MP Police Constable : (3 Dec 2025) Memory-Based Paper (Previous Year Paper)

The correct answer is Punjab.

Key Points

• The 48^th Constitutional Amendment inserted a new provision in clause (5) of Article 356 of the Constitution in order to provide that in the case of the Proclamation issued by the President on 6 October 1983 with respect to the State of Punjab, Parliament may pass any resolution with respect to the continuance in force of the Proclamation for a period up to two years.
• Article 356 of the Indian Constitution includes provisions in case of failure of constitutional machinery in the State.
• It empowers the President to issue a proclamation if he is satisfied that a situation has arisen in which the government of a state cannot be carried on in accordance with the provisions of the Constitution. Notably, the president can act either on a report of the governor of the state or otherwise too (i.e., even without the governor’s report).
• A Proclamation imposing President’s rule must be approved by both the Houses of Parliament within two months from the date of its issue.
• President's rule can be imposed in a state under any one of the following different circumstances:
• A state legislature is unable to elect a leader as Chief Minister for a time prescribed by the Governor of that state.
• Breakdown of a coalition leading to the Chief minister having minority support in the house and the Chief minister fails/will definitely fail to prove otherwise, within a time prescribed by the Governor of that state.
• Loss of majority in the Assembly due to a vote of no-confidence in the house.
• Elections postponed for unavoidable reasons like war, epidemic, pandemic, or natural disasters.
• On the report of the Governor of the state if said state's Constitutional machinery or legislature fails to abide by Constitutional norms.

Additional Information

The correct answer is CaCO3.

• CaCO3 is the chemical formula of Calcium carbonate.
• Limestone is a carbonate sedimentary rock composed primarily of calcium carbonate (CaCO3).
• Limestone is the raw material used in the process of manufacturing cement.
• Limestone released carbon dioxide gas while heating.
• Limestone is used as:
• Building material.
• Essential component cement industry.
• Aggregate for the base of roads.
• Filler in products such as toothpaste or paints.
• CaO is the chemical formula of Calcium oxide.
• Calcium oxide is the most abundant in ordinary Portland Cement.
• Calcium oxide is used for the dehydration of gases.
• CaSO4 is the chemical formula of Calcium Sulphate.
• MgSO4 is the chemical formula of Magnesium Sulphate.

Given equation : 42 ÷ 23 + 870 × 3 - 5 = 541

Checking with the options

option 1) + and ×

42 ÷ 23 × 870 + 3 - 5

= 1.826 × 870 + 3 - 5

= 1588.62 + 3 - 5

= 1586.62

option 2) ÷ and -

42 - 23 + 870 × 3 ÷ 5

= 42 - 23 + 870 × 0.6

= 42 - 23 + 522

= 541

option 3) × and ÷ 

42 × 23 + 870 ÷ 3 - 5

= 42 × 23 + 290 - 5

= 966 + 290 - 5

= 1251

option 4) + and -

42 ÷ 23 - 870 × 3 + 5

= 1.83 - 2610 + 5

= - 2603.17

Hence, the answer is ÷ and -

Key Points

Don't do the whole calculation starting from option 1.

Focus on the division part first, those which give integer then proceed further.

Shortcut Trick

If each observation in a set is multiplied by a constant 'k', the average of the set is also multiplied by 'k'.

Original Average = 11

Multiplier (k) = 7

New Average = 11 × 7 = 77

∴ The correct answer is 77.

Alternate Method

Given:

Number of observations (n) = 10

Original Average = 11

Formula Used:

Average = Sum of observations ÷ Total number of observations

Avg = 11
Initial State

Every item × 7

New Avg = 77
Final State

Result: 11 × 7 = 77

Calculations:

⇒ Original Sum = Average × Number of observations

⇒ Original Sum = 11 × 10 = 110

⇒ Since every number is multiplied by 7, the sum is also multiplied by 7.

⇒ New Sum = 110 × 7 = 770

⇒ New Average = New Sum ÷ Number of observations

⇒ New Average = 770 ÷ 10 = 77

∴ The correct answer is 77.

Additional Information

Addition/Subtraction Property

If a constant 'k' is added to or subtracted from every observation, the new average will be (Old Average + k) or (Old Average − k) respectively.

Division Property

If every observation is divided by a non-zero constant 'k', the new average is equal to (Old Average ÷ k).

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the new average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

The correct answer is Article 112.

Key Points

• Annual Financial Statement
• Under the Article 112 of the Indian Constitution, the government is required to present before the Parliament a financial statement of estimated receipts and expenditure in respect of every financial year.
• In India, the government's financial year runs from 1 April to 31 March.
• It is divided into three parts
• Consolidated Fund
• Contingency Fund
• Public Account.

Additional Information

• Article 156 : Term of office of Governor
• The Governor shall hold office during the pleasure of the President.
• Governor shall hold for a term of five years from the date on which he enters upon his office.
• The Governor may, resign his office by writing under his hand addressed to the President.
• Governor shall continue to hold office until his successor enters upon his office.
• Article 234
• Recruitment of persons other than district judges shall be made by the Governor of the State.
• After consultation with the State Public Service Commission and with the High Court exercising jurisdiction
• Article 134
• Appellate jurisdiction of Supreme Court in regard to criminal matters

The correct answer is cellulose.

• Viscose fibre is obtained from cellulose.

Key Points

• Viscose is made from natural cellulose like tree wood pulp, beech, pine, and eucalyptus.
• It is also obtained from bamboo.
• After the processing of viscose, it becomes semi-synthetic by the use of chemicals like sodium hydroxide and carbon disulfide.
• The fibre is absorbent, lightweight, breathable, soft and proves to be an ideal fabric for making clothes.

The positional value of letters according to the English alphabetical series is,

The logic followed here is,

D = 4, H = 8, P = 16, ( The positional value of the first letter is written last and the second letter is written second last, and so on).

The pair that follows the same logic is,

Hence, The correct answer is "XBJ : 10224.

Given:

Train speed = 30 m/s

Bridge length = 650 m

Time to cross = 50 s

Concept:

The total distance covered when a train crosses a bridge is the sum of the length of the train and the length of the bridge. This total distance is equal to the speed of the train times the time it takes to cross the bridge.

Solution:

Total distance covered = speed × time = 30 × 50 = 1500 m

Length of train = total distance - bridge length = 1500 - 650 = 850 m

Hence, the length of the train is 850 metres (Option 3).

The correct answer is 360.

Key Points

• Financial Emergency:
• Article 360 empowers the president to proclaim a Financial Emergency if he is satisfied that a situation has arisen due to which the financial stability or credit of India or any part of its territory is threatened.
• The 38^th Amendment Act of 1975 made the satisfaction of the president in declaring a Financial Emergency final and conclusive and not questionable in any court on any ground.
• But, this provision was subsequently deleted by the 44^th Amendment Act of 1978 implying that the satisfaction of the president is not beyond judicial review.
• A proclamation declaring financial emergency must be approved by both the Houses of Parliament within two months from the date of its issue.
• A resolution approving the proclamation of financial emergency can be passed by either House of Parliament only by a simple majority, that is, a majority of the members of that house present and voting.

Additional Information

• Boric acid (H₃BO₃) is used in eye, to wash to and clean the eyes. It helps remove pollutants from the eye and provide soothing relief from irritants.
• Also known as hydrogen borate, boric acid is a weak acid which is exploited for its antiseptic, flame retardant, and insecticidal properties.

Statements:

All eggs are millets.

All millets are balloons.

All balloons are prisoners.

Venn diagram:

Conclusions:

I. All balloons are eggs → Does not follow → From the given information we can say that all eggs are balloons but it will be wrong to say that all balloons are eggs and the same can be seen in the Venn diagram thus the conclusion does not follow.

II. Some prisoners are millets → Follow → We have 'all millets are balloons' and 'all balloons are prisoners' so we can say that all millets are prisoners, therefore, the conclusion follows.

III. All prisoners are balloons → Does not follow → From the statement, 'all balloons are prisoners' we can only say that some prisoners are balloons but we have no information about all the prisoners thus the conclusion does not follow.

So only conclusion II follows.

Hence the correct answer is option 3)

Given 

Speed  of boat in downstream = 14 

Speed of boat in upstream = 8 

Formula used 

Speed of boat in still  water = (speed of boat in downstream + speed of upstream)/2

Calculation 

Speed of boat in still water = (14 + 8)/2 = 11km /hr 

∴ The required answer is 11 km/hr

According to the Hindu Mythology, "Garuda" is not a part of the ten incarnations of Lord Vishnu.

• According to Hindu Mythology, there are ten complete incarnations of the Lord Vishnu and, countless numbers of incomplete incarnations.
• According to the Vaishnava tradition of Hinduism, the ninth avatar of Vishnu is Gautama Buddha.
• Southern tradition: Balarama, the brother of Lord Krishna, is considered the ninth avatar.

Just because you know your colleague to be honest does not make the complaint any less effective. Hence it is your duty to investigate the case.

Hence options 1 and 3 are eliminated.

Since there are only accusations, your first action will be to find the details of the case before taking any action against your colleague.

Therefore option 2 is also incorrect. 

Hence, the correct answer is option 4.

Given:

Length = 24 cm

Breadth = 16 cm

Height = 12 cm

Concept: 

Volume of a cuboid = Length × Breadth × Height

Solution:

⇒ Volume = 24 cm × 16 cm × 12 cm = 4608 cm³

Therefore, the volume of the box is 4608 cm³.

The correct answer is Karnataka.

Key Points

Neolithic sites in India:

• The Neolithic period began around 10700 to 9400 BC in Tell Qaramel in Northern Syria.
• In South Asia, the date assigned to the Neolithic period is 7000 BC and the earliest example is Mehrgarh Culture.
• Neolithic Revolution or Neolithic Demographic Transition, sometimes called the Agricultural Revolution, was the world’s first historically verifiable revolution in agriculture.
• There are mainly four groups of Neolithic agriculture-based regions in India as follows:
• Indus Valley
• Ganga Valley
• Western India (including northern Deccan) and
• Southern Deccan.
• One of the most important Neolithic agricultural settlements in the Indian subcontinent is Mehrgarh.
• It is now considered oldest agricultural settlement in the Indian subcontinent.
• It flourished in the seventh millennium B.C.
• It is located on the Bolan River, a tributary of the Indus, at the eastern edge of the Baluchistan plateau.
• In 1974, Mehrgarh was excavated by the French Archaeologist Jean Francois Jarrige.

Additional Information

• Other important Neolithic sites include Gufkral and Burzahom in Kashmir; Mahgara, Chopani Mando, and Koldihwa in Belan valley in Uttar Pradesh; Chirand in Bihar, etc.
• Belan valley sites have provided the oldest evidence of rice cultivation in any part of the world.
• The people in Burzahom lived in pit dwellings, rather than building houses on the ground.
• In South India, the important Neolithic sites include Kodekal, Utnur, Nagatjunikonda, Palavoy in Andhra Pradesh; Tekkalkolta, Maski, Narsipur, Sangankallu, Hallur, and Brahmagiri in Karnataka; Pariamlpalli in Tamil Nadu etc.

CONCEPT:

Diamagnetic Substance:

• Diamagnetic substances are those which develop feeble magnetization in the opposite direction of the magnetizing field.
• Such substances are feebly repelled by magnets and tend to move from stronger to weaker parts of a magnetic field.
• Magnetic susceptibility is small and negative i.e. -1 ≤ X ≤ 0.
• Examples: Bismuth, copper, lead, zinc, etc.

Explanation:

From the above explanation, we can see that when diamagnetic material is placed in an external magnetic field the magnetic dipoles of the diamagnet  will be aligned in the opposite direction of the applied magnetic field

Hence the net magnetic moment will always be zero for a diamagnetic material when subjected to an external magnetic field.

1. Blacksmith : anvil → A blacksmith uses tools like anvil to create objects from metal.

2. Carpenter : saw → A carpenter uses tools like saw to make furniture from wood.

3. Barber : scissor → A barber uses tools like scissor to cut hair.

4. Goldsmith : ornaments → A goldsmith is a person who makes ornaments.

Here in all options except “goldsmith : ornaments”, the first term is the “Professional person” and the second term is the prime tool require for that particular profession is given.

Hence, ‘Goldsmith : Ornaments’ is the odd one out.

Given:

Base area of the cone = 154 cm²

Height of the cone = 24 cm

π = 22/7

Concept used:

The formula for the slant height and curved surface area of a cone.

Solution:

Radius of the cone, r = √(Base Area/π) = √(154/(22/7)) = 7 cm

Slant height, l = √(r² + h²) = √(7² + 24²) = 25 cm

Curved Surface Area = πrl = (22/7) × 7 × 25 = 550 cm²

Therefore, the curved surface area of the cone is 550 cm².

The correct answer is option Ca (calcium).

CONCEPT:

• As we move from top to bottom in a group the atomic size increases and it decreases as we move from left to right in a period.

EXPLANATION:

• I denotes Iodine, N denotes Nitrogen, Ca denotes Calcium and Mg denotes Magnesium.

• Iodine size - 198 pm

• Nitrogen size - 65 pm

• Calcium size - 231 pm

• Magnesium size - 173 pm

• The decreasing order of the atomic size of the elements mentioned: Ca > I > Mg > N

• Atomic size and electronegativity are inversely proportional to each other.

Toothpastes are derived from a wide variety of substances including fluorides, detergents, and abrasives.

• It is slightly basic in nature.
• This is because it is used to neutralize the acid residue left by the bacteria in our mouth.
• It thus helps in maintaining hygiene with respect to the mouth.
• A small amount of calcium phosphate is used in some toothpastes which helps in remineralization of the tooth enamel.
• However, option 3 is more appropriate

According to the given information:

The codes in tabular form :

Thus, the code for 'leaves' is '7'.

Hence, the correct answer is "7".

Let the two numbers be x and y.

Given,

xy = 2500

And x is four times y.

⇒ x = 4y      ----(1)

Putting the value of x in (1), we get

⇒ 4y² = 2500

⇒ y² = 625

⇒ y = 25

The numbers are x = 4 × y = 100 and y = 25

Sum of two numbers = 100 + 25 = 125

The correct answer is Uttar Pradesh.

Key Points

• Charkula Dance:
• Charkula is a traditional dance form that originates from the state of Uttar Pradesh in India, particularly in the Braj region.
• It is typically performed during festive occasions, especially during the celebration of the Hindu festival of Radha Ashtami.
• In this dance, a pyramid-like structure is placed on the head of a female dancer, adorned with numerous lit oil lamps.
• The dancer balances this structure while performing intricate movements and patterns.

Additional Information

• Festivals of Tamil Nadu
• Pongal
• Tamil New Year (Puthandu)
• Karthigai Deepam
• Thaipusam
• Panguni Uthiram
• Aadi Perukku
• Chithirai Thiruvizha
• Natyanjali Dance Festival
• Thai Poosam
• Arudra Darshanam
• Panguni Brahmotsavam (Meenakshi Temple)
• Festivals of Andhra Pradesh:
• Ugadi
• Sankranti/Pongal (Bhogi, Sankranti, Kanuma)
• Dasara (Navaratri)
• Bathukamma
• Makara Sankranti
• Krishnashtami (Janmashtami)
• Bonalu (Hyderabad)
• Visakha Utsav (Visakhapatnam)
• Festvials of Tripura:- 
• Durga Puja
• Kharchi Puja
• Garia Puja
• Diwali
• Saraswati Puja
• Pous Sankranti
• Ashokastami Mela
• Dolyatra (similar to Holi)
• Kartik Puja
• Ker Puja

The correct answer is the valency of an element.

Key Points

• The chemical behavior of an element is determined by the valency of an element.
• The capacity of an element to combine with other atoms when it forms chemical compounds or molecules is known as valence or valency.

Additional Information

• Valence or valency can be calculated by two equivalent formulas:

1. valence = number of electrons in the valence shell of the free atom – number of nonbonding electrons on an atom in a molecule.

• The oxidation state of an atom in a molecule provides the number of valence electrons it has gained or lost.

The pattern follows here is,

Working in rows:

6² + 8 = 44

7² + 11 = 60

9² + 18 = 99

Similarly,

8² + 22 = 86

Hence 86 is correct answer.

Given

Invalid votes = 25% of total votes

Winner's votes = 2/3 of total valid votes

Concept:

The number of valid votes is (1 - invalid votes %) of total votes.

Calculation:

Let the total votes are 100x.

25% invalid, so remaining are 75x

According to question

 75x × 2/3 = 7500

x = 150

Total invalid votes = 25 × 150 = 3750

The difference in votes of the winner and invalid votes is = 7500 - 3750 = 3750.

Therefore, the difference in votes of the winner and invalid votes is 3750.

The correct answer is Wetlands for Life.

In News

• The International Film Festival and Forum on Environment and Wildlife, Vatavaran, was inaugurated with the theme "Wetlands for Life."

Key Points

• The festival aims to raise awareness and promote the conservation of wetlands.
• Around 6% of Indians depend on wetlands for their livelihoods, highlighting their importance.
• The event encourages discussions on significant environmental issues.
• Bilateral cooperation between India and Germany has been successful in wetland conservation.

Additional Information

• Wetlands
• Ecological systems that provide numerous benefits including water purification, flood control, and habitat for wildlife.
• Support livelihoods for millions of people through fishing, agriculture, and tourism.
• Vatavaran
• An international film festival focusing on environmental and wildlife issues.
• Uses film as a medium to engage the public and raise awareness about conservation efforts.

The correct answer is magnetic flux.

Key Points

• Magnetic flux is a measurement of the total magnetic field which passes through a given area.
• Magnetic flux is the product of the average magnetic field times the perpendicular area that it penetrates.
• The SI unit of magnetic flux is Weber (Wb).

Important Points

• Conductance explains the ease with which electric current flows through a substance.
• Magnetic flux density is defined as the amount of magnetic flux in an area taken perpendicular to the magnetic flux's direction.
• Capacitance is the ability of a body to hold an electrical charge.

The conclusion I doesn’t follow as it cannot be inferred that only those people who learn at the young age can time the ball well. Also, Conclusion II doesn’t follow as there is no definite correlation between young players and stroke players.

Hence, none of the conclusions follows.

Given:

Profit percentage = 380% and Increase in cost price = 20%

The selling price of the articles remains constant.

Formula used:

Percentage of profit = Gain value ÷ Selling price × 100

Calculation:

Let Cost price = 100

Profit = 380

Selling price = 380 + 100 = 480

Increased cost price = 120

Percentage = \(\dfrac{480-120}{480}\) × 100

⇒ \(\dfrac{360}{480}\) × 100 = 75%

∴ The profit Percentage is 75% of the selling price.

Option 3 is correct, i.e. Convex.

Key Points

Human eye:

• Retina is the part of the human eye where the image is formed.
• The cornea is a transparent layer that forms the front of the eye.
• The optic nerve or the cranial nerve is responsible for transferring visual information from the retina to the brain.
• Iris is a circular, thin structure in the eye that is responsible for controlling the size and diameter of the pupil.
• Convex lens present in the eye.

The correct answer is Infinite images.

Key Points

• Infinite images are formed if two parallel mirrors face each other.
• Because an image formed by one mirror can act as an object for the second mirror.
• And every image formed by the second mirror can act as an object for the first mirror.

Additional Information

• Reflection From Plane Mirror:
• The image is virtual and laterally inverted.
• The size of the image is equal to that of the object.
• The distance of the image from the mirror is equal to the distance of the object from the mirror.
• If an object moves towards (or away from) a plane mirror with speed u, relative to the object, the image moves towards (or away) with a speed of 2u.

Statement:

"Drop the mail in the mailbox", said John to his assistant.

Assumptions:

1. The assistant knows the address where the mail needs to be sent → This assumption is not valid because nothing such information is stated above.
2. The assistant will follow orders → This assumption is implicit here because this is an imperative statement, John is giving command to his assistant. So it is assumed that his assistant will follow his orders.

Hence, 'option 1' is the correct answer.

Given

Pipe A can fill a tank in 5 hours

Pipe Q can empty a tank in 12 hours

Calculation

Total capacity of the tank = 60 (L.C.M of 5 and 12)

Tank filled in 1 hour = (1/5) - (1/12)

⇒ (12 - 5)/60

⇒ 7/60

⇒ 60/7

\(8{4\over 7} hours\)

∴ Time taken by pipe A and Q to fill the tank is \(8{4\over 7} hours\)

The correct answer is Agriculture.

Key Points

• The Indian Constitution divides the legislative powers between the Centre and the States. The State List contains 61 subjects over which the State Legislatures have exclusive power to legislate.
• Agriculture is one of the subjects included in the State List. This means that the State Governments have the power to make laws and policies related to agriculture within their respective states.
• Banking is a subject that falls under the Union List, which means that the Central Government has the power to legislate on matters related to banking. However, cooperative banks and regional rural banks come under the purview of both the Centre and the States.

Additional Information

• Ports are also a subject that falls under the Union List, which means that the Central Government has the power to legislate on matters related to ports. However, the State Governments can also make laws and policies related to minor ports within their respective states.
• Railways are a subject that falls under the Union List.

The least possible Venn diagram is as follows:

Conclusions:

I. Some bugs are ants.→ False (it is possible but not definite)

II. No bug is a beetle. → False (it is possible but not definite)

III. No frog is an ant. → True ( as no frog is beetle and and all ants are beetles)

Hence, only conclusion III follows

Shortcut Trick

Net change in weight = Correct weight − Incorrect weight

⇒ Net change = 66 − 76 = −10 kg

Change in average = Net change ÷ Total boys = −10 ÷ 20 = −0.5 kg

Correct average = Initial average + Change in average

⇒ Correct average = 65 − 0.5 = 64.5 kg

∴ The correct answer is 64.5 kg.

Alternate Method

Given:

Number of boys (n) = 20

Calculated average weight = 65 kg

Incorrect weight read = 76 kg

Correct weight = 66 kg

Formula Used:

Average = Total sum of values ÷ Total number of values

Correct Sum = Incorrect Sum − Incorrect Value + Correct Value

Initial Average of 20 boys = 65 kg

Sum correction: 66 kg - 76 kg = -10 kg
Average change: -10 / 20 = -0.5 kg

Correct Average = 64.5 kg

Calculations:

⇒ Incorrect sum of weights = 20 × 65 = 1300 kg

⇒ Correct sum of weights = Incorrect sum − Incorrect weight + Correct weight

⇒ Correct sum = 1300 − 76 + 66

⇒ Correct sum = 1300 − 10 = 1290 kg

⇒ Correct average = 1290 ÷ 20

⇒ Correct average = 64.5 kg

∴ The correct answer is 64.5 kg.

Additional Information

Combined Average

If group A has n₁ items with average A₁ and group B has n₂ items with average A₂, then combined average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Replacing a Member

If a new person replaces an old person and the average increases, New weight = Old weight + (Increase in average × Total members).

Including a New Member

If a new person joins the group, New value = Old Average + [Total New Members × Change in Average ÷ Total Members].

The correct answer is December, 1992.

Key Points

• The Constitution 73^rd and 74^th Amendment Act was passed in December,1992.
• The Act gave state governments the authority to take the required actions to formalise Panchayati Raj Institutions and enable them to function as self-governing entities.

Additional Information

• According to Article 40 of the Directive Principles of State Policy in the Indian Constitution, the government must make it easier for Gram Panchayats to get started and run efficiently.
• The central government of India passed the 73^rd Amendment Act in 1992 to solve these problems and enhance local self-governments.
• The Constitution now contains a new chapter called "Part IX: The Panchayats" as a result of this Act.

The correct answer is Displacement.

Key Points

• The product of velocity and time gives Displacement.
• It is the shortest distance between the initial and final position. It is a vector quantity i.e. it has both magnitude and direction.
• Distance can’t be zero but Displacement is zero in some cases like for example when the person/thing returns to its initial position.
• Similarly, the average speed of a moving body can never be zero, but the average velocity of a moving body can be zero.

1) 1, 2, 5, 6, 4, 3

2) 2, 4, 1, 3, 6, 5

3) 3, 1, 6, 2, 5, 4

4) 5, 1, 3, 4, 2, 6

'ACTING' is a meaningful English word.

Hence, '3, 1, 6, 2, 5, 4'  is the correct answer.

The area of the equilateral triangle = (√3 a²)/4

 = (√3 × 2²)/4 = √3 sq. cm

The volume of a right triangular prism can be found by multiplying the area of base and the height.

Volume = √3 × 7√3 cubic cm

 = 21 cubic cm

The correct answer is house - hold consumer expenditure.

Key Points

• In India, household consumption expenditures are often used to determine and measure the poverty level.
• The Planning Commission (formerly known as NITI Aayog) uses data from several surveys, including the National Sample Survey (NSS), to determine the official poverty estimates in India.
• These surveys gather data on household consumption and spending habits, among other things, in order to establish poverty thresholds and calculate the number of persons living below them.
• The income or expenditure threshold below which people or households are deemed to be impoverished is known as the poverty line. The criteria used to establish the poverty line consider a number of things, including the amount of food consumed, non-food products, and other requirements.

Hence, Poverty level in India is established on the basis of house - hold consumer expenditure .

The correct answer is option i.e Potash alum. 

• Potash alum is a combination of double sulphate of potash and aluminium salts.
• Its chemical formula is KAl(SO4)2 or, AlK(SO4)2·12 H2O
• Potash alum is also known as an astringent.
• Astringents are substances that cause contraction or shrinkage of tissues and that dry up secretion.
• Used as a post-shaving treatment, it can eliminate bleeding from superficial wounds.
• It has also shown in vitro anti-microbial activity.
• The alum used for purifying water is known as potash alum.
• Potash alum is generally used in water purification, fireproof textiles etc. It is also used in leather tanning.

The given series is: 4 T 6 $ 2 A D & C E 2 4 + & 7 6 U 5 H U K 8 E W @ E A & P

Number of vowels which are immediately preceded by a number and also immediately followed by a consonant:

→ 4 T 6 $ 2 (A) D & C E 2 4 + & 7 6 U 5 H U K 8 (E) W @ E A & P

Here, we can see that there are two such vowels.

Hence, the correct answer is "Two".

Given:

Sohan alone can do a work in 18 days.

Mohan alone can do the same work in 36 days.

Formula Used:

Work done together in 1 day = \(\frac{1}{\text{Sohan's time}} + \frac{1}{\text{Mohan's time}}\)

Total time to complete work together = \(\frac{1}{\text{Work done together in 1 day}}\)

Calculation:

Work done by Sohan in 1 day = 1/18

Work done by Mohan in 1 day = 1/36

Work done together in 1 day = \(\frac{1}{18} + \frac{1}{36}\)

Work done together in 1 day = \(\frac{2}{36} + \frac{1}{36}\)

Work done together in 1 day = \(\frac{3}{36}\)

Work done together in 1 day = 1/12

Total time to complete work together = \(\frac{1}{\left( \frac{1}{12} \right)}\)

Total time to complete work together = 12 days

The correct answer is option 1: 12 days.

The correct answer is Option 1.

Key Points

• Newton’s Second law of motion: The rate of change of momentum of any object is directly proportional to the applied force on the body.
• \({\rm{Force\;}}\left( {\rm{F}} \right) = ma =m×\frac{{V_f~-~V_i}}{{Δ T}}\)
• F × ΔT  = ΔP
• Where Δ P = Change in momentum and Δ T = change in time taken
• The above equation is known as Impulse Momentum equation and states that the impulse or force intensity is equal to change in momentum.
• According to the impulse-momentum equation, the change in momentum of an object depends on both the net force acting on the object and duration of the net force.

Additional InformationMomentum:

• Momentum is the product of an object's mass and velocity (p = m * v).
• Conservation of momentum applies to isolated systems without external forces.
• Impulse, the change in momentum, results from force applied over time (J = F * Δt).
• Momentum is crucial in analyzing collisions.
• Units: kilogram meters per second (kg·m/s).

The correct answer is 3.

• Isotopes are atoms of the same element with a different number of Neutrons.
• Isotopes are atoms with the same number of protons but that have a different number of neutrons.
• For example - Uranium-235 and Uranium-239 are two different isotopes of the element uranium.
• the atomic number is equal to the number of protons.
• the atomic mass is the sum of protons and neutrons.
• Isotopes are elements with the same atomic number but different mass numbers.

Key Points

• There are three isotopes of the element hydrogen: hydrogen, deuterium, and tritium.
• Hydrogen has no neutron, deuterium has one, and tritium has two neutrons.​​​​

The Logic followed here is:

Square of any number - 4 = number

For (192, 140, 252) 

(14)² - 4 = 192;

(12)2 - 4 = 140

(16)² - 4 = 252;

Option 1: (165, 140, 192) 

(13)² - 4 = 165

(12)2 - 4 = 140

(14)2 - 4 = 192;

Option 2: (221, 192, 252) 

(15)2 - 4 = 221;

(14)2 - 4 = 192;

(16)2 - 4 = 252;

Option 3: (186, 134, 246) 

(14)2 - 4 = 192 ≠ 186

(12)2 - 4 = 140 ≠ 134

(16)2 - 4 = 252 ≠ 246

Option 4: (165, 117, 221) 

(13)2 - 4 = 165

(11)2 - 4 = 117

(15)2 - 4 = 221;

But this pattern is not applicable in option C.

So, this pattern is not applicable.

Shortcut Trick

As we know, Simple interest is same in all years

⇒ SI for 1 year is = 7% of 12000

⇒ SI for 1 year is = Rs. 840

⇒ SI for 3 year is = 840 × 3

⇒ SI for 3 year is = Rs. 2,520

Amount = P + SI

⇒ Amount = 12,000 + 2,520

⇒ Amount = Rs. 14,520

∴ The total amount received by Virendra is Rs. 14,520.

Traditional method:

Given: 

Principal = Rs. 12,000

Time = 3 years

Rate = 7%

Formula used:

SI = (PRT)/100

Amount = P + SI

where, SI = Simple interest, P = principal, R = Rate and T = Time

Calculations:

According to the question, we have

The simple interest is 

SI = (PRT)/100

⇒ SI = (12,000 × 3 × 7)/100

⇒ SI = 120 × 3 × 7

⇒ SI = Rs. 2,520

Total amount received by Virendra is 

Amount = P + SI

⇒ Amount = 12,000 + 2,520

⇒ Amount = Rs. 14,520

∴ The total amount received by Virendra is Rs. 14,520.

The correct answer is Sonipat.

Key Points

• Coal is a combustible black or brownish black sedimentary rock with a high amount of carbon and hydrocarbons.
• It is a important source of non-renewable energy.
• It is known as black diamond.
• Sonipat was earlier known as Sonprastha, which later became Svarnaprastha (Golden City), which is derived from two Sanskrit words, Svarna (Gold) and Prastha (Place).

Additional Information

• ​ Neyveli
• It is situated in Tamil Nadu.
• It is the principal lignite reserve Centre.
• Lignite is used for generation of electricity.
• Korba
• This Coalfield is located in Korba district in the Indian state of Chhattisgarh.
• It is situated in the basin of the Hasdeo River which is a tributary of the Mahanadi.
• Singareni
• It is a village located in Khammam district, Telangana, India.
• ​It is a coal reserve centre.

• The Tone is the sound of a single frequency.
• A sound produced after the mixing of several frequencies is known as a note.
• Pitch is the degree of lowness or highness of a tone.
• Hertz is the SI unit of frequency

The family tree can be drawn using the given statement and symbol notation as: 

or

Here, the gender of U is not defined, so the number of females cannot be determined.

So, the answer will be cannot be determined.

Shortcut Trick

Ratio 5 years ago = 5 : 6

Ratio 7 years hence = 11 : 12

Difference in ratio units = 11 − 5 = 6 units (same for both)

Total time gap = 5 + 7 = 12 years

6 units = 12 years ⇒ 1 unit = 2 years

Rohan age 5 years ago = 6 units = 12 years

Present age of Rohan = 12 + 5 = 17 years

∴ The correct answer is 17 years.

Alternate Method

Given: Ratio 5 years ago = 5 : 6; Ratio 7 years hence = 11 : 12.

Formula Used: Ratio × constant = Age.

⇒ Let ages 5 years ago be 5x and 6x.

⇒ Present ages = (5x + 5) and (6x + 5).

⇒ Ages after 7 years = (5x + 5 + 7) and (6x + 5 + 7).

⇒ (5x + 12) / (6x + 12) = 11 / 12

⇒ 12 × (5x + 12) = 11 × (6x + 12)

⇒ 60x + 144 = 66x + 132

⇒ 6x = 12 ⇒ x = 2

⇒ Rohan age 5 years ago = 6 × 2 = 12 years.

⇒ Present age of Rohan = 12 + 5 = 17 years.

∴ The correct answer is 17 years.

Additional Information

Ratio Difference Method

If the difference between ratio terms is constant, the difference in units equals the total years elapsed.

Age Gap Property

The difference between the ages of two persons remains constant throughout their lives.

Calculation of Present Age

Present Age = Age (n years ago) + n = Age (m years hence) − m.

The correct answer is Shamsuddin Iltutmish.

Key Points

• The Iqta System or Iqtadari System was introduced by Shamsuddin Iltutmish of the Delhi Sultanate.
• The Iqtadari System was a powerful instrument for centralisation.
• The Iqtadari System was based on the division of territories between Sultans and Nobility.
• The land was divided into small tracts and given to the nobles, the officers, and the soldiers.
• The areas directly under Sultan came to be known as Khalisa and the rest of the areas were known as Iqra.

Additional Information

• Regin of Iltumish - 1211-1236 AD.
• Iltumish was son-in-law of Aibak.
• He was a Turkic slave.
• He was the greatest of the Slave rulers of Delhi.
• The Slave dynasty was established by Qutb-us-din Aibak.
• Dynasty lasted from 1206 to 1290.
• It was the first of the dynasties to rule as Sultanate in Delhi.
• This dynasty was succeeded by Khilji Dynasty.

Explanation:

Oxides of nitrogen

• When fossil fuel is burnt,In an automobile engine, (at high temperature) dinitrogen and dioxygen combine to yield significant quantities of nitric oxide (NO) and nitrogen dioxide ( NO₂ ).

• NO reacts instantly with oxygen to give NO₂

• The irritant red haze in the traffic and congested places is due to oxides of nitrogen.

• Higher concentrations of NO2 damage the leaves of plants and retard the rate of photosynthesis.

• Nitrogen oxides also cause acute respiratory disorders.

Correct option is oxides of nitrogen

Additional InformationOxides of Sulphur

• They causes respiratory diseases e.g., asthma, bronchitis, emphysema in human beings.
• Sulphur dioxide causes irritation to the eyes, resulting in tears and redness.
• High concentration of SO₂ gas is responsible for stiffness of flower buds which eventually fall off from plants.

The correct option from the given options that can make a full square. (3 of the 5 images below) is shown below:

Hence, ‘1, 2, 3’ is the correct answer.

Given:

Principal = Rs. 10000

The rate of interest = 22% per annum

Formula Used:

C.I = P[{1 + (R/100)}^T - 1]

Where,

C.I = Compound Interest

P = Principal

R = Rate of Interest

T = Time

Calculation:

According to the question, we have

C.I = 10000[{1 + (22/100)}² - 1]

⇒ 10000[(122/100)² - 1]

⇒ 10000 × (122/100 × 122/100) - 10000

⇒ 14884 - 10000

⇒ 4884

∴ The compound interest is Rs. 4884.

Shortcut Trick

 Concept Used:

Total rate% of 2 years (at C.I) = X% + X% + (X%)²/100

Calculation:

Total rate% of 2 years = 22 + 22 + (22)²/100

⇒ 44 + 4.84

⇒ 48.84%

According to the question, we have

C.I = 10000 × (48.84/100)

⇒ 4884

∴ The compound interest is Rs. 4884.

CONCEPT:

• Work-energy theorem: It states that the sum of work done by all the forces acting on a body is equal to the change in the kinetic energy of the body i.e.,

Work done by all the forces = Kf - Ki

\(W = \frac{1}{2}m{v^2} - \frac{1}{2}m{u^2} = {\bf{Δ }}K\)

Where v = final velocity, u = initial velocity and m = mass of the body

EXPLANATION:

• According to the work-energy theorem, the work done will be equal to the change in kinetic energy.
• Hence option 3 is correct.

According to the given information:

Bala studies in class Q with only Deepak who likes red colour.

Arun Studies in class R and does not like either blue or green.

Vijay does not study in class R and likes yellow colour.

Praveen and Sonu study in the same class but not with Arun.

Sonu likes brown colour.

Praveen does not like blue colour. 

None of those who study in class P likes white.

The one who likes black studies in class Q.

Thus, Praveen likes Green color.

Hence, the correct answer is "Green".

Given:

Mohan sold a laptop at the price of Rs. 50,000.

When profits are raised by 10%, the selling price rises to Rs. 53,000.

Concepts used:

Profit % = (Profits/C.P.) × 100

Profits = S.P. – C.P.

Calculation:

Let price of laptop be Rs.

x. A laptop is sold by Mohan at the price of Rs. 50,000.

⇒ Profits = 50,000 – x

When profits are raised by 10%, the selling price rises to Rs. 53,000.

⇒ New profits = (50,000 – x) × {1 + (10/100)} = {55,000 – (11x/10)}

⇒ 53,000 – x = 55,000 – (11x/10)

⇒ x = Rs. 20,000

∴ Cost price of laptop is Rs. 20,000. 

Alternate Method

Mistake Points 

Some are assuming 100% of Profit as Cost price of laptop which is wrong.

The correct answer is option 2.

In News

• China has started live-fire military exercises in the Gulf of Tonkin after Vietnam published a map defining its territorial claims in the water body.

Key Points

• The Gulf of Tonkin, also called Beibu Gulf in Chinese and Bac Bo Gulf in Vietnamese, is a crescent-shaped, shallow, semi-enclosed water body in the northwestern South China Sea.
• It is bordered by Northern Vietnam (west and northwest), China's Guangxi Zhuang Autonomous Region (north), Leizhou Peninsula, and Hainan Island (east).
• It is connected to the South China Sea via its southern mouth and to the Hainan Strait in the northeast.
• Major Ports:
• Vietnam: Haiphong, Ben Thuy
• China: Beihai (Pakhoi)
• Hence, option 2 is correct.

Persons : A, B, C, D, E and F

Colours : Red, green, blue, black, orange and white

Cities : Delhi, Mumbai, Hyderabad, Chennai, Bangalore and Kolkata

1) A has a home in Delhi, F has a home in Bangalore and likes red colour, D has a home in Hyderabad, C likes green colour and lives in Chennai and E likes orange colour.

2. A does not like orange and white colours. (It means he likes either blue or black)

3) B does not like blue and black colours and does not live in Mumbai. (It means he likes white colour and lives in Kolkata)

4. D likes either blue or black colour.

B lives in Kolkata and likes white colour.

Hence, 'option 3' is the correct answer.

Given:

A bag contains coins of five rupees, two rupees and one rupee in a ratio of 2 : 3 : 5.

Their total value is Rs. 273

Calculation:

Let the number of five, two, one rupee coin be 2x, 3x and 5x

According to the question,

2x × 5 + 3x × 2 + 5x × 1 = 273

⇒ 10x + 6x + 5x

⇒ 21x = 273

⇒ x = 13

So, number of two rupee coins = 3 × 13 = 39

Amount = 39 × 2 = Rs. 78

∴ The amount of two rupees coins is Rs. 78.

The Correct Answer is Prevent misinformation and promote media integrity.

In News

• WAVES Declaration Adopted at Global Media Dialogue in Mumbai with 77 Nations Participating.

Key Points

• The WAVES Declaration was adopted during the Global Media Dialogue.
• 77 countries participated in the dialogue, held at the Jio World Convention Centre in Mumbai.
• The declaration focuses on preventing the spread of misinformation and disinformation.
• It promotes media integrity, fact-based journalism, and responsible advertising.
• The declaration emphasizes supporting content that respects human rights and cultural sensitivities.
• Countries agreed to foster cross-border collaborations to deepen shared understanding.
• The critical role of media and entertainment in promoting development and harmony was acknowledged.
• The member nations recognized that AI can enhance market efficiency, creativity, and audience engagement, but emphasized the ethical use of AI to minimize harms and reduce biases.

The logic followed here is:

Similarly,

Hence, 'MLPQBA' is the correct answer.

Given:

Average of 4 numbers = 52

Average of first two numbers is thrice the average of the other two numbers.

Concept:

To find the sum of the first two numbers, use the concept of averages and algebraic equations.

Calculation:

Let the first two numbers be a and b, and the other two numbers be c and d.

Average of 4 numbers = (a + b + c + d) / 4 = 52

⇒ a + b + c + d = 52 × 4

⇒ a + b + c + d = 208

Let the average of the other two numbers (c and d) be xxxxxx .

Then, the average of the first two numbers (a and b) is 3x.

⇒ c + d = 2x

⇒ a + b = 6x

We know that:

a + b + c + d = 208

Substitute the values:

⇒ 6x + 2x = 208

⇒ 8x = 208

⇒ x = 208 / 8

⇒ x = 26

Therefore, the sum of the first two numbers:

⇒ a + b = 6x

⇒ a + b = 6 × 26

⇒ a + b = 156

∴ The sum of the first two numbers is 156.

The correct answer is Malwa Plateau

Key Points

• The Malwa Plateau region of Madhya Pradesh has a temperate (equable) climate.
• This region is known for its temperate climate because it is neither too hot in summer nor too cold in winter.
• It roughly forms a triangle based on the Vindhyan Hills, bounded by the Aravali Range in the west and Madhya Bharat Pathar to the north.
• The other regions of Madhya Pradesh generally have a subtropical monsoon climate with hot, humid summers and cool, dry winters.
• The average temperature in summer is 40-42 degrees Celsius, and the average temperature in winter is 10-12.5 degrees Celsius.

Additional Information

• The Vindhyan/Satpura Mountain Region
• This is a hilly terrain, so the summers are not too hot, and the winters are moderate.
• This climatic zone includes well-known hill stations like Pachmari and Amarkantak.
• Malwa Plateau is composed of extensive lava flow and is covered with black soils, with a general slope towards the north.