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

The correct answer is Bhopal.

Key Points

• Madhya Pradesh Tribal Museum located at Bhopal.
• The Indian state of Madhya Pradesh borders five other Indian states, making the area a hub of cultural diversity.
• The Tribal Museum in Bhopal, Madhya Pradesh is India’s first museum of its kind and gives visitors an immersive experience of local tribal culture.
• A total of six galleries exhibit the lifestyles of the seven main tribes of Madhya Pradesh – Gond, Bhil, Korku, Baiga, Sahariya, Kol, and Bhariya.
• The strikingly beautiful building of the tribal museum is designed by Revathi Kamath, the renowned Indian architect.

Additional Information

• Attractions in the museum:
• A shop 'Chinhari' in the museum is a must-visit.
• It is basically a retail outlet for handicraft connoisseurs and -exhibits a huge collection of beautiful artefacts all available for sale.
• One can even take a look at the 'Choumasa' Magazine editions, an in-house magazine of the museum with detailed information on the tribal lifestyle.

Drawing the Venn diagram,

Conclusion 1: Some stationery are papers → True (This is definitely true)

Conclusion 2: No stationery is paper → False(This is definitely false)

Conclusion 3: No book is stationery → False (This is definitely false)

Conclusion 4: Some books are papers → True (This is definitely true)

Hence, “only conclusions 1 and 4” follow.

Given:

Current age ratio of Samir to Tanuja = 8 ∶ 15

After 9 years, age ratio of Samir to Tanuja = 11 ∶ 18

Calculation:

Let the current ages of Samir and Tanuja be 8k and 15k respectively.

After 9 years:

Samir's age ⇒ 8k + 9

Tanuja's age ⇒ 15k + 9

The ratio then ⇒ (8k + 9) ∶ (15k + 9) = 11 ∶ 18

⇒ 18 × (8k + 9) = 11 × (15k + 9) ⇒ 144k + 162 = 165k + 99

⇒ 165k - 144k = 162 - 99 ⇒ 21k = 63 ⇒ k = 3

Samir's age = 8 × 3 = 24 years

Tanuja's age = 15 × 3 = 45 years

⇒ 45 - 24 = 21 years

The difference between their ages is 21 years.

Pattern followed is:

8 × 3 = 24; 8 × 7 = 56

Similarly,

3 × 3 = 9; 7 × 3 = 21

Hence, 9 : 21 is the correct answer.

Given:

The area of the base of the cylinder = 616 m²

The height of the cylinder (h) = 8 m

Formula used:

Value of π = 22/7

The area of the base of the cylinder = π r ²

The curved or lateral surface area of the cylinder = 2 π r h

where r = radius, h = height

Calculation:

The area of the base of the cylinder = 616 m²

⇒ π r ²  = 616

⇒ (22/7) × r² = 616

⇒ r² = 196

⇒ r = 14 m

The radius of the cylinder = 14 m

The curved surface area (C.S.A.) of the cylinder = 2 π r h

⇒ 2 π r h = 2 × (22/7) × 14 × 8

= 2 × 44 × 8

= 704 m²

∴ The curved surface area of the cylinder is 704 m²

Additional Information 

The correct answer is Kuchipudi.

Key Points

• Vempati Chinna Satyam
• Born on October 25, 1929, in Kuchipudi village in Krishna district.
• The Kuchipudi dance originated in the same place.
• Chinna Satyam strove to popularise the unique dance form across the world.
• He began dancing at the age of six.
• Over a period of two decades received training from famous teachers such as Tadepalli Perrayya Sastry, Vedantam Lakshminarayana Sastry, and later from his elder brother Vempati Pedda Satyam.
• He founded Kuchipudi Art Academy in Chennai, in 1963.
• He trained hundreds of students at the Kuchipudi Art Academy in Chennai.
• Branches of this academy were later established in cities such as Visakhapatnam, Mumbai, and Calcutta in India and several cities in the USA.
• His students include veteran actors and dancers like Hemamalini, Rekha, Vyjayanthimala Bali, and Manju Bhargavi of ‘Shankarabaranam’s fame.
• He also gave performances in over 60 countries.

According to the given information :

what time between the 3 and 4 clockwise, the needles of hours and minute will be opposite each other or make an angle of 180°.

The angle between the hour hand and the minute hand is given by :

M (11)/2) = 30 × h + Ɵ

Ɵ  = 180º given

H = 3, M = ?

M (11/2) = 30 × 3 + Ɵ

M (11/2) = 90 + 180º

M (11/2) = 270º

M = \(\dfrac{540}{11}\)

M = \(49\dfrac{1}{11}\)

Thus the time between the 3 and 4 clockwise, the needles of hours and minute will be opposite each other or make an angle of 180° = \(3:49\dfrac{1}{11}\)

Hence, the correct answer is "Option 3".

Formula Used:

Probability = (Number of successful outcomes/Total number of outcomes)

P(E) = (nE)/(nS), where nE = Number of events and nS = Number of sample space 

Calculation:

When an unbiased coin is tossed three times, we'll get following cases;

HHH, HHT, HTH, THH, HTT, THT, TTH, TTT

Total possible outcomes = 8

Here, H = Head, T = Tail

At least 2 heads outcomes = 4

P(E) = (nE)/(nS) = 4/8 = 1/2

∴ Probability of getting at least two heads are 1/2.

Preparing the family tree using the following symbols:

A possible tree diagram will be:

Hence, the man is the cousin of the woman.

Shortcut Trick

Merchant uses a dishonest weight of 800 g instead of 1000 g.

Profit% = (Error ÷ True Value − Error) × 100

Error = 1000 g − 800 g = 200 g

Profit% = (200 ÷ 800) × 100 = 1/4 × 100 = 25%

∴ The correct answer is 25%.

Alternate Method

Given: True weight = 1000 g, False weight = 800 g.

Formulas: Profit% = (Profit ÷ Cost Price) × 100. In weight cases, Cost Price is proportional to the weight actually given, and Selling Price is proportional to the weight claimed.

⇒ Let the cost of 1 g be 1 unit.

⇒ Cost Price (CP) for merchant = Cost of 800 g = 800 units.

⇒ Selling Price (SP) for merchant = Price charged for 1000 g = 1000 units.

⇒ Profit = SP − CP = 1000 − 800 = 200 units.

⇒ Profit% = (200 ÷ 800) × 100 = 25%.

∴ The correct answer is 25%.

Additional Information

Dishonest Dealer Concept

When a dealer sells goods at cost price but uses less weight, the profit is calculated on the actual weight delivered to the customer, not the claimed weight.

Ratio Method

The ratio of Weight is 1000:800 (5:4). Since Price is inversely proportional to weight for the same amount, the Price ratio (CP:SP) becomes 4:5, leading to a 25% profit.

The correct answer is Dhar.

Key Points

• The famous Bagh Caves are situated in the Dhar district of Madhya Pradesh.
• Bagh Caves are rock-cut monasteries and shrines.
• They are situated on the banks of the Bagh river.
• They comprise 9 Buddhist caves and were developed in the 6^th century AD.

Additional Information

• The rock-cut architecture is a kind of Rock Art in which a natural rock is carved to create a structure.
• Other famous rock-cut caves in India are:
• Udayagiri Caves
• Ajanta Caves
• Ellora Caves
• Jogimara Caves
• Barabar Caves
• Nagarjuni Caves

The correct answer is CaO + H2O → Ca(OH)2.

Key Points

• Neutralization Reaction:
• It is a chemical reaction in which an acid and base react together to form salt and water as products.
• Example of the neutralization reaction.
• Ca(OH)2 + H2CO3 → CaCO3 + 2H2O
• H3PO4 + 3KOH → K3PO4 + 3H2O
• HNO3 + KOH → KNO3 + H2O
• The reaction between calcium oxide (CaO) and water (H2O) to form calcium hydroxide (Ca(OH)2) is an example of a combination reaction and not a neutralisation reaction.

Additional Information

• Other types of Chemical Reactions:
• Decomposition reaction: The opposite of a combination reaction, a complex molecule breaks down to make simpler ones. Such reactions are represented by equations of the following form: AB → A + B.
• Precipitation reaction: Two solutions of soluble salts are mixed resulting in an insoluble solid (precipitate) forming. Such reactions are represented by equations of the following form: A + Soluble salt B  → Precipitate + soluble salt C.
• Combination reaction: It is a reaction where two or more elements or compounds combine to form a single compound. Such reactions are represented by equations of the following form: X + Y → XY.
• Combustion reaction: Oxygen combines with a compound to form carbon dioxide and water. These reactions are exothermic, meaning they give off heat. Such reactions are represented by equations of the following form: A + O2 → H2O + CO2.
• Displacement reaction: One element takes place with another element in the compound. Such reactions are represented by equations of the following form: A + BC → AC + B.

Relocation from village to cities does not impact the work of government officers. So, conclusion 1 does not follow. Increase in transport facilities between cities and villages will improve the connectivity between the two, but will not impact the relocation from village to cities. Hence conclusion 2 does not follow.

Given:

Circumference of the circle = 33 cm

Concept used:

The circumference of a circle = 2πr, 

where "r" is the radius of the circle.

The area of a circle = πr²

Calculation:

C = 2πr

⇒ 33 = 2πr

⇒ r = \(\dfrac{21}{4}\)

⇒ Area = π × \(\dfrac{21}{4}^2\)

⇒ Area = \(\dfrac{22 \times 21 \times 21}{7 \times 4 \times 4}\) = \(\dfrac{693}{8}\)

∴ The area of the circle is \(\dfrac{693}{8} \) cm².

Present Day - Monday

Find - Day after 61 days

First, we have to find the number of odd days in these 61 days.

Odd days = 61 ÷ 7 = 5 days (Remainder)

Thus, day after 61 days = Monday + 5 days = Saturday

Hence, Saturday is correct.

Given: 

x + y = 10 and x - y = 8

Calculation:

x + y = 10     ----(i)

x - y = 8      ----(ii)

By adding  eq (i) and eq (ii) we get

2x = 18

⇒ x = 9

So, y = 1

Now,

x2 y2 = 9² × 1²

⇒ 81 × 1

⇒ 81

∴ The required answer is 81.

The correct answer is Mirzapur.

• Indian Standard Time (IST) is the time zone followed throughout the country. It is the actual time of  Mirzapur.

Key Points

• Mirzapur has the time along the Standard Meridian of India which is 82° 30' E.
• Hence, it is taken as the standard time for the whole country.
• The Indian Standard Time (IST) is 5 hours 30 minutes ahead of the Greenwich Mean Time (GMT)..

Additional Information

• Local Time (L) and Time Zones:
• The earth is divided into 24 longitudinal zones, each being 15 degrees or 1 hour apart in time (360 degrees = 24 hours, 360/24=15 degree in 1 hour) or 1 degree in 4 minutes is called Standard Time Zones.
• Russia has as many as 11 time zones.
• Both the USA and Canada have five time zones.
• Longitudes are measured from zero to 180° east and 180° west (or 180°) and both 180° longitudes share the same line, in the middle of the Pacific Ocean.
• International Date Line (IDL)
• The International Date Line (IDL) is an imaginary line on the surface of the Earth, that runs from the north to the south pole and demarcates one calendar day from the next.
• It passes through the middle of the Pacific Ocean, roughly following the 180° longitude but it deviates at Aleutian Islands, Fiji, Samoa, and the Gilbert Islands.
• The International Dateline is on the opposite side of the Earth-Prime Meridian.
• The Prime Meridian helps to define Universal Time and is the meridian from which all other time zones are calculated.

The correct answer is Fungi.

• Fungi acts as principal decomposers in ecological systems.
• The scientific study of fungi is called mycology.
• Examples of fungi are yeasts, molds, mushrooms, symbionts of plants, animals, and other fungi, parasites, etc.
• They have chitin in their cell wall.
• Ethnomycology is the study of the historical uses and sociological impact of fungi.

Image of fungi:

.jpg&ehk=ls0EFUQLx9YGadlKnrOLZLduFsSRWB6arOS%2f0uKlFBs%3d&risl=&pid=ImgRaw)

• Ferns are members of a vascular group of the plant which reproduces via spores and have neither seeds nor flowers.
• They have specialized tissues that transport water and nutrients and have life cycles in which the sporophyte is the dominant phase.
• Their leaves are called megaphylls and they are more complex than the microphylls of clubmosses.
• Most of the ferns are leptosporangiate ferns.
• Some Ferns are used as food, medicine, biofertilizer, ornamental plants, and for remediating contaminated soil.

Image of fern:

• Algae are classified as blue-green algae, red algae, brown algae, and green algae.
• They have the ability to do photosynthesis and they are a diverse group of aquatic organisms.
• Examples of algae are seaweeds, such as kelp or phytoplankton, pond scum, or the algal blooms in the lake.
• They are capable of producing oxygen by the method of photosynthesis.
• Algaes are not only helpful but also crucial for the existence of life on earth.

Image of algae:

• Mosses are a phylum of non-vascular plants.
• They do not grow flowers, wood, or true roots instead of seeds they reproduce by spores.
• They have rhizoids in place of roots.
• They are found in wet environments such as rainforests, wetlands, and alpine ecosystems.
• There are approximately 14,500 species of moss in the world which makes 75% of all bryophyte species.

Image of mosses:

Hence, Leela and the girls are cousins.

Given:

p2 + \(\frac{1}{p^2}\) = 14

Concept used:

If (a + \(\rm \frac{1}{a}\)) = k

Then,

a3 + \(\rm \frac{1}{a^3}\) = k3 - 3k

Calculation:

p2 + \(\frac{1}{p^2}\) = 14

By adding 2 in both sides

p2 + \(\frac{1}{p^2}\) +2 = 14 + 2

⇒ (p2 + \(\frac{1}{p^2}\) )² = 16

⇒ p + \(\frac{1}{p}\) = 4

Now,

p3 + \(\frac{1}{p^3}\) = 4³ - 3 × 4

⇒ 64 - 12

⇒ 52

∴ The required answer is 52.

The logic followed here is:

Therefore, '383 is the missing number in the given series.

Hence, the correct answer is "Option 1".

Given:

Distance covered by the car in 5 hours = 275 km

Distance to cover = 300 km

Speed reduction = 5 km/h

Formula Used:

Time = Distance / Speed

Calculation:

Initial speed of the car = 275 km / 5 hr = 55 km/h

New speed = 55 km/h - 5 km/h = 50 km/h

Time to cover 300 km at 50 km/h

Time = 300 km / 50 km/h

Time = 6 hours

The car will take 6 hours to cover a distance of 300 km at the reduced speed.

The correct answer is the shedding of the ownership or management.

Key Points

Privatization:

It is defined as "The transfer of ownership, property or business from the government to the private sector is termed privatization. The government ceases to be the owner of the entity or business"

The process of privatization includes all the activities that increase the hold of private companies than the Government itself. The major impact of privatization is that the stocks of such companies are not traded over the stock market, which implies that the general public of the country does not have the right to supply the capital to such firms. The advantage of privatization is that privately-owned companies are that they are generally more efficient and bring objectivity to the company.

All the ownership and management of the Government are shredded and passed on to the hands of a few private people. The features of privatization are:

1. Ownership Measures: The ownership of all public enterprises ultimately shifts to private owners. The denationalization can be complete or partial.
2. Organizational Measures: This is where we limit the control of the state in public companies.

Some methods include holding company structuring, leasing. restructuring of the enterprises etc. 3. Operational Measures: Public organizations and companies were running into huge losses. So the efficiency of these companies was to be increased.

Important Points

Industrial Reforms in India, 1991:

There were some major reforms bought about in India in 1991, privatization was one of the major decisions taken by the Government of India. The Government had proposed the policy of privatization of some of the Government-owned industries in order to improve the slow growth of these industries. Two major decisions were taken with respect to privatization in India-

• The disinvestment of the government’s equity in public sector undertakings, and
• The opening up of hitherto closed areas to private participation.

The correct answer is option(2) i.e. Force = mass × acceleration.

Explanation:

• Newton's second law is often stated as F = ma, which means the force (F) acting on an object is equal to the mass (m) of object times its acceleration (a). This means the more mass an object has, the more force you need to accelerate it, and the greater the force, the greater the object's acceleration.
• Force(F) = Mass(m) × Acceleration(a).
• Unit of Force = SI unit of Force is in Newtons (N).
• 1 Newton is equal to 1 kgms^-2.
• Acceleration of an object is directly related to the net force and inversely related to its mass.
• Acceleration of an object depends on two things, force and mass.
• Mass is a measure of the amount of matter in an object.
• Mass is usually measured in grams (g) or kilograms (kg).
• An object's mass is constant in all circumstances, contrast this with its weight, a force that depends on gravity.

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

Conclusions:

I. Some birds are pink → Does not follow (As some pigs are birds and all pink are pigs. So it is possible but not definite.)

II. Some pigs are pink → Follow (As all pink are pigs. As whole pinks comes in pigs, therefore it is true.)

III. Some pigs are roses → Follow (As some roses are pink and all pink are pigs. As whole pinks comes in pigs and has some part common with roses, therefore it is true.)

IV. Some birds are roses → Does not follow (As some roses are pink, all pink are pigs and some pigs are birds. So it is possible but not definite.)

∴ Here, Only II and III follow.

Hence, "Option 1" is the correct answer.

From the following figure,

In Isosceles triangle ABC

∠ACB = ∠ABC [AC = AB]

Given, ∠BAC = 80°

In ΔABC

∠ACB + ∠ABC + ∠BAC = 180°

⇒ 2∠ACB = 180° - 80° = 100°

⇒ ∠ACB = 100°/2 = 50°

The pattern followed for DOGS is:-

Similarly, for CATS:-

​ 

Hence, the correct answer is "LHYV".

Given, AB = 25 cm, BP = 5 cm, CP = 10 cm

Then, AP = AB – PB = 25 – 5 = 20 cm.

If the chords AB and CD intersect at a point P inside the circle, then their lengths satisfy the relation:

AP × BP = CP × DP

⇒ 20 × 5 = 10 × DP

⇒ DP = 100/10 = 10 cm

The correct answer is New Delhi.

Key Points

• The Central Reserve Police Force (CRPF) is India's largest Central Armed Police Force.
• The Headquarters of CRPF is in New Delhi.
• It functions under the authority of the Ministry of Home Affairs (MHA) of the Government of India.
• The CRPF's primary role lies in assisting the State/Union Territories in police operations to maintain law and order and counter-insurgency.
• It came into existence as the Crown Representative's Police on 27 July 1939.
• After Indian Independence, it became the Central Reserve Police Force on the enactment of the CRPF Act on 28 December 1949.

Additional Information

• Union Minister of Home Affairs is Amit Shah.
• Union Minister of Defence is Rajnath Singh.
• The tagline of CRPF is Service and Loyalty.
• The Director-General of CRPF is Anish Dayal Singh.

The correct answer is large distance of stars and fluctuations in the density of air.

Key Points

• To solve this type of question we must first know the basic concept of the twinkling of stars and then will see the options.
• Concept
• Atmospheric refraction of starlight is responsible for the twinkling of stars.
• Explanation
• The atmosphere has to change density layers hence when light rays cross the atmosphere, refraction of light rays occurs.
• Hence the eye some times receives more light with the result that the star appears brighter and sometimes it receives only a few rays or no rays which make the star appear fainter.
• This continuous brighter and fainter appearance is known as the twinkling of the stars.
• Hence, twinkling of stars in on account of two major factors-
• Large distance of stars.
• Fluctuations in the density of the air.

The positional values of the English alphabet is as follows:

The pattern followed here is:

'TYRE' is written as 'UZQD'

'SALE' is written as 'TBKD'

Similarly, 'DISH' will be written as:

Hence, 'option 1' is the correct answer.

Given:

Average of three numbers = 20

Sum of first two numbers = 40

Concept:

Average = (sum of all numbers) / (number of numbers)

Calculation:

Let the three numbers be a, b, and c

According to the average given, (a + b + c) / 3 = 20

Therefore, a + b + c = 20 × 3 = 60

It's given that a + b = 40

Subtracting the sum of the first two numbers from the total sum:

60 - 40 = 20

Hence, the third number is 20.

Drawing the diagram according to the given information,

So, the distance between the starting and ending point = 4 km

Hence, 4 km is the correct answer.

Shortcut Trick

Let Initial Income = 100. Expenditure = 60, Savings = 40.

New Income = 100 + 30% = 130.

New Expenditure = 60 + 20% = 72.

New Savings = 130 − 72 = 58.

Increase in Savings = 58 − 40 = 18.

% Increase = (18 ÷ 40) × 100 = 45%.

∴ The correct answer is 45%.

Alternate Method

Given:

Initial Income = I₁, Expenditure = E₁, Savings = S₁

Formula Used:

Income = Expenditure + Savings

Percentage Increase = [(New Value − Old Value) ÷ Old Value] × 100

Calculations:

⇒ Let initial Income = 100

⇒ Initial Expenditure = 60% of 100 = 60

⇒ Initial Savings = 100 − 60 = 40

⇒ New Income = 100 × (1 + 30/100) = 130

⇒ New Expenditure = 60 × (1 + 20/100) = 72

⇒ New Savings = 130 − 72 = 58

⇒ Increase in Savings = 58 − 40 = 18

⇒ Percentage Increase in Savings = (18 ÷ 40) × 100

⇒ Percentage Increase = 0.45 × 100 = 45%

∴ The correct answer is 45%.

Additional Information

Income-Expenditure Relation

The fundamental equation is Income = Expenditure + Savings. Any change in two variables directly dictates the change in the third.

Percentage Change

Percentage change is always calculated on the original base value. Formula: % Change = (Change ÷ Original Value) × 100.

Alligation Method

This can also be solved using Alligation between Expenditure increase and Savings increase to find the total Income increase.

The Correct Answer is My Favorite Photo.

In News

• World Photography Day: 19 August.

Key Points

• World Photography Day is celebrated annually on August 19 to honor the art, science, and impact of photography.
• The 2025 theme for World Photography Day is “My Favorite Photo.”
• World Photography Week 2025 runs from August 12–26, encouraging people to share meaningful photographs using #WorldPhotographyWeek.
• In 1826, Joseph Nicéphore Niépce produced the first permanent photograph.
• In 1837, Louis Daguerre invented the Daguerreotype process, the first commercial photography method.
• On August 19, 1839, the French government made photography freely available to the world, marking the origin of World Photography Day.
• Homai Vyarawalla was India’s first female photojournalist.
• Raghu Rai is a globally acclaimed photographer and a member of Magnum Photos.

The correct answer is Option 2 : Convince your mother about the national importance of your duty and continue.

• Qualities Projected in this situation:  (Speed of decision, Sense of responsibility, Determination, and Courage).

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:

Shortcut Trick

Given, 30 × CP = 40 × SP

⇒ SP / CP = 30 / 40 = 3 / 4

Here, CP = 4 units and SP = 3 units.

Loss = CP − SP = 4 − 3 = 1 unit.

Loss % = (1 / 4) × 100 = 25%.

∴ The correct answer is 25%.

Alternate Method

Given:

Cost price of 30 tables = Selling price of 40 tables

Formula Used:

Loss = CP − SP

Loss % = (Loss / CP) × 100

Calculations:

Let the Cost Price (CP) of 1 table be ₹1.

⇒ Total CP of 40 tables = 40 × 1 = ₹40

According to the given condition,

⇒ Total SP of 40 tables = CP of 30 tables = 30 × 1 = ₹30

Now, analyzing the transaction for 40 tables:

⇒ Total CP = ₹40

⇒ Total SP = ₹30

⇒ Loss = Total CP − Total SP

⇒ Loss = 40 − 30 = ₹10

⇒ Loss % = (Loss / Total CP) × 100

⇒ Loss % = (10 / 40) × 100

⇒ Loss % = 25%

∴ The correct answer is 25%.

Additional Information

Profit and Loss Formula

Profit occurs when SP > CP. Profit = SP − CP, and Profit % = (Profit ÷ CP) × 100.

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). SP = MP − Discount.

Successive Discount

If two successive discounts of x% and y% are given, the single equivalent discount is (x + y − xy÷100)%.

By checking the options:

(1) TXCJ

(2) DHSZ

(3) GKPW

(4) NRJQ

(here, J is not the opposite of R, I is the opposite of R)

Hence, NRJQ is the odd one.

Given:

x + y = 3

Concept used:

(a + b)³ = a3 + b3 + 3ab(a + b)

Calculation:

x + y = 3

By cubing both sides we get,

x3 + y3 + 3xy(x + y) = 27

⇒ x3 + y3 + 3xy(3) = 27

⇒ x3 + y3 + 9xy = 27

∴ The required answer is 27.

The correct answer is the Industrial Finance Corporation of India.

Key Points 

• Industrial Finance Corporation of India
• ​It was established on July 1, 1948
• The primary goal of establishing this development bank was to help the industrial sector meet its medium- and long-term financial demands.
• The IFCI's authorized capital is 250 crores.
• People's deposits are not accepted
• When a firm issues shares or debentures, the Industrial Finance Corporation of India may choose to underwrite securities.
• The IFCI also insures the loans that these industrial enterprises take out.
• It also ensures deferred payments for loans taken out in foreign currency from foreign banks.

Additional Information 

• The National Housing Bank Act,1987 envisaged the setting up of National Housing Bank (NHB) in 1988.
• National Housing Bank is an apex-level financial institution for promoting the housing sectors at both regional and local levels.
• The Head office of NHB is in New Delhi.
• The Export-Import Bank of India (EXIM Bank) is a financial institution of India that was established on 1 January 1982 under the Export-Import Bank of India Act 1981.
• Its main objective is to provide financial assistance to promote Indian exports.
• Industrial Development Bank of India was established in 1964 and came into operation on July 1, 1964, to provide credit and other financial facilities for the development of industries in India.
• IDBI Bank has been categorized as a private sector bank by the Reserve Bank of India, with effect from January 21, 2019.

The correct answer is (v-u)/t.

CONCEPT:

• Acceleration: The rate of change in velocity is called acceleration. It is denoted by a.
• The SI unit of acceleration is m/s².
• Equation of motion: The mathematical equations used to find the final velocity, displacements, time, etc of a moving object without considering force acting on it are called equations of motion.
• V = u + at
• Where, V = final velocity, u = initial velocity, a = acceleration of body under motion, and t = time taken by the body under motion.

EXPLANATION:

From the above equation of motion:

V = u + a t

So a = (V - u)/t

• The formula for finding acceleration is (v-u) / t. So option 4 is correct.

Additional Information

• The product of velocity and time (v x t) represents the displacement of a body which represents the shortest distance between two points.
• The reciprocal of time (1 / t) represents the frequency of oscillations which gives the value of the total number of oscillations in the given time.
• The work per unit time (W / t) represents power which is the measurement of the rate of doing work.

In the given statement, the facilities of government and private schools are compared and after analyzing we find that health and safety facilities in private schools are much better than government school because though the government is concerned about the health and safety, but it is unable to deliver it. So assumption I is not implicit and from the statement we can also assume that private schools give utmost importance to the facilities they need to provide, so II is implicit

Given:

Average weight of 73 notebooks = 7.3 kg

Number of notebooks = 73

Weight of the single new notebook = 7.4 kg

Formula Used:

Total weight of all notebooks = Average weight × Number of notebooks

Calculation:

Total weight of 73 notebooks = 7.3 kg × 73

Total weight of 73 notebooks = 532.9 kg

Now, there are 74 notebooks (73 old notebooks + 1 new notebook), and the new average weight is 7.4 kg.

Total weight of 74 notebooks = 7.4 kg × 74

Total weight of 74 notebooks = 547.6 kg

Weight of the new notebook = Total weight of 74 notebooks - Total weight of 73 notebooks

Weight of the new notebook = 547.6 kg - 532.9 kg

Weight of the new notebook = 14.7 kg

The weight of the new notebook is 14.7 kg.

Given:  Government is supplying free medicines from 2014 and 75,000 people have been benefitted from this till now, although the size of the affected population is 100 times this number.

Conclusion 1: The number of affected people is higher than the number of beneficiaries → "Follows" (Because, the size of the affected population is 100 times the number of people who have benefited (75,000) from the government's free medicine program).

Conclusion 2:  The government has to spread awareness about this scheme because most people are unaware of it → **"Follows" (**Because, To reach more of the affected population, the government would need to increase outreach and awareness efforts about the scheme.)

Therefore, both i and ii follows.

Hence, the correct answer is "Option 2".

Given:

Length and breadth ratio = 5:4

Perimeter = 144 m

Formula Used:

Perimeter of a rectangle = 2 × (Length + Breadth)

Area of a rectangle = Length × Breadth

Calculation:

Let the length be 5x and the breadth be 4x.

Perimeter = 2 × (Length + Breadth)

⇒ 144 = 2 × (5x + 4x)

⇒ 144 = 2 × 9x

⇒ 144 = 18x

⇒ x = 144 / 18

⇒ x = 8

Length = 5x = 5 × 8 = 40 m

Breadth = 4x = 4 × 8 = 32 m

Area = Length × Breadth

⇒ Area = 40 × 32

⇒ Area = 1280 m²

The area of the rectangle is 1280 m².

The correct answer is Dhupgarh.

 Key Points

• Dhupgarh Peak, near Pachmarhi in south-central Madhya Pradesh, is the highest point in the state.
• To the northwest of the Vindhya range lies the Malwa plateau.
• Mount Dhupgarh or Dhupgarh is the highest point in the Mahadev Hills, Madhya Pradesh, India.
• Located at Pachmarhi in the Hoshangabad district, its elevation is 1,352 meters.

Additional Information

Concept:

• Fibers are materials that form clothing.
• Fibers are of two types, Natural and Synthetic (or artificial).
• Natural fibers are obtained from organic sources (plants and animals). Examples: jute, cotton, silk, wool
• Synthetic fibers are chemically processed. Examples: rayon, nylon, dacron, polymer, etc,

Explanation:

• Artificial fibers came into use because they were cheap and easy to maintain compared to natural fibers.
• The cloths made up of artificial fibers get easily dried up when washed.
• They get less wrinkled and are resistant to bugs.
• Though they are not so comfortable compared to natural ones. Cotton cloths are more comfortable in summer compared to synthetic alternatives.
• Also, fire catches easily in synthetic cloths. Therefore, it is recommended to wear cotton clothes while burning crackers on Diwali.
• So, Synthetic fibers are not fire-resistant. They are cheaper, easy to maintain bus less comfortable.

The correct option here is 'They are fire-resistant.'

1. + and ×

24 + 108 - 36 ÷ 6 × 18 = 84

⇒ 24 + 108 - 6 × 18 = 84

⇒ 24 + 108 - 108 = 84

⇒ 132 - 108 = 84

⇒ 24 ≠ 84

2. ÷ and -

24 × 108 ÷ 36 - 6 + 18 = 84

⇒ 24 × 3 - 6 + 18 = 84

⇒ 72 - 6 + 18 = 84

⇒ 90 - 6 = 84

⇒ 84 = 84

3. - and +

24 × 108 + 36 ÷ 6 - 18 = 84

⇒ 24 × 108 + 6 - 18 = 84

⇒ 2592 + 6 - 18 = 84

⇒ 2598 - 18 = 84

⇒ 2580 ≠ 84

4. + and ÷

24 × 108 - 36 + 6 ÷ 18 = 84

⇒ 24 × 108 - 36 + 0.34 = 84

⇒ 2592 - 36 + 0.34 = 84

⇒ 2592.34 - 36 = 84

⇒ 2556.34 ≠ 84

Hence, ‘÷ and -’ is the correct answer.

Concept:

BODMAS Rule:

Calculation:

(1500 − 275) ÷ 25 ÷ 7 + 300 = ?

1225 ÷ 25 ÷ 7 + 300 = ?

49 ÷ 7 + 300 = ?

? = 7 + 300 = 307

Shortcut Trick

We know that: HCF × LCM = Product of two numbers

⇒ HCF × 3528 = 148176

Check the unit digit: 8 × (unit digit of HCF) must end in 6.

Since 8 × 2 = 16 (ends in 6), the unit digit of the HCF must be 2.

Among the given options, only 32 and 42 end with 2. By estimating, 3500 × 40 = 140000, so 42 is the correct fit.

∴ The correct answer is 42.

Alternate Method

Given:

Product of the two numbers = 1,48,176

Least Common Multiple (LCM) = 3,528

Formula Used:

For any two given numbers:

Product of numbers = HCF × LCM

Calculations:

⇒ 148176 = HCF × 3528

⇒ HCF = 148176 ÷ 3528

⇒ HCF = 42

∴ The correct answer is 42.

Additional Information

Product Rule Validity

The formula (Product of numbers = HCF × LCM) is strictly valid ONLY for two numbers. It does not apply directly to three or more numbers.

HCF and LCM of Fractions

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

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

Co-prime Numbers

Two numbers are said to be co-prime if their HCF is 1. In such cases, their LCM is always equal to the product of the two numbers.

The correct answer is Saraswati River.

• Rani-ki-Vav, on the banks of the Saraswati River, was initially built as a memorial to a king in the 11^th century AD. It is **located in **Gujarat.
• It is an exceptional example of a distinctive form of subterranean water architecture of the Indian subcontinent.
• This stepwell was built by the Solanki dynasty’s queen Udayamati in the 11^th century as a memorial to her deceased husband Bhimdev I.
• Over the years, as the Saraswati river changed its course, the massive structure was flooded and lay buried until its excavation by the Archaeological Survey of India in the late 1980s.
• Rani-ki-Vav highlights the sanctity of water as it is designed as an inverted temple under the earth’s surface.

​

• The new 100 rupee note (colored Lavender)  features the motif of 'Rani ki Vav', Queen's Stepwell, a UNESCO World Heritage site in Gujarat's Patan.

The correct answer is Osteoporosis.

• Calcium deficiency occurs at any stage.
• It can result in rickets, osteoporosis, and osteopenia.
• Osteoporosis occurs at later stages of life and is a disease in which bone becomes more fragile and more likely leading to fractures.

Additional Information

• Anaemia is occurs due to the deficiency of iron and it may also leads to tiredness and shortening of breath.
• Osteomalacia refers to softening of bones, caused by severe vitamin D deficiency.
• Rickets usually occurs due to the lack of vitamin D or calcium and it is a condition which affects bone development in children.

Statement I: Not sufficient

Date of birth of Ram is not known so, his anniversary date cannot be determined.

Statement II: Not sufficient

Month of birth of Ram is not clear so, his anniversary date cannot be determined.

Therefore, neither of the statements is sufficient to answer the question.

Concept used:

Calculation:

⇒ 144 ÷ 12 + 42 - 44 + 54 ÷ 3 × 2

⇒ 12 + 16 - 44 + 18 × 2

⇒ 12 + 16 - 44 + 36

⇒ 64 - 44 = 20

∴ The correct answer is 20.

Given: Each of six sports persons, Falak, Bala, Renu, Rekha, Priya and Pallavi, has a different weight. 

1) Pallavi is the heaviest.

Pallavi > _ > _ > _ > _ > _

2) Rekha is heavier than only Falak and Renu but lighter than Bala and Priya.

Pallavi > Bala/Priya > Bala/Priya > Rekha > Falak/Renu > Falak/Renu

3) Priya is heavier than Bala and Falak is heavier than Renu.

Pallavi > Priya > Bala > Rekha > Falak > Renu

Thus, according to the final arrangement, Renu is the lightest among all the sports persons.

Hence, "Option 3" is the correct answer.

Given:

Numbers: 2, 3, 8.

Concept:

The Least Common Multiple (LCM) of numbers is the smallest multiple that is divisible by each of the numbers.

Calculation:

Find the prime factors of each number:

2 = 2

3 = 3

8 = 2 × 2 × 2 = 2³

Identify the highest power of each prime factor:

2³

3¹

Multiply the highest powers together to find the LCM:

LCM = 23 × 3¹ = 8 × 3 = 24.

Therefore, the LCM of 2, 3, and 8 is 24.

The correct answer is Sattriya.

Key Points

• This dance which is said to be the amalgamation of Ojapali and Devadasi is known as Sattriya.
• Sattriya:
• Sattriya is one of the 8 classical dances of India.
• It originated in the state of Assam.
• This dance includes Nritta, Nritya and Natya.
• It was introduced by Saint Shankaradeva in the 15^th century.
• The dance derives its name from the word 'Sattras' which means Vaishnava monasteries.
• The subject matter of this dance is mainly mythological stories of Lord Vishnu.
• It is known for its hand gestures and footwork.
• 'Ankia Naat' is a type of Sattriya dance which is a musical drama portraying the story of Lord Krishna.

Important Points

• Important performers of the Sattriya dance:
• Guru Jatin Goswami
• Guru Ghanakanta Bora
• Manik Barbayan
• Bhabananda Barbayan
• Late Moniram Dutta
• Muktiyar Barbayan
• Late Roseshwar Saikia Barbayan
• Late Dr Maheswar Neog
• Late Ananda Mohan Bhagawati
• Sharodi Saikia
• Indira PP Bora
• Anita Sharma
• Anwesha Mahanta
• Mallika Kandali

Additional Information

• Ojapali is a dance form founded in Assam.
• The devadasi community of Tamil Nadu are the founder of the classical dance form called Bharatanatyam.
• Mahari is a ritualistic dance form that originated from the state of Odisha that used to be performed at the Jagganath Temple of Puri by devadasi dancers who were known as Maharis.

The Correct Answer is Option 2 i.e Noble gases.

• Group Number 18 of the Modern Periodic table contains noble gases.
• They are called noble gases because they in general, don't react with anything. They possess very low chemical reactivity.
• The elements belonging to group number 18 are helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), radon (Rn), and Oganesson (Og).
• They are all colorless and odorless gases.
• Non-metals form acidic oxides when a non-metal reacts with oxygen it gives an oxide which on reaction with water gives an acid.
• Non-metal oxides are acidic in nature while metal oxides are basic in nature.
• Metals lose electrons to form cations (positive charge) whereas non-metals gain electrons to form anions (negative charge).
• Metals are good conductors of electricity because of a lot of free electrons while non-metals are bad conductors of electricity because they have no free electrons.
• Metalloid and has both metal and non-metal qualities.

P @ M % H # A @ G & B → P is daughter of M, M is wife of H, H is brother of A, A is daughter of G, G is husband of B.

By using the symbols in the table given below, we can draw the following family tree:

Clearly, B is paternal grandmother, i.e., father's mother of P.

Hence, ‘Father’s mother’ is the correct answer.

Shortcut Trick

Using the unitary method for direct proportions:

Cost of 6 mangoes = ₹90

Cost of 1 mango = 90 ÷ 6 = ₹15

Cost of 10 mangoes = 10 × 15 = ₹150

∴ The correct answer is ₹150.

Alternate Method

Given:

Cost of 6 mangoes = ₹90

Formula Used:

Cost of N items = N × (Total Cost ÷ Given Quantity)

Calculations:

⇒ First, find the cost of a single mango.

⇒ Cost of 1 mango = 90 ÷ 6 = ₹15

⇒ Now, multiply this unit cost by the required quantity.

⇒ Cost of 10 mangoes = 10 × 15

⇒ Cost of 10 mangoes = ₹150

∴ The correct answer is ₹150.

Additional Information

Unitary Method

A technique for solving problems by first finding the value of a single unit and then multiplying that unit value to find the required quantity.

Direct Proportion

Two quantities are in direct proportion if an increase in one causes a proportional increase in the other. It is represented by the formula: x₁ ÷ y₁ = x₂ ÷ y₂.

Inverse Proportion

Two quantities are in inverse proportion if an increase in one causes a proportional decrease in the other. It is represented by the formula: x₁ × y₁ = x₂ × y₂.

Statement: Is ‘Maruti Car’ twice as fuel efficient as an ordinary car?

⇒ Here, a question is being asked which seeks to compare the fuel efficiency of ‘Maruti Car’ vis-à-vis an ordinary car. This question also asks if the fuel efficiency is double in a 'Maruti Car'.

Assumption I: A large number of people use ‘Maruti Car’. ⇒ This assumption is not implicit as the number of people buying the 'Maruti Car' does not speak to its fuel efficiency, just to its popularity. 

Assumption II: The sale of ‘Maruti Car’ has increased ⇒ This assumption is not implicit because the recent sales could be because of anything. There’s data regarding sales of ‘Maruti Car’ not fuel efficiency of ‘Maruti Car’. This is not enough to answer the question in the statement. 

Hence, neither I nor II follows.

Given:

2.5 × [144 ÷ 198 × {121 × 81 ÷ (11 × 9)}] 

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

2.5 × [144 ÷ 198 × {121 × 81 ÷ (11 × 9)}] 

⇒ 2.5 × [144 ÷ 198 × {121 × 81 ÷ 99}] 

⇒ 2.5 × [144 ÷ 198 × {99}] 

⇒ 2.5 × [72] 

⇒ 180

∴ The value is 180.

The correct answer is Option 1, i.e Article 153.

• There shall be a Governor for each state (Article 153 of the Constitution of India).
• The executive power of the State shall be vested in the Governor and shall be exercised by him either directly or through officers subordinate to him in accordance with the Constitution of India (Article 154).
• Article 148: It states that there shall be a Comptroller and Auditor-General of India who shall be appointed by the President by warrant under his hand and seal and shall only be removed from office in like manner and on like grounds as a Judge of the Supreme Court.
• Article 61: It provides for the Impeachment of the President of India. The President can be removed from office by impeachment for violation of the Constitution.
• Article 178: Every Legislative Assembly of a State shall, as soon as may be, choose two members of the Assembly to be respectively Speaker and Deputy Speaker thereof and, so often as the office of Speaker or Deputy Speaker becomes vacant, the Assembly shall choose another member to be Speaker or Deputy Speaker, as the case may be.

The correct answer is Abscisic acid.

Key Points

• The plant hormone, Abscisic acid inhibits the growth of the plant.
• Auxin, Gibberellins, and cytokinins promote the growth of the plant.
• Abscisic Acid (ABA) is involved in the closure of stomata, seeds dormancy, and inhibit other hormonal actions.
• It plays an important role in seed maturation.
• It also has an important role in the synthesis of proteins and compatible osmolytes, which enable plants to tolerate stresses due to environmental or biotic factors.

Additional Information

• Cytokinins, Gibberellins, Auxins are responsible for plant growth.
• They are produced within the plant and occur in very low concentrations.
• They control all aspects of plant growth and development, regulation of organ size, embryogenesis, stress tolerance, etc.

The correct answer is Option 3: Question them and ask them to either repair the mobile or pay for the losses they caused.

Qualities Projected in this situation:  (Effective intelligence and reasoning ability).

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:

Shortcut Trick

Ratio of numbers = 4 : 5. Let numbers be 4x and 5x.

New ratio is 1 : 1, which means the modified values are equal.

⇒ 4x + 3 = 5x − 7

⇒ 5x − 4x = 3 + 7

⇒ x = 10

⇒ Numbers are 4 × 10 = 40 and 5 × 10 = 50.

∴ The correct answer is 40, 50.

Alternate Method

Given:

Ratio of two numbers = 4 : 5

Smaller number = 4x, Larger number = 5x

Calculations:

⇒ According to the question: (4x + 3) / (5x − 7) = 1 / 1

⇒ 4x + 3 = 5x − 7

⇒ 5x − 4x = 7 + 3

⇒ x = 10

⇒ First number = 4 × 10 = 40

⇒ Second number = 5 × 10 = 50

∴ The correct answer is 40, 50.

Additional Information

Ratio and Proportion

A ratio compares two quantities by division. If a : b = c : d, then a × d = b × c (Product of extremes = Product of means).

Cross Multiplication Method

For problems involving changes in ratios, the cross-multiplication technique can quickly find the value of one unit by comparing initial and final ratios with the absolute changes.

The logic follows here is :-

Given statements are :

M ≥ N ≥ O = P, G > H < I = J, M < L ≥ K ≥ J

On combining the given statements we get :

G > H < I = J ≤ K ≤ L > M ≥ N ≥ O = P

Conclusions:

I. M > P → False (As M ≥ N ≥ O = P, the possible relation between M and P should be M ≥ P, but given M > P so , false)

II. P = M → False (As M ≥ N ≥ O = P, the possible relation between M and P should be M ≥ P, but given P = M so , false)

Here conclusions I and II form a complimentary pairs as possible relation is M ≥ P, Either M > P or M = P

Hence, Either conclusions I or II follows.

Key Points

Conditions for Either - or

I. Subject and predicate should be same.

II. Both the individual conclusions must be false

Given:

Principal (P) = ₹3500

Rate (r) = 3% per year

Time (t) = 2 years

Formula used:

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

Calculations:

SI = \(\frac{3500 \times 3 \times 2}{100}\)

⇒ SI = \(\frac{21000}{100}\)

⇒ SI = ₹210

∴ The correct answer is option 1.

The correct answer is Developing heritage cities.

In News

• The Scheme 'HRIDAY' is associated with Developing heritage cities

Key Points

• The scheme 'HRIDAY' is associated with the development of heritage cities in India.
• HRIDAY is an acronym that stands for Heritage City Development and Augmentation Yojana.
• HRIDAY scheme was launched on 21^st January 2015.
• The 100% funding of this scheme is sponsored by the government of India.
• The budget amount of the HRIDAY scheme is ₹500 crore.
• It was launched by the ministry of housing and urban affairs.

​

Important Points

• In the initial phase**, 12 heritage cities in India** have been identified which will be rejuvenated and developed under HRIDAY:

1. Ajmer.
2. Amaravati.
3. Kanchipuram.
4. Mathura.
5. Puri.
6. Varanasi.
7. Velankanni.
8. Warangal.
9. Amritsar.
10. Badami.
11. Dwarka.
12. Gaya.

The correct answer is Malleability.

Key Points

• The property by virtue of which metals can be beaten into thin sheets is known as malleability.
• Metals are malleable.
• Malleability is a substance's ability to deform under pressure.
• Malleability is a property of material by which in can be beaten to form its thin sheets. Most of the metals are malleable.
• The crystal structure of harder metals such as antimony and bismuth, makes it more difficult to press atoms into new positions without breaking. This is because the rows of atoms in the metal don't line-up.
• Example of Malleable Metals are bellow.
• Gold.
• Silver.
• Iron.
• Copper.
• Tin.

Additional Information

Shouting loudly will disturb students giving the exam.

Relocating the student based on a doubt is not appropriate. If the examiner is sure that the student is cheating then relocating the student is correct but it should not be done on the basis of a doubt.

Telling the nearby students about my doubt will create a negative impact on the student if the student was not cheating. It should not be done on the basis of a doubt.

Keeping the concerned student under vigilance and verify if your doubt is actually, true is the most preferred course of action.

Hence, ‘option 4’ is the correct answer.

Given:

A & B together do a work in 12 days.

B & C together do in 15 days.

C & A together do in 20 days.

Formula used:

Work done by 2A, 2B, and 2C together in one day = (1/A & B) + (1/B & C) + (1/C & A)

Calculation:

Work done by A & B in one day = 1/12

Work done by B & C in one day = 1/15

Work done by C & A in one day = 1/20

⇒ Work done by 2(A + B + C) in one day:

⇒ (1/12) + (1/15) + (1/20)

Finding LCM of 12, 15, and 20 = 60

⇒ (5/60) + (4/60) + (3/60)

⇒ 12/60

⇒ 1/5

⇒ Work done by (A + B + C) in one day:

⇒ 1/2 × 5 

⇒ 1/10

So, A, B, and C together can complete the work in 10 days.

To find the number of days to complete 2/5^th of the work:

⇒ Total work = 10

⇒ 2/5^th of the work = (2/5) × 10

⇒ 4 days

∴ The correct answer is option (3).

As per the given information;

Distance between A and B = 5 + 4 = 9 km

Hence, A is 9 km far away from B.