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

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Explanation:

Bakelite is a polymer that is made up of the monomers phenol and Formaldehyde. This phenol-Formaldehyde is a Thermosetting polymer.

Some important properties of Bakelite are listed below.

• It can be easily Molded.
• Very smooth molding can be obtained from this polymer.
• Bakelite moldings are heat resistant and scratch-resistant.
• Owing to its low electrical conductivity, bakelite is resistant to electric current.

Bakelite structure:

Important Points

• Bakelite is used for making electrical switches.
• Melamine is used for floor tiles.

(I) Rs. 500 crores is not sufficient for developing smart cities project in India. – False

The statement does not mentions whether the amount allocated is sufficient or not.

(II) Rs. 500 crores is adequate for developing smart cities project in India. – False

The statement does not mentions whether the amount allocated is sufficient or not.

But I and II are complementary statements.

Hence, if either conclusion (I) or (II) follows

Given:

The average of six consecutive odd numbers is 66.

Formula used:

Average = Sum of all terms / Number of terms

Calculation:

Let the six consecutive odd numbers be x, x + 2, x + 4, x + 6, x + 8, x + 10

⇒ Average = (x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10)/6 = 66

⇒ (6x + 30)/6 = 66

⇒ 6x + 30 = 66 × 6 = 396

⇒ 6x = 396 - 30 = 366

⇒ x = 366/6 = 61

The lowest number = x = 61

And the highest number = (x+10) = 61 + 10 = 71

Average = (Lowest + Highest)/2

⇒ (61 + 71)/2 = 132/2 = 66

∴ The average of the lowest and highest odd numbers out of these is 66.

The condition to make a five-member team is:-

1. M4 and M7 are to be selected together.

2.M3 and M6 are to be selected together. 3. Either M2 or M1 is to be chosen with M6.

Option 1. M3, M4, M5, M6, M8❌

Here, M4 and M7 are not selected together. But according to the conditions M4 and M7 are to be selected together.

Hence, this option is incorrect.

Option 2. M2, M3, M4, M6, M8❌

Here, M4 and M7 are not selected together. 

Hence, this option is incorrect.

Option 3. M2, M3, M5, M6, M8✅

This option fulfill all conditions.

Hence, this option is correct.

Option 4. M1, M2, M3, M5, M8 ❌

Here, M3 and M6 are not selected together.

Hence, this option is incorrect.

Hence, the correct answer is M2, M3, M5, M6, and M8.

Given:

Distance covered = 2.5 km

Time taken = 4 minutes 10 seconds = 4 + 10/60 = 4 + 1/6 = 25/6 minutes

New distance = 6 km

Formula Used:

Time = Distance / Speed

Calculation:

Speed = Distance / Time

Speed = 2.5 / (25/6)

Speed = 2.5 × 6 / 25

Speed = 15 / 25

Speed = 3 / 5 km/min

Time to cover 6 km = Distance / Speed

Time to cover 6 km = 6 / (3/5)

Time to cover 6 km = 6 × 5 / 3

Time to cover 6 km = 30 / 3

Time to cover 6 km = 10 minutes

Therefore, the correct answer is option 4.

The correct answer is Lakshadweep.

Key Points

• According to Census 2011, Lakshadweep, with a literacy rate of 91.8%, is the Union Territory with the highest literacy rate in India.
• And according to the Census of 2011 Lakshadweep ;has the second-highest literacy rate in India.
• Kerala ranks the highest in terms of literacy rate with a 94.00% literacy rate.

Additional Information

• As per the 2011 census,
• The literacy rate of India is 74.04 %.
• Male literacy rate = 82.14%.
• Female literacy rate = 65.46%.
• The top five states and UTs where the literacy rate is the highest are:
• Kerala (94%)
• Lakshadweep (91.8%)
• Mizoram (91.3%)
• Goa (88.7%)
• Tripura (87.2%).
• Among the State/UTs, the male and female literacy rate is highest in Kerala (male: 96.11%, female 92.07%) and lowest in Bihar (male: 71.2%, female: 51.5%).

The correct answer is Distillation.

Key Points

• Distillation, or classical distillation, is the process of separating the components or substances from a liquid mixture by using selective boiling and condensation.
• Dry distillation is the heating of solid materials to produce gaseous products.
• Examples of uses of distillation include purification of alcohol, desalination, crude oil refining, and making liquefied gases from the air.
• Vacuum distillation is distillation performed under reduced pressure, which allows the purification of compounds not readily distilled at ambient pressures or simply to save time or energy.

Additional Information

• Filtration is a process used to separate solids from liquids or gases using a filter medium that allows the fluid to pass through but not the solid.
• Evaporation is a type of vaporization that occurs on the surface of a liquid as it changes into the gas phase.
• Condensation is the change of the physical state of matter from the gas phase into the liquid phase and is the reverse of vaporization.

The pattern followed here is:

The least possible Venn diagram is shown below according to the given information.

Statements:

Some ships are cups.

No cup is a stool.

All windows are cups.

Conclusions:

I. Some ships being windows is a possibility → Follow → As some ships are cups and No cup is a stool and all windows are cups. So some ships being windows is a possibility is definitely followed.

II. No window is a stool → Follow → As No cup is a stool and All windows are cups. So No window is a stool is definitely followed.

III. All cups are windows → Does not follow → As all windows are cups. So all cups are windows is not definitely followed.

IV. No ship is a stool → Does not follow → As some ships are cups and No cup is a stool and all windows are cups. So No ship is a stool is not followed because it is a possibility that some ships are stool. So it is definitely not followed.

So, the only conclusions I and II follow.

Hence, the correct answer is "Option 3".

Given:

a = 32

b = 162

Formula used:

Mean Proportional = √(ab)

Calculation:

Mean Proportional = √(32 × 162)

⇒ √5184

⇒ 72

The mean proportion is 72.

The table shows the place value of the alphabet from A to Z.

The logic followed here is:

Given series is HJLN : SQOM : : DFHJ : ?

As, HJLN : SQOM

Similarly, DFHJ : ?

Hence, the correct answer is "DFHJ : WUSQ".

Assume a + b = x

x² – 2x – 80 = 0

x = 10

ab = 16

a = 8, b = 2

3 × a – 19b = −14

Alternate MethodHere, (a + b)2 − 2(a + b) = 80 and ab = 16

⇒(a + b)2 − 2(a + b) = 80

Adding 1 in both the sides , we get

⇒ (a + b)2 − 2(a + b) + 1 = 80 + 1

⇒ (a + b) 2 − 2 ×(a + b) × 1 + (1)² = 81

⇒ {(a + b) - 1}² = 81

⇒ (a + b - 1) = 9

⇒ (a + b) = 10

Since ab = 16 = 8 × 2 and a + b = 10

⇒ a = 8 and b = 2

∴ 3a - 19b = 3 × 8 - 19 × 2 = -14

The Correct Answer is 7^th August.

 

Key Points

• August 7 is celebrated as the National Handloom Day.
• Prime Minister Narendra Modi inaugurated the first National Handloom Day in 2015.
• It was a salute to weavers and others in the industry to promote the handmade and the handwoven.

 

Important Points

• August 7 was chosen as the National Handloom Day to commemorate the Swadeshi Movement.
• The Swadeshi Movement was launched on August 7 in 1905 in the Calcutta Town hall to protest against partition of Bengal by the British Government.
• The movement had aimed at reviving domestic products and production processes.

The correct answer is Reduce high blood pressure.

Key Points

• Reserpine is used to treat high blood pressure.
• It also is used to treat severe agitation in patients with mental disorders.
• Reserpine is in a class of medications called rauwolfia alkaloids.
• It works by slowing the activity of the nervous system, causing the heartbeat to slow and the blood vessels to relax.

Additional Information

• Reserpine lowers blood pressure by slowing down your nervous system.
• This allows your blood vessels to relax and dilate (widen), which helps your heartbeat more slowly and improves blood flow.
• Reserpine is used to treat hypertension (high blood pressure).

Given:

Today is Saturday

Calculation:

A week has 7 days.

Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.

Then, Sunday again.

71 days have 10 weeks' worth of days and then one extra day.

After each week or every seven days, a day of the week is repeated. 

So, the 70^th day will be Saturday again

Thus, the 71^st day will be Sunday

∴ After 71 days it will be Monday.

Given:

Difference between cost price (CP) and selling price (SP) = Rs. 180

Profit percentage = 12%

Formula Used:

Profit = SP - CP

Profit Percentage = (Profit / CP) × 100

SP = CP + Profit

Calculation:

Let CP be x.

Profit = Rs. 180

Profit Percentage = 12%

\(\frac{180}{x} \times 100\) = 12

⇒ 18000 / x = 12

⇒ x = 18000 / 12

⇒ x = 1500

CP = Rs. 1500

SP = CP + Profit

⇒ SP = 1500 + 180

⇒ SP = 1680

The selling price is Rs. 1680.

The logic followed here is:

Hence, "G56H" is the correct answer.

Shortcut Trick

Total Work = LCM(18, 24) = 72 units.

Efficiency: C = 4 units/day, B = 3 units/day (Total = 7 units/day).

Work completed in 8 days = 8 × 7 = 56 units.

Remaining work = 72 − 56 = 16 units.

Time for B = 16 ÷ 3 = 5¹/₃ days.

∴ The correct answer is 5¹/₃ days.

Alternate Method

Given:

Time taken by C to complete the work = 18 days

Time taken by B to complete the work = 24 days

Time they worked together = 8 days

Formula Used:

Total Work = Efficiency × Time

Time Taken = Total Work ÷ Efficiency

Calculations:

⇒ Efficiency of (C + B) = 4 + 3 = 7 units/day

⇒ Work done by C and B in 8 days = 7 × 8 = 56 units

⇒ Remaining work = 72 − 56 = 16 units

⇒ Time taken by B to finish remaining work = 16 ÷ 3 = 5¹/₃ days

∴ The correct answer is 5¹/₃ days.

Additional Information

Total Work (LCM Method)

Taking Total Work as the Least Common Multiple (LCM) of the given times ensures efficiency values are integers, making calculations faster: Total Work = LCM of Days.

Efficiency & Time Relation

Efficiency is inversely proportional to Time when Total Work is constant. The formula to remember is: Total Work = Efficiency × Time.

Mid-way Joining or Leaving

When individuals join or leave during a project, always calculate the exact work completed up to that point. Subtract it from Total Work to find Remaining Work, which is then divided by the efficiency of the remaining active workers.

The correct answer is Maruthur Gopalan Ramachandran.

Key Points

• The highest civilian award of India is the Bharat Ratna.
• Bharat Ratna was started in 1954 for the first time in India.
• Bharat Ratna is given to a maximum of three nominees every year. To date, 53 people had been awarded the Bharat Ratna.
• The three recipients who received Bharat Ratna for the first time were C. Rajagopalachari, Sarvepalli Radhakrishnan, and C.

V. Raman.

• In 2019 Bharat Ratna was awarded to Nanaji Deshmukh (posthumous), Bhupen Hazarika (posthumous), and Pranab Mukherjee.
• Maruthur Gopalan Ramachandran was the third Chief Minister of Tamil Nadu from 1977 to1987 to be awarded the highest civilian award Bharat Ratna posthumously.
• Maruthur Gopalan Ramachandran's resting place is known as MGR Memorial.
• Maruthur Gopalan Ramachandran belongs to the All India Anna Dravida Munnetra Kazhagam party.
• Maruthur Gopalan Ramachandran was a Film actor, Producer, Director, Politician, and Philanthropist by Profession.

Image of Maruthur Gopalan Ramachandran

Important Points

• The five recipients of the Bharat Ratna award in 2024 were: 
• M. S. Swaminathan: An agricultural scientist and the "Father of the Green Revolution". He was a key figure in the changes to farming in the 1960s and 1970s that helped India achieve food security. He also worked in biodiversity, biotechnology, and environmental conservation.
• Karpoori Thakur: A former Chief Minister of Bihar.
• **P.

V. Narasimha Rao**: A former Prime Minister.

• Chaudhary Charan Singh: A former Prime Minister.
• L. K. Advani: A veteran BJP leade

The correct answer is amino acids.

Key Points

• All proteins are polymers of a-amino acids which are linked together through a peptide linkage.
• Proteins make up 15% of the mass of our body.
• Amino acids
• Amino acids are the basic building units of proteins.
• Their molecule possesses both an amino group as well as a carboxylic group.
• The amino acids having amino and carboxyl groups are attached to the same carbon.
• Example- Glycine, Alanine, etc.

Additional Information 

• Sugars
• Carbohydrates that are sweet in taste are called sugars.
• Example- Sucrose, lactose, etc.
• Fatty acids
• Fatty acids are the building blocks of the fat in our bodies and in the food we eat.
• Example- fats, oils, cholesterol, and steroids.

The logic followed here is,

HF 16 is related to KI 8,

RP 10 is related to US 5,

Similarly,

NL 6 is related to,

Hence, the correct answer is "QO 3".

Given:

 \(x+\frac{1}{x}=2\) 

Concept used:

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

Calculation:

 \(x+\frac{1}{x}=2\) 

Squaring both side, we get

⇒  \([x+\frac{1}{x}]^2=2^2\) 

⇒ x² + 1/x² + 2 = 4

⇒ x2 + 1/x2 = 2---(i)

∴  \([x-\frac{1}{x}]^2\) = x² + 1/x² - 2 = 2 - 2 = 0 (from (i))

Given- ELJB is the code for HOME.

So, DUKE would be written as ARHB.

Concept:

In an isosceles triangle, the median to the base is perpendicular to the base and bisect it into two equal parts. 

Given:

PQ = PR = 25 cm, PS = 7 cm

Formula used:

Pythagoras Theorem

Hypotenuse² = Base² + Perpendicular²

Calculation:

In triangle PSQ 

PQ² = PS² + QS²

⇒25² = 7² + QS²

⇒ QS = 24 cm 

∵ QS = 1/2 × QR

∴ QR = 2 × 24 = 48 cm

The correct answer is Firoz Shah Tughlaq.

Key Points

• Jaunpur, city, southeastern Uttar Pradesh state, northern India.
• It straddles the Gomati River, about 35 miles (55 km) northwest of Varanasi (Benares).
• Jaunpur probably was originally founded in the 11^th century but was washed away by the Gomati floods.
• It was rebuilt in 1359 by Firoz Shah Tughluq, whose fort still stands.
• The city was the capital of the independent Muslim kingdom of the Sharqi dynasty.
• It was conquered by the Mughal emperor Akbar in 1559 and fell under British rule in 1775.
• Jaunpur contains several old mosques, including the Aṭala Mosque (1408) and the Jamiʿ Masjid (Great Mosque; 1478).
• A splendid bridge, built in the 16^th century, spans the Gomati.
• Jaunpur is an important road and rail junction.
• The city houses numerous colleges of Deen Dayal Upadhyaya Gorakhpur University in Gorakhpur.

Additional Information

• Tughluq dynasty emerged during the period of medieval India and was of Turk-Indian Origin.
• The dynasty majorly ruled over the Sultanate of Delhi.
• The Tugluq dynasty emerged in 1320 and ended in 1413 and was ruled by many rulers like Ghazi Malik, Muhammad-bin-Tughluq, etc.
• ​Firoz Tughlaq (1351-1388 A.D.)
• In 1351A.D. Firoz Tughlaq was the son of Ghiyas - ud - din Tughlaq’s younger brother.
• He succeeded the throne.
• ​He withdrew all Taquavi (agricultural) loans granted by Mohammed-bin-Tughlaq.
• He raised the salary of the revenue officers. He brought to an end all unlawful and unjust taxes.
• He collected four important taxes which are:
• Kharaj- 1/10 of the produce of the land
• Khams- 1/5 of the war booty
• Jizya-  this tax was meant to be like a protection fee or for exemption from military service or even to practice non-Muslim faith in the rule of a Muslim ruler given by a non-Muslim subject to its Muslim ruler.
• Zakat- Tax on Muslims for specific religious purposes

The correct answer is Helium.

Key Points

• A balloon is a flexible bag that can be inflated with helium gas.

Additional Information

• Helium can be liquefied, but its condensation temperature is the lowest among all the known substances.
• Helium has many unique properties: low boiling point, low density, low solubility, high thermal conductivity, and inertness, so it is used for any application which can exploit these properties.
• The atomic number of helium is 2, meaning each atom of helium has two protons.
• Helium has the lowest melting point and boiling point of the elements, so it only exists as a gas, except under extreme conditions.
• Helium is the second-lightest element.

Given

Statements:

P > Q; Q > R; R > S; S > T.

On combining: P > Q > R > S > T

Conclusions

I. T < Q → True (as Q > R > S > T → Q > T)

II. R < P → True (as P > Q > R → P > R)

Hence, both of the conclusions are true.

Given:

Numbers to find HCF of: 620 and 248.

Formula Used:

Euclidean Algorithm: HCF(a, b) = HCF(b, a mod b)

Calculation:

Step 1: Apply Euclidean Algorithm:

⇒ 620 mod 248 = 124

Step 2: Apply Euclidean Algorithm again:

⇒ 248 mod 124 = 0

The HCF of 620 and 248 is 124.

Let the present age of Nandini be x and her daughter of y.

6 years ago

→ x - 6 = 5(y - 6)

→ x - 6 = 5y - 30

5y - x = 24.....(i)

After 4 years

→ x + 4 = 2(y +4) + 5

→x + 4 = 2y + 8 + 5

→ x - 2y = 9.....(ii)

from (i) and (ii)

→ (5y - x = 24) × 2 ; (x - 2y = 9) × 5

→10y - 2x = 48 ; -10y + 5x = 45

→ 3x = 93; x = 31;

Hence, Nandini is 31 years old today.

Given:

(x₁, y₁) = (4, 3) and (x₂, y₂) = (0, 0)

Concept:

Use of distance formula for calculating the distance between two points

Formula used:

\(PO = \sqrt {{{\left( {{x_1}} \right)}^2} + {{\left( {{y_1}} \right)}^2}}\)

Calculation:

\(PO = \sqrt {{{\left( 4 \right)}^2} + {{\left( 3 \right)}^2}}\)

\( \Rightarrow PO = \sqrt {16 + 9}\)

∴ PO = 5 units

The correct answer is Ujjain.

Key Points

• Madhya Pradesh Sports Youth Welfare Department opened Malkham Academy in Ujjain on the lines of other sports academies running in the state. Hence, Option 1 is correct.
• This is the first Malkhamb Academy in the country.
• Apart from Madhya Pradesh, training will also be given to the players interested in this game from other states.
• This game has been included in the list of major sports of the state by the state government.
• Presently there are training centers in Indore, Ujjain, Khargone, Shajapur, Shivpuri, Gwalior, Datia, Jabalpur, Panna, Tikamgarh, Chhatarpur, Datia, and Sagar districts in the state.

The correct answer is Arteries.

Key Points

• The blood vessels that carry blood from the heart to the various parts of the body are called Arteries.
• The main artery is the aorta, the principal high-pressure duct linked to the left ventricle of the heart.
• The smaller branches of the arteries are called capillaries and arterioles.
• Veins are vessels of the blood which carry blood to the heart.
• The septum is the cartilage that divides the heart into right and left chambers, this prevents the mixing of blood.

The pattern followed here is:

Given:

Similarly,

For "When % SSR 2 meet shall you":

Thus, this statement "When % SSR you 2 meet shall" will be the step 2.

Hence, the correct answer is "Option 3".

Shortcut Trick

Using the multiplying factor method for successive percentage decreases:

Original Population × (1 − 10/100) × (1 − 25/100) = Final Population

P × (9/10) × (3/4) = 2025

P = (2025 × 40) ÷ 27 = 3000

∴ The correct answer is 3000 people.

Alternate Method

Given:

Percentage of people who died due to cholera = 10%

Percentage of remaining people who left the village = 25%

Final remaining population = 2025

Concept Used:

Successive percentage change calculated over the dynamically remaining base value.

Original
100% (x)

−10%

Remaining
90%

−25%

Final: 2025
67.5%

Total reduction to 67.5% corresponds to 2025 people

Calculations:

⇒ Let the original population of the village be 100%.

⇒ People who died due to cholera = 10%

⇒ Remaining population = 100% − 10% = 90%

⇒ People who left the village = 25% of 90% = (25 ÷ 100) × 90% = 22.5%

⇒ Final remaining population = 90% − 22.5% = 67.5%

⇒ We are given that the final population is 2025.

⇒ 67.5% of Original Population = 2025

⇒ Original Population = (2025 ÷ 67.5) × 100

⇒ Original Population = 30 × 100 = 3000

∴ The correct answer is 3000 people.

Additional Information

Successive Percentage Change

When a value is changed by x% and then the newly altered value is changed again by y%, it represents successive percentage change. The net effect is not a simple addition of percentages but calculated sequentially on the updated base value.

Base Value Identification

In percentage problems, keywords like "of the remaining" indicate that the base for the subsequent calculation is the reduced value from the previous step, rather than the initial total base (100%).

Successive Multiplying Factor

Final Value = Initial Value × (1 − r₁/100) × (1 − r₂/100), where r₁ and r₂ are the percentage decreases.

According to the given statements vien diagram wil be:

 

Conclusion:

1) some wheels are ovens > May be follow (some bicycles are wheels and some bycycles are Ovens then there is possibilites that some wheels can be oven.)

2) No wheel is oven. > Depands on 1 conclusion (If some wheels are oven then this conclusion does not follow. If no wheels are oven then this conclusion follow.)

Both conclusion can't be true at same time.

Hence, the correct answer is "Option(4)".

Given:

If two hemispheres of curved surface area 8π cm² each are joined together to form a sphere.

Concept Used:

In this type of question, the total surface area of the sphere can be calculated by adding two hemispheres of curved surface area.

Calculation:

Total surface area of the sphere = (8π + 8π) cm²

∴ Total surface area of the sphere = 16π cm²

The correct answer is the International Monetary Fund.

• The IMF was conceived at the United Nations Conference in July 1944 at Bretton Woods, New Hampshire, United States.
• The IMF was formally formed on 27 December 1945.
• The member nation of the World Bank automatically becomes a member of the IMF.
• The IMF is an international financial institution that monitors the global economic situation of its member countries.

Key Points

The correct answer is Anisole.

Key Points

• Anisole or methoxybenzene is an organic compound with the formula CH₃OC₆H₅.
• It is a colourless liquid with a smell reminiscent of an anise seed, and many of its derivatives are found in natural and artificial fragrances.
• The compound is mainly made synthetically and is a precursor to other synthetic compounds.
• It is mainly used to make perfumes, favouring and as a solvent.

Additional Information

• Toluene (C₇H₈) is a substituted aromatic hydrocarbon, which is a colourless, water-insoluble liquid. with a smell associated with paint thinners.
• It is mainly used in oil refining and manufacturing of paints, dyes, explosives and glues.
• Aniline (C₆H₅NH₂) is an organic compound that is the simplest aromatic amine.
• It is used to make a wide variety of products such as agricultural chemicals, the rubber industry, varnishes etc.

The logic followed here is:

'now or never' is coded as 'ak bj ut' 

'never be late' is coded as 'bj tl cv'

Here, the codes for

now / or - ak / ut

be / late - tl / cv

So, the code for 'never' is 'bj'

Hence, the correct answer is "Option 3".

Shortcut Trick

In cyclic quadrilateral PQRS, sum of opposite angles ∠PSR and ∠PQR = 180°.

∠PQR = 180° − 105° = 75°.

Angle in a semi-circle ∠PRQ = 90° (since PQ is the diameter).

In ▵PQR: ∠QPR = 180° − (90° + 75°) = 15°.

∴ The correct answer is 15°.

Alternate Method

Given: ∠PSR = 105° and PQ is the diameter of the circle.

Formula Used:

1. Opposite angles of a cyclic quadrilateral add up to 180°.
2. The angle subtended by a diameter at any point on the circumference is 90°.
3. Sum of angles in a triangle = 180°.

Calculations:

⇒ In cyclic quadrilateral PQRS, ∠PSR + ∠PQR = 180°

⇒ 105° + ∠PQR = 180°

⇒ ∠PQR = 180° − 105° = 75°

⇒ Since PQ is the diameter, ∠PRQ = 90° (Angle in a semi-circle)

⇒ In ▵PQR, ∠QPR + ∠PRQ + ∠PQR = 180°

⇒ ∠QPR + 90° + 75° = 180°

⇒ ∠QPR + 165° = 180°

⇒ ∠QPR = 180° − 165° = 15°

∴ The correct answer is 15°.

Additional Information

Cyclic Quadrilateral Property

A quadrilateral is cyclic if all its vertices lie on a circle. The sum of each pair of opposite angles is always 180°.

Thales Theorem (Angle in a Semi-circle)

Any triangle inscribed in a circle with one side as the diameter is a right-angled triangle, with the right angle (90°) opposite the diameter.

Angles in the Same Segment

Angles subtended by the same arc (or chord) at any point on the remaining part of the circle are equal.

 

Therefore, Option 4 is the correct answer.

Given:

Amount in one year = 650

Amount in two years = 676

Concept used:

Amount = P(1 + R/100)T

Calculation:

Let the principal be x.

For one year,

⇒ x(1 + R/100)1 = 650      ----(1)

For two years,

⇒ x(1 + R/100)2 = 676      ----(2)

Dividing equation (2) and (1),

\(\frac{x(1 + R/100)^2}{x(1 + R/100)^1} = \frac{676}{650}\)

⇒ (1 + R/100) = 26/25

From equation (1),

⇒ x(26/25) = 650

⇒ x = (650 × 25)/26

⇒ x = 25 × 25

⇒ x = 625

∴ The principle is Rs. 625.

The physical features of India can be grouped under the following physiographic divisions.

• The Himalayan Mountains
• The Northern Plains
• The Peninsular Plateau
• The Indian Desert
• The Coastal Plains
• The Islands

The Himalayan mountain range is separating the plains of the Indian subcontinent from the Tibetan Plateau. 

Tibetan Plateau:

• The Tibetan Plateau is also known in China as the Qinghai–Tibet Plateau or the Qing–Zang Plateau or as the Himalayan Plateau in India, is a vast elevated plateau in Central Asia, South Asia, and East Asia, covering most of the Tibet Autonomous Region, Northwestern Yunnan, the Western half of Sichuan, Southern Gansu and Qinghai provinces in Western China, Indian regions of Ladakh and Lahaul and Spiti (Himachal Pradesh) as well as Bhutan.

Additional Information

Therefore, from the above discussion, we may say that the Elevated peninsula region is not a part of the Indian physiographic division.

The correct answer is Ascorbic acid.

Key Points

• Vitamin C (also known as ascorbic acid and ascorbate) is a vitamin found in various foods and sold as a dietary supplement.
• It is used to prevent and treat scurvy.
• Vitamin C is an essential nutrient involved in the repair of tissue and the enzymatic production of certain neurotransmitters.
• It is required for the functioning of several enzymes and is important for immune system function.
• It also functions as an antioxidant.

​​​​

Additional Information​

Seven houses: M, N, O, P, Q, R, S

1. S is third from the left.

2. O is at the left end.

3. M is second from the right end.

4. P is not at any end and R is to the immediate right of P.

There is only one consecutive vacant place for P and R.

5. N is not beside O.

The final arrangement will be as follows:

Q is located second from left end.

Hence, the correct answer is "Second from the left".

Given:

The average of six numbers = 74

7^th = 79

Concept used:

Average calculation formula: Total sum of numbers ÷ Total count of numbers

Calculation:

The total sum of the six numbers = 74 × 6

⇒ Total sum of the six numbers = 444

Total sum of all seven numbers = Total sum of six numbers + 7^th number

⇒ Total sum of all seven numbers = 444 + 79

⇒ Total sum of all seven numbers = 523

Average of all seven numbers = Total sum of all seven numbers ÷ Total count of numbers

⇒ Average of all seven numbers = 523 ÷ 7

⇒ Average of all seven numbers = 74.71

∴ The average of all seven numbers is 74.71

The logic followed here is:

​

​

Hence, "Option 4" is the correct answer.

Calculations:

\(\sqrt{324}× 65\div26+54=?\) = 18 × 65  /26 + 54 = 1170/26 + 54

⇒ 1170/26 + 54 = 1170/26 + 54 = 45 + 54 = 99

Hence, The Correct option is 4.

The correct answer is Trygve Lie.

Key Points

• Trygve Halvdan Lie was elected the first Secretary-General of the United Nations on February 1, 1946.
• On February 2, 1946, the General Assembly formally inaugurated him at its 22^nd meeting. Mr. Lie was re-elected by the General Assembly on November 1, 1950, for a third term beginning February 1, 1951.
• In November 1952, he resigned as Secretary-General of the United Nations.
• The United Nations Secretary-General (UNSG or SG) is the UN's highest administrative officer and heads the UN Secretariat, one of the UN's six main institutions.
• Chapter XV (Articles 97 to 101) of the United Nations Charter defines the secretary and general's secretariat's roles.

Important Points

• Carl Hammarskjöld was a Swedish economist and diplomat who served as the UN's second Secretary-General from April 1953 until September 1961, when he died in a plane crash.
• U Thant was a Burmese diplomat who served as the UN's third Secretary-General from 1961 to 1971, the first non-Scandinavian to do so.
• Kofi Atta Annan was a Ghanaian diplomat who served as the United Nations' seventh Secretary-General from 1997 to 2006.

The correct answer is Amino acids.

• Enzymes are made up of Amino acids.

Key Points

• Enzymes are made of chains of amino acids chemically bonded to one another.
• These bonds give the enzyme a unique structure, which determines its function.
• Enzymes help in processes like digestion, blood clotting, and hormone production.
• They either catalyze or speed up chemical reactions that take place in the bodies of living things.
• Types of enzymes in the human body:
• Lactase
• Pectinase.
• Bromelain
• Papain
• Catalase

Additional Information

• Carbohydrates are organic compounds in which the ratio of Carbon, Hydrogen and Oxygen is 1: 2: 1.
• **���**Carbohydrate works as fuel during the process of respiration, glucose break into CO₂ and H₂O with the release of energy.
• One gram of glucose gives 4.2 kilocalories energy.
• Nucleic acids are polymers of nucleosides and nucleotides and contain pentose sugar.
• Fat is an ester of glycerol and fatty acid.
• Normally fat remains as solid at 20°C temperature, but if it is in liquid form at this temperature, this is called oil.
• 9.3 kilocalorie energy is liberated from 1 gram fat.

According to the given information:

1)  Anamika is the 13^th from the left side, and Mridula is the 17^th from the right side.

=> The number of students in a row = Mridula's position from left + Mridula's position from right - 1.

=> Mridula's position from left = The number of students in a row - Mridula's position from right + 1.

=> Mridula's position from left = 67 - 17 + 1 = 51.

=> Students between Anamika and Mridula = Mridula's position from left - Anamika's position from left - 1.

=> Students between Anamika and Mridula = 51 - 13 - 1 = 37

Hence, the correct answer is "37".

Alternate MethodAccording to the given information:

1) Anamika is the 13^th from the left side.

2) Mridula is the 17^th from the right side.

3) There are 67 students in total.

12 + Anamika + 37 + mridula + 16 = 67 students

Hence, the correct answer is "37".

GIVEN:

Radius of sphere = 9cm and radius of bullet = 0.3 cm

CONCEPT:

Number of bullets = (Volume of the sphere)/(Volume of each bullet)

FORMULA USED:

Volume of sphere = 4/3πr³

CALCULATION:

Let n be the number of bullets that can be made out of the sphere.

Volume of the sphere = (4/3) × π × (9)³

Volume of each bullet = (4/3) × π × (0.3)³

Now,

⇒ n = [(4/3) × π × (9)³]/[(4/3) × π × (0.3)³]

⇒ n = (9)³/(0.3)³

⇒ n = 27000

The logic is:

Except the first two letters of the word, the remaining letters are written from right to left and the first two letters are then written after it, to obtain the code.

Similarly,

Hence, ‘HTIMSDLGO’ is the correct answer.

Shortcut Trick

Use the direct algebraic identity: (l + b + h)² = (l² + b² + h²) + 2(lb + bh + hl)

Here, (l² + b² + h²) = Diagonal² and 2(lb + bh + hl) = Total Surface Area (TSA).

Shortcut formula: TSA = (Sum of dimensions)² − (Diagonal)²

⇒ TSA = 38² − 22² = 1444 − 484 = 960 cm².

∴ The correct answer is 960 cm².

Alternate Method

Given:

Sum of length, breadth, and height (l + b + h) = 38 cm

Length of the diagonal (d) = 22 cm

Formula Used:

1. Diagonal of a cuboid = √(l² + b² + h²)
2. Total Surface Area (TSA) = 2(lb + bh + hl)
3. Algebraic identity: (l + b + h)² = l² + b² + h² + 2(lb + bh + hl)

Calculations:

⇒ Diagonal = √(l² + b² + h²) = 22

⇒ Squaring both sides: l² + b² + h² = 22² = 484

⇒ We know (l + b + h) = 38

⇒ Squaring both sides: (l + b + h)² = 38²

⇒ l² + b² + h² + 2(lb + bh + hl) = 1444

⇒ 484 + TSA = 1444

⇒ TSA = 1444 − 484

⇒ TSA = 960 cm²

∴ The correct answer is 960 cm².

Additional Information

Volume of a Cuboid

The space occupied by a cuboid is given by the product of its three dimensions: Volume = l × b × h.

Lateral Surface Area (LSA)

The area of the four side walls of the cuboid (excluding top and bottom) is LSA = 2h(l + b).

Special Case: Cube

When l = b = h = a, the cuboid becomes a cube. Diagonal = a√3, TSA = 6a², and Volume = a³.

The Correct Answer is Martha Graham.

Key Points

• Martha Graham was a monumental figure in the development of modern dance.
• Her choreographic style, characterized by expressive movement, reshaped dance and is still taught worldwide.
• Graham’s dance technique and choreography explore the depth of human emotions and the complexities of the human experience.
• She founded the Martha Graham Dance Company, one of the oldest dance companies in America.
• Her work has influenced many generations of dancers and choreographers, including Merce Cunningham and Paul Taylor.

The correct answer is Water.

Key Points

Xylem:

• Water Transport: Xylem is responsible for the transport of water and dissolved minerals from the roots to other parts of the plant.
• It forms a network of interconnected tubes that extend from the root system to the leaves.
• Structure and Components: Xylem tissue is composed of several types of specialized cells.
• The main conducting cells in xylem are called tracheary elements, which include tracheids and vessel elements. These cells have thick, lignified cell walls that provide structural support and prevent collapse under the tension created during water transport.
• Unidirectional Flow: The movement of water through xylem occurs in a unidirectional manner, primarily driven by transpiration, which is the loss of water vapor through the stomata on the leaves.
• This process creates a negative pressure or tension, pulling water upward from the roots to the upper parts of the plant.

Phloem:

• Nutrient Transport: Phloem is responsible for the transport of organic nutrients, such as sugars, amino acids, and hormones, from the site of production (usually leaves) to other parts of the plant.
• It allows the distribution of these nutrients to areas of growth, storage, or metabolic activity.
• Structure and Components: Phloem tissue consists of several cell types, including sieve tube elements, companion cells, phloem fibers, and phloem parenchyma cells.
• The main conducting cells are the sieve tube elements, which form sieve tubes. These cells lack nuclei and have perforated sieve plates that allow the movement of nutrients between adjacent cells.
• Bidirectional Flow: The movement of nutrients through phloem can occur in both upward (from source to sink) and downward (from sink to source) directions.
• This bidirectional flow is facilitated by pressure gradients and active transport mechanisms. Source tissues, such as mature leaves, produce sugars and load them into the phloem, while sink tissues, such as developing fruits or roots, consume the nutrients.

Correct option 4. Both arguments I and II are strong.

The statement asks whether online gambling should be banned in India.

Argument I suggests that it should be banned because credit card or account details of gamblers may be vulnerable to capture, and funds may be vulnerable to theft by computer hackers. Therefore, argument I is strong.

Argument II states that a ban should not be imposed because if the government regulates the regime it can supplement its income by way of imposing taxes. Therefore, argument II is strong.

Hence, option 4 is correct.

Given:

Number of boys (n_b) = 20

Average weight of boys (avg_b) = 60 kg

Number of girls (n_g) = 30

Average weight of all (avg_all) = 54 kg

Formula Used:

Sum of weights = Number of individuals × Average weight

Calculation:

Total weight of 20 boys = n_b × avg_b = 20 × 60 = 1200 kg

Total number of boys and girls = n_b + n_g = 20 + 30 = 50

Total weight of all boys and girls = (n_b + n_g) × avg_all = 50 × 54 = 2700 kg

Total weight of 30 girls = Total weight of all - Total weight of boys

⇒ Total weight of girls = 2700 - 1200 = 1500 kg

Average weight of 30 girls = Total weight of girls / n_g

⇒ Average weight of girls = 1500 / 30 = 50 kg

The average weight of 30 girls is 50 kg.

Given: P, Q, R, S, T, U and V live on seven different floors of the same building.

The lowermost floor in the building is numbered 1, the floor above it is number 2, and so on till the topmost floor is numbered 7.

1. Q lives on floor number 2.

2. R lives on the topmost floor.

3. R lives on the floor immediately above U's floor.

 

4. Only one person lives between the floors of R and P.

5. Only three persons live between the floors of T and P.

 

6. S is on the floor immediately below V's floor.

 

So, P lives on the 5^th floor.

Hence, the correct answer is "Option 2".

Given:

side of equilateral triangle ABC = 28cm

Formula:

Area of an equilateral triangle = √3/4 × side²

Calculation:

Area of equilateral triangle ABC with side 28cm = √3/4 × 28² = 196√3 sq.cm

Area of equilateral triangle PQR = 16 × 196√3 sq.cm

Then,

⇒ 16 × 196√3 = √3/4 × (side of triangle PQR)²

∴ Side of an equilateral triangle PQR = 112 cm

Alternate MethodTwo equilateral triangles are always similar.

Area of ΔABC/Area of ΔPQR = (Side of ABC/Side of PQR)²

⇒ 1/16 = (28/x)²

⇒ 28/x = 1/4

⇒ x = 112 cm

∴ Side of an equilateral triangle PQR = 112 cm

The correct answer is 1909.

• The Morley - Minto Reform, drafted by John Morley, was enacted in 1909.

Key Points

• Indian Council Act of 1909 AD or Morley-Minto Reforms:
• The act was named after the Secretary of State for India John Morley and the Viceroy of India Minto.
• A separate electorate was introduced for Muslims.
• Lord Minto came to be known as the father of the Communal Electorate.
• Non-officials to be elected indirectly.
• Thus, the election was introduced for the first time.
• For the first time, one Indian was to be on Viceroy’s executive council.
• Satyendra Prasad Sinha was the first Indian to join the council as a Law member.
• Annulment of Partition in 1911 AD, the government announced the annulment of the partition of Bengal.

The correct answer is Carbon dioxide.

Key Points

• Lime water reacts with carbon dioxide during respiration, forming calcium carbonate (CaCO₃).
• This makes lime water milky.
• Carbon dioxide (CO₂) -
• It is a colourless and odourless gas.
• It is found naturally on the earth.
• In the atmosphere, this gas is about 0.03% by volume.

Additional Information

• Oxygen -
• It is the element found in the largest amount (about 46.6%) on the earth's crust.
• Its volume in the atmosphere is about 21%.
• Sulfur dioxide -
• It is produced by burning things like factories, coal, or oil.
• It is used as a bleach in the paper industry and wool, silk goods.
• Its chemical formula is SO₂.
• Oxygen is the element found in the largest amount (about 46.6%) on the earth's crust.
• In 1774 AD Joseph Priestley prepared oxygen gas by heating mercuric oxide.
• In 1772 AD Carl Sheele prepared oxygen gas by heating potassium nitrate.

The logic followed here is:-

Hence, the 'option 1' is the correct answer.

Given:

First number: 3² × 4² × 9

Second number: 3³ × 4⁴ × 9¹⁰

Formula used:

HCF is calculated by taking the smallest powers of common prime factors.

Note:

9 = 3².

Calculation:

Rewrite the numbers in terms of prime factors:

First number = 3² × 4² × (3²) = 3⁴ × 2⁴

Second number = 3³ × 4⁴ × (3²⁰) = 3²³ × 2⁸

HCF = Take the smallest powers of 3 and 2:

For 3: min(4, 23) = 4

For 2: min(4, 8) = 4

HCF = 3⁴ × 2⁴

HCF = 81 × 16 = 1296

∴ The HCF is 1296.

Persons; Riya, Mahima, Jagat, Kabir, Sita, Tanu, and Garima.

i) Tanu sits third to the right of Garima. 

 

ii) Sita is sitting exactly left of Tanu.

iii) Kabir is sitting exactly between the Riya and Jagat and Jagat is not a neighbour of Garima.

Hence Jagat is sitting to the right of Tanu.

iv) Neither Sita nor Gita sitting next to Garima.

v) Therefore the Mahima is sitting to the right to the Garima.

Thus we can say from the above arrangement that Mahima sits immediate left of Sita in the neighbourhood.

Hence, the correct answer is "Option 3".

Shortcut Trick

Since the number of boys remains constant, equate the boys' ratio in both cases.

Initial Ratio (Boys : Girls) = 4 : 5 ≡ 12 : 15

New Ratio (Boys : Girls) = 6 : 7 ≡ 12 : 14

Decrease in girls' ratio = 15 − 14 = 1 part ≡ 100 girls.

Number of boys = 12 parts = 12 × 100 = 1200.

∴ The correct answer is 1200.

Alternate Method

Given:

Initial ratio of boys and girls = 4 : 5

Number of girls who left the school = 100

New ratio of boys and girls = 6 : 7

Calculations:

Let the number of boys be 4x and girls be 5x.

⇒ Number of girls after 100 leave = 5x − 100

⇒ New ratio = 4x / (5x − 100) = 6 / 7

⇒ 4x × 7 = 6 × (5x − 100)

⇒ 28x = 30x − 600

⇒ 30x − 28x = 600

⇒ 2x = 600

⇒ x = 300

⇒ Number of boys = 4x = 4 × 300 = 1200

∴ The correct answer is 1200.

Additional Information

Equivalent Ratios

Multiplying or dividing both terms of a ratio by the same non-zero number does not change its value. For example, a : b = ak : bk.

Constant Quantity Concept

In mixture or ratio problems, if one quantity is changed while the other remains constant, making the constant quantity equal in both ratios simplifies the calculation significantly.

Cross-Multiplication Method

When equating two fractions or ratios like a/b = c/d, their cross-products are always equal: a × d = b × c.

Maulana Azad opposed Jinnah's two-nation theory.

Key Points

• Azad was born in Mecca to a Bengali father and an Arab mother.
• Well-versed in many languages, Azad was a scholar of Islam and an exponent of the notion of what-i-deen, the essential oneness of all religions.
• An active participant in Gandhian movements and a staunch advocate of Hindu-Muslim unity, he was opposed to Jinnah’s two-nation theory.
• Maulana Azad rejected this idea and advocated for a united India where people of all religions could live together in harmony.
• He believed that India's diversity was its strength and that a partition based on religion would be disastrous for the country.
• Despite being a Muslim himself, he argued that religion should not be the sole basis for political identity or division.
• Maulana Azad played a significant role in the Indian independence movement and was India's first Education Minister after independence.

Hence we conclude that Maulana Azad opposed Jinnah's two-nation theory.

Additional Information

• Sardar Vallabhbhai Patel is also known as the Iron Man of India. He is remembered as a very strong and dynamic freedom fighter of India. He had actively contributed to the Indian Freedom Movement
• Khan Abdul Ghaffar Khan, also known as Bacha Khan, was a Pashtun independence activist who campaigned to end the rule of the British Raj in India. He was nicknamed as Frontier Gandhi. Khan Abdul Ghaffar Khan worked towards the formation of a united, independent, secular India.
• Veer Savarkar was also known as Swatantryaveer Savarkar. This renowned freedom fighter was also the President of Hindu Mahasabha from 1937 to 1943 and founded a secret organization called Abhinav Bharat Society.

The correct answer is Amalgam.

Important Points

• Amalgam is a special class of alloys in which one metal is mercury.
• Silver amalgam is the amalgam used for a dental filling.
• Gold amalgam is the amalgam used in the extraction of gold from ore.
• The metal mercury is kept inside an iron container because iron doesn't form an amalgam with mercury.
• Mercury is a chemical element with atomic number 80.
• Mercury is also known as quicksilver.
• Mercury is the metal that is liquid at room temperature.
• Mercury is the first known superconductor.
• Cinnabar is the ore of mercury.

Additional Information

• Brass is the alloy of copper and zinc.
• Nichrome is the alloy of nickel, chromium, and iron.
• Electrum is the alloy of gold and silver.

Conclusion:

I. Talat did not cry after failing the Hindi test → False (as Talat always starts crying in situations which are difficult and failing in the Hindi examination was a difficult situation for her, means Talat did cried)

II. Talat cried after failing in Hindi exam → True (as Talat always starts crying in situations which are difficult and failing in the Hindi examination was a difficult situation for her, means Talat did cried)

Hence, only conclusion II follows.

Given:

Perimeter of triangle = 600 m

Ratio of sides of triangle = 12 : 13 : 15

Concept used:

Sum of all sides of triangle = Perimeter of triangle

Calculation:

Sum of all sides of triangle 

⇒ 12x + 13x + 15x = 40x

⇒ 40x = 600

⇒ x = 15

Longest side = 15x

⇒ 15 × 15 = 225 cm

∴ The longest side is 225 cm.

Statement:

Farmers are unable to sell their produce due to low demand.

As statement says Farmers are unable to sell their products due to low demand.

Course of action:

I: The government should buy products from farmers at a price below the cost price and export them at a higher price.

If the government buys their product below the cost price this will not help them to recover their loss, hence this is not the right statement to help the farmers.

Hence, the course of action I do not follows.

II: Government should not interfere in this situation as it will cause trouble to the farmers.

Government should interfere in this situation otherwise how farmers sell their product on a large scale. Hence, this is also not the right statement to help farmers.

Hence, the course of action II do not follows.

Hence, Option (1) is correct.

Additional Information

Some rules to solve Statements and Course of action questions must be kept in mind while solving it.

Rule 1. Have an unbiased and neutral mind frame. Individual perception must not be used to judge the course of action to be taken.

Rule 2. The first step should be to identify the root cause of the problem. Once the problem is solved, a logical mindset should be employed to figure out the course of action.

Rule 3. There must be no extremity involved in the course of action.

Rule 4. A course of action must be able to solve, reduce, or minimize the problem given in the situation.

Rule 5. The course of action can be said to solve/reduce the problem when it is an established fact, when it is logically possible and when it is known from experience.

Shortcut Trick

Equate the ratio difference by making the age gap constant between the mother and son.

Present Ratio = 4 : 1 (Gap = 3 units) | Future Ratio (after 14 years) = 2 : 1 (Gap = 1 unit).

Multiply the future ratio by 3 to equalize gaps: Future Ratio = 6 : 3.

Increase in units for Mother = 6 − 4 = 2 units → 2 units = 14 years → 1 unit = 7 years.

Present age of Mother = 4 units × 7 = 28 years.

∴ The correct answer is 28 years.

Alternate Method

Given:

Present age ratio (Mother : Son) = 4 : 1

Ratio after 14 years = 2 : 1

Calculations:

Let the present age of the Mother be 4x and the Son be x.

⇒ According to the question, after 14 years:

⇒ (4x + 14) / (x + 14) = 2 / 1

⇒ 4x + 14 = 2 × (x + 14)

⇒ 4x + 14 = 2x + 28

⇒ 4x − 2x = 28 − 14

⇒ 2x = 14

⇒ x = 7

⇒ Present age of Mother = 4x = 4 × 7 = 28 years.

∴ The correct answer is 28 years.

Additional Information

Constant Age Difference

The numerical difference between the ages of two persons always remains constant, regardless of how many years pass.

Ratio Balancing Method

To solve age problems quickly, multiply the ratios by the difference of the other ratio to ensure the unit change is consistent with the time elapsed.

Cross-Product Method

For a ratio a:b becoming c:d after x years, use the formula: 1 unit = [x × (c − d)] / [(a × d) − (b × c)].

The correct answer is 226.

Key Points 

• Under Article 226, a writ petition can be filed in a High court for issuing one of the five writs as per the case.
• A High Court is empowered to issue directions, orders, or writs for the enforcement of a Fundamental Right and for any other purpose those include:
• Habeas corpus
• Mandamus
• Prohibition
• Quo warranto
• Certiorari.
• The Supreme Court is considered the protector and guarantor of fundamental rights(Article 32).

Additional Information

• Article 32  of the Indian Constitution has been described as the ‘heart and soul’ of the Indian Constitution by Dr B. R. Ambedkar.
• It gives a citizen the right to approach the Supreme Court to get resorted to any of the fundamental rights in case of their violation.
• It is also known as the Right to Constitutional Remedies.