MP Police Constable : (2 Dec 2025 Shift 1) Memory-Based Paper (Previous Year Paper)

The correct answer is LignoSat.

In News

• Japan is set to test the world's first wooden satellite named LignoSat.

Key Points

• LignoSat was developed by Kyoto University and Sumitomo Forestry.
• It will be launched next week on a SpaceX rocket to the International Space Station.
• The satellite aims to test how wood withstands the extreme environment of space for six months.
• Wood can burn harmlessly in the atmosphere, offering a sustainable alternative to traditional satellites.

Additional Information

• LignoSat
• The name comes from the Latin word for wood.
• It is an innovative project that combines sustainability with space exploration.
• Takao Doi
• A former astronaut who advocates for using natural materials in space technology.
• Involved in the development of LignoSat as part of a sustainable future initiative.
• Magnolia tree (Japanese honoki)
• The wood used for LignoSat comes from this type of tree.
• It is known for its strength and resistance to shattering.
• Sustainable materials in space
• The concept aims to minimize pollution and use eco-friendly resources in future space missions.
• Wood's natural properties allow it to serve as a potential building material for habitats on other planets.

The correct answer is option 3 i.e. Cu (Copper).

• Bell metal is a hard alloy used for making bells and different musical instruments.
• It is made of 80% copper and 20% tin (Sn) with some amount of Zinc and Lead.
• Bell metal is known for its resonance and attractive sound.
• Some other important alloys are:
• German Silver - Cu + Zn + Ni
• Gun Metal - Cu + Sn + Zn + Pb
• Solder - Pb + Sn
• Brass - Cu + Zn
• Stainless steel - Fe + Cr + Ni + C

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

Conclusions:

I. Some thread is fruit → Does not follow (As all threads are soft and some soft are fruit. So, it is possible but not definitely true)

II. Some fruit is yellow → Follow (As all fruit is yellow. So, as whole fruit comes in yellow therefore it is definitely true)

∴ Here, Only conclusion (II) follow.

Hence, the correct answer is "Option - (3)".

Given:

PQ is a diameter.

∠QOR = 100°

Concept used:

the angle subtended by the chord at the centre of the circle is twice

the angle subtended at any point on the circle's circumference. 

Calculation:

⇒ ∠QOR + ∠ROP = 180°

⇒ ∠ROP = 180 - 100 = 80°

∠ROP = 2 × ∠PSR

⇒ ∠PSR = 80/2 = 40°

∴ The correct answer is 40°.

The correct answer is Narendra Modi.

In News

• Prime Minister Narendra Modi launched Mission Mausam during the 150^th Foundation Day celebration of the India Meteorological Department (IMD).
• The event was held at Bharat Mandapam, New Delhi.

Key Points

• Mission Mausam aims to make India weather-ready and climate-smart through advanced surveillance technologies.
• It will enhance forecast accuracy and provide critical air quality data to support sectors like agriculture and the blue economy.

Additional Information

• The mission includes deploying next-generation radars and advanced surveillance technologies for better weather forecasting.

The correct answer is option 1.

Note: Both hydra and yeast reproduce asexually by budding. Thus, both option 1 and 2 are factually incorrect. But, we have marked the correct answer as Option 1 according to the official answer key.

Source: https://ncert.nic.in/textbook/pdf/gesc108.pdf

Key Points

• Hydra reproduces asexually through a process called budding, not multiple fission.
• Yeast primarily reproduces asexually through budding rather than spore formation.
• Plasmodium is known for reproducing through multiple fission within its host cells.
• Leishmania reproduces asexually through a process called binary fission.
• Each organism has specific methods of asexual reproduction, which are key to their biological processes.

Additional Information

• Budding
• This is a form of asexual reproduction where a new organism develops from an outgrowth or bud on the parent organism.
• Hydra and yeast commonly use this method for reproduction.
• Binary Fission
• This is a method of asexual reproduction where a single organism divides into two parts, each of which becomes a new organism.
• Binary fission is common in prokaryotic organisms such as bacteria and protozoa like Leishmania.
• Multiple Fission
• In this type of asexual reproduction, the parent cell divides into multiple daughter cells simultaneously.
• Plasmodium, the malaria-causing parasite, reproduces using multiple fission within the red blood cells of its host.

The pattern followed here is as follows,

Hence, “H19S” is the correct answer.

Shortcut Trick

Area = (1/2) × d₁ × d₂ ⇒ 216 = (1/2) × 24 × d₂ ⇒ d₂ = 18 m.

Side of rhombus = √[(d₁/2)² + (d₂/2)²]

Side = √[12² + 9²] = √[144 + 81] = √225 = 15 m.

∴ The correct answer is 15 m.

Alternate Method

Given: Area = 216 m², Diagonal 1 (d₁) = 24 m.

Formula Used: Area = (d₁ × d₂) / 2; Side (a) = √[(d₁/2)² + (d₂/2)²]

⇒ 216 = (24 × d₂) / 2

⇒ 216 = 12 × d₂

⇒ d₂ = 216 / 12 = 18 m

⇒ Half of diagonals are 12 m and 9 m.

⇒ In a right-angled triangle formed by the intersection of diagonals:

⇒ Side² = 12² + 9²

⇒ Side² = 144 + 81 = 225

⇒ Side = √225 = 15 m

∴ The correct answer is 15 m.

Additional Information

Properties of Rhombus

All sides are equal and diagonals bisect each other at 90°.

Perimeter of Rhombus

Perimeter = 4 × side = 4a.

Relation between Side and Diagonals

4a² = d₁² + d₂², where 'a' is the side and d₁, d₂ are diagonals.

The correct answer is Larsen & Toubro

In News

• The indigenous light tank Zorawar was developed jointly by the Defence Research and Development Organisation (DRDO) and Larsen & Toubro (L&T).

Key Points

• The prototype of Zorawar is ready and will soon undergo extensive trials.
• The tank is currently powered by a Cummins engine, with a project underway to develop a new engine domestically.
• It is designed to operate in extreme weather and high-altitude conditions with minimal logistic support.
• The tank will be subjected to various trials over the next six months, including tests in summer, winter, and high-altitude environments.
• The development of Zorawar was expedited to meet the Indian Army's needs for a lightweight, agile tank that can be deployed at high altitudes.
• The tank is versatile, built in a modular fashion, and capable of future upgrades, enhancing its tactical and operational mobility.

The correct answer is ​Moon's lower gravitational force.

Key Points

• Weight refers to the force exerted on a body by gravity while Mass refers to the amount of matter in a substance.
• The Earth's Moon has considerably less mass than the Earth itself.
• Not only is the Moon smaller than the Earth, but it is only about 60 per cent as dense as Earth.
• Thus, the gravitational attraction on the Moon is only one-sixth that of the Earth. Hence option 3 is the correct answer.
• As the force gravity exerts on a person determines the weight of a person.
• A person's weight is generally one-sixth of their weight on Earth.
• One thing to note here is that it is only the value of weight that changes from Earth to the moon, while the mass remains the same.

Given : [{(38 × 23) - (4 ÷ 3)} + (6 - 3)] ÷ 2

So, after interchanging the signs :

⇒[{(38 - 23) + (4 × 3)} ÷ (6 + 3)] × 2

⇒[{15 + 12} ÷ (6 + 3)] × 2

⇒[27 ÷ 9] × 2

⇒3 × 2

⇒6

Hence, "6" is the correct answer.

Shortcut Trick

Runs scored in 30 overs = 30 × 5 = 150 runs.

Runs required in remaining 20 overs = 20 × 10 = 200 runs.

Target for the chasing team = 150 + 200 = 350 runs.

First team score = Target − 1 = 350 − 1 = 349 runs.

∴ The correct answer is 349.

Alternate Method

Given:

Total overs = 50

Current progress = 30 overs at 5 runs/over

Remaining requirement = 20 overs at 10 runs/over

Calculations:

⇒ Current Score = 30 × 5 = 150 runs

⇒ Remaining Runs Needed = (50 − 30) × 10 = 20 × 10 = 200 runs

⇒ Total Target = 150 + 200 = 350 runs

⇒ Since the Target is always 1 run more than the First Team Score:

⇒ First Team Score = 350 − 1 = 349 runs

∴ The correct answer is 349.

Additional Information

Run Rate Calculation

Run Rate = Total Runs ÷ Total Overs. It represents the average runs scored per over.

Required Run Rate

Required Run Rate = Remaining Runs Needed ÷ Remaining Overs. This is the pace needed to reach the target.

Target vs Score

In limited-overs cricket, the Target for the team batting second is always (First Team Score + 1).

The correct answer is Kanauj.

Key Points

• Gahadavalas:-
• The Gahadavalas were a dynasty of Indian rulers who held power in the region of Kanauj during the medieval period.
• The Gahadavalas came to power in the 11^th century CE and ruled over Kanauj for several centuries. They were known for their patronage of the arts and their support of Hinduism.
• The Gahadavalas faced numerous challenges during their rule, including invasions by Muslim rulers from the north and internal power struggles. Despite these difficulties, they were able to maintain their hold on Kanauj for several centuries.

Additional Information

• Kanauj:-
• It was an important political and cultural center in northern India during this time.
• It was located on the banks of the Ganges River and was known for its wealth and strategic location.
• Ajmer:-
• It was a city located in present-day Rajasthan that was ruled by various dynasties throughout history.
• Malwa:-
• It was a region in central India that was ruled by the Paramara dynasty during the medieval period.
• Patan:-
• It was a city in present-day Gujarat that was ruled by the Solanki dynasty during the medieval period.

The Correct answer is Equal to its weight.

Explanation:

• The buoyant force acting on an object is equal to the weight of the fluid displaced by the object. In this case, the object is floating, so the buoyant force is equal to the weight of the object.
• The buoyant force is caused by the pressure difference between the top and bottom of the object. The pressure is greater at the bottom of the object because the fluid is denser at the bottom. This pressure difference creates a force that pushes the object upward.
• When the buoyant force is greater than the weight of the object, the object floats. If the buoyant force is less than the weight of the object, the object will sink. If the buoyant force is equal to the weight of the object, the object will rise to the surface of the liquid.

So, the buoyant force acting on an object that floats in a liquid with half of its volume submerged in the liquid is equal to its weight.

Important Points

• When the buoyant force of liquid is less than the weight of the object, the object will be submerged or sank.
• When the buoyant force of the liquid is greater than the weight of the object, the object will float on the surface of the liquid.
• NOTES: Buoyancy is the tendency of a liquid to exert an upward force on an object immersed in it.
• The buoyancy of a liquid depends upon the density of the fluid and the volume of the object immersed in the liquid.
• Thus we can say the buoyant force is greater if the volume of an object submerged in a liquid is Larger.

The pattern follow here is

Hence, JIM is the odd one.

Formula used:

Distance = Speed × Time

Calculation:

Since, 1 km/hr = 5/18 m/s:

60 km/h = 60 × (5/18) = 50/3 m/s

We know that, Distance = Speed × Time

Distance = (50/3) × 9 = 150 m 

∴ The length of the train is 150 meters.

The correct answer is Harsha Vardhan 

Key Points

• Harshavardhana:-
• He was a prominent Indian emperor of the 7^th century CE.
• He ruled over a vast empire that stretched across northern and northwestern India, with the Narmada River as its southern boundary.
• His capital was at Kannauj (present-day Kannauj, Uttar Pradesh state), and he reigned for nearly four decades, from 606 to 647 CE.
• Harshavardhana was born into the Pushyabhuti dynasty, a powerful family that had ruled over Thanesar (present-day Haryana) for several generations.
• His father, Prabhakaravardhana, was a successful ruler who had defeated the Huna invaders and extended his control over neighboring states.
• He sent an envoy to the Chinese court in 641 AD.

Additional Information

• Narasimhavarman I:-
• He was a Pallava emperor who reigned from 630 CE to 668 CE.
• He was the son of Mahendravarman I and is considered one of the greatest Pallava rulers.
• Narasimhavarman I was a skilled military leader and diplomat, and he is credited with reviving Pallava power and prestige.
• He is also known for his patronage of the arts, and he is credited with commissioning the construction of several magnificent temples, including the Shore Temple at Mamallapuram.
• Narsimhavarman II:-
• He was a Pallava monarch who reigned from 690 CE to 725 CE.
• He was the son of Parameswaravarman I and is considered one of the greatest Pallava rulers.
• Pulakeshin I:-
• He was the first sovereign ruler of the Chalukya dynasty of Vatapi (modern Badami).
• He ruled parts of the present-day Maharashtra and Karnataka states in the western Deccan region of India.

Concept:

• The area under the velocity-time graph for a particle moving in a straight line with uniform acceleration gives the net displacement of the particle.
• In physics, displacement refers to the change in position of an object or particle.
• It is a vector quantity that indicates both the magnitude (distance) and direction of the change.
• When a particle undergoes uniform acceleration, its velocity changes at a constant rate.
• The velocity-time graph represents the velocity of the particle as a function of time. The area under this graph, between two specific time points, represents the displacement of the particle during that time interval.

The correct answer is option (2)

Additional Information

• If the velocity-time graph is a straight line segment, the area under the graph is a trapezoid.
• The base of the trapezoid is the time interval, and the height is the average velocity during that interval. The formula for the area of a trapezoid is given by:

Area = (1/2) × (sum of parallel sides) × (height)

In this case, the parallel sides are the initial and final velocities of the particle, and the height is the time interval. Therefore, the area under the velocity-time graph is:

Area = (1/2) × (initial velocity + final velocity) × (time interval)

This area represents the displacement of the particle during the given time interval.

As, Biology is a natural science that studies life and living organisms, including their physical structure, chemical processes, molecular interactions, physiological mechanisms, development and evolution. Where as, Zoology is the branch of biology that studies the animal kingdom, including the structure, embryology, evolution, classification, habits and distribution of all animals, both living and extinct and, Zoography is a branch of Zoology concerned with the description of animals, their habitats etc.

So, Under Biology, Zoology will come and under zoology, zoography will come. The correct Venn diagram which shows the relation between these three is :

Hence, option 3 is the correct answer.

Shortcut Trick

Apply the Direct formula for OR/AND type questions:

Required Days = Given Days ÷ [(And Men / Or Men) + (And Women / Or Women)]

Required Days = 19 ÷ [(3 / 5) + (6 / 9)]

Required Days = 19 ÷ [(3 / 5) + (2 / 3)] = 19 ÷ [19 / 15]

Required Days = 19 × (15 / 19) = 15 days.

∴ The correct answer is 15 days.

Alternate Method

Given: 5 Men = 9 Women, Days = 19, Target Group = 3 Men + 6 Women

Formula Used: Total Work = Efficiency × Time

⇒ Efficiency of 1 Man = 1/5

⇒ Efficiency of 1 Woman = 1/9

⇒ Total Efficiency of (3 Men + 6 Women) = 3 × (1/5) + 6 × (1/9)

⇒ Combined Efficiency = 3/5 + 2/3 = (9 + 10) / 15 = 19/15

⇒ Required Time = Total Work ÷ Combined Efficiency

⇒ Required Time = 19 ÷ (19/15) = 19 × (15/19) = 15 days

∴ The correct answer is 15 days.

Additional Information

Work and Wages

Wages are always distributed in the ratio of the work done by individuals, which is also the ratio of their efficiencies if they work for the same amount of time.

Pipes and Cisterns

This concept is similar to Time and Work, where filling pipes have positive efficiency and leakage or outlet pipes have negative efficiency.

Alternate Day Work

When persons work on alternate days, work is calculated in cycles (e.g., 2-day cycles), and the remaining work is handled by the person whose turn comes next.

The correct answer is Magnetic waves. 

• MRI scanners use strong magnetic fields, magnetic field gradients, and radio waves to generate images of the organs in the body.
• MRI does not involve X-rays or the use of ionizing radiation, which distinguishes it from CT or CAT scans and PET scans.

Key Points

• MRI can be also known or called Magnetic Resonance imaging.
• In MRI the body is placed in a high strength magnetic field.
• This field is generated by a superconducting magnetic coil which is immersed in liquid helium.
• This field causes the alignment of the spins of the protons in the body of the patient.
• Pulses of radio waves are then used to excite the nuclei causing the alignment of the spins to undergo decoherence.
• When the spins realign, they release a radio signal which is picked up by antennae placed close to the body.
• from this signal and by modulating the radio wave pulses different types of MR images are reconstructed.
• This is the basis of MR imaging.

• The Point at which all the rays converge is termed as Focus.
• The straight line that goes through the center of the lens at right angles to the lens surface is called principle axis.
• Pole is the mid point of the Lens.

The pattern followed here is:

Similarly,

Hence, the correct answer is HODVQDPV.

GIVEN:

 \((4^3+4)\) ÷ [\(5^2 - (7^2 -41)\) )]

FORMULA USED : 

CALCULATION :

⇒ \((4^3 +4 )\) ÷ [\(5^2 - (7^2 -41)\))]

⇒ (64 + 4) ÷ [ 25 -  8]

⇒ 68 ÷ 17

⇒ 4

∴ The value is 4.

The correct answer is 1 and 3 only.

Key PointsGeothermal Plants

• Geothermal energy is the thermal energy in the Earth's crust.
• The high temperature and pressure in Earth's interior cause some rock to melt and solid mantle to behave plastically.
• It originates from the:
• Formation of the planet.
• Radioactive decay of materials.
• Parvati Valley near Manikaran in Himachal Pradesh is used for harnessing geothermal energy. Hence 1 is correct.
• Puga Valley is situated in the Changthang Valley in the southeastern part of Ladakh.  Hence 3 is correct. 
• ​It is a region of great significance known for its natural beauty and geothermal activities.
• Puga is also visited for its hot sulfur spring.
• Following are the six most promising geothermal energy sites in India:
• Tattapani in Chhattisgarh
• Puga in Ladakh
• Cambay Graben in Gujarat
• Manikaran in Himachal Pradesh
• Surajkund in Jharkhand
• Chhumathang in Ladakh
• Madras Atomic Power Station (MAPS) is located at Kalpakkam about 80 kilometres (50 mi) south of Chennai, India. Hence 2 incorrect.
• Narora Atomic Power Station (NAPS) is a nuclear power plant located in Narora Uttar Pradesh, India. Hence 4 is incorrect.
• Geothermal resources in India have been mapped by the Geological Survey of India (GSI).
• A broad estimate suggests that there could be 10 GW of geothermal power potential.

Uses:

• Geothermal reservoirs located near the earth's surface, mostly located in the western U.S
• Hot water or steam reservoirs deep in the earth are accessed by drilling.
• The shallow ground near the Earth's surface maintains a relatively constant temperature of 50-60°F.

The correct answer is "Tonometer".

Key Points 

Tonometer 

• A tonometer is used to measure the pressure inside the eyes
• Tonometry is a test to measure the pressure inside the eyes.
• The test is used to screen for glaucoma.
• It is also used to measure how well glaucoma treatment is working.

Additional Information

Odometer

• the word odometer is derived from the Greek word hodos, meaning "road" or "trip".
• An odometer for automobiles records the distance a car has run for.
• An odometer shares space on your dashboard with a speedometer, a tachometer, and maybe a "tripmeter"

Viscometer

• Viscometers measure the viscosity and flow properties of fluids
• Viscosity arises from the internal friction of a fluid and is defined as a liquid’s resistance to flow or shear stress.

Machmeter

• The machmeter is designed to measure the ratio of pitot excess pressure (the difference between pitot and static) and static pressure

The figure that will replace the question mark (?) in the following figure is:

Hence, the correct answer is "Option (1)".

Shortcut Trick

Direct identity: (sin α + cos α)² = 1 + 2 / (tan α + cot α)

Substitute the given value: (2/√3)² = 1 + 2 / (tan α + cot α)

⇒ 4/3 = 1 + 2 / (tan α + cot α)

⇒ 1/3 = 2 / (tan α + cot α)

⇒ tan α + cot α = 6

∴ The correct answer is 6.

Alternate Method

Given:

sin α + cos α = 2/√3

Formula Used:

(a + b)² = a² + b² + 2 × a × b

sin² α + cos² α = 1

tan α = sin α / cos α and cot α = cos α / sin α

Calculations:

Squaring both sides of the given equation:

⇒ (sin α + cos α)² = (2/√3)²

⇒ sin² α + cos² α + 2 × sin α × cos α = 4/3

Substitute sin² α + cos² α = 1:

⇒ 1 + 2 × sin α × cos α = 4/3

⇒ 2 × sin α × cos α = 4/3 − 1

⇒ 2 × sin α × cos α = 1/3

⇒ sin α × cos α = 1/6

Now evaluate (tan α + cot α):

⇒ tan α + cot α = (sin α / cos α) + (cos α / sin α)

⇒ tan α + cot α = (sin² α + cos² α) / (sin α × cos α)

⇒ tan α + cot α = 1 / (sin α × cos α)

Substitute the value of sin α × cos α:

⇒ tan α + cot α = 1 / (1/6)

⇒ tan α + cot α = 6

∴ The correct answer is 6.

Additional Information

Basic Trigonometric Identities

sin² α + cos² α = 1, sec² α − tan² α = 1, and cosec² α − cot² α = 1.

Reciprocal Relations

tan α = 1 / cot α, sin α = 1 / cosec α, and cos α = 1 / sec α.

Key Shortcut Formula

The expression tan α + cot α frequently simplifies to 1 / (sin α × cos α), which is a direct and standard substitution for trigonometric simplifications.

The correct answer is 'Two members'.

Key Points

• The Protection of Human Rights Act of 1993 provides for the creation of not only the National Human Rights Commission but also a State Human Rights Commission at the State Level.
• The State Human Rights Commission is charged with the protection of Human Rights or investigating any violations that occur within their respective state.
• The State Human Rights Commission is a multi-member body consisting of a chairperson and two members.
• Thus, a State Human Rights Commission can have two members. (Excluding Chairperson).
• The chairperson and members hold office for a term of three years or until they attain the age of 70 years, whichever comes first.
• Although the chairperson and members of a State Human Rights Commission are appointed by the Governor they can only be removed by the President (and not by the Governor).

Hence, the correct answer is Two members.

Explanation:

Atomic radius and its trends:

• It specifies the radius of the atom i.e distance between the nucleus and the outermost shell.
• The size of the atom reduces in moving from left to right along a period.
• Hence, the atomic radius decreases in moving from left to right along a period.
• Atomic radius increases from top to bottom within a group.

Metallic character and its trends :

• It specifies the tendency of an element to lose electrons and form positive ions or cations**.**
• On moving downwards in a group the metallic character increases.
• On moving from left to right in a period the metallic character decreases

Trends of valence electrons and the number of shells:

• The number of electron shells increases on moving down a group.
• Since the elements in the same group have the same number of electrons in their outer shell, the valence electrons remain constant.
• For example, all the elements in group 1 have 1 electron in their outer shell.

Key Points Periodic table:

• It's an arrangement of all the known elements.
• All elements are arranged (from left to right and top to bottom) in order of increasing atomic number and recurring chemical properties.
• All the rows represent periods.
• All the columns represent groups.
• Elements in the same group have the same valence electron configuration and therefore same chemical properties.
• Elements in the same period have an increasing order of valence electrons.
• The elements are arranged in 7 horizontal rows, called periods, and 18 vertical columns, called groups.

Given:

A × B means that A is the mother of B.

A – B means that A is the father of B.

A ÷ B means that A is the sister of B.

Evaluating the given expressions in the options, we get

1) P ÷ R – Q

P ÷ R → P is the sister of R, R – Q → R is the father of Q

So, P ÷ R – Q shows that P is the paternal aunt of Q.

2) P × Q ÷ R

P × Q → P is the mother of Q, Q ÷ R → Q is the sister of R

So, P × Q ÷ R shows that P is the mother of R.

3) Q × P – R

Q × P → Q is the mother of P, P – R → P is the father of R.

So, Q × P – R shows that Q is the paternal grandmother of R.

4) P × Q – R

P × Q → P is the mother of Q, Q – R → Q is the father of R

So, P × Q – R shows that P is the paternal grandmother of R.

Hence, the correct answer is "Option 4".

Formula Used:

Work Done = Efficiency × Days

Calculation:

Let total work done = LCM (12, 24, 36) = 72

Total Efficiency = 6 + 3 + 2 = 11

No. of days required by A + B + C = 72/11 = \(6\frac{6}{11}\)

∴ The correct option is \(6\frac{6}{11}\)

Concept:

Stefan's Law: 

• According to it the radiant energy emitted by a perfectly black body per unit area per sec (i.e. emissive power of black body) is directly proportional to the fourth power of its absolute temperature i.e.

\(E \propto {T^4}\)

\( \Rightarrow E = \sigma {T^4}\)

Where, is a constant called Stefan’s constant.

Calculation:

From the above equation, we can write energy emitted per second per square meter by the black body at 303 K is proportional to  303⁴.

The correct answer is Angular Velocity.

• Angular Velocity is a vector quantity.

Key Points

• Vector Quantities
• Physical quantities which have magnitude and direction both and which obey triangle law are called vector quantities.
• Example: Displacement, Velocity, angular velocity etc.
• Angular Velocity
• The time rate of change of the angular displacement of a particle relative to its origin is angular velocity.
• Its direction is given by the right-hand thumb rule.
• Scalar Quantities
• Physical quantities which have magnitude only and no direction are called scalar quantities.

Example: Mass, Speed, Volume, etc.

• Angular frequency is the magnitude of Angular velocity, hence it is a scalar quantity.

Additional Information

Given:

1. Rupali is at the 13^th position from the left and Neelam is at the 18^th position from the right.

2. They interchange their positions, Rupali becomes 21^st from the left.

=> The total number of persons = Rupali position from left + Rupali position from right - 1

=> The total number of persons = 21 + 18 - 1 = 38

Neelam position from the right:

=> The total number of persons = Neelam position from left + Neelam position from right - 1

=> 38 = 13 + Neelam position from right - 1

=> Neelam position from right = 38 - 13 + 1 = 39 - 13 = 26

Hence, Neelam position from right  is “26”.

Shortcut Trick

Ratio of Present ages of A : B = 5 : 4

Difference in ages is constant. Let ratio be 5x and 4x.

Given: (5x − 3) − (4x + 4) = 2 ⇒ x − 7 = 2 ⇒ x = 9

Total Ratio units = 5 + 4 = 9 units

Total Age = 9 × 9 = 81 years

∴ The correct answer is 81 years.

Alternate Method

Given: Present age ratio A : B = 5 : 4. Let age of A = 5x and B = 4x.

Condition: Age of A (3 years ago) = Age of B (4 years hence) + 2

⇒ (5x − 3) = (4x + 4) + 2

⇒ 5x − 3 = 4x + 6

⇒ 5x − 4x = 6 + 3

⇒ x = 9

⇒ Present age of A = 5 × 9 = 45 years

⇒ Present age of B = 4 × 9 = 36 years

⇒ Total present age = 45 + 36 = 81 years

∴ The correct answer is 81 years.

Additional Information

Age Ratio Concept

If the ratio of ages is given as a:b, we assume the ages to be ax and bx. The constant difference between two people's ages remains the same throughout their lives.

Past and Future Ages

If the present age is 'x', then age 'n' years ago is (x − n) and age 'n' years hence is (x + n).

Sum and Ratio Relation

The total sum of ages at any point is the sum of their individual ratio parts multiplied by the common variable factor 'x'.

The correct answer is 14^th century.

Key Points

• Murder was not considered a crime in the English Society till 14^th century.
• The 14^th century saw the passage of the Statute of Winchester, which established a number of reforms to the criminal justice system in England.
• These reforms included the creation of a system of coroners to investigate suspicious deaths and the introduction of the death penalty for murder.

Additional Information

• In India, the death penalty for a person who commits murder comes under IPC section - 302.

Key Points

Explanation:

• Normal rain has a pH of about 5.6; it is slightly acidic because carbon dioxide (CO2) dissolves into it forming weak carbonic acid.
• Acid rain usually has a pH between 4.2 and 4.4.
• Acid rain, or acid deposition, is a broad term that includes any form of precipitation with acidic components. such as sulfuric or nitric acid that falls to the ground from the atmosphere in wet or dry forms.
• This can include rain, snow, fog, hail or even dust that is acidic.
• Acid rain results when sulfur dioxide (SO2) and nitrogen oxides (NOX) are emitted into the atmosphere and transported by wind and air currents.
• The SO2 and NOX react with water, oxygen, and other chemicals to form sulfuric and nitric acids.

SO₂ + H2O → H₂SO₃

• These then mix with water and other materials before falling to the ground.

Drawing the diagram as per the given information:

Thus we can say starting point is in the North of ending point.

Important PointsThus we can conclude that:

i) The direction of ending point with respect to starting point is South.

ii) The direction of starting point with respect to ending point is North.

Mistake PointsIf the question is framed in such a way that (In which direction is the starting point from the endpoint), then the answer would have been South, but here it is asked in reverse (In which direction is the starting point from the endpoint) ∴ answer would be North.

Hence, the correct answer is "North".

Given:

Total number of voters (N) = 90000

Percentage of votes polled = 70%

Percentage of votes in favor of candidate A = 60%

Formula:

Number of votes received by a candidate = (Percentage of votes × Total number of voters) / 100

Solution:

Number of votes polled = (70/100) × 90000

Number of votes polled = 63000

Number of votes in favor of candidate A = (60/100) × 63000

Number of votes in favor of candidate A = 37800

Since there were only two candidates, the remaining votes would be in favor of candidate B.

Number of votes received by candidate B = Total number of votes polled - Number of votes in favor of candidate A

Number of votes received by candidate B = 63000 - 37800

Number of votes received by candidate B = 25200

Therefore, candidate B received 25,200 votes.

Shortcut Trick 60% of polled votes were in favour of A

So, votes received by B = 40% of the polled votes

ATQ, votes received by B = 40% of (70% 0f 90000) = 25200

The correct answer is Gulf of Mannar.

Key Points

Gulf of Mannar:

• Gulf of Mannar is a marine national park, an inlet of the Indian Ocean located between southeastern India and western Sri Lanka.
• It is bounded to the northeast by Rameswaram (island), Adam's (Rama's) Bridge (a chain of shoals), and Mannar Island.
• The gulf is 80–170 miles (130–275 km) wide and 100 miles (160 km) long.
• It receives several rivers, including the Tambraparni (India) and the Aruvi (Sri Lanka).
• The port of Tuticorin is on the Indian coast.
• The gulf is noted for its pearl banks and sacred chank (a gastropod mollusk).

Additional Information

• Bhitar-Kanika
• Bhitar Kanika mangrove wetland is one of the most productive ecosystems.
• It adds to coastal fishery production.
• The rivers and creeks in the wetland are a major source of a variety of indigenous fish.
• The sheltered waters of mangroves provide nursery ground for commercially harvested prawns and shrimps.
• Several fish species come to the estuary for breeding.
• Fishing is the mainstay of the villagers who do not have any landed property.
• In addition, the local people depend on the mangrove vegetation for the collection of honey, wax, and medicinal plants.
• Around 50 quintal of honey is available per year in Bhitar Kanika forests.
• Sundarbans
• Sundarbans was formerly Sunderbans, a vast tract of forest and saltwater swamp forming the lower part of the Padma (Ganges [Ganga])-Brahmaputra River delta in southeastern West Bengal state, northeastern India, and southern Bangladesh.
• The tract extends approximately 160 miles (260 km) west-east along the Bay of Bengal from the Hugli River estuary in India to the western segment of the Meghna River estuary in Bangladesh and reaches inland for about 50 miles (80 km) at its broadest point.
• A network of estuaries, tidal rivers, and creeks intersected by numerous channels, it encloses flat, densely forested, marshy islands.
• The total area of the Sundarbans, including both land and water, is roughly 3,860 square miles (10,000 square km), about three-fifths of which is in Bangladesh.
• Gahirmatha
• Gahirmatha is the lone mass nesting spot in the Indian Ocean region and the only turtle sanctuary in Odisha.
• The Olive Ridley turtles travel across the South Pacific to breed on the coast of Gahirmatha.
• Million of Olive Ridley turtles visit the beach during mass nesting every year.
• Olive Ridley turtles usually nest during nighttime.
• The sanctuary is also home to a variety of flora and fauna.
• Wild boar, barking deer, bear, leopard, crocodile, jungle fowl, samber, and wild dogs are among the other wildlife seen in the sanctuary.

The correct answer is land and water body both.

The International Date Line (IDL) - 

• The International Date line is an imaginary line that passes through the Pacific Ocean.
• Along with the IDL, the date changes by exactly one day when it is crossed.
• A traveller crossing the International Date Line from West to East gains a day while crossing the International Date Line from East to West loses a day.

Why is there gain or loss of the day?

• 180^o E is GMT +12hrs and 180^o W is GMT -12hrs, hence the difference between 180^o E and 180^o W is 24hrs.
• The time difference on either side of the IDL is 24hours, so the date changes as soon as one crosses IDL.

Does it pass through the water body only?

• The International Date Line (IDL) is intentionally drawn in a zig-zag manner to avoid passing through land masses, but it does cross some islands (e.g., Fiji, Kiribati, Aleutian Islands).
• Therefore, it passes through land and water body both.

Given: NERVOUS

Arranging in alphabetical order:

NERVOUS → ENORSUV

The letter 'R' is fourth from the left and the letter 'U' is second from the right.

Here, two letters 'S' and 'T' come between the letters 'R' and 'U'.

Hence, the correct answer is "Option (1)".

Given 

X is a number when divided by 19 gives remainder 7 

Concept used:

Dividend = Divisor × Quotient + Remainder

Calculation:

According to the question,

Then, x = 19k + 7 [where, k is any natural number]

To make calculation easier put k = 1, 2, 3, 4...

We have to check, k = 1,

x = 19 × 1 + 7 = 26, this is not perfect square

k = 2,

x = 19 × 2 + 7 = 45, this is not perfect square

k = 4,

x = 19 × 3 + 7 = 64, this is perfect square.

∴ Answer will be option 3.

The correct answer is 15^th.

Key Points

• The 15^th Finance Commission was constituted on 27^th November 2017 in terms of Article 280 of the Constitution of India.
• Shri N.K. Singh is the Chairman of the 15^th Finance Commission of India.
• The 15^th Finance Commission on 16 November 2020 submitted to Prime Minister Narendra Modi its report on the ratio in which tax is to be divided between the Centre and states over the next five years. The report titled ‘Finance Commission in COVID Times' was submitted to Finance Minister Nirmala Sitharaman on the next day.

Additional Information

• The Commission submitted two reports — the first report consisted of recommendations for the financial year 2020-21 and the final with recommendations for 2021-26.
• The recommendations of the 15^th Finance Commission for 2021-22 to 2025-26 have not been disclosed as it has not been tabled in Parliament.
• The Commission was asked to give its recommendations on wide-ranging issues. Apart from the vertical and horizontal tax devolution, local government grants, disaster management grants, it was also asked to examine and recommend performance incentives for States in many areas like the power sector, adoption of direct benefit transfer, solid waste management, etc.
• The Commission was also asked to examine whether a separate mechanism for funding of defense and internal security ought to be set up and if so, how such a mechanism could be operationalized.

The correct answer is the Gulf Stream.

• Gulf Stream does not flow into the Pacific Ocean. It is a warm Atlantic Ocean Current which originates from the Gulf of Mexico.
• An ocean current is a continuous, directed movement of seawater generated by a number of forces acting upon the water, including wind, the Coriolis effect, waves, and temperature and salinity differences.

List of Ocean Currents of the World

Given:

Statement:

Apartment complexes have decided to charge a heavy penalty on residents who do not segregate their dry waste and wet waste.

Now,

Arguments:

I. The government has mandated segregation of wet waste and dry waste by all homeowners - True (As the statement says the government has mandated waste segregation, apartment complexes are legally obligated to enforce it within their premises. This is strong argument).

II. All apartments have been provided with separate bins for dry waste and wet waste to facilitate garbage segregation - True (As the statement clearly mentioned that Apartment complexes have decided to charge because they provided the bins for dry waste and wet waste to facilitate garbage segregation).

So, Both arguments I and II strengthen the statement.

Hence, the correct answer is "Option 1".

Given:

The original speed of Shikha's car = 60 km/hr

Original time taken to cover the distance = 2 hrs 30 min = 2.5 hrs

New time taken to cover the distance = 4 hrs

Formula Used:

Distance = Speed × Time 

Calculation:

According to the question, 

The distance covered in both cases is the same.

So, 

S₁ × T₁ = S₂ × T₂

⇒ 60 × 2.5 = S₂ × 4

⇒ 60 × (5/2) = S₂ × 4

⇒ S₂ = 150/4

⇒ S₂ = 37.5 km/hr

∴ The speed of Shikha's car to travel the same distance in 4 hrs is 37.5 km/hr.

The correct answer is Ustad Mansoor.

Key Points

• Mansur was a leading nature painter in the court of Jahangir, who lived early 17^th century.
• Mansur was extraordinarily talented in scientific documentation.
• His detailed careful depictions of plants and animals avoided all personal expression and are extremely valuable for their scientific accuracy as well as their artistic perfection.
• Mansur became known as Ustad Mansur, and the emperor bestowed the title Nadir-ul- 'Asr ("Miracle of the Age") on him.
• Mansur accompanied Jahangir on some of his travels and was then in charge of the documentation of plants and animals.
• **Jahangir's memoirs state that during a trip into the Kashmir Valley Mansur painted over 100 flowers.**​

Additional Information

• Abul Hasan
• He was the son of the Iranian painter Aqa Reza, in the service of the future Mughal emperor, Jahangir.
• He grew up in the prince's household and became so valued as a court artist that he was called "Nadiru'l Zaman" - Wonder of the Age.
• The superbly finished frontispiece to the Jahangir Nama to which there is the reference by the Emperor Jahangir; the moving portrait of a fragile old pilgrim standing, perilously close to the end of his life; the scene of the emperor Jahangir giving audience —jharokha darshan — from a window of the palace Some of his works are copied from European works was not the only, groove in which Abu’l Hasan’s talent moved.
• He made some of the most beautiful and precious paintings under Mughal Emperors.​

According to the given information:

The distance can be calculated using Pythagoras theorem as:

Distance from his home = (16² +12²)^1/2 = (256 + 144)^1/2 = 20 km

Hence, Abhinav is 20 km far in Northwest direction from his house.

Shortcut Trick

Use the Option Verification method to find the Original Price quickly.

If the original price is ₹12:

Original Quantity = 288 ÷ 12 = 24 articles.

New Price after ₹4 reduction = 12 − 4 = ₹8.

New Quantity = 288 ÷ 8 = 36 articles.

Difference = 36 − 24 = 12 articles (Matches the given condition).

∴ The correct answer is ₹12.

Alternate Method

Given:

Total expenditure = ₹288

Reduction in price = ₹4

Increase in quantity = 12 articles

Let the Original Price of each article be x.

Original quantity = 288 ÷ x

New price = x − 4

New quantity = 288 ÷ (x − 4)

According to the question:

⇒ 288 ÷ (x − 4) − 288 ÷ x = 12

⇒ 288 [ (x − (x − 4)) ÷ (x(x − 4)) ] = 12

⇒ 288 × 4 ÷ (x² − 4x) = 12

⇒ 1152 = 12(x² − 4x)

⇒ 96 = x² − 4x

⇒ x² − 4x − 96 = 0

⇒ x² − 12x + 8x − 96 = 0

⇒ x(x − 12) + 8(x − 12) = 0

⇒ (x − 12)(x + 8) = 0

⇒ x = 12 or x = −8

Since the price cannot be negative, x = 12.

∴ The correct answer is ₹12.

Additional Information

Constant Expenditure Rule

When the total expenditure remains constant, the price is inversely proportional to the quantity (Consumption ∝ 1/Price).

Percentage Change Relation

If the price decreases by r%, then the consumption must increase by [r ÷ (100 − r)] × 100% to keep expenditure the same.

Quadratic Formula

For an equation ax² + bx + c = 0, the roots are given by x = [−b ± √(b² − 4ac)] ÷ 2a.

The correct option is Light cannot travel through Vacuum.

Key Points

• Light is an electromagnetic wave, no physical medium is required for its propagation. It can therefore travel in a vacuum.
• The speed of light in Vaccum is 3 x 10⁸ meters per second (approx). This is greater than sound speed.
• Light travels in a straight line.
• Some basic properties of light are Reflection, Refraction, Polarization, etc.

Electromagnetic wave:

• The oscillations between an electric field and a magnetic field produce waves known as electromagnetic waves or EM waves.
• An electromagnetic wave may pass through any medium, including vacuum, solid materials, and air.
• It may spread or move from one area to another without the use of a medium.
• Transverse waves are electromagnetic waves.
• A variety of frequencies may be created by dividing up electromagnetic waves known as the electromagnetic spectrum.
• Example: Radio waves, microwaves, infrared waves, X-rays, gamma rays, and other types of waves are EM waves.

Additional InformationVacuum: 

• It is a region of space empty of matter or with pressure so low that any particles there has no impact on any actions taking place there.

Reflection:

• The bouncing back of light from any shiny surface is known as reflection.

Polarization:

• A characteristic of electromagnetic radiations in which vibrating electric fields have a specified relationship between their direction and magnitude.

Refraction:

• The change in direction of a wave passing from one medium to another is caused by its change in speed. For example, light travels faster in the air as compared to water.

The logic followed here is :-

Hence, the correct answer is "78".

Shortcut Trick

Present sum of ages of A, B, and C = 3 × (24 + 5) = 87 years.

Present sum of ages of B and C = 2 × (19 + 6) = 50 years.

Present age of A = 87 − 50 = 37 years.

Age of A after 13 years = 37 + 13 = 50 years.

∴ The correct answer is 50 years.

Alternate Method

Given:

The average age of Akram (A), Bikram (B), and Chandra (C) 5 years ago = 24 years

The average age of Bikram (B) and Chandra (C) 6 years ago = 19 years

Calculations:

⇒ Sum of ages of A, B, and C 5 years ago = 3 × 24 = 72 years

⇒ Present sum of ages of A, B, and C = 72 + (3 × 5) = 87 years    ... (Equation 1)

⇒ Sum of ages of B and C 6 years ago = 2 × 19 = 38 years

⇒ Present sum of ages of B and C = 38 + (2 × 6) = 50 years    ... (Equation 2)

⇒ Present age of A = (Present sum of A, B, and C) − (Present sum of B and C)

⇒ A = 87 − 50 = 37 years

⇒ Age of Akram 13 years from the present = 37 + 13 = 50 years

∴ The correct answer is 50 years.

Additional Information

Present Age from Past Average

If the average age of n people t years ago was A, then their present average age is directly calculated as (A + t). Their present total sum will be n × (A + t).

Net Change in Average

When calculating average ages in the future or past, the average increases or decreases by exactly the number of years passed, provided the individuals in the group remain identical.

Sum of Ages Rule

The sum of ages in the present = Sum of ages t years ago + (n × t), where n is the number of individuals. This rule ensures every individual's age increment is correctly accounted for.

The correct answer is Dhar.

Key Points

• Unlike the other princely states of the country, the royal history of Amjhera under the Dhar district is very unique.
• Raja Bakhtawar Singh was hanged to death at the present MTH compound in Indore on February 10, 1858, since he had refused to surrender before the British and enter into a treaty with them.
• Maharana Bakhtawar Singh was the ruler of Amjhera town in Dhar district of Madhya Pradesh, who fought with the British in Madhya Pradesh in the freedom struggle of 1857. Hence, Option 2 is correct.
• After a long struggle, he was imprisoned by the British fraudulently.
• He was hanged on 10 February 1858 on a neem tree in the Maharaja Yashwant Hospital premises of Indore.
• His family moved to Ringnod Fort, which was the second fort of Amjhera, the last ruler of Amjhera was Rao Laxman Singh Ji Rathore.
• Deep Singh Ji was the son of Chhadavad. Rani Bhatiani Ji who lived in Ringnod Fort adopted Laxman Singh Ji.
• Rao Laxman Singh Ji was the last ruler of Amjhera state where his dynasty is found in the form of Chhadavad Jagir.
• The Madhya Pradesh government has declared the fort of Maharana Bakhtawar Singh at Amjhera as a state-protected building.
• It is 27 km from the district headquarters, on the Indore-Ahmedabad state road.

Additional Information

• Dhar district
• It is a district of Madhya Pradesh state in central India.
• The historic town of Dhar is the administrative headquarters of the district.
• The district has an area of 8,153 km².
• Population: 21.9 lakhs (2011)
• Division: Indore
• Headquarters: Dhar

Drawing Venn diagram according to given information,

Conclusion 1: All cars are either roads or metros → false (This is definitely false)

Conclusion 2: Some care are metros → True (This is definitely true)

Hence, “only conclusion 2” follows.

Given:

Cost price (C.P.) = Rs. 225

Repair cost = Rs. 15

Selling price (S.P.) = Rs. 300

Concept Used:

Profit percent calculation

Formula Used:

Profit = S.P. - (C.P. + Repair cost)

Profit Percent = (Profit / (C.P. + Repair cost)) × 100

Calculation:

⇒ Total Cost Price = C.P. + Repair cost

⇒ Total Cost Price = 225 + 15

⇒ Total Cost Price = Rs. 240

⇒ Profit = S.P. - Total Cost Price

⇒ Profit = 300 - 240

⇒ Profit = Rs. 60

⇒ Profit Percent = (Profit / Total Cost Price) × 100

⇒ Profit Percent = (60 / 240) × 100

⇒ Profit Percent = 0.25 × 100

⇒ Profit Percent = 25%

∴ The correct answer is option 3.

The correct answer is Karakoram Mountain Range

Key Points

• Hispar Glacier is situated in the Karakoram Mountain Range.
• The Karakoram range spans the borders between Pakistan, India, and China, and is home to some of the highest peaks in the world, including K2.
• The glacier is one of the longest in the Karakoram range and is known for its dramatic landscapes and challenging trekking routes.
• The Karakoram range is part of the larger complex of mountain ranges in the region, which also includes the Himalayas and the Hindu Kush.

Additional Information

• The Karakoram Mountain Range is known for its significant glaciation and is one of the most heavily glaciated areas outside the polar regions.
• It serves as a critical water source for the Indus River, which is vital for agriculture and human consumption in the region.
• The region is also notable for its geological activity and is part of the tectonic collision zone between the Indian and Eurasian plates.
• The Karakoram range has a rich history of exploration and mountaineering, attracting adventurers from around the world.
• Environmental concerns such as climate change and glacial melting are significant issues impacting the region, with potential consequences for water resources and local communities.

The logic followed here is:

1. All the elements including the center element shifts clockwise.

Thus, the final series is:

Hence, "Option 1" is the correct answer.

Given:

Rahul's time to complete the work alone = 10 days

Sonu's time to complete the work alone = 15 days

Number of days they work together = 4 days

Formula used:

Work done = (Work rate) × (Time)

Rahul's work rate per day = 1/10 (as he completes the work in 10 days)

Sonu's work rate per day = 1/15 (as he completes the work in 15 days)

Combined work rate per day = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6

Now, let's calculate the work done by Rahul and Sonu together in 4 days:

Work done in 4 days = (Combined work rate per day) × (Number of days they work together)

Work done in 4 days = (1/6) × 4 = 4/6 = 2/3

This means that they have completed 2/3 of the total work in 4 days.

To find the remaining part of the total work, we subtract the work done from the total work:

Remaining work = 1 - 2/3 = 1/3

Therefore, the remaining part of the total work is 1/3.

The correct answer is 22 January 1947.

Key PointsObjective Resolution to the Constitution of India

• Jawaharlal Nehru proposed the Objective Resolution to the Constitution of India on 13^th December 1946 which laid down the principles of the constitution.
• The Objective Resolution provides the philosophy of the constitution.
• The Resolution was adopted by the Constituent Assembly on 22 January 1947.
• The Resolution proclaimed India as a sovereign Republic which is now independent of any external ruler.
• The Resolution stated that the citizens of India must be guaranteed justice, freedom and equality.
• It also talked about adequate safeguards for the minorities in the Indian society.
• The Objective resolution later took the form of Preamble of the Constitution of India.

According to BODMAS rule:

Let us analyze each option:

Given: 56 – 8 + 42 ÷ 6 × 5 = 19

i) – and ×

⇒ 56 × 8 + 42 ÷ 6 – 5 = 19

⇒ 56 × 8 + 7 - 5 = 19

⇒ 448 + 7 - 5 = 19

⇒ 455 - 5

= 450 ≠ 19

ii) + and –

⇒ 56 + 8 – 42 ÷ 6 × 5 = 19

⇒ 56 + 8 – 7 × 5

⇒ 56 + 8 – 35

⇒ 64 – 35 

= 29  ≠ 19

iii) ÷ and –

⇒ 56 ÷ 8 + 42 – 6 × 5 = 19

⇒ 7 + 42 – 6 × 5 = 19

⇒ 7 + 42 - 30 

= 49 - 30 = 19

iv) + and ÷ 

⇒ 56 – 8 ÷ 42 + 6 × 5

⇒ 56 – 0.19 + 6 × 5

⇒  56 - 0.19 + 30 

⇒ 86 - 0.19

= 85.81 ≠ 19

Hence, '÷ and –' is the correct answer.

Shortcut Trick

Simple Interest for 1 year = 7% of ₹1,900 = 19 × 7 = ₹133.

Total Interest given = ₹798.

Time period = Total Interest ÷ Interest per year

Time = 798 ÷ 133 = 6 years.

∴ The correct answer is 6 years.

Alternate Method

Given:

Principal (P) = ₹1,900

Simple Interest (SI) = ₹798

Rate (R) = 7% per annum

Formula Used:

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

Calculations:

⇒ 798 = (1900 × 7 × T) ÷ 100

⇒ 798 = 19 × 7 × T

⇒ 798 = 133 × T

⇒ T = 798 ÷ 133

⇒ T = 6

∴ The correct answer is 6 years.

Additional Information

Simple Interest (SI)

It is the interest calculated only on the Principal amount for the entire period. Formula: SI = (P×R×T)/100.

Amount (A)

The total sum of money returned after the time period, calculated as Amount = Principal + Simple Interest.

Effective Rate of Interest

For Simple Interest, the total percentage increase over T years is simply (R × T)% of the Principal.

Rate and Time Relationship

If the SI and Principal are constant, the Rate is inversely proportional to Time (R ∝ 1/T).

From the given

Statement:

Should the government encourage young entrepreneurs? 

Now we consider the given

Arguments:

Ⅰ. Yes, they will reduce the burden of unemployment: Many entrepreneurs have innovative and great ideas but those ideas are not sufficiently implemented and if the government encourages young entrepreneurs, it will definitely reduce unemployment on large scale. Thus the argument is strong.

Ⅱ. Yes, they will contribute to the development of the country: With more and more interest in entrepreneurship from the young generation, it will be huge diversification of different fields and it will ultimately lead to the development of the country and this initiative from the government will inspire many young minds from an early age to think out of the box and come up with something different and new ideas. Therefore the argument is strong.

So, both arguments Ⅰ and Ⅱ are strong.

Hence the correct answer is option 1).

Given:-  

12 ÷ (1/2) + {(35 ÷ 7) of 40} + 20 - 15 of 10

Concept used:- 

Calculation:- 

⇒ 12 ÷ (1/2) + {(35 ÷ 7) of 40} + 20 - 15 of 10  

⇒ 12 ÷ (1/2) + {(5) of 40} + 20 - 15 of 10 

⇒ 12 ÷ (1/2) + 5 × 40 + 20 - 150 

⇒ 12 × 2 + 200 + 20 - 150 

⇒ 244 - 150 = 94

∴ The required answer is 94.

The correct answer is CO_2.

Key Points

• There is a certain amount of carbon dioxide gas dissolved in cold beverages and various other drinks.
• It undergoes a chemical reaction to create aqueous carbonic acid when the gaseous carbon dioxide comes into contact with water.
• It is carbonic acid that gives your mouth an acidic taste and a sweet feeling.
• Carbon dioxide is highly soluble in water; indeed, it is the most soluble of the highly soluble common, non-toxic gases.
• At normal atmospheric pressure, about 1.5 litres of carbon dioxide can be dissolved in 1 litre of water.
• When combined with water, carbon dioxide is remarkably stable, unlike many other gases.
• In addition, carbon dioxide is readily available, so it also helps to reduce the price.
• Also, carbon dioxide does a great job preserving drinks for extended periods of time.

Carbonated drinks:

The given statement gives the fact that now the Indians have begun to opt for cars manufactured within the countries instead of those which are imported.

The first statement indicates that indigenously manufactured cars are cheaper and better suited to Indian conditions. This is in an assumption that is inherent in the given statement since it follows from logic that indigenously manufactured cars will be cheaper since they can avoid a lot of duties and taxes imposed on imported cars. Also, since the customers prefer them over imported cars, it can be assumed that they are better suited to the conditions here.

Hence, it is an assumption that can be safely made.

The word ‘ostracize’ means to completely boycott or avoid something. This assumption is not true since the statement indicates that the customers are simply preferring indigenously manufactured cars over imported ones, and not completely avoiding foreign companies. Hence, this assumption cannot be made.

Hence, option 1 is the given answer.

Additional Information

1. Read the statement with an approach that the assumptions would be true with regard to the statement.
2. Do not go too logical with the statements. Analyze the given information and the assumption must only be made based on the information in the statement. Do not over-complicate it.
3. Common assumptions can always be followed but other than that do not align the statement with General Knowledge or other facts
4. Use the elimination method if you are unable to apprehend the answer. Read the statement and then the assumptions given in the options, you shall notice that a few of them will most definitely not follow. Eliminate them and then choosing from lesser options may prove to be more convenient
5. One thing to make a note of is that the assumption is something that the author believes to be true so while choosing the correct option, keep this thought in mind as well. If any option contradicts the statement, then that assumption will not follow.

Given

The marked price is 25% more than the cost price.

The desired profit is 10%.

Concept:

MP/CP = (100 + Profit%)/(100 - Discount%)

Calculation:

MP/CP = (100 + Profit%)/(100 - Discount%)

⇒ MP is 25% more than CP.

⇒ 5/4 = (100 + 10)/(100 - Discount%)

⇒ 5/4 = (110)/(100 - Discount%)

⇒ 100 - Discount% = 88

⇒ Discount% = 12 

Therefore, a 12% discount on the marked price should be given to earn a 10% profit.

The Correct Answer is ​Jitendra Singh.

In News

• India introduces 'Battery Aadhaar' to monitor batteries from manufacturing to recycling.

Key Points

• The Battery Aadhaar Initiative was launched by Science and Technology Minister Jitendra Singh.
• It aims to track the full life cycle of batteries — from manufacturing to disposal.
• Each battery pack will get a unique digital identity, called Battery Aadhaar.
• The initiative will help monitor:
• Manufacturing origin
• Battery chemistry
• Safety certifications
• Performance data throughout the battery’s lifecycle
• It tracks thermal events, charge-discharge cycles, and end-of-life status.
• It supports predictive maintenance and efficient recycling.
• The initiative also fights counterfeit batteries and boosts consumer confidence.
• It promotes a circular economy and sustainability.
• It integrates with Battery Management Systems (BMS), AI diagnostics, and national EV databases.
• It strengthens India’s battery intelligence ecosystem.

Option 1 is incorrect course of action. The Boss is correct. Arresting a person without enough evidence clearly implies the decision has been taken in a haste. 

Option 2 is incorrect course of action. One cannot take legal actions against anyone just because a liking or disliking against anyone.

Option 3 is incorrect course of action. Planting an evidence against the arrested person would simply mean accusing an innocent person for a crime that he did not do.

Option 4 is the correct course of action. Arresting a person without enough evidence clearly implies the decision has been taken in a haste and one should apologies for it.

Hence, 'option 4' is the correct answer.

Given:

70% of (A – B) = 49% of (A + B)

Calculation:

According to question:

70 × (A - B)/100 = 49(A + B)/100

⇒ 70(A - B) = 49 (A + B)

⇒ 10(A - B) = 7(A + B)

⇒ 10A – 10B = 7A + 7B

⇒ 10A – 7B = 7A + 10B

⇒ 3A = 17B

⇒ A/B = 17/3

∴ A ∶ B = 17 ∶ 3

The correct option is 1 i.e. 17 ∶ 3

The correct answer is To enhance the efficiency and safety of solid rocket motor manufacturing.

Key Points

• The vertical planetary mixer developed by ISRO in February 2025 is designed to enhance the efficiency and safety in the production of solid rocket motors.
• This technology supports precise mixing of propellant ingredients, ensuring consistent quality and composition for better performance of rockets.
• Solid rocket motors are critical components in many launch vehicles, including those used for satellite deployment and interplanetary missions.
• The mixer integrates advanced mechanical design and automation features to reduce human intervention, minimizing risks associated with hazardous materials.
• ISRO has been focusing on innovations to streamline the manufacturing process of solid propulsion systems, which are vital for India’s space missions.

Additional Information

• Solid Rocket Motors:
• Solid rocket motors use a solid propellant mixture that is ignited to produce thrust.
• They are simpler and more reliable compared to liquid propulsion systems but require meticulous manufacturing processes for consistent results.
• Propellant mixtures generally include oxidizers, fuel, and binders.
• Planetary Mixers:
• Planetary mixers are specialized machines designed for mixing viscous materials uniformly.
• They are widely used in industries like food, chemical, and aerospace manufacturing.
• The "vertical" design enhances efficiency by reducing material settling and ensuring thorough mixing.
• ISRO’s Advancements in Propulsion:
• ISRO has developed several propulsion technologies, including cryogenic engines and solid rocket boosters.
• Solid propulsion systems are used in the PSLV and GSLV series for launching satellites into orbit.
• Continuous advancements aim to improve reliability, safety, and cost-effectiveness.
• Safety Considerations in Propellant Manufacturing:
• Propellant manufacturing involves handling hazardous chemicals and explosive materials.
• Automation and specialized equipment like vertical planetary mixers reduce the risks associated with human errors.
• Safety protocols and advanced designs are integral to ensuring worker safety and environmental protection.