Kolkata Police SI (Prelims) 28 Jan 2024 Official Paper (Previous Year Paper)

The correct answer is 1942.

Key Points

• The Cripps Mission came to India in 1942.
• The mission was led by Sir Stafford Cripps, a member of the British Cabinet. 
• It aimed to secure Indian cooperation and support for the British war efforts during World War II.
• The mission proposed Indian dominion status after the war, which was rejected by Indian leaders.
• The failure of the Cripps Mission led to the intensification of the Indian independence movement, including the Quit India Movement.

Additional Information

• The Cripps Mission was part of a series of attempts by the British government to secure Indian support during World War II.
• Despite its failure, it marked a significant moment in the Indian struggle for independence.
• The proposals included the establishment of an Indian Union with full Dominion status, which was to be created after the war.
• Provinces and princely states were given the option to opt-out of the Union, which was a contentious point for Indian leaders.

Given:

Principal (P) = 1,000

Rate (R) = 10%

Time (T) = 3 years

Formula Used:

1. Simple Interest (SI) = P × R × T / 100
2. Compound Interest (CI) = P × (1 + R/100)^T - P
3. Difference = CI - SI

Calculation:

Simple Interest:

SI = 1,000 × 10 × 3 / 100

⇒ SI = 300

Compound Interest:

CI = 1,000 × (1 + 10/100)³ - 1,000

CI = 1,000 × (1 + 0.1)³ - 1,000

CI = 1,000 × (1.1)³ - 1,000

CI = 1,000 × 1.331 - 1,000

CI = 1,331 - 1,000

⇒ CI = 331

Difference:

Difference = CI - SI

Difference = 331 - 300

⇒ Difference = 31

The difference in interest yielded in 10% compound rate and simple rate on a sum of 1,000 for 3 years is 31.

The correct answer is Tropical Evergreen.

Key Points

• The North-Eastern states of India are predominantly covered with Tropical Evergreen forests.
• Tropical Evergreen forests are characterized by high rainfall and a warm climate throughout the year. 
• These forests remain green all year round and are known for their dense canopy.
• Some key features of Tropical Evergreen forests include:
• High biodiversity.
• Multiple layers of vegetation, including tall trees, shrubs, and undergrowth.
• Presence of valuable timber species like mahogany, ebony, and rosewood.
• These forests play a crucial role in maintaining ecological balance and supporting diverse wildlife.

Additional Information

• Other types of forests in India include:
• Tropical Deciduous forests: Found in regions with seasonal rainfall, these forests shed their leaves in the dry season.
• Coastal forests: Found along the coastal regions, these include mangroves and other salt-tolerant species.
• Tropical Desert forests: Found in arid regions with sparse vegetation, mainly consisting of thorny bushes and cacti.

The correct answer is Frequency.

Key Points

• Hertz (Hz) is a unit of frequency.
• Frequency refers to the number of cycles per second of a periodic wave.
• One Hertz is equivalent to one cycle per second.
• It is used to measure phenomena such as sound waves, radio waves, and electrical signals.

Additional Information

• Density is a measure of mass per unit volume.
• Wavelength is the distance between successive crests of a wave.
• Energy is the capacity to do work or produce heat.

The correct answer is Antimony.

Key Points

• Antimony is a chemical element with the symbol Sb and atomic number 51.
• Unlike most substances, antimony expands upon cooling. This is a key characteristic that sets it apart from other elements.
• When antimony solidifies from its liquid state, its volume decreases, which is contrary to the behavior of most other metals.

Additional Information

• Most substances expand when they transition from a liquid to a solid state due to the decrease in density.
• For example, ice, the solid form of water, occupies more volume than liquid water, which is why ice floats.
• Similarly, metals like aluminum and bismuth also expand upon solidification, increasing their volume.

Preparing the family tree using the following symbols,

Let's check each option,

1) W × R × F

2) W + R - F + T 

3) W ÷ R × F

4) W + R × F - T

 ⇒ Here, F is daughter of W.

Hence, the correct answer is "W + R × F - T".

The correct answer is Flagellar.

Key Points

• Locomotion of Euglena is done by flagellar.
• Flagella are long, whip-like structures that act as a propeller to move the organism.
• Euglena uses its flagellum to move through water.
• The flagellum is attached at the anterior end of the organism, and it rotates to propel Euglena forward.

Additional Information

• Cilia are short, hair-like structures that can move fluid or cells over their surface. They are not used by Euglena for locomotion.
• Pseudopodia are temporary projections of eukaryotic cell membranes or unicellular protists. They are used by amoebae for locomotion and feeding, not by Euglena.
• Fins are typically associated with aquatic animals like fish and are not relevant to Euglena.

Given:

Total sum = ₹ 2000

Interest from first part = 10%

Interest from second part = 20%

Total interest received = ₹ 320

Formula Used:

Total Interest = Interest from first part + Interest from second part

Calculation:

Let the first part be ₹ x.

Then the second part = ₹ (2000 - x).

Interest from first part = x × 10% = 0.1x

Interest from second part = (2000 - x) × 20% = 0.2(2000 - x)

Total Interest = 0.1x + 0.2(2000 - x)

Total Interest = 0.1x + 400 - 0.2x

Total Interest = 400 - 0.1x

Given Total Interest = ₹ 320

⇒ 400 - 0.1x = 320

⇒ 0.1x = 80

⇒ x = 800

The first part of the sum is ₹ 800.

The least possible venn diagram is shown below,

Conclusions:

I. Some trucks are pens → True (All pens are chairs, and all chairs are trucks implies that some trucks are pens).

II. Some trucks are chairs → True (All chairs are trucks implies that some trucks are definitely chairs).

III. Some trees are pens → False (All pens are chairs, all chairs are trucks and all trees are trucks implies that some trees can be pens. This is possible but not definite).

IV. Some trees are chairs → False (All chairs are trucks and all trees are trucks implies that some trees can be chairs. This is possible but not definite).

Hence, the correct answer is "Only I and II follow".

The correct answer is Judicial System.

Key Points

• The Ilbert Bill was introduced in 1883 during the tenure of Viceroy Lord Ripon.
• The bill was aimed at allowing Indian judges to preside over cases involving British citizens in India.
• It was a significant step towards judicial equality and was part of the broader reforms under Lord Ripon's administration.
• The bill faced strong opposition from the British community in India, leading to its modification.

Additional Information

• The opposition to the Ilbert Bill highlighted the racial tensions and the colonial mindset prevalent during British rule in India.
• The controversy eventually led to the bill being passed in a diluted form, allowing Indian judges to try European British subjects only in the presence of a jury with at least half of its members being Europeans.

The correct answer is 3^rd.

Key Points

• When lifting anything with the help of the hand, the hand acts as a third-class lever.
• In a third-class lever, the effort is applied between the fulcrum and the load.
• This type of lever is used to gain speed rather than force.
• Examples of third-class levers include human arms, tweezers, and fishing rods.
• In the context of lifting with the hand, the elbow joint acts as the fulcrum, the hand provides the effort, and the load is the object being lifted.

Additional Information

• First-class lever: The fulcrum is located between the effort and the load (e.g., seesaw).
• Second-class lever: The load is located between the fulcrum and the effort (e.g., wheelbarrow).
• Third-class lever: The effort is applied between the fulcrum and the load (e.g., human arm).

Let's count the number of triangles in the given figure,

Hence, the correct answer is "16".

The correct answer is Odisha.

Key Points

• Daringbari is a popular tourist spot located in the state of Odisha.
• It is often referred to as the "Kashmir of Odisha" due to its scenic beauty and pleasant climate.
• The place is known for its pine forests, coffee plantations, and beautiful valleys.
• Daringbari is situated in the Kandhamal district and is a well-known hill station in eastern India.
• The region attracts tourists for its natural beauty, waterfalls, and trekking opportunities.

Additional Information

• Odisha is a state located in eastern India, known for its rich cultural heritage and natural beauty.
• The state is home to several historical monuments, temples, and wildlife sanctuaries.
• ​Odisha's coastline along the Bay of Bengal is famous for its beaches and marine life.
• Popular tourist destinations in Odisha include Puri, Konark, and Bhubaneswar, known for their ancient temples and cultural festivals.

The correct answer is Madhya Pradesh.

Key Points

• Kanha National Park is located in the state of Madhya Pradesh.
• It is one of the largest national parks in India and is known for its significant population of Bengal tigers.
• The park is also home to a variety of other wildlife including leopards, wild dogs, and the rare hardground barasingha (swamp deer).
• Kanha National Park was established in 1955 and is part of the Kanha Tiger Reserve, which was created in 1973 under Project Tiger.

Additional Information

• Kanha National Park is divided into two core zones: Kanha and Kisli.
• The park's landscape is a mix of dense forests, open meadows, and rivers, making it an ideal habitat for a diverse range of flora and fauna.
• Visitors to the park can enjoy a variety of activities including jungle safaris, bird watching, and nature walks.

The correct answer is New Delhi.

Key Points

• The first Lok Adalat in India was held in New Delhi.
• Lok Adalats are an alternative dispute resolution mechanism.
• They are a forum where disputes/cases pending in the court of law or at pre-litigation stage are settled/compromised amicably.
• The first Lok Adalat was held on March 14, 1982.
• Lok Adalats have the powers of a Civil Court and their decisions are final and binding on all parties.

Additional Information

• Lok Adalats are governed under the Legal Services Authorities Act, 1987.
• They provide a platform for the common man to settle disputes without having to go through the lengthy and expensive process of litigation.
• Lok Adalats are also known for their quick and efficient resolution of cases.
• They help in reducing the burden on regular courts.
• They ensure that justice is accessible to all sections of society.

The logic followed here is,

SPORADIC: QNORDJEB

\

Similarly,

TROUBLES: ?

Hence, the correct answer is "TNQSTFMC".

The correct answer is Paris.

Key Points

• UNESCO stands for United Nations Educational, Scientific and Cultural Organization.
• The headquarters of UNESCO is located in Paris, France.
• Paris is known for being a hub of international organizations and cultural institutions.
• UNESCO was founded in 1945 and its headquarters have been in Paris since its inception.
• UNESCO's mission is to contribute to the building of peace, the eradication of poverty, sustainable development, and intercultural dialogue through education, the sciences, culture, communication, and information.

Additional Information

• UNESCO has 193 member states and 11 associate members.
• ​It pursues its objectives through five major programs:
• Education
• Natural sciences
• Social/human sciences
• Culture
• Communication and information

The logic followed here is:

1. 149 → It is a prime number.

2. 159 → It is not a prime number (Divisible by 3)

3. 113 → It is a prime number.

4. 127 → It is a prime number.

Here, we can see that Option 2 is different from others.

Hence, the correct answer is "159".

The correct answer is Nitric Acid.

Key Points

• Aqua Fortis is a historical name for nitric acid.
• Nitric Acid (HNO₃) is a highly corrosive and toxic strong acid.
• It was called "Aqua Fortis" which means "strong water" in Latin, due to its powerful reactivity.
• It is used in various applications such as fertilizer production, explosives, and metal processing.

Additional Information

• Hydrochloric Acid (HCl) is a strong acid commonly used in cleaning and pickling of metals.
• Acetic Acid (CH₃COOH) is a weak acid found in vinegar.
• Sulphuric Acid (H₂SO₄) is another strong acid used in battery acid and industrial processes.

The correct answer is Mohinder.

Key Points

• The names in a telephone directory are arranged in alphabetical order.
• Comparing the given options:
• Mahindra comes before Mahendra because "i" comes before "e".
• Mahendra comes before Mohindar because "a" comes before "o".
• Mohindar comes before Mohinder because "a" comes before "e".
• Thus, Mohinder will come last in a telephone directory.

The correct answer is Earthworm.

Key Points

• The nephridium is an excretory organ present in earthworms.
• Nephridia are tubular excretory structures that perform a function similar to kidneys in vertebrates.
• They help in removing metabolic wastes from the body fluids.
• Nephridia are found in many invertebrates, including annelids like earthworms.
• There are different types of nephridia, such as protonephridia and metanephridia, based on their structure and function.

Additional Information

• Planaria have a different excretory system based on flame cells.
• Rats have kidneys as their excretory organs.
• Cockroaches use Malpighian tubules for excretion.

The correct answer is Hoon.

Key Points

• Attila was the leader of the Huns, also known as the Hoon community.
• The Huns were a nomadic tribe known for their invasions and conquests in Europe during the 4^th and 5^th centuries.
• Attila ruled the Huns from 434 until his death in 453, and he was one of the most feared enemies of the Western and Eastern Roman Empires.
• Under Attila's leadership, the Huns became one of the most powerful and formidable groups during that era.

Additional Information

• The Huns originated from Central Asia and migrated into Europe, causing significant upheaval in the regions they invaded.
• Attila's campaigns extended from the Ural River to the Rhine River and from the Danube River to the Baltic Sea.
• Despite his fearsome reputation, Attila's death in 453 led to the rapid decline of the Hun Empire.

The logic followed here is:

Logic: Iron, Zinc, and Chlorine are all individual elements. Whereas Mica is not an element, but a mineral composed of different elements, making it structurally different from the others.

Hence, the correct answer is "Mica".

The correct answer is 14.

Key Points

• The Rajya Sabha must return the Money Bill to the Lok Sabha within 14 days from the date of its receipt.
• If the Rajya Sabha fails to return the Money Bill within this period, it is deemed to have been passed by both Houses in the form originally passed by the Lok Sabha.

Additional Information

• A Money Bill is defined under Article 110 of the Indian Constitution.
• The Lok Sabha has more power over Money Bills compared to the Rajya Sabha.
• Only the Lok Sabha can introduce and pass Money Bills, while the Rajya Sabha can only make recommendations.

According to the given information,

1) If A is placed below E.

2) D is placed above E.

3) C is placed above D.

4. B is placed below A

Here, we can see that B touches the table.

Hence, the correct answer is "B".

The correct answer is Waterflow.

Key Points

• Rill erosion is an example of erosion caused by waterflow.
• Waterflow erosion occurs when running water removes the soil surface, creating small channels or rills.
• These rills can merge to form larger channels, further contributing to soil erosion.
• Water is a powerful agent of erosion, shaping landscapes by transporting soil and sediment over time.

Additional Information

• Other types of erosion include:
• Wind erosion: Caused by the movement of air, which can remove topsoil and transport it to different locations.
• Glacial erosion: Caused by the movement of glaciers, which can carve out valleys and shape mountains.
• Thermal erosion: Caused by temperature changes, which can expand and contract rocks, leading to their breakdown.
• Prevention of soil erosion includes practices like planting vegetation, using erosion control mats, and building terraces.

The correct answer is Treaty of Purandar.

Key Points

• The Treaty of Purandar was signed between Shivaji Maharaj and the Mughal Empire in 1665.
• This treaty was a result of the Mughal Emperor Aurangzeb's campaign against Shivaji.
• Under the terms of the treaty, Shivaji agreed to surrender 23 out of 35 forts to the Mughals and pay a compensation of 400,000 rupees.
• This treaty marked a temporary setback for Shivaji but he soon regained his strength and continued his resistance against the Mughals.

Additional Information

• Shivaji Maharaj was a Maratha warrior king and the founder of the Maratha Empire in western India.
• He is known for his innovative military tactics, pioneering non-conventional methods of warfare, and administrative reforms.
• The Mughal Empire was one of the largest empires in Indian history, known for its rich cultural heritage and architectural achievements.
• It was founded by Babur in 1526 and reached its zenith under Akbar, Jahangir, Shah Jahan, and Aurangzeb.
• The empire began to decline after Aurangzeb's death in 1707.

According to the given information,

BOARD: 53169

NEAR: 2416

Using the given codes for the letters,

NODE: ?

Hence, the correct answer is "2394".

The correct answer is Copper & Zinc.

Key Points

• Brass is an alloy of copper and zinc.
• The proportions of zinc and copper can vary to create a range of brasses with varying properties.
• Brass is typically used for decoration due to its bright gold-like appearance.
• Brass is also used for applications where low friction is required such as locks, gears, bearings, doorknobs, ammunition casings, and valves.
• It is known for its acoustic properties, making it an ideal material for musical instruments such as horns and bells.

Additional Information

• Brass has higher malleability than bronze or zinc.
• It is a good conductor of heat and is often used in heat exchangers.
• The melting point of brass varies depending on the composition, typically ranging from 900 to 940 °C (1,650 to 1,720 °F).

According to the given information,

Hence, the correct answer is "2".

The correct answer is Phosphine.

Key Points

• Phosphine smells like rotting fish.
• Phosphine is a toxic, flammable gas.
• It is often associated with a foul odor similar to that of decaying fish.
• Phosphine is used in various industrial applications but is highly hazardous.
• It is important to handle phosphine with care due to its toxic properties.

Additional Information

• Ozone has a distinct sharp smell, often described as similar to chlorine.
• Chlorine has a strong, pungent smell often associated with bleach.
• Acetylene gas has a garlic-like odor.

Shortcut Trick

Efficiency Ratio (A : B) = 3 : 1 ⇒ Time Ratio (A : B) = 1 : 3.

Difference in time units = 3 − 1 = 2 units.

Given 2 units = 16 min ⇒ 1 unit = 8 min (Time for Pipe A) and 3 units = 24 min (Time for Pipe B).

Combined time = (A × B) ÷ (A + B) = (8 × 24) ÷ (8 + 24) = 192 ÷ 32 = 6 min.

∴ The correct answer is 6 min.

Alternate Method

Given: Capacity of Pipe A is thrice that of Pipe B. Time difference between A and B to fill the tank is 16 min.

⇒ Let Efficiency of Pipe B = 1 unit/min. Then Efficiency of Pipe A = 3 units/min.

⇒ Let Time taken by Pipe B = t min. Time taken by Pipe A = (t − 16) min.

⇒ Since Total Work is constant: Efficiency_A × Time_A = Efficiency_B × Time_B

⇒ 3 × (t − 16) = 1 × t ⇒ 3t − 48 = t ⇒ 2t = 48 ⇒ t = 24 min.

⇒ Combined Efficiency (A + B) = 3 + 1 = 4 units/min.

⇒ Time taken together = Total Work ÷ Combined Efficiency = 24 ÷ 4 = 6 min.

∴ The correct answer is 6 min.

Additional Information

Efficiency and Time Relation

For a fixed work, Efficiency is inversely proportional to Time. If efficiency ratio is a:b, then time ratio is b:a.

Combined Work Formula

If two pipes can fill a tank in x and y minutes respectively, then both together can fill it in (xy) ÷ (x + y) minutes.

Work-Efficiency Product

Total Work = Efficiency × Time. This constant product helps in establishing equations between different pipes.

The correct answer is Jyotiba Phule.

Key Points

• Jyotiba Phule founded the Satyasodhak Samaj in 1873.
• The main objective of the Satyasodhak Samaj was to achieve social justice and to provide equal rights to the underprivileged sections of society.
• Jyotiba Phule was a prominent social reformer and activist who worked towards the upliftment of women and lower castes in India.

Additional Information

• Jyotiba Phule, along with his wife Savitribai Phule, was a pioneer in women's education in India.
• He also fought against the caste system and untouchability, advocating for the rights of oppressed classes.
• The Satyasodhak Samaj's principles were based on human rights, dignity, and social justice.

The logic followed here is:

 

All of the options are the pair of secondary colors, 

Whereas,

Blue - Red are the primary colors.

Hence, the correct answer is "Option 4".

Important Points

The correct answer is 2.

Key Points

• Humans have a total of 46 chromosomes in each cell, arranged in 23 pairs.
• Among these 23 pairs, one pair is the sex chromosomes.
• Females have two X chromosomes (XX).
• Males have one X and one Y chromosome (XY).
• Sex chromosomes determine the biological sex of an individual.

Additional Information

• Autosomes are the other 22 pairs of chromosomes that are not sex chromosomes.
• These chromosomes contain the bulk of an individual's genetic information.
• Chromosomes are structures within cells that contain DNA and many genes.
• They play a crucial role in heredity and the functioning of cells.

According to the given information,

1) A man is facing towards West and turns through 45° clockwise.

2. Again turns 180° clockwise.

3. Then turns through 270° anticlockwise.

Here, we can see that he is now facing southwest direction.

Hence, the correct answer is "Southwest".

The correct answer is Asmaka.

Key Points

• Asmaka was one of the sixteen Mahajanapadas mentioned in ancient Indian texts.
• It was located in the southern part of India, specifically in the region that is now part of Maharashtra and Andhra Pradesh.
• The capital of Asmaka was Potali or Podana, which is identified with modern-day Bodhan in Telangana.
• The Mahajanapadas were a set of sixteen kingdoms or oligarchic republics that existed in ancient India from the 6^th to 4^th centuries BCE.

Additional Information

• The other Mahajanapadas were primarily located in the northern and eastern parts of India.
• Koshala and Anga were located in the northern region, while Malaba is not recognized as one of the sixteen Mahajanapadas.
• The Mahajanapadas played a crucial role in the political and cultural development of ancient India.

The logic followed here is:

Logic: The terms of the series are the resultant of consecutive prime numbers + 1.

Hence, the correct answer is "32, 38".

The correct answer is Niels Bohr.

Key Points

• Niels Bohr explained the structure of the atom using Quantum Theory.
• Quantum Theory describes the behavior of particles at the atomic and subatomic levels.
• Bohr's model introduced the idea that electrons orbit the nucleus at specific distances.
• This model was a significant advancement in understanding atomic structure and laid the groundwork for modern quantum mechanics.

Additional Information

• Other notable scientists:
• Oppenheimer: Known for his role in the Manhattan Project.
• Albert Einstein: Developed the theory of relativity.
• Rutherford: Known for the gold foil experiment and the discovery of the nucleus.
• Bohr's contributions:
• He received the Nobel Prize in Physics in 1922 for his work on the structure of atoms.
• Bohr's work helped to explain the periodic table and the chemical behavior of elements.

Given:

A's capacity to complete a work is thrice that of B.

A completes the work 20 days prior to B.

Formula Used:

Work Done = Capacity × Time

When working together, combined capacity = Sum of individual capacities

Time = Work / Combined capacity

Calculation:

Let B's capacity be x.

Then, A's capacity = 3x.

Let B takes T days to complete the work.

⇒ A takes (T - 20) days to complete the work.

Since Work Done = Capacity × Time:

B's work done = x × T

A's work done = 3x × (T - 20)

Since both are completing the same work:

⇒ x × T = 3x × (T - 20)

⇒ T = 3(T - 20)

⇒ T = 3T - 60

⇒ 2T = 60

⇒ T = 30

So, B takes 30 days, and A takes 10 days to complete the work.

Combined capacity = x + 3x = 4x

Let total work be W. Then W = x × 30 = 30x.

Time taken to complete the work together:

⇒ Time = Work / Combined capacity

⇒ Time = 30x / 4x

⇒ Time = 30 / 4

⇒ Time = 7.5 days

They can complete the work together in 7.5 days.

The correct answer is 1576.

Key Points

• The Battle of Haldighat took place in 1576.
• It was fought between the forces of Maharana Pratap, the ruler of Mewar, and the Mughal army led by Man Singh I of Amber.
• The battle was significant in the history of Rajasthan and is remembered for the valor and bravery of Maharana Pratap.
• The battle took place in the Aravalli Range at Haldighati, which is a mountain pass in Rajasthan.

Additional Information

• Maharana Pratap is regarded as a symbol of Rajput valor and resistance against Mughal domination.
• The battle did not result in a decisive victory for either side, but it showcased the determination of Maharana Pratap to defend his kingdom.
• Despite the Mughal forces being larger and better equipped, Maharana Pratap's guerrilla warfare tactics inflicted significant damage on the Mughal army.

According to the given information,

LACK: 396

Similarly,

BACK: ?

Hence, the correct answer is "66".

The correct answer is 15.

Key Points

• The United Nations Security Council (UNSC) has a total of 15 members.
• The members consist of:
• 5 permanent members: China, France, Russia, the United Kingdom, and the United States.
• 10 non-permanent members elected for two-year terms by the General Assembly.
• The Security Council is one of the six principal organs of the United Nations and is charged with ensuring international peace and security.

Additional Information

• The Security Council can convene at any time whenever peace is threatened.
• Each of the five permanent members has veto power over substantive resolutions.
• The presidency of the Security Council rotates monthly among its members.

The correct answer is Sandhyakar Nandi.

Key Points

• Sandhyakar Nandi is the author of 'Ramacharit'.
• He was a renowned Sanskrit scholar and poet of ancient India.
• 'Ramacharit' is one of the significant works in Sanskrit literature.
• Sandhyakar Nandi's contributions to Sanskrit literature are highly regarded.

Additional Information

• Sandhyakar Nandi was a court poet of Pala dynasty.
• He lived during the c 1084-1155 AD.
• Sandhyakar Nandi's literary works provide valuable insights into the socio-political and cultural aspects of his time.
• His works are considered masterpieces of classical Sanskrit literature.

The logic followed here is,

Logic: Final output = (Sum of the digits of first number) - (Sum of the digits of second number)

84 × 13 = 8

→ (8 + 4) - (1 + 3)

→ (12) - (4) = 8

37 × 13 = 6

→ (3 + 7) - (1 + 3)

→ (10) - (4) = 6

Similarly,

56 × 22 = ?

→ (5 + 6) - (2 + 2)

→ (11) - (4) = 7

Hence, the correct answer is "7".

The correct answer is Siddhanta.

Key Points

• The compilation of preachings of Mahavir is known as Siddhanta.
• Mahavir, also known as Vardhamana, was the 24^th and the last Tirthankara of Jainism.
• His teachings form the core of Jain philosophy and are compiled in texts known as Siddhanta.
• Siddhanta encompasses the principles, doctrines, and ethics taught by Mahavir.
• These texts are considered sacred in Jainism and guide the spiritual and ethical practices of its followers.

Additional Information

• Jainism is an ancient Indian religion that emphasizes non-violence, truth, and asceticism.
• It was founded by a lineage of 24 Tirthankaras, with Mahavir being the last.
• The religion has two major sects: Digambara and Svetambara.
• Both sects follow the teachings of Mahavir, though they have some differences in practices and interpretations.

Given:

Discount given = 15%

Profit earned after discount = 19%

Formula Used:

Profit = Selling Price - Cost Price

Calculation:

Let the marked price be M and the cost price be C .

Selling Price (SP) with discount = M \(\times (1 - \frac{15}{100})\) = 0.85M

19% Profit implies: 0.85M = \(C \times (1 + \frac{19}{100})\) = 1.19C

To find the profit without discount, Selling Price without discount = M

Profit Percentage without discount = \(\left(\frac{M - C}{C}\right) \times 100\)

From the given conditions:

\( 0.85M = 1.19C \)

⇒ \( M = \frac{1.19C}{0.85} \)

⇒ \( M = 1.4C \)

Now, Profit Percentage without discount:

\( \left(\frac{M - C}{C}\right) \times 100 \)

⇒ \( \left(\frac{1.4C - C}{C}\right) \times 100 \)

⇒ \( \left(\frac{0.4C}{C}\right) \times 100 \)

⇒ \( 0.4 \times 100 \)

⇒ 40%

The correct answer is option 2.

The correct answer is Dolomite.

Key Points

• Dolomite is not an ore of Aluminium.
• Dolomite is a mineral composed of calcium magnesium carbonate.
• It is used as a source of magnesium and calcium and as a building material.
• Bauxite, Gibbsite, and Feldspar are ores of Aluminium.
• Bauxite is the primary ore of Aluminium.
• Gibbsite and Feldspar also contain Aluminium.

Additional Information

• Aluminium is extracted primarily from Bauxite ore through the Bayer process.
• Feldspar is a group of minerals that contain Aluminium along with potassium, sodium, and calcium.

The correct answer is Pepsin.

Key Points

• Pepsin is the enzyme that converts protein into peptone.
• Pepsin is a digestive enzyme found in the stomach.
• It breaks down proteins into smaller peptides known as peptones.
• Pepsin is activated from its inactive form, pepsinogen, by the acidic environment in the stomach.
• It is one of the main digestive enzymes in the gastric juice.

Additional Information

• Trypsin is another digestive enzyme, but it acts in the small intestine and breaks down peptides into smaller amino acids.
• Erypsin further breaks down peptones into amino acids.
• Renin (or rennin) is an enzyme that coagulates milk, found in the stomach of young ruminants.

Given:

Numbers: 123, 178, 244

Formula Used:

To find the greatest number that leaves the same remainder when dividing multiple numbers, we calculate the Greatest Common Divisor (GCD) of the differences between the numbers.

Calculation:

Calculate the differences between the numbers:

178 - 123 = 55

244 - 178 = 66

244 - 123 = 121

Find the GCD of these differences:

GCD of 55, 66, and 121

Prime factorization:

55 = 5 × 11

66 = 2 × 3 × 11

121 = 11²

Common factor: 11

GCD = 11

The greatest number that leaves the same remainder when dividing 123, 178, and 244 is 11.

Given:

Initial ratio of the two numbers = 3 ∶ 5

When 10 is added to both numbers, the ratio becomes 5 ∶ 7.

Formula Used:

Ratio equation: \(\frac{a+10}{b+10} = \frac{5}{7}\)

Calculation:

Let the numbers be 3x and 5x.

According to the problem:

\(\frac{3x + 10}{5x + 10} = \frac{5}{7}\)

Cross-multiplying gives:

⇒ 7(3x + 10) = 5(5x + 10)

⇒ 21x + 70 = 25x + 50

⇒ 21x - 25x = 50 - 70

⇒ -4x = -20

⇒ x = 5

The two numbers are:

First number = 3x = 3 × 5 = 15

Second number = 5x = 5 × 5 = 25

Sum of the two numbers = 15 + 25 = 40

The sum of the two numbers is 40.

The correct answer is Glucagon.

Key Points

• Glucagon is a hormone secreted by the alpha cells of the pancreas.
• It plays a crucial role in glucose metabolism and homeostasis.
• Glucagon increases blood glucose levels by promoting gluconeogenesis and glycogenolysis in the liver.
• It acts in opposition to insulin, which lowers blood glucose levels.
• Glucagon is essential for maintaining normal blood sugar levels, especially during fasting or between meals.

Additional Information

• Insulin, another pancreatic hormone, is secreted by the beta cells and helps lower blood sugar levels by facilitating cellular glucose uptake.
• The pancreas also secretes other hormones:
• Somatostatin from delta cells, which regulates the secretion of both insulin and glucagon.
• Pancreatic polypeptide from PP cells, which helps regulate pancreatic secretions and gastrointestinal motility.

Given:

Initial milk in the container = 20 litres

Milk withdrawn in each step = 4 litres

Water added in each step = 4 litres

Process repeated = 2 times

Formula Used:

Remaining milk after each step = \(Initial milk × (1 - \frac{milk\ withdrawn}{total\ liquid}) \)

Calculation:

Initial milk = 20 litres

Milk withdrawn = 4 litres

Remaining milk = \(20 × (1 - \frac{4}{20})\)

⇒ Remaining milk = \(20 × \frac{16}{20}\)

⇒ Remaining milk = 16 litres

Initial milk = 16 litres

Milk withdrawn = 4 litres

Total liquid after adding water = 20 litres

Remaining milk = \(16 × (1 - \frac{4}{20})\)

⇒ Remaining milk = \(16 × \frac{16}{20}\)

⇒ Remaining milk = 12.8 litres

There will be 12.8 litres of milk left after the process is repeated twice.

Given:

The sum of marks obtained by Arun in English and Mathematics is 170.

The difference in marks obtained by Arun in English and Mathematics is 10.

Formula Used:

Let the marks in English be E and in Mathematics be M .

From the given conditions:

E + M = 170      ......(1)

E - M = 10     ......(2)

Calculation:

Adding equation (1) and (2):

⇒ (E + M) + (E - M) = 170 + 10

⇒ 2E = 180

⇒ E = 90

Substituting the value of E in equation (1):

⇒ 90 + M = 170

⇒ M = 80

Now, the ratio of marks in English to Mathematics is:

⇒ E : M = 90 : 80

⇒ 9 : 8

The ratio of marks obtained by Arun in English and Mathematics is 9 ∶ 8.

The correct answer is Cerebellum.

Key Points

• The Cerebellum is a crucial part of the brain that plays a significant role in maintaining body balance and coordination.
• It is located at the back of the brain, underneath the occipital lobes of the cerebral cortex.
• The cerebellum is responsible for fine-tuning motor activities and ensuring smooth, balanced muscular activity.
• It also helps in maintaining posture and equilibrium, making it essential for everyday activities such as walking, running, and other physical movements.

Additional Information

• The Medulla Oblongata is responsible for regulating vital functions such as heartbeat and breathing.
• The Thalamus acts as a relay station for transmitting sensory and motor signals to the cerebral cortex.
• The Mid Brain is involved in functions such as vision, hearing, eye movement, and body movement.

The logic followed here is :

Hence the correct answer is Option 4.

The correct answer is Common Salt.

Key Points

• Common salt (sodium chloride) is a crystalline solid.
• Amorphous solids are solids that do not have a long-range order of atoms.
• Examples of amorphous solids include substances like chalk, coal tar, and wood.
• Common salt has a well-defined crystalline structure, unlike amorphous solids.

Additional Information

• Amorphous solids have a disordered arrangement of atoms or molecules.
• Crystalline solids have a highly ordered arrangement of atoms or molecules, which contributes to their unique physical properties.
• Common salt is an example of a crystalline solid, characterized by its regular and repeating pattern of sodium and chloride ions.

According to the given information,

Let's check each option,

1) 3 × 4 > 2 - 9 + 3 < 3 

→ 3 + 4 × 2 = 9 ÷ 3 - 3 

→ 3 + 4 × 2 = 3 - 3

→ 3 + 8 = 3 - 3

→ 11 = 3 - 3

→ 11 = 0 ⇒ This is not true.

2) 5 × 3 < 3 ÷ 8 + 4 × 4

→ 5 + 3 - 3 > 8 ÷ 4 + 4

→ 5 + 3 - 3 > 2 + 4

→ 8 - 3 > 6

→ 5 > 6 ⇒ This is not true.

3) 3 × 2 < 4 ÷ 16 > 2 + 4 

→ 3 + 2 - 4 > 16 × 2 ÷ 4 

→ 3 + 2 - 4 > 16 × 1/2 

→ 3 + 2 - 4 > 8

→ 5 - 4 > 8

→ 1 > 8 ⇒ This is not true.

4) 5 > 8 + 4 = 10 < 4 × 8 

→ 5 × 8 ÷ 4 < 10 - 4 + 8 

→ 5 × 2 < 10 - 4 + 8 

→ 10 < 10 - 4 + 8 

→ 10 < 18 - 4

→ 10 < 14 ⇒ This is true.

Hence, the correct answer is "5 > 8 + 4 = 10 < 4 × 8".

Given:

Speed of A = 8 metres/second

Speed of B = 5 metres/second

Initial distance between A and B = 180 metres

Time = 70 seconds

Formula Used:

Relative Speed = Speed of A - Speed of B

Distance covered = Relative Speed × Time

New Distance between A and B = Initial Distance - Distance covered

Calculation:

Relative Speed = 8 - 5

Relative Speed = 3 metres/second

Distance covered in 70 seconds = 3 × 70

⇒ Distance covered = 210 metres

New Distance between A and B = 210 - 180

⇒ New Distance = 30 metres

The distance between A and B after 70 seconds is 30 metres.

The correct answer is Africa.

Key Points

• Madagascar is located in the Indian Ocean, off the southeastern coast of Africa.
• It is the fourth largest island in the world and is part of the African continent.
• The capital city of Madagascar is Antananarivo.
• Madagascar is known for its unique biodiversity and is home to many species that are not found anywhere else in the world.

Additional Information

• Madagascar separated from the Indian subcontinent around 88 million years ago, allowing its flora and fauna to evolve in relative isolation.
• The island is famous for its lemurs, baobab trees, and unique ecosystems.
• Due to its isolation, Madagascar has a high rate of endemism, with many species that are found nowhere else on Earth.

Preparing the family tree using the following symbols,

The family tree can be drawn based on the given information as shown below,

Here, we can see that M is the father of Q.

Hence, the correct answer is "Father".

Given:

Initial investment by A on 1^st January = ₹40,000

Initial investment by B on 1^st January = ₹60,000

Additional investment by A on 1^st March = ₹20,000

Withdrawal by B on 1^st June = ₹10,000

Total profit till 31^st December = ₹33,250

Formula Used:

Profit share = (Investment by partner × Time period) / Sum of (Investment × Time period for all partners)

Calculation:

Investment by A:

From 1^st Jan to 1^st Mar (2 months): ₹40,000

From 1^st Mar to 31^st Dec (10 months): ₹40,000 + ₹20,000 = ₹60,000

Investment by B:

From 1^st Jan to 1^st Jun (5 months): ₹60,000

From 1^st Jun to 31^st Dec (7 months): ₹60,000 - ₹10,000 = ₹50,000

Total investment by A:

₹40,000 × 2 + ₹60,000 × 10

⇒ ₹80,000 + ₹600,000

⇒ ₹680,000

Total investment by B:

₹60,000 × 5 + ₹50,000 × 7

⇒ ₹300,000 + ₹350,000

⇒ ₹650,000

Sum of investments:

₹680,000 + ₹650,000

⇒ ₹1,330,000

B's share in profit:

\(\left( \frac{\text{B's investment} \times \text{Total profit}}{\text{Total investment}} \right)\)

\(\left( \frac{650,000 \times 33,250}{1,330,000} \right)\)

⇒ \(\left( \frac{21,612,500}{1,330,000} \right)\)

⇒ ₹16,250

The share of B in the profit is ₹16,250.

The correct answer is Morarji Desai.

Key Points

• In 1967, Morarji Desai was designated as the Deputy Prime Minister of India.
• Morarji Desai served as Deputy Prime Minister under Prime Minister Indira Gandhi.
• He also held the position of Finance Minister during this time.
• Morarji Desai later became the Prime Minister of India in 1977.

Additional Information

• Chowdhry Charan Singh, Shri Jagjivan Ram, and Sardar Ballav Bhai Patel also held significant positions in the Indian government but were not designated as Deputy Prime Minister in 1967.
• Sardar Ballav Bhai Patel served as the first Deputy Prime Minister of India from 1947 to 1950.

The correct answer is Mandamus.

Key Points

• Mandamus is a writ issued by a higher court to compel a lower court or a government officer to perform mandatory or purely ministerial duties correctly.
• It ensures that public authorities fulfill their legal duties.
• It cannot be issued to compel a private individual or body.
• The term Mandamus means "We Command" in Latin.
• This writ is a powerful tool for judicial review of administrative actions.

Additional Information

• Certiorari is a writ issued by a higher court directing a lower court to send the record of a proceeding for review.
• Prohibition is a writ issued by a higher court to prevent a lower court from exceeding its jurisdiction.
• Habeas Corpus is a writ requiring a person under arrest to be brought before a judge or into court.

Given:

Speed of the train = 45 km/hr

Speed of the person = 5 km/hr

Time taken to cross the person = 18 seconds

Formula Used:

Length of the train (in metres) = Relative speed × Time

Calculation:

Relative speed = Speed of the train + Speed of the person

Relative speed = 45 km/hr + 5 km/hr

Relative speed = 50 km/hr

Convert relative speed to m/s:

Relative speed = 50 × (1000 / 3600) m/s

Relative speed = 50 × (5 / 18) m/s

Relative speed = 250 / 18 m/s

Relative speed = 125 / 9 m/s

Length of the train = Relative speed × Time

Length of the train = (125 / 9) × 18

Length of the train = 125 × 2

Length of the train = 250 metres

The length of the train is 250 metres.

The correct answer is Madras.

Key Points

• Annie Besant established the Home Rule League in Madras in 1916.
• The Home Rule League was an Indian political organization aimed at achieving self-governance and dominion status for India within the British Empire.
• The league played a crucial role in the Indian independence movement.
• Annie Besant was a prominent British socialist, theosophist, and supporter of Indian nationalism.
• The Home Rule League campaigned for the cause through public meetings, petitions, and extensive propaganda.

Additional Information

• Another Home Rule League was established by Bal Gangadhar Tilak in Pune around the same time.
• Both leagues worked in tandem to promote the idea of self-governance.
• The efforts of the Home Rule Leagues eventually led to greater political awareness and participation among Indians.
• This laid the groundwork for subsequent movements leading to India's independence in 1947.

The correct answer is Total internal reflection.

Key Points

• Mirage is an example of total internal reflection.
• Total internal reflection occurs when a wave hits a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface.
• Mirages are optical phenomena where light rays bend to produce a displaced image of distant objects or the sky.
• This bending of light usually occurs due to the temperature gradient in the atmosphere.

Additional Information

• Refraction is the bending of light as it passes from one medium to another.
• A spectrum is a range of different colors produced when light is dispersed by a prism.
• Reflection is the bouncing back of light from a surface.
• Mirage involves the bending of light rays due to total internal reflection, resulting in optical illusions.

Shortcut Trick

Separate the integer and fractional parts to calculate rapidly.

Integers: 12 + 10 − 7 − 1 = 14

Fractions: 1/3 + 5/6 − 2/3 − 4/7 = −1/3 + 5/6 − 4/7 = 3/6 − 4/7 = −1/14

Combine parts: 14 − 1/14 = 13 + (14/14 − 1/14) = 13 13/14

∴ The correct answer is 13 13/14.

Alternate Method

Given:

12 1/3 + 10 5/6 − 7 2/3 − 1 4/7

Calculations:

⇒ Converting mixed fractions to improper fractions:

⇒ 37/3 + 65/6 − 23/3 − 11/7

⇒ Grouping terms with denominator 3:

⇒ (37/3 − 23/3) + 65/6 − 11/7

⇒ 14/3 + 65/6 − 11/7

⇒ Taking LCM of 3 and 6, which is 6:

⇒ (28 + 65)/6 − 11/7

⇒ 93/6 − 11/7

⇒ Simplifying the fraction:

⇒ 31/2 − 11/7

⇒ Taking LCM of 2 and 7, which is 14:

⇒ (31 × 7 − 11 × 2) / 14

⇒ (217 − 22) / 14

⇒ 195 / 14

⇒ 13 13/14

∴ The correct answer is 13 13/14.

Additional Information

Mixed Fractions

A mixed fraction represents the sum of a whole number and a proper fraction. It can be split into two parts for easier addition and subtraction: A B/C = A + B/C.

BODMAS Rule

It dictates the correct order of mathematical operations: Brackets, Orders, Division/Multiplication, and Addition/Subtraction. Operations of the same rank are solved from left to right.

LCM for Fractions

When adding or subtracting fractions with different denominators, always find the Least Common Multiple (LCM) of the denominators to create equivalent fractions.

The correct answer is Laterite Soil.

Key Points

• Laterite soil is ideal for coffee plantation.
• Laterite soils are rich in iron and aluminum, which are beneficial for coffee plants.
• These soils are well-drained, which is a crucial requirement for coffee cultivation.
• Laterite soil is commonly found in regions with a high amount of rainfall, which suits the water needs of coffee plants.

Additional Information

• Red soil is also used for coffee cultivation but is not as ideal as laterite soil.
• Alluvial soil is more suited for crops like rice, wheat, and sugarcane.
• Black soil is ideal for cotton cultivation due to its moisture-retentive capacity.

Given:

Amount after 1 year (A₁) = Rs. 5,500

Amount after 3 years (A₃) = Rs. 6,655

Formula Used:

Compound Interest Formula: \(A = P \left(1 + \frac{r}{100}\right)^n\)

Calculation:

Let the principal amount be P and the rate of interest be r%.

From the given data, we have:

A₁ = \(P \left(1 + \frac{r}{100}\right)^1\)

5,500 = \(P \left(1 + \frac{r}{100}\right) \)

A₃ = \(P \left(1 + \frac{r}{100}\right)^3\)

6,655 = \(P \left(1 + \frac{r}{100}\right)^3 \)

Dividing the two equations:

\(\frac{A_3}{A_1} = \left(1 + \frac{r}{100}\right)^3 / \left(1 + \frac{r}{100}\right)\)

\(\frac{6,655}{5,500} = \left(1 + \frac{r}{100}\right)^2\)

⇒ \(\frac{6655}{5500} = \left(1 + \frac{r}{100}\right)^2\)

⇒ \(\frac{6655}{5500} = 1.21\)

⇒ \(\left(1 + \frac{r}{100}\right)^2 = 1.21\)

⇒ \(1 + \frac{r}{100} = \sqrt{1.21}\)

⇒ \(1 + \frac{r}{100} = 1.1\)

⇒ \( \frac{r}{100} = 0.1\)

⇒ r = 10%

The rate of interest is 10%.

Given:

Amount for elder daughter (A_elder) = ₹38,000

Amount for younger daughter (A_younger) = ₹38,000

Rate of interest (r) = 15%

Time for elder daughter (t_elder) = 18 - 12 = 6 years

Time for younger daughter (t_younger) = 18 - current age

Extra amount for elder daughter = ₹4,800

Formula used:

A = P\((1+\frac{r}{100})^t\)

Where,

P = Principal

A = Amount

r = Rate of interest

t = Time

Calculation:

For elder daughter:

38,000 = P_elder\((1+\frac{15}{100})^6\)

⇒ 38,000 = P_elder\((1+0.15)^6\)

⇒ 38,000 = P_elder(1.15)⁶

⇒ 38,000 = P_elder × 2.313

⇒ P_elder = \( \dfrac{38,000}{2.313} \)

⇒ P_elder ≈ ₹16,425

For younger daughter:

P_younger = P_elder - ₹4,800

⇒ P_younger = 16,425 - 4,800

⇒ P_younger ≈ ₹11,625

∴ The amount he kept for his younger daughter is ₹11,625.

The correct answer is Mahatma Gandhi.

Key Points

• Mahatma Gandhi represented the Indian National Congress in the Second Round Table Conference.
• The Second Round Table Conference was held in London from September to December 1931.
• Gandhi was the sole representative of the Indian National Congress, as the Congress had decided to boycott the conference initially but later sent Gandhi as their representative.

Additional Information

• The First Round Table Conference was held in London from November 1930 to January 1931 and was boycotted by the Indian National Congress.
• The Third Round Table Conference took place from November to December 1932, but by this time, the Congress had again boycotted the conference.
• The Round Table Conferences were a series of conferences organized by the British Government to discuss constitutional reforms in India.

Given:

Percentage of voters who restrained from voting = 25%

Percentage of invalid votes = 2%

Percentage of votes won by the candidate = 75%

Votes won by the candidate = 9261

Formula Used:

Total voters = Total votes cast / (1 - Percentage of voters who restrained from voting)

Valid votes = Total votes cast × (1 - Percentage of invalid votes)

Votes won by the candidate = Valid votes × Percentage of votes won by the candidate

Calculation:

Let the total number of voters be V.

Total votes cast = V × (1 - 0.25) = 0.75V

Valid votes = 0.75V × (1 - 0.02) = 0.75V × 0.98 = 0.735V

Votes won by the candidate = 0.735V × 0.75

⇒ 0.735V × 0.75 = 9261

⇒ 0.55125V = 9261

⇒ V = (9261)/(0.55125)

⇒ V = 16800

The total number of voters was 16800.

The logic followed here is: 

Logic: Along the row → Third number = (First number + Second number) × 2 + Second number

Let's check each row as per the logic,

Third row:

→ 59 = (13 + 11) × 2 + 11

→ 59 = 24 × 2 + 11

→ 59 = 48 + 11

Second row: 

→ 69 = (9 + 17) × 2 + 17

→ 69 = 26 × 2 + 17

→ 69 = 52 + 17

First row:

→ 49 = (? + 13) × 2 + 13

→ 49 = 2 × ? + 26 + 13

→ 49 = 2 × ? + 39

→ 10 = 2 × ? 

→ 10/2 = ?

→ 5 = ?

Hence, the correct answer is "5".

The correct answer is Narmada.

Key Points

• The Sardar Sarovar Multi-purpose Project is situated on the Narmada River.
• The Narmada River is one of the major rivers in India that flows westwards over a length of approximately 1,312 kilometers (815 miles).
• It originates from the Amarkantak Plateau in Madhya Pradesh.
• The project aims to provide water for irrigation, hydroelectric power generation, and drinking purposes.
• The Sardar Sarovar Dam is one of the largest dams constructed on the Narmada River.

Additional Information

• The Narmada River flows through the states of Madhya Pradesh, Maharashtra, and Gujarat before draining into the Arabian Sea.
• The river is considered sacred by Hindus and is often referred to as the "Life Line of Gujarat and Madhya Pradesh."
• The Sardar Sarovar Project is part of the Narmada Valley Development Plan, which includes multiple dams and canals to harness the river's potential.
• The project has been both praised for its benefits and criticized for its environmental and social impacts.

Given:

First day savings = ₹1

Second day savings = ₹2

Third day savings = ₹4

Fourth day savings = ₹8

Number of days = 12

Formula used:

The savings form a geometric series with the first term (a) = 1 and common ratio (r) = 2.

The sum of the first n terms of a geometric series is given by:

S_n = a(1 - rⁿ) / (1 - r)

Calculation:

For 12 days:

a = 1, r = 2, n = 12

S₁₂ = 1 × (1 - 2¹²) / (1 - 2)

⇒ S₁₂ = (1 - 4096) / (-1)

⇒ S₁₂ = -4095 / (-1)

⇒ S₁₂ = 4095

∴ The total savings in 12 days is ₹4095.

The correct answer is Gurusikhar.

Key Points

• Gurusikhar is the highest peak of the Aravalli range.
• The peak is located in Mount Abu, Rajasthan, and it rises to a height of about 1,722 meters (5,650 feet) above sea level.
• It offers a panoramic view of the surrounding area and is a popular tourist destination.
• The Aravalli range is one of the oldest mountain ranges in India, stretching approximately 800 km from Gujarat to Delhi.
• Mount Abu is the only hill station in the state of Rajasthan and is known for its cool climate and lush green surroundings.

Additional Information

• Dodabeta is the highest peak of the Nilgiri Hills in Tamil Nadu.
• Gorgaburu is a peak in the Ajodhya Hills of West Bengal.
• Panchmari is a hill station in Madhya Pradesh, but not a peak in the Aravalli range.

Given:

Perimeter of the rectangular field = 20 cm

Area of the rectangular field = 24 sq cm

Formula used:

Perimeter of rectangle = 2(length + breadth)

Area of rectangle = length × breadth

Calculation:

Let the length be L and the breadth be B.

From the perimeter:

2(L + B) = 20

⇒ L + B = 10

From the area:

L × B = 24

We have two equations:

1. L + B = 10
2. L × B = 24

Substitute B = 10 - L into the area equation:

L(10 - L) = 24

⇒ 10L - L² = 24

⇒ L² - 10L + 24 = 0

Solving the quadratic equation:

L = \(\dfrac{10 ± \sqrt{(10)^2 - 4×1×24}}{2×1}\)

⇒ L = \(\dfrac{10 ± \sqrt{100 - 96}}{2}\)

⇒ L = \(\dfrac{10 ± \sqrt{4}}{2}\)

⇒ L = \( \dfrac{10 ± 2}{2}\)

So, L = 6 or L = 4

If L = 6, then B = 4

If L = 4, then B = 6

The difference between length and breadth:

⇒ |L - B| = |6 - 4| = 2

∴ The difference of length and breadth of the field is 2 cm.

The mirror image of the given figure is shown below,

Hence, the correct answer is "Option 1".

The correct answer is Gopal Krishna Gokhale.

Key Points

• Gopal Krishna Gokhale was a prominent Indian political leader and a social reformer during the Indian independence movement.
• He founded the 'Servants of India Society' in 1905. 
• The objective of the society was to train and raise a group of selfless and dedicated individuals to serve India and promote social and human welfare.
• Gokhale was a senior leader of the Indian National Congress and was known for his moderate views and advocacy for constitutional methods of agitation.
• He played a significant role in the Indian National Congress and was a mentor to Mahatma Gandhi.

Additional Information

• The 'Servants of India Society' worked in the fields of education, healthcare, and rural development.
• It aimed to promote Indian nationhood and to serve the underprivileged sections of society.
• Gopal Krishna Gokhale believed in the principles of non-violence and constitutional means to achieve political goals.
• He was also associated with the Deccan Education Society and Fergusson College in Pune.
• His efforts laid the foundation for various social reforms in India.

The logic followed here is:

Logic: In the triangle, First number = (Second number + Third number)/ 2

Let's check each triangle,

In triangle 1,

→ 6 = (7 + 5)/ 2

→ 6 = 12/ 2

In triangle 3,

→ 7 = (10 + 4)/ 2

→ 7 = 14/2

Similarly, In triangle 2,

→ ? = (8 + 6)/ 2

→ ? = 14/ 2 = 7

Hence, the correct answer is "7".

The correct answer is Lamarck.

Key Points

• Lamarck was a pioneering biologist and is best known for his theory of inheritance of acquired characteristics.
• The law of use and disuse suggests that parts of the body that are used extensively become larger and stronger, while those that are not used deteriorate.
• Lamarck's ideas were an important early attempt to explain evolution, although they have been largely superseded by Darwin's theory of natural selection.

Additional Information

• Jean-Baptiste Lamarck was a French naturalist who lived from 1744 to 1829.
• Although his theories were eventually overshadowed by Darwinian evolution, Lamarck's work laid important groundwork for the field of evolutionary biology.
• His ideas were some of the first to suggest that complex organisms evolved from simpler ones over time.

Given:

Average age of 10 students = 10.3 years

Average age of 3 students = 12 years

Average age of 5 students = 9 years

Formula Used:

Average age = Total age of students / Number of students

Calculation:

Total age of 10 students = 10 × 10.3

Total age of 10 students = 103 years

Total age of 3 students = 3 × 12

Total age of 3 students = 36 years

Total age of 5 students = 5 × 9

Total age of 5 students = 45 years

Total age of remaining 2 students = Total age of 10 students - Total age of 3 students - Total age of 5 students

Total age of remaining 2 students = 103 - 36 - 45

Total age of remaining 2 students = 22 years

Average age of remaining 2 students = Total age of remaining 2 students / Number of remaining students

Average age of remaining 2 students = 22 / 2

The average age of the remaining 2 students is 11 years.

The correct answer is France.

Key Points

• Emmanuel Macron is the current President of France.
• He has been serving as the President since May 14, 2017.
• Macron is a former civil servant and investment banker.
• He founded the political party La République En Marche! in 2016.

Additional Information

• Before becoming President, Emmanuel Macron served as the Minister of the Economy, Industry, and Digital Affairs from 2014 to 2016.
• He is one of the youngest Presidents in French history, assuming office at the age of 39.
• Macron's policies focus on economic reform, labor laws, and European Union integration.

Given:

Numbers: 21, 36, and 66

Formula used:

To find the least perfect square divisible by given numbers, we first find the Least Common Multiple (LCM) of these numbers and then ensure the LCM is a perfect square.

Calculation:

Prime factorization:

21 = 3 × 7

36 = 2² × 3²

66 = 2 × 3 × 11

LCM is found by taking the highest power of all prime factors present in any of the numbers:

LCM = 2² × 3² × 7 × 11

⇒ LCM = 4 × 9 × 7 × 11

⇒ LCM = 2772

To make 2772 a perfect square, all prime factors must be raised to an even power:

2772 = 2² × 3² × 7 × 11

Missing factors for a perfect square:

We need another 7 and another 11:

Therefore, the least perfect square = 2772 × 7 × 11

⇒ Least perfect square = 2772 × 77

⇒ Least perfect square = 213,444

∴ The least perfect square divisible by 21, 36, and 66 is 213,444.

The correct answer is Wellington.

Key Points

• Wellington is not a cricket field in South Africa.
• Wellington is actually the capital city of New Zealand.
• It is known for its cricket ground, the Basin Reserve.
• The cricket fields in South Africa include:
• Johannesburg (Wanderers Stadium)
• Durban (Kingsmead)
• Centurion (SuperSport Park)
• South Africa is known for its rich cricketing history and has several prominent cricket grounds where international matches are held.

Additional Information

• Cricket is a popular sport in South Africa, with a strong domestic and international presence.
• Other notable cricket grounds in South Africa include:
• Newlands in Cape Town
• St George's Park in Port Elizabeth
• Boland Park in Paarl

According to the given information,

Here, we can see that I's position is 9. It has the same position in English alphabet.

Hence, the correct answer is "I".

The correct answer is Coromondol Coast.

Key Points

• The Coromandel Coast receives significant winter rainfall.
• This is primarily due to the northeast monsoon winds.
• These winds pick up moisture from the Bay of Bengal and bring rainfall to the region.
• Other coastal areas like Gujarat Coast, Konkan Coast, and Malabar Coast do not experience significant winter rainfall.
• The northeast monsoon is also known as the retreating monsoon.

Additional Information

• The northeast monsoon typically occurs from October to December.
• During this period, the Coromandel Coast receives the bulk of its annual rainfall.
• The southwest monsoon, which occurs from June to September, brings rainfall to other parts of India.
• The Coromandel Coast does not receive much rainfall from the southwest monsoon.

According to the given information,

→ A watch gets slow by 6 minutes in every hour.

Number of minutes the watch gets delayed in 9 hours i.e from 7 am to 4 pm:

→ 6 minutes × 9 = 54 minutes.

Number of minutes it gets delayed in 20 minutes = 6/3 = 2 minutes.

Now, total number of minutes the watch gets delayed between 7 am and 4 pm:

→ (54 + 2) = 56 minutes.

So, the time faulty watch will show when the original time is 4 past 20 minutes is:

→ (4 past 20 minutes - 56 minutes) = 3 past 24 mins

Hence, the correct answer is "3 past 24 mins".

The correct answer is Fa Hiyen.

Key Points

• Fa Hiyen was a Chinese Buddhist monk and a renowned traveller.
• He came to India during the reign of Chandragupta II to study Buddhism and collect Buddhist scriptures.
• His journey to India is well documented and provides valuable insights into the history and culture of the time.
• He traveled through Central Asia and reached India around the early 5^th century AD.

Additional Information

• Al Beruni was a Persian scholar who visited India during the reign of Mahmud of Ghazni in the 11^th century.
• Ibn Battuta was a Moroccan traveller who visited India during the reign of Muhammad bin Tughlaq in the 14^th century.
• Hiuen Tsang was another Chinese Buddhist monk who visited India during the reign of Harsha in the 7^th century AD.

The correct answer is Chhattisgarh.

Key Points

• Bailadila Iron ore mine is located in the state of Chhattisgarh.
• It is one of the largest iron ore mines in India and is operated by the National Mineral Development Corporation (NMDC).
• It is known for its high-grade iron ore reserves.
• The Bailadila range of hills is located in the Dantewada district of Chhattisgarh.
• The iron ore from Bailadila is exported to Japan and South Korea, apart from being supplied to domestic steel plants.

Additional Information

• Chhattisgarh is rich in minerals such as iron ore, coal, limestone, and bauxite.
• The state is known for its significant contribution to India's mineral production.
• NMDC (National Mineral Development Corporation) is a state-controlled mineral producer of the Government of India.
• It is involved in the exploration of a wide range of minerals including iron ore, copper, limestone, dolomite, and gypsum.
• NMDC is one of the leading mining companies in India.

In a clock, when it is 6, the bell tolls 6 times and takes 10 seconds.

• For 6 o'clock:
• There are 6 tolls, which creates exactly 5 intervals between them.
• Total time taken = 10 seconds.
• Time for 1 interval = 10 ÷ 2 = 5 sec
• For 12 o'clock:
• There are 12 tolls, which creates exactly 11 intervals between them.
• Time for 11 intervals = 11 × 2 = 22.

Thus, It takes 22 seconds for the clock to toll 12 times at 12 o'clock.

Hence, the correct answer is "Option 4".

The correct answer is Formic acid.

Key Points

• Formic acid is the chemical responsible for the painful sensation caused by ant stings.
• Formic acid is also known as methanoic acid.
• It is a naturally occurring substance, found not only in ant venom but also in the stings and bites of other insects.
• Formic acid is used by ants as a defense mechanism to protect themselves from predators.

Additional Information

• Formic acid is the simplest carboxylic acid.
• It is used industrially in leather production and as a preservative in livestock feed.
• In nature, formic acid is also found in the stings of bees and certain caterpillars.

Given:

Profit earned = 25%

Cost Price (CP) = Selling Price (SP)

Formula used:

SP = CP + Profit

Calculation:

Let's assume the Cost Price (CP) of 1 metre of cloth is ₹100.

Profit = 25% of CP

⇒ Profit = 25% of ₹100

⇒ Profit = ₹25

Selling Price (SP) = CP + Profit

⇒ SP = ₹100 + ₹25

⇒ SP = ₹125

Since the businessman sells the cloth at cost price (₹100), he is giving cloth worth ₹125 at a price of ₹100.

The actual length of cloth he gives for ₹100:

Let x be the actual length of cloth given in metres.

Therefore, cost of x metres of cloth at ₹125 per metre = ₹100

⇒ x × ₹125 = ₹100

⇒ x = \(\dfrac{100}{125}\)

⇒ x = 0.8 metres

Converting metres to centimetres:

1 metre = 100 cm

0.8 metres = 0.8 × 100 cm

⇒ 0.8 metres = 80 cm

∴ While selling 1 metre of cloth, he actually gives 80 cm of cloth.