RRB Technician Grade III Official Paper (Held On: 27 Dec, 2024 Shift 2) (Previous Year Paper)

Shortcut Trick

Ratio of Boys : Girls = 9 : 7

Given, 7 units (Girls) = 189

Value of 1 unit = 189 ÷ 7 = 27

Number of Boys = 9 units = 9 × 27 = 243

∴ The correct answer is 243.

Alternate Method

Given:

Ratio of Boys to Girls = 9 : 7

Total number of girls = 189

Formula Used:

If the ratio of two quantities is a : b, and the value of one quantity is known, the other can be found using the unitary method or the constant of proportionality (x).

Calculations:

⇒ Let the number of boys in the school be 9x and girls be 7x.

⇒ According to the question, 7x = 189

⇒ x = 189 ÷ 7

⇒ x = 27

⇒ Now, number of boys = 9x

⇒ Number of boys = 9 × 27

⇒ Number of boys = 243

∴ The correct answer is 243.

Additional Information

Ratio and Proportion

A ratio is a comparison of two quantities of the same kind by division. If a/b = c/d, then a, b, c, d are in proportion.

Scaling of Ratios

Multiplying or dividing both terms of a ratio by the same non-zero number does not change the ratio (a : b = am : bm).

Mean and Extreme Proportional

In the proportion a : b :: c : d, the product of extremes (a × d) is always equal to the product of means (b × c).

G iven, statements:

All tablets are screens.

All screens are gadgets.

Possible venn diagram is,

Conclusions:

(I) Some gadgets are tablets. → Follow (As from venn diagram, all tablets are gadgets then some gadgets are tablets is true.)

(II) No gadgets are tablets. → Not Follow (As from venn diagram, all tablets are gadgets then no gadgets are tablets is not true.)

Hence the correct answer is "Option 4"

Additional Information

The correct answer is IIT Ropar.

Key Points

• IIT Ropar unveiled a Mechanical Knee Rehabilitation Device in November 2024.
• This device is a Completely Mechanical Passive (CPM) machine, unlike traditional motorized CPM machines.
• The device eliminates the need for electricity, batteries, and motors.
• It is designed to assist in knee rehabilitation without any external power source.
• The innovation aims to be cost-effective and accessible for patients in remote and resource-limited settings.

Additional Information

• Completely Mechanical Passive (CPM) Machine:
• CPM machines are used in physical therapy to help patients recover range of motion in their joints post-surgery.
• Traditional CPM machines are motorized and require a power source.
• Knee Rehabilitation:
• Knee rehabilitation is crucial for recovery post-injury or surgery to restore function and reduce pain.
• Exercises and mechanical devices are often used to assist in the rehabilitation process.
• IIT Ropar:
• Indian Institute of Technology Ropar is a premier engineering and technology institute in India.
• It is known for its innovative research and contributions to various fields of science and technology.
• Accessibility in Medical Devices:
• Creating medical devices that do not rely on electricity can significantly benefit rural and underdeveloped areas.
• Such innovations ensure that essential medical care is accessible to a broader population.

The correct answer is behind the mirror at the focus F.

Key Points

• A convex mirror always forms a virtual, erect, and diminished image of an object placed in front of it.
• When an object is placed at an infinite distance from a convex mirror, the image formed is highly diminished and point-sized.
• The position of this highly diminished, virtual image is located at the focal point (F) of the convex mirror, behind the mirror.
• This property of convex mirrors makes them suitable for use as rearview mirrors in vehicles, as they provide a wider field of view.

Additional Information

• Focal Point (F): The point at which parallel rays of light either converge or appear to diverge after reflecting off the mirror.
• Centre of Curvature (C): The center of the sphere from which the mirror segment is cut. For convex mirrors, it lies behind the mirror.
• Principal Axis: The line passing through the center of curvature and the midpoint of the mirror.
• Ray Diagrams for Convex Mirrors: Useful for understanding the image formation, showing the path of rays and how they reflect to form images.
• Applications of Convex Mirrors: Used in vehicle rearview mirrors, security mirrors, and in places requiring a wide-angle view.

The Logic follows here is,

For, SOLD - DLSO-SLOD

And also for: TEAR-RATE - TAER

Only 'Option 1' follows the same logic.

1) VOID - DIVO - VIOD 

Hence the correct answer is "Option 1"

Logic followed here is,

Logic: Every letter is increased by 5.

Given,

ROSP is related to WTXU

For, TQUR is related to YVZW

Similarly for OLPM is related to TQUR.

Hence the correct answer is "Option 2"

Shortcut Trick

Let the HCF of the numbers be x.

The numbers in the ratio 1 : 2 : 5 are x, 2x, and 5x.

The LCM of 1, 2, and 5 is 10. Thus, LCM of the numbers is 10 × x = 10x.

Given 10x = 1600 ⇒ x = 160.

∴ The correct answer is 160.

Alternate Method

Given: Ratio of three numbers = 1 : 2 : 5, and their LCM = 1600.

Formula Used: For numbers ax, bx, and cx where x is the HCF, their LCM is x × LCM(a, b, c).

Let the common multiplier be x, which also represents the HCF of the three numbers.

⇒ First number = 1x

⇒ Second number = 2x

⇒ Third number = 5x

⇒ LCM of (1x, 2x, 5x) = x × LCM(1, 2, 5)

⇒ LCM = x × 10 = 10x

⇒ 10x = 1600

⇒ x = 160

∴ The HCF of the numbers is 160.

∴ The correct answer is 160.

Additional Information

LCM and HCF Relationship

For any set of numbers, their HCF is always a factor of their LCM. The ratios of the numbers, when multiplied by their HCF, yield the original numbers.

Product of Two Numbers Formula

For any two numbers A and B, the product of the numbers is equal to the product of their HCF and LCM: A × B = HCF × LCM.

The correct answer is Both proteins and lipids.

Key Points

• The plasma membrane is primarily composed of a bilayer of lipids, mainly phospholipids, with embedded proteins.
• Phospholipids form the fundamental structure, creating a semi-permeable membrane.
• Proteins in the plasma membrane serve various functions including transport, signal transduction, and acting as enzymes.
• The fluid mosaic model describes the plasma membrane as a dynamic arrangement of phospholipids and proteins.

Additional Information

• Phospholipids:
• Composed of a hydrophilic (water-attracting) "head" and two hydrophobic (water-repelling) "tails".
• They arrange themselves into a bilayer in aqueous environments, with heads facing outward and tails inward.
• Integral Proteins:
• Span the entire membrane and are involved in transport and communication across the membrane.
• Peripheral Proteins:
• Located on the surface of the membrane and play a role in cell signaling and maintaining the cell's shape.
• Cholesterol:
• Present within the lipid bilayer, it helps to stabilize the fluidity of the membrane.
• Glycoproteins and Glycolipids:
• Carbohydrate chains attached to proteins and lipids, involved in cell recognition and signaling.

Logic follow here is that the first letter is decreased by 1 and second letter is increased by 5.

Option 1) GC-FH

Option 2) JF-IL

Does not follow the same logic.

Option 3) MI-LN

Option 4) EA-DF

Hence the correct answer is "Option 2"

Shortcut Trick

Let the sides of the rectangle be l and b. The diagonal is d = √(l² + b²).

The area of the square on the diagonal is d² = l² + b².

Given, d² = Area of rectangle + 108(1/3)% of Area ⇒ l² + b² = (25/12) × lb.

Since perimeter 2(l + b) = 28 ⇒ l + b = 14. By triplet testing: if l = 8 and b = 6, then l + b = 14, and l² + b² = 64 + 36 = 100, while (25/12) × 48 = 100. This perfectly matches.

Difference between sides = l − b = 8 − 6 = 2 units.

∴ The correct answer is 2 units.

Alternate Method

Given:

Perimeter of the rectangle = 28 units

Area of the square on the diagonal is 108(1/3)% more than the area of the rectangle.

Formula Used:

Perimeter of rectangle = 2(l + b)

Area of rectangle = l × b

Diagonal of rectangle (d) = √(l² + b²)

Area of square on diagonal = d² = l² + b²

Calculations:

⇒ 2(l + b) = 28

⇒ l + b = 14

⇒ percentage increase = 108(1/3)% = 325/3% = 325/300 = 13/12

⇒ Area of square on diagonal = l × b + (13/12) × l × b

⇒ l² + b² = (25/12) × lb

⇒ We know that (l + b)² = l² + b² + 2lb

⇒ 14² = (25/12) × lb + 2lb

⇒ 196 = (49/12) × lb

⇒ lb = (196 × 12) ÷ 49

⇒ lb = 4 × 12 = 48

⇒ Now, (l − b)² = (l + b)² − 4lb

⇒ (l − b)² = 14² − 4 × 48

⇒ (l − b)² = 196 − 192 = 4

⇒ l − b = √4 = 2

∴ The correct answer is 2 units.

Additional Information

Properties of a Rectangle

Opposite sides are equal and parallel, and all four angles are right angles (90°). The diagonals are equal and bisect each other.

Pythagorean Triplets in Rectangles

The diagonal forms a right-angled triangle with the length and breadth. Common integer triplets like (3, 4, 5), (5, 12, 13), and (6, 8, 10) frequently simplify geometry problems.

Shortcut Trick

In Compound Interest, if a sum becomes n times in T years, it becomes n^x times in x × T years.

Given: n = 2 times in T = 15 years.

We need 8 times, which is 2³ times.

Here, x = 3. Therefore, Required Time = 3 × 15 = 45 years.

∴ The correct answer is 45 years.

Alternate Method

Given: Sum becomes 2 times in 15 years.

Formula: Amount (A) = P(1 + r/100)^t

⇒ 2P = P(1 + r/100)¹⁵

⇒ 2 = (1 + r/100)¹⁵ --- (Equation 1)

To find time (t) for 8 times the sum:

⇒ 8P = P(1 + r/100)^t

⇒ 8 = (1 + r/100)^t

⇒ 2³ = (1 + r/100)^t

Substituting the value of 2 from Equation 1:

⇒ [(1 + r/100)¹⁵]³ = (1 + r/100)^t

⇒ (1 + r/100)⁴⁵ = (1 + r/100)^t

⇒ t = 45 years

∴ The correct answer is 45 years.

Additional Information

Compound Interest Formula

The formula for annual compounding is A = P(1 + r/100)ⁿ, where A is the amount, P is the principal, r is the rate, and n is the time in years.

Rule of doubling (CI)

In CI, the time taken for a sum to grow from 1 to 2, 2 to 4, 4 to 8, and so on, remains constant for a fixed interest rate.

SI vs CI growth

Simple interest grows linearly (constant addition), whereas Compound Interest grows exponentially (constant multiplication).

The correct answer is DNA copying.

Key Points

• Variations are crucial for the survival and evolution of species, providing a way for organisms to adapt to changing environments.
• These variations occur due to errors in the DNA copying process during cell division.
• Such errors, known as mutations, can introduce new traits in organisms which may enhance their survival and reproduction.
• While some mutations can be harmful, others can be beneficial and contribute to the genetic diversity of a population.

Additional Information

• DNA Replication:
• DNA replication is the process by which a DNA molecule makes a copy of itself during cell division.
• It ensures that each new cell receives an exact copy of the organism's genetic material.
• The process involves enzymes like DNA polymerase, which helps in adding nucleotides to the growing DNA strand.
• Mutation:
• A mutation is a change in the DNA sequence that can lead to variations in the genetic code.
• Mutations can occur spontaneously or be induced by external factors such as radiation and chemicals.
• They play a critical role in evolution by introducing new genetic variations.
• Genetic Variation:
• Genetic variation refers to the differences in DNA sequences among individuals within a population.
• It is essential for natural selection, as it provides the raw material for evolutionary change.
• High genetic variation within a population increases its ability to adapt to environmental changes.
• Natural Selection:
• Natural selection is the process by which organisms with advantageous traits are more likely to survive and reproduce.
• Over time, these advantageous traits become more common within the population.
• Natural selection drives the evolution of species by favoring traits that enhance survival and reproductive success.

Shortcut Trick

Let the number be 100%.

Given: 85% + 24 = 100% ⇒ 15% = 24.

We need to find 75% of the number.

If 15% → 24, then 75% → 24 × (75 ÷ 15) = 24 × 5 = 120.

∴ The correct answer is 120.

Alternate Method

Given: 85% of a number + 24 = the number itself.

Formula: Value = (Percentage ÷ 100) × Total Number

⇒ Let the number be x.

⇒ 0.85x + 24 = x

⇒ x − 0.85x = 24

⇒ 0.15x = 24

⇒ x = 24 ÷ 0.15 = 160

⇒ 75% of 160 = 0.75 × 160

⇒ 75% of 160 = 120

∴ The correct answer is 120.

Additional Information

Percentage Change

Percentage change = (Difference ÷ Original Value) × 100. This is useful for finding the gap between 85% and 100%.

Fraction Equivalent

Converting percentages to fractions can simplify calculations: 75% = 3/4 and 15% = 3/20.

Base Change Rule

If 15% of a number is added to make it 100%, the added value is always equal to the remaining percentage of that total base.

Given:

Statement: Overweight and obesity are defined as abnormal or excessive fat accumulation that presents a risk to health.

Reason I:

Several factors can play a role in gaining and retaining excess weight. These include diet, lack of exercise, environmental factors, and genetics.

Reason II:

There are a number of scientifically proven ways you can keep the weight off, ranging from exercising, a proper diet to controlling stress.

Logic:

Reason I explains the causes of overweight and obesity, which directly relate to the statement and it is the possible reason to the statement.

Reason II explains the solutions to overweight and obesity, which also relate to the statement but it is not the reason to the statement.

Hence Only I is a possible reason.

The correct answer is Alkaline potassium permanganate.

Key Points

• Alkaline potassium permanganate (KMnO₄) is a strong oxidizing agent used to convert primary alcohols into carboxylic acids.
• The oxidation process involves the formation of an aldehyde intermediate, which further oxidizes to form the carboxylic acid.
• This reagent is often used in organic chemistry due to its effectiveness and relatively straightforward reaction mechanism.
• Alkaline potassium permanganate is preferred in many laboratory and industrial applications because of its ability to provide high yields of the desired carboxylic acid.

Additional Information

• Oxidation of Alcohols:
• Primary alcohols are oxidized to aldehydes and further to carboxylic acids.
• Secondary alcohols are oxidized to ketones, which generally do not undergo further oxidation under mild conditions.
• Tertiary alcohols are resistant to oxidation due to the absence of hydrogen atoms on the carbon bearing the hydroxyl group.
• Potassium Permanganate (KMnO₄):
• It is a dark purple, crystalline compound that is highly soluble in water.
• In its alkaline form, KMnO₄ provides an effective oxidizing environment.
• It is widely used for its disinfectant and oxidizing properties in various chemical reactions.
• Reaction Mechanism:
• The oxidation of a primary alcohol to a carboxylic acid involves the removal of hydrogen atoms and the addition of oxygen atoms.
• This process typically involves intermediate steps, including the formation of an aldehyde.
• The reaction is typically carried out under controlled conditions to ensure complete oxidation.
• Applications:
• Oxidation reactions are crucial in the synthesis of various organic compounds.
• They are used in the pharmaceutical industry for the production of active pharmaceutical ingredients (APIs).
• Such reactions are also important in the production of fine chemicals and in environmental chemistry for pollutant degradation.

The correct answer is Five.

Key Points

• The Union Budget 2024-25 introduced the Prime Minister's package comprising five schemes and initiatives.
• The package is aimed at providing employment, skilling, and other opportunities.
• It targets 4.1 crore youth over a five-year period.
• The initiative is part of the government's broader strategy to address unemployment and skill gaps in the country.
• These schemes are expected to boost economic growth by enhancing the employability of the youth.

Additional Information

• Employment Generation
• Employment generation refers to the creation of jobs and opportunities for the working-age population.
• It is a key indicator of economic health and social stability.
• Government schemes often target sectors with high potential for job creation, such as manufacturing and services.
• Skill Development
• Skill development focuses on training individuals to enhance their capabilities and job readiness.
• It includes vocational training, technical education, and soft skills improvement.
• Skilling initiatives are crucial for meeting the demands of a rapidly changing job market.
• Economic Growth
• Economic growth is the increase in the market value of goods and services produced by an economy over time.
• It is typically measured as the percent rate of increase in real gross domestic product (GDP).
• Employment and skill development are integral to sustaining long-term economic growth.
• Youth Unemployment
• Youth unemployment refers to the jobless rate among individuals aged 15-24.
• High youth unemployment can lead to social unrest and economic instability.
• Governments often implement specific programs to target youth unemployment and enhance employability.

Shortcut Trick

The volume of a sphere is proportional to the cube of its radius (V ∝ r³).

If the radius becomes 1/2 of its original value, the volume change ratio = (1/2)³.

Calculation: (1/2) × (1/2) × (1/2) = 1/8.

∴ The correct answer is 1/8 times.

Alternate Method

Given: Original radius = r, New radius = r/2

Formula Used: Volume of a Sphere (V) = (4/3)πr³

⇒ Original Volume (V₁) = (4/3) × π × r³

⇒ New Volume (V₂) = (4/3) × π × (r/2)³

⇒ V₂ = (4/3) × π × (r³ / 8)

⇒ V₂ = (1/8) × [(4/3) × π × r³]

⇒ V₂ = (1/8) × V₁

∴ The correct answer is 1/8 times.

Additional Information

Surface Area of a Sphere

The surface area is given by 4πr². If the radius is halved, the surface area becomes (1/2)² = 1/4 of the original.

Volume of a Hemisphere

A hemisphere is half of a sphere, and its volume is given by (2/3)πr³.

Ratio of Volumes

For any similar 3D shapes, the ratio of their volumes is the cube of the ratio of their corresponding linear dimensions (Side₁/Side₂)³.

Given:

X : 40 :: 18 : Y

Logic: (first number - 2) × 2 = second number

Checking each Option:

Option 1: X = 24, Y = 38

For X: (24 - 2) × 2 = 22 × 2 = 44 (not 40)

For Y: (18 - 2) × 2 = 16 × 2 = 32 (not 38)

Option 2: X = 20, Y = 40

For X: (20 - 2) × 2 = 18 × 2 = 36 (not 40)

For Y: (18 - 2) × 2 = 16 × 2 = 32 (not 40)

Option 3: X = 28, Y = 56

For X: (28 - 2) × 2 = 26 × 2 = 52 (not 40)

For Y: (18 - 2) × 2 = 16 × 2 = 32 (not 56)

Option 4: X = 22, Y = 32

For X: (22 - 2) × 2 = 20 × 2 = 40

For Y: (18 - 2) × 2 = 16 × 2 = 32

Follow the same logic.

∴ The correct answer is option (4).

The correct answer is Three.

Key Points

• Amphibians, such as frogs and salamanders, have a three-chambered heart.
• The heart consists of two atria and one ventricle.
• The three-chambered heart allows for some separation of oxygenated and deoxygenated blood.
• This structure is an evolutionary adaptation suited to their dual life in water and on land.

Additional Information

• Oxygenation Process:
• In amphibians, the heart pumps both oxygenated and deoxygenated blood, which partially mixes in the single ventricle.
• This mixed blood is then sent to the lungs and skin for oxygenation and to the rest of the body.
• Circulatory System:
• Amphibians have a double circulatory system, with separate pulmonary and systemic circuits.
• This system is more efficient than a single circulatory system but less efficient than a four-chambered heart.
• Comparison with Other Vertebrates:
• Fish have a two-chambered heart (one atrium and one ventricle).
• Birds and mammals have a four-chambered heart (two atria and two ventricles), which allows for complete separation of oxygenated and deoxygenated blood.
• Evolutionary Significance:
• The three-chambered heart of amphibians represents an intermediate stage in the evolution of the more complex hearts of higher vertebrates.
• This adaptation is essential for amphibians' survival in both aquatic and terrestrial environments.

The correct answer is 4)C6H5OH.

Key Points

• Homologous series are groups of chemical compounds with a similar general formula, differing by a CH2 unit.
• CH3OH (methanol), C2H5OH (ethanol), and C3H7OH (propanol) are members of the alcohol homologous series (CnH2n+1OH).
• C6H5OH (phenol) is not a member of the alcohol homologous series; it belongs to the phenols, which have different properties and structures.
• Phenol (C6H5OH) has an aromatic ring and a hydroxyl group directly bonded to the benzene ring, distinguishing it from alcohols with aliphatic chains.

Additional Information

• Homologous Series:
• These are series of compounds with the same functional group and similar chemical properties, where each successive member differs by a CH2 unit.
• Examples include the alkane series (CnH2n+2), alkene series (CnH2n), and alcohol series (CnH2n+1OH).
• Phenol:
• Phenol (C6H5OH) is an aromatic compound where a hydroxyl group (-OH) is bonded to a benzene ring.
• It exhibits different chemical behavior compared to aliphatic alcohols, including higher acidity and reactivity with electrophiles.
• Alcohols:
• Alcohols are organic compounds containing one or more hydroxyl (-OH) groups attached to a saturated carbon atom.
• They are classified as primary, secondary, or tertiary based on the carbon atom to which the hydroxyl group is attached.
• Functional Groups:
• Functional groups are specific groups of atoms within molecules that determine the characteristic chemical reactions of those molecules.
• Common functional groups include hydroxyl (-OH), carboxyl (-COOH), and amino (-NH2).

The correct answer is the atmospheric refraction of light from the star.

Key Points

• The twinkling of stars is primarily caused by the atmospheric refraction of light as it passes through different layers of Earth's atmosphere.
• As the light from a star travels through the Earth's atmosphere, it constantly changes direction due to the varying density and temperature of the atmospheric layers.
• This continuous change in direction causes the star's light to appear as if it is twinkling when observed from the Earth's surface.
• The phenomenon is more pronounced for stars closer to the horizon because their light passes through a greater thickness of the Earth's atmosphere.
• Planets do not twinkle as much as stars because they have a larger apparent size, which averages out the variations in light due to atmospheric refraction.

Additional Information

• Atmospheric Refraction:
• Refraction is the bending of light as it passes from one medium to another, caused by a change in the speed of light in different media.
• In the context of stars, atmospheric refraction is the bending of starlight as it passes through the Earth's atmosphere, which has varying densities and temperatures.
• Scintillation:
• Scintillation refers to the rapid variations in the brightness and color of stars caused by atmospheric turbulence. It is often used synonymously with "twinkling."
• Light Pollution:
• Light pollution from urban areas can also affect the visibility of stars, making the twinkling effect less noticeable in cities compared to rural areas.
• Seeing Conditions:
• "Seeing" refers to the steadiness of the Earth's atmosphere. Poor seeing conditions, caused by atmospheric turbulence, can enhance the twinkling effect of stars.

Statements:

All screens are mouse.

Some mouses are keyboards.

Possible venn diagram is,

Conclusions:

(I) Some screens are keyboards.→ Not follow(As there is no direct link between screen and keyboards)

(II) No screen is a keyboard. → Not follow(As there is no direct link between screen and keyboards)

Hence the correct answer is "Option 1"

Additional Information

The correct answer is Option 4.

Key Points

• Voltage (V) is defined as the work done (W) per unit charge (Q).
• The correct formula for voltage is V = W / Q.
• Option 4 represents the correct relationship: Voltage = (Work done) / (current × Time).
• This is because current (I) multiplied by time (t) gives charge (Q), and the formula becomes V = W / (I × t).

Additional Information

• Voltage (V):
• Also known as electric potential difference or electric pressure.
• Measured in volts (V).
• It is a scalar quantity.
• Current (I):
• The flow of electric charge.
• Measured in amperes (A).
• It is a vector quantity.
• Work Done (W):
• Energy transferred by a force.
• Measured in joules (J).
• In electrical context, it is the energy used to move a charge through a potential difference.
• Charge (Q):
• Measured in coulombs (C).
• One coulomb is equal to the charge of approximately 6.242×10¹⁸ electrons.

Given:

Weight of Apples = 67 kg

Weight of Oranges = 85 kg

Weight of Pineapple = 69 kg

Weight of Bananas = 95 kg

Weight of Guava = 71 kg

Weight of Pear = 53 kg

Weight of Papaya = 85 kg

Formula used:

Average = (Sum of all values) / (Number of values)

Calculations:

Total weight of fruits = 67 + 85 + 69 + 95 + 71 + 53 + 85 = 525 kg

Number of fruits = 7

⇒ Average weight = 525 / 7

⇒ Average weight = 75 kg

∴ The average weight of fruits bought is 75 kg.

Given

52, 34, 69, 56, 86, 78, 103, ?

Logic follow here is,

Logic 

So, next number is 100.

Hence the correct answer is "Option 4"

The correct answer is Paramecium.

Key Points

• Paramecium is a unicellular organism belonging to the phylum Ciliophora, characterized by the presence of cilia.
• It is commonly found in freshwater environments, such as ponds and lakes.
• The cilia covering its body are used for locomotion and feeding, creating water currents to direct food into the oral groove.
• Paramecium exhibits a complex behavior of movement known as taxis, which helps it respond to environmental stimuli.
• It reproduces asexually through binary fission and can also engage in conjugation, a form of genetic exchange.

Additional Information

• Cilia:
• Hair-like structures that cover the surface of Paramecium and are used for movement and feeding.
• They beat in coordinated waves to propel the organism and to move food particles towards the oral groove.
• Binary Fission:
• A method of asexual reproduction in which Paramecium divides into two genetically identical daughter cells.
• This process ensures rapid population growth under favorable conditions.
• Conjugation:
• A sexual process where two Paramecia exchange genetic material through a temporary cytoplasmic bridge.
• This process increases genetic diversity within the population.
• Taxis:
• Directional movement in response to environmental stimuli, such as light or chemical signals.
• Helps Paramecium navigate towards favorable conditions and avoid harmful environments.
• Phylum Ciliophora:
• A group of protists characterized by the presence of cilia.
• Includes other genera like Tetrahymena and Vorticella, which also possess cilia for movement and feeding.

The correct answer is Option 2.

Key Points

• Evaporation is the process where liquid turns into vapor.
• The rate of evaporation is directly proportional to the surface area.
• When the surface area is increased, more molecules are exposed to air, hence the rate of evaporation increases.
• This principle is commonly observed in everyday life, such as drying clothes faster when they are spread out.

Additional Information

• Factors Affecting Evaporation:
• Temperature: Higher temperatures increase the rate of evaporation.
• Humidity: Lower humidity levels increase the rate of evaporation.
• Wind Speed: Higher wind speeds increase the rate of evaporation by moving saturated air away from the surface.
• Surface Area: Larger surface areas increase the rate of evaporation.
• Applications of Evaporation:
• Drying Clothes: Clothes dry faster when spread out due to increased surface area.
• Cooling Mechanisms: Sweat evaporates from the skin, cooling the body.
• Industrial Processes: Used in processes like salt extraction from seawater.
• Evaporation vs. Boiling:
• Evaporation occurs at any temperature, while boiling occurs at a specific boiling point.
• Evaporation happens only at the surface, while boiling occurs throughout the liquid.

Shortcut Trick

Present Ratio (Teacher : Sum of Students) = 1.5 : 1 ⇒ 3 : 2

Ratio after 6 years = 6 : 5

Since there are 2 students, the sum of their ages increases by 6 × 2 = 12 years, while the teacher's age increases by 6 years.

Let present ages be 3x and 2x. ⇒ (3x + 6) / (2x + 12) = 6 / 5

⇒ 15x + 30 = 12x + 72 ⇒ 3x = 42 years.

∴ The correct answer is 42 years.

Alternate Method

Given:

Let the present sum of ages of the two students be S.

The present age of the teacher T = 1.5S = (3/2)S.

Calculations:

⇒ T / S = 3 / 2 ⇒ T = 3x and S = 2x.

⇒ After 6 years, Teacher age = T + 6 = 3x + 6.

⇒ After 6 years, Sum of students age = S + (6 × 2) = 2x + 12 (since there are two students).

⇒ Given ratio after 6 years: (3x + 6) / (2x + 12) = 6 / 5

⇒ 5 × (3x + 6) = 6 × (2x + 12)

⇒ 15x + 30 = 12x + 72

⇒ 3x = 42

⇒ Teacher present age T = 3x = 42 years.

∴ The correct answer is 42 years.

Additional Information

Ages of Multiple Persons

When calculating the sum of ages for n people after t years, always add n × t to the initial sum.

Ratio and Proportion in Ages

If the ratio of ages is given as a:b, it is often easiest to assume the values as ax and bx to form linear equations based on time shifts.

The correct answer is Alkane.

Key Points

• Alkanes are saturated hydrocarbons containing only single bonds between carbon atoms (C-C).
• The general formula for alkanes is C_nH_2n+2, where n is the number of carbon atoms.
• Examples of alkanes include methane (CH₄), ethane (C₂H₆), and propane (C₃H₈).
• They are typically less reactive than alkenes and alkynes due to the absence of double or triple bonds.
• Alkanes are found in natural gas and petroleum and are used as fuels and solvents.

Additional Information

• Alkynes:
• These are unsaturated hydrocarbons containing at least one carbon-carbon triple bond (C≡C).
• The general formula for alkynes is C_nH_2n-2.
• Examples include ethyne (acetylene) C₂H₂.
• Ethylene:
• Also known as ethene, it is an unsaturated hydrocarbon with the formula C₂H₄.
• Ethylene contains a carbon-carbon double bond (C=C).
• It is widely used in the chemical industry, particularly in the production of polyethylene.
• Alkenes:
• These are unsaturated hydrocarbons containing at least one carbon-carbon double bond (C=C).
• The general formula for alkenes is C_nH_2n.
• Examples include ethene (C₂H₄) and propene (C₃H₆).
• Saturation and Unsaturation:
• Saturated compounds have single bonds between carbon atoms, making them more stable and less reactive.
• Unsaturated compounds have double or triple bonds between carbon atoms, which makes them more reactive.
• Hydrogenation is the process of converting unsaturated compounds to saturated ones by adding hydrogen.

The correct answer is Option 3.

Key Points

• Saponification is the reaction between an ester and a base (such as sodium hydroxide) to form a sodium salt of a carboxylic acid and an alcohol, not the reaction of ethanol with conc. H₂SO₄ to form ethene.
• Esterification is correctly matched as it involves the reaction of an acid (such as ethanoic acid) with an alcohol (such as ethanol) in the presence of an acid catalyst to form an ester and water.
• Dehydration typically refers to the removal of water from a molecule, such as the dehydration of alcohols to form alkenes, not the reaction of esters with sodium hydroxide.
• The correct match here is only the esterification reaction: the reaction of ethanoic acid with ethanol in the presence of an acid catalyst to form an ester.

Additional Information

• Saponification:
• This is a process that involves the conversion of fat or oil into soap and alcohol by the action of aqueous alkali.
• The general equation for saponification is: Fat/Oil + NaOH → Soap + Glycerol.
• Esterification:
• This is the chemical reaction between an acid and an alcohol, usually in the presence of a catalyst, to form an ester and water.
• Commonly used in producing fragrances and flavors due to the pleasant smell of esters.
• Dehydration Reaction:
• A chemical reaction that involves the loss of a water molecule from the reacting molecule.
• Commonly seen in the conversion of alcohols to alkenes using a strong acid such as sulfuric acid.
• Hydrolysis of Esters:
• This is the reaction of an ester with water, leading to the formation of an alcohol and a carboxylic acid.
• In basic conditions, it is known as saponification.

Given:

Total students = 51

Tinu's position from left = 24^th

Shivangi's position to the right of Tinu = 11^th

Calculations:

Shivangi's position from left = Tinu's position from left + Shivangi's position to the right of Tinu

⇒ Shivangi's position from left = 24 + 11 = 35^th

Shivangi's position from right = Total students - Shivangi's position from left + 1

⇒ Shivangi's position from right = 51 - 35 + 1 = 17^th

∴ Shivangi's position from the right end of the row is 17^th.

Shortcut Trick

Product of numbers = HCF × LCM

96 × Other Number = 6 × 1824

Other Number = (6 × 1824) ÷ 96 = 1824 ÷ 16 = 114

∴ The correct answer is 114.

Alternate Method

Given:

HCF = 6

LCM = 1824

First Number (n₁) = 96

Formula Used:

n₁ × n₂ = HCF × LCM

Calculations:

⇒ 96 × n₂ = 6 × 1824

⇒ n₂ = (6 × 1824) ÷ 96

⇒ n₂ = 10944 ÷ 96

⇒ n₂ = 114

∴ The correct answer is 114.

Additional Information

HCF and LCM Relation

For any two positive integers a and b, HCF(a, b) × LCM(a, b) = a × b. This rule only applies to two numbers.

HCF of Fractions

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

LCM of Fractions

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

The correct answer is Option 2.

Key Points

• Copper is more reactive than Silver (Ag).
• Copper (Cu) is more reactive than noble metals such as gold (Au) and platinum (Pt).
• The reactivity series places Copper below Hydrogen, indicating it is less reactive compared to elements above it.
• Silver (Ag) is used in various applications due to its low reactivity, making it less likely to tarnish or corrode.

Additional Information

• Reactivity Series:
• A list of elements ordered by their reactivity from highest to lowest.
• Helps predict how metals will react with acids, water, and other substances.
• Displacement Reactions:
• More reactive metals can displace less reactive metals from their compounds.
• Example: Copper can displace Silver from Silver nitrate (AgNO3) solution.
• Uses of Copper:
• Due to its good conductivity, Copper is widely used in electrical wiring and electronics.
• It is also used in plumbing, roofing, and industrial machinery.
• Corrosion Resistance:
• Copper develops a protective layer of copper oxide, which prevents further corrosion.
• This characteristic is exploited in various industrial and architectural applications.

Shortcut Trick

Prime numbers have only two factors: 1 and themselves.

For any two distinct prime numbers, the only common divisor they share is 1.

Therefore, their Highest Common Factor (HCF) is always 1.

∴ The correct answer is 1.

Alternate Method

Given: Two distinct prime numbers, let them be p and q.

Formula Used: HCF is the largest positive integer that divides each of the integers.

Calculations:

⇒ Let us assume two distinct prime numbers: 3 and 5.

⇒ Factors of 3 = 1, 3

⇒ Factors of 5 = 1, 5

⇒ Common Factor = 1

⇒ HCF(3, 5) = 1

⇒ This property holds true for any pair of distinct prime numbers.

∴ The correct answer is 1.

Additional Information

Coprime Numbers

Any two numbers whose HCF is 1 are called coprime numbers. Thus, any two distinct prime numbers are always coprime.

LCM of Prime Numbers

The Least Common Multiple (LCM) of any two distinct prime numbers p and q is always their product, i.e., p × q.

Lowest Prime Number

The number 2 is the smallest prime number and the only even prime number in existence.

Shortcut Trick

Relative Speed (Opposite Direction) = 42 + 30 = 72 km/h

Convert Speed to m/s: 72 × (5/18) = 20 m/s

Total Distance = Sum of lengths = 120 + 280 = 400 m

Time Taken = 400 ÷ 20 = 20 seconds

∴ The correct answer is 20 sec.

Alternate Method

Given:

Length of Train 1 (L₁) = 120 m

Length of Train 2 (L₂) = 280 m

Speed of Train 1 (S₁) = 42 km/h

Speed of Train 2 (S₂) = 30 km/h

Formula Used:

Time = Total Distance ÷ Relative Speed

Relative Speed (Opposite) = S₁ + S₂

Calculations:

⇒ Total Distance = 120 + 280 = 400 m

⇒ Relative Speed = 42 + 30 = 72 km/h

⇒ Speed in m/s = 72 × (5/18) = 20 m/s

⇒ Time = 400 ÷ 20

⇒ Time = 20 seconds

∴ The correct answer is 20 sec.

Additional Information

Relative Speed Rules

When two objects move in opposite directions, relative speed is S₁ + S₂. In same direction, relative speed is |S₁ − S₂|.

Unit Conversion

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

Train Crossing Concepts

When a train crosses another train or a bridge, total distance is the sum of their lengths. When crossing a pole or a person, distance equals the train's length only.

Shortcut Trick

Area of Equilateral Triangle = (√3 / 4) × Side²

25√3 = (√3 / 4) × Side²

Side² = 100 ⇒ Side = 10 cm

Perimeter = 3 × Side = 3 × 10 = 30 cm

∴ The correct answer is 30 cm.

Alternate Method

Given: Area of equilateral triangle = 25√3 cm²

Formula Used:

Area = (√3 / 4) × a²

Perimeter = 3a (where a is the side length)

Calculations:

⇒ Area = (√3 / 4) × a² = 25√3

⇒ a² = (25√3 × 4) / √3

⇒ a² = 100

⇒ a = √100 = 10 cm

⇒ Perimeter = 3 × a = 3 × 10

⇒ Perimeter = 30 cm

∴ The correct answer is 30 cm.

Additional Information

Height of Equilateral Triangle

The altitude or height (h) is given by the formula h = (√3 / 2) × a.

Inradius and Circumradius

For an equilateral triangle, Inradius (r) = a / (2√3) and Circumradius (R) = a / √3.

Properties of Equilateral Triangle

All three sides are equal and each interior angle measures exactly 60°.

The correct answer is Bacteria.

Key Points

• Bacteria are microorganisms that play a crucial role in the decomposition of biodegradable materials.
• They break down complex organic substances into simpler compounds through various biochemical processes.
• The activity of bacteria is essential for the recycling of nutrients in ecosystems, contributing to soil fertility.
• Different species of bacteria are involved in the degradation process, each specializing in breaking down specific types of organic matter.

Additional Information

• Biodegradation: The process by which organic substances are broken down by living organisms, primarily by microorganisms like bacteria and fungi.
• Decomposers: Organisms, including bacteria and fungi, that break down dead or decaying organisms, facilitating the recycling of nutrients back into the ecosystem.
• Aerobic Decomposition: Decomposition that occurs in the presence of oxygen, typically resulting in the rapid breakdown of organic material.
• Anaerobic Decomposition: Decomposition that occurs in the absence of oxygen, often resulting in the production of methane and other gases.
• Composting: A managed process of aerobic decomposition of organic waste, leading to the production of compost, a nutrient-rich soil amendment.

Family tree

In a certain code language,

'P + Q' means 'P is the son of Q',

'P - Q' means 'P is the husband of Q',

'P × Q' means 'P is the daughter of Q' and

'P ÷ Q' means 'P is the wife of Q'.

Given,

 A + B - C × D ÷ E

So,  A is Daughter's son to E

Hence the correct answer is "Option 3"

Logic:

first number × 3 + 5 = second number

Given:

16 × 3 + 5 = 48 + 5 = 53

21 × 3 + 5 = 63 + 5 = 68

Calculations:

Option 1: 25, 70

⇒ 25 × 3 + 5 = 75 + 5 = 80 ≠ 70

Option 2: 28, 84

⇒ 28 × 3 + 5 = 84 + 5 = 89 ≠ 84

Option 3: 19, 62

**⇒ 19 × 3 + 5 = 57 + 5 = 62(**second number)

Option 4: 12, 31

⇒ 12 × 3 + 5 = 36 + 5 = 41 ≠ 31

∴ The correct answer is option (3).

Shortcut Trick

Identify prime numbers in each decade from 51 to 100.

51 to 60: 53, 59 (Sum = 112)

61 to 70: 61, 67 (Sum = 128)

71 to 80: 71, 73, 79 (Sum = 223)

81 to 90: 83, 89 (Sum = 172)

91 to 100: 97 (Sum = 97)

Total Sum = 112 + 128 + 223 + 172 + 97 = 732

∴ The correct answer is 732.

Alternate Method

Given: Range for prime numbers is 51 to 100.

Formula Used: Sum of numbers = n₁ + n₂ + n₃... + n_x

⇒ Prime numbers are numbers having only two factors: 1 and itself.

⇒ List: 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

⇒ Sum = 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97

⇒ Sum = 112 + 128 + 144 + 162 + 186 (grouped addition)

⇒ Sum = 732

∴ The correct answer is 732.

Additional Information

Prime Numbers from 1 to 100

There are a total of 25 prime numbers between 1 and 100. The sum of prime numbers from 1 to 50 is 328.

Smallest and Largest Prime

2 is the only even prime number and the smallest prime number. 97 is the largest two-digit prime number.

Twin Primes

Pairs of prime numbers with a difference of 2 are called twin primes (e.g., 71 and 73).

The correct answer is Marathi, Pali, Prakrit, Assamese, and Bengali.

Key Points

• In October 2024, the Government of India granted classical language status to five Indian languages: Marathi, Pali, Prakrit, Assamese, and Bengali.
• This recognition aims to highlight and preserve the rich cultural and linguistic heritage associated with these languages.
• Classical language status provides certain benefits, including financial assistance for the development of the language, and academic research and funding for translation projects.
• Only languages with a rich heritage and history of more than 1500-2000 years are considered for classical status by the Government of India.
• The announcement was made by the Ministry of Culture, which oversees the promotion and protection of Indian languages and cultural heritage.

Additional Information

• Classical Languages of India:
• As of 2024, India recognizes 11 classical languages, including Tamil, Sanskrit, Kannada, Telugu, Malayalam, Odia, Marathi, Pali, Prakrit, Assamese and Bengali.
• The criteria for classical language status include a significant body of ancient literature, a long history, and an original tradition.
• Benefits of Classical Language Status:
• Classical languages receive financial support for setting up centers of excellence for study and research.
• The status facilitates the translation of classical texts into other Indian languages and English.
• Pali and Prakrit:
• Pali is an ancient language, primarily used in the Theravada Buddhist scriptures.
• Prakrit refers to a group of middle Indo-Aryan languages that were spoken in ancient India.
• Assamese and Bengali:
• Assamese is the easternmost Indo-Aryan language, spoken mainly in the state of Assam.
• Bengali is the second most spoken language in India and has a rich literary heritage, including works by Nobel Laureate Rabindranath Tagore.

Shortcut Trick

Arrange the 10 data points in ascending order: 0, 1, 2, 2, 3, 3, 3, 4, 5, 6.

Since the number of observations (n) is 10 (even), the median is the average of the 5^th and 6^th terms.

The 5^th term is 3 and the 6^th term is 3.

Median = (3 + 3) ÷ 2 = 3.

∴ The correct answer is 3.

Alternate Method

Given: Wickets taken in 10 matches: 2, 6, 4, 5, 0, 3, 1, 3, 2, 3.

Formula Used:

When the number of observations (n) is even:

Median = [(n/2)^th term + (n/2 + 1)^th term] ÷ 2

Calculations:

⇒ Total number of matches (n) = 10

⇒ Arrange the data in ascending order: 0, 1, 2, 2, 3, 3, 3, 4, 5, 6

⇒ n/2 = 5^th term = 3

⇒ n/2 + 1 = 6^th term = 3

⇒ Median = (3 + 3) ÷ 2 = 6 ÷ 2 = 3

∴ The correct answer is 3.

Additional Information

Median for Odd Number of Terms

If n is odd, the median is the value of the ((n + 1) ÷ 2)^th term after arranging the data in ascending order.

Mode of Data

The mode is the value that appears most frequently in a data set. For this dataset, the mode is 3 as it appears three times.

Empirical Relationship

The relationship between mean, median, and mode is given by: Mode = 3 × Median − 2 × Mean.

The correct answer is 100 m.

Key Points

• The initial velocity (u) of the cycle is not given but can be calculated since the final velocity (v) is 0 m/s (cycle stops).
• The acceleration (a) is given as -2 m/s² (negative sign indicates deceleration).
• The time (t) taken to stop the cycle is 10 seconds.
• Using the first equation of motion: v = u + at, we get 0 = u - 2 * 10, therefore u = 20 m/s.
• Using the second equation of motion: s = ut + 0.5 * a * t², we get s = 20 * 10 + 0.5 * (-2) * 10² = 200 - 100 = 100 meters.

Additional Information

• Equations of Motion:
• The three equations of motion are: v = u + at, s = ut + 0.5 * a * t², and v² = u² + 2as.
• These equations are used to calculate final velocity, displacement, and final velocity squared respectively.
• Deceleration:
• Deceleration refers to a decrease in speed or velocity.
• It is represented by a negative acceleration in physics equations.
• Stopping Distance:
• The stopping distance is the distance a vehicle travels while coming to a complete stop.
• It is affected by the initial speed, the rate of deceleration, and the reaction time of the driver.
• Practical Applications:
• Understanding motion and deceleration is crucial in designing safe braking systems for vehicles.
• It helps in accident reconstruction and traffic safety analysis.

The correct answer is vas deferens.

Key Points

• The vas deferens is a long, muscular tube that transports mature sperm from the epididymis to the urethra in preparation for ejaculation.
• Surgical cutting or sealing of the vas deferens is known as a vasectomy, which is a common form of male sterilization.
• During a vasectomy, the vas deferens is either cut and sealed or tied, preventing sperm from mixing with the semen that is ejaculated from the penis.
• The procedure is highly effective at preventing pregnancy, with a success rate of over 99%.
• A vasectomy does not affect the production of male hormones, sexual function, or the ability to ejaculate semen.

Additional Information

• Prostate Gland
• The prostate gland produces fluid that nourishes and transports sperm during ejaculation.
• It is located just below the bladder and surrounds the urethra.
• Enlargement of the prostate gland can lead to urinary problems in older men.
• Fallopian Tube
• The fallopian tubes are part of the female reproductive system.
• They transport eggs from the ovaries to the uterus.
• Fertilization of the egg by sperm typically occurs in the fallopian tubes.
• Seminal Vesicles
• The seminal vesicles are glands that secrete a fluid rich in sugar that provides energy for sperm.
• They contribute approximately 60% of the fluid in semen.
• The fluid from the seminal vesicles mixes with sperm to form semen.

Shortcut Trick

Total Simple Interest % for 6 years = Rate × Time = 7.5% × 6 = 45%.

Amount % = 100% (Principal) + 45% (Interest) = 145%.

Total Amount = 145% of ₹75,000 = 1.45 × 75,000 = ₹1,08,750.

∴ The correct answer is ₹1,08,750.

Alternate Method

Given: Principal (P) = ₹75,000, Rate (R) = 7.5% per annum, Time (T) = 6 years.

Formula Used: Simple Interest (SI) = (P × R × T) ÷ 100; Amount (A) = P + SI

⇒ SI = (75000 × 7.5 × 6) ÷ 100

⇒ SI = 750 × 45

⇒ SI = ₹33,750

⇒ Amount = Principal + SI = 75,000 + 33,750

⇒ Amount = ₹1,08,750

∴ The correct answer is ₹1,08,750.

Additional Information

Simple Interest Properties

Simple Interest remains constant for every year if the principal and rate are unchanged. SI = P × R × T ÷ 100.

Amount Calculation

The total money returned after the tenure is called Amount. A = P(1 + RT/100).

Effective Rate of Interest

In Simple Interest, the effective rate for 't' years is simply (R × t)%. For Compound Interest, it follows successive percentage change.

Shortcut Trick

Ratio of students in Section A and Section B = 36 : 44 = 9 : 11.

Assume weighted average using deviation from 35 kg: [9 × (40 − 35) + 11 × (35 − 35)] ÷ (9 + 11).

Net deviation = (9 × 5) ÷ 20 = 45 ÷ 20 = 2.25 kg.

Actual Average = 35 + 2.25 = 37.25 kg.

∴ The correct answer is 37.25 kg.

Alternate Method

Given:

Students in Section A (n₁) = 36, Average (A₁) = 40 kg

Students in Section B (n₂) = 44, Average (A₂) = 35 kg

Formula Used:

Combined Average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂)

Calculations:

⇒ Total weight of Section A = 36 × 40 = 1440 kg

⇒ Total weight of Section B = 44 × 35 = 1540 kg

⇒ Total weight of class = 1440 + 1540 = 2980 kg

⇒ Total number of students = 36 + 44 = 80

⇒ Average weight of whole class = 2980 ÷ 80

⇒ Average weight = 37.25 kg

∴ The correct answer is 37.25 kg.

Additional Information

Weighted Average

It is used when groups have different sizes. Formula: W = (Σ n_iw_i) ÷ Σ n_i.

Deviation Method

New Average = Assumed Average + (Total Deviation ÷ Total Number). This simplifies large multiplications.

Alligation Rule

The ratio of quantities is inversely proportional to the difference between their averages and the mean average.

Given Equation: 44 A 4 C 12 B 2 D 1 = ?

BODMAS Rule:

Decoding the given information:

Now replacing the signs from left to right using BODMAS Rule, we get:

44 ÷ 4 + 12 × 2 - 1 = ?

⇒ 11 + 12 × 2 - 1 

⇒ 11 + 24 - 1 

⇒ 35 - 1 

⇒ 34 

Hence, the correct option is "Option 4".

Given Equation: 

13 + 11 ÷ 32 × 4 - 10 = ?

BODMAS Rule:

After interchanging '÷' and '×' , we get

13 + 11 × 32 ÷ 4 - 10 

⇒ 13 + 11 × 8 - 10 

⇒ 13 + 88 - 10 

⇒ 101 - 10 = 91 

Hence, the correct option is "Option 4".

Shortcut Trick

Expenditure on petrol = 30% of Income = ₹300.

⇒ 100% Income = (300 ÷ 30) × 100 = ₹1,000.

Remaining income after petrol = ₹1,000 − ₹300 = ₹700.

House rent = 1/4 of Remaining income = 700 ÷ 4 = ₹175.

∴ The correct answer is ₹175.

Alternate Method

Given:

Expenditure on petrol = 30% of total income

Value of petrol expenditure = ₹300

House rent = 1/4 of Remaining income

Calculations:

⇒ Let the total income be 'X'.

⇒ 30% of X = 300

⇒ (30/100) × X = 300

⇒ X = (300 × 100) ÷ 30 = ₹1,000

⇒ Remaining income = Total Income − Petrol expense

⇒ Remaining income = 1000 − 300 = ₹700

⇒ House rent = (1/4) × 700

⇒ House rent = ₹175

∴ The correct answer is ₹175.

Additional Information

Successive Percentage Change

When spending from a remaining amount, use the multiplying factor: Final = Initial × (1 − r₁) × (1 − r₂).

Fraction to Percentage Conversion

A fraction of 1/4 is equivalent to 25%. Calculating 1/4 of a value is the same as taking 25% of it.

Base Value Identification

Always identify if a percentage is applied to the total income or the remaining income to avoid calculation errors.

Logic followed here is,

Hence the correct answer is "Option 3"

The correct answer is blue.

Key Points

• Blue light has the shortest wavelength (about 450-495 nanometers) among the visible spectrum, which makes it scatter more than other colors when it enters the Earth's atmosphere.
• The scattering of blue light by air molecules causes the sky to appear blue during the daytime, a phenomenon known as Rayleigh scattering.
• When sunlight passes through the atmosphere, shorter wavelengths of light (blue and violet) are scattered in all directions by the gases and particles in the air.
• The human eye is more sensitive to blue light than to violet light, which is why we see the sky as blue rather than violet.

Additional Information

• Rayleigh Scattering:
• Named after the British scientist Lord Rayleigh, this type of scattering occurs when the particles causing the scattering are smaller than the wavelength of the light.
• It is responsible for the blue color of the sky and the reddening of the sun at sunrise and sunset.
• Visible Spectrum:
• The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye, ranging from approximately 380 to 750 nanometers.
• Colors in the visible spectrum include violet, blue, green, yellow, orange, and red.
• Wavelength and Frequency:
• Light waves are characterized by their wavelength (the distance between successive peaks) and frequency (the number of peaks passing a point per second).
• Shorter wavelengths correspond to higher frequencies and higher energy.
• Mie Scattering:
• This type of scattering occurs when the particles causing the scattering are about the same size as the wavelength of the light.
• Mie scattering is responsible for the white appearance of clouds, as it scatters all wavelengths of light equally.

Given D, E, F, G, L, M and N are sitting around a circular table facing the centre.

N sits third to the left of M.

M is an immediate neighbour of both E and L.

D is not an immediate neighbour of N.

L sits second to the left of G.

And F sits at remaining place.

Two people sit between F and L when counted from the right of F.

Hence the correct answer is "Option 2"

Given series:

(Left) 3 Ω 2 * £ 1 + & & % 4 6 @ 8 $ 7 $\mho$ 9 # 1 @ 5 (Right)

Condition to be checked:

After dropping all the symbols from the given series, we get:

3 2 1 4 6 8 7 9 1 5

In the new series, the seventh number from the left is 7.

∴ The correct answer is "Option 4"$.

Logic follow here is that the first letter is decreased by 5 and second letter is decreased by 10.

Option 1) TQ - OG

Option 2) ZW - UM

Option 3) GK - PW

Does not follow the same logic.

Option 4) BY - WO

Hence the correct answer is "Option 3"

The correct answer is 3) The gaseous state.

Key Points

• The gaseous state is characterized by particles that are far apart and move freely, making gases highly compressible.
• Compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure change.
• Gases can be compressed into much smaller volumes compared to solids and liquids.
• Due to the large amount of empty space between gas particles, they can be squeezed together under pressure.
• Examples of highly compressible gases include air, carbon dioxide, and helium.

Additional Information

• Solid State
• Solids have a fixed shape and volume with particles closely packed in a regular pattern.
• They are incompressible due to the minimal space between particles.
• Examples include ice, iron, and wood.
• Liquid State
• Liquids have a fixed volume but take the shape of their container.
• They are slightly compressible because particles are close together but can move past each other.
• Examples include water, oil, and mercury.
• Boyle's Law
• It states that the pressure of a given mass of gas is inversely proportional to its volume at a constant temperature.
• This law explains the compressibility of gases.
• Applications of Gas Compressibility
• Compressed natural gas (CNG) is used as a fuel for vehicles.
• Compressed air is used in pneumatic tools and machinery.

The correct answer is Only (i) and (iii).

Key Points

• In yeast, pyruvate is converted into ethanol and carbon dioxide during the process of fermentation.
• Pyruvate breakdown in the presence of oxygen takes place in the mitochondria, not in the chloroplast.
• In muscle cells, during anaerobic respiration, pyruvate is converted into lactic acid.
• The conversion of pyruvate to lactic acid in muscles occurs during intense exercise when oxygen supply is low.

Additional Information

• Fermentation:
• It is an anaerobic process where energy is produced without oxygen.
• Common in yeast and some bacteria, used in brewing and baking.
• Aerobic Respiration:
• Occurs in the mitochondria of cells.
• Involves complete oxidation of glucose to carbon dioxide and water.
• Produces a large amount of energy (ATP).
• Anaerobic Respiration:
• Occurs in the absence of oxygen.
• Produces less energy compared to aerobic respiration.
• In muscles, it results in the formation of lactic acid.
• Pyruvate:
• A key intermediate in several metabolic pathways.
• Formed by the breakdown of glucose during glycolysis.
• Can be further processed anaerobically or aerobically.

The correct answer is Tamil Nadu.

Key Points

• The Governor of Tamil Nadu launched the book titled 'Sri Rama in Tamilagam – An Inseparable Bond' in September 2024.
• The event highlighted the cultural and historical significance of Lord Rama in Tamil Nadu.
• The book emphasizes the deep-rooted connection between the Tamil region and the epic of Ramayana.
• This launch was part of a series of cultural initiatives aimed at promoting Tamil heritage and literature.
• The Governor's involvement underscores the state's commitment to preserving and celebrating its rich cultural traditions.

Additional Information

• Ramayana in Tamil Literature:
• The Ramayana has been a significant part of Tamil literature for centuries.
• Various Tamil poets and scholars have translated and interpreted the Ramayana, enriching the cultural tapestry of the region.
• Kambar's 'Kamba Ramayanam' is one of the most celebrated Tamil renditions of the Ramayana.
• Cultural Initiatives in Tamil Nadu:
• Tamil Nadu is known for its vibrant cultural heritage, including classical music, dance, and literature.
• The state regularly organizes festivals and events to promote its cultural legacy.
• Initiatives like the book launch highlight the ongoing efforts to preserve and celebrate Tamil culture.
• Role of the Governor:
• The Governor of a state in India often plays a ceremonial role in promoting cultural and educational activities.
• Such events are part of the Governor's efforts to engage with the public and support cultural initiatives.
• The Governor's participation lends official recognition and significance to cultural events.
• Historical Significance of Lord Rama:
• Lord Rama is a central figure in the Hindu epic, the Ramayana.
• His life and deeds are considered exemplary and continue to inspire millions.
• The story of Rama is celebrated in various forms of art, literature, and religious practices across India.

The correct answer is Option 2.

Key Points

• Isobars are atoms of different chemical elements that have the same atomic mass but different atomic numbers.
• Since they have the same atomic mass, their mass number (sum of protons and neutrons) is identical.
• Isobars have different numbers of protons, which leads to different atomic numbers and different chemical properties.
• Despite having the same mass number, the arrangement of electrons and their chemical behavior differ due to different atomic numbers.

Additional Information

• Isotopes: Atoms of the same element that have the same number of protons but different numbers of neutrons.
• Isotones: Atoms with the same number of neutrons but different numbers of protons.
• Atomic Mass: The mass of an atom, typically measured in atomic mass units (amu), which includes protons and neutrons.
• Atomic Number: The number of protons in the nucleus of an atom, which defines the chemical element.

The correct answer is A commitment to de-escalate tensions along the contested border.

Key Points

• During the 2023 BRICS summit, Xi Jinping and Narendra Modi held an informal meeting to address bilateral issues.
• One of the significant outcomes was a mutual commitment to de-escalate border tensions.
• Both leaders agreed to take steps to reduce the presence of troops along the Line of Actual Control (LAC).
• This commitment aims to foster a peaceful and stable border environment between India and China.

Additional Information

• Line of Actual Control (LAC):
• The LAC is the demarcation that separates Indian-controlled territory from Chinese-controlled territory.
• It is not a legally recognized international boundary but a practical border line.
• BRICS Summit:
• BRICS is an acronym for the association of five major emerging national economies: Brazil, Russia, India, China, and South Africa.
• The summit serves as a platform for collaboration on economic, political, and cultural issues.
• Border Disputes:
• India and China have a long-standing border dispute, particularly in regions like Aksai Chin and Arunachal Pradesh.
• The conflict has led to several military standoffs over the years.
• Military De-Escalation:
• De-escalation involves reducing military forces to minimize the risk of conflict.
• It often includes measures like troop withdrawals and the establishment of buffer zones.

Given:

Word: SHOWING

Vowels: O, I

Consonants: S, H, W, N, G

Logic:

Vowel change: Preceding letter in alphabet

Consonant change: Following letter in alphabet

Common letters: I, H, N, O

Count: 4

∴ 4 letters in the original word also appear in the group of letters thus formed.

Hence the correct answer is "Option 3"

Shortcut Trick

Total Work (LCM of 20, 30) = 60 units. Efficiency: Rahul = 3, Rohan = 2.

Combined Full Efficiency = 3 + 2 = 5 units/day; Half Efficiency = 2.5 units/day.

Work done in first 6 days (Full) = 6 × 5 = 30 units.

Work done in next 6 days (Half) = 6 × 2.5 = 15 units.

Remaining Work = 60 − (30 + 15) = 15 units.

Remaining Days = 15 ÷ 5 = 3 days.

∴ The correct answer is 3 days.

Alternate Method

Given:

Time taken by Rahul = 20 days

Time taken by Rohan = 30 days

Total work = LCM(20, 30) = 60 units

Calculations:

⇒ Total combined efficiency (Full) = 3 + 2 = 5 units/day

⇒ Total combined efficiency (Half) = 5 ÷ 2 = 2.5 units/day

⇒ Work completed in 1^st 6 days = 6 × 5 = 30 units

⇒ Work completed in 2^nd 6 days = 6 × 2.5 = 15 units

⇒ Total work done = 30 + 15 = 45 units

⇒ Remaining work = 60 − 45 = 15 units

⇒ Time taken to finish remaining work (Full efficiency) = 15 ÷ 5 = 3 days

∴ The correct answer is 3 days.

Additional Information

Work and Efficiency Relation

Efficiency is inversely proportional to the time taken to complete a task. Efficiency = Work ÷ Time.

Combined Efficiency

When multiple people work together, their individual efficiencies are added to find the total rate of work.

Variable Efficiency

If efficiency changes, the work done in a specific period is calculated by (New Efficiency × Duration).

Shortcut Trick

Put θ = 90° in the given expression.

⇒ [sin 90° / (1 + cos 90°)] + [(1 + cos 90°) / sin 90°]

⇒ [1 / (1 + 0)] + [(1 + 0) / 1] = 1 + 1 = 2.

Check options for θ = 90°: (2) 2 cosec 90° = 2 × 1 = 2.

∴ The correct answer is 2 cosec θ.

Alternate Method

Given: [sin θ / (1 + cos θ)] + [(1 + cos θ) / sin θ]

Formula Used: sin²θ + cos²θ = 1; cosec θ = 1 / sin θ

⇒ Take LCM of denominators: sin θ (1 + cos θ)

⇒ [sin²θ + (1 + cos θ)²] / [sin θ (1 + cos θ)]

⇒ [sin²θ + 1 + cos²θ + 2 cos θ] / [sin θ (1 + cos θ)]

⇒ [(sin²θ + cos²θ) + 1 + 2 cos θ] / [sin θ (1 + cos θ)]

⇒ [1 + 1 + 2 cos θ] / [sin θ (1 + cos θ)]

⇒ [2 + 2 cos θ] / [sin θ (1 + cos θ)]

⇒ 2(1 + cos θ) / [sin θ (1 + cos θ)]

⇒ 2 / sin θ = 2 cosec θ

∴ The correct answer is 2 cosec θ.

Additional Information

Trigonometric Identities

Fundamental identities include sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Reciprocal Relations

The function cosec θ is the reciprocal of sin θ, and sec θ is the reciprocal of cos θ.

The correct answer is N m² kg^-2.

Key Points

• The universal gravitational constant (G) appears in Newton's law of gravitation, which describes the gravitational force between two masses.
• The correct SI unit of G is N m² kg^-2, where:
• N stands for Newton (unit of force).
• m² stands for square meters (unit of distance squared).
• kg^-2 represents the inverse square of mass in kilograms.
• G is a proportionality constant that quantifies the strength of the gravitational force between two objects.
• The value of G is approximately 6.674 × 10^-11 N m² kg^-2.
• The universal gravitational constant is the same throughout the universe and is independent of the nature of the medium between the objects.

Additional Information

• Newton's Law of Gravitation:
• It states that every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
• The formula is: F = G (m₁m₂) / r², where F is the gravitational force, G is the gravitational constant, m₁ and m₂ are the masses, and r is the distance between their centers.
• Dimensional Formula of G: [G] = M^-1L³T^-2, where M stands for mass, L for length, and T for time.
• Importance of G: The value of G enables the calculation of gravitational forces in celestial mechanics, such as the orbits of planets, moons, and satellites.
• Gravitational Force vs. Electromagnetic Force:
• Gravitational force is much weaker compared to electromagnetic force but acts over long distances.
• It is always attractive, unlike electromagnetic force, which can be both attractive and repulsive.
• Discovery: The value of G was first determined experimentally by Henry Cavendish in 1798 using a torsion balance.

The correct answer is Ladakh.

Key Points

• The first leg of the 2024 Khelo India Winter Games was held in Ladakh.
• The event commenced in January 2024 and featured various winter sports.
• Ladakh is known for its cold desert climate, making it an ideal location for winter sports.
• The Khelo India Winter Games aim to promote winter sports in India and provide a platform for athletes to showcase their talent.

Additional Information

• Khelo India is a national program for the development of sports in India, launched by the Government of India.
• The objective of Khelo India is to identify talented athletes at the grassroots level and provide them with training and support to excel in their respective sports.
• Winter Games include sports such as skiing, snowboarding, ice hockey, and figure skating, among others.
• Ladakh's unique geographical and climatic conditions make it a prime location for hosting winter sports events.
• The Khelo India Winter Games also aim to boost tourism in the region by attracting sports enthusiasts and visitors.

The correct answer is Between 16% and 25%.

Key Points

• As per the Economic Survey of India 2023-24, Bihar has between 16% and 25% of the country's poor population.
• Bihar is one of the states with the highest poverty rates in India, according to recent surveys and reports.
• The state has been implementing various poverty alleviation programs, but significant challenges remain.
• Poverty in Bihar is attributed to several factors including limited industrialization, high population density, and low agricultural productivity.

Additional Information

• Economic Survey of India:
• An annual document released by the Ministry of Finance, Government of India.
• It provides a detailed report on the state of the economy in the past year and outlines the economic outlook and policy directions for the coming year.
• The Economic Survey is presented in the Parliament ahead of the Union Budget.
• Poverty in India:
• India has made significant strides in poverty reduction, but a considerable portion of the population still lives below the poverty line.
• Poverty is measured using various indicators, including income levels, access to basic services, and living conditions.
• The government has launched several schemes like MGNREGA, PMAY, and NFSA to combat poverty.
• Factors Affecting Poverty:
• High population growth, unemployment, and underemployment are major factors contributing to poverty.
• Other factors include lack of access to education, healthcare, and social security.
• Rural poverty is often exacerbated by inadequate infrastructure and limited access to markets.
• Poverty Alleviation Programs:
• Various government programs aim to reduce poverty, such as the Public Distribution System (PDS), Mid-Day Meal Scheme, and National Rural Livelihood Mission (NRLM).
• These programs focus on improving income levels, providing employment opportunities, and ensuring food security.
• The effectiveness of these programs is regularly reviewed and updated to meet the changing needs of the population.

The correct answer is Different layers of the atmosphere have different density.

Key Points

• The phenomenon responsible for the apparent position of a star changing slightly is known as stellar scintillation or twinkling.
• This occurs because the Earth's atmosphere is composed of layers with different densities and temperatures.
• The varying densities cause the light from the star to bend or refract as it passes through the atmosphere.
• This continuous refraction due to atmospheric turbulence makes the star appear to change its position slightly.

Additional Information

• Refraction: It is the bending of light as it passes from one medium to another with different densities.
• Atmospheric Turbulence: This is the chaotic movement of air masses in the atmosphere, which causes variations in the refractive index.
• Scintillation: The fluctuation in the apparent brightness or position of a distant luminous object viewed through the Earth's atmosphere.
• Adaptive Optics: A technology used in telescopes to reduce the distortion caused by the Earth's atmosphere.
• Star’s Own Light: Stars emit their own light through nuclear fusion processes happening in their cores, unlike planets which reflect the light of stars.

Given, Seven people, A, B, E, F, P, Q and R are sitting in a row, facing north.

Only B sits to the left of A.

Only four people sit between B and Q.

Only E sits between R and P and R is not an immediate neighbour of Q.

F sit at remaining place.

F sits at the extreme right of the row.

Hence the correct answer is "Option 4"

Shortcut Trick

Net efficiency = Efficiency of Filling Pipe − Efficiency of Emptying Pipe.

Total Capacity (LCM of 8, 72) = 72 units.

Filling efficiency = 9, Emptying efficiency = 1 → Combined efficiency = 8 units/hr.

Time for 1/3^rd tank = (72 ÷ 3) ÷ 8 = 24 ÷ 8 = 3 hours.

∴ The correct answer is 3 hours.

Alternate Method

Given: Filling time = 8 hours, Emptying time = 72 hours.

Formula: Total Work = LCM of times; Efficiency = Total Work ÷ Time.

⇒ Combined Efficiency of (A + B) = 9 − 1 = 8 units/hr

⇒ Required capacity to fill = 1/3 × 72 = 24 units

⇒ Time required = 24 ÷ 8 = 3 hours

∴ The correct answer is 3 hours.

Additional Information

Inlet and Outlet Pipes

Inlet pipes add water (positive efficiency) while outlet/leakage pipes remove water (negative efficiency).

Combined Rate Formula

If pipe A fills in 'x' hours and pipe B empties in 'y' hours, net rate per hour = (1/x − 1/y).

Time and Work Relation

Time taken to complete a specific fraction of work = (Fraction × Total Work) ÷ Combined Efficiency.

Given:

POKED = 85263

TOKED = 36584

Logic:

Direct letter to number mapping.

Comparing the two codes O K E D is common in both the code language and 3 6 5 8 is common in both the code.

And code for,

P = 8

T = 4

∴ The code for ‘T’ is 4.

Logic followed here is,

Hence the correct answer is "Option 4"

The correct answer is 1) Nervous tissue.

Key Points

• The spinal cord is primarily composed of nervous tissue, which includes neurons and neuroglial cells.
• Neurons in the spinal cord transmit electrical signals between the brain and the rest of the body.
• Neuroglial cells provide support, protection, and nutrition to the neurons.
• The spinal cord is part of the central nervous system (CNS), which also includes the brain.
• Nervous tissue in the spinal cord is organized into white matter and gray matter.

Additional Information

• White Matter:
• Composed of myelinated axons, which are nerve fibers that transmit signals rapidly over long distances.
• Organized into tracts that carry information up and down the spinal cord.
• Gray Matter:
• Contains neuron cell bodies, dendrites, and unmyelinated axons.
• Organized into regions called horns, which are involved in processing information.
• Central Nervous System (CNS):
• Consists of the brain and spinal cord.
• Responsible for processing and transmitting information throughout the body.
• Neurons:
• The basic functional units of nervous tissue.
• Specialized for the transmission of electrical impulses.
• Neuroglial Cells:
• Support cells for neurons, providing structural support, protection, and nutrients.
• Types include astrocytes, oligodendrocytes, and microglia.

The correct answer is 1, 2 and 3.

Key Points

• Metals exhibit the property of malleability, which allows them to be beaten into thin sheets. This is a key characteristic that distinguishes metals from non-metals.
• Metals possess ductility, enabling them to be drawn into thin wires without breaking.
• Metals are known for being good conductors of heat, which makes them essential in applications requiring efficient heat transfer.
• Common examples of malleable metals include gold, silver, and aluminum, while copper and iron are well-known for their ductility.

Additional Information

• Malleability: This is the ability of a metal to withstand deformation under compressive stress, often demonstrated by hammering or rolling.
• Ductility: This property refers to the ability of a metal to be stretched into a wire. It is a critical property for materials used in electrical wiring and construction.
• Conductivity: Metals like copper and aluminum are widely used in electrical applications due to their high electrical conductivity.
• Thermal Conductivity: Metals such as silver and copper are utilized in applications where rapid heat dissipation is required, such as in heat sinks and cookware.
• Other Properties: Metals also generally have high melting points, are dense, and have a shiny appearance, which can be attributed to their free electron structure.

The correct answer is Gravitational.

Key Points

• The gravitational force is the force of attraction between two masses.
• It was first described by Sir Isaac Newton in his law of universal gravitation.
• Gravitational force is responsible for keeping the planets in their orbits around the Sun.
• This force acts over a distance and decreases with the square of the distance between the objects.

Additional Information

• Newton's Law of Universal Gravitation states that every point mass attracts every other point mass by a force acting along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.
• Gravitational Constant (G) is a proportionality factor used in the equation of the law of universal gravitation, and its value is approximately 6.674 × 10^-11 N(m/kg)^2.
• Orbital Mechanics involves the study of the motions of objects in space, governed by gravitational forces.
• Kepler's Laws of Planetary Motion describe the orbits of planets around the Sun, which are elliptical, with the Sun at one focus.
• Einstein's Theory of General Relativity provides a more comprehensive description of gravitation, describing it as the curvature of spacetime caused by mass and energy.

The correct answer is IIT Madras.

Key Points

• IIT Madras hosted the International Chess Federation (FIDE)-rated Rapid Chess Tournament in March 2024.
• The event was part of the institution's efforts to promote chess and enhance the intellectual capabilities of students and participants.
• The tournament attracted players from various parts of the world, contributing to the global chess community.
• IIT Madras has a history of organizing significant chess events, highlighting its commitment to fostering a competitive spirit and strategic thinking.

Additional Information

• FIDE (International Chess Federation)
• Founded in 1924, FIDE is the international governing body of chess.
• It is responsible for organizing world chess championships and regulating international chess competitions.
• FIDE's mission is to promote chess globally and ensure fair play and integrity in the game.
• Rapid Chess
• Rapid chess is a form of chess with faster time controls than classical chess.
• Each player is typically given 15 to 60 minutes for the entire game.
• Rapid chess allows for a more dynamic and exciting game, often leading to unexpected outcomes.
• IIT Madras
• Indian Institute of Technology Madras is one of the premier engineering institutions in India.
• Established in 1959, it is known for its excellence in education, research, and innovation.
• IIT Madras frequently hosts various national and international events, fostering a vibrant academic and cultural environment.
• Chess in Education
• Chess is used as an educational tool to develop critical thinking, problem-solving, and strategic planning skills.
• Many educational institutions incorporate chess into their curriculum to enhance cognitive abilities and concentration among students.
• Studies have shown that regular chess practice can improve academic performance and intellectual development.

Given, 

Gaurav starts from point A and drives 3 km South.

He then takes a left turn and drives 2 km.

He takes another left turn and drives 2 km.

He then takes a right turn and drives 3 km.

He takes a final left turn and drives 1 km to reach point B.

He should drive 5 km in west direction to reach Point A again

Hence the correct answer is "Option 4"

The correct answer is Atoms consist of a positively charged nucleus and negatively charged electrons..

Key Points

• Rutherford's gold foil experiment demonstrated that atoms have a small, dense, positively charged nucleus.
• Most of the atom's volume is empty space, with electrons orbiting the nucleus.
• Only a few alpha particles were deflected, indicating that the nucleus occupies a very small region of the atom.
• The experiment disproved the earlier plum pudding model proposed by J.J. Thomson, which suggested a uniform positive charge.
• The nucleus contains protons and neutrons, while electrons are located outside the nucleus.

Additional Information

• Alpha Particles:
• Alpha particles are positively charged particles consisting of two protons and two neutrons.
• They were used in Rutherford's experiment to probe the structure of the atom.
• Nucleus:
• The nucleus is the dense central part of an atom, containing protons and neutrons.
• It accounts for almost all the mass of the atom but occupies only a tiny fraction of its volume.
• Electron Cloud:
• The electron cloud is the region surrounding the nucleus where electrons are likely to be found.
• Electrons are negatively charged and move rapidly around the nucleus.
• Plum Pudding Model:
• Proposed by J.J. Thomson, it suggested that atoms were made up of electrons scattered within a "soup" of positive charge.
• This model was refuted by Rutherford's gold foil experiment.

The correct answer is 10 B.

Key Points

• The magnetic field (B) created by a coil is directly proportional to the number of turns (N) in the coil.
• If a single-turn coil produces a magnetic field B, then a coil with 10 turns will produce a magnetic field proportional to 10 times the single-turn coil.
• The relationship can be expressed as B_{10 turns} = N * B_{single turn}, where N is the number of turns.
• Therefore, for 10 turns, the magnetic field B_{10 turns} = 10 * B.
• Hence, the magnetic field due to a circular coil with 10 turns will be 10 B.

Additional Information

• Magnetic Field:
• It is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.
• The symbol for the magnetic field is B, and it is measured in teslas (T).
• Electromagnetic Induction:
• It is the production of an electromotive force (EMF) across an electrical conductor in a changing magnetic field.
• This principle is fundamental in the operation of transformers, inductors, and many types of electrical generators and motors.
• Right-Hand Rule:
• It is a mnemonic for understanding the direction of the magnetic field relative to the direction of the current.
• If you point your thumb in the direction of the current, the curl of your fingers shows the direction of the magnetic field loops.
• Solenoid:
• A solenoid is a coil wound into a tightly packed helix, which generates a magnetic field when an electric current passes through it.
• The magnetic field inside a solenoid is uniform and parallel to the axis of the solenoid.

Logic follow here is,

Logic: RES is common in both the language and 5 2 9 is common in both the code.

So, code for,

T = 4

H = 7

Hence the correct answer is "Option 1"

Shortcut Trick

Ratio of Selling Prices is proportional to (100 + Profit%).

Initial SP : New SP = (100 + 30) : (100 + 40) = 130 : 140 = 13 : 14.

Given 13 units = 19.50 ∴ 1 unit = 19.50 ÷ 13 = 1.50.

The increase in SP is (14 − 13) = 1 unit.

Value of 1 unit = 1.50.

∴ The correct answer is ₹1.50.

Alternate Method

Given: Initial SP = 19.50, Initial Profit = 30%, Target Profit = 40%.

Formulas: CP = [SP × 100] ÷ [100 + Profit%], New SP = CP × [100 + New Profit%] ÷ 100.

⇒ Cost Price (CP) = (19.50 × 100) ÷ 130 = 1950 ÷ 130 = 15.

⇒ New Selling Price = 15 × (140 ÷ 100) = 15 × 1.4 = 21.

⇒ Increase in SP = New SP − Old SP = 21 − 19.50 = 1.50.

∴ The correct answer is ₹1.50.

Additional Information

Cost Price & Selling Price Relationship

When Cost Price is constant, the ratio of any two Selling Prices is equal to the ratio of their respective (100 ± Profit/Loss%).

Profit Calculation

Profit is always calculated on the Cost Price unless specified otherwise. Profit = SP − CP.

Shortcut Trick

Identify two numbers whose sum is 20 and product is 84.

Factors of 84: 14 × 6 ⇒ 14 + 6 = 20. So, x = 14 and y = 6.

Value = x² + y² = 14² + 6² = 196 + 36 = 232.

∴ The correct answer is 232.

Alternate Method

Given:

x + y = 20

xy = 84

Formula Used:

(x + y)² = x² + y² + 2xy

Calculations:

⇒ (20)² = x² + y² + 2(84)

⇒ 400 = x² + y² + 168

⇒ x² + y² = 400 − 168

⇒ x² + y² = 232

∴ The correct answer is 232.

Additional Information

Algebraic Identity for Squares

(x − y)² = x² + y² − 2xy is used when the difference and product are given.

Sum and Difference Relation

(x + y)² − (x − y)² = 4xy. This helps find the difference if the sum is known.

The correct answer is 4) Both Statements I and II.

Key Points

• A current-carrying coil indeed produces a magnetic field. This phenomenon is described by Ampère's circuital law, which relates the circulating magnetic field in a closed loop to the electric current passing through the loop.
• A solenoid, which is a type of coil, generates a uniform magnetic field inside it when current flows through it, effectively behaving like a bar magnet with distinct north and south poles.
• Statement I is correct as the magnetic field around a current-carrying conductor is a fundamental principle in electromagnetism.
• Statement II is correct because a solenoid with current behaves like a bar magnet, creating a magnetic field similar to that of a permanent magnet.

Additional Information

• Magnetic Field: A region around a magnetic material or a moving electric charge within which the force of magnetism acts.
• Solenoid: A cylindrical coil of wire acting as a magnet when carrying electric current, used in various applications such as electromagnets and inductors.
• Ampère's Circuital Law: This law states that the integrated magnetic field around a closed loop is proportional to the electric current passing through the loop.
• Electromagnetism: A branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.
• Permanent Magnet: An object made from a material that is magnetized and creates its own persistent magnetic field.

Shortcut Trick

For a continued proportion a : b :: b : x, the third proportional is x = b² ÷ a.

Here, a = 1.6 and b = 0.6.

⇒ x = (0.6 × 0.6) ÷ 1.6 = 0.36 ÷ 1.6 = 0.225.

∴ The correct answer is 0.225.

Alternate Method

Given: 1.6 : 0.6 :: 0.6 : x

Formula Used: Product of Extremes = Product of Means

⇒ 1.6 × x = 0.6 × 0.6

⇒ 1.6x = 0.36

⇒ x = 0.36 ÷ 1.6

⇒ x = 36 ÷ 160

⇒ x = 9 ÷ 40

⇒ x = 0.225

∴ The correct answer is 0.225.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(a × b).

Fourth Proportional

For a : b :: c : d, the fourth proportional d is given by (b × c) ÷ a.

Third Proportional

In the ratio a : b :: b : c, c is the third proportional to a and b, calculated as c = b² ÷ a.

The correct answer is sperms.

Key Points

• The male organ, the penis, is primarily involved in the transfer of sperms during sexual intercourse.
• Sperms are the male gametes that are necessary for fertilization of the female egg (ovum).
• During ejaculation, sperms are released from the male reproductive system and deposited into the female reproductive tract.
• This transfer of sperms is crucial for natural conception to occur.

Additional Information

• Male Reproductive System
• The male reproductive system includes the testes, vas deferens, seminal vesicles, prostate gland, and penis.
• The testes produce sperms and the hormone testosterone.
• Sperms are stored and matured in the epididymis.
• Spermatogenesis
• Spermatogenesis is the process by which sperms are produced in the testes.
• This process begins at puberty and continues throughout a man's life.
• Fertilization
• Fertilization occurs when a sperm successfully penetrates an egg, leading to the formation of a zygote.
• This process typically occurs in the fallopian tubes of the female reproductive system.
• Role of Hormones
• Testosterone is the primary male sex hormone responsible for the development of male reproductive tissues and secondary sexual characteristics.
• Follicle-stimulating hormone (FSH) and luteinizing hormone (LH) are also crucial in regulating spermatogenesis.