MP Police Constable : (24 Nov 2025, Shift 2) Memory-Based Paper (Previous Year Paper)

In animals like sponges and hydra, transport of food and oxygen is done by water only.

Animals such as sponges and Hydra do not have a circulatory system. The water they live in provides food and oxygen to their bodies.

Water carries waste materials and carbon dioxide as it passes out. Thus these species do not require a blood-like circulatory fluid.

Sponges live mainly in seawater, while hydra lives in freshwater.

Sponges and hydra do not have lungs, blood or heart.

Important Points

• Transport  is a life process in which the substance consumed by one portion of the body of the organism is transferred to other parts of the body.
• Amoeba and paramecium are both small creatures that live in water and have no blood in them.

The correct answer is Phylum-Class-Order-Family-Genus-Species.

Key Points

• Taxonomy, the science of classifying organisms.
• The classification system of Phylum-Class-Order-Family-Genus-Species is primarily attributed to Carl Linnaeus.
• who developed the hierarchical system of taxonomy in the 18^th century.
• This system is known as Linnaean taxonomy.

Additional InformationAristotle (384-322 BC):

• Known as the “Father of Science.”
• Introduced the early concepts of classification and binomial definition

Carl Linnaeus (1707-1778):

• Developed the binomial nomenclature system.
• Known as the “Father of Modern Taxonomy.”
• Published “Systema Naturae,” which laid the foundation for modern taxonomy

Charles Darwin (1809-1882):

• Proposed the theory of evolution by natural selection.
• His work influenced the classification of organisms based on evolutionary relationships

Robert Whittaker (1920-1980):

• Proposed the five-kingdom classification system (Monera, Protista, Fungi, Plantae, Animalia).
• His system was based on cell structure, mode of nutrition, and other factorsclassification of humans:
• Phylum: Chordata
• Class: Mammalia
• Order: Primates
• Family: Hominidae
• Genus: Homo
• Species: Homo Sapien

The position values of the letters according to the English alphabet series:

The pattern followed is,

Similarly,

Hence, "YTQM" is the correct answer.

Given:

The work efficiency of Mahendra, Viraj and Ronit is 1 ∶ 2 ∶ 4

Concept Used:

Time ∝ 1/Efficiencey

If a person can complete a work in t days then in 1 day he will do 1/t part of the work.

Calculation:

Ratio of work efficiency of Mahendra, Viraj and Ronit is 1 ∶ 2 ∶ 4

⇒ Ratio of time taken by Mahendra, Viraj and Ronit to complete the work is 1 : 1/2 : 1/4

⇒ 4 : 2 : 1

Let the time taken by Mahendar, Viraj and Ronit be 4x, 2x and x days respectively

Together they can finish the work in 40 days

⇒ (1/4x) + (1/2x) + (1/x) = 1/40

⇒ 7/4x = 1/40

⇒ x = 70

∴ Viraj can complete the work in = 2x = 2 × 70 = 140 days

Ronit can complete the work in = x = 1 × 70 = 70 days

Together they can finish the work

⇒ (1/140) + (1/70) = 6/280 = 3/140

∴ Time taken by Viraj and Ronit to do the work together is 140/3 days

Alternate Method

The correct answer is option 1, i.e. Chandragupta Vikramaditya.

• The Mehrauli Iron Pillar located near the Qutub Minar belongs to the period of Chandragupta Vikramaditya.
• The Iron pillar of Delhi (Mehrauli Iron Pillar) is 7.2 m which is equal to 23 ft and 8 inches.
• It is also known as Kirti Stambha.
• It is originally erected and dedicated as 'dhvaja' (banner) to Hindu deity Lord Vishnu.
• Chandragupta Vikramaditya was also known as Chandragupta II.
• Chandragupta Vikramaditya was one of the most powerful emperors of the Gupta Empire in northern India.

The correct answer is Ernest Rutherford.

Key PointsErnest Rutherford

• E. Rutherford (1871-1937) was born at Spring Grove on 30 August 1871.
• He was known as the ‘Father’ of nuclear physics.
• He is famous for his work on radioactivity and the discovery of the nucleus of an atom with the gold foil experiment.
• He got the Nobel prize in chemistry in 1908.

J.J. Thomson

• J.J. Thomson (1856- 1940) a British physicist was born in Cheetham Hill, a suburb of Manchester, on 18 December 1856.
• He was awarded the Nobel prize in Physics in 1906 for his work on the discovery of electrons.
• He directed the Cavendish Laboratory at Cambridge for 35 years and seven of his research assistants subsequently won Nobel prizes.

Neils Bohr

• Neils Bohr (1885-1962) was born in Copenhagen on 7 October 1885.
• He was appointed professor of physics at Copenhagen University in 1916.
• He got the Nobel prize for his work on the structure of the atom in 1922.

The logic followed here is:

The total number of letters is the code of that word.

• JUNIOR is written as 6.
• the total number of letters in JUNIOR is 6.

And, 

• LABOURER is written as 8.
• Here, the total number of letters is the code of that word.

Similarly,

• JOSEPHINE is written as 9.
• the total number of letters in JOSEPHINE is 9.

Hence, "option 1" is the correct answer.

Shortcut Trick

Find the prime factors of each number: 15 = 3 × 5, 18 = 2 × 3², 24 = 2³ × 3.

To find the LCM, take the highest power of all prime factors present.

LCM = 2³ × 3² × 5¹

LCM = 8 × 9 × 5 = 360

∴ The correct answer is 360.

Alternate Method

Given: The numbers are 15, 18, and 24.

Formula Used: Common Division Method for Least Common Multiple (LCM).

⇒ List the numbers: 15, 18, 24.

⇒ Divide by the prime factors 2, 3, and 5 sequentially until all quotients are 1.

⇒ The divisors are: 2, 2, 2, 3, 3, 5.

⇒ LCM = 2 × 2 × 2 × 3 × 3 × 5 = 360.

∴ The correct answer is 360.

Additional Information

HCF (Highest Common Factor)

The largest positive integer that divides each of the integers without leaving a remainder. For 15, 18, 24, the HCF is 3.

LCM and HCF Relation

For any two numbers a and b: a × b = HCF(a, b) × LCM(a, b).

LCM of Fractions

LCM of fractions = (LCM of Numerators) ÷ (HCF of Denominators).

The correct answer is Sanchi.

Key PointsSanchi first solar city in Madhya Pradesh:

• On March 4, 2023, Dr Prabhuram Chaudhary, Minister of Public Health and Family Welfare of Madhya Pradesh, performed Bhoomi Pujan for making Sanchi city a solar city in Nagauri village of Sanchi development block of Raisen district of the state. Hence, Option 1 is correct.
• Public Health and Family Welfare Minister Dr Prabhuram Chowdhary told that Sanchi is world famous for stupas and Buddhist pilgrimage sites.
• Sanchi is being developed as the country's second and the state's first solar city to meet the power requirements and make it self-sufficient in power supply.
• Electricity will be generated for Sanchi city and surrounding rural areas by using solar energy.
• A 3 MW solar plant is being set up in Nagauri and a 5 MW solar plant is in Gulgaon.
• The work of developing Sanchi as a Solar City was to be completed by 15 April 2023.
• Due to some reasons, the deadline for the construction of Solar City has been set as May 3, 2023.

The correct answer is P - waves.

Key Points

• Seismic waves:
• Seismic waves are waves of energy that travel through the Earth's layers.
• Seismic waves are caused by the sudden movement of materials within the Earth, such as slipping along a fault during an earthquake, Volcanic eruptions, explosions, landslides, avalanches, and even rushing rivers can also cause seismic waves.
• Types of seismic waves:
• There are three basic types of seismic waves: P-waves, S-waves, and surface waves.
• P-waves and S-waves are sometimes collectively called body waves.

Additional Information

• P-waves:
• P-waves, also known as primary waves or pressure waves, travel at the greatest velocity through the Earth.
• When they travel through the air, they take the form of sound waves – they travel at the speed of sound (330 ms-1) through the air but may travel at 5000 ms-1 in granite.
• Because of their speed, they are the first waves to be recorded by a seismograph during an earthquake.
• S-waves:
• S-waves, also known as secondary waves, shear waves, or shaking waves, are transverse waves that travel slower than P-waves.
• In this case, particle motion is perpendicular to the direction of wave propagation.
• Surface waves:
• Surface waves are similar in nature to water waves and travel just under the Earth’s surface.
• They are typically generated when the source of the earthquake is close to the Earth’s surface.
• Although surface waves travel more slowly than S-waves, they can be much larger in amplitude and can be the most destructive type of seismic wave.
• There are two basic kinds of surface waves:
• Rayleigh waves, also called the ground roll, travel as ripples similar to those on the surface of the water.
• Love waves cause horizontal shearing of the ground. They usually travel slightly faster than Rayleigh waves.

The total number of students in the row is 16.

Reeta's position = 11^th from the right of the row.

so, Reeta's position = (16 - 11) + 1 i.e. 6^th from the left of the row.

Given, Madhuri is 14^th from the left.

So, there have 7 students between Reeta and Madhuri.

As Riya is exactly in the middle of Reeta and Madhuri.

The diagram will follow:

Therefore, the position of Riya from the left 

= Reeta's position from left + 4

= 6 + 4

= 10^th.

Hence, the correct answer is "10^th".

Given:

The sum becomes five times itself

Time = 8 years

Formula Used:

Simple interest = (P × R × T)/100

P → Principal

R →Rate of interest

T →Time 

Calculation:

Let the sum of money be P

After 8 years it becomes 5 times.

The simple interest = 5P – P = 4P

4P = (P × R × 8)/100

R = 400/8 = 50%

∴The Rate of interest per annum is 50%

The correct answer is Satpura National Park.

Key Points

• Satpura National Park is famous for Black deer.
• The park extends from Satpura hills in the Hoshangabad district and is part of Pachmarhi Biosphere Reserves.
• Satpura National Park was established in 1981.
• It becomes part of the Tiger project in the year 1999.
• Total Area: 524 sq km.

Additional Information

• Kanha Kisli National Park:
• Located in Mandla and Balaghat district
• Total Area: 940 sq km.
• It is the largest national park of Madhya Pradesh
• It was founded as Wildlife Sanctuary in 1933.
• It was established as a National Park in the year 1955.
• In 1974, it was included in the Tiger Project.
• It is the first National Park included in the Tiger Project in MP.
• A maximum number of Tigers is found in this park.
• It is the natural habitat of Barasingha Swamp Dear.
• Hallo and Banjar Valley are situated here.
• Park Interpretation Scheme is being launched in this National Park with the help of USA.
• Sanjay Gandhi National Park:
• Located in Sidhi and some parts of Chhatisgarh.
• In Chhatisgarh, it is known as Guru Ghasidas National Park.
• Established as National Park in 1981.
• Included in Project Tiger in the year 2008.
• It was the largest national park before the division of Madhya Pradesh.
• Madhav National Park: 
• Located in Shivpuri.
• Established in 1958 as National Park.
• Famous for forest density and good roads.
• Sakhya Sagar lake is situated here.
• George Castle is situated in this park.

The correct answer is Beriberi.

Beriberi:

• It is a disorder that can occur when a person lacks thiamine or vitamin B-1.
• The deficiency in this nutrient can lead to lasting damage to the nervous system and heart.

Answer: Option 1 i.e., only assumption I is implicit.

I. Environmental activists are concerned with the welfare of the environment so if they have demanded a ban on plastics, it implies that the use of plastics is negatively affecting the environment. Hence assumption I is implicit.

II. Marine animals form a part of the environment but it is not clear to us about the kind of impact plastics have on them. Hence assumption II is not implicit.

Shortcut Trick

15% of 120 = 18

Given: 30% of Number = 18 + 21 = 39

If 30% → 39, then 10% → 13

So, 100% → 130

∴ The correct answer is 130.

Alternate Method

Given:

15% of 120 = (15 ÷ 100) × 120 = 18

Let the unknown number be 'x'.

⇒ 30% of x = 15% of 120 + 21

⇒ 0.30 × x = 18 + 21

⇒ 0.30x = 39

⇒ x = 39 ÷ 0.30

⇒ x = 3900 ÷ 30

⇒ x = 130

∴ The correct answer is 130.

Additional Information

Percentage Change

To find a value after a percentage increase: Final Value = Initial Value × (1 + r/100).

Base Change Rule

If A is x% more than B, then B is [x/(100+x)] × 100% less than A.

Fraction Equivalents

Always remember common fractions: 15% = 3/20 and 30% = 3/10 for faster calculation.

The correct answer is Kuchipudi.

Key Points

• Kuchipudi is a classical dance form that originated in the village of Kuchipudi in Andhra Pradesh, India.
• It takes its name from the village and has a rich history that dates back several centuries.
• Kuchipudi is known for its dynamic footwork, fast-paced movements, and the blend of dance, music, and acting.
• The dance form encompasses both masculine (Tandava) and feminine (Lasya) aspects and combines elements of Nritta (pure dance), Nritya (expressional dance), and Natya (dramatic aspect).
• Kuchipudi was created as a way to worship Krishna, a Hindu deity.

Additional InformationBharatanatyam-

• Bharatanatyam is a classical dance form that originated in Tamil Nadu.
• It is characterized by intricate footwork, hand gestures, facial expressions, and elaborate costumes.
• Bharatanatyam is known for its technical precision and expressive storytelling.

Mohiniyattam-

• Mohiniyattam is a classical dance form from the state of Kerala.
• It is predominantly performed by female dancers and is known for its graceful movements and subtle expressions.
• Mohiniyattam combines elements of dance, music, and drama to convey stories from Hindu mythology.

Manipuri-

• Manipuri is a classical dance form from the northeastern state of Manipur.
• It is deeply rooted in the traditions and mythology of Manipur and reflects the region's cultural heritage.
• Manipuri dance is characterized by its graceful and gentle movements, intricate hand gestures, and devotion to Lord Krishna and Radha.

The correct answer is I × V.

Key Points

• The power in an electrical circuit is calculated using the formula, \(P=IV\), where I is the current and V is the voltage.
• This formula represents the rate at which electrical energy is converted into another form of energy.
• The unit of power is the watt (W), where 1 watt is equal to 1 ampere of current flowing through a potential difference of 1 volt.
• This relationship is derived from Ohm's Law and the definition of power in physics.

Additional Information

• Ohm's Law
• Ohm's Law states that, \(V=IR\) where V is the voltage, I is the current, and R is the resistance.
• This fundamental principle is crucial for analyzing electrical circuits.
• Watt
• The watt (W) is the SI unit of power.
• It is defined as one joule per second.
• Electrical Energy
• Electrical energy is the energy derived from electric potential energy or kinetic energy.
• It is used to power various devices and systems.
• Power in Resistive Circuits
• In purely resistive circuits, the power dissipated is purely due to resistance.
• The power formula \(P=I^2R\) can also be used in such cases.

We can see from the given figure that, the question figure can be found only in the option 3 figure. Rest all of the figure does not contain two diagonals.

Shortcut Trick

56% of Y = 182

Divide both sides by 14 to simplify:

4% of Y = 13

Multiply by 25 to find 100%:

100% of Y = 13 × 25 = 325

∴ The correct answer is 325.

Alternate Method

Given:

Percentage = 56%

Value of 56% = 182

Formula Used:

Total Value (Y) = (Given Value ÷ Percentage Rate) × 100

0%
56% = 182
100% = Y

Total length represents the unknown value Y
Y = (182 ÷ 56) × 100

Calculations:

⇒ 56% of Y = 182

⇒ (56/100) × Y = 182

⇒ Y = (182 × 100) ÷ 56

⇒ Y = 18200 ÷ 56

⇒ Y = 325

∴ The correct answer is 325.

Additional Information

Percentage to Fraction Conversion

To convert a percentage to a fraction, divide by 100. Example: 56% = 56/100 = 14/25.

Finding the Base Value

If x% of a number is A, then the number is (A × 100) ÷ x. This is the standard base-finding formula in percentage problems.

Successive Percentage Change

When a value is increased by a% and then by b%, the net percentage change is given by [a + b + (a × b)/100]%.

The correct answer is Residual Mountain.

Key Points

• Residual Mountain
• Mountain which is worn down due to a process of erosion for a long time by agents like wind, air, water.

Important Points

• Graben

• Graben is a depressed block of the crust of a planet due to internal disturbances.

• Horst

• A horst is a raised fault block bounded by normal faults.

• A horst is a raised block of the Earth's crust that has lifted or has remained stationary, while the land on either side (graben) has subsided.

• Rift Valley

• A rift valley is a linear-shaped lowland between several highlands or mountain ranges created by the action of a geologic rift or fault. A rift valley is formed on a divergent plate boundary, a crustal extension or spreading apart of the surface, which is subsequently further deepened by the forces of erosion.

Additional Information

• Internal forces of the earth result in earthquakes and volcanoes.
• The forces which originate from within the earth’s crust or inside the earth are called internal or endogenetic forces.
• The sources providing them energy are the internal heat, chemical reactions taking place within the earth.

The correct answer is Henry.

• Henry is the SI unit of mutual inductance.

Key Points

• Mutual Inductance is the interaction of one coil's magnetic field on another coil as it induces a voltage in the adjacent coil.
• It is the basic operating principle of the transformer, motors, generators, and many other electrical components that interact with another magnetic field.
• The mutual inductance between the two coils can be greatly increased by positioning them on a common soft iron core or by increasing the number of turns.

Additional Information

• Weber is the SI unit of magnetic flux.
• Farad is the SI unit of electrical capacitance.
• Tesla (T) is SI unit of magnetic flux density or magnetic field strength.

• The correct answer is Option 3: take out another pen carried by him and finished the examination.

• Qualities Projected in this situation:  (Effective intelligence and Organising abilities).

Key Points

• Checklist for attempting SRT questions:

1. Read the question and options carefully.
2. Look for options that are realistic, optimistic, and reflect officer-like qualities.
3. Do not skip any situation.
4. Relegate the negative sentences and choose the most logical option among the remaining. As time is an important factor, hence your thinking ability should be swift.
5. React quickly and be logical.

Additional Information

Officer qualities:

Given:

The lengths of the three sides of a triangle are in the ratio of 2 : 2 : 3.

Calculation:

Let the sides be 2x, 2x, and 3x

2x + 2x + 3x = 42

⇒ 7x = 42

⇒ x = 6

So, the length of the largest side = 6 × 3

⇒ 18 cm

∴ The length of the largest side is 18 cm.

Environmental protection refers to the practice of safeguarding the natural environment and its resources from degradation, pollution, overexploitation, and other detrimental impacts caused by human activities.

Key Points

• The goal is to ensure the sustainable use of natural resources, preserve biodiversity, and maintain the overall health and balance of ecosystems.
• Environmental protection involves adopting measures to minimize pollution, conserve energy, manage waste responsibly, protect endangered species, and promote sustainable practices in industries, agriculture, and daily life.
• It also emphasizes the importance of environmental awareness, education, and policies to address global challenges like climate change and loss of biodiversity.

The correct answer is Fluoridation.

Key Points

• Water fluoridation is the process of adjusting the amount of fluoride in drinking water to a level recommended for preventing tooth decay.
• Fluoride has been proven to protect teeth from decay.
• Bacteria in the mouth produce acid when a person eats sugary foods.
• This acid eats away minerals from the tooth’s surface, making the tooth weaker and increasing the chance of developing cavities.
• Fluoride helps to rebuild and strengthen the tooth’s surface, or enamel.
• Water fluoridation prevents tooth decay by providing frequent and consistent contact with low levels of fluoride.
• Fluoride stops cavities from forming and can even rebuild the tooth’s surface.

Additional Information

• Iodisation
• ​Salt iodization has been the preferred strategy to control and eliminate iodine deficiency disorders (IDD).
• The World Health Organization (WHO) recommends that the salt must have an iodine content of 15 parts per million (ppm) or more.
• Chlorination​
• ​Chlorination is the process of adding chlorine to drinking water to kill parasites, bacteria, and viruses.
• Chlorine levels up to 4 milligrams per liter (mg/L or 4 parts per million (ppm)) are considered safe in drinking water.
• Carbonization ​
• ​Carbonization is the conversion of organic matter like plants and dead animal remains into carbon through destructive distillation.
• The gradual process of coal formation from dead vegetation is known as carbonization.

The pattern followed here is shown below:

4 × 3 - 2 = 12 - 2 = 10

10 × 3 - 2 = 30  - 2 = 28

28 × 3 - 2 = 84 - 2 = 82

82 × 3 - 2 = 246 - 2 = 244 

244 × 3 - 2 = 732 - 2 = 730

So, 28 will complete the series.

Hence,"28"  is the correct answer.

Shortcut Trick

We can solve this instantly by checking the given options against the conditions.

Condition 1: The ratio of the two numbers must be 5 : 9.

Condition 2: (Greater number + 6) = 6 × (Smaller number − 6).

Testing Option 2 (10 and 18): (18 + 6) = 24 and (10 − 6) = 4.

Since 24 = 6 × 4, both conditions are perfectly satisfied.

∴ The correct answer is 10 and 18.

Alternate Method

Given:

Ratio of two numbers = 5 : 9

New greater number = Original greater + 6

New smaller number = Original smaller − 6

Calculations:

⇒ Let the original smaller number be 5x and the greater number be 9x.

⇒ According to the given condition:

⇒ 9x + 6 = 6 × (5x − 6)

⇒ 9x + 6 = 30x − 36

⇒ 30x − 9x = 36 + 6

⇒ 21x = 42

⇒ x = 2

⇒ Smaller number = 5 × 2 = 10

⇒ Greater number = 9 × 2 = 18

∴ The correct answer is 10 and 18.

Additional Information

Ratio & Proportion Basics

A ratio represents a quantitative relation between two amounts, showing the number of times one value contains or is contained within the other. It is primarily used to assign a common variable to the actual values.

Cross-Multiplication Method

Often used in ratio problems where a constant is added or subtracted to the terms of a ratio to get a new relation. Constructing linear equations effectively helps find the missing variables.

Ages and Numbers Problems

Questions involving ages or generic numbers often use a common multiplier 'x' to represent actual baseline values from a given ratio before applying arithmetic conditions.

The correct answer is 1946.

Important Points

• Full form of UNICEF- United Nations International Children's Emergency Fund / United Nations Children's Fund.
• UNICEF was created by United Nations General Assembly on 11 Dec 1946.
• UNICEF is the successor of the International Children's Emergency Fund (ICEF) which was created in 1946 by the U.N. Relief Rehabilitation Administration with the prime objective of providing immediate relief to children and mothers affected by World War II.
• The primary objective of the agency is to provide humanitarian and development aid to children worldwide.
• UNICEF is having more than 150 country offices across the globe & having a presence in 192 countries & Territories.
• Via a specific partnership mechanism established with the host country, UNICEF depends on national offices to help carry out its mission.

                  The UNICEF Flag

The correct answer is Aperture

Key Points

• Aperture refers to the opening of the diaphragm of a lens that spatially limits the propagation of light.
• It is a crucial component in optics, determining the amount of light that enters the lens and thereby affecting the image's brightness and depth of field.
• A larger aperture allows more light to pass through, which is beneficial in low-light conditions but may result in a shallower depth of field.
• A smaller aperture allows less light, providing a greater depth of field but requiring more light for a proper exposure.

Additional Information

• Aperture is usually expressed as an f-number (e.g., f/2.8, f/16), which is the ratio of the lens's focal length to the diameter of the aperture.
• The concept of aperture is not only limited to photography but is also used in various optical instruments like telescopes and microscopes.
• Adjusting the aperture is one of the primary methods photographers use to control exposure and achieve desired artistic effects in their images.

The logic followed here is:

So, 122 will come next in the given series.

Hence, the correct answer is 'Option 1'.

Shortcut Trick

Total Distance = 325 km

Time 1 = 125 ÷ 25 = 5 hours

Time 2 = (325 − 125) ÷ 40 = 200 ÷ 40 = 5 hours

Average Speed = Total Distance ÷ Total Time = 325 ÷ (5 + 5) = 32.5 km/hr

∴ The correct answer is 32.5 km/hr.

Alternate Method

Given:

First part distance (d₁) = 125 km, Speed (s₁) = 25 km/hr

Total distance (D) = 325 km, Speed (s₂) = 40 km/hr

Formula Used:

Average Speed = Total Distance ÷ Total Time

Time = Distance ÷ Speed

Calculations:

⇒ Remaining distance (d₂) = Total Distance − d₁

⇒ d₂ = 325 − 125 = 200 km

⇒ Time taken for first part (t₁) = 125 ÷ 25 = 5 hours

⇒ Time taken for second part (t₂) = 200 ÷ 40 = 5 hours

⇒ Total Time (T) = t₁ + t₂ = 5 + 5 = 10 hours

⇒ Average Speed = 325 ÷ 10 = 32.5 km/hr

∴ The correct answer is 32.5 km/hr.

Additional Information

Average Speed (Equal Distances)

If a person covers two equal distances at speeds x and y, the average speed is (2xy) ÷ (x + y).

Average Speed (Equal Time)

If a person travels at speeds x and y for equal intervals of time, the average speed is (x + y) ÷ 2.

Relative Speed

For two objects moving in the same direction, relative speed is |s₁ − s₂|. In opposite directions, it is s₁ + s₂.

The correct answer is Ministry of Drinking Water and Sanitation.

Key Points

• The Ministry of Drinking Water and Sanitation (MDWS) launched the 'Ganga Gram Project'.
• This project is for sanitation based integrated development of all 4470 villages along the River Ganga,  at a multi-stakeholder sammelan held at Vigyan Bhawan, New Delhi today.
• The Ganga Gram Swachhta Sammelan was attended by more than 1400 delegates including 500 village sarpanches from all five Ganga States (Uttarakhand, Uttar Pradesh, Bihar, Jharkhand and West Bengal), State and District government officials, NMCG Members and Ganga Swachhta Manch volunteers.
• Source: Click

The correct answer is Magnetism.

Key Points

• Moving electric charges, such as in a current-carrying wire, generate a surrounding magnetic field, as Ampere's Law explains.
• The Lorentz force governs the interaction between electric currents and magnetic fields, forming the foundation of electromagnetism.
• Electromagnetism is one of the four fundamental forces of nature, unifying electric and magnetic phenomena through Maxwell's Equations.
• Electromagnetic principles are applied in devices like electric motors, generators, and inductors, which are crucial in modern technology.
• Electromagnetic Waves: Oscillating electric and magnetic fields travel as waves, forming the basis of technologies like radio communication, microwaves, and optics.

Additional Information

The Mirror image is as follows:

Hence, the correct answer is "Option 3".

Given:

\(36 \div 4\;of\frac{1}{2} + \frac{3}{4} \times \frac{3}{2}\)

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

\(36 \div 4\;of\frac{1}{2} + \frac{3}{4} \times \frac{3}{2}\)

\(36 \div 2 + \frac{3}{4} \times \frac{3}{2}\)

\(= 18 + \frac{9}{8}\)

\( = \frac{{153}}{8} = 19\frac{1}{8}\)

∴ \(19\frac{1}{8}\)

The correct answer is Option 3.

Key Points

The climate of Madhya Pradesh

• It has a subtropical climate with three distinct seasons: winter (December to February), summer (March to May) and the rainy season (June to October). Hence, Statement 1 is correct.
• Madhya Pradesh experiences a monsoon climate, receiving most rainfall from the southwest monsoon during the summer. Hence, Statement 2 is correct.
• The southeastern part of the state receives relatively higher rainfall.
• The southeastern part of Madhya Pradesh, including districts like Mandla, Balaghat, and Chhindwara, receives relatively higher rainfall. This region is influenced by the southwesterly monsoon winds, resulting in more rainfall compared to other parts of the state.
• The climate of Madhya Pradesh is influenced by the Tropic of Cancer which passes through its central part. Hence, Statement 4 is correct.
• The southern parts of Madhya Pradesh have a tropical wet and dry climate with a distinct dry season in the winter. Hence, Statement 3 is not correct.
• The Dhar district of Madhya Pradesh is located in the temperate zone. It receives the majority of its annual rainfall during the southwest monsoon period, which is from June to September.

Raman Effect was jointly discovered by Sir C.V. Raman and K.S. Krishnan. According to Raman effect, when a beam of light traverses a dust-free, chemical compound, a fraction of the light emerges in directions other than that of the incident. Most of this scattered light is of unchanged wavelength however a small part has different wavelengths from that of the incident light. This phenomenon was discovered by Raman and Krishnan in 1928. The change in wavelength of light due to this scattering is studied through Raman spectrometer. 

Only Conclusion 3 follows. According to the statement, National Aluminium Company has moved Georgia from a position of shortage in the past to self-sufficiency in the present. This means that previously, Georgia had to import aluminium. So, the conclusion I follow. Also, it can be deduced that if production increases at the same rate, Georgia can export it in future. So, conclusion II also follows.

Shortcut Trick

Using the chain rule (M₁D₁ = M₂D₂):

⇒ 40 × 56 = 32 × D₂

⇒ D₂ = (40 × 56) ÷ 32

⇒ D₂ = 2240 ÷ 32 = 70

∴ The correct answer is 70 days.

Alternate Method

Calculations:

⇒ Assuming the efficiency of 1 mechanic is 1 unit/day.

⇒ Total Work = Efficiency of 40 Mechanics × Days

⇒ Total Work = 40 × 56 = 2240 units

⇒ Days required by 32 Mechanics = Total Work ÷ Efficiency of 32 Mechanics

⇒ Days = 2240 ÷ 32

⇒ Days = 70

∴ The correct answer is 70 days.

Additional Information

Chain Rule (MDH Formula)

(M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂, where M is Men, D is Days, H is Hours, and W is Work.

Inverse Proportion

When the amount of work is constant, the number of workers is inversely proportional to the number of days required (M × D = Constant). More mechanics will take fewer days, and fewer mechanics will take more days.

The correct answer is Assam.

Key Points

• Nameri Tiger Reserve
• The Nameri Tiger Reserve (NTR) is situated in the northern part of the Sonitpur district of Assam.
• It is situated along the foothills of Arunachal Pradesh.
• The habitat is biologically rich and is famous for the **white-winged wood duck.**​

Additional Information

• Other National Parks in Assam
• Kaziranga National Park
• Dibru - Saikhowa National Park
• Rajiv Gandhi Orang National Park
• Manas National Park
• Nameri National Park
• ​​Project Tiger was launched by the Indira Gandhi government in 1973 from the Jim Corbett National Park in Uttarakhand.
• The tiger is an endangered species in the world.

Important Points 

The correct answer is eukaryotic cells.

Key Points

• Eukaryotic cells are characterized by a well-organized nucleus enclosed by a nuclear membrane.
• This is where the cell's DNA is stored.
• These cells are generally larger and more complex than prokaryotic cells.
• Eukaryotic cells have various types of organelles, including mitochondria, endoplasmic reticulum, and Golgi apparatus, which are enclosed by membranes and have specific functions.
• Eukaryotic cells can be found in a wide variety of organisms, including plants, animals, and fungi.
• The complex structure of eukaryotic cells allows for compartmentalization and specialization of functions, which enables these cells to perform more complex tasks than prokaryotic cells.

Additional Information

In option 1, 2 and 3, three is added in the positional value of first letter to get the second letter, then again three is added in the positional value of second letter to get the third letter and then four is subtracted from the positional value of third letter to get the fourth letter.

But in option 4, three is added in the positional value of first letter to get the second letter, then again three is added in the positional value of second letter to get the third letter and then five is subtracted from the positional value of third letter to get the fourth letter.

The pattern followed here is :

Hence, C-F-I-D is the correct answer.

Given:

The ratio of the father's age to the son’s age is 3 ∶ 1

The product of their ages is 147.

Calculation:

Let the age of father is = 3x

The age of son is = x

According to question, 

3x × x = 147

3x² = 147

x² = 147/3 = 49

x = √49

x = 7

So, father's age is = 3 × 7 = 21 years

Son's age = 7 years

The age of father after 5 years = 21 + 5 = 26 years

The age of son after 5 years = 7 + 5 = 12 years

Ratio = 26 ∶ 12 = 13 ∶ 6

Hence, the correct answer is "13 : 6".

The correct answer is Bhagat Singh.

Key PointsBhagat Singh:

• Bhagat Singh is also known as Shahid-e-Azam.
• Born as Bhaganwala on the 28^th September 1907, Bhagat Singh grew up in a petty-bourgeois family of Sandhu Jats settled in the Jullundur Doab district of Punjab.
• In 1924 in Kanpur, he became a member of the Hindustan Republican Association, started by Sachindranath Sanyal a year earlier.
• The main organiser of the Association was Chandra Shekhar Azad and Bhagat Singh became very close to him.
• In 1925, Bhagat Singh returned to Lahore and within the next year he and his colleagues started a militant youth organisation called the Naujawan Bharat Sabha.
• In April 1926, Bhagat Singh established contact with Sohan Singh Josh and through him the 'Workers and Peasants Party' which brought out the monthly magazine Kirti in Punjabi.
• In 1928, Bhagat Singh changed the name of the Hindustan Republican Association to the Hindustan Socialist Republican Association (HSRA).
• To take revenge for the death of Lala Lajpat Rai, Bhagat Singh and his associates plotted the assassination of James A. Scott, the Superintendent of Police. However, the revolutionaries mistakenly killed J.P. Saunders. The incident is famously known as Lahore Conspiracy case (1929).
• Bhagat Singh and B.K. Dutt threw a bomb on 8^th April, 1929 in the Central Legislative Assembly, in protest against the passing of two repressive bills, the Public Safety Bill and the Trade Dispute Bill.
• Bhagat Singh was arrested for the murder of J.P. Saunders and bomb manufacturing in the Lahore Conspiracy case. He was found guilty in this case and was hanged on 23^rd March, 1931 in Lahore along with Sukhdev and Rajguru.
• Every year, 23^rd March is observed as Martyrs’ Day as a tribute to freedom fighters Bhagat Singh, Sukhdev, and Rajguru.

The correct answer is ₹100 crore.

Key Points

NABARD:

• NABARD came into existence on 12 July 1982 by transferring the agricultural credit functions of RBI and refinance functions of the then Agricultural Refinance and Development Corporation (ARDC).
• Set up with an initial capital of Rs.100 crore, its’ paid-up capital stood at Rs.14,080 crore as of 31 March 2020.
• Initially, it is owned by the Government of India and RBI.
• NABARD today is fully owned by the Government of India.
• Vision - Development Bank of the Nation for Fostering Rural Prosperity.
• Mission - Promote sustainable and equitable agriculture and rural development through participative financial and non-financial interventions, innovations, technology, and institutional development for securing prosperity.

Additional Information

• The Reserve Bank of India (RBI) at the insistence of the Government of India, constituted a Committee to Review the Arrangements For Institutional Credit for Agriculture and Rural Development (CRAFICARD) to look into these very critical aspects.
• The Committee was formed on 30 March 1979, under the Chairmanship of Shri B. Sivaraman, a former member of Planning Commission, Government of India.
• The Committee’s interim report, submitted on 28 November 1979, outlined the need for a new organizational device for providing undivided attention, forceful direction, and pointed focus to credit-related issues linked with rural development.
• Its recommendation was the formation of a unique development financial institution that would address these aspirations and the formation of the National Bank for Agriculture and Rural Development (NABARD) was approved by the Parliament through Act 61 of 1981.

Two ends of a battery is called terminals. While two ends of a magnet is called poles.

Thus, ‘Magnet’ is related to ‘Poles’.

Given:

Radius of big spherical ball = 4 cm

Radius of small spherical ball = 2 cm

Formula Used:

Volume of sphere = 4/3πr³,  here r = radius

Number of balls = Volume of a big sphere/Volume of a small sphere

Calculation:

Let n be the number of small spherical balls

Volume of big spherical ball = n × Volume of a small spherical ball

4/3π(4 cm)³ = n × 4/3π(2 cm)³ 

⇒ 8n = 64

⇒ n = 64/8 

⇒ n = 8

∴ 8 small spherical balls are formed from a big spherical ball.

Concept:

• Groundwater is the water found under the ground in soil spaces, cracks of earth's crust etc
• The presence of groundwater in soil enables the plant to take it up to fulfil its water requirements
• It also indicates a healthy soil
• Groundwater is the main source of drinking water as well as irrigation in many parts of the country.

Explanation:

• The rainwater and water from other sources such as rivers and ponds seeps through the soil and fills the empty spaces and cracks deep below the ground.
• The process of seeping water into the ground is called infiltration.
• The groundwater thus gets recharged by this process.
• At places, the groundwater is stored between layers of hard rock below the water table. This is known as an aquifer.
• Water in the aquifers can be usually pumped out with the help of tube wells or handpumps.

Additional Information

• Groundwater is one of the most important water source in the country especially in rural areas
• However, with increasing stress on natural resources because of human demand, groundwater resources are being depleted.
• They have also got polluted because of the use of chemicals in the soil
• A large part of the country's economy depends on agriculture, which is dependent on groundwater.
• Hence there is a need to conserve groundwater.
• According to recent reports, 22% of groundwater has already dried up.
• Urban cities are facing huge water shortage because of low groundwater levels, especially in Tamil Nadu.

The correct answer is Insects.

Key Points

• All living organisms respire to get energy from food.
• The process of breakdown of food in the cell with the release of energy is called cellular respiration.
• A network of tubes called tracheae are the respiratory organs of insects.
• Tracheal tubes help insects to transport atmospheric air within the body.
• Oxygenated air rushes through spiracles into the tracheal tubes, diffuses into the body tissue, and reaches the body cell.
• Carbon dioxide from the cells moves to the tracheal tubes and moves out through spiracles.

Additional Information

• Reptiles, birds, and mammals respire through the lungs.
• Amphibians like frogs can respire through their moist skin.
• Earthworms breathe through their moist skins(cuticle).
• Fishes use gills for gas exchange.
• Mussels breathe through their gills.

The logic followed here is:

59 : 44 → 5³ – 9² = 125 – 81 = 44

Similarly,

78 : ? → 7³ – 8² = 343 – 64 = 279

Hence, ‘279’ is the correct answer.

Shortcut Trick
If one pipe fills a tank in x hours and another pipe empties it in y hours (where y > x), the total time taken to fill the tank together is given by:
⇒ Time = (x × y) ÷ (y − x)
⇒ Time = (4 × 6) ÷ (6 − 4)
⇒ Time = 24 ÷ 2 = 12 hours
∴ The correct answer is 12 hours.

Alternate Method
Given:
Time taken by Pipe A to fill the tank = 4 hours
Time taken by Pipe B to empty the tank = 6 hours
Formula Used:
Total Capacity = LCM of individual times
Efficiency = Total Capacity ÷ Time

Pipe
Hours
Total Capacity (Units)
Efficiency (Units/hr)

A (Filling)
4
12
+3

B (Emptying)
6
−2

Calculations:
⇒ Net combined efficiency = +3 − 2 = +1 unit/hour
⇒ Total time required to fill the tank = Total Capacity ÷ Net Efficiency
⇒ Total time = 12 ÷ 1 = 12 hours
∴ The correct answer is 12 hours.

Additional Information
Two Pipes Filling Simultaneously
If two individual pipes can fill a tank in x and y hours respectively, the combined time taken to fill the tank is (x × y) ÷ (x + y).
Emptying Pipe Concept (Negative Work)
The efficiency of an emptying pipe, leak, or outlet is always taken as negative because it acts against the process of filling the cistern.
Work and Efficiency Relation
Efficiency is inversely proportional to the time taken. If pipe A is twice as fast as pipe B, it takes half the time compared to B to complete the same work.

The correct answer is M.Adhikari.

Key Points

• The Advocate General office of M.P. came into existence in November 1956 upon the formation of the State of M.P. as per the State Re-Organisation Act 1956 when the High Court of M.P. was established.
• On the formation of the new State of M.P., Shri M. Adhikari became the first Advocate General for the State of Madhya Pradesh.
• The AG's Office presents all the cases in which the Govt. of Madhya Pradesh is one of the parties, in the High Court of M.P. Central Administrative Tribunal (CAT).

Important Points

• Prashant Singh is the Advocate General at present. (Feb 2022)

Additional Information

The correct answer is Amino acids.

Key Points

• In animal digestion proteins breaks downs to form amino acid.
• Amino acids are responsible for the breaking down of food.
• Amino acids are the building blocks of life.
• Examples of Amino acids are Glutamine, Tyrosine, and Tyrosine.
• Lipid molecules are a combination of oil and fats.
• Sugar is a source of energy for the human body.

The following symbols are used:

Let Anjali’s sister be X,

Anjali’s sister's brother be Y and Y’s father be Z.

From the above figure it can be seen that Y is the brother of Anjali.

Thus the required relationship is brother.

Given:

Coins = 480 

Conis of 1 Rupee, 50 Paise & 25 Paise

Value ration = 2 : 3 : 4

Calculation:

Ratio  =  1 Rs : 50 p : 25 p

Value =     2 : 3 : 4

Coin   =     2 : 6 : 16

⇒ 1 : 3 : 8

Total coins are 12x

⇒ 12x = 480

⇒ x = 480/12

⇒ x = 40

⇒ 1 : 3 : 8

⇒ 40 : 120 : 320

Coin of 1 Rupee = 40 

Coin of 50 Paise = 120

Coin of 25 Paise = 320

The value of 40 coins of 1 rupee is Rs.40

The value of 120 coins of 50 paise is Rs.60

The value of 320 coins of 25 paise is Rs.80

Total Value is (40 + 60 + 80) = 180

∴ The answer is Rs.180.

Alternate Method Let the value of 1 Rupee, 50 Paise, and 25 Paise coins be 2x, 3x, and 4x respectively.

Number of coins = Total value/value of each coin

Therefore,

Number of 1 Rupees coins = 2x/1 = 2x 

Number of 50 paise coins = 3x/(1/2) = = (3x) × 2 = 6x 

Number of 25 paise coins = 4x/(1/4) = = (4x) × 4 = 16x  

Since total number of coins = 480

2x + 6x + 16x = 480

24x = 480

x = 20

Therefore, the total amount 

⇒ 2x + 3x + 4x = 9x 

⇒ 9 × 20 = 180 Rs.

Shortcut Trick  

Total value of all coins together = Rs. (40 + 60 + 80) = Rs. 180

The correct answer is Four.

• Four parathyroid glands are present on the backside of the thyroid gland in humans​.

Key Points

• Parathyroid Gland:
• The glands are small pea-sized glands located in the neck just behind the butterfly-shaped thyroid gland.
• Everyone has four parathyroid glands, with two parathyroid glands lying behind each 'wing' of the thyroid gland.
• Parathyroid hormone: This hormone is secreted when there is a deficiency of calcium in the blood.
• Calcitonin: This hormone is released when there is an excess of calcium in the blood.
• A hormone secreted by the parathyroid gland controls the quantity of calcium in the blood.

Additional Information

• Exocrine glands: Glands which have duct are called exocrine glands. Secretion of enzymes passes through it.
• Example: Lactic gland, Sweat gland.
• Endocrine glands: These are ductless glands. Hormones are secreted by these glands.
• Hormones are sent to the different parts of the body through blood plasma.
• Example: Pituitary gland, Thyroid gland.

The correct answer is  Gamma rays.

Key Points

Alpha particles

• Charge - Positive
• Velocity - 2*10^7  m/s.
• It is the same as the Helium nucleus.
• It has very low penetrating power.
• It has very high ionizing power.

Beta particles

• Charge - Negative.
• Velocity = 2*10^8 m/s.
• It is the same as Electrons.

Gamma particles

• It is charge-less.
• Velocity = 3*10^8 m/s.
• It is the same as an electromagnetic wave
• It has a very high penetrating power.
• It has very low ionising power.

The logic followed here is:

Similarly,

Hence, "NPRTV" is the correct answer.

Concept used:

Follow BODMAS rule to solve this question, as per the order given below,

Calculation:

 1 - [5 - {2 + (-5 + 6 - 2)2}] = ? 

 1 - [5 - {2 + (-1)2}] = ? 

 1 - [5 - {2 - 2}] = ? 

 1 - [5 - 0] = ? 

 1 - 5 = ? 

∴ ? = - 4

The correct answer is Art and Science of cultivating forest trees.

• Silviculture is the art and science of cultivating forest trees.
• It is the practice of controlling the establishment and management of forest stands.
• The term silviculture comes from the Latin word 'silvi' means forest and 'culture' as in growing.
• It will increase the forest cover necessary for the conservation of wildlife.

The correct answer is Beriberi.

Key Points

• Beriberi is the classical manifestation of chronic dietary deficiency in vitamin B1.
• Before the discovery of thiamine, it was a major health problem in East Asian countries, where polished rice was the staple food.
• Beriberi is a polyneuritis syndrome, mainly affecting the lower limbs.
• Symptoms of “dry” beriberi include weakness and pain in the limbs, weight loss, and partial paralysis.
• In “wet” beriberi, there are also cardiac symptoms, including cardiac insufficiency and enlargement, with a tendency to edema.

According to the question,

Sandeep is 10^th from left and Lalit is 5^th from right.

After interchanging, Sandeep becomes 15^th from the left.

Consider the position of Sandeep,

Sandeep is 15^th from the left and there are 4 boys to the right of Sandeep.

Therefore, the total number of persons in the line = 15 + 4 = 19 boys

Total number of persons in the line = Lalit's position from the right + Lalit's position from the left - 1

⇒ 19 = Lalit's position from the right + 10 - 1

⇒ Lalit's position from the right = 19 - 9

⇒ Lalit's position from the right = 10

Therefore, Lalit is 10^th from the right.

Hence, the correct answer is 10^th.

Shortcut Trick

Hearts and diamonds make up all the red cards in a standard deck.

Total red cards = 13 (Hearts) + 13 (Diamonds) = 26.

Required Probability = Total red cards ÷ Total cards in deck.

Required Probability = 26 ÷ 52 = 1/2.

∴ The correct answer is 1/2.

Alternate Method

Given:

Total number of cards in a deck, n(S) = 52

Number of heart cards, n(H) = 13

Number of diamond cards, n(D) = 13

Formula Used:

Probability P(E) = Number of favorable outcomes ÷ Total possible outcomes

For mutually exclusive events A and B: P(A or B) = P(A) + P(B)

Calculations:

⇒ Probability of getting a heart, P(H) = 13 ÷ 52 = 1/4

⇒ Probability of getting a diamond, P(D) = 13 ÷ 52 = 1/4

⇒ Since a single drawn card cannot be both a heart and a diamond, these are mutually exclusive events.

⇒ Probability of getting a heart or diamond = P(H) + P(D)

⇒ P(Heart or Diamond) = 1/4 + 1/4

⇒ P(Heart or Diamond) = 2/4

⇒ P(Heart or Diamond) = 1/2

∴ The correct answer is 1/2.

Additional Information

Standard Deck of Cards

A standard deck consists of 52 cards, divided equally into 4 suits: Hearts (red), Diamonds (red), Clubs (black), and Spades (black). Each suit contains exactly 13 cards.

Mutually Exclusive Events

Two events are mutually exclusive if they cannot occur simultaneously. The probability of either event occurring is the sum of their individual probabilities: P(A or B) = P(A) + P(B).

Face Cards

Jacks, Queens, and Kings are known as face cards. There are 3 face cards per suit, resulting in a total of 12 face cards in a standard 52-card deck.

Independent Events

Two events are independent if the outcome of one does not affect the outcome of the other. For independent events A and B, P(A and B) = P(A) × P(B).

The correct answer is B.V. Doshi.

Key Points

• B.V. Doshi is known as the Father of Indian Architecture.
• Balkrishna Vithaldas Doshi is the first Indian architect to win Pritzker Prize.
• Pritzker Prize is often referred to as the Nobel Prize for architecture.
• B.V Doshi has also been honoured with France’s highest honour for arts the 'Officer of the Order of Arts and Letters' in 2011.
• Balkrishna Vithaldas Doshi is an Indian Architect.
• He is the first Indian who won the Pritzker Prize in 2018.
• The prestigious Pritzker Prize, considered architecture field’s Nobel, has been awarded to renowned Indian architect Balakrishna Doshi for 2018.
• Doshi has designed many educational institutions like IIM Bangalore, IIM Lucknow, etc. and is noted for his contributions to many low - cost housing projects.

The correct answer is Mushroom.

Key Points

• Mushroom
• Mushroom is a Heterotrophic Plant.
• Heterotrophic means which depends on others for food. Hence, Option 2 is correct.
• They cannot make their food themselves as Autotrophs.
• Also, they are a non-green plant that doesn't part in photosynthesis.
• While others are Autotrophs; they can make their food themselves.
• Also, they can take part in photosynthesis as they are green plants
• Mushroom is a Fungi.
• Scientific Name: "Agaricus bisporus" (Edible Mushroom).
• Any of various fungi having a stalk topped by a fleshy, often umbrella-shaped cap.
• Ecology of Mushrooms:
• Sporophores: The spore-producing organ of a fungus or slime mold.
• Two types of Sporophores are: The term Mushroom is used to identify the edible sporophores,
• The term Toadstool is often reserved for inedible or poisonous sporophores.
• Mushrooms contain no chlorophyll which means they can not photosynthesize.
• Mushrooms are a low-calorie source of fibre, protein, and antioxidants.
• Mushrooms are a good source of B vitamins.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. All Rackets are Sticks → False (As Some Rackets are Bats so, All Rackets are Sticks is definitely False as shown below)

II. Some Rackets are not Sticks → False (As Some Rackets are Bats and All Bats are Sticks so, Some Rackets are not Sticks is definitely False as shown below)

III. Some Sticks are Rackets → True (As Some Rackets are Bats and All Bats are Sticks so, Some Sticks are Rackets is True)

∴ Here Conclusion I and II does not form complimentary pairs because both are false and there is no possibility from given statements.

Hence, the correct answer is "Only conclusion III follows".

Shortcut Trick

For an equilateral triangle, distances are equal (d₁ = d₂ = d₃).

Average Speed = 3 ÷ (1/s₁ + 1/s₂ + 1/s₃)

Average Speed = 3 ÷ (1/12 + 1/24 + 1/8) = 3 ÷ [(2 + 1 + 3)/24]

Average Speed = (3 × 24) ÷ 6 = 12 kmph.

∴ The correct answer is 12 kmph.

Alternate Method

Given: Speeds s₁ = 12 kmph, s₂ = 24 kmph, s₃ = 8 kmph. Distance is equal for all sides.

Let the length of each side of the equilateral triangle be the LCM of (12, 24, 8) = 24 km.

⇒ Total Distance = 24 + 24 + 24 = 72 km

⇒ Time taken for side 1 (t₁) = 24 ÷ 12 = 2 hours

⇒ Time taken for side 2 (t₂) = 24 ÷ 24 = 1 hour

⇒ Time taken for side 3 (t₃) = 24 ÷ 8 = 3 hours

⇒ Total Time = 2 + 1 + 3 = 6 hours

⇒ Average Speed = Total Distance ÷ Total Time = 72 ÷ 6 = 12 kmph

∴ The correct answer is 12 kmph.

Additional Information

Average Speed (Equal Distances)

For two equal distances with speeds x and y, Average Speed = 2xy/(x + y). For three equal distances, use the Harmonic Mean formula.

Equilateral Triangle Property

In an equilateral triangle, all three sides are equal in length, which is why we assume the distance for each speed to be identical.

LCM Method for Speed

Assuming distance as the Least Common Multiple of given speeds simplifies calculations by providing whole number time values.

The Correct Answer is ​Measurements for all times, for all people.

In News

• World Metrology Day: 20 May.

Key Points

• World Metrology Day is celebrated every year on May 20.
• It highlights the importance of measurement science (metrology) in everyday life.
• 2025 marks the 150^th anniversary of the Metre Convention.
• The Metre Convention was signed on May 20, 1875 in Paris.
• This agreement laid the foundation for the metric system and global unit standardisation.
• The celebration began in 1999 by the International Committee for Weights and Measures (CIPM).
• The 2025 theme is: "Measurements for all times, for all people."

The correct answer is Cynology.

Key Points

• The scientific study of domestic dogs is called Cynology.
• The Scientific name of Dog is Canis lupus.