lines, Shinkansen routes are strictly off-limits to any other kind of traffic.
• This network makes use of viaducts and tunnels to go through the obstacles, rather than going around them, thereby saving time spent on covering the distance.
• Due to the lighter vehicles used, chances of damage to the tracks are minimal. These trains offer fast acceleration & deceleration and are electric multiple units.
• Route Map of the Bullet Train:

Given:

Sales of printer model L-1102 in 2018 = 1245

Sales of printer model L-1102 in 2014 = 678

Formula used:

Percentage increase = $\frac{(New\ value - Old\ value)}{Old\ value} \times 100$

Calculation:

Percentage increase = $\frac{(1245 - 678)}{678} \times 100$

⇒ Percentage increase = $\frac{567}{678} \times 100$

⇒ Percentage increase = 83.63% ≈ 84%

∴ The approximate percentage increase is 84%.

Given:

A bought a horse for ₹4,500.

He sold it to B at a profit of 5%.

B sold it to C at a profit of 20%.

Formula Used:

Cost price (CP) of horse for B = CP for A + Profit percentage on CP for A

Cost price (CP) of horse for C = CP for B + Profit percentage on CP for B

Calculation:

CP for A = ₹4,500

Profit for B = 5% of ₹4,500

Profit for B = 5/100 × 4500

Profit for B = 225

CP for B = 4500 + 225

CP for B = 4725

Profit for C = 20% of ₹4725

Profit for C = 20/100 × 4725

Profit for C = 945

CP for C = 4725 + 945

CP for C = 5670

The cost price of the horse for C is ₹5670.

The correct answer is Aravidu.

Key Points

• Aravidu
• Dynastic Shift to Aravidu: By 1542, power in the Vijayanagara Empire had transitioned to the Aravidu dynasty, marking a significant shift from the Tuluva dynasty, which had previously held control.
• Battle of Talikota (1565): This critical battle saw the forces of the Vijayanagara Empire under the rule of the Aravidu dynasty face off against a coalition of Deccan Sultanates comprising Bijapur, Ahmadnagar, and Golconda. The battle took place near the villages of Rakshasi (Demons) and Tangadi (Mustard), often collectively referred to as Talikota.

Additional Information

• The Vijaynagar empire was ruled by four important dynasties:
• Sangama
• Saluva
• Tuluva
• Aravidu
• The Vijayanagara Empire was founded by Harihara and Bukka and the reign was from 1336 A.D to 1646 A.D.
• The Tuluva dynasty was founded by Vir Narsingh.
• This Tuluva dynasty ruled from 1491 to 1570.
• The last king of the Tuluva dynasty was Sadasiva Raya (1542-1570).
• The most popular king of the Tuluva dynasty was Krishna Deva Raya (1509-1529).
• During his rule, the empire reached its Zenith.

Given:

Principal (P) = ₹1,000

Amount after 2 years (A) = ₹1,061

Time (t) = 2 years

Formula:

A = P (1 + r/100)^t

Solution:

1061 = 1000 (1 + r/100)²

1.061 = (1 + r/100)²

Take the square root:

1.03 = 1 + r/100

Solve for r:

r = 3%

∴ The rate of compound interest per annum is 3%.

The correct answer is Karnataka.

Key Points

• Kaiga Nuclear Power Plant is the third-largest nuclear power plant in India.
• Kaiga Atomic Power Station (KAPS), located in Uttara Kannada district, is near river Kali.
• The plant has been in operation since 2000 and is operated by the Nuclear Power Corporation of India.
• The Kaiga Atomic Power Station supplies 67% of the power generated through its nuclear reactors to Telangana, Andhra Pradesh, Tamil Nadu, Kerala, and Puducherry.
• The remaining 33% is reserved for the Karnataka.​

Additional Information

Indian Nuclear Power station:

The correct answer is Military Demarcation Line.

Key Points

• The Military Demarcation Line (MDL) lies between North Korea and South Korea.
• It was established as part of the Korean Armistice Agreement in 1953, ending the Korean War.
• The MDL runs roughly along the 38th parallel, forming the boundary between the two countries.

Additional Information

The correct answer is Aurobindo Ghose.

Key Points

• Aurobindo Ghose​
• Aurobindo Ghose (Sri Aurobindo) was born in Calcutta (now Kolkata) on 15th August 1872.
• He was a yogi, guru, poet, Indian philosopher and an Indian freedom fighter.
• He was a part of Anushilan Samiti, an organisation which supported revolutionary violence for ending British Rule.
• Aurobindo was arrested and tried in Alipore Bomb case in 1908
• He was eventually set free after which he retired from active politics and moved to Pondicherry choosing spiritual path.
• He founded the Aurobindo Ashram in Pondichery in 1926.
• Some of his Literary works are:
• The life Divine, The synthesis of Yoga and Savitri​**

Additional Information

• Rabindranath Tagore​
• Rabindranath Tagore was born on 7th May 1861 in Kolkata.
• He was a poet, litterateur, philosopher, playwright, composer, and painter.
• He was awarded the Nobel Prize for Literature in 1913 for the creation of the world-famous epic Gitanjali.
• He is the only Indian to win the Nobel in the field of literature.
• Rabindra Nath Tagore gave up his 'Knighthood' in protest of the Jallianwala Bagh Massacre.
• He was awarded the knighthood in the year 1915 by King George V.
• He gave Gandhiji the title of Mahatma.
• He is the only poet whose two compositions became the national anthem of two countries.
• The national anthem of India - Jana-Gana-Mana.
• The national anthem of Bangladesh - Amar Sonar Bangla.
• Tagore established Santiniketan with trees, gardens, and a library in the lap of nature.
• Tagore also established the Vishwabharati University here.
• On 7 August 1941, he breathed his last in Kolkata.
• ​Gopal Krishna Gokhale​
• In the 1905, Gopal Krishna Gokhale founded 'Servants of India Society'. 
• The Servants of India Society was formed in Pune on June 12, 1905, for the expansion of Indian education.
• Servants of India Society's aim was to unite and train Indians of different ethnicities and religions in welfare work.
• It was the first secular organization in that country to devote itself to the underprivileged, rural and tribal people, and other social causes.
• Members go through a five-year training period and agree to serve on extremely modest salaries.
• Mahatma Gandhi​
• Mohandas Karamchand Gandhi was born on October 2, 1869 in Porbandar.
• He was a lawyer, anti-colonial nationalist, and political ethicist.
• He led the non-violent movement for the independence of the nation from the British Raj.
• Major movements for India’s Independence –
• Champaran agitation – 1917 in Bihar
• Kheda agitation – 1918
• Khilafat movement – 1919
• Non-cooperation movement – 1920
• Dandi March (Salt Satyagraha) – 1930
• Round Table Conferences – 1931-32
• Quit India Movement – 1942
• Independence and Partition – 1947

The logic followed here is:

Knight, Bishop, Pawn all are Chess pieces,

Whereas,

Ace is a Playing card.

Hence, the correct answer is "Ace".

Given:

A profit of 25% is made when an article is sold for ₹750.

Formula Used:

Cost Price (CP) = Selling Price (SP) / (1 + Profit Percentage)

Profit Percentage = [(Selling Price (SP) - Cost Price (CP)) / Cost Price (CP)] × 100

Calculation:

Let the Cost Price (CP) be x.

Given, Selling Price (SP) = ₹750 and Profit Percentage = 25%

Using the formula for CP:

CP = 750 / (1 + 0.25)

⇒ CP = 750 / 1.25

⇒ CP = 600

Now, the new Selling Price (SP) = ₹660

Using the formula for Profit Percentage:

Profit Percentage = [(660 - 600) / 600] × 100

⇒ Profit Percentage = (60 / 600) × 100

⇒ Profit Percentage = 0.1 × 100

⇒ Profit Percentage = 10%

The profit percentage when the article is sold for ₹660 is 10%.

Given:

Rate of interest (r₁) = 5% for 6 years

Rate of interest (r₂) = 8% for 3 years

Let the principal be P in both cases.

Formula used:

Simple Interest (SI) = $\frac{P \times r \times t}{100}$

Calculation:

Simple Interest at 5% for 6 years = $\frac{P \times 5 \times 6}{100} = \frac{30P}{100} = 0.30P$

Simple Interest at 8% for 3 years = $\frac{P \times 8 \times 3}{100} = \frac{24P}{100} = 0.24P$

Now, the ratio of the simple interest earned is:

Ratio = $\frac{0.30P}{0.24P} = \frac{30}{24} = \frac{5}{4}$

∴ The required ratio is 5:4.

Given:

Rama can finish a piece of work in 50 days.

He worked for 10 days but then stopped.

Ravi finished the remaining work alone in 32 days.

Formula Used:

Work rate of Rama = 1/50 work/day

Work rate of Ravi = 1/remaining work days

Combined work rate = Work rate of Rama + Work rate of Ravi

Time taken by Rama and Ravi together = Total work / Combined work rate

Calculation:

Work done by Rama in 10 days = 10 × (1/50) = 1/5

Remaining work = 1 - 1/5 = 4/5

Time taken by Ravi to finish the remaining work = 32 days

Work rate of Ravi = (4/5) / 32 = 1/40 work/day

Combined work rate = (1/50) + (1/40)

Combined work rate = (4 + 5) / 200

Combined work rate = 9/200 work/day

Time taken by Rama and Ravi together to finish the work = 1 / (9/200)

Time taken by Rama and Ravi together = 200/9 days

Time taken by Rama and Ravi together = 22 (2/9) days

The correct answer is option 4.

Given: Four girls, Radha, Neena, Mohita and Jyoti, are to be served in a sequence by a service provider.

Limitations as follows:

1. Mohita and Jyoti cannot be served one after the other;

2. Neena cannot be served at the third number in sequence;

3. And Radha and Neena are to be served one after the other.

Considering the given information: 

Option 1) Mohita cannot be served first. - False (It can be possible)

Option 2) Mohita will be served first. - False (It can be possible)

Option 3) Radha will be served third. - True (This statements is compulsorily true)

Option 4) Jyoti will be served first - False (It can be possible)

Hence, the correct answer is "Option 3".

Shortcut Trick

To find the intercepts of a plane ax + by + cz = d, divide the constant term d by the coefficients a, b, and c.

Given equation: 3x − 4y − 2z = 6

x-intercept = 6 ÷ 3 = 2

y-intercept = 6 ÷ (−4) = −3/2

z-intercept = 6 ÷ (−2) = −3

∴ The correct answer is 2, − (3)/(2) , −3.

Alternate Method

Given: Equation of the plane is 3x − 4y − 2z = 6.

Formula Used: The intercept form of a plane is (x/a) + (y/b) + (z/c) = 1, where a, b, and c are the intercepts on the x, y, and z axes respectively.

Calculations:

⇒ 3x − 4y − 2z = 6

Divide the entire equation by the constant term on the RHS (6) to make it 1:

⇒ (3x/6) − (4y/6) − (2z/6) = 6/6

⇒ (x/2) − (2y/3) − (z/3) = 1

Write the equation in standard intercept form by making the numerators of variables unity and signs positive:

⇒ (x/2) + (y/(−3/2)) + (z/(−3)) = 1

Comparing with (x/a) + (y/b) + (z/c) = 1:

⇒ a = 2, b = −3/2, c = −3

∴ The correct answer is 2, − (3)/(2) , −3.

Additional Information

General Equation of a Plane

The linear equation ax + by + cz + d = 0 represents a plane where (a, b, c) are the direction ratios of the normal to the plane.

Distance from Origin to Plane

The perpendicular distance from the origin (0, 0, 0) to the plane ax + by + cz = d is given by |d| ÷ √(a² + b² + c²).

Direction Cosines of the Normal

If the equation is converted to lx + my + nz = p (where l²+m²+n²=1), then l, m, n are the direction cosines of the normal.

Given:

\(\left{ \left( 2 - \frac{1}{3} \right) + \left( \frac{2}{3} \times 1 \frac{1}{5} \right) \right} + \frac{3}{5} \times 2 \frac{5}{7}\)

Formula used:

We solve the expression by simplifying the terms inside the brackets and multiplying.

Calculations:

$2 - \frac{1}{3} = \frac{6}{3} - \frac{1}{3} = \frac{5}{3}$

$1 \frac{1}{5} = \frac{6}{5}$

$\frac{2}{3} \times \frac{6}{5} = \frac{12}{15} = \frac{4}{5}$

Now solve the bracket:

$\frac{5}{3} + \frac{4}{5} = \frac{25}{15} + \frac{12}{15} = \frac{37}{15}$

Next, simplify:

$2 \frac{5}{7} = \frac{19}{7}$

$\frac{3}{5} \times \frac{19}{7} = \frac{57}{35}$

Now, add both results:

$\frac{37}{15} + \frac{57}{35} = \frac{37 \times 7}{15 \times 7} + \frac{57 \times 3}{35 \times 3} = \frac{259}{105} + \frac{171}{105} = \frac{430}{105} = \frac{86}{21}$

∴ The final result is $\frac{86}{21}$.

The correct answer is Asphalt.

Key Points

• Ozone layer:
• The ozone layer or ozone shield is a region of the Earth’s stratosphere that absorbs most of the Sun’s Ultraviolet (UV) radiation.
• It is a layer in the earth’s stratosphere that contains high levels of ozone.
• This layer protects the earth from the Sun’s harmful UV radiation. Hence, option 4 is correct.
• It absorbs 97 – 99% of the UV radiation from the Sun.
• Ozone screens all of the most energetic, UV-c, radiation, and most of the UV-b radiation.​

Additional Information

• Millions of individuals would be vulnerable to skin conditions including cancer and compromised immune systems in the absence of ozone layer.
• UV radiation would also affect the environment adversely leading to decreased productivity.
• Fauna on earth is also adversely affected by ozone layer depletion.
• Ozone (O3) is a highly reactive gas whose molecules are comprised of three oxygen atoms.

The correct answer is Lokyukta can't question Prime Minister on the allegation of abuse of power.

Key Points

• Lokayuktas:
• Even much before the enactment of the Lokpal and Lokayuktas Act (2013) itself, many states had already set up the institution of Lokayuktas.
• It must be noted here that the institution of Lokayukta was established first in Maharashtra in 1971.
• Although Odisha had passed the Act in this regard in 1970, it came into force only in 1983.
• Structural Variations:
• The structure of the Lokpal and Lokayuktas is not the same in all the states.
• Some states like Rajasthan, Karnataka, Andhra Pradesh, and Maharashtra have created the Lokayukta as well as a Upalokayukta, while some others like Bihar, Uttar Pradesh, and Himachal Pradesh have created only the Lokayukta.
• There are still other states like Punjab and Orissa that have designated officials as Lokpal.
• This pattern was not suggested by the ARC in the states.
• Appointment:
• The Lokayukta and upalokayukta are appointed by the governor of the state. Hence, statement 3 is correct.
• While appointing, the governor in most of the states consults (a) the chief justice of the state high court, and (b) the leader of Opposition in the state legislative assembly.

The correct answer is Odisha.

Key Points

• Bhutan shares a  699 km long border with India.
• It adjoins the Indian states of Assam, Arunachal Pradesh, West Bengal and Sikkim.
• Bhutan is known as the Land of Thunder Dragon.
• Capital of Bhutan - Thimphu
• Currency - Bhutanese Ngultrum.

Given:

Principal (P) = ₹10,000

Time (T) = 6 months

Rate of Interest (R) = 5 paise per rupee per month

Formula Used:

Simple Interest (SI) = (P × R × T) / 100

Calculation:

Convert the rate from paise to rupees:

R = 5 paise per rupee per month = 5 / 100 = 0.05 rupees per rupee per month

R = 0.05 × 12 = 0.6 rupees per annum

Time in years = 6 months / 12 = 0.5 years

Now, substitute the values in the formula:

SI = (₹10,000 × 0.6 × 0.5)

⇒ SI = ₹10,000 × 0.6 × 0.5

⇒ SI = ₹10000 × 0.3

⇒ SI = ₹3000

The simple interest is ₹3000.

Given Statement: "Moral education should be compulsory at primary school level." - A part of the Education Minister's speech.

Now, 

Assumptions:

1. Only young children can be provided moral education - Not Implicit (The statement does not imply that only young children can be provided moral education, it only emphasizes the importance of moral education at the primary school level.)
2. Older children do not require moral education - Not Implicit (The statement does not suggest that older children do not require moral education, it simply focuses on making it compulsory at the primary school level.)

Here, neither assumption 1 nor 2 are implicit.

Hence, the correct answer is "Option 4".

The logic followed here is:

Hence, the correct answer is "Option 4".

The correct answer is Guglielmo Marconi.

Key Points 

• Guglielmo Marconi
• Italian physicist and inventor of the successful wireless telegraph (1896).
• He received the Nobel Prize for Physics in 1909.
• He worked on the development of shortwave wireless communication, which constitutes the basis of nearly all modern long-distance radio.
• It meant a giant leap – from an era of communication using wires to communicating without using wires (Wireless).​

Additional Information

The correct answer is Stortinget.

Key Points

• The parliament of Norway is called the Stortinget.
• The word Stortinget is Norwegian for "the Great Thing".
• The Stortinget was established in 1814 by the Constitution of Norway.

Additional Information

The logic followed here is:

RATE is written as IZGV.

Similarly,

FUND be written as:

Hence, the correct answer is "Option 3".

Given:

Points: (-2, 5) and (1, 3)

Formula used:

Equation of a line passing through two points is:

y - y₁ = m(x - x₁)

Where slope (m) = (y₂ - y₁) / (x₂ - x₁)

Calculation:

m = (3 - 5) / (1 - (-2))

⇒ m = -2 / 3

Now, using the point (1, 3):

y - 3 = (-2/3)(x - 1)

⇒ y - 3 = (-2/3)x + 2/3

⇒ y = (-2/3)x + 2/3 + 3

⇒ y = (-2/3)x + 2/3 + 9/3

⇒ y = (-2/3)x + 11/3

⇒ 2x + 3y - 11 = 0

∴ The equation of the line is: 2x + 3y - 11 = 0.

Given:

$\sqrt {107 + ;\sqrt {192 + ;\sqrt {11 + ;\sqrt {25} } } }$

Formula used:

To simplify the nested square roots.

Calculation:

$\sqrt {107 + ;\sqrt {192 + ;\sqrt {11 + ;\sqrt {25} } } }$

⇒ $\sqrt {107 + ;\sqrt {192 + ;\sqrt {11 + 5 } } }$

⇒ $\sqrt {107 + ;\sqrt {192 + 4 } }$

⇒ $\sqrt {107 + ;\sqrt {196 } }$

⇒ $\sqrt {107 + 14 }$

⇒ $\sqrt {121} = 11$

∴ The value of the expression is 11.

The correct answer is Electric motor.

Key Points

• Electric motor​
• An electrical motor converts electrical energy into mechanical energy.
• An electrical motor works on the principle of electromagnetic induction.
• Types of the electric motor:
• AC motor: It converts alternating current into mechanical power.
• DC motor: It converts direct current into mechanical power.

Additional Information

• A simple motor has the following parts:
• Power supply: DC for a simple motor.
• Field Magnet: Could be a permanent magnet or an electromagnet
• Commutator: It is the rotating interface of the armature coil with a stationary circuit.
• Field Magnet: The magnetic field helps to produce a torque on the rotating armature coil by virtue of Fleming’s left-hand rule.
• Armature Core: Holds the armature coil in place and provides mechanical support.
• Armature Coil: It helps the motor to run.
• Brushes: It is a device that conducts current between stationary wires and moving parts, most commonly the rotating shaft.
• Uses of an Electric Motor
• Drill machine, Water Pumps, Hard Disc Drives, Washing Machines, Industrial Equipment etc.

The correct answer is e-Granthalaya.

Key Points 

• e-Granthalaya is a Digital Platform developed by the National Informatics Centre, Ministry of Electronics and Information Technology, Government of India.
• Version 4.0 of e Granthalaya was the first version which is a Cloud Ready Application to facilitate web-based data entry with a Centralized Database.
• e-Granthalaya was started as an in-house project at 'The Karnataka State Centre of NIC in 2002 for the automation of public libraries in the Karnataka state.

The correct answer is 7th April.

Key Points

• The Assembly decided to celebrate 7 April of each year, with effect from 1950, as World Health Day.
• World Health Day is held to mark WHO's founding and is seen as an opportunity by the organization to draw worldwide attention to a subject of major importance to global health each year.
• On World Health Day 2022, under the theme “Our planet, our health”.
• It is an enterprise taken by the World Health Organization (WHO) to raise awareness about the overall health and well-being of people across the world. Each year, there is a specific theme for World Health Day.

Additional Information

• ​World environment day is celebrated on June 5 every year and this day is commemorated to raise awareness about environmental issues, increasingly deteriorating conditions, climate change, etc.
• "Universal Social Protection to End Child Labour" The 2022 theme of the world day calls for increased investment in social protection systems and schemes to establish solid social protection floors and protect children from child labour.

Given:

The salary paid by the company (in 10 lakh ₹) over 5 years:

2014: 340

2015: 398

2016: 409

2017: 456

2018: 479

Formula used:

Average salary = (Sum of salaries for all years) ÷ (Number of years)

Calculation:

⇒ Total salary paid = 340 + 398 + 409 + 456 + 479

⇒ Total salary = 2082

⇒ Average salary = 2082 ÷ 5

⇒ Average salary = 416.4

∴ The average salary paid by the company over the 5 years is 416.4 (in 10 lakh) ₹.

Given:

The diagonal of a cube = 6√2 cm.

Formula Used:

The formula for the diagonal of a cube is $√{3} × \text{side}$.

The formula for the surface area of a cube is $\text{6} × \text{side}^2$.

Calculation:

Let the side of the cube be aaaaa cm.

According to the given diagonal:

$√{3} × a = 6√{2}$

⇒ a = $\frac{6√{2}}{√{3}}$

⇒ a = 6 × $\frac{√{2}}{√{3}}$

⇒ a = 6 × $√{\frac{2}{3}}$

⇒ a = 6 × $√{\frac{2}{3}} × \frac{√{3}}{√{3}}$

⇒ a = 6 ×  $\frac{√{6}}{3}$

⇒ a = 2√6 cm

Now, the surface area of the cube:

Surface Area = 6 × (side)²

Surface Area = 6 × (2√6)²

⇒ Surface Area = 6 × 4 × 6

⇒ Surface Area = 144 cm²

The surface area of the cube is 144 cm².

The correct answer is Madhya Pradesh.

Key Points

• Madhya Pradesh saw the highest number of tigers at 526 , closely followed by Karnataka at 524 with Uttarakhand at number 3 with 442 tigers.
• Madhya Pradesh has the maximum number of tiger reserves.
• Madhya Pradesh is also known as the 'Tiger State' has 6 Tiger reserves within the state.
• Madhya Pradesh harbors nearly 20% of India's Wild Tiger Population and nearly 10% of the world's tiger population as per the current estimates.
• Six tiger reserves of MP are:
• Kanha Tiger Reserve, Pench Tiger Reserve, Panna Tiger Reserve, Bandhavgarh Tiger Reserve, Satpuda Tiger Reserve, and Sanjay Tiger Reserve.

Additional Information 

• There are a total of 51 tiger reserves throughout India.
• Project Tiger was launched by the Government of India in the year 1973 to save the endangered species of tiger in the country.  Starting from nine (9) reserves in 1973-2016 the number is grown up to fifty-one (51).

The correct answer is Poles

Key Points

• Acceleration Due to Gravity:
• The force of attraction exerted by the earth on a body is called gravitational pull or gravity.
• We know that when a force acts on a body, it produces acceleration. Therefore, a body under the effect of gravitational pull must accelerate.
• The acceleration produced in the motion of a body under the effect of gravity is called acceleration due to gravity, it is denoted by g.
• If g is the acceleration due to gravity, then
• $g = \frac{{GM}}{{{R^2}}}$
• Where G = universal gravitational constant, M = mass of the earth and R = radius of the earth
• The distance from the center of the earth to its poles is lesser-than the distance to the equator region.
• Therefore g value is slightly greater at poles and its value is 9.83m/s2. Option (2) is correct.

Additional Information

• The value of g at the equator is 9.78m/s2.
• The difference between gravity and gravitation is Gravity is the force between a body and earth while gravitation is the force acting between two bodies.

The logic followed here is:

To find the probability that the number 5 has appeared at least once given that the sum of the two dice is 10, we can follow these steps:

1. Determine the total outcomes where the sum is 10: The possible pairs (x, y)

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         (x, y) where          
   
   

x + y = 10x + y = 10 are:

Valid outcomes are:

So, the total outcomes where the sum is 10 are 3.

• (4, 6)
• (5, 5)
• (6, 4)
• (3, 7) - not possible since 7 is not on a die.
• (2, 8) - not possible.
• (1, 9) - not possible.
• (4, 6)
• (5, 5)
• (6, 4)

2. Determine the favorable outcomes where at least one die shows a 5: The pairs where at least one die is a 5 are:

So, the favorable outcomes are 1.

• (5, 5)

3. Calculate the probability: The probability PPP P that at least one die shows a 5 given that the sum is 10 is given by:

• P = Number of favorable outcomes / Total outcomes = 1 / 3
• Thus, the probability that the number 5 has appeared at least once given that the sum is 10 is 1/3.

Hence, the correct answer is  "Option 4".

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The correct answer is Shivaji Sagar Lake

Key Points

• Shivaji Sagar Lake is the largest artificial freshwater lake in India.
• It is formed by the Koyna Dam on the Koyna River in Maharashtra.
• It is an artificial reservoir and one of the largest in India.
• The lake plays a crucial role in providing hydroelectric power through the Koyna Hydroelectric Project.
• It is surrounded by the scenic Western Ghats, making it a tourist attraction.

Additional Information

• Nainital Lake
• Nanital lake is situated in the state of Uttarakhand.
• This has a form in the shape of a kidney or a crescent and an outfall at the south-east end.
• Nainital is the most prominent hill-station in the Kumaon district.
• It is famous for its Naini Lake located in the center of the town, as well as several other nearby lakes.
• It is one of the four lakes in Kumaon Hills; the other three are the Sattal Lake, the Bhimtal Lake, and the Naukuchiyatal Lake.
• Kolleru Lake
• A natural freshwater lake, situated between the Krishna and Godavari deltas in Andhra Pradesh.
• Kolleru is a wildlife sanctuary and home to numerous migratory birds, especially in winter.
• It serves as a crucial ecosystem and supports local fishing industries.
• Though a natural lake, it sometimes undergoes changes due to human intervention like drainage.
• Kodai Lake
• An artificial lake located in Kodaikanal, Tamil Nadu.
• It was created in 1863 by Sir Vere Henry Levinge, the then Collector of Madurai.
• The lake is star-shaped and is popular for boating, cycling, and horse riding along its perimeter.
• Surrounded by the Palani Hills, it is a major tourist attraction in Kodaikanal.

The correct answer is Kanpur

Key Points

• As per the Guinness World Records 2020 analysis of a World Health Organization (WHO) report, Kanpur in India was listed as the most polluted city in the world
• Kanpur, in Uttar Pradesh, topped the list of the most polluted cities due to extremely high levels of particulate matter (PM2.5).
• The city faces severe air pollution issues mainly due to industrial emissions, vehicular pollution, and dust.
• Poor air quality in Kanpur is linked to serious health risks, including respiratory and cardiovascular diseases.
• The WHO report highlighted several other Indian cities among the most polluted globally.

Additional Information

• Delhi consistently ranks among the most polluted cities in the world in terms of air quality, especially during the winter months.
• High levels of PM2.5 (fine particulate matter) and PM10 due to vehicular emissions, industrial activities, construction dust, and seasonal stubble burning in neighboring states.
• Lahore also ranks among the most polluted cities globally, particularly during winter.
• Major sources of pollution include vehicular emissions, industrial pollution, and crop burning.
• The city also faces air quality problems due to dust and seasonal fog (smog).
• While Karachi experiences high pollution levels, it tends to rank lower than Lahore and Delhi in terms of severity.

Given:

The number of students from various schools participating in different games:

Formula used:

Sum of students in each school = Total number of students in each row

Calculation:

⇒ Total students for School A = 34 + 21 + 12 + 9 + 98 = 174

⇒ Total students for School B = 67 + 40 + 22 + 13 + 121 = 263

⇒ Total students for School C = 23 + 26 + 19 + 7 + 78 = 153

⇒ Total students for School D = 78 + 32 + 16 + 12 + 84 = 222

⇒ Total students for School E = 56 + 29 + 21 + 6 + 67 = 179

Conclusion:

The school with maximum participation is School B with 263 students.

The school with minimum participation is School C with 153 students.

∴ The correct answer is option 1.

Given:

The equation to solve is: 3(5x + 2) - 4 = 2(1 - 4x)

Formula Used:

Solve for x by isolating the variable on one side of the equation.

Calculation:

Start by expanding both sides:

⇒ 3(5x + 2) - 4 = 2(1 - 4x)

⇒ 15x + 6 - 4 = 2 - 8x

Simplify the equation:

⇒ 15x + 2 = 2 - 8x

Combine like terms:

⇒ 15x + 8x = 2 - 2

⇒ 23x = 0

Divide both sides by 23:

⇒ x = 0

The value of the variable x is 0.

Shortcut Trick

Apply the Cosine Rule directly: cos A = (b² + c² − a²) / (2bc)

Substitute the values: a = 25, b = 45, c = 30

cos A = (45² + 30² − 25²) / (2 × 45 × 30)

cos A = (2025 + 900 − 625) / 2700 = 2300 / 2700 = 23/27

∴ The correct answer is 23/27.

Alternate Method

Given: Sides of triangle ABC are a = 25, b = 45, and c = 30.

Formula Used: In any triangle ABC, the Law of Cosines states:

cos A = (b² + c² − a²) / 2bc

Calculation:

⇒ a² = 25² = 625

⇒ b² = 45² = 2025

⇒ c² = 30² = 900

⇒ cos A = (2025 + 900 − 625) / (2 × 45 × 30)

⇒ cos A = (2925 − 625) / 2700

⇒ cos A = 2300 / 2700

⇒ cos A = 23/27

∴ The correct answer is 23/27.

Additional Information

Cosine Rule for Other Angles

Similarly, cos B = (a² + c² − b²) / 2ac and cos C = (a² + b² − c²) / 2ab.

Sine Rule

The relationship between sides and angles is given by a / sin A = b / sin B = c / sin C = 2R, where R is the circumradius.

SSS Condition

When all three sides (Side-Side-Side) are known, the angles of the triangle can be uniquely determined using the Cosine Rule.

The correct answer is the Young Party

Key Points

• The organisation that was NOT a part of the revolutionary movement for Indian Independence is Young Party.
• This name does not appear in historical records or literature related to Indian freedom movements.

Additional Information

• Anushilan Samiti
• A revolutionary organization based in Bengal, founded in the early 20th century.
• It played a major role in the Indian independence movement, focusing on violent methods to overthrow British rule.
• It carried out a number of attacks against British officials and institutions.
• Jugantar
• A branch of Anushilan Samiti, also centered in Bengal.
• Involved in numerous revolutionary activities, including assassinations, bombing campaigns, and organizing armed struggles against British rule.
• Prominent revolutionaries like Barindra Kumar Ghosh and Bagha Jatin were part of this group.
• Abhinav Bharat
• A secret revolutionary society founded by Vinayak Damodar Savarkar in 1904.
• It aimed to incite armed rebellion against the British Empire and inspired many revolutionaries through its radical approach.
• It was involved in conspiracies, bomb-making, and assassinations of British officials.

The correct answer is Article 280

Key Points

• The article that deals with the formation of the Finance Commission is Article 280
• Article 280 of the Indian Constitution provides for the formation of a Finance Commission by the President of India.
• It outlines the commission’s duties, such as recommending the distribution of taxes between the Union and the States,
• determining financial relations, and providing advice on fiscal matters.

Additional Information

• Article 279
• This article provides the framework for determining and calculating the net proceeds of taxes or duties levied by the Government of India.
• The term "net proceeds" refers to the total revenue collected from a tax after deducting the costs of collection.
• Article 282
• This article allows the Union or State Governments to make grants for any public purpose, even if the purpose is not within their legislative competence.
• This provides flexibility for governments to allocate funds for unforeseen or special needs that may arise.
• Article 281
• Article 281 outlines how the recommendations of the Finance Commission are to be laid before each house of Parliament.
• Once the Finance Commission submits its report, the recommendations are reviewed and considered for implementation.

The correct answer is Article 41

Key Points

• The article that is directed to establish the right to work, to education, and to public assistance in certain cases is  Article 41
• Article 41 of the Indian Constitution, part of the Directive Principles of State Policy (DPSP),
• ​directs the state to make provisions for securing the right to work, to education, and to public assistance in cases of unemployment, old age, sickness, and disablement.
• This is subject to the state’s economic capacity and development.

Additional Information

• Article 40
• Article 40 directs the state to take steps to organize village panchayats and endow them with powers and authority to function as units of local self-government.
• It emphasizes the decentralization of power to local levels for better governance.
• Article 42
• Article 42 requires the state to ensure that just and humane conditions of work are provided and to make provisions for maternity relief.
• This relates to workers' welfare and the protection of women’s rights, particularly concerning maternity benefits.
• Article 43
• Article 43 directs the state to ensure that workers are provided with a living wage, suitable conditions of work, and a decent standard of life.
• It aims to improve the welfare of workers and promote cottage industries.

The correct answer is Prolactin

Key Points

• Prolactin is a hormone produced in the pituitary gland of animals, including humans.
• It primarily regulates lactation (milk production) and has various roles in metabolism,
• regulation of the immune system, and development of the reproductive system.
• It is not involved in plant growth or development, which is why it is not classified as a plant hormone.

Additional Information

• Gibberellins
• Gibberellins are a group of plant hormones that promote stem elongation, seed germination, and flowering.
• They help in breaking dormancy in seeds and are involved in various developmental processes in plants.
• They are particularly important in processes such as fruit development and leaf expansion.
• Ethylene
• Ethylene is a gaseous plant hormone involved in the regulation of fruit ripening, flowering, and the response to stress conditions.
• It plays a key role in the ageing process of plants.
• It is well known for promoting the ripening of fruits and is used commercially to control the timing of ripening in various fruits.
• Abscisic Acid (ABA)
• Abscisic acid is a plant hormone that primarily promotes leaf abscission (the shedding of leaves), helps plants respond to stress conditions (such as drought), and regulates seed dormancy.
• It plays a crucial role in maintaining plant water balance and is involved in signalling pathways that help plants cope with environmental stresses.

The correct answer is a rail magazine

Key Points

• Rail Bandhu is  a rail magazine.
• Rail Bandhu is a passenger-friendly magazine published by Indian Railways.
• It provides information about train schedules, services, tourism, and various other topics related to rail travel.
• The magazine aims to enhance the travel experience by keeping passengers informed and engaged during their journey.

Additional Information

• Important facts about Indian Railways:
• ​It has the largest rail network in Asia and is the second-largest in the world, after the United States.
• The total length of the railway tracks in India is around 68,000 kilometers, spanning across the country, connecting remote and urban areas.
• The first passenger train in India ran on April 16, 1853, from Mumbai to Thane, covering a distance of 34 kilometers.
• Indian Railways is divided into 18 zones and further into divisions.
• Some of the major zones include Northern Railway, Eastern Railway, Southern Railway, and Western Railway.
• Around 75% of the railway network is electrified, and the Indian government aims to achieve 100% electrification in the near future to reduce dependence on fossil fuels.

The logic followed here is:

ABLE is written as 3781,

HAIR is written as 4365

TOOL is written as 9008.

Then, RATTEL be written as:

Hence, the correct answer is "Option 3".

Given:

Height of the cylinder (h) = 14 cm

Curved surface area (CSA) = 660 cm²

Formula Used:

CSA of a cylinder = 2πrh

Volume of a cylinder = πr²h

Calculation:

From CSA, we have:

2πrh = 660

⇒ 2 × 22/7 × r × 14 = 660

⇒ 88r = 660

⇒ r = 660 / 88

⇒ r = 7.5 cm

Now, Volume (V) = πr²h

⇒ V = (22/7) × (7.5)² × 14

⇒ V = (22/7) × 56.25 × 14

⇒ V = 22 × 8.04 × 14

⇒ V = 2475 cm³

The volume of the cylinder is 2475 cm³.

Given:

Evaluate: (0.2)³ - (0.02)³

Formula Used:

Difference of cubes: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

Calculation:

Let a = 0.2 and b = 0.02

(0.2)³ - (0.02)³

= $(0.2 - 0.02) \left( (0.2)^2 + (0.2 \times 0.02) + (0.02)^2 \right)$

= $0.18 \left( 0.04 + 0.004 + 0.0004 \right)$

= $0.18 \left( 0.0444 \right)$

⇒ 0.18 × 0.0444

⇒ 0.007992

The correct answer is option 1.

Given:

The number is 2893#$ and it is divisible by 8 and 5.

Formula Used:

1. A number is divisible by 5 if its last digit is 0 or 5.
2. A number is divisible by 8 if its last three digits form a number that is divisible by 8.

Calculation:

Since the number is divisible by 5, the last digit $ must be 0.

Hence, the number becomes 2893#0.

Now, the number must be divisible by 8. So, the last three digits 3#0 must form a number divisible by 8.

We test values for #:

If # = 0: Last three digits = 300, 300 ÷ 8 = 37.5 (Not divisible)

If # = 1: Last three digits = 310, 310 ÷ 8 = 38.75 (Not divisible)

If # = 2: Last three digits = 320, 320 ÷ 8 = 40 (Divisible)

⇒ # = 2 and $ = 0

The correct answer is option 3.

Given:

Height of the pole = 6√3 metres

Length of the shadow = 6 metres

Formula Used:

tan(θ) = Opposite / Adjacent

Calculation:

Let the angle of elevation be θ.

tan(θ) = Height of the pole / Length of the shadow

tan(θ) = 6√3 / 6

tan(θ) = √3

⇒ θ = 60º

The angle of elevation of the sun is 60º.

Given:

Mohan's salary = ₹1600

Ravi's salary is 20% more than Mohan's salary.

Formula Used:

Ravi's salary = Mohan's salary + 20% of Mohan's salary

Calculation:

20% of Mohan's salary = 20/100 × ₹1600

20% of Mohan's salary = 0.2 × ₹1600

20% of Mohan's salary = ₹320

Ravi's salary = ₹1600 + ₹320

⇒ Ravi's salary = ₹1920

The correct answer is option 2.

The correct answer is Nandan Bal.

Key Points

• Nandan Bal is a renowned Indian tennis coach who has significantly contributed to the sport.
• He has been instrumental in coaching and mentoring numerous young tennis players in India.
• His dedication to the sport and his contributions to developing tennis in India earned him the prestigious Dhyan Chand Award in 2020.
• The Dhyan Chand Award is India’s highest award for lifetime achievement in sports and games, which recognizes his lifelong dedication and achievements in tennis.

Additional Information

• Dhyan Chand Award
• The Dhyan Chand Award is the highest award for lifetime achievement in sports and games in India.
• It is named after the legendary Indian hockey player Dhyan Chand, who is regarded as one of the greatest hockey players of all time.
• The award is given by the Ministry of Youth Affairs and Sports, Government of India.
• The award comprises a bronze statuette of Dhyan Chand, a certificate, and a cash prize.
• Arokia Rajiv
• Arokia Rajiv is an Indian sprinter who specializes in the 400 meters.
• He has represented India in various international events, including the Asian Games and Commonwealth Games.
• Sikki Reddy
• N. Sikki Reddy is an Indian badminton player specializing in doubles.
• She has won several medals in international competitions, including the Commonwealth Games and South Asian Games.
• Rajat Chauhan
• Rajat Chauhan is an Indian archer who competes in the compound archery discipline.
• He has won medals in events like the Asian Games and World Archery Championships.

Given:

Distance covered by the cyclist = 650 m.

Time taken = 2 min 10 sec = 2 × 60 + 10 = 130 seconds.

Formula Used:

Speed (in km/hr) = $\frac{Distance (in meters)}{Time (in seconds)} × \frac{18}{5}$

Calculation:

Distance = 650 m

Time = 130 sec

Speed (in m/s) = $\frac{650}{130}$

⇒ Speed (in m/s) = 5 m/s

Speed (in km/hr) = 5 × $\frac{18}{5}$

⇒ Speed (in km/hr) = 18 km/hr

The speed of the cyclist is 18 km/hr.

The correct answer is Widow remarriage

Key Points

• The Widow Remarriage Act was enacted in 1856 during Lord Canning's administration.
• This act aimed to improve the status of widows in Indian society by allowing them to remarry, challenging the stigma associated with widowhood.
• In 19th-century India, widowhood was a highly stigmatized state for women.
• Widows were often subjected to social ostracism and were expected to live a life of austerity, frequently following practices like Sati (self-immolation on the husband’s funeral pyre) or leading a life of seclusion.
• The social reform movement in India gained momentum during this period, driven by intellectuals and social reformers who sought to challenge and change entrenched social norms.
• Prominent figures like Ishwar Chandra Vidyasagar, a leading reformer, actively campaigned for widow remarriage.

Additional Information

• Doctrine of Lapse
• The Doctrine of Lapse was a policy introduced by the British East India Company, primarily under Lord Dalhousie (Governor-General from 1848 to 1856).
• It allowed the British to annex any Indian princely state if the ruler died without a direct male heir.
• This doctrine was a major factor leading to the Indian Rebellion of 1857, as many Indian rulers lost their states due to this policy.
• For example, the annexation of Awadh (Oudh) was a significant event attributed to this doctrine.
• Morley-Minto Reforms
• These reforms were enacted in 1909 and aimed to increase Indian participation in government through a series of legislative reforms, including the introduction of separate electorates for Muslims.
• It is named after John Morley (Secretary of State for India) and Lord Minto (Viceroy), these reforms were part of an effort to address growing political discontent in India and manage communal tensions.
• Prohibition of Sati
• The practice of Sati, where widows self-immolated on their husbands' funeral pyres, was banned in 1829 by Lord William Bentinck.
• This was a significant social reform aimed at protecting women's rights and dignity.
• Raja Rammohan Roy, the great Hindu reformer from Bengal fought many social evils prevalent in the Hindu society of Bengal and Sati pratha was one of the chief ones.

Given:

The least square number that is exactly divisible by 4, 5, 8, 16, and 32.

Formula Used:

The least square number divisible by given numbers is the LCM of the numbers raised to the power of 2.

Calculation:

Prime factorization of the given numbers:

4 = 2²

5 = 5¹

8 = 2³

16 = 2⁴

32 = 2⁵

LCM is obtained by taking the highest power of each prime factor:

LCM = 2⁵ × 5¹

To make it a perfect square, all exponents in the prime factorization should be even:

LCM = 2⁶ × 5²

Now calculate the number:

LCM = 2⁶ × 5²

LCM = 64 × 25

⇒ LCM = 1600

The least square number that is exactly divisible by 4, 5, 8, 16, and 32 is 1600.

The correct answer is London

Key Points

• The 2012 Summer Olympics were held in  London
• The 2012 Summer Olympics, officially known as the Games of the XXX Olympiad, took place in London, United Kingdom, from July 27 to August 12, 2012.
• London made history by becoming the first city to host the modern Olympic Games three times, having previously hosted the games in 1908 and 1948.

Additional Information

• Tokyo:
• Tokyo hosted the Summer Olympics in 1964 and later in 2021 (officially the 2020 Summer Olympics, which were postponed due to the COVID-19 pandemic).
• Rio:
• Rio de Janeiro, Brazil, hosted the Summer Olympics in 2016.
• Paris:
• Paris hosted the Summer Olympics in 1900 and 1924, and it is scheduled to host them again in 2024.

Given:

$\left( 3\frac{1}{7} + 4\frac{3}{7} \right) + \frac{7}{6}$

Formula used:

Mixed fractions: a ^b/_c = (a * c + b)/c

Calculations:

⇒ $\left( 3\frac{1}{7} = \frac{22}{7}\right) + \left( 4\frac{3}{7} = \frac{31}{7} \right)$

⇒ $\frac{22}{7} + \frac{31}{7} = \frac{53}{7}$

⇒ $\frac{53}{7} + \frac{7}{6}$

Finding the LCM of 7 and 6 = 42

⇒ $\frac{53 \times 6}{42} + \frac{7 \times 7}{42} = \frac{318}{42} + \frac{49}{42} = \frac{367}{42}$

∴ The correct answer is option 3,

The correct answer is Argon

Key Points

• In October 2019, the noble gas detected on the lunar exosphere by the Chandrayaan-2 orbiter was Argon-40.
• It is produced from the radioactive decay of Potassium-40 in the Moon’s interior.
• The detection of Argon-40 is significant for studying the lunar exosphere and
• understanding the processes taking place on and below the Moon’s surface, such as volcanic and radioactive decay activities.

Additional Information

• Helium:
• Helium, particularly Helium-3, has been detected on the lunar surface in previous missions,
• It is considered a potential resource for future energy use due to its possible application in nuclear fusion.
• Neon:
• Neon is known to exist in the Moon’s exosphere.
• It is released by solar wind particles striking the lunar surface.
• Neon contributes to the extremely thin lunar atmosphere (exosphere)
• Krypton:
• Krypton is a noble gas that has not been prominently detected on the Moon.
• Its atomic number is 36
• A noble gas, about three times heavier than air, monatomic, and does not react with anything except fluorine gas

The correct answer is IIT BHU

Key Points

• Recently, the Indian Institute of Science (IISc) Bengaluru installed the supercomputer 'Param Pravega'.
• It has a supercomputing capacity of 3.3 petaflops.
• It has been installed under the government’s National Supercomputing Mission.
• India’s first supercomputer was PARAM 8000.
• PARAM Shivay, the first supercomputer assembled indigenously, was installed in IIT (BHU), followed by PARAM Shakti, PARAM Brahma, PARAM Yukti, PARAM Sanganak at IIT-Kharagpur, IISER, Pune, JNCASR, Bengaluru and IIT Kanpur respectively.
• In 2020, PARAM Siddhi, the High-Performance Computing-Artificial Intelligence (HPC-AI) supercomputer, achieved a global ranking of 62nd in the Top 500 most powerful supercomputer systems in the world.

Additional Information

• National Supercomputing Mission
• In 2015, the National Supercomputing Mission was launched to enhance the research capacities and capabilities
• To form a Supercomputing grid, with National Knowledge Network (NKN) as the backbone.
• The NKN project is aimed at establishing a strong and robust Indian network that will be capable of providing secure and reliable connectivity.
• It supports the government's vision of 'Digital India' and 'Make in India' initiatives.
• The Mission is being jointly steered by the Department of Science and Technology (DST) and the Ministry of Electronics and Information Technology (MeitY).

Given:

2^x = 4^{y + 1} and 3^y = 3^{x - 9}

Formula used:

Using properties of exponents:

a^m = aⁿ implies m = n

Calculations:

1. Start with 2^x = 4^{y + 1}

4 can be written as 2², so the equation becomes:

⇒ 2^x = (2²)^{y + 1}

⇒ 2^x = 2^{2y + 2}

Since the bases are the same, equate the exponents:

⇒ x = 2y + 2

2. Now, solve 3^y = 3^{x - 9}

Equate the exponents:

⇒ y = x - 9

3. Substitute y = x - 9 into x = 2y + 2:

⇒ x = 2(x - 9) + 2

⇒ x = 2x - 18 + 2

⇒ x - 2x = -16

⇒ -x = -16

⇒ x = 16

4. Substitute x = 16 into y = x - 9:

⇒ y = 16 - 9

⇒ y = 7

∴ The values of x and y are 16 and 7, respectively.

The correct answer is Fourth Schedule

Key Points

• The Fourth Schedule of the Indian Constitution enumerates the allocation of Rajya Sabha seats to states and union territories.
• It provides details on how many Rajya Sabha seats each state or union territory is allotted based on their population.
• The allocation can be revised based on changes in population and other constitutional amendments.

Additional Information

• Sixth Schedule:
• The Sixth Schedule deals with the administration of tribal areas in the states of Assam, Meghalaya, Tripura, and Mizoram.
• It provides for Autonomous District Councils to govern these tribal areas with a degree of autonomy.
• It aims to protect the rights and culture of tribal communities by granting them the ability to make laws on certain subjects like land, forest, and water.
• First Schedule:
• The First Schedule lists the names of States and Union Territories of India and their territorial jurisdictions.
• It defines the geographical extent of India by including the newly formed states and union territories.
• This schedule is amended when new states are formed or the boundaries of existing ones are altered.
• Tenth Schedule:
• The Tenth Schedule contains provisions relating to anti-defection laws.
• It deals with the disqualification of members of Parliament and state legislatures on grounds of defection to another political party
• Its main aim is to curb political defections by preventing elected representatives from switching parties after elections.

Given:

The least number that when divided by 9, 16, 20 or 24, leaves 3 as remainder in each case.

Formula Used:

Let the least number be N .

Then N = LCM(9, 16, 20, 24) + R , where R is the remainder.

R = 3

Calculation:

First, find the LCM of 9, 16, 20, and 24.

Prime factorization:

9 = 3²

16 = 2⁴

20 = 2² × 5

24 = 2³ × 3

LCM = 2⁴ × 3² × 5

LCM = 16 × 9 × 5

LCM = 720

Therefore, the least number N is:

N = 720 + 3

N = 723

The least number that when divided by 9, 16, 20, or 24, leaves 3 as remainder in each case is 723.

According to the given information:

A is older than B, D is younger than B.

• A > B > D

C is older than D but younger than B.

• A > B > C > D

Thus, D is the youngest among all.

Hence, the correct answer is "Option 4".

The correct answer is 1576 AD

Key Points

• The Battle of Haldighati was a battle fought on 18 June 1576.
• It was fought between the Rana of Mewar, Maharana Pratap, and the Mughal emperor Akbar.
• The Mughal force was led by Man Singh I of the Amber.
• Abul Fazl says that the Mughal army was forced to retreat in the initial phase of the battle.
• Haldighati is a region in the Aravalli mountain range, which links Rajsamand and Pali districts in Rajasthan, the name for which is inspired by its yellow-turmeric-colored soil.
• The two armies fought a four-hour-long war in which the Mughals suffered heavy casualties and Maharana escaped unhurt.

The correct answer is Belgium

Key Points

• Belgium is a European country that doesn't have the Alps range located within its geographical boundary
• The Alps are the highest and most extensive mountain range system that lie in south-central Europe. The mountain range stretches approximately 750 miles (1,200 kilometers) in a crescent shape across eight Alpine countries: France, Switzerland, Monaco, Italy, Liechtenstein, Austria, Germany, and Slovenia.
• The Alps are one of the world's largest and highest mountain ranges, and the highest mountain in the Alps is Mont Blanc, which spans the French–Italian border.
• The Alps were formed over millions of years when the African and Eurasian tectonic plates collided.
• The range's size and altitude impact the climate in Europe, and the mountains have distinct climatic zones and varying precipitation levels.

Given:

Value = $5\frac{44}{49}$

Formula Used:

$\sqrt{a + \frac{b}{c}} = \sqrt{\frac{ac + b}{c}}$

Calculation:

We need to find the square root of $5\frac{44}{49}$.

First, convert the mixed fraction to an improper fraction:

$5\frac{44}{49} = \frac{5 \times 49 + 44}{49}$

⇒ $5\frac{44}{49} = \frac{245 + 44}{49}$

⇒ $5\frac{44}{49} = \frac{289}{49}$

Now, find the square root:

$\sqrt{\frac{289}{49}}$

⇒ $\frac{\sqrt{289}}{\sqrt{49}}$