MP Police Constable : (26 Nov 2025, Shift 2) Memory-Based Paper (Previous Year Paper)

The correct answer is Radon.

• In the modern periodic table, group 18 belongs to noble gases.
• This group of a series of gases includes:
• Argon. Helium, Neon, Krypton, Xenon, and Radon.
• Radon is the only radioactive out of all and it's also not present in the Atmosphere.

Important Points

• Their outer shell of valence electrons is considered to be "full", giving them little tendency to participate in chemical reactions, so they are considered the most stable elements of the periodic table.
• Noble gases are also known as inert and rare gases.
• Neon, argon, krypton, and xenon are obtained from air in an air separation unit using the methods of liquefaction of gases and fractional distillation.
• Helium is sourced from natural gas fields that have high concentrations of helium in natural gas, using cryogenic gas separation techniques.
• Radon is usually isolated from the radioactive decay of dissolved radium, thorium, or uranium compounds.

Key Points

• Nobel gases are odourless, non-flammable, colourless, and monoatomic gas with low chemical reactivity.
• All noble gases are insoluble in water.
• Nobel gases conduct electricity and fluorescence which can be needed in many conditions to maintain a constant and safe environment.
• They have a complete octet that makes them very stable, so they hardly react with other elements. Xenon is the only noble gas that may form compounds either with fluoride or oxide.

Additional Information

• Noble gases have several important applications in industries such as lighting, welding, and space exploration.
• Helium-oxygen breathing gas is often used by deep-sea divers at depths of seawater over 55 m (180 ft).
• After the risks caused by the flammability of hydrogen became apparent, it was replaced with helium in blimps and balloons.

The correct answer is Suspension.

Key Points

• All solutions will be considered homogeneous because the dissolved material is present in equal amounts throughout the solution.
• A characteristic of mixtures is that they can be separated into their components.
• A suspension is a heterogeneous mixture in which solid particles settle to the bottom without settling.

Additional Information

• A homogeneous mixture is a mixture in which the composition is uniform throughout the mixture. Examples of Homogeneous mixtures are - Blood, milk, brass, steel, Vinegar, Wine, etc.
• A heterogeneous mixture has components whose proportions vary throughout the sample or is simply and mixture that is not uniform in composition.

Given equation: 96 ÷ 6 - 16 + 12 × 8 = 40.

BODMAS Table: 

Let's check each option one by one.

Option 1) 6 and 16

Given: 96 ÷ 6 - 16 + 12 × 8 = 40

After interchanging the numbers we get;

⇒ 96 ÷ 16 - 6 + 12 × 8 = 40

⇒ 6 - 6 + 12 × 8 = 40

⇒ 6 - 6 + 96 = 40

⇒ 102 - 6 = 40

⇒ 96 ≠ 40

⇒ LHS ≠ RHS

Option 2) 96 and 16

Given: 96 ÷ 6 - 16 + 12 × 8 = 40

After interchanging the numbers we get;

⇒ 16 ÷ 6 - 96 + 12 × 8 = 40

⇒ 2.66 - 96 + 12 × 8 = 40

⇒ 2.66 - 96 + 96 = 40

⇒ 2.66 ≠ 40

⇒ LHS ≠ RHS

Option 3) 6 and 8

Given: 96 ÷ 6 - 16 + 12 × 8 = 40

After interchanging the numbers we get;

⇒ 96 ÷ 8 - 16 + 12 × 6 = 40

⇒ 12 - 16 + 12 × 6 = 40

⇒ 12 - 16 + 72 = 40

⇒ 84 - 16 = 40

⇒ 68 ≠ 40

⇒ LHS ≠ RHS

Option 4) 6 and 12

Given: 96 ÷ 6 - 16 + 12 × 8 = 40

After interchanging the numbers we get;

⇒ 96 ÷ 12 - 16 + 6 × 8 = 40

⇒ 8 - 16 + 6 × 8 = 40

⇒ 8 - 16 + 48 = 40

⇒ 56 - 16 = 40

⇒ 40 = 40

⇒ LHS = RHS

Hence, the correct answer is "Option 4".

Shortcut Trick

For two entities, if (A+B) takes X days and A takes Y days, then B takes (X × Y) ÷ (Y − X) days.

Here, X = 20 days and Y = 24 days.

Days for B = (20 × 24) ÷ (24 − 20)

Days for B = 480 ÷ 4 = 120 days.

∴ The correct answer is 120 days.

Alternate Method

Given: A and B together take 20 days. A alone takes 24 days.

Formula: Efficiency = Total Work ÷ Days

⇒ Total Work = LCM of 20 and 24 = 120 units.

⇒ Efficiency of (A + B) = 120 ÷ 20 = 6 units/day.

⇒ Efficiency of A = 120 ÷ 24 = 5 units/day.

⇒ Efficiency of B = Efficiency of (A + B) − Efficiency of A = 6 − 5 = 1 unit/day.

⇒ Time taken by B = Total Work ÷ Efficiency of B

⇒ Time taken by B = 120 ÷ 1 = 120 days.

∴ The correct answer is 120 days.

Additional Information

Work and Wages

Wages are distributed in the ratio of the efficiency of the workers when they work for the same amount of time.

Pipes and Cisterns

Similar to time and work, but inlet pipes have positive efficiency and outlet (leak) pipes have negative efficiency.

Alternate Day Work

Calculate the work done in one cycle (e.g., 2 days if A and B work alternately) and then find the total cycles needed.

The correct answer is Dichloro diphenyl trichloro ethane.

Key Points

• Dichloro diphenyl trichloroethane is a chemical compound commonly used as Insecticide.
• Dichlorodiphenyltrichloroethane is commonly known as DDT.
• It is also called 1,1,1-trichloro-2,2-bis(p-chlorophenyl)ethane.
• It was first developed by Othmar Zeidler in 1874.
• The insecticidal action of DDT was discovered by the Swiss chemist Paul Hermann Müller in 1939.
• Paul Hermann Müller was awarded the Nobel Prize in Physiology in 1948 "for his discovery of the high efficiency of DDT as a contact poison against several arthropods".
• Dichloro diphenyl trichloroethane became infamous for its environmental impacts.
• It was used to limit the spread of the insect-born diseases malaria and typhus among civilians and troops during the second half of World War II.
• The United States banned the use of DDT in 1972, but some countries still use the chemical.
• DDT can be absorbed by eating, breathing, or touching products contaminated with DDT.
• It is one of 12 pesticides recommended by the WHO for indoor residual spray programs.

Additional Information

• Bordeaux mixture is an effective fungicide and bactericide used to control diseases of fruit and nut trees, vine fruits, and ornamental plants.
• 2, 4-Dichloro phenoxy acetic acid is a systemic herbicide.
• Arsenic is a natural component of the earth’s crust that is highly toxic in its inorganic form.

The correct answer is Dispersion and total internal reflection.

Key Points

• The order of a rainbow is determined by the number of light reflections inside the water droplets that create it:
• One reflection results in the first-order or primary rainbow; two reflections create the second-order or secondary rainbow.
• More internal reflections cause bows of higher orders—theoretically unto infinity.

​

Additional Information

• Total internal reflection, in physics, complete reflection of a ray of light within a medium such as water or glass from the surrounding surfaces back into the medium.
• The phenomenon occurs if the angle of incidence is greater than a certain limiting angle, called the critical angle.
• Dispersion
• In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.
• Media having this common property may be termed dispersive media

The logic followed here is :-

Hence, the correct answer is "7411".

Given

Bag contains Rs. 1, 50 paise, coins

The ratio of value is 30 : 11

The total no. of coins are 520

Concept used

Ratio concept used

Calculation

Value of Rs. 1 and 50 paise coins = 30 : 11

Number of coins = 30 : 22

⇒ 52 part = 520

⇒ 1p = 10

⇒ 22p = 10 × 22

⇒ 220

Calculation:

Rs. 1 = 100 paise 

Let the total number of 100 paise coins be x

Then 50 paise coins are 520 – x

According to the question,

⇒ 100x/50(520 – x) = 30/11

⇒ 11 × 100x = 30 × 50(520 – x)

⇒ 1,100x = 7,80,000 – 1,500x

⇒ 2,600x = 7,80,000

⇒ x = 7,80,000/2,600

⇒ x = 300

50 paise coins,

⇒ 520 – 300 = 220

∴ 50 paise coins are 220.

The correct answer is To use digitally fetched data for automated MSME loan appraisals.

In News

• The Union Finance Minister and MoS, Finance launched a new credit assessment model for MSMEs leveraging digital footprints.

Key Points

• The model uses digitally fetched data such as Name and PAN authentication, GST data, and bank statement analysis for MSME loan appraisals.
• The new system provides instant in-principle sanctions and reduces the paperwork and branch visits for MSMEs.
• The model aims to improve loan processing speed, reduce turnaround time (TAT), and offer credit based on objective data.
• It enables MSMEs without a formal accounting system to apply for loans, improving accessibility for smaller businesses.

Additional Information

• Digital Footprints
• Digital footprints refer to data that can be collected electronically, such as bank statements, GST records, PAN details, and mobile verification, which are used for the credit assessment process.
• By using these footprints, the new model automates and streamlines the loan application process, making it faster and more transparent.
• CGTMSE
• The Credit Guarantee Fund Trust for Micro and Small Enterprises (CGTMSE) is a scheme that provides credit guarantees to financial institutions to encourage lending to MSMEs.
• This new credit assessment model allows MSMEs to access loans under the CGTMSE scheme without the need for physical collateral, promoting ease of access to finance.
• Straight Through Process (STP)
• STP refers to the automatic, seamless processing of transactions or processes without manual intervention.
• In this context, it ensures faster loan processing and reduced waiting times for MSME applicants.
• Turnaround Time (TAT)
• TAT refers to the total time taken to process a request or transaction from start to finish.
• The new credit assessment model aims to significantly reduce the TAT for MSME loans, making the system more efficient and accessible.

The correct answer is Inbreeding.

Key Points

• Self-pollination occurs when the pollen from the anther is deposited on the stigma of the same flower, or another flower on the same plant.
• Self-pollination leads to the production of plants with less genetic diversity, since genetic material from the same plant is used to form gametes, and eventually, the zygote.

Additional Information

• Self-pollination or cross-pollination can be an advantage when the number of flowers is small or they are widely spaced.
• During self-pollination, the pollen grains are not transmitted from one flower to another.
• As a result, there is less wastage of pollen.

The Position and positional values of English Alphabets are:

The logic followed here is:

So, 805Y will complete the series.

Hence, the correct answer is 'Option 3'.

Shortcut Trick

When the time intervals are equal (T₁ = T₂ = 3 hr), the Average Speed is simply the Arithmetic Mean of the speeds.

Average Speed = (30 + 50) ÷ 2 = 40 km/h

Average of Speeds = (30 + 50) ÷ 2 = 40 km/h

Required Percentage = (40 ÷ 40) × 100 = 100%

∴ The correct answer is 100%.

Alternate Method

Given:

Speed 1 (v₁) = 30 km/h, Time 1 (t₁) = 3 hr

Speed 2 (v₂) = 50 km/h, Time 2 (t₂) = 3 hr

Formula Used:

Total Distance = (v₁ × t₁) + (v₂ × t₂)

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Distance for first part = 30 × 3 = 90 km

⇒ Distance for second part = 50 × 3 = 150 km

⇒ Total Distance = 90 + 150 = 240 km

⇒ Total Time = 3 + 3 = 6 hr

⇒ Average Speed = 240 ÷ 6 = 40 km/h

⇒ Average of Speeds = (30 + 50) ÷ 2 = 80 ÷ 2 = 40 km/h

⇒ Percentage = (Average Speed ÷ Average of Speeds) × 100

⇒ Percentage = (40 ÷ 40) × 100 = 100%

∴ The correct answer is 100%.

Additional Information

Average Speed (Equal Distances)

If a person covers two equal distances at speeds x and y, the average speed is 2xy ÷ (x + y).

Average Speed (Equal Time Intervals)

If a person travels at speeds x and y for equal time intervals, the average speed is (x + y) ÷ 2.

General Formula

Average Speed = (Total Distance) ÷ (Total Time) = (d₁ + d₂ + ...) ÷ (t₁ + t₂ + ...).

Unit Conversion

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

The correct answer is Nuclear Energy.

Key Points

• Homi Bhabha
• Homi Bhabha award is given for special contribution in the field of Nuclear Energy.
• He is often considered the father of the Indian nuclear program.
• He founded a nuclear research center at Trombay which was later renamed the Bhabha Atomic Research Centre (BARC).
• CAP-CRM Prize is the award given to recognize research excellence in the fields of theoretical and mathematical physics.
• Aryabhatta Award is presented to individuals with notable lifetime contributions in the field of astronautics and aerospace technology in India.

Additional Information

• Nuclear Reactor
• Nuclear energy is energy in the nucleus (core) of an atom.
• A nuclear reactor consists of nuclear reactor fuel, control rods, moderators, pressure vessels, coolant, and containment.
• The moderator in the nuclear reactor slows down the neutrons in the reactor to sustain the chain reaction.
• Examples of moderators used are water, beryllium, graphite, heavy water, etc.
• Nuclear reactors operate on the principle of nuclear fission, in which a heavy atomic nucleus splits into two smaller fragments.
• The heat generated by the fission process turns the water into steam, which spins a turbine to produce carbon-free electricity.
• Coolants include heavy water, air, carbon dioxide, helium, liquid sodium, etc.

The correct answer is Zinc.

Key Points

Explanation:

Galvanization

• The process of putting a protective zinc coating to iron to prevent rusting is known as galvanization.
• It extends the life of iron parts by establishing a membrane between the metal and the air, which prevents iron oxide from developing on its layer.
• Galvanization also provides greater corrosion protection to parts that are exposed to air.
• Galvanizing protects against rust and corrosion in several ways:

1. It acts as a barrier, preventing corrosive chemicals from reaching the iron beneath.
2. The zinc acts as a sacrificial anode, meaning that even if the coating is damaged, the exposed steel is still protected by the zinc that remains on it.
3. The zinc surface reacts with the environment to generate a dense, adhering patina that is impervious to moisture.

The statement asserts that people do not condone a particular trend for a long time and want to change it quite often. The first inference cannot be drawn as nothing about the authors’ mind set can be inferred. Thus only inference II follows because the public wants a change and wants something original all the time. Thus, literature is altered every six months to suit the taste of the public.

Shortcut Trick

When a sphere is melted into 'n' equal smaller spheres, the new radius becomes r = R ÷ n^1/3.

Here, n = 8, so the new radius r = 10 ÷ 8^1/3 = 10 ÷ 2 = 5 cm.

Surface area of each new small ball = 4πr²

⇒ Surface Area = 4 × (22/7) × 5² = 2200/7 = 314 2/7 cm².

∴ The correct answer is 314 2/7 cm².

Alternate Method

Given:

Radius of the original solid sphere (R) = 10 cm

Number of identical spherical balls formed (n) = 8

Formula Used:

Volume of a sphere = 4/3 × π × r³

Surface Area of a sphere = 4 × π × r²

R = 10
Original Sphere

Melted into
8 balls

r = ?
8 Equal Balls

Calculations:

Let the radius of each newly formed small spherical ball be r.

Since the large sphere is melted to form 8 identical balls, the total volume remains conserved.

⇒ Volume of large sphere = 8 × Volume of one small ball

⇒ 4/3 × π × R³ = 8 × (4/3 × π × r³)

⇒ R³ = 8 × r³

⇒ 10³ = 8 × r³

⇒ 1000 = 8r³

⇒ r³ = 1000 ÷ 8

⇒ r³ = 125

⇒ r = 5 cm

⇒ Surface Area of each small ball = 4 × π × r²

⇒ Surface Area = 4 × (22/7) × 5²

⇒ Surface Area = 4 × (22/7) × 25

⇒ Surface Area = 100 × (22/7)

⇒ Surface Area = 2200/7 cm²

⇒ 2200 ÷ 7 = 314 with a remainder of 2

⇒ Surface Area = 314 2/7 cm²

∴ The correct answer is 314 2/7 cm².

Additional Information

Volume Conservation

When a 3D object is melted and recast into other shapes, the total volume always remains constant, even though the combined surface area changes significantly.

Sphere Formulas

Volume of a Sphere = 4/3 × π × r³

Surface Area of a Sphere = 4 × π × r²

Hemisphere Formulas

Volume of a Hemisphere = 2/3 × π × r³

Curved Surface Area = 2 × π × r²

Total Surface Area = 3 × π × r²

The correct answer is Kuchipudi

Key Points

• Bhaamaakalaapam is a traditional dance-drama from Andhra Pradesh.
• This dance-drama is associated with the Kuchipudi dance style.
• It narrates the story of Lord Krishna and his queen Satyabhama.
• The performance is known for its expressive dance movements and dramatic storytelling.
• Kuchipudi is one of the eight major Indian classical dances and is renowned for its graceful movements and strong narrative element.

Additional Information

• Kuchipudi originated in a village named Kuchipudi in the Indian state of Andhra Pradesh.
• It combines dance, music, and acting to depict stories from Hindu epics and scriptures.
• The dance form was traditionally performed by male Brahmins, but now it is performed by both men and women.
• Kuchipudi performances often include intricate footwork, dramatic expressions, and elaborate costumes.
• The dance form has evolved over time and continues to be a significant cultural heritage of India.

The correct answer is Vitamin C.

• The disease scurvy occurs because of a lack of Vitamin C.

Key Points

Some of the vitamins and their deficiency diseases are listed below:

The statement says that Leela is considering recommending the movie to her friends.

Therefore, we can conclude that Leela liked the movie and wants her friends to watch it.

Hence, both the conclusions follow.

Shortcut Trick

Marked Price (MP) = Rs. 1600

Discount% = 10%

Multiplier for SP = (100 − 10) ÷ 100 = 0.9

Selling Price (SP) = 1600 × 0.9 = 1440

∴ The correct answer is Rs. 1440.

Alternate Method

Given: Marked Price = Rs. 1600, Discount Rate = 10%

Formulas: Discount = MP × (Discount% ÷ 100) | SP = MP − Discount

⇒ Discount = 1600 × (10 ÷ 100) = Rs. 160

⇒ Selling Price (SP) = 1600 − 160

⇒ Selling Price (SP) = Rs. 1440

∴ The correct answer is Rs. 1440.

Additional Information

Marked Price (MP)

The price printed on an item or the label price is called the Marked Price. Discounts are always calculated on this value.

Selling Price (SP)

The actual price at which the item is sold to the customer after deducting the discount from the MP.

The correct answer is option 4.

Key Points

• Implementation of Public Policy:
• Bureaucracy in India functions as the permanent executive responsible for the implementation of government policies and programs.
• It plays a crucial role in translating the decisions made by the political leadership into actionable policies and services.
• Hence, option 4 is correct.
• Widening the Scope of Parliamentary Democracy:
• While bureaucracy supports the democratic process, its primary role is not to widen the scope of parliamentary democracy but to ensure the effective execution of policies enacted by the elected representatives.
• Therefore, option 1 is incorrect.
• Strengthening the Structure of Federalism:
• Bureaucracy operates at both the central and state levels, but its main function is not specifically to strengthen federalism.
• Its role in federalism is more about administration rather than structural strengthening.
• Thus, option 2 is incorrect.
• Facilitating Political Stability and Economic Growth:
• While a stable and effective bureaucracy can contribute to political stability and economic growth, these are not its primary functions.
• Its main focus is on the execution of public policies as directed by the government.
• Hence, option 3 is incorrect.
• In summary, the bureaucracy is primarily characterized by its role as an agency for the implementation of public policy, ensuring that the administrative framework works effectively under the political leadership.

The correct answer is Protein.

Key Points

• Wool and silk fibre are obtained from animals.
• The protein fibre of silk is composed mainly of fibroin.
• The silk fibre is drawn from the cocoon of the silkworm.
• Wool is obtained from the fleece of sheep or goat.
• It is also obtained from the hair of rabbits, yak and camels.
• So, silk fibre is primarily made up of protein.

The logic followed here is:

So, '45' will complete the series.

Hence, the correct answer is "Option 2".

Given :

Radius of right circular cone and cylinder(r) = 5 cm

Height of right circular cone and cylinder(h) = 9 cm

Formula used :

Volume of right circular cylinder(V₁) = πr²h

The volume of the right circular cone (V₂) = \(\dfrac{1}{3}\)πr2h

Calculation :

Volume of remaining solid = V₁ - V₂ 

⇒ \(π× 5^2× 9 - \dfrac{1}{3}× π× 5^2× 9\) 

⇒ π × 5² × 9 (1 - \(\dfrac{1}{3}\))

⇒ \(\dfrac{2}{3}× π× 5^2× 9\)

⇒ 150π

∴ The answer is 150π .

The correct answer is Drums.

Key Points

• Sivamani, known by his stage name Drums Sivamani, is a renowned percussionist from India. He plays many instruments including drums, octoban, darbuka, udukai, ghatam, and kanjira.
• Over his career, he has performed in various stages and for different types of events, including the IPL Championships in 2008 and 2010.
• He has been associated with prominent musicians, like A.R. Rahman, and has performed for various compositions across film industries.

​

Additional Information

• List of Famous Musicians with Instruments:
• Santoor: Pt Shiv Kumar Sharma
• Sarod: Allauddin Khan,Amjad Ali Khan.
• Sitar: Pt Ravi Shankar, Budhaditya Mukherjee.
• Surbahar: Annapurna Devi, Sajjad Hussain.
• Rudra Veena: Asad Ali Khan, Zia Moin-ud-din Khan.

The correct answer is Silver

• Silver articles when exposed to air become black after some time.
• This is because the silver metal reacts with the sulphur present in the atmosphere and forms silver sulphide (black colour).

Key Points

• The silver article turns black when kept in the air because the silver article reacts with sulphur compounds such as hydrogen sulphide (H₂S) present in the air. Ag+H₂S→Ag₂S+H₂
• ​The phenomenon is called corrosion. For silver particularly, it is called tarnishing of silver.
• Silver sulphide (Ag₂S) is the black substance formed.

The image embedded in given figure is as shown below:

Hence, "Option 3" is the correct answer.

Shortcut Trick

When a wire is reshaped, Perimeter of Square = Circumference of Circle.

Area of Square (a²) = 154 ⇒ Side (a) = √154 cm.

Perimeter = 4 × √154 cm.

Area of Circle = (Perimeter²) ÷ (4 × π) = (16 × 154) ÷ (4 × 22/7).

Area of Circle = (4 × 154 × 7) ÷ 22 = 4 × 7 × 7 = 196 cm².

∴ The correct answer is 196 cm².

Alternate Method

Given: Area of square = 154 cm²

Formula Used: Area of square = a²; Perimeter = 4a; Circumference = 2πr; Area of circle = πr²

⇒ a² = 154

⇒ a = √154 cm

⇒ Length of wire = Perimeter of square = 4 × √154 cm

⇒ Circumference of ring = 2 × (22/7) × r = 4√154

⇒ r = (4√154 × 7) ÷ 44 = (√154 × 7) ÷ 11

⇒ Area of ring = πr² = (22/7) × [(√154 × 7) ÷ 11]²

⇒ Area = (22/7) × (154 × 49) ÷ 121

⇒ Area = (22 × 154 × 7) ÷ 121

⇒ Area = (2 × 154 × 7) ÷ 11 = 2 × 14 × 7 = 196 cm²

∴ The correct answer is 196 cm².

Additional Information

Constant Perimeter Rule

When a wire of fixed length L is bent into different shapes, the circle encloses the maximum area compared to any polygon.

Area-Perimeter Relation

For a circle, Area = C² ÷ (4π). For a square, Area = P² ÷ 16. If P = C, then Area_circle ÷ Area_square = 4 ÷ π ≈ 14 ÷ 11.

Square Properties

Diagonal of a square = a√2. Area can also be expressed as (Diagonal²) ÷ 2.

The correct answer is - Budget deficit + Net government borrowings

Key Points

• Fiscal Deficit
• Fiscal deficit in a budget represents the total amount by which the government's expenditure exceeds its income, excluding borrowings.
• It is a key indicator of the financial health of a government and shows the gap between the government's revenue and its spending.
• The correct formula to calculate fiscal deficit is: Fiscal Deficit = Budget Deficit + Net Government Borrowings.
• The budget deficit is the difference between the total revenue (excluding borrowings) and total expenditure.

Additional Information

• Revenue Deficit
• The revenue deficit is the excess of revenue expenditure over revenue receipts.
• It indicates the shortfall in the government's current receipts compared to its current expenditure.
• Capital Deficit
• Capital deficit refers to the shortfall in the government's capital receipts compared to its capital expenditure.
• It is not a commonly used term in public finance.
• Primary Deficit
• The primary deficit is the fiscal deficit minus interest payments on previous borrowings.
• It indicates the borrowing requirement of the government excluding interest payments.

The correct answer is None of these.

Key Points

• Hugo de Vries studied the inheritance of flower colour in Evening Primrose and proposed mutation theory that says that mutations are sudden, random, and inheritable and discontinuous variations which serve as raw material for evolution.
• Hence option 2 is correct.

​​​

Additional Information

• Darwin proposed a theory of natural selection that explains the process of evolution by means of natural selection which in turn refers to an unequal ability of individuals to survive and reproduce based on suitability of their inherited characters to prevailing environmental conditions.
• Lamarck gave the theory of inheritance of acquired characters that explains evolution as the inheritance of acquired characters under influence of needs as posed as changing environmental conditions.
• The term new systematic was proposed by Huxley that emphasize three attributes of species; the phylogenetic relationship between different species, mutability, and ability of gradual modification.

The logic followed here is:

Asha is sitting at 532 from the right and 462 from the left end.

Total number of person in that row = Rank of Asha from Right + Rank of Asha from Left - 1.

= 532 + 462 - 1

= 994 - 1

= 993.

Hence, the correct answer is 'Option 4'.

Shortcut Trick

Stoppage time per hour = [(Faster Speed − Slower Speed) ÷ Faster Speed] × 60 min

Stoppage time per hour = [(90 − 75) ÷ 90] × 60

Stoppage time per hour = (15 ÷ 90) × 60

Stoppage time per hour = (1 ÷ 6) × 60 = 10 minutes

∴ The correct answer is 10 minutes.

Alternate Method

Given:

Speed without stoppages = 90 kmph

Speed with stoppages = 75 kmph

Without Stoppage (90 kmph)

Distance covered in 1 hr = 90 km
With Stoppage (75 kmph)

Distance covered in 1 hr = 75 km

15 km

10 min stop

Calculations:

⇒ Distance covered in 1 hr without stop = 90 km

⇒ Distance covered in 1 hr with stop = 75 km

⇒ Decrease in distance due to stoppage = 90 − 75 = 15 km

⇒ Stoppage time = Time taken to cover the lost 15 km at normal speed of 90 kmph

⇒ Stoppage time (in hr) = Distance ÷ Speed = 15 ÷ 90 = 1 ÷ 6 hr

⇒ Stoppage time (in min) = (1 ÷ 6) × 60 = 10 minutes

∴ The correct answer is 10 minutes.

Additional Information

Direct Stoppage Time Formula

Stoppage time per hour = (Difference in Speed ÷ Speed without Stoppages) × 60 minutes.

Average Speed

Average Speed = Total Distance ÷ Total Time. It represents the uniform speed needed to cover the same distance in the same total time.

Unit Conversions

To convert kmph to m/s, multiply by 5 ÷ 18. To convert m/s to kmph, multiply by 18 ÷ 5.

The correct answer is Gwalior.

• The Indian Mutiny of 1857 effectively ended in the city of Gwalior.

Key Points

• The Indian Mutiny of 1857 was a major revolt in India in 1857–58 against the rule of the British East India Company, which acted as a sovereign power on behalf of the British Crown.
• The rebellion began on 10 May 1857 as a mutiny by soldiers of the Company's army in the garrison town of Meerut.
• The rebellion posed a great threat to British power in that region and was only contained with the defeat of the rebels at Gwalior on 20 June 1858.
• Its name has been contested and has been described as the Sepoy Mutiny, the Indian Rebellion, the Great Rebellion, the Rebellion of 1857, the Indian Rebellion, and the First War of Independence.

Additional Information

The correct answer is Upwards.

Key Points

• The electron moves undeflected through the field if the electric force acts on the electron are equal and opposite to the magnetic field.
• Using Fleming's left-hand rule, the magnetic field should be applied in the vertically upward direction.
• Fleming's left-hand rule states that:
• Whenever a current-carrying conductor is placed in a magnetic field, it experiences a force due to the magnetic field.
• The middle finger points in the direction of the current.
• The thumb gives the direction of force or motion acting on the conductor.

Additional Information

• Flemings right-hand rule:
• ​The direction of the current induced by changing magnetic field is given by the right-hand rule.

​

The logic followed here is :-

Hence, the correct answer is "RMZK".

Given:

In an elections there are two candidates. One got 38% votes and lost by 9600 votes.

Calculations:

Let, total votes be 100x.

One candidate got 38% = 100x × \(\dfrac{38}{100}\)

= 38x

Then another candidate got (100x - 38 x) = 62x

Now, lost by 9600 votes, 62x - 38x = 9600

24x = 9600

x = \(\dfrac{9600}{24}\) = 400

So, total votes = 100x = 100 × 400 = 40000

∴ The answer is 40000.

The correct answer is Zn.

Key Points

• An amphoteric oxide is an oxide that can act as either an acid or base in a reaction to produce salt and water.
• Amphoterism depends on the oxidation states available to a chemical species.
• Because metals have multiple oxidation states, they form amphoteric oxides and hydroxides.
• Metals that display amphoterism include copper, zinc, lead, tin, beryllium, and aluminium.
• Al2O3 is an amphoteric oxide.
• When reacted with HCl, it acts as a base to form the salt AlCl3.
• When reacted with NaOH, it acts as an acid to form NaAlO2.

Mistake Points

• Zn and Mn both are amphoteric oxides, but due to the official answer key option, 1 is marked as the correct answer.

The correct answer is Alpha ray.

Key Points

• The alpha particle is the heaviest.
• It is produced when the heaviest elements decay.
• Alpha and beta rays are not waves.
• They are high-energy particles that are expelled from unstable nuclei.

Important Points

• Alpha particles carry a positive charge, beta particles carry a negative charge, and gamma rays are neutral.
• An alpha particle is made up of two protons and two neutrons bound together.
• Beta particles are high energy electrons.
• Gamma rays are waves of electromagnetic energy or photons.

The figure that will replace the question mark (?) in the following figure series is shown below:

1. For ''

element → Flipping horizontally subsequently.

2. For '

' element →  Rotating 90º clockwise in forward and backward direction.

3. For '

' element → No change

Final series is

Hence, ‘option - (3)’ is the correct answer.

Given:

The cost price of the item is Rs.950.

The selling price of the item is Rs.1,150.

Concept:

The percentage profit is calculated by the formula:

((Selling price - Cost price)/Cost price) × 100%.

Solution:

⇒ The percentage profit = ((1,150 - 950)/950) × 100% = 21%.

Therefore, her percentage profit is 21%

The Correct Answer is Bundela Rajputs.

• Chaturbhuj Temple, dedicated to Vishnu, is located in Madhya Pradesh, India.
• The name Chaturbhuj is a combination of 'Chatur' meaning 'four' and 'bhuj' meaning 'arms' which literally translates to 'one who has four arms' and refers to Rama and Avatar of Vishnu.
• The temple has a dynamic multi-story structural view that incorporates the architectural features of the temple, the fortress, and the palace.
• The temple was originally constructed to deify the image of Rama as the chief deity installed in the Rama Raja Temple in the Orchha Fort complex.
• The portrait of Radha Krishna is now worshipped in the temple.
• The temple is considered to have one of the tallest Vimana among the Hindu temples standing at 344 feet.

Important Points

• The temple was founded during the reign of Mughal emperor Akbar by the Bundela Rajputs of the kingdom of Orchha.
• Its construction began with Madhukar Shah and was completed by his son, Vir Singh Deo, in the 16^th century. Madhukar Shah has constructed a temple for his wife, Rani Ganeshkuwari.
• The Chaturbhuj temple has tall spires, shaped like pine cones, constructed on a raised platform 4.5 meters (15 ft) high.
• The total height of the temple is 105 meters (344 ft) high and its architecture is compared to that of the Basilica and it is designed to imitate the four arms of Vishnu for which it was constructed.

The correct answer is Helium.

Key Points

• The noble gas family has zero valencies.
• The valency of an element is related to how many electrons are in the outer shell.
• The electronic configuration of Helium (He) is 2, 0.
• Hence, the Valency of the element Helium is 0.
• Neon, Radon, and Argon have zero valencies because they have their outer shell completely filled and are chemically inert gas.

Additional Information

• The combining capacity of an atom is known as its valency.
• The number of bonds that an atom can form as part of a compound is expressed by the valency of the element.
• Valence electrons are those electrons that are present in the outermost orbit of the atom.
• These electrons have a weak attraction towards the atomic nucleus; thus, atoms can easily remove or share these electrons with other atoms.
• By sharing, gain or donating electrons, chemical bonds are formed between the atoms.
• Lithium has one valency.
• Beryllium has two valencies.
• Fluorine has one valency.

​

The logic followed here is:

So, 'HZL' will complete the series.

Hence the correct answer is "HZL".

Given:

secC = cosec(C – 30°)

Concepts used:

Calculation:

secC = cosec(C – 30°)

⇒ secC = sec(90° - (C – 30°))

On comparing,

⇒ C = 90° + 30° - C

⇒ 2C = 120°

⇒ C = 60°

 cotC – tanC = cot60° - tan60° = (1/√3) – (√3) = -2/√3

 ∴ Value of cotC – tanC is -2/√3.

The correct answer is Shah Jahan.

Key Points

• Shah Jahan, whose name means "King of the World" in Persian, was the fifth Mughal emperor, who ruled from 1628 to 1658.
• Known for his patronage of the arts, Shah Jahan commissioned many magnificent architectural projects during his reign, with the Sheesh Mahal in Agra being one of them.
• Sheesh Mahal, also known as "Glass Palace", is situated inside the Agra Fort. It's renowned for its intricate mirror work.
• Shah Jahan is most famous for the construction of the Taj Mahal, built in memory of his beloved wife, Mumtaz Mahal.
• His architectural style often involved white marble and precious stones, leading to some of the most beautiful and iconic structures in India.

Additional Information

The correct answer is Clove.

• Clove spices are obtained from flower buds.

Key Points

• Cloves are the flower buds of the clove tree which is an evergreen tree.

• Its scientific name is Syzygium aromaticum.

• Cloves are a rich source of manganese.

• Clove was introduced to India as early as 1800 from Mauritius.

Additional Information

• Zanzibar is called the Island of Cloves.
• Cumin is the dried seed of Cuminum cyminum.
• As its name suggests the Coriander seeds are dry fruits of coriander.
• Nutmeg is also a seed.

Given: A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 6.

1) F lives on an even numbered floor but not 6.

2) The sum of floors on which F and C live is 3.

3) The sum of floors on which D and F live is 7.

4. B lives immediately above A.

After positioning B and A only one position is left which will be occupied by the only person left i.e. E.

Thus, one person live between B and F.

Hence, "Option 1" is the correct answer.

Given:

Average of nine numbers = 60

Average of first five numbers = 55 and average of next three numbers = 65

Tenth number = Ninth number + 10

Concept used:

Average = Total sum of all numbers / (Count of the numbers)

Calculation:

The sum of nine numbers = 60 × 9 = 540

The sum of the first five numbers = 55 × 5 = 275

The sum of the next three numbers = 65 × 3 = 195

Ninth number = (540 – 275 – 195) = (540 – 470) = 70

∴ Tenth number = 70 + 10 = 80

Mistake PointsWe have details about 10 numbers but the average is given only of 9 

numbers. To calculate the 10^th number, we have a relationship that is

the ninth number is 10 less than the tenth number. So after calculating

the 9^th number, use this relation to find the next number. Don't take

the average of 10^th number.

The Correct Answer is ​Amaravati.

In News

• Amaravati to host India’s first Quantum Computing Valley.

Key Points

• India’s first Quantum Computing Valley will be launched in Amaravati, Andhra Pradesh by January 2026.
• It aims to employ lakhs of professionals, promoting research, innovation, and industrial growth.
• The park will be accessible to states, government bodies, and institutions across India.
• The main goal is to make quantum technology benefit human society.
• The initiative is aligned with the National Quantum Mission (NQM).
• Focus areas: Productivity enhancement and wealth creation through quantum technologies.
• The NQM was approved in 2023, covering the period from 2023–24 to 2030–31.

The correct answer is Glycogen.

Key Points

• The carbohydrates are stored in the animal body as glycogen.
• It is also known as animal starch because its structure is similar to amylopectin and is rather more highly branched.
• It is present in the liver, muscles, and brain and is found in yeast and fungi.
• When the body needs glucose, enzymes break the glycogen down to glucose.
• Polysaccharides contain a large number of monosaccharide units joined together by the glycosidic linkages.
• These are the most commonly encountered carbohydrates in nature.
• They mainly act as food storage or structural materials.

The statement highlights the new government policy which aims to reduce carbon emissions by 50% within the next decade. It doesn't mention any steps that government will take to achieve this goal. So, we can't say that the government will ban all the vehicles that run on fossil fuel immediately. Hence, Conclusion I don't follow.

The statement also doesn't mention anything regarding the steps that it will take for coal-fired power plants. Hence, Conclusion II don't follow.

Hence, the correct answer is "Neither Conclusion I nor Conclusion II follows".

Shortcut Trick

Let the two numbers be 9x and 9y, where x and y are co-prime.

Product of numbers = HCF × LCM ⇒ 9x × 9y = 9 × 252.

81xy = 2268 ⇒ xy = 28.

Possible co-prime pairs for xy = 28 are (1, 28) and (4, 7).

For (4, 7), Sum = 9 × (4 + 7) = 9 × 11 = 99.

∴ The correct answer is 99.

Alternate Method

Given:

HCF of two numbers = 9

LCM of two numbers = 252

Formula Used:

Product of two numbers = HCF × LCM

Calculations:

Let the numbers be a and b.

⇒ a = 9x and b = 9y (where HCF(x, y) = 1)

⇒ 9x × 9y = 9 × 252

⇒ 81xy = 2268

⇒ xy = 28

⇒ The factors of 28 that are co-prime are (4, 7).

⇒ x = 4 and y = 7

⇒ a = 9 × 4 = 36

⇒ b = 9 × 7 = 63

⇒ Sum = a + b = 36 + 63 = 99

∴ The correct answer is 99.

Additional Information

LCM and HCF Relationship

For any two numbers 'a' and 'b', a × b = HCF(a, b) × LCM(a, b).

HCF of Fractions

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

LCM of Fractions

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

Co-prime Property

Two numbers are co-prime if their Highest Common Factor is 1.

The correct answer is option 3 i.e. Tamil Nadu.

• This refinery is a plant for industrial processes where crude oil is transformed into useful products like petroleum, diesel, naphtha etc.
• Manali refinery is located in the state of Tamil Nadu.
• It is managed by Chennai Petroleum Corporation Limited.
• It comes under the Public sector industries.

The correct answer is Freon.

Key Points

• Freon is one of the several simple fluorinated aliphatic organic compounds that are used in commerce and industry.
• In addition to fluorine and carbon, Freons often contain hydrogen, chlorine, or bromine.
• Thus, Freons are types of chlorofluorocarbons (CFCs), hydrochlorofluorocarbons (HCFCs), and related compounds.
• The name Freon is a trademark registered by E.I. du Pont de Nemours & Company.
• The Freons are colourless, odourless, nonflammable, noncorrosive gases or liquids of low toxicity that were introduced as refrigerants in the 1930s; they also proved useful as propellants for aerosols and in numerous technical applications.
• Their low boiling points, low surface tension, and low viscosity make them especially useful refrigerants.
• They are extremely stable, inert compounds.
• The Freons neither present a fire hazard nor give off a detectable odour in their circulation through refrigerating and air-conditioning systems.

Additional Information

• Methane:
• Methane is a colourless, odourless gas that occurs abundantly in nature and as a product of certain human activities.
• Methane is the simplest member of the paraffin series of hydrocarbons and is among the most potent of the greenhouse gases.
• Its chemical formula is CH₄.
• Methane is lighter than air, having a specific gravity of 0.554. It is only slightly soluble in water.
• It burns readily in air, forming carbon dioxide and water vapour; the flame is pale, slightly luminous, and very hot.
• The boiling point of methane is −162 °C (−259.6 °F) and the melting point is −182.5 °C (−296.5 °F).
• Methane, in general, is very stable, but mixtures of methane and air, with the methane content between 5 and 14 per cent by volume, are explosive.
• Butane:
• ​Butane, either of two colourless, odourless, gaseous hydrocarbons (compounds of carbon and hydrogen), members of the series of paraffinic hydrocarbons.
• Their chemical formula is C₄H₁₀.
• The compound in which the carbon atoms are linked in a straight chain is denoted normal butane or n-butane; the branched-chain form is isobutane.
• Both compounds occur in natural gas and in crude oil and are formed in large quantities in the refining of petroleum to produce gasoline.
• Commercially, n-butane can be added to gasoline to increase its volatility.
• Transformed to isobutane in a refinery process known as isomerization, it can be reacted with certain other hydrocarbons such as butylene to form valuable high-octane constituents of gasoline.
• Chloroform:
• ​Chloroform (CHCl3), also called trichloromethane, nonflammable, clear, colourless liquid that is denser than water and has a pleasant etherlike odour.
• It was first prepared in 1831, by the Scottish physician, Sir James Simpson of the University of Edinburgh was the first to use it as an anesthetic in 1847.
• Chloroform has a relatively narrow margin of safety and has been replaced by better inhalation anaesthetics.
• In addition, it is believed to be toxic to the liver and kidneys and may cause liver cancer.
• Chloroform was once widely used as a solvent, but safety and environmental concerns have reduced this use as well.
• Chloroform is prepared by the chlorination of methane.
• The major use of chloroform is in the preparation of chlorodifluoromethane (HCFC-22).
• HCFC-22 contributes to the depletion of the ozone layer.
• Chloroform is formed by the reaction of chlorine with organic substances present in water and thus can occur in drinking water that has been chlorinated.

Explanation:

From the given information: A denotes ‘+’, B denotes ‘×’, C denotes ‘−’, and D denotes ‘÷’

We substitute the values in the given equation and solve it using BODMAS rule:

54 C 34 A 24 D 8 B 2 

54 - 34 + 24 ÷ 8 × 2

54 - 34 + 3 × 2 

54 - 34 + 6

60 - 34

26 = Answer

Hence the correct answer is option (3).

Given:

The average age of 6 brothers = 15 years

The age of youngest brother = 5 years

Formula used:

Average = sum of the ages/number of persons

Calculations:

Sum of the 6 persons = 6 × 15

⇒ 90

When the youngest brother born the sum of the remaining 6 brothers = 90 - 6 × 5

⇒ 90 - 30 = 60

Average of the group of brothers when the younger one born = 60/5

⇒ 12 years

∴ The average age of 6 members when younger one born is 12 years

Important Points

At the time of birth, the age of the newly born baby is 0

So, the average age of 6 boys = 60/6 = 10 years

But here, no such option is available in the official paper so we have to consider at the time of birth of the baby number of boys = 5

And then their average age was 60/5 = 12 years.

If both 10 & 12 are available in option, then 10 will get more priority.

Explanation:

• Liquefied petroleum gas (LPG) mainly consists of propane and butane.
• Ethyl Mercaptan (CH3CH2SH) is an organic sulphur compound. It has a distinct smell that is used to detect the leakage of otherwise odourless LPG cooking gas.

The correct answer is Melting of ice.

Key Points

• Melting of ice is a reversible change.
• As an ice cube melts, its shape changes as it acquires the ability to flow. However, its composition does not change.
• Melting is an example of a physical change.
• Physical changes can further be classified as reversible or irreversible.
• The melted ice cube may be refrozen, so melting is a reversible physical change.

Additional Information

• The Curdling of milk is an example of the denaturation of the protein.
• Burning wood is an example of a chemical reaction in which wood in the presence of heat and oxygen is transformed into carbon dioxide, water vapour, and ash.
• During the ripening of fruits or growing of plants into a tree, a chemical change occurs which helps in the ripening and growing of plants into a tree and cannot be reversed.

Premises :

(i) All religious persons are emotional.

(ii) Ram is a religious person

Conclusion:

(a) Ram is emotional → True (As, All religious persons are emotional and Ram is a religious person → so, Ram being a Religious person is emotional)

(b) All emotional persons are religious → False (As All religious persons are emotional → but the reverse of this statement is possibly true but it is not definitely true)

(c) Ram is not a non-religious person → True (As Ram is a religious person)

(d) Some religious persons are not emotional → False (As All religious persons are emotional)

Hence, ‘(a) and (c) only’ is the correct answer.

Given:

Average of 4 consecutive odd numbers = 10

Formula used:

Average = Sum of all the observations/Number of observations

Calculations:

Let the first odd number be n

⇒ [n + (n + 2) + (n + 4) + (n + 6)]/4 = 10

⇒ n + (n + 2) + (n + 4) + (n + 6) = 40

⇒ 4n + 12 = 40

⇒ 4n = 28

⇒ n = 7

The largest odd number = n + 6

⇒ 7 + 6

⇒ 13

∴ The largest odd number is 13

The correct answer is Bhind.

Key Points

• Vankhandeshwar Temple

• ​It is located in Bhind district.

• The temple is dedicated to Lord Shiva.

• It was constructed by Prithviraj Chauhan in 1175 AD.

• The 'eternal flame' present there is burning since its establishment.

• A fair is organized every year on the occasion of Mahashivratri.

• Bhind

• It is a part of the Chambal division.

• It was established as a district on 28^th May 1948.

• It is named after Sage Bhindi.

• Major rivers: Chambal, Sindh, Kuwari, and Puhuj.

• Tourist places: Ater Fort, Gohad Fort, Tomb of Malhar Rao Holkar, Mata Renuka Temple, etc.

• The district has the least Scheduled Tribe population.

• Gohad is famous for "Kali much" rice.

• Bajra and Mustard are grown here.

• Total area: 4459 km²

The correct answer is nitrous oxide.

• Laughing gas, used by doctors as anaesthesia is nitrous oxide.
• Laughing gas is a colourless and odourless sweet-smelling gas.

Key Points

• Nitrous oxide was discovered by Joseph Priestly in 1793.
• Nitrous oxide, is a chemical compound, an oxide of nitrogen with the formula N2O.
• It is a non-flammable gas.
• It is soluble in water.

Additional Information

• Nitrogen is the chemical element with the symbol N.
• It has the atomic number 7.
• The Earth's atmosphere is 78% nitrogen gas.

The subjects are: Hindi, English, Mathematics, Science, History, and Geography.

1. History has to be immediately after Geography.
2. Science has to be earlier than History.

3. Mathematics period is scheduled before Science. 4. English has to be earlier than Mathematics. 5. English has to be either immediately before or immediately after Hindi.

Case - 1 and Case -2 and Case - 3 is elimintaed.

Hence, Geography is scheduled in the 5^th period.

Shortcut Trick

Total work = LCM(8, 4, 16) = 16 units.

Efficiency: A = 2, B = 4, C = 1.

Work done in 2 days (cycle): Day 1 (A alone) = 2 units, Day 2 (A+B+C) = 7 units ⇒ Total 9 units in 2 days.

Remaining work = 16 − 9 = 7 units. Day 3 (A alone) completes 2 units. Remaining = 5 units.

Time for Day 4 (A+B+C) = 5/7 days. Total time = 3 + 5/7 = 26/7 days.

∴ The correct answer is 26/7 days.

Alternate Method

Given:

Time taken by A = 8 days

Time taken by B = 4 days

Time taken by C = 16 days

Concept Used:

Total work is the LCM of the days taken by each person.

Efficiency = Total Work ÷ Days

Calculations:

⇒ Work done by A on 1^st day = 2 units

⇒ Work done by A, B, and C together on 2^nd day = 2 + 4 + 1 = 7 units

⇒ Total work done in 1 cycle of 2 days = 2 + 7 = 9 units

⇒ Remaining work after 2 days = 16 − 9 = 7 units

⇒ Work done by A on the 3^rd day = 2 units

⇒ Remaining work after 3 days = 7 − 2 = 5 units

⇒ On the 4^th day, A, B, and C work together. Time taken to do 5 units = 5 ÷ 7 days

⇒ Total time taken = 3 days + 5/7 days = (21 + 5)/7 = 26/7 days

∴ The correct answer is 26/7 days.

Additional Information

Alternate Day Work Concept

When individuals work on alternate days or in a specific cyclic pattern, calculate the total work done in one complete cycle (e.g., 2 or 3 days). Multiply the cycle to get as close to the total work as possible without exceeding it, then calculate the remaining work day by day.

Work and Wages

Wages are always distributed in proportion to the total work done by each individual. If workers work together for the exact same duration, their wages are directly proportional to their individual efficiencies.

Pipes and Cisterns

Works exactly like Time & Work problems, but an outlet pipe or a leak is considered to do negative work, which is subtracted from the total filling efficiency to find the net work rate.

The correct answer is 'Sodium bicarbonate'.

Key Points

• Sodium bicarbonate is the chemical name of Baking soda.
• It is a chemical compound with the formula NaHCO₃.
• Sodium bicarbonate is a white, crystalline substance that is odorless, and commonly found as a fine powder.
• It tastes slightly salty and alkaline and is basic in nature.
• It is used as a component of baking powder, in fire extinguishers, and to neutralize the acidity of the stomach.

Important Points

The correct answer is Isobars.

Key Points

• Elements that have the same mass number, but different atomic numbers, are called isobars.
• The reason for the variation in the atomic number of isotopes is the varying number of protons in the nuclei of those elements.
• For example, Argon (18Ar⁴⁰), Potassium (₁₉K⁴⁰), and Calcium (₂₀Ca⁴⁰) are Isobars, because all three of them have the same mass numbers.
• Isobars have the following properties:
• Most of the physical properties of isobars are different from each other.
• The chemical properties of isobars are completely different from each other.
• The physical properties of isobars are the same, which depend on the atomic mass.

 Important Points Isotopes:

• Isotopes are atoms that have the same number of protons and electrons, but a different number of neutrons.
• For example, Hydrogen has three isotopes, whose atomic number is 1 but their mass number is 1, 2, and 3 respectively.
• Hydrogen's three isotopes are Protium (₁H¹), Deuterium (₁H²), and Tritium (₁H³).
• Isotones:
• Those Elements whose atomic number and mass number are both different, but whose nucleus has the same number of neutrons, are called Isotones.
• For example, Phosphorus (₁₅P³¹) and Sulphur (₁₆S³²) are isotones, as they each have 16 neutrons in their nucleus.

Given:

Chair ⇒ Butter ⇒ Milk ⇒ Soap ⇒ Ghee ⇒ Chair

We use Soap for bathing.

But here, Soap ⇒ Ghee

Hence, the correct answer is "Option (3)".

GIVEN:

Numbers are 3,8,13, 23......

FORMULA USED :

a_n = a + (n - 1) d 

Where a_n = nth term , a = 1^st term, n = number of terms , d= common difference (second term - first term)

CALCULATION:

Here, we have a = 1^st term = 3 , 2^nd term = 8  n = 50 , d = ( 2^nd term - 1^st term) = ( 8 - 3) = 5

⇒ So, a_n = a + (n - 1) d 

⇒ a₅₀ = 3 + (50 - 1)5 = 3 + 49 × 5 = (3 + 245) =  248.

Hence, 50^th term is 248.

The correct answer is option 4.

Key Points

• Meerut is famous for its hand-forged scissors, and the craft of making these Meerut scissors has been awarded a Geographical Indication (GI) tag.

 Additional Information

• Geographical Indication (GI) is a sign used on products that have a specific geographical origin and possess qualities, reputation, or characteristics essentially attributable to that location.
• Example: Darjeeling Tea, Banarasi Saree, Kashmir Saffron.
• Legal Basis in India
• Governed by the Geographical Indications of Goods (Registration and Protection) Act, 1999.
• Came into force in 2003.
• Administered by the Controller General of Patents, Designs, and Trade Marks (CGPDTM) under the Ministry of Commerce & Industry.
• International Basis
• Protected under TRIPS Agreement (1994) of the World Trade Organization (WTO).
• GI is a type of intellectual property right (IPR), like trademarks and patents.
• Key Features of GI Tags
• Valid for 10 years → can be renewed.
• GI is given to communities or groups, not individuals.
• Helps prevent unauthorized use or imitation of the registered product.
• Promotes local culture, heritage, and rural economy.