MP Police Constable : (5 Dec 2025) Memory-Based Paper (Previous Year Paper)

The correct answer is USD 30 trillion.

In News

• India is aiming to become a USD 30 trillion economy by 2047, according to the Department of Financial Services.

Key Points

• India is targeting a USD 30 trillion economy by 2047 as part of its long-term growth strategy.
• This vision is aligned with the country's economic policies and development goals over the coming decades.
• Growth in sectors like banking and financial services, such as the Regional Rural Banks (RRBs), will contribute to this vision.

Additional Information

• Regional Rural Banks (RRBs)
• RRBs have been a crucial part of India's financial inclusion strategy, serving the rural population and driving economic growth in remote areas.
• The consolidation of RRBs is expected to enhance their contribution to India's GDP, increasing from 3.7% in FY24 to 5.2% by FY30.
• India's Economic Growth
• The vision of a USD 30 trillion economy is part of India's aspiration to strengthen its global economic position by 2047, marking 100 years of independence.

From the statement given “Should the Integrity of Wildlife Sanctuaries be maintained?”, argument I holds strong because it gives reason that we should “give endangered species a special place to live in” and that will “promote ecological balance”.

Argument II talks about generating income. That piece of information is not given in the statement. The fact is that the main purpose of wildlife sanctuary is to protect endangered species and not to generate income. So, the argument II does not hold strong.

Hence, “Only argument 1 is a ‘strong’ argument”

According to the given information,

A square of side 14 cm is inscribed in a circle.

Diameter of circle, d = diagonal of square = 14√2 cm

⇒ Radius of circle = (14√2)/2 = 7√2 cm

∴ Area of circle = πr² = π × (7√2)² = 98π cm²

The Correct Answer is India and Morocco.

In News

• India and Morocco Sign Legal Cooperation Agreements: Enables Cross-Border Enforcement of Judicial Summons, Settlements and Arbitral Awards.

Key Points

• India and Morocco have signed a Mutual Legal Assistance Treaty (MLAT) and an MoU.
• The MLAT focuses on civil and commercial matters.
• Areas of cooperation include:
• Service of judicial documents
• Taking of evidence through Letters of Request
• Execution of judgments, decrees, settlements, and arbitral awards
• Also includes exchange of legal expertise, training, and research.
• A joint coordination committee will be formed to plan annual cooperation programmes.
• Morocco is a mountainous country in western North Africa.
• It lies across the Strait of Gibraltar from Spain.
• Borders Algeria, Western Sahara, the Atlantic Ocean, and the Mediterranean Sea.
• It is the only African country with a coastline on both the Atlantic and Mediterranean.

The correct answer is Velocity.

Key Points

Additional Information

• All laws of motion given by Newton was published in 1687.
• Newton's first and second laws are valid only in an inertial reference frame.
• Force = mass * Acceleration

The logic is :

Addition of previous number to find next number in series.

Hence, '196' is the correct answer.

Volume of cone = (1/3)πr²h

Volume of sphere = (4/3)πR³

r = 2R

Volume of cone = Volume of sphere

(1/3)πr²h = (4/3)πR³

(1/3)π(2R)²h = (4/3)πR³

h = R

⇒ h : R = 1 : 1

The correct answer is: 2) Eastern Satpura hill range.

In News

• 4 elephants in Bandhavgarh reserve dead and 5 were found critically ill.

Key Points

• Bandhavgarh Tiger Reserve is situated in the eastern Satpura hill range of Umaria and Katni districts. The reserve is renowned for its rich biodiversity, featuring hills, valleys, rivers, and meadows that support a wide range of vegetation.
• It is also significant for its mythological connection, where the name "Bandhavgarh" refers to the fort given by Lord Rama to his brother Lakshman.
• Rich biodiversity: Includes 34 species of mammals, 260 bird species, and 70 species of butterflies.

Additional Information

• Total area of the reserve is 1,536.93 sq km, comprising a core area of 716.90 sq km and a buffer area of 820.03 sq km.
• Known for a healthy tiger population and diverse vegetation.

The reason for more number of failures in exams would be anything apart from excess usage of mobiles among students as well. Harmful radiation coming from mobiles might be hazardous to heath but linking to the exam failure is not correct. Hence neither 1^st nor 2^nd statement is implicit.

Formula used:

The perimeter of a circle = 2πr 

Area of circle = πr²

Calculation:

Perimeter of a circle = 2πr = 48π units

So, radius, r = 24 units

Radius is reduced to one-third of its value

New radius = \(\dfrac{{24}}{3} \) = 8 units

Area of the new circle = π(8)² = 64π sq. units

Explanation:

M, L, T & I represent Mass, Length, Time, and Current respectively, which are some of the useful dimensions of the basic physical quantity

Option 1:

Weight (W) = mg ⇒ [M1L1T-2]

Force (F) = ma ⇒ [M1L1T-2]

∴ both of them have the same dimensions.

Option 2:

Force (F) = ma ⇒ [M1L1T-2]

Momentum (p) = mv ⇒ [M1L1T-1]

Options 3 and 4 have inertia in common and inertia does not have any dimensions.

The below figure can be formed from the pieces given in the figure (X).

Hence, the answer is the figure (1).

Let the radii of the two spheres be ‘R’ cm and ‘r’ cm, such that R > r

∵ Surface area of sphere = 4π × (radius)²

⇒ Ratio of sum and difference of surface areas = (4πR² + 4πr²)/(4πR² – 4πr²) = (R² + r²)/(R² – r²)

⇒ (R² + r²)/(R² – r²) = 13/5

⇒ 5R² + 5r² = 13R² – 13r²

⇒ 4R² = 9r²

⇒ R/r = 3/2

⇒ R³/r³ = 27/8      ----(1)

Now,

Volume of sphere = (4/3)π × (radius)³

⇒ Ratio of sum and difference of volumes = (R³ + r³)/(R³ – r³) = (R³/r³ + 1)/(R³/r³ – 1)

Substituting from (1),

∴ Ratio of sum and difference of volumes = (35/8)/(19/8) = 35 ∶ 19

The correct answer is Volcanoes and Earthquakes.

Volcanoes and Earthquakes:

• The Ring of Fire is an area in the basin of the Pacific Ocean. Here a large number of earthquakes and volcanic eruptions occur.
• It covers about 40,000 km in a horseshoe shape.
• It has a continuous series of oceanic trenches, volcanic arcs, and volcanic belts, and plate movements.
• More than 75% of the world's active and dormant volcanoes are at this place.
• The Ring of Fire is a direct outcome of plate tectonics.

The correct answer is Can see but not very clearly.

• Translucent objects are the objects through which we can see but not very clearly.
• Translucent objects allow a part of incident light to pass through it.
• Examples for translucent objects are: Oil paper, Butter paper, wax paper, ground glass, thin sheets of plastic.
• Transparent objects are the objects through which we can see clearly.
• Transparent objects allow the incident light to pass through it.
• Examples for transparent objects are: glass, air, and water.
• Opaque objects are the objects through which we cannot see at all.
• Opaque objects do not allow the incident light to pass through it.
• Examples for opaque objects are: Cardboard, stone.

Given:

Saroj walks 24 km towards north. She turns right and walks 20 km. She turns left and walks 30 km. She rotates by 90 degrees in clockwise direction and walks 15 km. she turns right and walks 30 km. She finally rotates by 90 degrees in clockwise direction and walks 25 km. 

Solutions:

Direction of starting point from finishing point is South-west.

Distance between the two points = √(24² + 10²)

= √(576 + 100)

= √676

= 26 km

Hence, the answer is 26 km, South-west.

Given-

A piece of wire, bent in the shape of a square having 44 cm as its side, is subsequently bent to form a circle. 

Formula Used- 

The perimeter of a Square = 4 × Side

The perimeter of a Circle = 2πr

Calculation- 

Let the radius of the circle be r cm

According to the question-

Perimeter of Square = Perimeter of Circle

⇒ 4 × 44 = 2 × (22/7) × r

⇒ r = 28 cm

∴ The radius of the circle is 28 cm.

The Correct Answer is 42^nd Constitutional Amendment.

Key Points

• The Provision for the creation of "All India Judicial Service" is made by the 42^nd  Constitutional Amendment.
• The All India Judicial Service was first proposed by the 14^th report of the Law Commission in the year 1958.
• 42^nd Constitutional Amendment Act, 1976
• It is the most comprehensive amendment made so far to the constitution of India.
• It is known as the ‘Mini-Constitution’.
• It gave effect to the recommendations of the Swaran Singh Committee and added Fundamental Duties (as Part IV A).
• It also amended Preamble, which added three new words; socialist, secular and integrity, to the Preamble.

Additional Information

• 48^th Constitutional Amendment of the Indian Constitution
• It inserted a new provision in clause (5) of Article 356 of the Indian Constitution.
• 28^th Amendment act of the Indian constitution
• It deals with the secretary of state or the secretary of state in council to a civil service appointed by the crown in India.
• 22^nd Amendment of the Indian Constitution
• It inserted new article 244A in the Constitution of India to authorize Parliament to approve a law for constituting an independent State within the State of Assam and also to provide the Sovereign State .

The correct answer is Fathometer.

Key Points

• A fathometer is used to measure the depth of the ocean.
• The average depth of the ocean is about 12,100 feet.
• The deepest part of the ocean is called the Challenger Deep and is located beneath the western Pacific Ocean at the southern end of the Mariana Trench.

Important Points

• The first depth measurements in the Mariana Trench were made by the British survey ship HMS Challenger, which was used by the Royal Navy in 1875 to conduct research in the trench.
• A fathometer is a depth finder that uses sound waves to determine the depth of water.

Additional Information 

The description is as follows:

Hence, ‘Luminosity’ is the odd one out.

Shortcut Trick

If the area of a new circle is equal to the sum of the areas of two circles with radii r₁ and r₂, the radius R of the new circle is simply given by the Pythagorean relation: R = √(r₁² + r₂²).

Given, r₁ = 15 cm and r₂ = 8 cm.

R = √(15² + 8²)

R = √(225 + 64) = √289

R = 17 cm.

∴ The correct answer is 17 cm.

Alternate Method

Given:

Radius of the first circle (r₁) = 15 cm

Radius of the second circle (r₂) = 8 cm

Formula Used:

Area of a circle = πr²

Calculations:

Let the radius of the larger circle be R.

⇒ Area of new circle = Area of first circle + Area of second circle

⇒ πR² = π(r₁)² + π(r₂)²

⇒ πR² = π × (15² + 8²)

⇒ R² = 225 + 64

⇒ R² = 289

⇒ R = √289

⇒ R = 17 cm

∴ The correct answer is 17 cm.

Additional Information

Pythagorean Triplets

Three positive integers a, b, and c that satisfy a² + b² = c² form a Pythagorean triplet. Common examples are (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25). Spotting these saves calculation time.

Circumference Sum Relation

If the circumference of a circle equals the sum of the circumferences of two circles with radii r₁ and r₂, then the radius R of the new circle follows a direct linear addition: R = r₁ + r₂.

Area of Semicircle and Quadrant

Area of a Semicircle = ½ πr² and its Perimeter = πr + 2r. Area of a Quadrant = ¼ πr² and its Perimeter = πr/2 + 2r.

The correct answer is Alaudddin Khalji – Jalaluddin Khalji

Key Points

• Khilji Dynasty (1290-1320)
• Jalaluddin Khilji (1290-96)
• He was the founder of the Khilji Dynasty
• Alauddin Khilji (1296-1316)
• He was a nephew and son-in-law of Jalaluddin Khilji.
• Alauddin Khilji killed him and succeeded the throne in 1296.
• Tughlak Dynasty (1320-1414)
• Ghiyasuddin Tughlak (1320-25)
• He was the founder of the Tughlak Dynasty.
• He was succeeded by Mohammad bin Tughlak.
• Mohammad bin Tughlak (1325-51)
• His name was Ulugh Khan and after succeeding Ghiyasuddin Tughlak he was named under the title of Mohammad bin Tughlak.
• Firoz Shah Tughlak (1351-88)
• He was the cousin of Mohammad bin Tughlak.

Additional Information

• Slave Dynasty (1206-90)
• Founded by Qutubuddin Aibak.
• Khilji Dynasty (1290-1320)
• Founded by Jalaluddin Khilji
• Tughlak Dynasty (1320-1414)
• Founded by Ghiyasuddin Tughlak
• Sayyid Dynasty ( 1414-50)
• Founded by Khizr Khan.
• Lodhi Dynasty (1451-1526)
• Founded by Behlol Lodhi

The correct answer is option 2, i.e., Parallel to the principal axis.

• A ray of light appearing to meet at the principal focus of a concave lens emerge after refraction will be parallel to the principal axis.
• In the case of a convex lens, the ray passing through the principal focus after refraction becomes parallel to the principal axis.

The least possible Venn diagram is:

Conclusions:

I. All yellow are roses. → Does not follow (As, Some roses are yellow and Some yellow are buses → Some yellow are roses)

II. Some buses are yellow. → Follows (As, Some yellow are buses)

III. All yellow are green. → Does not follow (As, Some yellow are buses and All buses are green → Some yellow are green)

Hence, 'Only conclusion II follows' is the correct answer.

GIVEN:

Lateral surface areas = 198 m² and 220 m²

FORMULA USED:

Lateral surface area of cone = πrl

CALCULATION:

Let l₁, l₂ be slant heights of two cones.

Here, radius of each cone = 1/2 = 0.5 m

⇒ (π × 0.5 × l₁) : (π × 0.5 × l₂) = 198 : 220

⇒ l₁ : l₂ = 9 : 10

∴ required ratio of their slant heights are 9 : 10

The correct answer is Mandan.

• Mandan and Jaita were the Architects (Shilpacharya) of Chittor during the reign of Maharana Kumbha.

Key Points

• Rana Kumbha was the ruler of Mewar who ruled from 1433 to 1468.
• Kumbha built the chief citadel of Mewar - The fort of Kumbhalgarh.
• He built 32 of 84 fortresses that form the defense of Mewar.
• Maharana Kumbha built Vijay Stambh to commemorate his victory over the Army of Malwa and Gujarat.
• He wrote treatises on music called Sangeet raj, Sangeet mimansa, Sangeet Ratnakar, and Shudprabandha.

The positional values of English alphabet is as follows :

The pattern followed here is :

 'BLISS' is coded as 'MAITR' 

 'JAPAN' is coded as 'BIPOZ

Similarly, 'GLOBE' will be written as :

Hence, "MFOFA" is the correct answer.

Given:

Aarti can type 85 pages in 10 hours

Aarti and Bina together can type 500 pages in 40 hours

Formula Used:

Efficiency = Work done/Time Taken

Calculation:

By using the above formula

The efficiency of Aarti is = 85/10 = 8.5 pages/hr

The efficiency of Aarti and Bina  = 500/40= 12.5 pages/hr

The efficiency of Bina = 12.5 - 8.5 = 4 pages/hr

The time taken by Bina to type 40 pages will be

⇒ 40/4= 10 hr

∴ The Time taken by Bina is 10 hours.

The correct answer is the National Institution for Transforming India.

• The full form of NITI Ayog is the National Institution for Transforming India.​

Key Points 

• NITI Aayog:
• NITI Aayog or National Institution for Transforming India Aayog is the replacement of the Planning Commission of India.
• National Institution for Transforming India (NITI) Aayog was created in accordance with the announcement made by Prime Minister, Narendra Modi on 15 August 2014.
• The Government of India, in keeping with its reform agenda, constituted the NITI Aayog to replace the Planning Commission instituted in 1950.
• The Planning Commission was replaced by a new institution – NITI AAYOG (National Institution for Transforming India) on January 1, 2015.
• It focuses upon the ‘Bottom-Up’ approach to Planning.
• Administrative Skeltal:
• Vice-Chairman - Dr. Suman Bery
• CEO - Parameswaran Iyer
• Chairperson: Prime Minister Narendra Modi.

• Acetic Acid is the common name of ethanoic acid.
• The chemical Formulae for Acetic Acid is CH₃COOH.
• It belongs to a group called carboxylic acid and hence they are weak acids.
• When acetic acid is diluted in water with a percentage of 5-8 then vinegar is formed.
• The melting point of acetic acid is 290k and it often freezes at room temperature, hence it has another name called Glacial Acetic Acid.

Realistic and Fictional are antonyms.

Similarly,

The antonym for Appreciation is Criticism.

‘Criticism’ is related to the third word in the same way as the second word is related to the first word.

Hence, “criticism” is the correct answer.

Shortcut Trick

Using the product-over-difference formula for two opposing rates.

Time taken by leakage = (Filling time × Filling time with leakage) ÷ (Filling time with leakage − Filling time)

Time = (30 × 50) ÷ (50 − 30) = 1500 ÷ 20 = 75 hours.

∴ The correct answer is 75 hr.

Alternate Method

Given:

Time taken by Pipe A to fill = 30 hours

Time taken by Pipe A + Leakage L = 50 hours

Calculations:

⇒ Let total tank capacity (LCM of 30 and 50) = 150 units.

⇒ Efficiency of Pipe A = 150 ÷ 30 = 5 units/hr.

⇒ Combined efficiency of Pipe A and Leakage L = 150 ÷ 50 = 3 units/hr.

⇒ Efficiency of Leakage L = Combined efficiency − Efficiency of A

⇒ Efficiency of Leakage L = 3 − 5 = −2 units/hr (negative denotes emptying).

⇒ Time taken by Leakage to empty tank = Total Work ÷ Efficiency of L

⇒ Time = 150 ÷ 2 = 75 hours.

∴ The correct answer is 75 hr.

Additional Information

Pipes and Cisterns Efficiency

If a pipe fills a tank in 'x' hours and another empties it in 'y' hours (where y > x), the net part filled in 1 hour is (1/x − 1/y).

Combined Time Formula

When two pipes operate together, the total time T taken is given by 1/T = 1/T₁ + 1/T₂, where emptying pipes have negative values.

Leakage Impact

A leak always reduces the net efficiency of the filling pipe, thereby increasing the total time required to fill the tank.

The correct answer is Attorney General of India.

Key Points

• The Attorney General of India is the chief legal advisor to the Government of India.
• He/she is appointed by the President of India under Article 76 of the Constitution.
• The Attorney General represents the Government of India in all legal matters, including the Supreme Court.
• He/she holds office during the pleasure of the President and has the right to speak and take part in the proceedings of both Houses of Parliament but cannot vote.

Additional Information

• When Magnesium (Mg) ribbon is burnt in air, Magnesium Oxide (MgO) is formed.
• A bright white light is produced when the ribbon is burnt and powdery ash i.e. MgO is formed.
• The reaction is a highly exothermic reaction, i.e. a lot of heat is produced.
• The oxygen in the air reacts with Mg to form MgO.
• 2Mg + O₂ → 2MgO + energy; is the balanced equation for this reaction.

Thus, the correct answer is option 1.

Given:

Difference between compound interest and simple interest = Rs. 31

Annual interest rate (r) = 10% (0.10 in decimal form)

Time (t) = 3 years

Concept used:

Difference between compound interest (CI) and simple interest (SI) for a given time period = P [(1 + (r/n))^t - 1] - (P × r × t)

Calculation:

⇒ 31 = P [(1 + 0.10)³ - 1] - (P × 0.10 × 3)

⇒ 31 = P [1.331 - 1] - 0.30P

⇒ 31 = P (0.331) - 0.30P

⇒ 31 = 0.031P

⇒ P = 31 / 0.031 = Rs. 1000

⇒ Principal amount (sum) = Rs. 1000

∴ The sum is Rs. 1000.

• The correct answer is Budda.

Key Points

• Siddhartha Gautama, after attaining enlightenment referred to as the Buddha ("the awakened").

Additional Information

• The real name of Gautama Buddha was "Siddharth Gautama".
• Gautama Buddha was the originator of Buddhism. He was born in 563 BC and "Mahaparinirvana" in 483 BC.
• He was born in Lumbini near Kapilavastu, the capital of the Shakya Republic.
• Distressed by worldly problems, Siddharth left home at the age of 29.
• This renunciation is known as "Mahabhinishkramana" in Buddhism.
• In search of knowledge, Siddhartha first took the initiation of "Sankhya philosophy" from Alar Kalam of Vaishali.
• At the age of 35, he realized the knowledge in Uruvela (Bodh Gaya) under the Peepal tree on the banks of river Niranjana.
• After the attainment of knowledge in Uruvela, people started addressing them in the name of "Tathagata or Buddha".
• This place was also later known as "Bodh Gaya".

Given:

Kapil's position from top : 14^th

Kapil's position from bottom; 48^th

Formula used:

The total number of students = Position of the person from Top + Position of the person from Bottom - 1.

Therefore,

The total number of students = 14 + 48 - 1 = 61

Hence, the correct answer is "61".

Shortcut Trick

Pass Marks = Marks Obtained + Shortfall Marks

⇒ Pass Marks = 40 + 20 = 60 marks.

Given that the minimum pass percentage is 40%.

⇒ Total Marks = 60 × (100 ÷ 40) = 150 marks.

∴ The correct answer is 150 marks.

Alternate Method

Given:

Marks obtained by the student = 40 marks

Marks by which the student failed = 20 marks

Passing percentage for the exam = 40%

Formula Used:

Total Marks = (Passing Marks ÷ Pass Percentage) × 100

Obtained
Gap
Total Marks (100%)

40 Marks

• 20

Pass Marks = 60
0%
40%
100%

Total = 150 marks

Calculations:

⇒ Minimum pass marks = 40 (obtained) + 20 (shortfall) = 60 marks.

⇒ 40% of the Total Marks = 60

⇒ (40 ÷ 100) × Total Marks = 60

⇒ Total Marks = (60 × 100) ÷ 40

⇒ Total Marks = 6000 ÷ 40 = 150

∴ The correct answer is 150 marks.

Additional Information

Percentage Basics

Percentage means per hundred. To find a percentage of a given number: Value = (Percentage ÷ 100) × Total Quantity.

Base Change in Percentage

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

Successive Percentage Change

If a number is changed by X% and then by Y%, the net percentage change is given by the formula: X + Y + (X × Y ÷ 100)%.

The correct answer is Nitric acid.

Key Points

• Nitric acid (HNO₃), is a highly corrosive and poisonous strong mineral acid that is normally colorless but turns yellow due to the accumulation of oxides of nitrogen when stored for long periods.
• Nitric acid is used in the purification of gold and silver.
• The acid mixture aqua regia, or royal water, dissolves gold and is used to purify scrap alloy containing gold.
• Aqua regia is a mixture of hydrochloric acid and nitric acid in the ratio 3:1.
• Nitric acid is a nitrogen oxoacid of the formula HNO₃ in which the nitrogen atom is bound to a hydroxyl group and the remaining two oxygen atoms by equal bonds.

Additional Information

• Sulphuric Acid:
• Sulphuric acid is a strong mineral acid commonly used in various industrial processes.
• It is not typically used by goldsmiths for cleaning gold and silver articles due to its highly corrosive nature.
• Hydrochloric Acid:
• Hydrochloric acid is another strong mineral acid.
• While it can dissolve some metal oxides, it is not commonly used alone for cleaning gold and silver in jewelry making.
• Hydrochloric acid is often used in combination with nitric acid to form aqua regia, a mixture with powerful oxidizing properties.
• Phosphoric Acid:
• Phosphoric acid is a weaker acid compared to nitric, sulfuric, and hydrochloric acids.
• It is often used in certain rust-removing products and as a food additive, but it is not a common choice for cleaning precious metals like gold and silver.

Goldsmiths commonly use nitric acid to clean silver articles because it reacts with impurities or other metals (like copper) that may be present in the alloy, helping to purify or clean the surface. However, pure gold does not react with nitric acid, which helps in distinguishing it from counterfeit or impure metals — this property is also used in the acid test for gold.

⚠️

Note:

For dissolving gold, a mixture of nitric acid and hydrochloric acid (called aqua regia) is used — but for cleaning, nitric acid alone is often sufficient, especially for silver articles.

The correct answer is Option 4: Refuse the offer as safety comes first.

• Qualities Projected in this situation:  (Courage, Determination, Dedication, and Social adaptability)

Key Points

• Checklist for attempting SRT questions:

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

Additional Information

Officer qualities:

Shortcut Trick

Total weight increase in the group = Total players × Increase in average weight

Total weight increase = 12 × 1.5 = 18 kg

New player weight = Old player weight + Total increase

New player weight = 63 kg + 18 kg = 81 kg

∴ The correct answer is 81 kg.

Alternate Method

Given:

Number of players = 12

Weight of the replaced player = 63 kg

Increase in average weight = 1.5 kg

Calculation:

⇒ Let the initial average weight of 12 players be 'A' kg.

⇒ Total weight of the group = 12A kg

⇒ New total weight after replacement = 12A − 63 + (New Player Weight)

⇒ New average = A + 1.5

⇒ (12A − 63 + New Player Weight) ÷ 12 = A + 1.5

⇒ 12A − 63 + New Player Weight = 12(A + 1.5)

⇒ 12A − 63 + New Player Weight = 12A + 18

⇒ New Player Weight = 18 + 63

⇒ New Player Weight = 81 kg

∴ The correct answer is 81 kg.

Additional Information

Replacement Rule in Average

When one item is replaced, the change in total weight is always equal to (Number of items × Change in average). New Value = Replaced Value + (n × ΔAverage).

Average of a Group

The average weight is the sum of weights of all members divided by the total number of members. Average = (Sum) ÷ (Count).

Effect of Addition vs Replacement

In replacement, the count (n) remains constant. In addition, the count increases to (n+1), which requires a different calculation for the new average.

The correct answer is option 2.

Key Points

• Montane forest: These forests are typically found on mountain slopes and vary with altitude, often transitioning from temperate forests to alpine vegetation. Hence, option 2 is correct.
• Tropical rainforest: Found in lowland equatorial regions with heavy rainfall.
• Deciduous forest: Found in areas with a distinct dry season, not typically on mountain slopes.
• Mangrove forest: Found in coastal, tidal areas, not on mountains.
• Hence, Montane forest is correct.

Hence option 1 is the correct answer. 

Mistake Points

Options 1 and 2 are different because the 4 corners of options 1 and 2 are different.

Shortcut Trick

In Simple Interest, interest is always calculated on the Principal.

Total effective interest rate = 4% + 5% = 9%

Total Payable Amount = 100% (Principal) + 9% (Total SI) = 109% of 25,000

Amount = 25,000 × (109 ÷ 100) = 250 × 109 = 27,250

∴ The correct answer is Rs. 27,250.

Alternate Method

Given:

Principal (P) = Rs. 25,000

Rate in 1^st year (R₁) = 4%

Rate in 2^nd year (R₂) = 5%

Time (T) = 2 years

Formula Used:

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

Total Amount (A) = Principal + Total SI

Calculations:

⇒ Interest for Year 1 = (25000 × 4 × 1) ÷ 100 = Rs. 1,000

⇒ Interest for Year 2 = (25000 × 5 × 1) ÷ 100 = Rs. 1,250

⇒ Total Simple Interest = 1,000 + 1,250 = Rs. 2,250

⇒ Total Amount = Principal + Total Interest

⇒ Total Amount = 25,000 + 2,250 = Rs. 27,250

∴ The correct answer is Rs. 27,250.

Additional Information

Effective Simple Interest Rate

For consecutive years with different rates R₁, R₂, ..., R_n, the net rate is R_eff = R₁ + R₂ + ... + R_n.

Simple Interest vs Compound Interest

In SI, interest is only on the Principal, whereas in CI, interest is calculated on (Principal + accumulated Interest).

Amount Formula

Amount = P × [1 + (R₁ + R₂ + ... + R_n) ÷ 100], where P is the initial sum.

• Conduction is the transfer of heat energy by direct contact.
• Convection is the movement of heat by actual motion of matter.
• Absorption is a physical or chemical phenomenon or a process in which atoms, molecules or ions enter some bulk phase, liquid or solid material.
• Advection is defined as the transfer of heat or matter by the flow of a fluid, especially horizontally in the atmosphere.

Hence, 4 is the correct option.

695, 395 and 885 are all the multiples of 5 whereas 489 is not a multiple of 5.

Hence, 489 is the odd one.

Given:

Three numbers are in the ratio 1 ∶ 2 ∶ 3

The sum of their squares is 2366.

Calculation:

Let the three numbers are 1x, 2x, and 3x.

According to the question statements,

(1x)² + (2x)² + (3x)² = 2366

⇒ 1x² + 4x² + 9x² = 2366

⇒ 14x2 = 2366

⇒ x2 = 2366/14 = 169

⇒ x = 13

The third number = 13 × 3 = 39

∴ The third number is 39.

The correct answer is 1981.

Key Points

• The Dhrupad Kendra Bhopal is an institution for training Dhrupad singers.
• It was established by the Government of Madhya Pradesh in the state capital Bhopal in 1981.
• Its goal is to impart training in the Indian teacher-apprentice or Guru-Shishya tradition of education in Dhrupad.

Additional Information

• Dhrupad:
• It is the oldest known style of major vocal styles associated with Hindustani classical music.
• Some famous artists of this style of music are Rahim Fahimuddin Dagar, Zia Fariuddin Dagar, Wasifuddin Dagar, Sayeedudin Dagar, etc.

The statement is a warning to the students who are trying to do copy in the exam. So, from this, we can assume that some students are doing copy during the exam and the invigilator is warning them so that they will not copy during the exam, hence statement 1 is implicit.

We cannot be certain about the impact of the warning and hence 2 is not implicit.

Hence, statement 1 is implicit.

Given :

Amount in 4 years =  Rs. 720

Amount in 6 years = Rs. 768

Formula used :

Principal = amount - simple interest 

Calculation:

If the amount of 4 years is subtracted from the amount of 6 years, then we will get S.I. for 2 years.

⇒ S.I. for 2 years = 768 - 720

⇒ S.I. for 2 years = 48

⇒ S.I. for 1 year  = 48/2 = 24

⇒ S.I. for 4 years = 24 × 4 = 96

⇒ Principal = 720 - 96 = Rs. 624

∴ The principal is Rs. 624

The correct answer is Casting vote.

Key Points

• A casting vote is exercised to resolve or break a deadlock.
• It is by the presiding officer of a council or legislative body.
• It is the deciding vote of the presiding officer made when the other votes are equally divided.

Additional Information

Hence, figure given in option 3 is the correct answer.

Shortcut Trick

Required number = LCM(6, 8, 12, 16) + Remainder

LCM of 6, 8, 12, 16 = 48

Required number = 48 + 3 = 51

∴ The correct answer is 51.

Alternate Method

Given: Divisors are 6, 8, 12, and 16. The remainder in each case is 3.

Formula Used: Smallest number = LCM(divisors) + remainder

⇒ Prime factorization of 6 = 2 × 3

⇒ Prime factorization of 8 = 2³

⇒ Prime factorization of 12 = 2² × 3

⇒ Prime factorization of 16 = 2⁴

⇒ LCM = 2⁴ × 3 = 16 × 3 = 48

⇒ Required number = 48 + 3 = 51

∴ The correct answer is 51.

Additional Information

LCM (Least Common Multiple)

The smallest positive integer that is divisible by each of the given numbers without leaving a remainder.

Different Remainders Case

If the remainders are different (r₁, r₂...) such that (Divisor − Remainder) = k (constant), then the number is LCM(divisors) − k.

HCF (Highest Common Factor)

The largest positive integer that divides each of the given numbers exactly. Relationship: LCM × HCF = Product of two numbers.

The correct answer is Tapi.

Key Points

• Tapi, also known as the Tapti River, is one of the most important rivers of peninsular India.
• It originates in the Satpura Range of Madhya Pradesh and flows through Maharashtra and Gujarat before draining into the Arabian Sea.
• The river has a total length of about 724 km, making it one of the longest rivers in peninsular India.
• The Tapi River is an important source of water for irrigation, hydropower generation, and drinking water supply for the people living in the region.
• The river is also known for its scenic beauty and is a popular tourist destination. The Tapi Riverfront project in Surat, Gujarat, has been developed as a recreational and entertainment hub for the local residents and tourists.

Important Points

• Satpura range arises parallel to Narmada and Tapi and is a source of both rivers.
• It is one of the major rivers of peninsular India with a length of around 724 km.
• Tapti River, a river in central India, rises in the Gawilgarh Hills of the central Deccan plateau in south-central Madhya Pradesh state.
• It flows westward between two spurs of the Satpura Range, across the Jalgaon plateau region in Maharashtra state, and through the plain of Surat in Gujarat state to the Gulf of Khambhat.

Additional Information

• Beas: The Beas River is a major river in northern India, flowing through the states of Himachal Pradesh and Punjab. It is a tributary of the Indus River and has a total length of about 470 km. The river is an important source of water for irrigation and hydropower generation.
• Palar: The Palar River is a major river in southern India, flowing through the states of Karnataka and Tamil Nadu. It has a total length of about 348 km and is an important source of water for irrigation and drinking water supply for the people living in the region.
• Bhavani: The Bhavani River is a major river in southern India, flowing through the states of Tamil Nadu and Kerala. It has a total length of about 217 km and is an important source of water for irrigation and drinking water supply for the people living in the region.

The pattern followed here is:

The given sentences are arranged according to the meaningful order.

S1: Several metro lines have been planned in the NCR. 2. They are expected to alleviate the problem of transportation.

1. Red line is the first among them.
2. It starts from Shahdara and terminates at Tiz-Hazari in the initial phase.
3. It caters to over 1 lakh commuters at present.

S6: Hopefully, the public transportation problem will not be as acute after all the metro lines are completed.

Hence, the correct answer is "2, 1, 3, 4".

Given:

Age of Nikhil = 26 years

Age of Simran (Daughter) = 4 years

Calculation:

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

⇒ (26 + x)/(4 + x) = 2/1

⇒ 26 + x = 2 × (4 + x)

⇒ 26 + x = 8 + 2x

⇒ x = 18

∴ After 18 years, Nikhil's age will be double of Simran's age.

The correct answer is 'Nitisara' by Kamandaka.

Key Points

• Nitisara is an ancient Indian treatise on politics and statecraft.
• It was authored by Kamandaka.
• Kamandaka was a disciple of Chanakya.
• It gives us a fair idea of the polity and administration of the Guptas.
• The work has been dedicated to Chandragupta.
• The book contains 20 sargas and 36 prakarans.
• It is based on Arthashastra written by Kautilya.
• Nitisara discusses social elements such as theories of social order, the state's structure, and the government's principles and policies**.**

 Thus, we can say that 'Nitisara' by Kamandaka gives us a fair idea of the polity and administration of the Guptas.

The positions of the letters according to the English alphabet series:

The pattern for this code is as follows;

Hence, "SV76" is the correct answer.

Concept:

Calculation:

50 - 4 of (17 - 12) + 4 × 7

⇒ 50 - 4 of 5 + 4 × 7

⇒ 50 - 20 + 4 × 7

⇒  50 - 20 + 28

⇒  50 + 8 = 58

∴ The correct answer is the 58.

The correct answer is Both 1 and 2.

Key Points

• Uttar Pradesh has 31 seats in Rajya Sabha. Hence statement 1 is correct.
• Uttar Pradesh has 80 seats in Lok Sabha. Hence statement 2 is correct.
• Among 80 seats in Lok Sabha 63 seats are general and 17 are reserved for SC/ST candidates.
• Uttar Pradesh has a maximum number of Lok Sabha seats among all states.

​

Additional InformationEligibility to Elected In Lok Sabha

• The candidate must be a citizen of India.
• The candidate must be at least 25 years of age.
• He/she should not have been sentenced to imprisonment.
• The person should not be declared as an insolvent by banks or courts of the country.

Eligibility to Elected In Rajya Sabha

• Be a citizen of India.
• Make and subscribe before some person authorized in that behalf by the Election Commission an oath or affirmation according to the form set out for the purpose in the Third Schedule to the Constitution.
• Be at least 30 years old. (Article 84 constitution of India)
• Be elected by the Legislative Assembly of States and Union territories by means of single transferable vote through proportional representation.

The pattern followed here is –

Left Side Number - Right Side Number = 20

1)  40 – 21 = 19 

2)  35 – 15  = 20

3)  60 – 40  = 20

4)  55 – 35  = 20

40 – 21 = 19 which is not equal to 20

Hence, 40 - 21 is the odd one among the given options.

Given:

By selling an article for Rs.770, a woman incurred a loss of 23%.

Formula used:

Selling Price = (100% + Profit%) × Cost Price

Selling Price = (100% - Loss%) × Cost Price

Calculation:

According to the question,

First case:

By selling an article for Rs.770, a woman incurred a loss of 23%.

⇒ 770 = (100% - 23%) of C.P

⇒ 770 = 77% of C.P

⇒ C.P = Rs. 1000

Second case:

Selling price S.P so that she makes a profit of 27%.

⇒ S.P = (100% + 27%) of 1000

⇒ S.P = (127%) of 1000

⇒ S.P = Rs. 1270

Therefore, "Rs. 1270" is the required answer.

The correct answer is Option B.

Key Points

• EVMs eliminate common issues with ballot papers, like invalid votes.
• They streamline the voting process by reducing the time needed for counting.
• EVMs help prevent booth capturing and bogus voting.
• They are also noted for reducing paper use and logistical complexities.
• The administrative convenience of EVMs speeds up the election process.
• These benefits are critical in large-scale elections like those in India.

• The correct answer is Option 3: seeing the management getting concerned about the developing situation, you volunteered to help in this operation.

• Qualities Projected in this situation: (Effective Intelligence, Strong Reasoning Ability, Sense of Responsibility, Cooperative Nature, Liveliness, Courage, willingness to take initiative).

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 average age of 8 coworkers = 16 years

2 new colleagues join the average age, increases by 1 year.

Formula Used:

Average = Sum of total observations / Total no. of observations

Calculation:

The sum of average age of 8 coworkers = 8 × 16 = 128 years

According to the question,

After adding the age of new 10 coworkers,

The average age is 17 years 

The sum of ages after adding new coworkers

⇒10 × 17 = 170 years

The age of new coworkers = 170 - 128 = 42 years

The average age of new colleagues = 42/2 = 21 years.

∴ The correct answer is 21 years.

The correct answer is Rajvalli Katha.

• Ravalli Katha is a Jaina text in which Bindusara is called Seemseri.
• Bindusara was the son of Chandragupta Maurya.
• Born in 320 BC, he ruled from 298 BC to 272 BC.
• Syrian King Antiochus-I sent Deimachus as his ambassador in the court of Bindusara.
• Jain literature is contained in the Agam(Sacred book of Jainism)..

The pattern followed here is:

Hence, the correct answer is "U35H".

Given:

Speed of a train is 46 km/hr

Length of the train is 805 metre

Concept Used:

1 km/hr = (5/18) m/s

1 sec = 1/60 minutes

Formula Used:

Speed = Distance/Time

Calculation:

Let T be the time required by the train to cross a man

Speed of a train = 46 × (5/18) = 115/9 m/s

⇒ T = \(\frac{805}{\frac{115}{9}}\) = \(\frac{805\times9}{115}\) = 63 seconds

⇒ T = 63 sec = 63/60 = 21/20 minutes

∴ The train will take 21/20 minutes to cross a man standing on the platform.

The correct answer is ​Its frequency 98.3 million hertz.

Key Points

• In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal.Frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave.
• In Frequency modulation, the carrier amplitude remains constant, but its frequency is changed in accordance with the modulating signal.
• FM Radio signals have bandwidth several times that of Amplitude Modulation (AM) signals. Bandwidth six times or larger are common.
• Frequency Modulation index is consistently over 1, requires high bandwidth in the range of 200 kHz, operates in a very high frequency range of 88 to 108 Megahertz.

The positions of the letters according to the English alphabet series:

The pattern for this is as follows;

Hence, "LR" is the correct answer.

Given:

sin2 60° cos2 45° + 2 tan2 60° – cosec2 30°

Formula used:

sin60° = √3/2

cos45° = 1/√2

tan60° = √3

cosec30° = 2

Calculation:

sin2 60° cos2 45° + 2 tan2 60° – cosec2 30°

⇒ (√3/2)² × (1/√2)² + 2 × (√3)² – (2)²

⇒ (3/4 × 1/2) + (2 × 3 – 4)

⇒ (3/8 + 2)

⇒ (3 + 16)/8

⇒ 19/8

∴ The required value is 19/8

The correct answer is 1992.

Key Points

• 71^st constitution amendment act 1992 deals with the addition of Konkani, Manipuri, and Nepali in the eighth schedule of the constitution of India.

Additional Information

• Eighth Schedule
• It is the list of 22 official languages.
• Part 17 of the Indian constitution describes the official languages in Articles 343 to 351.
• 14 languages were initially included in the constitution of India.
• 21^st constitution amendment act of 1967 deals with the addition of the Sindhi language.
• 92^nd constitution amendment act of 2003 deals with the addition of Bodo, Dogri, Maithili, And Santhali languages.

The correct answer is Option 3: Pay for that broken flask

• Qualities Projected in this situation:  (Effective intelligence and Sense of responsibility).

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:

x + \(\frac{1}{x}\) = 2

Concept Used:

(a + b)2 = a2 + b2 + 2ab

Calculation:

⇒ It is given that, x + \(\frac{1}{x}\) = 2

⇒ Squaring both sides, we get

⇒ x2 + \(\frac{1}{x^2} \) + 2 = 4

⇒ x2 + \( \frac{1}{x^2}\) = 2

⇒ Squaring again both sides, we get

⇒ x4 + \( \frac{1}{x^4} \) + 2 = 4

⇒  x4 + \( \frac{1}{x^4} \) = 2

Therefore, the value of \(x^4 + \frac{1}{x^4}\) is 2.