RRB NTPC CBT-I Official Paper (Held On: 27 Mar 2021 Shift 1) (Previous Year Paper)

The logic followed here is:

 

Tablet, Ointment, Injection all are forms of medications,

Whereas,

Treatment is a process, not a form of medication.

Hence, the correct answer is "Treatment".

The correct answer is Aluminium

Key Points

• Bauxite is a clay-like substance that contains aluminum, a mineral that is extracted from it:
• Aluminum
• Bauxite is a naturally occurring aluminum ore that's primarily made up of aluminum hydroxide minerals, such as boehmite, gibbsite, and diaspore.
• Other minerals
• Bauxite also contains other minerals and compounds, including silica, iron oxide, titania, and aluminosilicate.
• 9 Ore Deposits and Economic Minerals – Mineralogy
• Bauxite is a primary source of aluminum, which is used in many industrial applications.
• About 70% of the world's bauxite is refined into alumina, or aluminum oxide, using the Bayer chemical process.

The correct answer is Stephen Hawking.

Key Points

• Stephen Hawking:
• He was an English theoretical physicist, cosmologist, and author.
• He is the author of the best-selling book, "A Brief History of Time".
• Hawkings redefined cosmology by proposing that black holes emit radiation and later evaporate.
• Hawking was diagnosed with an early-onset slow-progressing form of motor neuron disease (amyotrophic lateral sclerosis "ALS" or Lou Gehrig's disease) that gradually paralyzed him over the decades.
• Stephen Hawking, the British Physicist, and the black hole theorist died on 14^th March.

Additional Information

• J.V. Narlikar: Jayant V. Narlikar is an Indian astrophysicist known for his work in cosmology. He has authored several books on science and astronomy,
• Satyendranath Bose: An Indian physicist known for his work on quantum mechanics, specifically Bose-Einstein statistics, in collaboration with Albert Einstein. He did not write A Brief History of Time.
• C.V. Raman: An Indian physicist renowned for discovering the Raman Effect, for which he won the Nobel Prize in Physics in 1930.

Given:

The height of the house = h

Length of the ladder = 5.2 m

Inclination with the horizontal ground = 45º

Formula Used:

In a right triangle, using trigonometry: h = L sin(θ)

Calculation:

Here, L = 5.2 m and θ = 45º

We know that sin(45º) = $\frac{\sqrt{2}}{2}$

Using the formula:

⇒ h = 5.2 × sin(45º)

⇒ h = 5.2 × $\frac{\sqrt{2}}{2}$

⇒ h = 5.2 × $\frac{\sqrt{2}}{2}$

⇒ h = 2.6 $\sqrt{2}$

Therefore, the height of the house is:

h = $\frac{13\sqrt{2}}{5}$ m

The correct answer is option 2.

The correct answer is Oxford

Key Points

• Rashmi Samant became the first Indian woman to be elected as the president of the Oxford University Student Union in February 2021.
• Her election was historic as it marked significant representation for Indian students at the prestigious university.
• Her election was one of the oldest and most prestigious universities in the world, had never before had an Indian woman leading its student body.
• Samant campaigned on themes such as inclusivity, environmental issues, and mental health support for students, which resonated with many at Oxford.
• Her win was celebrated by many in India and internationally as a step forward for diversity and representation in educational institutions globally.
• However, her presidency was brief, as she faced scrutiny and criticism over some past social media posts, which eventually led her to step down from the role.

The logic followed here is:

BEST is written as UTTSFECB

Similarly,

CHAIR is written as

Hence, "Option 1" is the correct answer.

Given:

Number 1: 285, leaving a remainder of 9

Number 2: 1249, leaving a remainder of 7

Formula Used:

Greatest number which divides both numbers leaving given remainders = HCF of (Number 1 - Remainder 1) and (Number 2 - Remainder 2)

Calculation:

Required number = HCF of (285 - 9) and (1249 - 7)

Required number = HCF of 276 and 1242

Using the Euclidean algorithm:

1242 = 276 × 4 + 138

276 = 138 × 2 + 0

So, HCF = 138

The greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively is 138.

Given:

Provisions for 150 men for 45 days.

After 10 days, 25 men left.

Formula Used:

Total provisions = Number of men × Number of days

Remaining provisions = Initial provisions - Provisions used in 10 days

New number of men = Initial number of men - Number of men left

Remaining days = Remaining provisions / New number of men

Calculation:

Total provisions = 150 × 45

Total provisions = 6750 man-days

Provisions used in 10 days by 150 men = 150 × 10

Provisions used = 1500 man-days

Remaining provisions = 6750 - 1500

Remaining provisions = 5250 man-days

New number of men = 150 - 25

New number of men = 125 men

Remaining days = 5250 / 125

Remaining days = 42 days

The provisions will last for 42 days.

Calculation:

Let's check each option one by one:

Option 1: $\left( √{2} + \frac{1}{√{8}} \right)^2$

Step 1: Simplify the terms.

$\frac{1}{√{8}} = \frac{1}{2√{2}}$

Step 2: Substitute in the original expression:

$\left( √{2} + \frac{1}{2√{2}} \right)^2$

Step 3: Apply the expansion formula $(a + b)^2 = a^2 + 2ab + b^2$

$a = √{2}, b = \frac{1}{2√{2}}$

⇒ 2 + 2 × √2 × $\frac{1}{2√{2}}$ + $(\frac{1}{2√{2}})^2$ = 4 + 1 + 1/8 = 41/8

Result:

This expression is a rational number.

Option 2: 2 - √{5}

This is a subtraction of a rational number and an irrational number √{5}. The result will be irrational.

Option 3: $\left( √{2} + √{5} \right)^2$

Step 1: Apply the expansion formula $(a + b)^2 = a^2 + 2ab + b^2$

$a = √{2}, b = √{5}$

Step 2: Simplify:

$a^2 = 2,\ b^2 = 5,\ 2ab = 2 × √{2} × √{5} = 2 √{10}$

The result will still involve irrational terms, so it is not a rational number.

Option 4: 2 + √{5}

This is a sum of a rational number and an irrational number √{5}. The result will be irrational.

∴ The correct answer is option 1.

The correct answer is Delhi

Key Points

• The Indian Navy and both IIT Delhi and IIT Kharagpur have signed a Memorandum of Understanding (MoU) for research in the underwater domain of Naval Electronic Systems:
• IIT Delhi
• The Indian Navy and IIT Delhi have a relationship that dates back to the 1970s.
• The research work conducted at IIT Delhi has been important for the Indian Navy's technological advances.
• IIT Kharagpur
• The Indian Navy and IIT Kharagpur signed an MoU on March 20, 2024 at Naval Headquarters, New Delhi.
• The partnership aims to promote academic cooperation, scientific understanding, and research projects in naval technology areas

Additional Information

• IIT Kanpur
• Located in Kanpur, Uttar Pradesh, IIT Kanpur is a public institute of technology.
• It's consistently ranked among India's top academic institutions. In 2024, it was ranked fourth in the NIRF Engineering list.
• IIT Bombay
• One of India's top engineering institutes, IIT Bombay was ranked third in the 2024 NIRF Engineering list.
• IIT Madras
• Established in 1959, IIT Madras has a Department of Mathematics

Given:

1/3 of a commodity is sold at the rate of 15% profit.

1/4 of the commodity is sold at the rate of 20% profit.

The rest is sold at the rate of 24% profit.

Total profit earned = Rs. 62

Formula Used:

Weighted Average Profit = (Sum of (Profit rate × Fraction of commodity))/Total fractions

Total Profit = (Weighted Average Profit) × (Cost Price)

Calculation:

Let the cost price of the commodity be Rs. x.

Fraction of commodity sold at 15% profit = 1/3

Fraction of commodity sold at 20% profit = 1/4

Fraction of commodity sold at 24% profit = 1 - (1/3 + 1/4)

⇒ Fraction of commodity sold at 24% profit = 1 - (4/12 + 3/12)

⇒ Fraction of commodity sold at 24% profit = 1 - 7/12

⇒ Fraction of commodity sold at 24% profit = 5/12

Weighted Average Profit = (15% × 1/3) + (20% × 1/4) + (24% × 5/12)

⇒ Weighted Average Profit = (15/100 × 1/3) + (20/100 × 1/4) + (24/100 × 5/12)

⇒ Weighted Average Profit = 5/100 + 5/100 + 10/100

⇒ Weighted Average Profit = 20/100

⇒ Weighted Average Profit = 20%

Total Profit = 20% of Cost Price

⇒ 62 = 20/100 × x

⇒ 62 = 0.2 × x

⇒ x = 62 / 0.2

⇒ x = 310

The cost price of the commodity is Rs. 310.

All conditions are as follows:

Therefore, Mr. A fulfills the eligibility criteria (i) to become a member of the library.

Hence, the correct answer is "Eligible only under (i)".

The correct answer is a bacterial disease

Key Points

• Citrus canker is a bacterial disease caused by the bacterium Xanthomonas citri subsp. citri:
• Symptoms
• Citrus canker causes lesions on the leaves, stems, and fruit of citrus plants. The leaves may drop and unripe fruit may fall to the ground.
• Impact
• Citrus canker affects the health of infected citrus trees and the marketability of infected fruit. While not harmful to humans, there is no cure for citrus canker.
• Spread
• Citrus canker is most severe in hot, wet areas. It is highly contagious and can affect all above-ground parts of citrus trees.
• Control
• To control citrus canker, you can:
• Reduce wind speeds with windbreaks
• Apply copper sprays to the fruit and leaves
• Practice sanitation
• Control leafminer

Additional Information

• Hormonal Disorder:
• A hormonal disorder refers to an imbalance or abnormality in the hormones in the body.
• Hormones are chemicals produced by glands and regulate various functions in the body, including growth, metabolism, and mood.
• Disorders like hypothyroidism, diabetes, and polycystic ovary syndrome (PCOS) are examples of hormonal disorders.
• Viral Disease:
• A viral disease is an illness caused by a virus, a microscopic agent that requires a living host to replicate.
• Viral infections can affect various parts of the body, such as the respiratory system (e.g., the flu), the digestive system (e.g., gastroenteritis), or the skin (e.g., chickenpox).
• Viruses can sometimes lead to chronic conditions, like HIV/AIDS.
• Fungal Disease:
• A fungal disease is an infection caused by fungi.
• Fungi are microorganisms that can live in the environment or on the skin and mucous membranes.
• When they grow out of control, they can cause diseases like athlete's foot, ringworm, and candidiasis (yeast infections).

The logic followed here is:

Logic: Activity and its category.

Here,

Tennis : Sport → Tennis is an activity that falls under the category of Sport.

Similarly,

Dance : Art → Dance is an activity that falls under the category of Art.

Hence, the correct answer is "Option 3".

The correct answer is Force

Key Points

• Force is not a scalar quantity, but rather a vector quantity.
• Scalar quantities have magnitude but no direction, while vector quantities have both magnitude and direction.
• Scalar quantities
• Distance and speed are scalar quantities because they have magnitude or size, but no defined direction.
• Vector quantities
• Force, velocity, and field strength are vector quantities because they have both magnitude and direction.

The correct answer is the Electoral College

Key Points

• The President of India is elected by an Electoral College.
• The Electoral College for the presidential election in India comprises:
• • Elected Members of Parliament (MPs) from both Houses (Lok Sabha and Rajya Sabha).
• Elected Members of the Legislative Assemblies (MLAs) of all Indian states and Union Territories with legislatures (like Delhi and Puducherry).
• This system is designed to provide a weighted representation from both the central and state governments.

Additional Information

• Direct Election: The President is not directly elected by the people.
• System of Universal Adult Franchise: This system is used to elect Members of Parliament and Members of Legislative Assemblies, not the President.
• Members of the Parliament: While MPs are part of the Electoral College, MLAs are also included, so it’s not limited to Parliament alone.

The correct answer is Pushkar 

Key Points Pushkar Fair:

• Pushkar fair is one of India's or the world's largest cattle (camel) fair.
• Pushkar Fair is also known as Pushkar Camel Fair or locally Kartik Fair.
• It is an annual fair that is also known as Kartik Mela or Pushkar ka Mela.
• It is held in the Pushkar city of Ajmer district of Rajasthan.
• The Pushkar fair is one of the largest camel, horse, and cattle fairs in India.
• Apart from the cattle trade, it is an important pilgrimage for Hindus to Pushkar Lake.
• Cultural events and competitions at this fair include Matka bust, longest moustache, contest, bridal contest, camel race, and others.

Additional Information 

Other important fairs of India:

Given:

5 + 5 × 5 ÷ (5 × 5) × 5

Formula Used:

Order of Operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Calculation:

Start with the parentheses:

5 + 5 × 5 ÷ (5 × 5) × 5

⇒ 5 + 5 × 5 ÷ 25 × 5

Next, handle multiplication and division from left to right:

⇒ 5 + (5 × 5 ÷ 25) × 5

⇒ 5 + (5 × 1/5) × 5

⇒ 5 + 1 × 5

⇒ 5 + 5

Finally, perform the addition:

⇒ 10

The correct answer is option 1.

Given:

K = 8

L = 5

N = 4

T = 28

Formula Used:

T ÷ N × L + K

Calculation:

T ÷ N = 28 ÷ 4

⇒ 7

7 × L = 7 × 5

⇒ 35

35 + K = 35 + 8

⇒ 43

The value of T ÷ N × L + K is 43.

The correct answer is Jawahar Lal Nehru

Key Points

• The second person to join the Individual Satyagraha movement in 1940 was Jawaharlal Nehru.
• The Individual Satyagraha movement was launched by Mahatma Gandhi in 1940 as a peaceful protest against British repression and to assert the right to free speech during World War II.
• Vinoba Bhave was the first Satyagrahi selected by Gandhi to launch this movement.
• Jawaharlal Nehru was chosen as the second Satyagrahi to participate in the movement, and he was subsequently arrested for delivering anti-war speeches, which was part of the protest against British involvement of India in World War II without consulting Indian leaders.

Additional Information

• Subhash Chandra Bose
• Subhash Chandra Bose was a prominent leader in the Indian independence movement, known for his radical and militant approach. Unlike Gandhi's non-violent methods, Bose believed in a more confrontation with British rule.
• Muhammad Ali Jinnah
• Muhammad Ali Jinnah was the leader of the All India Muslim League and a prominent advocate for the creation of Pakistan.
• By the 1940s, Jinnah was focused on advancing the idea of a separate Muslim state and distanced himself from the Indian National Congress’s campaigns.
• Vinoba Bhave
• Vinoba Bhave was the first person selected by Gandhi to initiate the Individual Satyagraha.
• Known for his deep commitment to Gandhi’s principles, Bhave’s selection was significant as he represented the moral and spiritual essence of satyagraha.

The correct answer is Mahayana

Key Points

• The worship of Buddha images became an important tradition in Mahayana Buddhism:
• Mahayana Buddhism is one of the two main branches of Buddhism.
• It emerged around the 1^st century CE after the Fourth Buddhist Council, when Mahayana followers began to worship Buddha images as divine beings.
• The word "Mahayana" means "Great Vehicle" in Sanskrit.
• In Buddhism, the image of Buddha is not an idol that is worshipped for its supernatural powers.
• Instead, the image helps people focus on and remember the Buddha's qualities and accomplishments.
• Many Buddhists keep shrines at home, and remove their shoes before entering the shrine room as a symbol of respect.
• The other main branch of Buddhism is Hinayana, which means "Small Vehicle" in Sanskrit.
• Hinayana adherents follow the Buddha's original teachings and emphasize individual redemption through self-discipline and concentration.

The correct answer is Kathakali

Key Points

• The South Indian classical dance form that literally means "story-play" is Kathakali.
• The word Kathakali comes from the Malayalam words katha, which means "story" or "conversation", and kaḷi, which means "performance" or "play".
• Kathakali originated in Kerala in the 18^th century.
• Kathakali is a combination of dance, drama, music, and ritual.
• It's performed with elaborate makeup and costumes, and actors use hand gestures, facial expressions, and eye movements to convey emotions.
• Kathakali performances often depict episodes from the Mahabharata and Ramayana, or the life of Krishna.
• Kathakali is considered one of the most difficult traditional dance forms.
• Other names: Kathakali is also known as the "Saga of East"

Additional Information

• Bharatanatyam, Kathak, and Mohiniyattam are all classical Indian dance forms:
• Bharatanatyam
• This dance form from Tamil Nadu is based on the ideas of Bharata's Natyashastra.
• It's characterized by strong lines, expressive hand gestures, and storytelling through facial expressions.
• Kathak
• This dance form from Uttar Pradesh is known for its fluid body movements, complex footwork, fast turns, and sudden stillness
• It's still widely practiced in Uttar Pradesh, Rajasthan, Delhi, Madhya Pradesh, and other regions of India.
• Mohiniyattam
• This dance form from Kerala is based on the Hindu myth of Vishnu taking the form of Mohini to distract the demon Bhasmasura

The correct answer is Antrix Corporation Limited

Key Points

• Antrix Corporation Limited (ACL) is the commercial and marketing arm of the Indian Space Research Organisation (ISRO):
• ACL was incorporated in September 1992.
• ACL is headquartered in Bangalore, India.
• ACL is under the administrative control of the Department of Space, which is directly overseen by the Prime Minister of India.
• ACL's services include:
• Supply of hardware and software
• Remote sensing data service
• Transponder lease service
• Launch services
• Mission support services
• Consultancy and training services
• Goals: ACL's goals include:
• Promoting and commercially exploiting space products
• Transferring technologies developed by ISRO
• Facilitating the development of space-related industrial capabilities in India
• Delivering space goods and services to foreign customers worldwide

Additional Information

• Research Corporation Technologies
• This is a private technology investment and management company based in the United States, focused on the advancement of research and technology, primarily in health sciences.
• Founded in 1912, it provides funding for research and early-stage companies developing new technologies.
• Indian National Space Promotion and Authorization Center (IN-SPACe)
• In India, IN-SPACe was established to allow private companies to participate in space research and development. This initiative is part of India’s broader space reforms to expand private sector involvement alongside ISRO (Indian Space Research Organisation).
• Several private players are now participating in space projects, satellite launches, and space technology development under IN-SPACe’s authorization.
• Corporations Related to Aerospace and Space Research
• In the United States, NASA collaborates with companies like SpaceX and Blue Origin.
• In Europe, Arianespace is known for launching satellites for a range of customers around the world.
• Space Corporation Limited and Sky Corporation Limited could imply companies focused on satellite technology, communication networks, or aerospace research.

The correct answer is YOUTHSAT

Key Points

• YOUTHSAT is an experimental satellite of the Indian Space Research Organisation (ISRO):
• YOUTHSAT is a joint Indo-Russian mission that studies the relationship between solar variability and the thermosphere-ionosphere.
• YOUTHSAT carries three payloads, two Indian and one Russian, to study the composition, energetics, and dynamics of the Earth's upper atmosphere.
• YOUTHSAT launched on April 20, 2011, on the PSLV-C16/RESOURCESAT-2 launch vehicle.

Additional Information

• RISAT-1 (Radar Imaging Satellite)
• RISAT-1 is designed for radar imaging to provide all-weather surveillance and earth observation, especially useful for agriculture, forestry, and disaster management.
• It uses synthetic-aperture radar (SAR), which allows it to capture images through cloud cover and in low light, which is advantageous during the monsoon season and natural disasters.
• Launched on April 26, 2012.
• RISAT-1 is one of India’s first radar imaging satellites, enhancing the country's surveillance capabilities and contributing to various fields such as agriculture monitoring and national security.
• 2. RESOURCESAT-1
• RESOURCESAT-1 is dedicated to resource monitoring in India.
• It was designed for advanced imaging to aid in land and water resource management, including agricultural planning, forestry, and environmental monitoring.
• It includes cameras with different resolutions and wavelengths to capture high-quality images of Earth’s surface.
• Launched on October 17, 2003.
• Part of ISRO’s long-standing remote sensing program, RESOURCESAT-1 provided valuable data for sustainable resource management and environmental conservation efforts in India.
• SCATSAT-1 (Scatterometer Satellite)
• SCATSAT-1 was launched primarily for weather forecasting and climate monitoring, with a focus on sea surface wind speed and direction.
• This is crucial for tracking cyclones and providing early warnings for severe weather conditions.
• The satellite uses a scatterometer, an instrument that measures the reflection or scattering effect produced when radar waves hit the ocean surface.
• This helps in predicting weather changes and monitoring wind patterns over oceans.
• Launched on September 26, 2016.
• SCATSAT-1 provides vital data for weather forecasting and cyclone prediction, aiding in disaster preparedness and response.

Important Points

• Other experimental satellites of ISRO include:
• Bhaskara-I: India's first experimental remote sensing satellite, which used TV camera imagery for hydrology and forestry
• Rohini Satellite RS-1: India's first indigenous satellite launch, which measured the in-flight performance of the second experimental launch of SLV-3
• Rohini Technology Payload (RTP): Launched on the SLV-3E1 launch vehicle
• APPLE: Launched on June 19, 1981, on the Ariane-1(V-3) launch vehicle
• INS-1C: Launched on January 12, 2018, on the PSLV-C40/Cartosat-2 Series Satellite Mission

Given: Seven friends P, Q, R, S, T, V and W are sitting around a circular table facing towards centre.

1) R sits to the immediate left of W and third to the left of P.

2. Only two friends sit between P and S.

3. Q sits to the immediate left of V.

After positioning Q and V only one position is left which will be occupied by the only boy left i.e. T.

Thus, T is third to the right of S.

Hence, "Option 2" is the correct answer.

The logic followed here is:

FACE is written as 6135

And,

DEAF is written as 4516

Similarly,

HIGH is written as

Hence, "Option 4" is the correct answer.

The correct answer is Kalpana Chawla

Key Points

• Kalpana Chawla was the first woman of Indian origin to go to space.
• She first flew on the Space Shuttle Columbia in 1997 as a mission specialist and primary robotic arm operator.
• Tragically, she lost her life during her second space mission in 2003 when the Space Shuttle Columbia disintegrated upon re-entering Earth's atmosphere.

Additional Information

• Sunita Williams: An astronaut of Indian descent, Sunita Williams flew to space in 2006 and again in 2012. However, she went to space after Kalpana Chawla and was the second woman of Indian origin to do so.
• Yamuna Krishnan: Yamuna Krishnan is a well-known scientist,
• Shawna Pandya: Shawna Pandya, a Canadian-born Indian-origin scientist and physician, trained with space programs but has not yet gone to space.

Shortcut Trick

Total Distance = Speed × Time = 45 km/h × 4 h = 180 km = 1,80,000 m.

Number of Intervals = Total Distance ÷ Distance between poles = 1,80,000 ÷ 50 = 3600.

Total Poles = Number of Intervals + 1 = 3600 + 1 = 3601.

∴ The correct answer is 3601.

Alternate Method

Given:

Distance between two telegraph poles = 50 m

Speed of the train = 45 km/h

Time taken = 4 h

Calculations:

⇒ Total distance covered = Speed × Time

⇒ Total distance = 45 × 4 = 180 km

⇒ Converting km to meters: 180 × 1000 = 1,80,000 m

⇒ Number of gaps between poles = 1,80,000 ÷ 50

⇒ Number of gaps = 3600

⇒ Since both the starting and ending poles are counted, Total poles = Number of gaps + 1

⇒ Total poles = 3600 + 1 = 3601

∴ The correct answer is 3601.

Additional Information

Linear Arrangement (Pole Counting)

In a straight line, if there are n intervals of equal length, the total number of points (poles/trees) is always n + 1 when both ends are included.

Unit Conversion

To convert Speed from km/h to m/s, multiply by 5/18. To convert Distance from km to m, multiply by 1000.

Relative Speed

If two objects move in the same direction, relative speed is the difference (S₁ − S₂); if in opposite directions, it is the sum (S₁ + S₂).

The correct answer is Tapti 

Key Points

• The Tapti River does not originate from the Western Ghats. Instead, it originates from the Satpura Range in central India.
• Tapti River: The Tapti River, also known as Tapi, originates in the Satpura Range in Madhya Pradesh.
• It flows westward through the states of Maharashtra and Gujarat before emptying into the Arabian Sea.
• It runs almost parallel to the Narmada River.

Additional Information

• Godavari River: The Godavari River, often referred to as the "Dakshina Ganga" or the "Ganges of the South," originates from Trimbakeshwar near Nashik in the state of Maharashtra, which is part of the Western Ghats. It is one of the longest rivers in India, flowing eastward across the Deccan Plateau and emptying into the Bay of Bengal.
• Krishna River: The Krishna River originates in the Western Ghats, specifically near Mahabaleshwar in the state of Maharashtra. It flows eastward across Maharashtra, Karnataka, and Andhra Pradesh, ultimately emptying into the Bay of Bengal.
• Kaveri River: The Kaveri River, also spelled Cauvery, originates at Talakaveri in the Western Ghats located in the Kodagu district of Karnataka. It flows southeast through Karnataka and Tamil Nadu, eventually reaching the Bay of Bengal.

Given:

(a + 1)(1 - a)(1 - a + a²)(1 + a + a²)(1 + a⁶)

Formula used:

(1 + x)(1 - x) = 1 - x2

x³ - y³ = (x - y)(x² + xy + y²)

Calculations:

(a + 1)(1 - a) = 1 - a²

(1 - a + a²)(1 + a + a²) = [(1 + a²)² - (a)²]

Now combining the results:

(a + 1)(1 - a)(1 - a + a2)(1 + a + a2)(1 + a6)

⇒ (1 - a²)[(1 + a2)2 - (a)2](1 + a⁶)

⇒ (1 - a2)[(1 + a2)2 - a2](1 + a6)

⇒ (1 - a2)[1 + a⁴ + 2×a² - a 2](1 + a6)

⇒ (1 - a2)[1 + a⁴ + a2](1 + a6) ------ (i)

Now, Solving (1 - a2)[1 + a4 + a2],

let 1 = x and  a² = y

expression becomes,

(x - y)(x² + y² + xy)

which is equal to x³ - y³

so,

(1 - a2)[1 + a4 + a2] = 1³ - (a²)³ = 1 - a⁶

Now, putting this value in equation (i),

⇒ (1 - a2)[1 + a4 + a2](1 + a6) 

⇒ (1 - a⁶)(1 + a6) = 1 - a¹²

∴ The correct answer is 1 - a¹².

The correct answer is Light-emitting diode

Key Points

• LED stands for Light Emitting Diode.

LED (light-emitting diode):

• The LED (light-emitting diode) is a PN junction device that emits light when a current pass through it in the forward direction, i.e. when LED is forward biased, it emits light.

• In an LED, this energy lies in the visible region of electromagnetic radiation, and the photon released is perceived as light.

• An LED in this way converts electrical energy into light energy.

• In reverse biased mode, it works like a normal diode and does not emit light.

• It is an optical semiconductor device that emits light when voltage is applied means it converts electrical energy into light energy.

• When Light Emitting Diode (LED) is forward biased, the free electrons from the n-side and the holes from the p-side are pushed towards the junction.

• Light-emitting diodes emit either visible light or invisible infrared light when forward biased.

• The LEDs which emit invisible infrared light are used for remote controls.

• LEDs that can emit red, yellow, orange, green, and blue light are available for commercial use.

The correct answer is Calcutta ( Kolkata), Bombay( Mumbai) and Madras( Chennai)

Key Points

• In the late 18^th century, the cities of Calcutta (Kolkata), Bombay (Mumbai), and Madras (Chennai) rose in importance as the Presidency cities of British India:
• These cities became the centres of British power in India.
• They were also the main centres of trade and economic activities for the English East India Company.
• The cities had a different layout from the older Indian towns, and their buildings were influenced by colonial architecture.
• Institutions were established to regulate economic activities and demonstrate British authority.

Given:

Rate of interest (R) = 4% per annum.

Time (T) = 8 years.

Interest = Sum lent - 340

Formula Used:

Simple Interest (SI) = (Principal × Rate × Time) / 100

Calculation:

Let the sum lent be P Rs.

Simple Interest (SI) = $\frac{P × 4 × 8}{100} = \frac{32P}{100} = \frac{8P}{25}$

According to the question:

SI = P - 340

⇒ 8P/25 = P - 340

⇒ 8P = 25P - 8500

⇒ 25P - 8P = 8500

⇒ 17P = 8500

⇒ P = 8500/17

⇒ P = 500

The sum lent is Rs. 500.

The correct answer is 1978

Key Points

• The property right was removed from the list of fundamental rights in India in 1978 when the 44^th Amendment to the Constitution was passed:
• The 44^th Amendment Act of 1978 removed the right to property from the list of fundamental rights.
• The amendment repealed Article 19(1)(f) and Article 31 of the Constitution and replaced Article 31 with Article 300A.
• This made the right to property a legal right, rather than a fundamental right.
• The Morarji Desai government introduced the amendment as part of land reform policies.
• The right to property was a fundamental right in the Indian Constitution from its inception in 1950.

Given:

Total amount lent = Rs. 30,000

Interest rate for part 1 = 10% per annum

Interest rate for part 2 = 8% per annum

Total interest received after 3 years = Rs. 8,280

Formula Used:

Simple Interest = Principal × Rate × Time

Calculation:

Let the amount lent at 10% per annum be Rs. x.

Then, the amount lent at 8% per annum = 30000 - x.

Interest from amount lent at 10% per annum for 3 years = x × 10% × 3

Interest from amount lent at 10% per annum for 3 years = x × 0.1 × 3

Interest from amount lent at 10% per annum for 3 years = 0.3x

Interest from amount lent at 8% per annum for 3 years = (30000 - x) × 8% × 3

Interest from amount lent at 8% per annum for 3 years = (30000 - x) × 0.08 × 3

Interest from amount lent at 8% per annum for 3 years = 0.24(30000 - x)

Given, total interest received = Rs. 8,280

So, 0.3x + 0.24(30000 - x) = 8280

0.3x + 7200 - 0.24x = 8280

0.06x + 7200 = 8280

0.06x = 1080

x = 1080 / 0.06

x = 18000

The amount he lent at 10% per annum is Rs. 18,000.

Given:

x² = y + z

y² = z + x

z² = x + y

Calculation:

x² + x = y + z + x

x (x + 1) = x + y + z

1/(x + 1) = x/(x + y + z)

Similarly,

1/(y + 1) = y/(x + y + z)

1/(z + 1) = z/(x + y + z)

Add all three above equation,

${1\over x+1}+{1\over y+1}+{1\over z+1}$ = x/(x + y + z) + y/(x + y + z) + z/(x + y + z)

⇒ ${1\over x+1}+{1\over y+1}+{1\over z+1}$ = (x + y + z)/(x + y + z) = 1

∴ The value of 1/(x+1) + 1/(y+1) + 1/(z+1) is 1.

Given:

A can complete in 2 days as much of a task as B can complete in 3 days.

B can complete in 4 days as much of the task as C can complete in 5 days.

A alone can complete the task in 22 days.

Formula Used:

Work rate of A, B, and C combined = Work rate of A + Work rate of B + Work rate of C

Time to complete the task = 1 / Work rate of A, B, and C combined

Calculation:

Work rate of A = 1/22

Let the task be x units.

In 2 days, A completes (2/22) × x = (1/11) × x units.

In 3 days, B completes (3/33) × x = (1/11) × x units.

⇒ B's work rate = (1/33)

In 4 days, B completes (4/33) × x units.

In 5 days, C completes (5/55) × x = (1/11) × x units.

⇒ C's work rate = (1/55)

Combined work rate of A, B, and C = (1/22) + (1/33) + (1/55)

⇒ Combined work rate = (165 + 110 + 66) / (22 × 33 × 55)

⇒ Combined work rate = 341 / (22 × 33 × 55)

⇒ Combined work rate = 1 / 10

Time to complete the task = 1 / (1/10)

Time to complete the task = 10 days

The correct answer is option 2.

Given:

X = √(1 + (√3 / 2)) + √(1 - (√3 / 2))

Formula used:

√(a + b) and √(a - b) where b is a fraction

√3 = 1.732 

Calculation:

⇒ 1 + (√3 / 2) = 1 + 0.866 = 1.866

⇒ 1 - (√3 / 2) = 1 - 0.866 = 0.134

⇒ √(1.866) ≈ 1.366

⇒ √(0.134) ≈ 0.366

⇒ X = 1.366 + 0.366 = 1.732 = √3 

∴ The value of X is √3. 

Alternate Method $X=\sqrt{\left(1+{\sqrt3\over2}\right)}+\sqrt{\left(1-{\sqrt3\over2}\right)}$

squaring both sides,

X² = ${\left(1+{\sqrt3\over2}\right)}+{\left(1-{\sqrt3\over2}\right)} + 2× \sqrt{\left(1+{\sqrt3\over2}\right)}× \sqrt{\left(1-{\sqrt3\over2}\right)}$ 

⇒ X² = 2 + 2 × $\sqrt{\left(1+{\sqrt3\over2}\right)\left(1-{\sqrt3\over2}\right)}$

⇒ X² = 2 + 2× $\sqrt{ \left(1^2-({\sqrt3\over2})^2\right)}$

⇒ X2 = 2 + 2×$\sqrt{ \left(1-\frac{3}{4}\right)}$

⇒ X2 = 2 + 2×$\sqrt{ \left(\frac{1}{4}\right)}$

⇒ X2 = 2 + 2 × 1/2

⇒ X2 = 2 + 1

⇒ X2 = 3

⇒ X = $\sqrt{3}$

∴ The correct answer is option 4.

The logic followed here is:

Logic: (1^st number)² = 2^nd number, (2^nd number)² = 3^rd number.

Now,

For (9, 81, 6561):

⇒ (9)² = 81 and (81)² = 6561.

Similarly, for (2, 4, 16):

⇒ (2)² = 4 and (4)2 = 16.

Hence, the correct answer is **"**Option 3".

The correct answer is Kalidasa

Key Points

• Kalidasa was a renowned classical Sanskrit poet and playwright in ancient India, whose works are celebrated for their literary excellence, vivid imagery, and emotional depth.
• He is often compared to William Shakespeare because, like Shakespeare, he made significant contributions to literature and created timeless works that depict human emotions and nature with great sensitivity.
• Kalidasa's famous works include "Shakuntala" (Abhijnanashakuntalam), "Meghaduta" (The Cloud Messenger), and "Raghuvamsha"

Additional Information 

• Panini: An ancient Sanskrit philologist and grammarian, known for his work on Sanskrit grammar, particularly his text "Ashtadhyayi".
• Kautilya (Chanakya): An ancient Indian philosopher, economist, and advisor to Emperor Chandragupta Maurya, known for his treatise "Arthashastra" on statecraft and military strategy.
• Vishnu Sharma: The author traditionally attributed to the Panchatantra, a collection of animal fables,

Given:

Service time before overhauling = 5/6 hours every 90 days

Service time after overhauling = 5/6 hours every 120 days

Formula Used:

Fraction of service time saved = (Service time before overhauling - Service time after overhauling) / Service time before overhauling

Calculation:

Service time before overhauling in a year (360 days) = (5/6) × (360/90)

Service time before overhauling in a year = (5/6) × 4

Service time before overhauling in a year = 20/6

Service time before overhauling in a year = 10/3 hours

Service time after overhauling in a year (360 days) = (5/6) × (360/120)

Service time after overhauling in a year = (5/6) × 3

Service time after overhauling in a year = 15/6

Service time after overhauling in a year = 5/2 hours

Fraction of service time saved = ((10/3) - (5/2)) / (10/3)

Fraction of service time saved = ((20/6) - (15/6)) / (10/3)

Fraction of service time saved = (5/6) / (10/3)

Fraction of service time saved = (5/6) × (3/10)

Fraction of service time saved = 15/60

Fraction of service time saved = 1/4

The fraction of the pre-overhauling service time saved is 1/4.

The correct answer is 2010

Key Points

• ​The National Green Tribunal Act was passed by the Indian parliament in 2010.
• The NGT was established on October 18, 2010.
• The NGT was established to: 
• Resolve environmental disputes in a timely manner
• Enforce legal rights related to the environment
• Provide relief and compensation for damages to people and property
• The NGT Act amends the: 
• Water (Prevention and Control of Pollution) Act, 1974
• Water (Prevention and Control of Pollution) Cess Act, 1977
• Forest (Conservation) Act, 1980

Given: Seven boys B1, B2, B3, B4, B5, B6, and B7 are sitting in a row facing towards south.

1) B2 sits at one of the extreme ends and is the neighbour of B4.

2) B3 is to the immediate right of B4 but is not the neighbour of B5.

3) Only two boys sit between B1 and B5.

4) B7 is not the neighbour of B1.

After positioning B1 only one position is left which will be occupied by the only person left i.e. B6.

Thus, according to the final arrangement, B6 is immediate right of B1.

Hence, "Option 2" is the correct answer.

According to the given Venn diagram:

The shaded region represents the engineers who live in urban areas and are in government jobs.

So, the engineers who live in urban areas and are in government jobs = 'C'

Hence, the correct answer is "Option 1".

The correct answer is Home Page

Key Points

• The main page of a website is called the home page. It's the first page that a visitor sees when they access a website.
• The term "home page" can also refer to the start page that appears in a web browser when it first opens.
• Some other things to know about home pages:
• They are usually located at the root of the website's domain or subdomain.
• They can be used to attract users.
• They can include welcome messages and copy blocks that explain the benefits of the website or brand.
• In web marketing, it's recommended to design the home page in a way that's consistent with the company or product branding

Given:

Numbers to evaluate: 1296, 836, 1156, 576

Formula Used:

Identify if the number is a perfect square.

Calculation:

1296 = 36²

836 is not a perfect square.

1156 = 34²

576 = 24²

Conclusion:

836 is not a perfect square, while the others are perfect squares.

The correct answer is option 2.

The correct answer is Godavari

Key Points

• The Hemavati is a tributary of the Kaveri River
• It originates from the Western Ghats in the Chikmagalur district of Karnataka and joins the Kaveri River near the town of Krishna Raja Sagara.
• The Hemavati is one of the major tributaries that contribute to the flow of the Kaveri, which is an important river in southern India, flowing through Karnataka and Tamil Nadu.

Additional Information

• Krishna: The Krishna River is one of the major rivers in India, flowing through Maharashtra, Karnataka, Telangana, and Andhra Pradesh.
• Mahanadi: The Mahanadi River flows through the states of Chhattisgarh and Odisha.it is part of the Kaveri River system.
• Godavari: The Godavari River is another major river of India, flowing primarily through Maharashtra, Telangana, Andhra Pradesh, and Odisha.

Given:

Data: 25, 18, 20, 16, 8, 10, 15, 20, 13, 30

Formula Used:

Median = Middle value of the sorted data

If the number of data points (n) is odd, Median = (n+1)/2^th value

If the number of data points (n) is even, Median = Average of (n/2)^th and (n/2 + 1)^th values

Calculation:

Sorted data: 8, 10, 13, 15, 16, 18, 20, 20, 25, 30

Number of data points (n) = 10 (even)

Median = Average of (10/2)^th and (10/2 + 1)^th values

⇒ Median = (16 + 18) / 2

⇒ Median = 34 / 2

⇒ Median = 17

The correct answer is option 4.

The correct answer is 1951

Key Points

• The First Five-Year Plan in India was presented in 1951 and it was the first step toward planned economic development in the country.
• The plan focused on agriculture and irrigation, with the goal of boosting food production, particularly after India’s independence when the economy was facing various challenges like poverty and food shortages.
• It was officially launched on April 1, 1951.
• Subsequent plans followed the model of five-year periods, with each plan focusing on different sectors of the economy to drive growth and development.

Given:

The data is arranged in ascending order: 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

The median of the data is 63.

Formula Used:

For an even number of data points, the median is the average of the two middle numbers.

Calculation:

Number of data points = 10

Middle numbers are the 5^th and 6^th elements.

Median = (5^th element + 6^th element) / 2

Given median = 63

5^th element = x

6^th element = x + 2

63 = (x + (x + 2)) / 2

⇒ 63 = (2x + 2) / 2

⇒ 63 × 2 = 2x + 2

⇒ 126 = 2x + 2

⇒ 126 - 2 = 2x

⇒ 124 = 2x

⇒ x = 124 / 2

⇒ x = 62

The correct answer is option 1.

The correct answer is 1949

Key Points

• The first nationalization of banks in India took place in 1949 when the Reserve Bank of India (RBI) was nationalized.
• The RBI was made the central bank of the country, taking over the responsibility for regulating and controlling the monetary system, which was previously under private ownership.
• However, the major nationalization of commercial banks occurred later, in 1969, when the Government of India nationalized 14 major commercial banks to increase control over the banking sector and to ensure that credit was provided to key sectors of the economy, such as agriculture and industry.
• The aim was to direct the banks to contribute to the nation’s development and reduce dependence on foreign banks.
• So, while 1949 marks the nationalization of the RBI, 1969 is often cited as the year of the first significant nationalization of commercial banks.

The correct answer is 150 million km

Key Points

• The average distance between the Earth and the Sun is about 93 million miles (150 million kilometres).
• This distance is also known as one astronomical unit (AU).
• The Earth's orbit around the Sun is elliptical, not a perfect circle, so the distance between the two bodies changes throughout the year:
• Perihelion
• The point when the Earth is closest to the Sun, which occurs during winter in the northern hemisphere.
• At this time, the distance is about 91.4 million miles (147.1 million kilometers).
• Aphelion
• The point when the Earth is farthest from the Sun, which occurs about six months after perihelion.
• At this time, the distance is about 94.5 million miles (152.1 million kilometers).
• Light from the Sun travels at a speed of 186,000 miles (300,000 kilometers) per second, so it takes about 8 minutes to reach Earth.

The diagram that best represents the relationship between Parrot, Bird, and Tiger is shown below :

Parrot is a type of bird.

Birds and tiger are two different sets.

Thus, figure 'd' best represents the relationship between Parrot, Bird, and Tiger.

Hence, "Option 2" is the correct answer.

The correct answer is Bangar

Key Points

• Old alluvial soil is known as Bhangar.
• Bhangar is a system of older alluvium that is deposited away from flood plains and forms terraces along river beds that are higher than the floodplain.
• Bhangar is not very fertile and is not suitable for agriculture.
• In contrast, newer alluvial soil is called Khadar.
• Khadar is more fertile than Bhangar and is used extensively for agriculture.
• Khadar is deposited by rivers in their flood plains and is replenished every year. Khadar is also known as Nali or Naili.
• Alluvial soil is made up of clay, gravel, sand, silt, boulders, and other particles, along with organic matter that makes the soil fertile.
• Alluvial soil differs in texture because it is a transported soil deposited by rivers.

The logic followed here is:​

Hence, "Option 2" is the correct answer.

The correct answer is Printer

Key Points

• A printer is an output device in a computer.
• An output device is a piece of hardware that converts digital data into a human-readable form, such as text, graphics, audio, or video.
• Other examples of output devices include:
• Monitors, Speakers, Headphones, Projectors, GPS devices, Optical mark readers, and Braille readers.

Additional Information

• A scanner, mouse, and webcam are all input devices that allow users to interact with a computer and provide it with data:
• Scanner: Scans documents and pictures and converts them into digital images that can be saved to a computer
• Mouse: A primary input device that controls the pointer on the computer screen
• Webcam: Captures a video image of the scene in front of it and sends it to the computer for processing
• Other input devices include:
• Keyboard, Microphone, Light pen, Barcode reader, Touch screen, and Joystick.

Given:

The incomes of A and B are in the ratio 3 ∶ 2.

The expenditures of A and B are in the ratio 5 ∶ 3.

Each saves Rs. 2,000.

Formula Used:

Income - Expenditure = Savings

Calculation:

Let the incomes of A and B be 3x and 2x respectively.

Let the expenditures of A and B be 5y and 3y respectively.

For A: 3x - 5y = 2,000

For B: 2x - 3y = 2,000

We have the system of equations:

3x - 5y = 2,000         (1)

2x - 3y = 2,000         (2)

To eliminate y, multiply equation (2) by 5 and equation (1) by 3:

5(2x - 3y) = 5(2,000)

10x - 15y = 10,000         (3)

3(3x - 5y) = 3(2,000)

9x - 15y = 6,000         (4)

Subtract equation (4) from equation (3):

(10x - 15y) - (9x - 15y) = 10,000 - 6,000

⇒ 10x - 9x = 4,000

⇒ x = 4,000

Substitute x = 4,000 in equation (2):

2(4,000) - 3y = 2,000

⇒ 8,000 - 3y = 2,000

⇒ -3y = 2,000 - 8,000

⇒ -3y = -6,000

⇒ y = 2,000

The incomes of A and B are 3x = 3(4,000) = 12,000 and 2x = 2(4,000) = 8,000 respectively.

The difference between their incomes is:

12,000 - 8,000 = 4,000

The difference between their incomes is Rs. 4,000.

Given:

We need to find the least number which is a perfect square and contains 3675 as its factor.

Formula Used:

If a number is a perfect square, all the exponents in its prime factorization must be even.

Calculation:

Prime factorization of 3675:

3675 = 3 × 5² × 7²

Therefore, 3675 = 3 × 5² × 7²

To make it a perfect square, we need to multiply it by the necessary primes to make all exponents even:

We need one more 3,

Required number = 3675 × 3

Required number = 11025

Checking if 11025 is a perfect square:

Square root of 11025 = 105

Therefore, the least number which is a perfect square and contains 3675 as its factor is:

11025

The correct answer is option 2.

The  correct answer is 48^th

Key Points

• India ranked 48^th in the 2020 Global Innovation Index (GII):
• The GII is a yearly ranking of countries based on their innovation capacity and success.
• The World Intellectual Property Organization (WIPO), Cornell University, and INSEAD jointly developed the GII.
• The 2020 GII ranked 131 economies based on 80 indicators across 7 pillars.
• India's performance
• India's 2020 ranking was its first time in the top 50. It also ranked third among lower-middle-income economies.
• India improved the most in the following pillars: 
• Institutions (61^st)
• Business sophistication (55^th)
• Creative outputs (64^th)
• Other findings
• The 2020 GII also found that:
• Innovation is gradually shifting from the West to the East.
• China, India, the Philippines, and Vietnam have made the most progress on the index in recent years.
• India ranked in the top 15 for indicators such as Information and Communication Technology (ICT) services exports and Government online services.

Given:

The broken upper part of the tree = 10 m.

The distance from the foot of the tree to the point where the upper part touches the ground = 6 m.

Formula Used:

Using the Pythagorean theorem for the right triangle formed:

$a^2 + b^2 = c^2$

Where:

a = height of the tree from the break point to the ground.

b = distance from the foot of the tree to the point where the upper part touches the ground.

c = length of the broken upper part of the tree.

Calculation:

Let the height of the tree from the break point to the ground be h meters.

$h^2 + 6^2 = 10^2$

⇒ $h^2 + 36 = 100$

⇒ $h^2 = 100 - 36$

⇒ $h^2 = 64$

⇒ $h = \sqrt{64}$

⇒ $h = 8$ meters.

The total height of the tree = height from the foot to the break point + length of the broken part.

Total height = 8 + 10 = 18 meters.

The height of the tree is 18 meters.

The logic followed here is:

Hence, "Option 1" is the correct answer.

Given:

A reduction of 10% in the price of mangoes enables a person to buy 10 mangoes more for Rs. 2250.

Formula Used:

Let the original price per mango be Rs. x .

Price after reduction = x - 0.1x = 0.9x

Number of mangoes bought originally = 2250 / x

Number of mangoes bought after reduction = 2250 / 0.9x

Difference in the number of mangoes bought = 10

Calculation:

⇒ (2250 / 0.9x ) - (2250 / x ) = 10

⇒ 2250 × (1 / 0.9x ) - 2250 × (1 / x ) = 10

⇒ 2250 × (1 - 0.9) / 0.9x = 10

⇒ 2250 × 0.1 / 0.9x = 10

⇒ 225 / 0.9x = 10

⇒ 225 = 9x

⇒ x = 225 / 9

⇒ x = 25

Price per dozen after reduction:

Price per mango after reduction = 0.9 × 25 = 22.5

Price per dozen after reduction = 22.5 × 12 = 270

The price per dozen after reduction is Rs. 270.

Given:

Decimal representation = 0.666...

Formula Used:

Let x be the repeating decimal, then multiply by a power of 10 to shift the decimal point.

Calculation:

Let x = 0.666...

Multiply by 10:

⇒ 10x = 6.666...

Subtract the original x from this equation:

⇒ 10x - x = 6.666... - 0.666...

⇒ 9x = 6

Solving for x :

⇒ x = 6 / 9

⇒ x = 2 / 3

The fraction form of 0.666... is 2/3.

The logic followed here is:

 

Jupiter, Saturn, Venus all are Planets,

Whereas,

Moon is a Natural Satellite.

Hence, the correct answer is "Moon".

Given:

Rate at which rubber bands are sold = 32 a rupee

Loss percentage = 40%

Desired gain percentage = 20%

Formula Used:

Cost Price (CP) = Selling Price (SP) / (1 - Loss%)

New Selling Price (SP') = CP × (1 + Gain%)

Number of rubber bands for a rupee = Total rubber bands / SP'

Calculation:

Given SP for 32 rubber bands = 1 rupee

Loss = 40%

⇒ CP = SP / (1 - Loss%)

⇒ CP = 1 / (1 - 0.4)

⇒ CP = 1 / 0.6

⇒ CP = 5/3 rupees

Desired gain = 20%

⇒ New SP' = CP × (1 + Gain%)

⇒ New SP' = (5/3) × (1 + 0.2)

⇒ New SP' = (5/3) × 1.2

⇒ New SP' = 2 rupees

Number of rubber bands for 1 rupee = 32 / New SP'

⇒ Number of rubber bands for 1 rupee = 32 / 2

⇒ Number of rubber bands for 1 rupee = 16

The correct answer is option 1: 16 rubber bands per rupee.

The correct answer is 11^th February 

Key Points

• The United Nations International Day of Women and Girls in Science is celebrated annually on February 11
• The day promotes gender equality in science and technology by: 
• Encouraging women and girls to participate fully and equally in science
• Raising awareness of the challenges women face in STEM fields
• Advocating for more opportunities and support for women in STEM
• UNESCO and UN Women work with other institutions and civil society partners to implement the day

Additional Information

• 15^th February: This date is observed as International Childhood Cancer Day, which raises awareness and promotes efforts to support children and adolescents with cancer, survivors, and their families.
• 15^th January: This day is celebrated as Indian Army Day in India to honor the bravery and sacrifice of the Indian Army personnel. It marks the day in 1949 when General K.M. Cariappa took command of the Indian Army from the British.
• 29^th January: This day is observed as World Leprosy Day (on the last Sunday of January, though it sometimes falls on 29^th) to increase public awareness about leprosy, eliminate stigma, and support those affected by the disease.

The correct answer is Green Book

Key Points

• Green Book won the Best Picture award at the 91^st Academy Awards in 2019: 
• The movie about a white chauffeur and his Black client in the segregated United States also won Best Supporting Actor for Mahershala Ali and Best Original Screenplay.
• Green Book overcame mixed reviews and awards-season setbacks to win the top prize.
• Other winners at the 91^st Academy Awards included:
• Bohemian Rhapsody: Won the most awards of the night, with four
• Black Panther: Won three awards
• Roma: Won three awards
• Regina King: Won Supporting Actress for her role in If Beale Street Could Talk
• Free Solo: Won Best Documentary Feature

The correct answer is Gravitational force

Key Points

• Gravitational force is the weakest of the four fundamental forces of nature:
• Gravitational force:
• The weakest force, but it works across infinite distances and is responsible for the universe's structure.
• It's always attractive in nature.
• Gravity is weaker on a smaller scale, like when you walk on Earth, but it's stronger on a larger scale, like when the Sun holds the planets in alignment.
• Electromagnetic force: A blend of electrical and magnetic forces that operates between electrically charged particles.
• It's stronger than gravitational force because it deals with microscopic particles like electrons and protons.
• Nuclear force: The strongest force.

Additional Information

• Electric force is a type of electromagnetic force, one of the four fundamental forces of nature: 
• Electric force: A type of electromagnetic force that exists between charged particles
• Nuclear force: There are two types of nuclear force: strong and weak
• Strong nuclear force: Holds together nuclei
• Weak nuclear force: Responsible for radioactive decay
• Buoyant force: The force that acts on an object immersed in a liquid or fluid

The correct answer is 14^th Century

Key Points

• The Vijayanagara Empire was founded in the 14^th century, in 1336:
• Brothers Harihara and Bukka Raya founded the empire.
• The empire was based in the Deccan region of peninsular and southern India.
• The empire succeeded the prosperous Hindu kingdoms of the Hoysalas, the Kakatiyas, and the Yadavas.
• The empire lasted for more than two centuries as the dominant power in south India.
• The empire's centre was Hampi, which was originally called Hastinavati.
• The empire included people who spoke different languages and followed different religious traditions

Given:

x = a(b - c)

y = b(c - a)

z = c(a - b)

Formula used:

If a + b + c = 0

Than, a³ + b³ + c³ = 3abc

Calculation:

Step 1: Simplify each term:

(x/a) = a(b - c)/a = (b - c)

(y/b) = b(c - a)/b = (c - a)

(z/c) = c(a - b)/c = (a - b)

Adding all three equations,

(x/a) + (x/b) + (x/c) = 0

Using the formula,

If a + b + c = 0

Than, a3 + b3 + c3 = 3abc

$({x\over a})^3+({y\over b})^3+({z\over c})^3$ = $3\frac{xyz}{abc}$

∴ The correct answer is option 3.

The correct answer is Kalpakkam

Key Points

• India's Prototype Fast Breeder Reactor (PFBR) is located at Kalpakkam in Tamil Nadu.
• This reactor is part of India’s nuclear power program and is managed by the Indira Gandhi Centre for Atomic Research (IGCAR).
• The PFBR is designed to use plutonium-uranium mixed oxide as fuel and aims to generate more fuel than it consumes, a process called "breeding."
• This technology is part of India's goal to achieve energy security and self-sufficiency in nuclear fuel

Additional Information

• Kudankulam: This location in Tamil Nadu is home to a nuclear power plant built in collaboration with Russia, known for its VVER-type reactors
• Tarapur: Situated in Maharashtra, Tarapur houses India's first nuclear power station but is not a site for fast breeder reactors.
• Kaiga: Located in Karnataka, Kaiga has pressurized heavy water reactors (PHWRs) but does not host a fast breeder reactor.

The correct answer is  Food grains

Key Points

• The buffer stock created by the Indian government is a stock of food grains, such as wheat and rice:
• The government procures food grains from farmers in states with surplus production through the Food Corporation of India (FCI).
• The grains are then stored in granaries.
• The government distributes the buffer stock to different parts of the country through the Public Distribution System.
• The government uses the buffer stock to: 
• Distribute food grains to poorer sections of society at a lower price than the market price
• Solve food shortages during adverse weather conditions or calamities

Additional Information

• Woof: This is commonly the sound made by a dog, an onomatopoeic word that imitates the barking sound.
• It can also mean the woven threads that run horizontally (weft) in fabric-making, crossing the warp (vertical threads) to form cloth.

Given:

Curved surface area of a cylindrical pillar = 66 m²

Volume of the cylindrical pillar = 231 m³

π  = 22/7

Formula Used:

Curved Surface Area (CSA) of a cylinder = 2πrh

Volume (V) of a cylinder = πr²h

Calculation:

From CSA, 2πrh = 66

⇒ 2 × 22/7 × r × h = 66

⇒ 44rh = 66 × 7

⇒ 44rh = 462

⇒ rh = 462/44

⇒ rh = 10.5

From Volume, πr²h = 231

⇒ 22/7 × r² × h = 231

⇒ 22r²h/7 = 231

⇒ 22r²h = 231 × 7

⇒ 22r²h = 1617

⇒ r²h = 1617/22

⇒ r²h = 73.5

We have rh = 10.5

⇒ r × 10.5 = 73.5

⇒ r = 73.5/10.5

⇒ r = 7 m

The correct answer is option 1.

Given:

Distance = 300 km

Increased speed = original speed + 5 km/h

Time difference = 2 hours

Formula Used:

Distance = Speed × Time

Calculation:

Let the original speed be x km/h.

Time taken at original speed = 300 / x

Time taken at increased speed = 300 / (x + 5)

Given that the time difference is 2 hours, we have:

$\frac{300}{x} - \frac{300}{x+5} = 2$

⇒ $\frac{300(x + 5) - 300x}{x(x + 5)} = 2$

⇒ $\frac{300x + 1500 - 300x}{x(x + 5)} = 2$

⇒ $\frac{1500}{x(x + 5)} = 2$

⇒ $1500 = 2x(x + 5)$

⇒ 1500 = 2x² + 10x

⇒ 2x² + 10x - 1500 = 0

⇒ x² + 5x - 750 = 0

Solving the quadratic equation:

$x = \frac{-b \pm \sqrt{b2 - 4ac}}{2a}$

Where a = 1, b = 5, c = -750

$x = \frac{-5 \pm \sqrt{52 - 4(1)(-750)}}{2(1)}$

$x = \frac{-5 \pm \sqrt{25 + 3000}}{2}$

$x = \frac{-5 \pm \sqrt{3025}}{2}$

$x = \frac{-5 \pm 55}{2}$

Taking the positive value:

$x = \frac{50}{2} = 25$

The original speed of the car is 25 km/h.

Given:

If P is a prime number and P divides Q²

Formula Used:

If a prime number P divides Q², then P divides Q.

Calculation:

Given P | Q²

Since P is a prime number:

⇒ P | Q

We need to determine which option P will NOT necessarily divide:

1. 3Q: P | Q ⇒ P | 3Q (True)

2. Q + 1: P | Q but P does not necessarily divide Q + 1 (False)

3. Q: P | Q (True)

4. 2Q²: P | Q² ⇒ P | 2Q² (True)

The correct answer is option 2.

The correct answer is Concurrent List

Key Points

• Marriage is a subject of the concurrent list in the Indian Constitution:
• List: Concurrent
• Subjects: Marriage, divorce, education, forests, trade unions, adoption, succession
• The concurrent list includes subjects that are of common interest to both the Union and the States.
• Both the Central and state governments can make laws on these subjects.
• However, the law made by the state government must be in conformity with the law made by the central government on the same subject.
• The Indian Constitution's 7^th Schedule divides powers between the Union and State governments through three lists: Union List, State List, and Concurrent List.

Additional Information

• The Union List, State List, and Concurrent List are three lists in the Seventh Schedule of the Constitution of India that divide the powers between the Union and State governments:
• Union List
• Subjects of national importance that only the Central Government can legislate on.
• Examples include defense, foreign affairs, atomic energy, and currency.
• State List
• Subjects of local and state interest that State Governments can legislate on.
• Examples include police, public health, agriculture, and local government.
• Concurrent List
• Subjects that both Parliament and State Legislatures can legislate on, but central laws take precedence in case of conflict.
• Examples include education, marriage and divorce, and bankruptcy and insolvency.
• The Central Government also has residual powers, which are subjects that came into existence after the constitution was written.
• Examples of residuary subjects include computer software, information technology, and space technology.

The correct answer is Concave

Key Points

• A concave mirror is used for shaving because it produces a magnified and erect image of the face, which makes it easier to shave:
• How it works
• When the face is placed close to the mirror, within its focus, the mirror produces a magnified and erect image
• Image type
• Produces images that are both genuine and reversed
• Other uses
• Also used for applying makeup
• Concave mirrors are curved, and as light hits the upper and lower portions of the mirror, the image is focused at a central point.
• The image changes depending on the distance between the item and the mirror.

Additional Information

• Opaque:
• Opaque materials do not allow light to pass through them.
• They block light completely, meaning you cannot see through opaque objects.
• Examples include wood, metal, and stone. In contrast to transparent or translucent materials, opaque materials prevent visibility through them.
• Transparent:
• Transparent materials allow light to pass through them completely, making objects behind them clearly visible.
• Glass, water, and clear plastic are examples of transparent materials.
• These materials enable us to see through them without distortion, as they allow most of the light to transmit.
• Convex Mirror:
• A convex mirror is a mirror that is curved outward, like the exterior of a sphere.
• Convex mirrors diverge light rays that strike them, meaning they spread out the reflected light.
• This property makes them useful in applications like car side mirrors and security mirrors, where a wide field of view is needed.
• Convex mirrors always produce virtual, upright, and diminished images.

The correct answer is Vision 2019-2021

Key Points

• The Reserve Bank of India's (RBI) vision document titled "Payment and Settlement Systems in India" is Vision 2019 - 2021.
• The document's core theme is "Empowering Exceptional (E)payment Experience".
• The vision aims to: 
• Make e-payment options safe, secure, convenient, quick, and affordable for all Indians
• Achieve a "highly digital" and "cash-lite" society
• Increase digital transactions fourfold in two years
• Reduce paper-based clearing as a percentage of retail payments
• The document also focuses on: innovation, cybersecurity, financial inclusion, customer protection, and competition.
• The RBI's Payments Vision 2025 builds on the initiatives of Vision 2019 - 2021.
• It emphasizes five anchor goalposts: integrity, inclusion, innovation, institutionalization, and internationalization