MP Police Constable : (10 Dec 2025) Memory-Based Paper (Previous Year Paper)

The correct answer is Samaveda.

Key Points

• The Narmada is also called Rewa and Purvaganga.
• It is said in Samaveda that a view of the river cleanses our sins.

Important Points

The correct answer is Double.

Key Points

• For many chemical reactions, the rate constant approximately doubles with a 10°C increase in temperature.
• This phenomenon is often referred to as the "rule of thumb" in chemical kinetics.
• The temperature dependence of the rate constant is described by the Arrhenius equation.
• According to the Arrhenius equation, the rate constant (k) is related to temperature (T) through the exponential factor involving activation energy (Ea) and the gas constant (R).

Additional Information

• Arrhenius Equation:
• The Arrhenius equation is k = A * exp(-Ea/(RT)), where k is the rate constant, A is the pre-exponential factor (frequency of collisions), Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
• This equation shows the relationship between the rate constant and temperature, indicating that as temperature increases, the rate constant increases exponentially.
• Activation Energy (Ea):
• Activation energy is the minimum energy that reacting molecules must possess to undergo a chemical reaction.
• Higher activation energy means that fewer molecules have sufficient energy to react at a given temperature.
• Gas Constant (R):
• The gas constant (R) is a physical constant that appears in many fundamental equations in physical sciences, such as the ideal gas law and the Arrhenius equation.
• The value of R is 8.314 J/(mol·K).
• Rule of Thumb in Chemical Kinetics:
• The "rule of thumb" in chemical kinetics suggests that for many reactions, the rate constant approximately doubles for every 10°C rise in temperature.
• This empirical rule helps chemists estimate the effect of temperature changes on reaction rates without detailed calculations.

The pattern followed is,

‘yb’ is followed by ‘by’ and ‘by’ is followed by ‘yb’ simultaneously.

The complete pattern is,

Hence, “ybby” is the correct answer.

Shortcut Trick

Direct formula for the difference between CI and SI for 3 years: D = P × (R/100)² × (300 + R)/100

⇒ 244 = P × (5/100)² × (305/100)

⇒ 244 = P × (1/400) × (61/20)

⇒ P = (244 × 8000) ÷ 61 = 4 × 8000 = 32000

∴ The correct answer is ₹32000.

Alternate Method

Given:

Difference between CI and SI (D) = ₹244

Rate (R) = 5% per annum

Time (T) = 3 years

Formula Used:

Effective SI for 3 years = 3R

Effective CI for 3 years = 3R + 3R²/100 + R³/10000

Simple Interest (SI)
Rate = 5% × 3 yrs
Total SI = 15%

Compound Interest (CI)
Effective % for 3 yrs
Total CI = 15.7625%

Difference = 0.7625% = ₹244

Calculations:

⇒ Effective SI % = 3 × 5% = 15%

⇒ Effective CI % = 3(5) + 3(5²)/100 + (5³)/10000 = 15 + 0.75 + 0.0125 = 15.7625%

⇒ Difference in effective % = 15.7625% − 15% = 0.7625%

⇒ This difference corresponds to ₹244.

⇒ 0.7625% of P = 244

⇒ P × (0.7625/100) = 244

⇒ P = (244 × 100) ÷ 0.7625

⇒ P = 24400 ÷ 0.7625 = 32000

∴ The correct answer is ₹32000.

Additional Information

CI vs SI Difference for 2 Years

The difference between compound interest and simple interest for exactly 2 years can be found directly using the formula: D = P × (R/100)².

Effective Compound Interest Rate

For an interest rate R%, the effective CI rate for 2 years is calculated using the successive percentage change formula: Effective Rate = R + R + (R×R)/100.

Rule of 72

A mental math shortcut used to estimate the time required to double an investment under compound interest: Approximate Time ≈ 72 ÷ Annual Interest Rate.

The correct answer is Geneva.

Key Points

• The World Meteorological Organization (WMO) is a specialized agency of the United Nations (UN) responsible for promoting international cooperation in meteorology, climatology, hydrology, and other related fields.
• The headquarters of the WMO is located in Geneva, Switzerland.
• It was established in 1950, succeeding the International Meteorological Organization (IMO), which was founded in 1873.
• The WMO has 193 member states and territories as of 2023 and provides leadership in monitoring and predicting changes in the Earth’s weather and climate.
• Geneva serves as a hub for many international organizations, making it an ideal location for the WMO's global coordination activities.

Additional Information

• World Meteorological Organization (WMO):
• The WMO works towards enhancing the understanding of weather, climate, and water resources globally.
• It is instrumental in implementing the Global Framework for Climate Services (GFCS) to improve climate-related decision-making.
• It regularly issues reports such as the State of the Global Climate and Greenhouse Gas Bulletin.
• Geneva as an International Hub:
• Geneva is home to several major international organizations, including the United Nations Office at Geneva (UNOG) and the World Health Organization (WHO).
• Switzerland’s policy of neutrality makes it a preferred location for global cooperation and diplomacy.
• Functions of WMO:
• It coordinates the activities of national meteorological and hydrological services worldwide.
• The WMO provides critical data and forecasts to mitigate natural disasters such as cyclones, floods, and droughts.
• It supports research on climate change, weather modeling, and atmospheric sciences.
• International Meteorological Organization (IMO):
• The IMO was the predecessor of the WMO, established in 1873 to promote international cooperation in meteorology.
• The IMO transitioned into the WMO in 1950, under the auspices of the United Nations.

The correct answer is Chloroethane.

Key Points

• Chloroethane with the chemical formula CH₃CH₂Cl is used as a blowing agent in foamed plastics.
• It was used as a promoter chemical in the aluminum chloride catalyzed process to produce ethylbenzene. Now, it is not widely used in any of these roles.
• Foam products are manufactured with chemical blowing agents that expand the plastic matrix before it solidifies.
• Chloroethane is produced by hydrochlorination of ethylene: C₂H₄ + HCl → C₂H₅Cl.
• Earlier chloroethane has been produced from ethanol and hydrochloric acid, from ethane and chlorine, or from ethanol and phosphorus trichloride, but these methods are no longer economical

Additional Information

• The chemical formula of 3-Chlorohexane is C6H13Cl.
• n-Propyl chloride (also 1-propyl chloride or 1-chloropropane) is a colorless, flammable chemical compound. It has the chemical formula C₃H₇Cl.
• Chloromethane, also called methyl chloride, Refrigerant-40, R-40 or HCC 40, is an organic compound with the chemical formula CH₃Cl.

The logical order of the money denominations in ascending order is as follows:

Ten - Hundred – Thousand – Million – Billion – Trillion

10 - 100 – 1,000 – 1,000,000 – 1,000,000,000 – 1,000,000,000,000

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

Shortcut Trick

When the distance travelled is the same for two different speeds, the average speed is given by the direct formula: (2 × x × y) ÷ (x + y)

Here, the onward speed x = 78 km/hr and return speed y = 91 km/hr.

Average speed = (2 × 78 × 91) ÷ (78 + 91)

Average speed = 14196 ÷ 169

Average speed = 84 km/hr.

∴ The correct answer is 84 km/hr.

Alternate Method

Given:

Speed from Kolkata to Ahmedabad (v₁) = 78 km/hr

Speed from Ahmedabad to Kolkata (v₂) = 91 km/hr

Let the one-way distance between Kolkata and Ahmedabad be d km.

Kolkata

Ahmedabad

Distance = d

Speed 1 = 78 km/hr

Speed 2 = 91 km/hr

Formula Used:

Average Speed = Total Distance ÷ Total Time

Time = Distance ÷ Speed

Calculations:

⇒ Total Distance for the round trip = d + d = 2d

⇒ Total Time taken = (Time taken for onward journey) + (Time taken for return journey)

⇒ Total Time = (d ÷ 78) + (d ÷ 91)

⇒ Taking the LCM of 78 and 91, which is 546.

⇒ Total Time = (7d + 6d) ÷ 546

⇒ Total Time = 13d ÷ 546 = d ÷ 42 hours

⇒ Average Speed = 2d ÷ (d ÷ 42)

⇒ Average Speed = 2 × 42 = 84 km/hr.

∴ The correct answer is 84 km/hr.

Additional Information

Average Speed for Three Equal Distances

If a journey involves covering 3 equal distances at speeds x, y, and z respectively, the average speed is (3 × x × y × z) ÷ (xy + yz + zx).

Relative Speed in the Same Direction

When two objects move in the same direction at speeds v₁ and v₂ (where v₁ > v₂), their relative speed is the difference of their speeds: (v₁ − v₂).

Relative Speed in Opposite Directions

When two objects move towards each other at speeds v₁ and v₂, their relative speed is the sum of their individual speeds: (v₁ + v₂).

The correct answer is Jharkhand.

Key Points

• The Tusu festival is primarily observed in Assam, the Tea-producing State, Northeastern Odisha, Southwest West Bengal, and Southeast Jharkhand.
• During this occasion, the goddess Tusu is worshipped. The focus is primarily on rivers. It is a unified expression of the agrarian society's shared trust and belief in the pleasure of crop gathering.
• It is thought that the term "Tusu" derives from the word "tush" for rice bran. Both a youthful child and a cosmic deity are representations of the Goddess Tusu.
• The ceremonies carried out during the Tusu Puja center on harvest-related ceremonies and songs of ethnic dedication chanted by women folk.
• Therefore, the Tusu festival is associated with Jharkhand.

Additional Information

State-Specific Festivals of India

The correct answer is pyruvate.

• One molecule of glucose is converted into two molecules of pyruvate, two hydrogen ions, and two molecules of water. Through this process, the high energy molecules of ATP and NADH are synthesized.
• The overall process is called Glycolysis.
• Glycolysis can be considered as a two-part process. Firstly, energy is consumed to generate high energy intermediates, which then go on to release their energy during the second phase:
• The energy investment phase – requires two ADP molecules to produce high energy intermediates.
• The energy pay-out phase – The intermediate is metabolized, producing four ATP molecules and two NADH molecules.
• The overall reaction of glycolysis which occurs in the cytoplasm is represented simply as:
• C₆H₁₂O₆ + 2 NAD⁺ + 2 ADP + 2 P → 2 (CH₃(C=O)COOH)+ 2 ATP + 2 NADH + 2 H⁺ ; where
• C6H12O6 = Glucose
• NAD = Nicotinamide Adenine Dinucleotide
• ADP = Adenosine Diphosphate
• Pyruvic acid = CH₃(C=O)COOH
• ATP = Adenosine Triphosphate
• NADH = Nicotinamide Adenine Dinucleotide Hydride

The correct Venn diagram representation is :

⇒As all graduates are educated and some graduates are unemployed. Therefore all graduates should come in educated and some part of graduates should be common with unemployed.

⇒Some educated are also unemployed, therefore some educated can be unemployed.

Hence, "Option - (2)" is the correct answer

Shortcut Trick

The required smallest number must be perfectly divisible by all given numbers, including 11.

Applying the divisibility rule of 11 (the difference between the sum of alternate digits must be 0 or a multiple of 11):

Only Option 4 (1144) satisfies this condition: (1 + 4) − (1 + 4) = 5 − 5 = 0.

Options 1, 2, and 3 give differences of 7, −2, and −4 respectively, none of which are divisible by 11.

∴ The correct answer is 1144.

Alternate Method

Given:

The set of numbers: 26, 8, 11, and 13.

Concept Used:

The smallest natural number exactly divisible by a given set of numbers is their Least Common Multiple (LCM).

Calculations:

⇒ First, find the prime factorization of each number:

⇒ 26 = 2 × 13

⇒ 8 = 2³

⇒ 11 = 11

⇒ 13 = 13

⇒ The LCM is the product of the highest power of each prime factor present.

⇒ LCM = 2³ × 11 × 13

⇒ LCM = 8 × 11 × 13

⇒ LCM = 88 × 13

⇒ LCM = 1144

∴ The correct answer is 1144.

Additional Information

Least Common Multiple (LCM)

The smallest non-zero common multiple of two or more numbers. It is obtained by multiplying the highest powers of all prime factors involved in the given numbers.

Highest Common Factor (HCF)

The largest positive integer that divides two or more numbers without leaving a remainder. It uses the lowest powers of common prime factors.

Relation between LCM and HCF

For any two numbers 'a' and 'b', the product of the numbers is strictly equal to the product of their HCF and LCM: a × b = HCF(a, b) × LCM(a, b).

Important Points

• There are six fundamental rights provided in the Constitution of India.
• Part III and Article 12 – 35 deal with fundamental rights in the Constitution of India.
• Right to equality - Articles 14-18
• Right to freedom - Articles 19-22
• Right against exploitation - Articles 23-24
• Right to freedom of religion - Articles 25-28
• Cultural and educational rights - Articles 29-30
• Right to constitutional remedies - Article 32 and 226

Key Points

Right to Equality finds its mention under Article 14 to 18 of the Constitution.

• Article 14 refers to equality before the law.
• Article 15 refers to the prohibition of discrimination on grounds of religion, caste, race, sex or place of birth.
• Article 16 refers to equal opportunities in public employment.
• Article 17 refers to the abolition of Untouchability.
• Article 18 refers to the abolition of titles.

Hence, ‘Abolition of untouchability’ is included in the Right to equality.

The correct answer is calcium carbonate.

Key Points

• Whitewashed walls appear to be shiny after three to four days due to the formation of calcium carbonate.
• The whitewash contains calcium hydroxide. It forms a thin layer of calcium carbonate on the walls by slowly reacting with carbon dioxide in the air.
• After three to four days of whitewashing, calcium carbonate is created.
• As a result, after three to four days, the walls have a shiny white finish.
• Ca(OH)_2(aq) + CO_2(g) → CaCO_3(s) + H₂O_(l)

Important Points

• The chemical compound calcium carbonate has the formula CaCO₃. It is the major component of eggshells, gastropod shells, shellfish skeletons, and pearls and is found in rocks such as the minerals calcite and aragonite.
• Calcium nitrate, is an inorganic chemical with the formula Ca(NO₃)_2x.
• Calcium sulphate and its hydrates are inorganic compounds with the formula CaSO₄.
• Calcium oxide, often known as lime or more particularly quicklime, is a white or greyish white solid made by burning calcium carbonate to remove carbon dioxide.

Numbers that are not divisible by 2 are odd numbers.

Given sequence of numbers is :

5 1 4 7 3 9 8 5 7 2 6 3 1 5 8 6 3 8 5 2 2 4 3 4 9 6 

(5,1) (7,3) (3,9) (5,7) (3,1) (1,5)

Hence, 6 is the correct answer.

Shortcut Trick

Let the given numbers be a and b.

The mean proportional between two numbers a and b is given by the formula √(a × b).

Mean proportional = √(2.8 × 0.7)

Mean proportional = √(1.96) = 1.4

∴ The correct answer is 1.4.

Alternate Method

Given:

The two numbers are 2.8 and 0.7.

Formula Used:

If x is the mean proportional between two numbers a and b, they form a continuous proportion such that a : x :: x : b.

x × x

2.8

:

x

::

x

:

0.7

2.8 × 0.7

Product of Means = Product of Extremes

Calculations:

⇒ Let the mean proportional be x.

⇒ 2.8 : x = x : 0.7

⇒ x × x = 2.8 × 0.7

⇒ x² = 1.96

⇒ x = √(1.96)

⇒ x = 1.4

∴ The correct answer is 1.4.

Additional Information

Third Proportional

If a : b :: b : c, then c is called the third proportional. It is calculated directly as c = b² ÷ a.

Fourth Proportional

If a : b :: c : d, then d is called the fourth proportional. It is calculated as d = (b × c) ÷ a.

Compound Ratio

The ratio of the product of antecedents to the product of consequents of two or more ratios is called the compound ratio. For a : b and c : d, it is (a × c) : (b × d).

The correct answer is Anginda.

Key Points

• Anamudi Peak is located on the border of Kothamangalam Taluka in the Ernakulam district and Devikulam Taluk of Idukki district of Kerala in India.
• It is the highest peak in the Western Ghats and South India at an altitude of 2,695 meters and a topographic prominence of 2,479 meters.
• The mountain derives its name from the Malayalam word Anamudi which means Elephant's head in the English language.
• It is the largest mountain in Kerala and it is also the highest mountain in peninsular India.
• It is also called "Everest of South India".
• Anginda Peak is the highest peak in Silent Valley National Park, Palakkad.
• It is a mountain in the Nilgiri Hills of the Western Ghats on the border of the Nilgiris District of Tamil Nadu and Palakkad district of Kerala.
• It has a height of 2,383 meters.
• The tributary of Bharathappuzha i.e River kunthipuzha arises from this peak.
• Devimala Peak is situated in the Anamalai Hills of Kerala and it is the highest peak in the Devikulam hill station.
• It is one of the fourteen highest peaks of the Western Ghats in Devikulam taluka of Idukki district.
• Perumal Peak is located in the Kodaikanal district of Tamilnadu and It is also known as the Perumal Malai Peak. 
• It has an elevation of a total of 2,440 meters​.

Image of Anginda Peak:

CONCEPT:

Substitution Reaction

• A substitution reaction is a chemical reaction during which one functional group in a chemical compound is replaced by another functional group.
• In organic chemistry, substitution reactions are common and are categorized as nucleophilic, electrophilic, or radical substitutions depending on the nature of the substituting species.

EXPLANATION:

• In the chlorination of methane:

CH₄ + Cl₂ → CH₃Cl + HCl

• Methane (CH₄) reacts with chlorine (Cl₂).
• One hydrogen atom in methane is replaced by a chlorine atom, forming chloromethane (CH₃Cl) and hydrochloric acid (HCl).
• This reaction involves the substitution of a hydrogen atom in methane with a chlorine atom, making it a substitution reaction.

Therefore, the chlorination of methane is an example of a substitution reaction.

Given equation : 40 × 5 - 30 + 24 ÷ 6 = 181

Going with the options we check the values

option 1) 5 and 6

40 × 6 - 30 + 24 ÷ 5

= 40 × 6 - 30 + 4.8

= 240 - 30 + 4.8

= 244.8 - 30

= 214.8

option 2 ) 40 and 30

30 × 5 - 40 + 24 ÷ 6

= 30 × 5 - 40 + 4

= 150 - 40 + 4

= 154 - 40

= 114

option 3) 30 and 24

40 × 5 - 24 + 30 ÷ 6

= 40 × 5 - 24 + 5

= 200 - 24 + 5

= 205 - 24

= 181

option 4) 24 and 6

40 × 5 - 30 + 6 ÷ 24

=40 × 5 - 30 + 0.25

= 200 - 30 + 0.25

= 200.25 - 30

= 170.25

Hence, the answer is 30 and 24.

Shortcut Trick

Total interest percentage for 4 years at 8% per annum = 8% × 4 = 32%.

This means 32% of the principal amount equals ₹824.

⇒ 1% of Principal = 824 ÷ 32 = ₹25.75

⇒ 100% of Principal = 25.75 × 100 = ₹2575

∴ The correct answer is ₹2575.

Alternate Method

Given:

Simple Interest (SI) = ₹824

Time (T) = 4 years

Rate of Interest (R) = 8% per annum

Formula Used:

SI = (P × R × T) ÷ 100

Where P is the Principal amount.

Principal (P) = 100%

SI = ₹824
Rate = 8% × 4 = 32%

32% of P = ₹824

Calculations:

⇒ 824 = (P × 8 × 4) ÷ 100

⇒ 824 = (P × 32) ÷ 100

⇒ P = (824 × 100) ÷ 32

⇒ P = 82400 ÷ 32

⇒ P = 2575

∴ The correct answer is ₹2575.

Additional Information

Amount Formula

The total amount (A) after a certain period is the sum of the Principal (P) and Simple Interest (SI): A = P + SI = P × (1 + RT/100).

Effective Interest Rate

In simple interest, the effective rate for multiple years is directly proportional to time. For 't' years at 'r'% rate, the total interest is (r × t)% of the principal amount.

Difference Between SI and CI

Simple Interest is calculated only on the initial principal sum, whereas Compound Interest is calculated on the principal plus any accumulated interest from previous periods.

• Rani Laxmibai dam is on Betwa River.

Other important Dams of UP:

The correct answer is Calcium hydrogen carbonate

Key Points

• Calcium hydrogen carbonate
• ​Ca(HCO3)2 is the chemical formula for calcium bicarbonate, often known as calcium hydrogencarbonate.
• It only exists in aqueous solutions containing calcium (Ca2+), bicarbonate ions, and dissolved carbon dioxide; the word does not refer to a known solid substance (CO2).
• The pH affects the relative quantities of these carbon-containing species, with bicarbonate predominating in fresh water between 6.36 and 10.25.

Additional Information

• The majority of natural waters that are drawn from streams, lakes, and especially wells can be thought of as diluted solutions of these bicarbonates because all waters that come into contact with the atmosphere absorb carbon dioxide.
• As these waters interact with rocks and sediments they pick up metal ions, most frequently calcium and magnesium.
• These hard fluids often result in carbonate scale building up in boilers and pipes, and when they interact with soap, they create an unfavourable scum.

The pattern followed in the given set is:

            The difference between the terms is 11.

Now we compare each option with the pattern:

Option 1) (161, 172, 195)

The pattern does not match.

Option 2) (119, 130, 141)

The pattern matches completely.

Option 3) (149, 160, 193)

The pattern does not match.

Option 4) (127, 149, 160)

The pattern does not match.

Hence the correct answer is option 2)

Shortcut Trick

Using the unitary method to find the 100% value directly:

2% of x = 348

1% of x = 348 ÷ 2 = 174

100% of x = 174 × 100 = 17400

∴ The correct answer is x = 17400.

Alternate Method

Given:

2% of x = 348

Formula Used:

p% of a number = (p ÷ 100) × number

2%
348

100% (Total)
x = ?

Calculations:

⇒ (2 ÷ 100) × x = 348

⇒ 2 × x = 348 × 100

⇒ 2x = 34800

⇒ x = 34800 ÷ 2

⇒ x = 17400

∴ The correct answer is x = 17400.

Additional Information

Percentage Basics

A percentage represents a part out of 100. To find p% of a number, use: Value = (p ÷ 100) × Base.

Percentage to Fraction

To convert a percentage to a fraction, divide the number by 100. Example: 2% = 2 ÷ 100 = 1 ÷ 50.

Finding the Base Value

If p% of an unknown number is equal to A, the total number (100%) can be found using: Total = (A × 100) ÷ p.

correct answer is Polythene bag.

 Key Points

• ​Biodegradable waste is a type of waste, typically originating from plant or animal sources, which may be degraded by other living organisms. Wastes that cannot be broken by other living organisms are called non-biodegradable.​
• Biodegradable waste can be commonly found in municipal solid waste (sometimes called biodegradable municipal waste, or BMW) as green waste, food waste, paper waste and biodegradable plastic.

Additional Information

• Biodegradable wastes are such waste materials which are and can be degraded by natural factors like microbes (e.g. bacteria, fungi and a few more), and abiotic elements like temperature, UV, oxygen.
• A Non-Biodegradable material can be defined as a kind of substance which cannot be broken down by natural organisms and acts as a source of pollution.
• They remain on earth for thousands of years without any degradation. Hence, the threat caused by them is also more critical.
• A notable example is plastics which are a commonly used material in almost every field. To give these plastics a long-lasting effect, improved quality plastics are being put to use.
• Other examples are cans, metals, and chemicals for agricultural and industrial purposes. They are the main causes of air, water and soil pollution and diseases like cancer.

The correct answer is Group-16.

 Key Points

• Chalcogens are a group of non-metal elements that have similar chemical properties.
• The word chalcogen comes from the Greek word "chalcos" which means copper.
• Group-2 elements are called alkaline earth metals.
• Group-17 elements are called halogens.
• Group-18 elements are called noble gases.

Additional Information 

• Chalcogens are located in Group-16 of the periodic table.
• They include oxygen, sulfur, selenium, tellurium, and polonium.
• Chalcogens are known for their ability to form compounds with metals and nonmetals.
• They are important elements in biological systems and have numerous industrial applications.

The pattern followed is:

Similarly,

Hence, “XSZOP” is the correct answer.

Shortcut Trick

Overall average of the 3 persons = 45 kg.

Total deviation of Mandar and Ketan from the overall average = (43 − 45) × 2 = −4 kg

Total deviation of Ketan and Tushar from the overall average = (48 − 45) × 2 = +6 kg

When two groups overlap exactly at one person, the overlapping value is given by:

Weight of Ketan = Overall Average + Net Total Deviation

⇒ Weight of Ketan = 45 − 4 + 6 = 47 kg

∴ The correct answer is 47 kg.

Alternate Method

Given:

Average weight of Mandar (M), Ketan (K), and Tushar (T) = 45 kg

Average weight of Mandar and Ketan = 43 kg

Average weight of Ketan and Tushar = 48 kg

Total Weight (M + K + T) = 135 kg

M + K = 86 kg

M
K
T

K + T = 96 kg

Overlap (K) = (86 + 96) − 135 = 47 kg

Calculations:

⇒ Total weight of M, K, and T = 45 × 3 = 135 kg  ... (Equation 1)

⇒ Total weight of M and K = 43 × 2 = 86 kg  ... (Equation 2)

⇒ Total weight of K and T = 48 × 2 = 96 kg  ... (Equation 3)

Adding Equation 2 and Equation 3 together gives the total weight of the sub-groups where Ketan's weight is counted twice:

⇒ (M + K) + (K + T) = 86 + 96

⇒ M + 2K + T = 182 kg

Subtracting the sum of all three members (Equation 1) from this total overlap gives Ketan's weight:

⇒ (M + 2K + T) − (M + K + T) = 182 − 135

⇒ K = 47 kg

∴ The correct answer is 47 kg.

Additional Information

Average Formula

Average = Sum of all observations ÷ Total number of observations.

Net Deviation Method

When analyzing overlapping subgroups within a common average, the exact value of the overlapping entity is equivalent to the Overall Average + Net total deviations of the overlapping groups.

Combined Average

When two separate groups containing sizes n₁ and n₂ have respective averages A₁ and A₂, the final combined average is calculated as (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

The correct answer is Central Highlands.

Key Points

• The Central Highlands lie to the north of the Narmada River and form the northern segment of the Peninsular Plateau in India.
• The region primarily consists of the Malwa Plateau, which is characterized by black soil and is rich in minerals.
• The Central Highlands are bounded by the Vindhya Range in the south and the Aravalli Hills in the northwest.
• These highlands slope eastward, leading to the drainage of rivers such as Chambal, Betwa, and Ken towards the Yamuna River.
• The Central Highlands are significant for agriculture, particularly the cultivation of wheat, soybeans, and pulses, due to the fertile soil and favorable climate.

Additional Information

• Peninsular Plateau:
• The Peninsular Plateau is a triangular landmass that forms the southern part of India.
• It is divided into two major regions: the Central Highlands (north of the Narmada River) and the Deccan Plateau (south of the Narmada River).
• The plateau is known for its stable geological structure and rich mineral resources.
• Malwa Plateau:
• The Malwa Plateau is a part of the Central Highlands and is known for its black soil, which is ideal for cotton cultivation.
• It is bounded by the Vindhya Range to the south and the Aravalli Hills to the northwest.
• Vindhya Range:
• The Vindhya Range acts as a natural boundary separating the Central Highlands from the Deccan Plateau.
• It is a prominent range running across central India and plays a crucial role in drainage patterns.
• Drainage System:
• The Central Highlands are drained by rivers such as Chambal, Betwa, and Ken, which flow towards the Yamuna River.
• These rivers contribute to the agricultural economy of the region by providing irrigation facilities.

The correct answer is Ignition temperature.

Key Points

• The ignition temperature:
• It is the least temperature of a substance at which the substance starts combustion.
• Substances that spontaneously ignite in a normal atmosphere at naturally ambient temperatures are termed pyrophoric.
• The autoignition temperature is also known as the kindling point.
• The kindling point of a substance is the lowest temperature in which it spontaneously ignites in a normal atmosphere without an external source of ignition, such as a flame or spark.

Additional Information

• Melting point
• The melting point is the temperature at which a substance changes its state from solid into liquid.
• For ice, the temperature in degree Celcius is 0 and in kelvin, it is 273.
• ​Boiling point
• The temperature at which the pressure exerted by the surroundings upon a liquid is equalled by the pressure exerted by the vapour of the liquid.
• Under this condition, the addition of heat results in the transformation of the liquid into its vapour without raising the temperature.
• The boiling point of water at normal pressure is 100°C.
• Normal temperature
• The normal temperature of the human body is 37 °C. A temperature above 100.4 °F(38°C) most often means you have a fever caused by an infection or illness.
• Normal human body temperature is the prototypical temperature range found in humans.
• The normal human body temperature border is typically stated as 36.5-37°C (97.7-98.6 °F)
• Human body temperature changes, it depends on gender, age, time of day, exertion level, health status, what part of the body the measurement is taken at, state of consciousness (waking, sleeping, sedated), and emotions.

Given: Five friends — Maha, Renu, Banu, Suji and Thanu travel to five different cities — 'P', 'Q', 'R', 'S' and 'T' by five different modes of transport —bus, train, aero plane, car and boat.

1) Banu travels to 'S' by car, and Renu travels to 'Q' by aero plane.

2) Suji travels by boat whereas Thanu travels by train.

As only one position is left in transport, therefore will be occupied by the mode of transport left i.e. Bus.

3) The person who travels to 'R', and 'P' does not travel by bus.

4) The person who travels to 'R' does not travel by boat.

As the person who travels to 'R' does not travel by neither bus nor boat, therefore will travel by only mode of transport left i.e. train.

As person who travels to 'P' does not travel by bus, therefore will travel by only mode of transport left i.e. boat.

As only one position for city is left, thus will be occupied by the only city left i.e. T.

Thus, according to the final arrangement Banu travels to the city 'S'.

Hence, "Option 1" is the correct answer.

Shortcut Trick

Let the Cost Price (CP) of the fan be 100%.

Since the profit is 32%, the Selling Price (SP) = 100% + 32% = 132%.

132% of CP = 7392

1% of CP = 7392 ÷ 132 = 56

100% of CP = 56 × 100 = 5600

∴ The correct answer is ₹5,600.

Alternate Method

Given:

Selling Price (SP) of the fan = ₹7,392

Profit Percentage = 32%

Formula Used:

CP = [100 ÷ (100 + Profit%)] × SP

CP = ?

SP = ₹7392

+32% Profit

132% of CP = SP

Calculations:

⇒ CP = [100 ÷ (100 + 32)] × 7392

⇒ CP = (100 ÷ 132) × 7392

⇒ CP = 100 × 56

⇒ CP = 5600

∴ The correct answer is ₹5,600.

Additional Information

Loss Percentage

When a product is sold at a loss, the Cost Price can be calculated using the formula: CP = [100 ÷ (100 − Loss%)] × SP.

Marked Price & Discount

Discount is always calculated on the Marked Price (MP). The relation between Cost Price, Marked Price, Profit% and Discount% is direct: CP × (100 + Profit%) = MP × (100 − Discount%).

Dishonest Dealer

If a seller sells goods at cost price but uses false weights, the profit percentage is calculated as: Profit% = [Error ÷ (True Value − Error)] × 100.

The correct answer is ₹125 crore.

In News

• The Union Budget 2025-26 has revised the MSME classification criteria, increasing both investment and turnover limits.

Key Points

• The investment limit for MSME classification has been increased by 2.5 times, and turnover limits have been doubled.
• New MSME classification as per investment and turnover limits:
• Micro Enterprises: Investment limit increased from ₹1 crore to ₹2.5 crore; turnover from ₹5 crore to ₹10 crore.
• Small Enterprises: Investment limit increased from ₹10 crore to ₹25 crore; turnover from ₹50 crore to ₹100 crore.
• Medium Enterprises: Investment limit increased from ₹50 crore to ₹125 crore; turnover from ₹250 crore to ₹500 crore.
• This revision aims to encourage MSMEs to expand, create jobs, and boost economic growth.

Additional Information

• Union Budget
• A budget is an elaborate statement of the expenditure and income of the government for the given financial year, which begins on April 1 and ends on March 31.
• The Constitution uses the term Annual Financial Statement instead of "Budget," as enshrined under Article 112 of the Constitution.
• MSMEs in India
• India has over 1 crore registered MSMEs, employing 7.5 crore people.
• MSMEs contribute 45% to India's exports and 36% to the manufacturing sector.
• Credit Support for MSMEs
• The credit guarantee cover for MSMEs has been enhanced, increasing loan limits for small enterprises from ₹5 crore to ₹10 crore.
• For startups, the loan limit has been raised from ₹10 crore to ₹20 crore, with a reduced guarantee fee of 1% for loans in 27 focus sectors.

The correct answer is Smelting.

Key Points

• Smelting is a process in which metals are extracted from their ores by heating beyond their melting point. During this process, the metal is separated from its impurities and a pure form of metal is obtained.
• Smelting is commonly used for extracting metals such as iron, copper, lead, and zinc from their ores. It is an important process in the metallurgical industry.
• Spinning is a process of twisting fibers together to make yarn or thread. It is not related to the extraction of metals from their ores.
• Heaving is not a process used in the extraction of metals from their ores. It is a term used to describe the upward movement of soil or rocks due to frost or ice.
• Extracting is a general term used for any process of separating a substance from its mixture or compound. It can refer to the extraction of metals, oil, or any other substance.

Additional Information

• Smelting is a highly energy-intensive process and requires a high temperature to melt the metal. The process can produce a lot of air pollution and greenhouse gases.
• Spinning is a process commonly used in the textile industry to make fabrics and clothing. It involves twisting fibers together to create a yarn or thread, which is then woven into fabric.
• Heaving is a geological process that occurs due to the expansion of soil or rocks when they freeze. The expansion can cause the soil or rocks to move upward, which can lead to landslides or other geological hazards.
• Extracting can refer to the extraction of any substance from its mixture or compound. For example, oil can be extracted from the ground using drilling and pumping techniques.

Hence, the answer is option 2.

Shortcut Trick

Total work = LCM of days taken by 1 man, 1 woman, and 1 boy = LCM(20, 30, 50) = 300 units.

Efficiency: 1 Man = 15, 1 Woman = 10, 1 Boy = 6.

Day 1 Work (2 Men + 6 Women) = 2 × 15 + 6 × 10 = 90 units.

Day 2 Work (5 Boys + 6 Women) = 5 × 6 + 6 × 10 = 90 units.

Since exactly 90 units of work are completed every single day, Total days = 300 ÷ 90 = 10/3 = 3 1/3 days.

∴ The correct answer is 3 1/3 days.

Alternate Method

Given:

20 men can finish in 1 day ⇒ 1 man finishes in 20 days.

30 women can finish in 1 day ⇒ 1 woman finishes in 30 days.

50 boys can finish in 1 day ⇒ 1 boy finishes in 50 days.

Formula Used:

Total Work = Efficiency × Time taken

Calculations:

⇒ Work done on Day 1 by 2 men and 6 women = 2 × 15 + 6 × 10 = 30 + 60 = 90 units.

⇒ Work done on Day 2 by 5 boys and 6 women = 5 × 6 + 6 × 10 = 30 + 60 = 90 units.

⇒ Work done in a complete 2-day cycle = 90 + 90 = 180 units.

⇒ Total work done in 3 days = 90 × 3 = 270 units.

⇒ Remaining work after 3 days = 300 − 270 = 30 units.

⇒ On Day 4, it is the turn of 5 boys and 6 women. Their combined efficiency is 90 units/day.

⇒ Time taken to complete the remaining work = 30 ÷ 90 = 1/3 day.

⇒ Total time taken to finish the work = 3 + 1/3 = 3 1/3 days.

∴ The correct answer is 3 1/3 days.

Additional Information

Total Work using LCM Method

Total work is assumed to be the LCM of the days taken by individuals to avoid fractional calculations. Efficiency = Total Work ÷ Time taken.

Alternate Day Work Concept

When individuals work on alternate days, calculate the total work done in one complete cycle (e.g., 2 days) and use it to find the number of full cycles required, then calculate the time needed for the remaining work.

The correct answer is Maharashtra.

• The ‘Lezim’ dance form is peculiar to Maharashtra states.

Key Points

• Lezim is a group dance that is performed in formations of two or four in the villages of Maharashtra.
• Lezim performed in colorful costumes, the dance involves a dholki and all the dancers carry Lezim which an instrument with jingling cymbals.
• It is often played during the Ganesh festival.
• Other important dances of Maharashtra: Lavani, Nakata, Koli, Gafa, Dahikala.

Additional Information

The correct answer is iron.

Key Points

• Ferrum is the Latin term for iron and the source of its chemical symbol Fe.
• Iron is a chemical element with the symbol Fe and atomic number 26.
• It is a metal that belongs to the first transition series and group 8 of the periodic table.
• It is, by mass, the most common element on Earth, right in front of oxygen, forming much of Earth's outer and inner core.
• Atomic mass: 55.845 u.
• **Electron configuration: [Ar] 3d64s2.**​

Additional Information

• The Latin name for zinc is Zincum, which means "white thin layer" or "white sediments".
• The symbol 'Cu' denotes the Latin name of copper, which is Cuprum.
• Niccolum is the Latin name for a Nickel.

Pattern is as follow:

Hence, "18" is the correct answer

Shortcut Trick

The product of two numbers is always equal to the product of their LCM and HCF.

Second Number = (LCM × HCF) ÷ First Number

⇒ Second Number = (168 × 14) ÷ 42

⇒ Second Number = 168 ÷ 3 = 56

∴ The correct answer is 56.

Alternate Method

Given:

LCM of the two numbers = 168

HCF of the two numbers = 14

First number = 42

Formula Used:

First Number × Second Number = LCM × HCF

Calculation:

Let the second number be x.

⇒ 42 × x = 168 × 14

⇒ x = (168 × 14) ÷ 42

⇒ x = 168 × (14 ÷ 42)

⇒ x = 168 × (1 ÷ 3)

⇒ x = 168 ÷ 3

⇒ x = 56

∴ The correct answer is 56.

Additional Information

LCM & HCF of Two Numbers

The product of any two given numbers is equal to the product of their LCM and HCF: a × b = LCM(a, b) × HCF(a, b). This rule applies strictly to exactly two numbers.

Co-prime Numbers

Two numbers are called co-prime if their HCF is 1. For any pair of co-prime numbers, their LCM is always equal to their product.

Fractions Rule

LCM of fractions = (LCM of numerators) ÷ (HCF of denominators). HCF of fractions = (HCF of numerators) ÷ (LCM of denominators).

The correct answer is Maharashtra.

• Khetial village is located on the border of Maharashtra and Madhya Pradesh.
• It is located in the Nandurbar district.

Key Points

• Nandurbar district was formed in 1998 by partitioning the Dhule district.
• Nandurbar district has two border boundaries. Gujarat is on the northwestern border of the state, while on the northeast border of the state of Madhya Pradesh.
• Khetia village is located in the Barwani district of Madhya Pradesh.

When marble chips are treated with HCL, carbon dioxide is liberated since marble contains calcium carbonate, which when reacts with hydrochloric acid, gives off CO₂.

CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂

The logic followed here is:-

• Import is the antonym of export.
• Similarly, expenditure is the antonym of revenue.

Hence, "option 3" is the correct answer.

Given:

Find the value of \(\left[(50 \div 5) \times\left\{\frac{72}{3}+\frac{12}{1} \times(8-7)\right\}\right]\)

Formula used:

Use BODMAS rule for calculation

Calculations:

[(50 ÷ 5) × {(72)/(3) + (12)/(1) × (8 - 7)}]

⇒ [(50 ÷ 5) × {24 + 12 × 1}]

⇒ [10 × {24 + 12}]

⇒ [10 × 36]

⇒ 360

∴ The correct answer is option 2.

The correct answer is Dhuppgarh Peak

Key Points

• Dhuppgarh Peak is the highest point in Madhya Pradesh.
• It is located in the Satpura Range in the Pachmarhi region.
• The peak stands at an elevation of approximately 1,352 meters (4,429 feet) above sea level.
• Dhuppgarh offers stunning views of the surrounding landscape and is a popular spot for trekking and nature enthusiasts.
• It is also known for its beautiful sunrises and sunsets, attracting tourists from all over the country.

Additional Information

• Madhya Pradesh is known for its rich cultural heritage and natural beauty.
• The Satpura Range is a series of hills that run through central India, forming a natural divide between the northern plains and the Deccan Plateau.
• Pachmarhi, where Dhuppgarh Peak is located, is often referred to as the "Queen of Satpura" and is the only hill station in Madhya Pradesh.
• The region is also home to several other attractions, including waterfalls, caves, and wildlife sanctuaries.
• Visitors to Dhuppgarh Peak can explore the surrounding Satpura National Park, which is known for its diverse flora and fauna.

The correct answer is Mercury.

Key Points

• Mercury is NOT an insulator.
• Insulators are material that does not conduct electricity.
• Examples - paper, plastic, rubber, glass, Ebonite, air, Styrofoam, etc.

Additional Information

• The Conductors are the material that conducts electricity.
• Examples - Metals, Aqueous solutions of salts ( ionic compounds dissolved in water),  Mercury, graphite.
• Please note that Mercury is a poor conductor of heat.
• Mercury forms weak bonds and is a liquid at room temperature.
• Atomic Number of Mercury-80,  Symbol-Hg

1. INTEGRAL → it can be formed.

2. GRUDGE → the letter U and D are not present in TRIANGLE, so it can’t be formed.

3. BANGLE → the letter B is not present in TRIANGLE, so it can’t be formed.

4. ALTERNATIVE → the letter V is not present in TRIANGLE, so it can’t be formed.

Hence, INTEGRAL can be formed from the letters used in TRIANGLE.

Shortcut Trick

The HCF must exactly divide the difference between any two given numbers: 153 − 117 = 36.

The factors of 36 are 36, 18, 12, 9, 6, 4, 3, 2, and 1.

Since 153, 117, and 405 are all odd numbers, their HCF cannot be an even number.

Eliminating the even factors of 36, the highest possible odd factor remaining is 9.

Checking divisibility, the sum of digits for all three numbers is 9, so they are perfectly divisible by 9.

∴ The correct answer is 9.

Alternate Method

Given:

The given numbers are 153, 117, and 405.

Method Used:

Prime factorisation method to find the Highest Common Factor (HCF).

Calculations:

⇒ 153 = 3 × 3 × 17 = 3² × 17

⇒ 117 = 3 × 3 × 13 = 3² × 13

⇒ 405 = 3 × 3 × 3 × 3 × 5 = 3⁴ × 5

⇒ The HCF is calculated as the product of the smallest powers of all common prime factors.

⇒ The only common prime factor among all three numbers is 3.

⇒ The smallest power of 3 present in the prime factorisations is 3².

⇒ HCF = 3² = 9

∴ The correct answer is 9.

Additional Information

Highest Common Factor (HCF)

It is the greatest number that divides two or more numbers completely without leaving any remainder. It is also known as Greatest Common Divisor (GCD).

Least Common Multiple (LCM)

It is the smallest common multiple of the given numbers. For any two numbers, Product of numbers = HCF × LCM.

HCF of Fractions

The HCF of given fractions can be calculated as (HCF of Numerators) ÷ (LCM of Denominators).

The correct answer is December 21.

Key Points

• The UN General Assembly declared December 21 as World Meditation Day.
• This decision was made through a resolution co-sponsored by multiple countries including India, Liechtenstein, Sri Lanka, Nepal, Mexico, and Andorra.
• The adoption of the resolution was a significant international acknowledgment of meditation's importance.
• The date, December 21, was specifically chosen for the observance of World Meditation Day.

Additional Information

• The UN General Assembly’s resolution to declare December 21 as World Meditation Day highlights the growing global recognition of meditation as an important practice for mental and physical well-being.
• The decision to officially observe the day on December 21 was driven by the collaborative efforts of several countries, with India playing a central role in promoting this cause.
• The date also holds significance, being the winter solstice in the Northern Hemisphere, symbolizing a time for inner reflection and peace.

The correct answer is blue, green.

Key Points

• When an iron nail is dipped into a solution of copper sulfate, the color of the solution changes due to a displacement reaction that occurs because iron is more reactive than copper.
• The blue colour of copper sulphate solution changes to green because of the formation of iron (II) sulfate.
• This is a type of single replacement reaction where iron replaces copper in the compound because iron is more reactive than copper.
• The equation for this reaction is:
• Fe(s) + CuSO4 (aq) -> FeSO4 (aq) + Cu(s)
• The green colour is due to the formation of FeSO4 or iron (II) sulfate in solution.

The correct answer is Option 4 : Work harder along with others to ensure the profit of the company.

• Qualities Projected in this situation:  (Effective Intelligence, Self-confidence, Sense of responsibility, Courage, Organizing ability and Speed of decision making).

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

Age of Teacher = New Average + (Old number of members × Increase in Average)

New Average = 38 years

Old number of members = 54 students

Increase in Average = 38 − 37 = 1 year

Age of Teacher = 38 + (54 × 1) = 38 + 54 = 92

∴ The correct answer is 92 years.

Alternate Method

Given:

Average age of 54 students = 37 years

Average age of whole group (54 students + 1 teacher = 55 members) = 38 years

Formula Used:

Sum of Ages = Average × Total Members

Average Age Distribution

54 Students (Avg: 37)

1 Teacher (Age: ?)

55 Members Combined (New Avg: 38)

Calculations:

⇒ Total age of 54 students = 54 × 37 = 1998 years

⇒ Total age of 55 members = 55 × 38 = 2090 years

⇒ Age of the teacher = Total age of 55 members − Total age of 54 students

⇒ Age of the teacher = 2090 − 1998 = 92 years

∴ The correct answer is 92 years.

Additional Information

Inclusion Principle

When a new entity is included in a group, its value can be directly found as: Value = New Average + (Old Count × Increase in Average).

Basic Average Formula

Average = Sum of all observations ÷ Total number of observations.

Weighted Average

Combined average of two groups with sizes n₁ and n₂ and averages A₁ and A₂ is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

The correct answer is Dharti Abba.

Key Points

• Birsa Munda Movement
• This movement was considered to be the most organized and widespread in Jharkhand.
• Birsa Munda, the protagonist of this movement was recognized as an incarnation of God and father of the World/Dharti Aba.
• Like other tribes, the Munda tribes were also dependent on agriculture and forests to preserve their traditions and beliefs.
• These tribes were one of the major tribes of the Chota Nagpur region and its people were as quite peaceful.
• The Munda people who fought lived otherwise peaceful life also from persecution and English plunder.
• One of the main reasons for the rebellion was influence of other culture on their culture.
• Some of the differences, which are found in every caste and tribe, also resided among the Munda people.

Given,

Statement:

Dengue has engulfed the majority of the population in Delhi in the year 2023 and there have been cases of deaths also.

Courses of Action:

I. Precautionary measures should be taken every year before the onset of diseases in the form of fogging and awareness campaigns - True (Because, taking preventive measures such as fogging and awareness campaigns can help in controlling the spread of dengue and reducing its impact on the population).

II. Medical facilities also need to be upgraded as the diseases are changing their mutant variations and becoming more and more fatal - True (Because, upgrading medical facilities can help in better diagnosing and treating the evolving and more fatal variations of diseases like dengue).

So, Both I and II follow.

Hence, the correct answer is "Option 2".

Shortcut Trick

Product of two numbers = LCM × HCF

33 × Second Number = 66 × 11

Second Number = (66 × 11) ÷ 33

Second Number = 2 × 11 = 22

∴ The correct answer is 22.

Alternate Method

Given:

LCM of two numbers = 66

HCF of two numbers = 11

First Number = 33

Formula Used:

First Number × Second Number = LCM × HCF

Calculation:

Let the second number be x.

⇒ 33 × x = 66 × 11

⇒ x = (66 × 11) ÷ 33

⇒ x = 726 ÷ 33

⇒ x = 2 × 11

⇒ x = 22

∴ The correct answer is 22.

Additional Information

Product Rule of LCM and HCF

For any two numbers a and b, a × b = LCM(a, b) × HCF(a, b). This rule applies only to exactly two numbers, not three or more.

HCF and LCM of Fractions

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

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

Co-prime Numbers

Two numbers are considered co-prime if their HCF is 1. Their LCM will always be equal to the product of the two numbers.

The Correct Answer is ​Sal tree.

In News

• Adivasis in Jharkhand and the larger Chhotanagpur region will welcome the new year and the spring season with the Sarhul festival.

Key Points

• Sarhul means worship of the Sal tree and celebrates the union of the Sun and the Earth.
• It marks the beginning of agricultural activities for Adivasis in Jharkhand and the Chhotanagpur region.
• Sal trees (Shorea robusta) are venerated as the abode of Sarna Maa, the deity who protects villages from natural forces.
• The festival lasts 3 days, with main rituals on day two at Sarna Sthals (sacred groves near villages).
• Tribes like Oraon, Munda, Santal, Khadia, and Ho celebrate Sarhul with unique traditions.
• Sarhul evolved from a hunting tradition to a focus on agriculture.
• The festival has spread to regions like Assam, Andaman and Nicobar Islands, Nepal, Bangladesh, and Bhutan.

The logical and meaningful order of the given words is:

2. nano : 10^-9
3. milli : 10^-3 
4. centi : 10^-2
5. mega : 10⁶
6. giga : 10⁹

The order is the arrangement of unit is ascending order i.e. 2, 1, 3, 5, 4.

Hence the correct answer is option 3)

Shortcut Trick

If two persons together can do a work in x days and one of them alone can do it in y days, the time taken by the other alone is (x × y) ÷ (y − x).

Time taken by Mona alone = (18 × 27) ÷ (27 − 18)

Time = (18 × 27) ÷ 9

Time = 18 × 3 = 54 days

∴ The correct answer is 54 days.

Alternate Method

Given:

Time taken by Ritu and Mona together = 18 days

Time taken by Ritu alone = 27 days

Method Used:

We use the LCM method to find the total work and individual efficiencies. Total Work is considered as the LCM of the given days.

Calculations:

⇒ Efficiency of Mona = Efficiency of (Ritu + Mona) − Efficiency of Ritu

⇒ Efficiency of Mona = 3 − 2 = 1 unit/day

⇒ Time taken by Mona alone = Total Work ÷ Mona's Efficiency

⇒ Time taken by Mona alone = 54 ÷ 1 = 54 days.

∴ The correct answer is 54 days.

Additional Information

Work & Wages

Wages are distributed in direct proportion to the amount of total work completed by each individual, or their efficiency if they all work for the exact same number of days.

Pipes & Cisterns

Filling a tank is treated as positive work, while emptying a tank (a leak) is treated as negative work. The LCM method applies here seamlessly.

Alternate Day Work

Calculate the combined work done in a pair of consecutive days. Divide the total work by this combined sum to find the number of full cycles required to finish the total work.

Carbon dioxide (CO2) is known as the greenhouse gas.

Important Points

• Greenhouse gases are gases that trap heat in the Earth's atmosphere and contribute to the greenhouse effect, which is the warming of the Earth's surface.
• Carbon dioxide is the most well-known greenhouse gas and is considered the primary driver of climate change caused by human activities.
• Other greenhouse gases include methane (CH4), nitrous oxide (N2O), and fluorinated gases such as hydrofluorocarbons (HFCs), perfluorocarbons (PFCs), and sulfur hexafluoride (SF6).
• These gases are released into the atmosphere through human activities such as burning fossil fuels, deforestation, and agriculture.
• Greenhouse gases are important for maintaining the Earth's temperature, but when their concentration in the atmosphere increases.
• They can cause the Earth's surface to warm up, leading to climate change and its associated impacts such as rising sea levels, more frequent extreme weather events, and changes in ecosystems

The logic follows here is:

As Nashik is situated on the banks of Godavari river. 

Similarly,

Gorakhpur, city, eastern Uttar Pradesh state, northern India. It lies along the Rapti River, a tributary of the Ghaghara River.

Hence, the correct answer is "Gorakhpur". 

Additional Information

• Nashik is best known for being one of Hindu pilgrimage sites, that of Kumbh Mela which is held every 12 years.
• Godavari river is also known as Dakshin Ganga or Vridha Ganga.
• It is the largest peninsular river and second largest river of India.
• Principal tributary are Penganga, Indravati, Pranhita, Manjra, Wainganga, Wardha and Pravara.

Shortcut Trick

Difference in percentage = 50% − 25% = 25%

Difference in marks = 68 (failed by) + 42 (passed by) = 110 marks

25% of total marks = 110 marks

Total maximum marks = 110 × 4 = 440 marks

∴ The correct answer is 440 marks.

Alternate Method

Given:

Marks scored by Candidate 1 = 25%

Marks failed by Candidate 1 = 68 marks

Marks scored by Candidate 2 = 50%

Marks passed by Candidate 2 = 42 marks

25%
Passing Mark
50%

+68 Marks

+42 Marks

Gap: 50% − 25% = 25% → 110 Marks

Formula Used:

Passing Marks = (Score% of Max Marks) + Marks Failed By

Passing Marks = (Score% of Max Marks) − Marks Passed By

Calculations:

Let the maximum marks for the examination be x.

⇒ Passing marks according to Candidate 1 = 25% of x + 68

⇒ Passing marks according to Candidate 2 = 50% of x − 42

Since the passing marks remain the same, we can equate both expressions:

⇒ 25% of x + 68 = 50% of x − 42

⇒ 50% of x − 25% of x = 68 + 42

⇒ 25% of x = 110

⇒ x × (25 ÷ 100) = 110

⇒ x ÷ 4 = 110

⇒ x = 110 × 4

⇒ x = 440

∴ The correct answer is 440 marks.

Additional Information

Percentage Difference Rule

When one value is below the passing mark and another is above, the absolute difference in their percentages equals the sum of their individual mark deviations.

Finding the Pass Percentage

Once maximum marks (M) are calculated, the pass percentage can be directly found as: Pass % = (Passing Marks ÷ M) × 100.

Base Value Concept

In examinations, the maximum possible score acts as the base value (100%). Finding the equivalent value of 1% allows calculating any required value by simple multiplication.

The Correct Answer is Option 1 i.e Suryavarman II.

• Angkor Wat:
• It is a Buddhist temple complex located in Cambodia.
• It was built in the 12^th century by King Suryavarman II of the Khmer empire in Angkor Wat style dedicated to Hindu God Vishnu.
• Later it was gradually transformed into a Buddhist temple towards the end of the 12^th century.
• It is designated as a UNESCO World Heritage site.
• Jayasimha Vallabha (633-666 AD):
• He founded a town called Sarvasiddhi in Vishakapatnam, which became the seat of provincial governors of Yelamanchili and Kalinga provinces.
• It was built after his title "Sarvasiddhi".
• Bhima (892-921 AD):
• Drakshrama is located in the East Godavari district of Andhra Pradesh. 
• The temple was built by the Eastern Chalukyan King, Bhima (892-921 AD).
• It is one of the five Pancharama Kshetras of Lord Shiva.
• Allauddin Khilji (1296-1316):
• He adopted the policy of blood and iron.
• He was the first among the Delhi sultanate to lay the foundation of standing army which was based on the Turkish model.
• He introduced the system of branding of horses and also maintained a list of soldiers.
• He built the famous Hauz Khas near Siri village.

Option 2. Only inference II follows.

The statement suggests that people in the present day world have become more conscious about their health as a result of the emergence of chronic diseases and they find refuge in modern yoga.

From what is supplied we can deduce cannot deduce anything about the people in the old world. So inference I do not follows.

But, from what is given it can be inferred that modern yoga deals with exercises that focus more on health. Therefore, inference II follows.

Hence, Option 2 is correct.

Shortcut Trick

Let initial expenditure be 100.

If consumption is unchanged, the expenditure will become 160 (since price increased by 60%).

But the desired target expenditure is 112 (only 12% increase from 100).

Reduction needed in consumption = [(160 − 112) ÷ 160] × 100

⇒ (48 ÷ 160) × 100 = 30%

∴ The correct answer is 30%.

Alternate Method

Given:

Increase in price of petrol = 60%

Required increase in expenditure = 12%

Formula Used:

Expenditure = Price × Consumption

Initial Expenditure = 100160Expenditure if consumption is unchanged (+60%)112Target Expenditure (+12%)Decrease = 48

Calculations:

⇒ Let the initial price be ₹100 per litre and initial consumption be 100 litres.

⇒ Initial Expenditure = 100 × 100 = ₹10000

⇒ New Price = 100 + 60% of 100 = ₹160 per litre

⇒ New Expenditure = 10000 + 12% of 10000 = ₹11200

⇒ New Consumption = New Expenditure ÷ New Price

⇒ New Consumption = 11200 ÷ 160 = 70 litres

⇒ Reduction in Consumption = Initial Consumption − New Consumption

⇒ Reduction = 100 − 70 = 30 litres

⇒ Percentage Reduction = (Reduction ÷ Initial Consumption) × 100

⇒ Percentage Reduction = (30 ÷ 100) × 100 = 30%

∴ The correct answer is 30%.

Additional Information

Price and Consumption Rule

Since Expenditure = Price × Consumption, if Expenditure remains constant, an increase of r% in Price leads to a reduction of [r ÷ (100 + r)] × 100% in Consumption.

Successive Percentage Formula

The net percentage change for two successive changes of a% and b% is calculated as: a + b + (a × b) ÷ 100.

Percentage Change

Percentage change is always calculated on the initial base value: % Change = (Difference ÷ Original Base) × 100.

The correct answer is Playa.

Key Points

• Playa
• It is also called pan, flat, or dry lake, flat-bottom depression found in interior desert basins and adjacent to coasts within arid and semiarid regions, periodically covered by water that slowly filtrates into the groundwater system or evaporates into the atmosphere, causing the deposition of salt, sand, and mud along the bottom and around the edges of the depression.
• It is defined as the flat-floored bottom of an undrained desert basin that becomes at times a shallow lake.
• They are the most kind of flattest known landforms.
• It occupies the flat central basins of desert plains.
• They require a drainage system from the place where evaporation takes place.
• When it floods, a la playa lake forms where fine-grained sediment and salts concentrate. Hence, Option 1 is correct.
• It is the process of inundation that develops and maintains the near-perfect flatness so characteristic of these arid-region landforms.

Additional Information

• An oasis
• It is a place in a desert where water comes up to the surface from deep underground.
• Drumlins
• ​They are smooth oval-shaped ridge-like features composed mainly of glacial till with some masses of gravel and sand.
• Natural levees
• It is embankments formed naturally after a river floods and recedes.

Given: 

The logic followed here is:

1. The top left corner symbol comes in the center, in each figure. So, in answer figure 

 should be in the center ⇒ option (4) eliminates. 2. The symbol in the center of the top line moves to the left corner of the figure in each step. So, in answer figure 

 should be in the top left corner ⇒ option (3) eliminates. 3. The symbol in the center of the figure comes in the bottom left corner in each step. So, in the answer figure

 should be in the bottom left corner ⇒ option (1) eliminates.

Thus, the final series is as follows,

Hence, option (2) is the correct answer.

Given:

a + b + c = 0

Concept:

Algebraic Identity - 

a3 + b3 + c3 - 3abc = (a + b + c)(a² - b² - c² - ab - bc - ca)

Solution:

According to the question,

a + b + c = 0

Substituting the value a + b + c = 0 in a3 + b3 + c3 - 3abc = (a + b + c)(a2 - b2 - c2 - ab - bc - ca) we will get

a3 + b3 + c3 - 3abc = (0)(a2 - b2 - c2 - ab - bc - ca)

a3 + b3 + c3 - 3abc = 0

a3 + b3 + c3 = 3abc  

Hence, option 3 is correct.

The correct answer is the Persian Gulf and the Gulf of Oman.

Key Points

Strait of Hormuz:

• It separates Iran and Oman linking the Persian Gulf to the Gulf of Oman and the Arabian Sea.
• The Strait is 33 km wide at its narrowest point.
• The shipping lane is just three km wide in either direction.
• Most crude exported from OPEC countries is shipped through this waterway.

Additional Information

Strait of Bosporus:

• It connects the Black Sea with the Sea of Marmara.
• It forms part of the continental boundary between Europe and Asia.
• It divides Turkey by separating Anatolia from Thrace.

Strait of Gibraltar:

• It is a narrow strait that connects the Atlantic Ocean to the Mediterranean Sea.
• It separates the Iberian Peninsula in Europe from Morocco in Africa.

The pattern followed here is :

(1^st number + 3^rd number) × 3 = 2^nd number

• (12, 81,15) → (12 + 15) × 3 = 27 × 3 = 81

Similarly,

1. (11, 69, 12) → (11 + 12) × 3 = 23 × 3 = 69
2. (15, 93, 16) → (15 + 16) × 3 = 31 × 3 = 93
3. (13, 85, 17) → (13 + 17) × 3 = 30 × 3 = 90 ≠ 85 (Not similar)
4. (8, 63, 13) → (8 + 13) × 3 = 21 × 3 = 63

Thus Option 3 set is not similar to the given set.

Hence, The correct  answer is "option 3".

Given:

7a - 3b = 40 →(1)

7b + 3a = 42 →(2)

Calculation:

7a - 3b = 40 →(1) × 7

3a + 7b = 42 →(2) × 3

From Eqn (1) and (2), we get

49a - 21b = 280 →(3)

9a + 21b = 126 →(4)

Adding Eqn (3) and (4), we have

58a = 406

⇒ a = 7

Putting the value of 'a' in Eqn (1), we have

7 × 7 - 3b = 40 →(1) 

⇒ 49 - 3b = 40

⇒ 3b = 9

⇒ b = 3

Now, a - b = 7 - 3 = 4

∴ The answer is 4.