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

The correct answer is P D Singh

In News

• Standard Chartered appoints P D Singh as India CEO, effective April 1, 2025.

Key Points

• He succeeds Zarin Daruwala, who will retire on March 31, 2025.
• Singh has 30 years of banking experience, previously serving as CEO of JP Morgan Chase India and holding leadership roles at HSBC.
• Sunil Kaushal, Co-Head of Corporate & Investment Banking, highlighted Singh’s market expertise and client relationships.
• Singh aims to drive sustained growth and strengthen Standard Chartered’s commitment in India.

The correct answer is Hydrogen.

Explanation:

• Combustion is a chemical reaction that produces heat when a substance reacts with oxygen.
• Combustible refers to a substance that can be burned. It is also known as a fuel. The fuel can be either solid, liquid, or gas.
• The amount of heat energy produced by the complete combustion of one kilogram of fuel is referred to as its calorific value.
• The calorific value of a fuel is expressed in kilojoule per kilogram (kJ/kg).
• Hydrogen has the highest caloric value and is highly combustible. Minor contact with a burning agent can result in a blast.

Calorific Values of Fuels

Hence, Hydrogen has highest calorific value.

Given:

Statements:

Some journals are novels.

Some novels are broachers.

All broachers are charts.

Conclusions:

I. Some charts are novels - True (Those part of Charts that is Broachers will be definitely Novels)

II. Some broachers are journals - False (There is no definite relation given between Broachers and Journals, so it is possible only)

So, Only conclusion I follows.

Hence, the correct answer is "Option 1".

Given:

The car covers 275 km with a speed = 50 km/h

The car covers 315 km with a speed = 70 km/h

Formula used:

Average speed = Total Distance/Total time

Calculation:

Time is taken to covers 275 km = 275/50 = 11/2 hours

Time is taken to covers 315 km = 315/70 = 9/2 hours

The average speed = (275 + 315)/(11/2 + 9/2) km/h

= 590/10 km/h

= 59 km/h

∴ The average speed (in km/h) for the entire journey is 59 km/h

The logic followed here is:

Given Sequence: t _ n s _ r t h _ s o _ t h _ s _ r

Now, putting the letters in the blank spaces given in the option one by one:

Option 1) nonrho → t n n s o r / t h n s o r / t h h s o r

Option 2) honrno → t h n s o r / t h n s o r / t h n s o r

Here, 'Option 2' followed a pattern.

Option 3) hornnr → t h n s o r / t h r s o n / t h n s r r

Option 4) hoonor → t h n s o r / t h o s o n / t h o s r r

Hence, the correct answer is "Option 2".

Formula used:

Average = Sum of all numbers/Total numbers

Calculation:

Let, the initial sum of observation is X.

We know that

Average = Sum of all numbers/Total numbers

⇒ 36 = Sum of all numbers/50

⇒ X = 1800          -----(1)

According to the question, 

Observation 48 was wrongly taken as 23

Hence, from equation (1)

New average = (1800 - 23 + 48)/50

⇒ New average = 1825/50 = 36.5

∴ Correct average is 36.5

The correct answer is Odisha.

Key Points

• Madhya Pradesh does not share its boundary with Odisha.
• Madhya Pradesh is the 2^nd largest state by area and the 5^th largest state by population.
• The Capital of Madhya Pradesh is Bhopal
• Madhya Pradesh shares its boundary with 5 states and details are mentioned about them.

The correct answer is DNA Polymorphism.

• DNA fingerprint is a technique to produce a pattern of the genome that is unique to an individual.
• It detects a lot of minisatellite in the genome and produces a pattern.
• It is also called DNA typing, DNA profiling, genotyping, genetic fingerprinting etc.
• DNA fingerprinting is based on short tandem repeats (STRs) which are unique to the individuals.
• Short tandem repeats are used in genetic profiling because of their polymorphism and high mutation rates.
• Polymorphism is a genetic marker of its own location in the chromosome and produced by changes in the nucleotide sequence and length.

The logic followed here is :-

Hence, the correct answer is "103".

Shortcut Trick

Let the common multiplier be x, which acts as the HCF of the numbers.

LCM of 4x, 5x, and 6x = x × LCM(4, 5, 6) = 60x.

Given LCM = 180 ⇒ 60x = 180 ⇒ x = 3.

∴ The correct answer is 3.

Alternate Method

Given:

⇒ Ratio of three numbers = 4  ∶ 5  ∶ 6

⇒ LCM of the numbers = 180

Concept Used:

⇒ If numbers are given in a ratio, their common multiplier 'x' represents their Highest Common Factor (HCF).

Calculations:

⇒ Let the actual numbers be 4x, 5x, and 6x.

⇒ LCM of 4, 5, and 6 = 60

⇒ Therefore, the LCM of 4x, 5x, and 6x = 60x

⇒ We are given that their overall LCM is 180.

⇒ 60x = 180

⇒ x = 180 ÷ 60

⇒ x = 3

⇒ Since x is the common multiplier, the HCF of the numbers is 3.

∴ The correct answer is 3.

Additional Information

LCM and HCF Relationship

For any two numbers 'a' and 'b', the product of the numbers is equal to the product of their LCM and HCF. Formula: a × b = LCM(a, b) × HCF(a, b). This rule does not directly extend to three numbers.

Co-prime Numbers

If the HCF of two or more numbers is 1, they are called co-prime numbers. For mutually co-prime numbers, their LCM is simply the product of the given numbers.

Ratio Multiplier as HCF

When numbers are expressed in their simplest simplified ratio, the common multiplier 'x' required to obtain the actual original numbers represents their Highest Common Factor (HCF).

Let’s solve this with the help of option.

B4 and G2 cannot be together. But they are together in the teams in options 1 and 2 hence both options 1 and 2 get eliminated.

B1 and G4 have to be together but in 4^th option, G4 is in the team without B1, hence 4^th one also gets eliminated.

Hence, ‘B1B2G4G1G2’ is the correct answer.

Given:

The angle subtended by a chord on the major arc of a circle is 132°.

Concept used:

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Calculation:

The major arc for the AB chord is ACB.

∠AGB = 132° 

According to the concept,

∠AGB  = 2 × ∠ACB

⇒ ∠ACB = 132°/2

⇒ ∠ACB = 66°

The angle ACB is 66°

The correct answer is P.V. Dixit.

• The Lokayukta is an anti-corruption ombudsman organization in the Indian states.
• The Lokayukta Organization in Madhya Pradesh came into existence in 1982.

Key Points

• P.V. Dixit  was the first Lokayukta of Madhya Pradesh.
• He served as the chief justice of the Madhya Pradesh high court from 1959 to 1969.
• It was created after the Madhya Pradesh Lokayuykt and Up-Lokayukta Act 1981.
• A bill was moved in the Madhya Pradesh legislative assembly for the creation of Lokayukta in the year 1975.
• The bill received the Presidential assent in September 1981.

Additional Information 

• All the committee members of the Lokayukta should be employees of the state government or members of the legislative assembly.
• The members are appointed by the governor.
• Naresh Kumar Gupta is the current Lokayukta of Madhya Pradesh.
• Prakash Chandra Sethi was the 8^th Chief Minister of Madhya Pradesh.

The correct answer Switch.

Key Points

• A switch is a simple device that is used to either break the electric circuit or to complete it.
• A resistor is a passive electrical component that resists the flow of electric current.
• A transistor is a semiconductor device that acts as both an amplifier and switch.
• A fuse is an electrical device for safety that removes electrical current from the circuit if the current gets too high.

Additional Information

• Transistors:
• Transistors are semiconductor devices, which are commonly used in amplifiers or electrically controlled switches
• Transistors are the basic building block that regulates the operation of computers, mobile phones, and all the other modern electronic circuits
• The most important transistor function is as a current amplifier and as a switch
• Transistors as current amplifiers are often used in amplifiers while transistors as switches are often found in automatic light circuits
• The functions of a transistor are variable resistors and switching devices.
• Capacitor:
• ​A capacitor is a device that stores electrical energy in an electric field.
• It is a passive electronic component with two terminals.
• The effect of a capacitor is known as capacitance.
• Capacitance: The capacitance is the capacity of the capacitor to store charge in it.
• Two conductors are separated by an insulator (dielectric) and when an electric field is applied, electrical energy is stored in it as a charge.
• The capacitance of a capacitor (C): The capacitance of a conductor is the ratio of charge (Q) to it by a rise in its potential (V), i.e.
• C = Q/V
• ​Resistor:
• A resistor is a passive element.
• It is represented by ‘R’ and is measured in ohms (Ω).
• Resistors are used to reduce current flow, adjust signal levels, to divide voltages.

Preparing the family tree using the following symbols:

A possible tree diagram will be:

Hence, the man is the cousin of the woman.

Given:

Meenu is 38 years old.

Her daughter is 8 years old.

Calculation:

Let, after x years will Meenu be double her daughter's age

As per the question,

⇒ 38 + x = 2 × (8 + x)

⇒  x = 22 years

∴ The correct option is 1

Statement: Country B has been importing 80% of its crude oil and petroleum from country Y for a few decades now to fulfil their fuel needs. However, owing to the current financial crisis in country Y, it exports the crude oil and petroleum to other countries at 30% higher prices now.

Conclusion I: The car resale industry in country B will be on verge of a total shut down in the coming months - False

(This is not the permanent solution, As, Country B has been importing 80% of its crude oil and petroleum from country Y for a few decades now to fulfil their fuel needs. So, it will not shut down in the coming months and also not mentioned in the statement) 

So, Conclusion I does not follow.

Conclusion II: Country B will increase fuel tax by 30% - False

(This is not the permanent solution, As, it exports the crude oil and petroleum to other countries at 30% higher prices now as mentioned in the statement).

So, Conclusion II does not follow.

Thus, 'Neither I nor II can be concluded from the given information'.

Given:

Loss on the article = 18%

Profit after adding ₹ 2,475 to SP = 12%

Formula used:

Selling Price = Cost Price - Cost Price × Loss%

Selling Price = Cost Price + Cost Price × Gain%

Calculation:

Let the cost price of the article be q

Original selling price = q - q × 18%

⇒q - (q × 18/100) =  0.82q

Desired selling price = q + q × 12%

⇒q + (q × 12/100) = 1.12q

According to the question,

1.12q - 0.82q = 2475

⇒ 0.3q = 2475

⇒ q = 2475/0.3

⇒ q = 8250

Now, the original SP of the article = 8250 × 0.82

⇒ ₹6765

∴ The selling price of the article was ₹6765.

Shortcut Trick 

Let CP be 100%, therefore

⇒ (100 - 18)% + 2475 = (100 + 12)%

⇒ 82 % + 2475 = 112%

⇒ 112% - 82% = 2475

⇒ 30% = 2475

⇒ 1% = 2475/30 = 82.5

Then SP = 82% (At 18% loss)

⇒ SP = 82.5 × 82 = 6765

∴ The selling price of the article was ₹6765.

The correct answer is Democratic politics.

Key Points

• India's federalism has been a tremendous success because of its democratic political system.
• India has a parliamentary system of government with federal and unitary components.
• It is a Sovereign Socialist Secular Democratic Republic. The Prime Minister serves as the head of the Council of Ministers, which provides advise to the President, who is the nation's constitutional leader.
• Federalism encourages political engagement.
• Federalism promotes economic equity throughout the nation.
• Federalism allows for several governmental tiers and allows for a range of viewpoints.
• India doesn't have a strict federal structure. Along with the union, states are sovereign in nature; they do not collaborate with the Center.
• In other words, it adheres to the principles of "quasi-federalism."

The correct answer is Ingestion.

Concept:

Human digestive system-

Explanation:

The digestive system includes 5 steps, They are in order as follows::

1. Ingestion

2. Digestion

3. Absorption

4. Assimilation

5) Egestion

• Ingestion: It is the process of taking food into the body by the animal.
• Digestion: It is the process in which food containing larger molecules is converted or break down into small water-soluble molecules.
• Absorption: It is the process in which digested food goes into the bloodstream.
• Assimilation: It is the process in which absorbed food is taken up by the body cells for their growth and energy.
• Egestion: It is the process in which undigested is discharged as faeces.

Table show alphabet serial number –

The pattern for the code is as follows,

 ‘RITU’ is written as ‘WLYX’

And,

 ‘AMAN’ is written as ‘FPFQ’

Similarly,

Hence, ‘MIRA’ is coded as ‘RLWD’.

Given:

sin 2A = cos(A - 60°)

Formula used:

sin x = cos(90° - x)

cos x = sin(90° - x)

Calculation:

sin 2A = cos(A - 60°)

⇒ cos(90° - 2A) = cos(A - 60°)

⇒ 90° - 2A = A - 60°

⇒ 2A + A = 90 + 60 = 150

⇒ 3A = 150

⇒ A = \(\dfrac{150}{3}\) = 50°

∴ The value of 'A' is 50°.

The pattern here is:

T + 1 = U; U + 1 = V; V + 1 = W; W + 1 = X

D + 2 = F; F + 2 = H; H + 2 = J; J + 2 = L

L + 3 = O; O + 3 = R; R + 3 = U; U + 3 = X

Hence, XLX is the correct answer.

Shortcut Trick

Fractional equivalent of 25% increase = +1/4

To keep the expenditure constant, the consumption must be reduced by the ratio: −1 ÷ (4 + 1) = −1/5

Percentage reduction = (1/5) × 100% = 20%

∴ The correct answer is 20%.

Alternate Method

Given:

Increase in the price of sugar = 25%

Formula Used:

Expenditure = Price × Consumption

Reduction % = [R ÷ (100 + R)] × 100% (where R is the percentage increase)

Calculations:

⇒ Let initial price = 100 units and initial consumption = 100 units.

⇒ Initial expenditure = 100 × 100 = 10000 units.

⇒ New price after 25% increase = 100 + 25 = 125 units.

⇒ Let the new consumption be C.

⇒ To keep expenditure constant: 125 × C = 10000

⇒ C = 10000 ÷ 125 = 80 units.

⇒ Decrease in consumption = 100 − 80 = 20 units.

⇒ Percentage reduction = (20 ÷ 100) × 100% = 20%.

∴ The correct answer is 20%.

Additional Information

Price and Consumption Rule

When Expenditure is constant, Price and Consumption are inversely proportional. An increase in price leads to a proportional decrease in consumption.

Percentage Increase / Decrease Concept

If value A is R% more than B, then B is less than A by exactly [R ÷ (100 + R)] × 100%.

Standard Fractional Equivalents

1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 ≈ 16.66%.

The correct answer is 1998.

• Dindori declared as a separate district in 1998.

Additional Information 

• Sohagpur area of Ramgarh was handed over to the king of Rewa.
• The remaining area annexed to Dindori tehsil which became a new district on 22^nd May 1998.
• Dindori District, formerly known as Ramgarh District, is a district of Madhya Pradesh state of central India.
• The town of Dindori is the district headquarters.
• The district is part of the Jabalpur Division.

The correct answer is Momentum.

CONCEPT:

• Conservation of Momentum: According to this principle, in an isolated system, the vector sum of linear momenta of all bodies of a system is conserved and is not affected due to their mutual action and reaction.
• If two bodies of different masses collide with each other and there is no external force acted on it then,

The initial momentum of bodies = Final momentum of bodies

​EXPLANATION:

• In a rocket, gasses at high temperatures and pressure are created by the combustion of fuel.
• They escape with a high constant velocity via a nozzle.
• The large, backward momentum of the gasses gives the rocket an equal forward momentum.
• However, due to the decrease in the mass of the rocket fuel system, the acceleration of the rocket continues to increase.
• Thus a rocket works on the principle of conservation of Momentum. So option 2 is correct.
• Since the energy of the rocket's fuel converts into heat energy that propels the rocket. So the energy of the rocket only is not conserved. The energy of the rocket and the surrounding will be conserved but not of the rocket.
• Similarly, the mass of the rocket decreases as the fuel burns. So mass is not conserved.
• There is no rotation in the rocket so no meaning of spin angular momentum here.

Correct option - 3

1. Three persons were seated between A and B. A was seated second to the right of F who was seated to the immediate left of D. A does not sit at any of the ends.

2. G was seated second to the right of C.

3) No two kids were seated together according to the English alphabetical order.

This implies that in case, C cannot sit between B and F.

Hence, case 2 and case 3 are invalid 

Thus, D was seated second to the left of C

Hence, option 3 is the correct answer

Shortcut Trick

Supplementary angles always sum up to 180°.

Subtracting the known angle: 180° − 80° = 100°.

The expression (3x − 5) must equal 100°.

Adding 5 to 100 gives 3x = 105.

Dividing 105 by 3 gives x = 35.

∴ The correct answer is 35°.

Alternate Method

Given:

Angle 1 = (3x − 5)°

Angle 2 = 80°

Formula Used:

Sum of supplementary angles = 180°

Calculations:

⇒ (3x − 5) + 80 = 180

⇒ 3x + 75 = 180

⇒ 3x = 180 − 75

⇒ 3x = 105

⇒ x = 105 ÷ 3

⇒ x = 35

∴ The correct answer is 35°.

Additional Information

Complementary

We compare the given phrase and their codes:

We get that, in both the combinations 'blue' is coded as '#'.

Hence the correct answer is option 3.

Given:

The average of 5 consecutive even numbers A, B, C, D, and E = 52

Formula used:

Average of n numbers = Sum of number/n 

Calculation:

Let A be = a 

⇒ B = a + 2 

⇒ C = a + 4 

⇒ D = a + 6 

⇒ E = a + 8 

Sum of 5 consecutive even numbers:

⇒ (A + B + C + D + E) = (a + a + 2 + a + 4 + a + 6 + a + 8) = 5a + 20

Average of 5 consecutive even numbers = (5a + 20)/5 

⇒ (5a + 20)/5 = 52 

⇒ 5a + 20 = 52 × 5 

⇒ 5a + 20 = 260 

⇒ 5a = 260 - 20 

⇒ 5a = 240 

⇒ a = 48 

A = 48

B = 48 + 2 = 50 

C = 48 + 4 = 52

D = 48 + 6 = 54

E = 48 + 8 = 56  

∴ The product of B and E = 50 × 56 

⇒ 2800

The correct answer is Charles Metcalfe.

Key Points 

• Charles Metcalf was assigned responsibility for signing treaties between the Rajput States in 1818 by the British Company.
• Sir Charles Metcalfe was appointed as Governor-General of India from 1835-36.
• He had succeeded Lord William Bentinck.
• Lord Hastings (1813-1823) wanted to establish British paramountcy in India for which destruction of the Marathas and the Pindaris were required.
• He looked upon the Rajputana States as his natural allies against the Marathas and the Pindaris.
• Charles Metcalf, the British Resident at Delhi, negotiated alliances with the princely states of Rajasthan.
• By these treaties, the princely States of Rajasthan came under the complete subordination of the British.

The correct answer is Roasting.

Key Points

• Roasting is a process of metallurgy where ore is converted into its oxide.
• It involves the heating of ores below their melting point in the presence of excess air.
• During the process of roasting moisture and non-metallic impurities in the form of volatile gases are removed.

Additional Information

• Calcination -  The process of heating and converting ore into an oxide. The moisture is also removed from the ore in this process.
• Corrosion - The natural process that converts refined metals into more stable compounds such as metal oxides, metal sulfides, or metal hydroxides.
• Extraction - It is the process of taking out metals from their ores through mining.

The logic followed here is:

PDLG : SFOI

And,

FTMN : IVPP

Similarly,

NKVH : ?

​

Hence, "Option 2" is the correct answer.

Shortcut Trick

Initial salary ratio of A and B = 5 : 6 (gap between terms is 1).

New salary ratio after ₹2000 increment = 11 : 13 (gap between terms is 2).

To make the gap equal, multiply the initial ratio by 2 → 10 : 12.

Now, the increment in ratio parts for both A and B = 11 − 10 = 13 − 12 = 1 part.

Since 1 ratio part = ₹2000, the new salary of A (11 parts) = 11 × 2000 = ₹22000.

∴ The correct answer is ₹22000.

Alternate Method

Given:

Initial salary ratio of A and B = 5 : 6

Increment for both = ₹2000

New salary ratio of A and B = 11 : 13

Calculations:

Let the initial salaries of A and B be 5x and 6x respectively.

After an increment of ₹2000, their salaries become (5x + 2000) and (6x + 2000).

⇒ (5x + 2000) ÷ (6x + 2000) = 11 ÷ 13

⇒ 13 × (5x + 2000) = 11 × (6x + 2000)

⇒ 65x + 26000 = 66x + 22000

⇒ 66x − 65x = 26000 − 22000

⇒ x = 4000

We need to find the new monthly salary of A.

⇒ New salary of A = 5x + 2000

⇒ New salary of A = 5 × 4000 + 2000

⇒ New salary of A = 20000 + 2000 = ₹22000

∴ The correct answer is ₹22000.

Additional Information

Compound Ratio

For two given ratios a : b and c : d, the compound ratio is calculated by multiplying the antecedents together and the consequents together, giving ac : bd.

Duplicate & Triplicate Ratios

The duplicate ratio of a : b is defined as a² : b². Similarly, the triplicate ratio is a³ : b³.

Invertendo & Alternendo

If four variables are in proportion a : b = c : d, then by the property of Invertendo b : a = d : c, and by Alternendo a : c = b : d.

The correct answer is Option 2: Place an ice pack and elevate it.

 

• Qualities Projected in this situation:  (Speed of decision and effective intelligence).

Key Points

• Checklist for attempting SRT questions:

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

Additional Information

Officer qualities:

Given :

The curved surface area of a solid right circular cone = 2145π cm²

The diameter of the base of the cone = 66 cm

Formula used:

The curved surface area of Right circular cone = πrl

Where

 r = Radius of the base of the cone

 l = Slant height of the cone

The volume of the right circular cone = \({1 \over 3}\)πr²h

Where

 r = Radius of the base of the cone

 h = Height of the right circular cone

Calculation :

radius of the cone = 33 cm   (∵ diameter is 66 cm)

⇒ π r l = 2145 π 

⇒ 33 × l = 2145

⇒ l = 65 cm

Also, we know that

 h² + r² = l²

⇒ h² = 65² - 33²

⇒ h = √3136 cm

⇒ h = 56 cm

Volume of right circular cone = (1/3)πr²h

⇒ (1/3)π × 33² × 56

⇒ 20328 π 

∴ The volume of the cone is 20328 π cm³

The correct answer is Odisha.

Key Points

• Udayagiri and Khandagiri are Located in Bhuvneshvar, Odisha.
• Built by King Kharavela of the Meghavahana dynasty, widely regarded as the most powerful king in the annals of the history of Odisha.
• These ancient rocks cut caves were first discovered by a young British Officer Andrew Sterling in the 19^th century AD.
• Eighteen caves are located in the Udaygiri hill and fifteen in the Khandagiri hill.
• The major Udaygiri caves are:-
• Hathigumpha.
• The Rani Gumpha.
• The Ganesh Gumpha.
• The VyagharaGumpha.

Important Points

• Important Caves
• Ajanta and Ellora Caves, Maharashtra.
• Badami, Karnataka.
• Tabo, Himachal Pradesh.
• Krem Liat Prah, Meghalaya.
• The Mystery Of Patal Bhuvaneshwar Cave Temple Uttarakhand.

CONCEPT:

• Convex mirror: It is an outward curved mirror that produces a diminished image.
• Convex mirrors either diverge a parallel beam of light into all directions or gather light from all directions and produce a parallel beam out of it.
• Focal length (f): The distance between the centre of the mirror and the focal point (where parallel rays of light meet or appear to meet) of the mirror is called the focal length.
• The radius of curvature (R): The distance between the centre of the lens or mirror to the vertex which is located on the local optical axis is called the Radius of Curvature.
• The focal length is half of the radius of curvature.

f = R/2

CALCULATION:

Given that:

Radius of curvature (R) = 30 cm,

The focal length (f) = R/2 = 30/2 = 15 cm

Given

Statement:

Looking at the family picture, Smriti said, "She is my father’s father-in-law’s wife’s son’s only sister."

Thus, according to the final family tree that person in the photo is wife of Smriti's father.

Hence, "Wife" is the correct answer.

Given:

Numbers are 28, 21, 39, 33, 36, 23.

Formula Used:

Arithmetic Mean = Sum of all numbers / Total number of numbers

Calculation:

Sum of numbers = 28 + 21 + 39 + 33 + 36 + 23

⇒ Sum = 180

Total number of numbers = 6

Arithmetic Mean = 180 / 6

⇒ Mean = 30

The arithmetic mean is 30.

The correct answer is option 4. Neither conclusion I nor II follows.

Investing in the tourism sector, providing financial assistance is a course of action and not a conclusion.

Therefore, conclusion I does not follow.

Similarly, setting up alternative sources of income for affected people too is a course of action and not a conclusion.

Therefore, conclusion II does not follow.

Hence, neither conclusion I nor conclusion II follows.

Shortcut Trick

Work done by Ramu in 12 days = 12 ÷ 36 = 1/3

Work done by Kanu in 12 days = 12 ÷ 32 = 3/8

Total work done together in 12 days = 1/3 + 3/8 = (8 + 9) / 24 = 17/24

Fraction of work left = 1 − 17/24 = 7/24

∴ The correct answer is 7/24.

Alternate Method

Given:

Time taken by Ramu to complete the work = 36 days

Time taken by Kanu to complete the work = 32 days

Number of days they worked together = 12 days

Calculations:

⇒ Total combined efficiency of Ramu and Kanu = 8 + 9 = 17 units/day

⇒ Total work done by both in 12 days = 17 × 12 = 204 units

⇒ Remaining work to be done = Total Work − Work Done = 288 − 204 = 84 units

⇒ Fraction of work left = Remaining Work ÷ Total Work

⇒ Fraction of work left = 84 ÷ 288 = 7/24

∴ The correct answer is 7/24.

Additional Information

Pipes and Cisterns

This topic follows the same logic as Time and Work, where inlet pipes fill a tank (positive work) and outlet pipes empty it (negative work).

Work and Wages

Wages are always distributed in the exact ratio of the work done by each individual. If they work for an equal number of days, wages are distributed directly in the ratio of their efficiencies.

Alternate Day Work

When two people work on alternate days, combine their individual day works to find the total work completed in a 2-day cycle before progressing to the remaining amount.

The correct answer is Chandragupta Maurya.

Key Points

• In classical Greek sources, Chandragupta Maurya Refers to Sandrocottus.
• Chandragupta Maurya (reign c.322 to c.298 BC) was the founder of the Mauryan Dynasty at Patliputra. With the help of Chanakya, he overthrew the Nanda Dynasty.
• His vast empire included Bihar, Bengal, Deccan, parts of current Tamil Nadu and parts of North East India, Eastern Afghanistan, Baluchistan and area west of Indus river.
• Seleucus, one of the generals of Alexander became his successor.Seleucus sent Megasthenes to Chandragupta’s Court.
• Chandragupta Maurya is believed to have spent his last days at Shravanabelagola.
• He is believed to have died by practising Santhara.

The correct answer is E.

Key Points

• Vitamin E is tocopherol.
• Vitamin E represents a group of compounds that contain both tocopherol and tocotrienol.
• It is good for the immune system and it fights toxins.
• It is a fat-soluble vitamin.
• It is a very powerful antioxidant.
• Weak muscles and fertility problems are signs of deficiency of vitamin E.
• Its deficiency also causes hair damage and skin problems.

Important Points

Given time: 6 : 45

Formula used: Angle = | \(\frac{{11}}{2}\) M - 30H |

Where, M = minutes and H = hours

Here, M = 45, H = 6

Therefore,

we get angle = | \(\frac{{11}}{2}\) × 45 - 30 × 6 |

= 247.5 - 180

= 67.5°

Hence the correct answer is "67.5°".

Shortcut Trick

Total Effective Interest Rate = Rate × Time

⇒ 7.5% × 4 years = 30%

Simple Interest = 30% of Principal (₹ 4650)

⇒ 0.3 × 4650 = ₹ 1395

∴ The correct answer is ₹ 1395.

Alternate Method

Given:

Principal (P) = ₹ 4650

Rate of Interest (R) = 7.5% per annum

Time Period (T) = 4 years

Formula Used:

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

Calculations:

⇒ SI = (4650 × 7.5 × 4) ÷ 100

⇒ SI = (4650 × 30) ÷ 100

⇒ SI = 46.5 × 30

⇒ SI = 465 × 3

⇒ SI = ₹ 1395

∴ The correct answer is ₹ 1395.

Additional Information

Total Amount Formula

The total amount (A) to be paid back is the sum of the Principal and Simple Interest: A = P + SI = P(1 + RT/100).

Relationship between SI and Time

Simple Interest is directly proportional to the time period if the Principal and Rate remain constant. Doubling the time doubles the interest.

Rate and Time Calculation

If SI, P, and R are known, Time (T) = (100 × SI) ÷ (P × R). Similarly, Rate (R) = (100 × SI) ÷ (P × T).

The logic followed here is:

Logic: First Number : First number +2

1) 31 - 33 = 31 : 31 + 2

2) 33 - 35 = 33 : 33 + 2

3) 37 - 39 = 37 : 37 + 2

4) 35 - 39 ≠  35 : 35 + 4

Hence, the correct answer is ’35 – 39’.

Given:

The sum of a positive number and its cube is 1740.

Calculation:

Let positive number = x

Its cube = x³

According to question, 

x + x³ = 1740

Now, check the option and verify your answer instead of solving the equation,

∴  x = 12 is absolutely correct answer.

The correct answer is Jupiter.

Key Points

• In our solar system, Jupiter is the fifth planet from the Sun.
• The planets in the solar system:
• Our Solar System consists of the Sun and 8 planets:
• Mercury (nearest to the sun).
• Venus.
• Earth.
• Mars.
• Jupiter.
• Saturn.
• Uranus and
• Neptune (farthest from the sun).

Additional Information

• Mercury:
• ​It is the nearest to the Sun and also the smallest planet in our solar system.
• Mars:
• It is called the red planet.
• Jupiter:
• It is the largest planet in the solar system.
• Saturn:
• It is yellowish in color and has rings around it.
• Venus:
• ​It is the brightest planet in our solar system it can be seen with the unaided eye from Earth.
• Venus because of its bright, consistent presence was given the nickname evening star and morning star.

The correct answer is Catenation.

Key Points

• Catenation is the ability of carbon atoms to link with each other to form long chains or rings, leading to the formation of a vast number of carbon compounds.
• This property arises from the unique ability of carbon to form strong covalent bonds with other carbon atoms.
• The tetravalency of carbon allows it to form stable bonds with four other atoms, which can be carbon or other elements.
• Carbon compounds can be straight chains, branched chains, or rings, which contributes to the diversity of organic compounds.
• Examples of catenation include hydrocarbons such as alkanes, alkenes, and alkynes.

Additional Information

• Allotropes of Carbon
• Carbon exists in different forms called allotropes, such as diamond, graphite, and fullerene.
• These allotropes exhibit different physical properties due to variations in the arrangement of carbon atoms.
• Hydrocarbons
• Hydrocarbons are compounds composed entirely of carbon and hydrogen.
• They can be classified into alkanes, alkenes, and alkynes based on the type of carbon-carbon bonds present.
• Functional Groups
• Functional groups are specific groups of atoms within molecules that determine the characteristic chemical reactions of those molecules.Examples include hydroxyl groups in alcohols, carboxyl groups in acids, and amino groups in amines.

Explanation:

It is given that, two days before yesterday was Friday, so today is Monday.

∴ the day after tomorrow will be Wednesday.

As we know,

Efficiency is inversely proportional to the time.

Efficiency ratio of A, B and C = 1/3 : 1/5 : 1/4 = 60/3 : 60/5 : 60/4 = 20 : 12 : 15

 

Note:

Multiple of 400 years i.e. 800, 1200, 1600, 2000 have 0 odd days.

Calculating leap year: For Finding number of leap year (1-99)yr, divide the number of years by 4 and the quotient will be the number of leap year.

Code for week days

 

Total odd days = 0 + 0 + 3 + 5 = 8 days = 1 week + 1 odd day

So , 1 is the code for "Monday".

Hence, Monday is the correct answer.

Given: 

37 - [19 - {6 ÷ 3 - (6 - 9 ÷ 3) ÷ 3}]

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

37 - [19 - {6 ÷ 3 - (6 - 9 ÷ 3) ÷ 3}]

⇒ 37 - [19 - {2 - (6 - 3) ÷ 3}]

⇒ 37 - [19 - {2 - 3 ÷ 3}]

​⇒ 37 - [19 - {2 - 1}]

⇒ 37 - [19 - 1]

⇒ 37 - 18 = 19

∴ 37 - [19 - {6 ÷ 3 - (6 - 9 ÷ 3) ÷ 3}] = 19

The correct answer is Education.

Key Points

• The Right to Education was made a fundamental right by the 86^th Constitutional Amendment Act 2002.
• 86^th Constitutional Amendment Act 2002 added Article 21 A which declares that the state shall provide free and compulsory education to all children of age six to fourteen years.
• It has made only elementary education a fundamental right but not professional of higher education.

Important Points

• For its implementation Parliament passed the Right of Children to Free and Compulsory Education Act in 2009.
• This act is also known as the Right of Children to Free and Compulsory Education Act because of its provision of, “the fundamental right of every child between the ages of 6 to 14 with specifies minimum norms in elementary schools.
• The RTE Act of the Parliament of India was enacted on 4 August 2009 and came into effect from 1^st April 2010.
• Earlier the right was there in the constitution under article 45 in Parts IV under the directive principle of state policy.

Concept:

Physical quantity:

• The quantities which are measurable are known as a physical quantities.
• Types of quantity are:
• Scalar
• Vector

Explanation:

Momentum:

• Momentum is the quantity of motion of a moving body.
• It is also measured as the product of its mass, and velocity.
• Its SI unit is Kgms^-1.

Impulse:

• Impulse is a term that quantifies the overall effect of a force acting over time.
• Its SI unit is Ns or  Kgms-1.

Thus, the correct answer is momentum, and impulse.

 Additional Information

Velocity:

• Velocity is a vector quantity that refers to the rate at which an object changes its position.
• Its SI unit is ms^-1.

Acceleration:

• Acceleration is a vector quantity that refers to the rate at which an object changes its velocity.
• Its SI unit is ms-2.

Given:

1. Navya's rank is 8^th from the top and Dharitri's rank is 12^th from the bottom. Shivalika's rank is exactly at the middle of Navya's and Dharitri's ranks.

2. Shivalika's rank is 15^th from the bottom

Number of students between Shivalika and Dharitri:

=> Number of students between Shivalika and Dharitri = Shivalika rank from bottom - Dharitri rank from the bottom - 1

=> Number of students between Shivalika and Dharitri = 15 - 12 - 1 = 3 - 1 = 2

Because Shivalika's rank is exactly at the middle of Navya's and Dharitri's ranks;

• So, the number of students between Shivalika and Navya's = the number of students between Shivalika and Dharitri = 2
• The number of students between Navya and Dharitri = students between Shivalika and Navya's + students between Shivalika and Dharitri + 1
• The number of students between Navya and Dharitri = 2 + 2 + 1 = 5

Dharitri rank from the top:

=> Dharitri rank from the top = Navya rank from the top +  Number of students between Navya and Dharitri + 1

=> Dharitri rank from the top = 8 + 5 + 1 = 14

Total number of students in the class:

=> Total number of students = Dharitri rank from the top + Dharitri rank from the bottom - 1

=> Total number of students = 14 + 12 - 1 = 26 - 1 = 25

Hence, "25" total number of students in the class.

Shortcut Trick

Income = Expenditure + Savings (Ratio 80 : 20 → 4 : 1)

Apply Alligation or Weighted Average: % Change in Income = (E% × E_ratio + S% × S_ratio) ÷ (Total Ratio)

12 = (17.5 × 4 + x × 1) ÷ 5

60 = 70 + x ⇒ x = −10%

Negative sign indicates a decrease.

∴ The correct answer is 10%.

Alternate Method

Given: Initial Income = 100, Expenditure = 80, Savings = 20.

Formula Used: Income = Expenditure + Savings

⇒ New Income = 100 + (12% of 100) = 112

⇒ New Expenditure = 80 + (17.5% of 80) = 80 + 14 = 94

⇒ New Savings = New Income − New Expenditure = 112 − 94 = 18

⇒ Decrease in Savings = Old Savings − New Savings = 20 − 18 = 2

⇒ Percentage Decrease = (Decrease ÷ Old Savings) × 100

⇒ Percentage Decrease = (2 ÷ 20) × 100 = 10%

∴ The correct answer is 10%.

Additional Information

Income-Expenditure Relationship

Total Income is always the sum of Expenditure and Savings. Any change in one must be balanced by the others.

Percentage Change Formula

Percentage change = [(Final Value − Initial Value) ÷ Initial Value] × 100.

Weighted Average in Income

% Change in Income = (% Change in Exp × Exp Ratio + % Change in Sav × Sav Ratio) ÷ (Total Ratio).

The logic followed here:

Therefore, by this logic, we see that 318 is the next number in the series. 

Hence, the correct answer is "Option 1".

Shortcut Trick

Ratio of corresponding sides of similar triangles ΔXYZ and ΔPQR is 6 ÷ 1.

Ratio of their areas = (Ratio of sides)² = (6)² ÷ (1)² = 36 ÷ 1.

Given, Area of ΔPQR = 6 cm².

Area of ΔXYZ = 36 × Area of ΔPQR = 36 × 6 = 216 cm².

∴ The correct answer is 216 cm².

Alternate Method

Given:

ΔXYZ ∼ ΔPQR

Ratio of sides XY ÷ PQ = 6 ÷ 1

Area of ΔPQR = 6 cm²

Formula Used:

For two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides:

Area(ΔXYZ) ÷ Area(ΔPQR) = (XY ÷ PQ)²

Calculations:

⇒ Area(ΔXYZ) ÷ 6 = (6 ÷ 1)²

⇒ Area(ΔXYZ) ÷ 6 = 36 ÷ 1

⇒ Area(ΔXYZ) = 36 × 6

⇒ Area(ΔXYZ) = 216

∴ The correct answer is 216 cm².

Additional Information

Area-Side Relationship Theorem

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding altitudes, medians, or angle bisectors.

Perimeter of Similar Triangles

The ratio of the perimeters of two similar triangles is equal to the ratio of their corresponding sides: P₁ ÷ P₂ = s₁ ÷ s₂.

Criteria for Similarity

Two triangles are similar if their corresponding angles are equal (AA) or if their corresponding sides are in the same proportion (SSS/SAS).

The correct answer is Pithampur.

Key Points

• Pithampur is an industrial town near Indore, Madhya Pradesh.
• The Pithampur city has the nickname the Detroit of India for its heavy concentration in the automotive industry.
• Pithampur city consists of a large number of manufacturing industries.​

Additional Information

• Jabalpur is one of the 100 smart cities of India.
• The famous Dhuandhar falls is located in Jabalpur.
• The High Court of Madhya Pradesh is located in Jabalpur.​
• Bhopal is the capital of Madhya Pradesh.
• The national judicial academy is located in Bhopal.
• The Indian Institute of Forest Management is located in Bhopal.
• Ashoknagar is well known for its Grain Mandi and Sharbati Gaihu(a type of wheat).

The correct answer is Stress.

Key Points

• Stress is a major risk factor for coronary heart disease.
• This disease can be overcome by controlling the following factors, which reduce your risk.
• These include the following -
• Smoking
• Diabetes
• High cholesterol
• High blood pressure
• Obesity, and
• Lack of exercise (the so-so-leisure lifestyle)
• Certain types of radiation therapy to the chest
• Stress
• High LDL "bad" cholesterol and low HDL "good" cholesterol.

Additional Information

• ​Coronary heart disease (CHD) -
• It is usually caused by a build-up of fatty deposits (atheroma) on the walls of the arteries around the heart (coronary arteries).

Given series: B E 6 D A U & 3 T I 1 8 9 C # 2 M % U 1 M W 7 5 J 8 L

Element, which is exactly in the middle of 3 and 1: 

B E 6 D A U & 3 T I 1 8 9 C # 2 M % U 1 M W 7 5 J 8 L

Hence, C is correct.

Given:

3x = 4y

Calculation:

3x = 4y

⇒ x/y = 4/3

Now,

(x + y)/(x - y)

⇒ (x/y + 1)/(x/y - 1)         [Dividing by y]

⇒ (4/3 + 1)/(4/3 - 1)

⇒ (7/3)/(1/3)

⇒ 7

∴ The value of (x + y)/(x - y) is 7.

From the above statement it is clear that the patient's condition would improve after the operation.

Assumptions:

I. The patient can be operated upon in this condition.⇒ From the above statement it clearly implies that the patient can be operated upon in this condition.

II. The patient can’t be operated upon in this condition.⇒ Not follows

So, I is implicit.

Hence, the correct answer is Only assumption I is implicit.

Given:-  14 ÷ 7 × 1 + 3 - [18 - {15 - (7 - 7 - 2)}]

Concept used:- 

Calculation:-

⇒ 14 ÷ 7 × 1 + 3 - [18 - {15 - (7 - 7 - 2)}]  

⇒ 14 ÷ 7 × 1 + 3 - [18 - {15 -( -2)}] 

⇒ 14 ÷ 7 × 1 + 3 - [18 - {17}] 

⇒ 14 ÷ 7 × 1 + 3 - [1]  

⇒ 2 × 1 + 3 - 1 

⇒ 5 - 1 = 4 

∴ The required answer is 4.

The correct answer is Kanha.

• Kanha National Park is a national park and a Tiger Reserve, located in the Mandla and Balaghat districts of Madhya Pradesh.
• It is the largest national park in Madhya Pradesh with 940 sq. km under it.
• Kanha National Park was created on 1 June 1955.
• The park has a significant population of Royal Bengal Tiger, Leopards, the Sloth Bear, Barasingha, and Indian wild dog.
• The Park is respected globally for saving the Barasingha from near extinction. It is also the first tiger reserve in India to officially introduce a mascot, "Bhoorsingh the Barasingha".
• The forest of the Kanha Tiger Reserve was originally inhabited by two indigenous tribes of Central India, the Gonds, and the Baigas.

Additional Information

• There are 101 existing national parks in India covering an area of 40,564.00 km2, which is 1.23% of the geographical area of the country (National Wildlife Database, December 2019).
• Madhya Pradesh has the maximum number of National Parks (10).
• Hemis National Park, located in Ladakh is the largest national park in India. It was formed in 1981.

The correct answer is Shigella.

• Dysentery is an infection of the intestines that causes diarrhea containing blood.

Important Points

• Dysentery is caused by shigella bacteria.
• It is spread by contaminated water and food
• Dysentery caused by Shigella is also called as Bacillary dysentery or shigellosis.
• Shigella is a rod-shaped bacteria under the Enterobacteriaceae family.
• Shigella is genetically closely related to E. coli.

Mistake Points

• Dysentery can be caused by bacteria as well as protozoa.
• The dysentery caused by protozoa is called amoebic dysentery or amoebiasis because the causative organism is Entamoeba histolytica.

Additional Information

• Cholerae is the disease caused by the Vibrio cholera bacteria.
• Tuberculosis is the disease caused by Mycobacterium tuberculosis bacteria.
• Diseases like rheumatic fever, impetigo, scarlet fever, puerperal fever are caused by Streptococcus pyogenes bacteria.

Hence, Option 2 is the correct answer.

Given:

Gain percent = 12% 

Formula used:

The profit is calculated on the cost price which is 100% of itself. 

Selling price = Cost price + Gain

Calculation:

Old selling Price = (100% + 12%) of Cost price = 112% CP 

It is given that if the article had been sold for Rs.33 more, there would a gain of 14%. 

⇒ New selling price = (100% + 14%) of Cost price = 114% 

Accordingly, New SP - Old SP = (114% - 112%) of CP = Rs.33

⇒ 2% of CP = Rs.33 

⇒ 100% of CP = Rs.33 ÷ 2% × 100% = Rs.1650

∴ The cost price of the article is Rs.1650

Shortcut Trick (114% - 112%) CP = 33

⇒ 100% CP = 33/2% × 100% = Rs.1650

Grouping them according to the given information,

A is always selected, so one member is selected out of the three.

Exactly one among B and C is always selected.

D will not participate if B is selected.

E will not play with C.

Possible members of a team can be ABE (or) ACD.

But there is ABE in the given options.

Hence, “ABE” is the correct answer.

Shortcut Trick

Value of a² + ab + b² = (a³ − b³) ÷ (a − b) = 488 ÷ 2 = 244.

Value of a² − 2ab + b² = (a − b)² = 2² = 4.

Difference 3ab = 244 − 4 = 240 ⇒ ab = 80.

Then a² + b² = (a² + ab + b²) − ab = 244 − 80 = 164.

∴ The correct answer is 164.

Alternate Method

Given:

a³ − b³ = 488

a − b = 2

Formula Used:

a³ − b³ = (a − b)³ + 3ab(a − b)

(a − b)² = a² + b² − 2ab

Calculations:

⇒ 488 = (2)³ + 3ab(2)

⇒ 488 = 8 + 6ab

⇒ 6ab = 480

⇒ ab = 80

Now, to find a² + b², we use the square identity:

⇒ (a − b)² = a² + b² − 2ab

⇒ (2)² = a² + b² − 2(80)

⇒ 4 = a² + b² − 160

⇒ a² + b² = 160 + 4

⇒ a² + b² = 164

∴ The correct answer is 164.

Additional Information

Difference of Cubes Identity

a³ − b³ = (a − b)(a² + ab + b²). This is a core Algebraic Identity used to factorize cubic expressions.

Sum of Cubes Identity

a³ + b³ = (a + b)(a² − ab + b²). Similar to the difference formula but with sign changes in the first and second terms.

Relationship between Squares and Cubes

a³ − b³ = (a − b)³ + 3ab(a − b). This form is highly efficient when the difference and product of terms are known.

The correct answer is Hiran.

Key Points

• Narmada River 
• It is the longest river in Madhya Pradesh, followed by the Chambal.
• The Source of the Narmada is Narmada Kund which is located at Amarkantak in Anuppur District, Madhya Pradesh.
• The Narmada is also known as the Rewa.
• People from Madhya Pradesh depend fully on the Narmada River, they consider Narmada as the Life Line of Madhya Pradesh.
• It is one of the major rivers in India that run from east to west along with the Tapti and the Mahi.
• It flows through the states of Madhya Pradesh (1,077 km), Maharashtra (74 km), and in Gujarat (161 km).
• List of Major Tributaries of Narmada:
• ​Right Bank:
• ​Hiran
• Tendoni
• Barna
• Kolar
• Man
• Uri
• Hatni
• Orsang
• Left Bank:
• ​Burhner
• Banjar
• Sher
• Shakkar
• Dudhi
• Tawa
• Ganjal
• Karjan

Chemical Equilibrium: Consider a general case of a reversible reaction

A + B ⇔ C + D

• With respect of time, the rate of forward reaction decreased, and the rate of backward reaction increased.
• With an instant of time, a stage is reached at which the rate of forward and reverse reaction become equal and the concentration of reactant and product becomes constant.

Given

Statement:

P = Q ≥ R > M

R < T ≤ L

Conclusions:

I. L ≥ M → False (As M < R < T ≤ L. So, M < L but not M = L therefore it is false.)

II. T > Q → False (As Q ≥ R < T. So, no relation between Q and T can be determined therefore it is false.)

Thus, Neither conclusion I nor II is true.

Hence, the correct answer is "Option 3".