RRB Technician Grade III Official Paper (Held On: 23 Dec, 2024 Shift 2) (Previous Year Paper)

The correct answer is self-pollination.

Key Points

• Self-pollination is the transfer of pollen grains from the stamen to the stigma of the same flower or another flower on the same plant.
• This process ensures genetic consistency and can occur in both monocots and dicots.
• It is a form of sexual reproduction in plants but does not promote genetic diversity as cross-pollination does.
• Plants that predominantly self-pollinate include wheat, rice, and tomatoes.
• Mechanisms such as cleistogamy (flowers that never open) ensure self-pollination in some plant species.

Additional Information

• Cross-pollination
• It involves the transfer of pollen from the stamen of one flower to the stigma of another flower, often requiring external agents like wind, water, or animals.
• Cross-pollination promotes genetic diversity and can lead to hybrid vigor in plants.
• Common examples include apples, pumpkins, and many types of flowers.
• Fertilization
• It is the process following pollination where male gametes from pollen grains unite with female gametes (ovules) to form a zygote.
• Fertilization results in the formation of seeds and fruit in flowering plants.
• It can occur in both self-pollinated and cross-pollinated plants.
• Spore Formation
• It is an asexual reproductive process found in fungi, algae, and some plants like ferns and mosses.
• Spores are usually single-celled and can develop into a new organism without the need for fertilization.
• Spores are highly resistant to environmental stresses and can remain dormant for extended periods.
• Stamen and Stigma
• The stamen is the male reproductive part of a flower, consisting of the anther and filament.
• The stigma is the female reproductive part of a flower that receives pollen during pollination.
• Both stamen and stigma are essential for sexual reproduction in flowering plants.

The correct answer is 5 W.

Key Points

• The power (P) is calculated using the formula $P=\frac{W}{t}$, where W is the work done and t is the time taken.
• Given: Work Done(W)= 50 Joules Time Taken(t)= 10 seconds.
• Substituting the values, $P=\frac{50J}{10s}=5Watts$.
• Power is measured in Watts (W), which is equal to one Joule per second.

Additional Information

• Work (W)
• Work is defined as the energy transferred to or from an object via the application of force along a displacement.
• The SI unit of work is the Joule (J).
• Work is calculated as $W=F.d.cos(\theta )$, where F is the force applied, d is the displacement, and θ is the angle between the force and the displacement direction.
• Time (t)
• Time is a measure of the duration of an event.
• In the context of power calculation, time is the duration over which the work is done.
• The SI unit of time is the second (s).
• Power (P)
• Power is the rate at which work is done or energy is transferred.
• The SI unit of power is the Watt (W), which is equivalent to one Joule per second.
• Power can also be calculated using the formula $P=V.I$ in electrical contexts, where V is voltage and I is current.
• Energy
• Energy is the capacity to do work.
• It exists in various forms such as kinetic, potential, thermal, electrical, chemical, and nuclear energy.
• Energy is conserved in all processes; it can neither be created nor destroyed, only converted from one form to another (First Law of Thermodynamics).

The correct answer is All in series.

Key Points

• When resistances are connected in series, the total resistance is the sum of individual resistances.
• The formula for total resistance in series is: $R_{total}=R_1+R_2+R_3$.
• For resistances of 3Ω, 4Ω, and 6Ω in series, the total resistance is 3 + 4 + 6 = 13Ω.
• In a series circuit, the current flowing through each resistor is the same.
• Resistors in series provide a higher total resistance than any individual resistor.

Additional Information

• Parallel Circuit:
• In a parallel circuit, the total resistance is less than the smallest resistor in the circuit.
• The formula for total resistance in parallel is $\frac{1}{R_{total}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$.
• Parallel circuits are used to reduce the overall resistance and to provide the same voltage across all components.
• Ohm's Law:
• Ohm's Law states that $V=IR$, where V is voltage, I is current, and R is resistance.
• This law is fundamental in understanding the behavior of electrical circuits.
• Applications of Resistors:
• Resistors are used to control current flow in circuits.
• They are essential in setting voltage levels and for timing applications in electronic devices.

The correct answer is nine.

Key Points

• The Union Budget 2024-25 focuses on nine key priorities to achieve the goal of 'Viksit Bharat' or Developed India.
• These priorities aim to create abundant opportunities for all citizens, ensuring inclusive growth and development.
• The strategy is designed to propel India towards becoming a developed nation by addressing critical areas such as infrastructure, healthcare, education, and innovation.
• Key initiatives include investments in renewable energy, digital infrastructure, skill development, and social welfare programs.

Additional Information

• Union Budget
• The Union Budget is the annual financial statement presented by the Government of India, detailing its revenue and expenditure for the upcoming fiscal year.
• It is presented by the Finance Minister in Parliament and is a key policy document outlining the government's economic strategy and priorities.
• The budget includes proposals for taxation, government spending, and allocation of resources to various sectors.
• It plays a crucial role in shaping the economic and social policies of the country.
• Inclusive Growth
• Inclusive growth refers to economic growth that is distributed fairly across society and creates opportunities for all, particularly the disadvantaged.
• It aims to reduce poverty and inequality by ensuring that the benefits of growth reach every section of society.
• Policies for inclusive growth typically focus on education, healthcare, social protection, and employment generation.
• This approach ensures sustainable development by promoting social stability and equity.
• Infrastructure Development
• Infrastructure development involves the construction and improvement of foundational services such as transportation, energy, water supply, and telecommunications.
• It is critical for economic growth as it enhances productivity, reduces costs, and improves the quality of life for citizens.
• Investment in infrastructure is a key priority for governments to boost economic activity and create jobs.
• Modern infrastructure also supports sustainable development by integrating green technologies and practices.

The correct answer is India and Australia.

Key Points

• The joint military exercise 'AUSTRAHIND' is conducted between the armies of India and Australia.
• The third edition of this exercise focuses on enhancing military cooperation and interoperability between the two nations.
• 'AUSTRAHIND' aims to improve tactical skills, practice joint operations, and increase mutual understanding.
• The exercise includes various drills, counter-terrorism operations, and humanitarian assistance operations.

Additional Information

• ​The Comprehensive Strategic Partnership (CSP) between India and Australia, established in June 2020, further strengthens bilateral defense ties.
• Joint military exercises improve coordination and interoperability between the armed forces of participating nations.
• They provide an opportunity to learn from each other’s best practices and operational experiences.
• The first edition of 'AUSTRAHIND' was conducted in 2016 with the aim of bolstering defense cooperation between India and Australia.

The logic followed here is:

For, JGLI is related to NKPM

For, PMRO is related to TQVS

Similarly, 

MJOL related ?

Hence, the correct answer is "Option 3".

Given:

 Pranay starts from Point A and drives 45 km towards North.

He then takes a right turn, drives 35 km, turns right and drives 75 km.

He then takes a right turn and drives 25 km.

He takes a final right turn, drives 30 km and stops at Point P.

Thus,  he drive 10 km towards West in order to reach Point A again.

Hence, the correct answer is "Option 2".

Shortcut Trick

Passing Marks = Marks Obtained + Failing Marks = 120 + 78 = 198

According to the question, 55% = 198

1% = 198 ÷ 55 = 3.6

100% (Total Marks) = 3.6 × 100 = 360

∴ The correct answer is 360.

Alternate Method

Given:

Marks scored by the candidate = 120

Marks by which the candidate failed = 78

Minimum Passing Percentage = 55%

Calculations:

⇒ Let the Total Marks of the examination be x.

⇒ Passing Marks = Marks Obtained + Failing Marks

⇒ Passing Marks = 120 + 78 = 198

⇒ According to the condition, Passing Marks = 55% of Total Marks

⇒ 198 = (55 ÷ 100) × x

⇒ x = (198 × 100) ÷ 55

⇒ x = 19800 ÷ 55

⇒ x = 360

∴ The correct answer is 360.

Additional Information

Passing Marks Calculation

Passing Marks = Obtained Marks + Failure Margin. Conversely, if a student passes with extra marks, Passing Marks = Obtained Marks − Extra Marks.

Percentage to Value

If a% of a number is N, then the number is (N ÷ a) × 100.

Total Marks Concept

The Maximum Marks or Total Marks in any exam-based problem is always considered as 100% for calculation purposes.

Shortcut Trick

When two objects move in opposite directions, their Relative Speed is the sum of their individual speeds.

Total Distance to cover = Sum of lengths of both trains = 135 + 155 = 290 m.

Relative Speed = 80 + 65 = 145 km/h = 145 × (5/18) m/s.

Time = Distance ÷ Relative Speed = 290 ÷ (145 × 5/18) = (290 × 18) ÷ (145 × 5) = 2 × 18 ÷ 5 = 36 ÷ 5 = 7.2 sec.

∴ The correct answer is 7.2 sec.

Alternate Method

Given: Length₁ = 135 m, Length₂ = 155 m, Speed₁ = 80 km/h, Speed₂ = 65 km/h.

Formula Used: Time = (Total Distance) ÷ (Relative Speed)

⇒ Total Length = 135 + 155 = 290 m

⇒ Relative Speed = (80 + 65) × (5/18) m/s

⇒ Relative Speed = 145 × 5 ÷ 18 = 725 ÷ 18 m/s

⇒ Time taken = 290 ÷ (725 ÷ 18)

⇒ Time taken = (290 × 18) ÷ 725

⇒ Time taken = 5220 ÷ 725 = 7.2 sec

∴ The correct answer is 7.2 sec.

Additional Information

Relative Speed Concepts

Same Direction: S_rel = S₁ − S₂ | Opposite Direction: S_rel = 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 Objects

When crossing another train, distance = sum of lengths. When crossing a pole/man, distance = length of the train.

The correct answer is Silver chloride turns grey in sunlight.

Key Points

• A decomposition reaction is a type of chemical reaction where one compound breaks down into two or more simpler substances.
• The reaction for silver chloride (AgCl) decomposing in sunlight can be represented as: 2AgCl(s) → 2Ag(s) + Cl2(g).
• This reaction is characterized by the breakdown of silver chloride into silver and chlorine gas.
• Silver chloride turns grey in sunlight due to the formation of metallic silver, which is grey in color.

Additional Information

• Decomposition Reaction
• It is a chemical reaction in which a single compound breaks down into two or more elements or new compounds.
• Decomposition reactions often require an input of energy in the form of heat, light, or electricity.
• Examples include the electrolysis of water and thermal decomposition of calcium carbonate.
• Thermal Decomposition
• It is a type of decomposition reaction where a compound is broken down into simpler substances by heating.
• Example: Calcium carbonate decomposes into calcium oxide and carbon dioxide when heated.
• Photochemical Reaction
• These reactions are initiated by the absorption of light.
• An example is the decomposition of silver chloride in sunlight.
• Redox Reaction
• Redox reactions involve the transfer of electrons between two species.
• These reactions include both oxidation and reduction processes.

The logic followed here is:

Option 1) FUT

Option 2) CEG

Option 3) JLN

Option 4) TVX

Hence, the correct answer is "Option 1".

Shortcut Trick

To double a sum of money, the Simple Interest must be equal to the Principal (100%).

Shortcut Formula: Rate × Time = 100 (when sum doubles)

Rate = 100 ÷ 16

Rate = 6.25%

∴ The correct answer is 6.25%.

Alternate Method

Given:

Let Principal (P) = ₹100

Since the sum doubles, Amount (A) = 2 × 100 = ₹200

Time (T) = 16 years

Formula Used:

Simple Interest (SI) = Amount − Principal

SI = (P × R × T) ÷ 100

Calculations:

⇒ SI = 200 − 100 = ₹100

⇒ 100 = (100 × R × 16) ÷ 100

⇒ 100 = R × 16

⇒ R = 100 ÷ 16

⇒ R = 6.25%

∴ The correct answer is 6.25%.

Additional Information

Sum 'n' times itself

If a sum becomes 'n' times itself in T years at simple interest, the rate R is given by: R = [(n − 1) × 100] ÷ T.

Simple Interest vs Compound Interest

In SI, the interest remains constant every year, whereas in CI, interest is calculated on the accumulated amount of previous years.

Rule of 72

A quick way to estimate the time to double money at Compound Interest is T ≈ 72 ÷ Rate.

Shortcut Trick

Assume Tanu age = 1 unit.

Then Kanu age = 2 units and Anu age = 2 units + 2 years.

Sum = 1 + 2 + 2 + 2 years = 5 units + 2 years = 32 years ⇒ 5 units = 30 years ⇒ 1 unit = 6 years.

Difference (Anu − Tanu) = (2 units + 2) − (1 unit) = 1 unit + 2 = 6 + 2 = 8 years.

∴ The correct answer is 8 years.

Alternate Method

Given:

Let Tanu age = x years.

Kanu age = 2x years.

Anu age = (2x + 2) years.

Calculations:

⇒ Total Age = x + 2x + (2x + 2) = 32

⇒ 5x + 2 = 32

⇒ 5x = 30

⇒ x = 6 years (Tanu age)

⇒ Anu age = 2(6) + 2 = 12 + 2 = 14 years.

⇒ Age difference = 14 − 6 = 8 years.

∴ The correct answer is 8 years.

Additional Information

Ratio and Proportion in Ages

If the ratio of ages of A and B is a : b and the sum is S, then A age = (a ÷ (a + b)) × S.

Age Difference Property

The difference between the ages of two persons remains constant throughout their lives, regardless of the number of years passed.

Given number series: 9 1 1 5 7 8 0 4 5 9 9 4 6 9 4 1 6 6 8 1 4 3 5 0 2 1 9 8 6 1

According to the question,

Condition:  perfect square - odd number - odd number

9 1 1 5 7 8 0 4 5 9 9 4 6 9 4 1 6 6 8 1 4 3 5 0 2 1 9 8 6 1

Thus, there are 5 odd numbers which are preceded by a perfect square and immediately followed by an odd digit.

911, 115, 157, 459, and 435.

Hence, "Option 4" is the correct answer.

The correct answer is Skin.

Key Points

• Stratified squamous epithelium is a type of epithelial tissue that consists of multiple layers of flat cells.
• The primary function of this tissue is to provide protection against mechanical stress, dehydration, and microbial invasion.
• The outermost layer of the skin, known as the epidermis, is composed of stratified squamous epithelium.
• These cells in the skin are keratinized, meaning they contain keratin, a protein that helps in waterproofing and providing strength.
• Stratified squamous epithelium is also found in other parts of the body, such as the oesophagus and oral cavity, but the skin's epidermis is the most prominent example.

Additional Information

• Epithelial Tissue
• Epithelial tissues are one of the four basic types of tissues in the body, along with connective tissue, muscle tissue, and nervous tissue.
• They cover the body surfaces, line body cavities, and form glands.
• Epithelial tissues are classified based on the number of layers (simple or stratified) and the shape of the cells (squamous, cuboidal, or columnar).
• Keratin
• Keratin is a type of protein found in the skin, hair, and nails.
• It provides structural strength and helps protect cells from damage or stress.
• Oesophagus
• The oesophagus is a muscular tube that connects the throat (pharynx) with the stomach.
• It is lined with non-keratinized stratified squamous epithelium, which provides protection from abrasion due to food passage.
• Skin Layers
• The skin is composed of three main layers: the epidermis, dermis, and hypodermis.
• The epidermis is the outermost layer, primarily made up of keratinized stratified squamous epithelium.
• The dermis lies beneath the epidermis and contains connective tissue, blood vessels, and nerve endings.
• The hypodermis, also known as the subcutaneous layer, contains fat and connective tissue that insulates and cushions the body.

The logic followed here is:

Logic: +3 in the each letter.

Hence, the correct answer is "Option 4".

Shortcut Trick

Ratio of efficiency A : B = 3 : 1

Total efficiency = 3 + 1 = 4 units/min

Total work = Total efficiency × Total time = 4 × 36 = 144 units

Time taken by A alone = Total work ÷ Efficiency of A = 144 ÷ 3 = 48 min

∴ The correct answer is 48 min.

Alternate Method

Given: Efficiency of Pipe A is 3 times that of Pipe B. Time taken together = 36 min.

Formula Used: Work = Efficiency × Time; Time = Work ÷ Efficiency

⇒ Let the efficiency of Pipe B be 1 unit/min.

⇒ Efficiency of Pipe A = 3 × 1 = 3 units/min.

⇒ Combined efficiency of (A + B) = 3 + 1 = 4 units/min.

⇒ Total capacity of the tank = 4 units/min × 36 min = 144 units.

⇒ Time taken by Pipe A alone = 144 units ÷ 3 units/min = 48 min.

∴ The correct answer is 48 min.

Additional Information

Efficiency and Time Relationship

The time taken to complete a work is inversely proportional to the efficiency. If Pipe A is 3 times faster than Pipe B, the ratio of time taken is 1 : 3.

Pipes and Cisterns Rule

If two pipes A and B fill a tank in x and y minutes respectively, then together they fill it in (x × y) ÷ (x + y) minutes.

Inlet and Outlet Concept

Inlet pipes carry positive efficiency, while outlet (leak) pipes carry negative efficiency when calculating total work per unit time.

Given: Six people - Adam, Brad, Clara, David, Emily and Farah - are sitting in a straight line, facing north.

Only one person sits to the left of Clara. Only one person sits between Clara and Brad.

David sits second to the right of Emily. Adam is neither an immediate neighbour of Clara nor sits at the extreme end of the line.

Thus, Farah sits at the extreme right end of the line.

Hence, the correct answer is "Option 1".

Shortcut Trick

In ΔPQR, sum of angles = 180° ⇒ ∠PRQ = 180° − (96° + 34°) = 50°.

Since QR || PS, alternate interior angles are equal ⇒ ∠SPR = ∠PRQ = 50°.

In ΔPRS, given PR = RS, so angles opposite to equal sides are equal ⇒ ∠PSR = ∠SPR = 50°.

Sum of angles in ΔPRS = 180° ⇒ ∠PRS = 180° − (50° + 50°) = 80°.

∴ The correct answer is 80°.

Alternate Method

Given: PQRS is a trapezium with QR || PS. PR = RS, ∠PQR = 96°, and ∠QPR = 34°.

Formula Used: Angle sum property of a triangle (Sum = 180°) and alternate interior angles property (when two lines are parallel).

Calculations:

⇒ In ΔPQR, ∠PQR + ∠QPR + ∠PRQ = 180°

⇒ 96° + 34° + ∠PRQ = 180°

⇒ 130° + ∠PRQ = 180°

⇒ ∠PRQ = 50°

⇒ Since QR || PS, ∠SPR = ∠PRQ (Alternate Interior Angles)

⇒ ∠SPR = 50°

⇒ In ΔPRS, given PR = RS, therefore ∠PSR = ∠SPR = 50° (Angles opposite to equal sides)

⇒ ∠PRS + ∠PSR + ∠SPR = 180°

⇒ ∠PRS + 50° + 50° = 180°

⇒ ∠PRS + 100° = 180°

⇒ ∠PRS = 80°

∴ The correct answer is 80°.

Additional Information

Isosceles Triangle Property

In a triangle, if two sides are equal, the angles opposite to those sides are also equal.

Parallel Lines & Transversals

When a transversal intersects two parallel lines, the alternate interior angles are always equal.

Angle Sum Property

The sum of all interior angles of any triangle is always 180°.

The correct answer is starch.

Key Points

• Plants store carbohydrates in the form of starch, which is a polysaccharide.
• Starch consists of two types of molecules: amylose (linear) and amylopectin (branched).
• It serves as an internal energy reserve for plants, used during periods of low photosynthetic activity.
• Starch is stored in plastids, such as chloroplasts and amyloplasts, within plant cells.
• When energy is required, starch is broken down into glucose by enzymatic processes.

Additional Information

• Cellulose
• Cellulose is a structural polysaccharide and a major component of the plant cell wall.
• It is composed of linear chains of glucose molecules linked by β-1,4-glycosidic bonds.
• Unlike starch, cellulose cannot be digested by humans but can be broken down by some herbivores and microorganisms.
• Glucose
• Glucose is a simple monosaccharide sugar that serves as a primary energy source for cells.
• It is directly used in cellular respiration to produce ATP.
• Excess glucose can be converted into starch for storage in plants.
• Glycogen
• Glycogen is a storage form of glucose in animals and fungi, similar to starch in plants.
• It is highly branched and stored mainly in the liver and muscle tissues.
• Glycogen is broken down into glucose when energy is needed by the body.

The correct answer is Sclerenchyma.

Key Points

• Sclerenchyma is a type of supportive tissue in plants, characterized by thickened, lignified cell walls.
• It is present in stems, around vascular bundles, in the veins of leaves, and the hard covering of seeds and nuts, providing structural support and strength.
• Sclerenchyma cells are typically dead at maturity and provide rigidity and support to the plant.
• This tissue is further divided into two types: fibers and sclereids, both contributing to the plant's mechanical strength.

Additional Information

• Apical Meristem
• It is a tissue found at the tips of roots and shoots, responsible for the primary growth of the plant.
• Cells in the apical meristem are undifferentiated and actively divide to allow the plant to grow in length.
• Epidermis
• It is the outermost layer of cells covering the leaves, flowers, roots, and stems of plants.
• The epidermis serves as a protective barrier against environmental stress and pathogens.
• Parenchyma
• This tissue is composed of living cells that are often involved in storage, photosynthesis, and tissue repair.
• Parenchyma cells have thin cell walls and are found throughout the plant.
• Collenchyma
• It is a type of plant tissue that provides support to growing parts of the plant, such as young stems and leaves.
• Collenchyma cells have unevenly thickened cell walls and are typically living at maturity.

Given series: (Left) 2 9 + % 8 4 5 3 @ $ 7 & Ω # 1 * £ (Right)

According to the question,

Condition:  symbols - symbols -  number

 2 9 + % 8 4 5 3 @ $ 7 & Ω # 1 * £

Thus, there are 3 symbols which are preceded by a symbols and immediately followed by number.

Hence, "Option 3" is the correct answer.

Shortcut Trick

Find the LCM of 8 and 12.

Multiples of 12: 12, 24, 36... Since 24 is divisible by 8, LCM(8, 12) = 24.

Smallest 3-digit number is 100. Divide 100 by 24: 100 ÷ 24 = 4 with remainder 4.

Next multiple of 24 after 100 is 24 × 5 = 120.

∴ The correct answer is 120.

Alternate Method

Given: Divisors are 8 and 12.

Formula Used: Required number = Smallest multiple of LCM(8, 12) that is ≥ 100.

⇒ Prime factorization of 8 = 2 × 2 × 2 = 2³

⇒ Prime factorization of 12 = 2 × 2 × 3 = 2² × 3

⇒ LCM(8, 12) = 2³ × 3 = 8 × 3 = 24

⇒ Smallest 3-digit number = 100

⇒ 100 ÷ 24: Quotient = 4, Remainder = 4

⇒ Smallest 3-digit multiple = 24 × (4 + 1) = 24 × 5 = 120

∴ The correct answer is 120.

Additional Information

LCM (Least Common Multiple)

The smallest positive integer that is divisible by both a and b. It is the product of the highest powers of all prime factors involved.

Divisibility Rule of 8

A number is divisible by 8 if its last three digits are divisible by 8. For 3-digit numbers, use direct division.

Divisibility Rule of 12

A number is divisible by 12 if it is simultaneously divisible by both 3 (sum of digits rule) and 4 (last two digits rule).

Shortcut Trick

Ratio of shares A : B : C = 5 : 7 : 15.

Given B's share (7 units) = ₹1,400.

Total units = 5 + 7 + 15 = 27 units.

Total amount = (1,400 ÷ 7) × 27 = 200 × 27 = ₹5,400.

∴ The correct answer is ₹5,400.

Alternate Method

Given:

Ratio of A, B, and C = 5 : 7 : 15

B's share = ₹1,400

Calculations:

⇒ Let the shares be 5x, 7x, and 15x.

⇒ 7x = 1,400

⇒ x = 1,400 ÷ 7 = 200

⇒ Total amount = 5x + 7x + 15x = 27x

⇒ Total amount = 27 × 200 = ₹5,400

∴ The correct answer is ₹5,400.

Additional Information

Concept of Ratio Distribution

To find an individual's share, use the formula: (Individual Ratio ÷ Sum of Ratios) × Total Amount.

Compound Ratio

If ratios are given as A:B and B:C, the combined ratio A:B:C is calculated by equating the common term B.

Direct Proportion in Sharing

The actual value of each share is directly proportional to its respective ratio part when the total amount is constant.

The correct answer is Solid particles are more closely packed than gas particles.

Key Points

• Solid particles are more closely packed than gas particles, leading to a fixed shape and volume for solids.
• In solids, the particles are in a fixed, orderly arrangement, resulting in a rigid structure.
• Gas particles are spread out and move freely, leading to no fixed shape or volume for gases.
• The close packing of solid particles results in higher density compared to gases.
• Solids have lower kinetic energy in their particles compared to gases, where particles move rapidly and randomly.

Additional Information

• States of Matter:
• Matter exists primarily in three states: solid, liquid, and gas.
• Each state is characterized by different arrangements and movements of its particles.
• Kinetic Theory of Gases:
• This theory explains the behavior of gas particles, stating that they are in constant, random motion.
• The temperature of a gas is a measure of the average kinetic energy of its particles.
• Density and Volume:
• Density is the mass per unit volume of a substance.
• Solids generally have higher density than gases due to closer particle packing.
• Intermolecular Forces:
• These are forces that hold particles together in a solid or liquid.
• In solids, intermolecular forces are strong, giving solids a definite shape and volume.
• In gases, these forces are negligible, allowing particles to move independently.

Given: 23 × 13 - 7 ÷ 14 + 7 = ?

According to the question,  '-' and '×' are interchanged and '+' and '+' are interchanged

23 × 13 - 7 ÷ 14 + 7 = ?

⇒ 23 - 13 × 7 + 14 ÷ 7 = ?

​⇒ 23 - 91 + 2

​⇒ 25 - 91 = -66

Hence, the correct answer is "Option 1".

The correct answer is Only (C).

Key Points

• Equation (C), $(v-u)=at$, is derived from the basic definition of acceleration: acceleration (a) is the rate of change of velocity with time (t).
• This equation applies directly to uniformly accelerated motion, such as that of a freely falling object under gravity.
• It relates the final velocity (v) of an object to its initial velocity (u), acceleration (a), and the time of travel (t).
• Equations (A) and (B) are not correctly written or applicable in the context of a freely falling object.

Additional Information

• Equations of Motion:
• There are three primary equations of motion that describe the behavior of objects in uniformly accelerated linear motion:
• $v=u+at$
• $s=ut+\frac{1}{2}at^2$
• $v^2=u^2+2as$
• These equations are essential in classical mechanics and are used to predict future motion based on current conditions.
• Uniform Acceleration:
• Uniform acceleration refers to a constant acceleration, meaning the velocity of the object changes at a constant rate.
• In the case of free fall, the acceleration due to gravity (g) is approximately 9.81 m/s² near the Earth's surface.
• Free Fall:
• Free fall is the motion of an object under the influence of gravitational force only.
• During free fall, the only force acting on the object is gravity, leading to a uniform acceleration downwards.
• Initial and Final Velocity:
• Initial velocity (u) is the velocity of the object before it starts accelerating.
• Final velocity (v) is the velocity of the object after it has been accelerating for a certain period of time.

The correct answer is Cytokinin.

Key Points

• Cytokinins are a class of plant hormones that promote cell division, or cytokinesis, in plant roots and shoots.
• They are present in higher concentrations in areas of rapid cell division such as growing tissues and meristems.
• Cytokinins work in conjunction with auxins to stimulate cell division, elongation, and differentiation.
• These hormones play a crucial role in various plant growth processes, including leaf expansion, chloroplast development, and delay of senescence (aging).

Additional Information

• Abscisic Acid (ABA)
• It is a plant hormone that plays a major role in plant stress responses, including stomatal closure during drought stress.
• ABA inhibits cell division and promotes leaf and fruit abscission (dropping).
• Gibberellins
• These are plant hormones that promote stem elongation, seed germination, and flowering.
• They work by breaking seed dormancy and aiding in the mobilization of nutrients during seed germination.
• Auxins
• Auxins are crucial for the regulation of plant growth and development.
• They are primarily involved in cell elongation, root initiation, and response to light (phototropism) and gravity (gravitropism).
• Plant Meristems
• Meristems are regions in plants where active cell division occurs, leading to the growth of new tissues.
• There are two main types of meristems: apical meristems (found at the tips of roots and shoots) and lateral meristems (responsible for secondary growth).

The logic followed here is:

Option 1) FAW

Option 2) XSN

Option 3) EZU

Option 4) WRM

Hence, the correct answer is "Option 1

The correct answer is 8.

Key Points

• According to the Bohr model, the second energy level can hold a maximum of 8 electrons.
• Electrons in an atom are arranged in energy levels or shells, which are denoted by the principal quantum number (n).
• The formula to determine the maximum number of electrons in a shell is given by 2n², where n is the principal quantum number.
• For the second energy level (n=2), the maximum number of electrons is calculated as 2(2)² = 8.
• This concept is foundational to understanding the electron configuration of atoms and their chemical properties.

Additional Information

• Principal Quantum Number (n)
• It denotes the energy level of an electron within an atom.
• The value of n determines the size and energy of the orbital.
• Higher values of n correspond to higher energy levels and larger orbitals.
• Bohr Model
• Proposed by Niels Bohr in 1913, it describes electrons orbiting the nucleus in fixed energy levels.
• Electrons can jump between energy levels by absorbing or emitting specific amounts of energy.
• The model helped explain the spectral lines of hydrogen.
• Electron Configuration
• It describes the distribution of electrons in the different energy levels or orbitals of an atom.
• It follows a specific order based on the Aufbau principle, Pauli exclusion principle, and Hund's rule.
• Electron configuration helps predict chemical behavior and bonding.
• Aufbau Principle
• It states that electrons fill lower energy orbitals first before moving to higher energy orbitals.
• This principle guides the order in which atomic orbitals are filled.

Shortcut Trick

Time taken to fill half the tank by 1 tap = 6 ÷ 2 = 3 hours.

The remaining half of the tank is filled by 4 identical taps (1 original + 3 new).

Time taken by 4 taps to fill the remaining half = Time taken by 1 tap ÷ 4 = 3 ÷ 4 hours = 45 minutes.

Total time = 3 hours + 45 minutes = 3 hours 45 min.

∴ The correct answer is 3 hours 45 min.

Alternate Method

⇒ Let the total capacity of the tank be the LCM = 6 units.

⇒ Efficiency of 1 tap = 1 unit/hour.

⇒ Time taken by 1 tap to fill half the tank (3 units) = 3 ÷ 1 = 3 hours.

⇒ Remaining work to be done = 6 − 3 = 3 units.

⇒ Now, 3 more similar taps are opened. Total taps operating = 1 + 3 = 4 taps.

⇒ Combined efficiency of 4 taps = 4 × 1 = 4 units/hour.

⇒ Time taken to complete the remaining work = Remaining work ÷ Efficiency = 3 ÷ 4 hours.

⇒ Converting into minutes = (3 ÷ 4) × 60 = 45 minutes.

⇒ Total time taken to fill the tank completely = 3 hours + 45 minutes = 3 hours 45 min.

∴ The correct answer is 3 hours 45 min.

Additional Information

Pipes & Cisterns Net Work

If pipe A fills a tank in x hours and pipe B fills it in y hours, their combined 1 hour work is (1/x + 1/y).

Efficiency of Multiple Identical Sources

When n identical taps are opened simultaneously, their combined efficiency becomes n times the efficiency of a single tap, effectively reducing the time required to 1/n.

Work Equivalence

Total Work = Number of identical workers (or taps) × Time taken × Efficiency. This is a direct application of the unitary method in Time & Work.

The correct answer is Kerala.

Key Points

• The 4^th Asmita Khelo India National Judo League/Ranking Judo Tournament 2024-25 was held in Kerala.
• This tournament is part of the Khelo India initiative, which aims to promote sports at the grassroots level across India.
• The event witnessed participation from various states, showcasing the best judo talents in the country.
• It serves as a platform for young athletes to gain national exposure and compete at a high level.
• The tournament is organized annually under the auspices of the Ministry of Youth Affairs and Sports, Government of India.

Additional Information

• Khelo India Programme
• Launched by the Government of India in 2018 to revive the sports culture in India at the grassroots level.
• Aims to encourage mass participation and excellence in sports.
• Focuses on building sports infrastructure and providing financial assistance to promising athletes.
• Includes initiatives like Khelo India Youth Games, Khelo India University Games, and the development of sports academies.
• Judo
• A modern martial art, combat, and Olympic sport created in Japan in 1882 by Jigoro Kano.
• The objective is to throw or takedown the opponent to the ground, immobilize them, or force them into submission.
• Judo became an official Olympic sport for men in 1964 and for women in 1992.
• It emphasizes the principles of maximum efficiency and mutual welfare and benefit.

The correct answer is First athlete of independent India to win two Olympic medals in a single edition.

Key Points

• Manu Bhaker became the first athlete of independent India to win two Olympic medals in a single edition at the 2024 Paris Olympics.
• She achieved this historic feat by securing medals in both the individual women's 10m air pistol event and the mixed team 10m air pistol event.
• This landmark achievement marks a significant milestone in India's Olympic history, showcasing her exceptional talent and dedication.
• Manu Bhaker's performance at the 2024 Paris Olympics has inspired many young athletes in the country to pursue their dreams in sports.

Additional Information

• Olympic Shooting Events:
• Shooting events in the Olympics are divided into rifle, pistol, and shotgun categories.
• Competitors aim to hit targets with precision to score points, with the highest scores winning medals.
• Events are held for both men and women, individually and in teams.
• 10m Air Pistol:
• This is a precision shooting event where competitors shoot at a target 10 meters away.
• It involves shooting 60 shots within a time limit, and the highest total score determines the winner.

Given Series: 2 % 8 4 5 3 @ # 1 * $ 7 & 9 + Ω 6 £ 

Condition: number - number - symbol

2 % 8 4 5 3 @ # 1 * $ 7 & 9 + Ω 6 £ 

Thus, here only 1 follow the condition.

Hence, the correct answer is "Option 1".

The correct answer is Violet.

Key Points

• When white light passes through a prism, it gets dispersed into its constituent colours, forming a spectrum.
• The deviation of light is due to the phenomenon of refraction, which occurs as light changes speed when passing through different media.
• Violet light deviates the most because it has the shortest wavelength among the visible spectrum.
• Due to its shorter wavelength, violet light is refracted at a greater angle compared to other colours.
• This increased deviation is why violet appears at the bottom of the spectrum when white light is dispersed by a prism.

Additional Information

• Dispersion of Light
• Dispersion occurs when light separates into its different colour components due to varying degrees of refraction for different wavelengths.
• This phenomenon is often observed with a prism or in natural occurrences like rainbows.
• Refraction
• Refraction is the bending of light as it passes from one medium to another with a different density.
• The amount of bending depends on the indices of refraction of the two media and the angle of incidence.
• Spectrum of Visible Light
• The visible spectrum consists of colours red, orange, yellow, green, blue, indigo, and violet (ROYGBIV).
• These colours correspond to wavelengths roughly between 400 nm (violet) and 700 nm (red).

Given:

Expression = 3 + 6 × (5 + 4) ÷ 3 − 7

Formula used:

BODMAS Rule (Brackets, Of, Division, Multiplication, Addition, Subtraction)

Calculations:

3 + 6 × (5 + 4) ÷ 3 − 7

⇒ 3 + 6 × 9 ÷ 3 − 7

⇒ 3 + 6 × 3 − 7

⇒ 3 + 18 − 7

⇒ 21 − 7

⇒ 14

∴ The correct answer is option (3).

Given:

Number to be subtracted from = −3/10

Number to be subtracted = −2

Formula used:

Result = (Value 1) − (Value 2)

Calculations:

Result = (−3/10) − (−2)

⇒ Result = −3/10 + 2

⇒ Result = (−3 + 20)/10

⇒ Result = 17/10

⇒ Result = 1 7/10

∴ The correct answer is option (4).

The logic followed here is:

Logic: The difference of number is 91.

Hence, the correct answer is "Option 1".

Given:

Exports by Company X in January = 95 crores

Exports by Company X in March = 85 crores

Exports by Company Y in January = 100 crores

Exports by Company Y in March = 100 crores

Formula used:

Total exports = Exports by Company X (Jan) + Exports by Company X (Mar) + Exports by Company Y (Jan) + Exports by Company Y (Mar)

Calculation:

⇒ Total exports = 95 + 85 + 100 + 100

⇒ Total exports = 380 crores

∴ The total exports by Company X and Y in January and March is 380 crores.

The correct answer is 40 m/s.

Key Points

• Formula: v = u + at
• Given: initial velocity (u) = 20 m/s, acceleration (a) = 4 m/s², and time (t) = 5 seconds.
• Substituting the values into the formula: v = 20 m/s + (4 m/s² * 5 s).
• The calculation yields: v = 20 m/s + 20 m/s = 40 m/s.
• Thus, the final velocity of the train after 5 seconds is 40 m/s.

Additional Information

• Uniform Acceleration:
• It occurs when an object's velocity changes at a constant rate.
• The equations of motion for uniformly accelerated motion are key tools in physics to predict the future position and velocity of an object.
• Equations of Motion:
• There are three main equations used to describe motion under uniform acceleration:
• $v=u+at$
• $s=ut+\frac{1}{2}at^2$
• $v^2=u^2+2as$
• These equations are essential for solving various problems in kinematics.
• Velocity:
• Velocity is a vector quantity that refers to the rate at which an object changes its position.
• It has both magnitude and direction, distinguishing it from speed, which is a scalar quantity.
• Acceleration:
• Acceleration is the rate of change of velocity of an object with respect to time.
• It is a vector quantity and can be caused by changes in speed, direction, or both.

The correct answer is It was linked to British colonial legacy..

Key Points

• The statue of John Nicholson was linked to the British colonial rule in India.
• John Nicholson was a British Army officer known for his role during the Indian Rebellion of 1857.
• The government's move aligns with the broader effort to address and rectify colonial-era symbols in public spaces.
• Removing such statues is part of the decolonization process and the reassertion of Indian historical and cultural identity.

Additional Information

• John Nicholson
• He was a British officer known for his role in suppressing the Indian Rebellion of 1857.
• He is often remembered for his brutal methods against Indian rebels.
• His actions and legacy are controversial, seen as oppressive by many in India.
• Indian Rebellion of 1857
• Also known as the First War of Indian Independence.
• It marked a significant resistance against British rule in India.
• The revolt led to the dissolution of the East India Company and the reorganization of British governance in India.
• Decolonization
• The process of decolonization involves the removal of colonial symbols and the reassertion of indigenous culture and history.
• It is aimed at addressing the historical injustices and colonial narratives.
• Many countries have undertaken similar initiatives to reclaim their cultural heritage.
• Government's Efforts
• The Indian government has been actively removing colonial-era statues and symbols.
• It is part of a broader initiative to promote national pride and cultural heritage.
• Such efforts include renaming streets and institutions that bear colonial names.

The correct answer is 0.4 m/s².

Key Points

• The initial velocity (u) of Raju's bicycle is 0 m/s as he starts from rest.
• The final velocity (v) reached by Raju's bicycle is 24 m/s.
• The time (t) taken to reach this velocity is 60 seconds (1 minute).
• Acceleration (a) can be calculated using the formula: $a=\frac{(v-u)}{t}$
• Substituting the values: a = (24 m/s - 0 m/s) / 60 s = 0.4 m/s².

Additional Information

• Acceleration
• Acceleration is the rate of change of velocity of an object with respect to time.
• It is a vector quantity, which means it has both magnitude and direction.
• Common units of acceleration are meters per second squared (m/s²).
• Velocity
• Velocity is the speed of an object in a given direction.
• It is also a vector quantity.
• The SI unit of velocity is meters per second (m/s).
• Distance and Displacement
• Distance is the total path covered by an object, irrespective of direction.
• Displacement is the shortest distance from the initial to the final position of an object in a straight line.
• Both are measured in meters (m).
• Kinematic Equations
• Kinematic equations relate the motion of an object to time, velocity, acceleration, and displacement.
• They are used to solve problems involving linear motion with constant acceleration.
• Examples include: 
• $v=u+at$
• $s=ut+\frac{1}{2}at^2$
• $v^2=u^2+2as$

The logic followed here is:

For, TX-VS-WY

For, UY-WT-XZ

Let's check options one by one:

Option 1) FJ-HE-IL

Option 2) OS-QN-RT

Here, it follow the pattern.

Option 3) LP-NK-OR

Option 4) IM-KH-LO

Hence, the correct answer is "Option 2".

The correct answer is Glomerulus.

Key Points

• The glomerulus is a network of capillaries located at the beginning of a nephron in the kidney.
• It is involved in the filtration of blood to form urine.
• The glomerulus allows the passage of water, ions, and small molecules from the blood into the Bowman's capsule.
• It retains large molecules like proteins and blood cells within the bloodstream.

Additional Information

• Nephron
• The nephron is the functional unit of the kidney responsible for urine formation.
• Each nephron includes a glomerulus and a renal tubule.
• There are approximately 1 million nephrons in each human kidney.
• The nephron performs essential functions like filtration, reabsorption, secretion, and excretion.
• Bowman's Capsule
• The Bowman's capsule is a cup-like sac that encases the glomerulus.
• It collects the filtrate that emerges from the glomerulus.
• This structure initiates the process of filtering blood to form urine.
• Renal Tubule
• The renal tubule processes the filtrate from the Bowman's capsule.
• It includes segments like the proximal convoluted tubule, loop of Henle, distal convoluted tubule, and collecting duct.
• Each segment plays a specific role in reabsorbing water and solutes or secreting substances into the filtrate.
• Filtration Barrier
• The filtration barrier in the glomerulus consists of three layers: endothelial cells, basement membrane, and podocytes.
• It selectively allows the passage of small molecules while preventing large molecules like proteins from passing through.
• This barrier is crucial for maintaining the composition of blood and filtrate.

The logic followed here is:

The code for "R" is "7".

Hence, the correct answer is "Option 4".

The correct answer is Binary fission.

Key Points

• Binary fission is a type of asexual reproduction common among prokaryotes such as bacteria.
• In binary fission, an organism duplicates its genetic material and then divides into two equal-sized daughter cells.
• This process ensures that each daughter cell receives a copy of the parent organism's genetic material.
• Binary fission is efficient and allows for rapid population growth, especially in favorable environments.

Additional Information

• Regeneration
• Regeneration is the process by which certain organisms can regrow lost or damaged parts of their body.
• Examples include the regrowth of limbs in starfish or tails in lizards.
• This is different from binary fission as it involves repairing or replacing damaged structures rather than creating new organisms.
• Budding
• Budding is another form of asexual reproduction where a new organism develops from an outgrowth or bud due to cell division at one particular site.
• It is commonly observed in yeast and some invertebrates like hydra.
• Unlike binary fission, budding results in the formation of a new organism while the parent organism remains.
• Spore formation
• Spore formation is a method of asexual reproduction that involves the formation of spores by the parent organism.
• These spores are typically resistant to extreme conditions and can remain dormant for long periods.
• When conditions become favorable, spores germinate to form new organisms.
• This is a common reproductive strategy among fungi and some bacteria.

The correct answer is Connective tissue.

Key Points

• Connective tissue is one of the four main types of tissue in the body, the others being epithelial, muscle, and nervous tissues.
• Nerve fibers are bound together by connective tissue, which provides structural support and protection.
• In nerves, connective tissue layers are classified into endoneurium, perineurium, and epineurium.
• The endoneurium surrounds individual nerve fibers, the perineurium surrounds bundles of nerve fibers (fascicles), and the epineurium surrounds the entire nerve.
• This hierarchical organization of connective tissue ensures that nerves are protected and can function effectively.

Additional Information

• Types of Connective Tissue:
• Loose connective tissue: Includes areolar, adipose, and reticular tissues.
• Dense connective tissue: Includes dense regular, dense irregular, and elastic tissues.
• Functions of Connective Tissue:
• Provides structural support to organs and tissues.
• Protects and insulates internal organs.
• Stores energy reserves, particularly in the form of fat.
• Transports substances within the body, particularly through blood, which is a type of connective tissue.
• Nerve Structure:
• Nerves are composed of neurons, the fundamental units of the nervous system that transmit signals.
• Neurons are surrounded by myelin sheaths, which are produced by Schwann cells in the peripheral nervous system.
• Connective Tissue Disorders:
• Examples include Ehlers-Danlos syndrome, Marfan syndrome, and systemic lupus erythematosus.
• These disorders can affect the integrity and function of connective tissues, leading to a variety of symptoms and complications.

The logic followed here is:

The code for "the" is "ot".

Hence, the correct answer is "Option 2".

The correct answer is Shri Nayab Singh Saini.

Key Points

• Shri Nayab Singh Saini took the oath as the new Chief Minister of Haryana after the Assembly Election 2024.
• He succeeded Shri Manohar Lal Khattar, who served as the Chief Minister of Haryana from 2014 to 2024.
• Shri Nayab Singh Saini is known for his work in the Haryana Legislative Assembly and his efforts towards the development of the state.
• His election as the Chief Minister marks a significant change in the political landscape of Haryana.

Additional Information

• Haryana Legislative Assembly
• The Haryana Legislative Assembly, also known as the Haryana Vidhan Sabha, is the unicameral state legislature of Haryana.
• It consists of 90 members who are elected every five years.
• The assembly meets at Vidhan Bhavan in Chandigarh, the capital of Haryana.
• Chief Minister of Haryana
• The Chief Minister of Haryana is the head of the government of the Indian state of Haryana.
• The Chief Minister is appointed by the Governor of Haryana.
• The term of the Chief Minister is for five years, subject to no term limits.
• Political Landscape of Haryana
• Haryana has a multi-party political system with major parties including the Bharatiya Janata Party (BJP), Indian National Congress (INC), and the Jannayak Janata Party (JJP).
• The state has seen significant political shifts over the years, with various parties forming the government at different times.
• Development Initiatives in Haryana
• Haryana has been focusing on various development initiatives across sectors such as agriculture, education, and infrastructure.
• Recent governments have emphasized the importance of industrial development and improving the ease of doing business in the state.

The correct answer is Only 2.

Key Points

• Double displacement reactions involve the exchange of ions between two compounds to form new compounds.
• In the reaction Na2SO4(aq) + BaCl2(aq) → BaSO4(s) + 2NaCl(aq), the sulfate (SO4^2-) and chloride (Cl^-) ions are displaced and form new products.
• This type of reaction typically produces a precipitate, a gas, or water.
• Double displacement reactions are also known as metathesis reactions.

Additional Information

• Single Displacement Reactions
• Involve one element being replaced by another in a compound.
• Example: Pb(s) + CuCl2(aq) → PbCl2(aq) + Cu(s).
• Combination Reactions
• Two or more substances combine to form a single product.
• Example: C(s) + O2(g) → CO2(g).
• Decomposition Reactions
• A single compound breaks down into two or more simpler substances.
• Example: CaCO3(s) → CaO(s) + CO2(g).
• Precipitation Reactions
• A type of double displacement reaction where an insoluble solid (precipitate) forms.
• Example: Na2SO4(aq) + BaCl2(aq) → BaSO4(s) + 2NaCl(aq).

Given:

Expression: 5 + 9 − 9 ÷ 3 × 4

Formula used:

The BODMAS/VBODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction) defines the order of operations.

Calculations:

Step 1: Perform Division (9 ÷ 3)

⇒ 5 + 9 − 3 × 4

Step 2: Perform Multiplication (3 × 4)

⇒ 5 + 9 − 12

Step 3: Perform Addition (5 + 9)

⇒ 14 − 12

Step 4: Perform Subtraction (14 − 12)

⇒ 2

∴ The correct answer is option (3).

Shortcut Trick

Sum of observations = Average × Number of observations.

Total sum of two numbers = M × 2 = 2M.

Other number = Total Sum − First Number = 2M − N.

∴ The correct answer is 2M-N.

Alternate Method

Given:

Average of two numbers = M

One number = N

Let the second number be x.

Formula Used:

Average = (Sum of all observations) ÷ (Total number of observations)

Calculations:

⇒ M = (N + x) ÷ 2

⇒ 2 × M = N + x

⇒ 2M = N + x

⇒ x = 2M − N

∴ The correct answer is 2M-N.

Additional Information

Definition of Average (Arithmetic Mean)

It is the central value of a set of data, calculated by dividing the total sum by the count of values.

Sum Calculation

The sum of n observations is always n × Average. This is the base for solving missing number problems.

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the new average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

The correct answer is cotton is a good absorber of water and exposes sweat to atmosphere for evaporation.

Key Points

• Cotton fabric is highly breathable, allowing air to circulate around the skin and sweat to evaporate.
• Cotton is a natural fiber known for its ability to absorb moisture effectively.
• When sweat is absorbed by cotton, it exposes a larger surface area for evaporation, which helps in cooling the body.
• Evaporation of sweat from cotton clothes results in a cooling effect on the body, making it a preferred choice for summer wear.
• Cotton’s moisture-wicking properties help in maintaining body temperature and prevent overheating during hot weather.

Additional Information

• Evaporation Process
• Evaporation is the process by which water changes from a liquid to a gas or vapor.
• This process requires heat energy, which is taken from the surroundings, resulting in a cooling effect.
• The efficiency of evaporation increases with higher temperatures and lower humidity levels.
• Breathable Fabrics
• Fabrics like cotton, linen, and some synthetic materials are designed to be breathable.
• Breathable fabrics allow air to pass through them, aiding in moisture wicking and temperature regulation.
• Such fabrics are ideal for active wear and hot weather clothing.
• Moisture-Wicking
• Moisture-wicking refers to the ability of a fabric to pull moisture away from the skin to the fabric's outer surface.
• This helps in quicker evaporation and keeps the body dry and comfortable.
• It is a key feature in athletic and performance clothing.
• Thermal Regulation
• Thermal regulation is the process by which the body maintains its core internal temperature.
• Proper clothing can assist in thermal regulation by providing insulation and aiding in heat dissipation.
• Cotton helps in maintaining thermal comfort by allowing heat to escape and sweat to evaporate.

The logic followed here is:

Logic: 1^st number × 6 = 2^nd number.

For, X : 72

⇒ X × 6 = 72

⇒ X = 72 ÷ 6 = 12.

Similarly,

For,  22 : Y

⇒ 22 × 6 = Y

⇒ 132 = Y.

Thus, X = 12, Y = 132

Hence, the correct answer is "Option 1".

The correct answer is Faraday.

Key Points

• Michael Faraday discovered the principle of electromagnetic induction in 1831.
• Faraday’s law of electromagnetic induction states that an electromotive force is induced in a conductor when there is a change in the magnetic field around it.
• This discovery laid the foundation for the development of electric generators and transformers.
• Faraday's experiments demonstrated that a changing magnetic field could produce an electric current, which is the basic principle behind many types of electrical devices.

Additional Information

• Electromagnetic Induction:
• It is the production of voltage across a conductor situated in a changing magnetic field or a conductor moving through a stationary magnetic field.
• Faraday’s law mathematically describes how a time varying magnetic field creates an electric field.
• Electromagnetic induction is the working principle behind electrical components like inductors and transformers.
• Lenz's Law:
• Formulated by Heinrich Lenz in 1834, it states that the direction of the induced current will be such that it opposes the change in the magnetic field that produced it.
• Lenz's Law is a consequence of the law of conservation of energy.
• Applications of Electromagnetic Induction:
• Used in the generation of electric power in power plants.
• Essential in the functioning of transformers, which transfer electric energy between circuits.
• Induction motors utilize this principle to convert electrical energy into mechanical energy.

The correct answer is The rate of diffusion of liquids is higher than that of solids..

Key Points

• Liquids have no fixed shape but take the shape of the container they are in.
• Liquids have a definite volume but no fixed shape.
• The intermolecular forces in liquids are weaker than in solids, allowing for higher rates of diffusion.
• The rate of diffusion in liquids is higher than that in solids due to the greater mobility of liquid molecules.

Additional Information

• Diffusion
• Diffusion is the process by which molecules spread from areas of high concentration to areas of low concentration.
• In liquids, diffusion occurs faster than in solids because the molecules are more mobile.
• Temperature affects the rate of diffusion; higher temperatures increase the rate.
• Intermolecular Forces
• Intermolecular forces are forces of attraction or repulsion between neighboring particles (atoms, molecules, or ions).
• In liquids, these forces are weaker than in solids, enabling easier movement of particles.
• Fluidity
• Fluidity is the ability of a substance to flow and take the shape of its container.
• Liquids and gases exhibit fluidity, with liquids being less compressible than gases.
• Viscosity
• Viscosity is a measure of a liquid's resistance to flow.
• Liquids with high viscosity flow slower than those with low viscosity.

The correct answer is Sahayogi Mahila Bagraisai.

Key Points

• Chami Murmu is an Indian environmental activist known for her significant contributions to environmental conservation.
• She founded the organization Sahayogi Mahila Bagraisai, which focuses on tree plantation and environmental sustainability.
• Under her leadership, the organization has planted over 3 million trees in the state of Jharkhand.
• In recognition of her efforts, she was awarded the Padma Shri in 2024, one of India's highest civilian honors.

Additional Information

• Padma Shri Award
• It is the fourth highest civilian award in the Republic of India.
• It is awarded to individuals for distinguished contributions in various fields including arts, education, industry, literature, science, sports, medicine, social service, and public affairs.
• The award is announced annually on Republic Day.
• Environmental Activism in India
• India has a rich history of environmental activism, addressing issues such as deforestation, pollution, and wildlife conservation.
• Notable environmental movements include the Chipko Movement and the Narmada Bachao Andolan.
• Tree Plantation Initiatives
• Tree plantation is a crucial activity in combating climate change and promoting biodiversity.
• Various NGOs and government schemes in India focus on large-scale tree plantation drives.
• Jharkhand
• Jharkhand is a state in eastern India known for its diverse flora and fauna.
• It is rich in mineral resources and has significant forest cover.

The correct answer is Vacuoles.

Key Points

• Vacuoles are membrane-bound organelles found in both plant and animal cells, but they differ significantly in size and function between the two.
• In plant cells, vacuoles are typically very large and can occupy up to 90% of the cell's volume, serving as storage for nutrients, waste products, and helping in maintaining turgor pressure.
• In animal cells, vacuoles are generally smaller and more numerous, primarily involved in storage, waste disposal, and intracellular digestion.
• The large central vacuole in plant cells plays a crucial role in maintaining the cell's shape and structure by exerting internal pressure against the cell wall.

Additional Information

• Lysosomes
• Lysosomes are small organelles containing digestive enzymes, primarily involved in breaking down waste materials and cellular debris.
• They are more prominent in animal cells and play a role in autophagy, the process of degrading and recycling cellular components.
• Plastids
• Plastids are a group of organelles found in plant cells and some algae, involved in the synthesis and storage of food.
• Chloroplasts, a type of plastid, are responsible for photosynthesis in plant cells.
• Golgi Apparatus
• The Golgi apparatus is involved in modifying, sorting, and packaging proteins and lipids for secretion or use within the cell.
• It is present in both plant and animal cells, but does not differ significantly in size between the two.

The correct answer is ISRO and JAXA.

Key Points

• The Lunar Polar Exploration Mission (LUPEX) is a collaborative lunar mission planned by the Indian Space Research Organisation (ISRO) and the Japan Aerospace Exploration Agency (JAXA).
• LUPEX aims to explore the south pole region of the Moon to assess the presence of water and other resources.
• The mission will include a lunar rover and a lander, with ISRO providing the lander and JAXA providing the rover.
• LUPEX is part of broader international efforts to explore and utilize lunar resources to support future human and robotic missions.

Additional Information

• ISRO (Indian Space Research Organisation)
• ISRO is the space agency of the Government of India, headquartered in Bengaluru.
• ISRO's primary objective is to harness space technology for national development while pursuing space science research and planetary exploration.
• ISRO has successfully launched numerous missions, including the Chandrayaan and Mangalyaan missions.
• JAXA (Japan Aerospace Exploration Agency)
• JAXA is the Japanese national aerospace agency responsible for space and planetary exploration.
• JAXA conducts various space missions, including satellite launches, human spaceflight, and lunar exploration.
• JAXA has been involved in international collaborations, such as the International Space Station (ISS).
• Lunar Exploration
• Lunar exploration involves the study and exploration of the Moon's surface, resources, and environment.
• It is critical for understanding the Moon's formation, geology, and potential for supporting future human missions.
• Key objectives include mapping the lunar surface, studying the presence of water ice, and assessing the feasibility of lunar habitation.
• Water on the Moon
• The presence of water on the Moon, particularly in the form of ice, is crucial for future lunar exploration and colonization.
• Water can be used for drinking, growing food, and producing oxygen for astronauts.
• Water can also be broken down into hydrogen and oxygen, which can be used as rocket fuel for missions beyond the Moon.

The correct answer is 1.01 × 10⁵ Pa.

Key Points

• One atmosphere (1 atm) is defined as being precisely equal to 101,325 Pa (Pascals).
• For practical purposes, it is commonly approximated as 1.01 × 10⁵ Pa.
• This unit of pressure is widely used in various fields, including physics, chemistry, and engineering.
• The value of 1 atm is derived from the average atmospheric pressure at sea level on Earth.
• It serves as a standard reference for pressure measurements and calculations.

Additional Information

• Pascal (Pa):
• The SI unit of pressure, equivalent to one newton per square meter.
• Bar:
• Another unit of pressure, where 1 bar = 100,000 Pa, slightly less than 1 atm.
• Standard Atmospheric Pressure:
• Often used in aviation, meteorology, and other fields to denote the pressure at sea level, defined as 101,325 Pa.
• Pressure Conversion:
• 1 atm = 1013.25 millibars (mbar)
• 1 atm = 760 mmHg (Torr)
• 1 atm = 14.696 psi (pounds per square inch)

The correct answer is Coal - digested in our body.

Key Points

• Coal is a fossil fuel formed from the remains of ancient plants and animals, and it is not a substance that can be digested by the human body.
• The human digestive system is designed to break down organic materials like carbohydrates, proteins, and fats found in food, not inorganic substances like coal.
• Materials that are undigestable by the human body are typically excreted as waste.
• Ingesting coal or other non-digestible substances can lead to serious health issues such as gastrointestinal blockage or poisoning.

Additional Information

• Digestion Process
• Digestion begins in the mouth where food is mechanically broken down by chewing and mixed with saliva.
• It continues in the stomach where gastric juices break down proteins and fats.
• The small intestine is where most nutrient absorption occurs with the help of enzymes produced by the pancreas and bile from the liver.
• Indigestible substances are passed into the large intestine where water is absorbed, and the remaining material is excreted as feces.
• Fossil Fuels
• Fossil fuels like coal, oil, and natural gas are formed over millions of years from the remains of plants and animals.
• They are used primarily for energy production but are harmful to the environment due to greenhouse gas emissions.
• Biodegradation
• Biodegradation is the process by which organic substances are broken down by living organisms, typically bacteria.
• Plastic and other synthetic materials are not easily biodegradable, leading to environmental pollution.
• Human Health
• Ingesting non-food substances can cause choking, poisoning, or internal injury.
• Medical attention should be sought immediately if non-food items are ingested.

Statements:

No car is a bus.

No bus is a plane.

The least possible Venn diagram is given:

Conclusions:

(I) No bus is a car - True(Because, No car is a bus, it implies that no bus is car).

(II) No car is a plane - False(Because, there is no direct relation given between them, so it can be possible only).

Thus, Only conclusion I follows

Hence, the correct answer is "Option 3".

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

Key Points

• The Principal Focus of a spherical mirror is a point on the principal axis where light rays parallel to the principal axis converge (in concave mirrors) or appear to diverge from (in convex mirrors).
• The Pole of a spherical mirror is the midpoint of the mirror's surface, lying on the principal axis.
• Both the principal focus and the pole always lie on the principal axis of a spherical mirror.
• The Point of incidence is the point where the light ray strikes the mirror, which does not necessarily lie on the principal axis.

Additional Information

• Spherical Mirror
• A spherical mirror is a mirror that has the shape of a piece cut out of a spherical surface. There are two types: concave and convex mirrors.
• Concave mirrors converge light rays, while convex mirrors diverge them.
• Principal Axis
• The principal axis is an imaginary line that passes through the pole and the center of curvature of the spherical mirror.
• It is the reference line for defining various properties and points related to the mirror.
• Center of Curvature
• The center of curvature is the center of the sphere from which the spherical mirror is a part.
• It lies on the principal axis, at a distance equal to the radius of curvature from the pole.
• Radius of Curvature
• The radius of curvature is the radius of the sphere from which the mirror is a part.
• It is twice the focal length in a spherical mirror.

Given:

Expression = 11/18 + 7/(−27)

Formula used:

Sum of fractions = (a/b) + (c/d) = (ad + bc) / (bd)

Calculations:

The given expression is 11/18 − 7/27

⇒ LCM of 18 and 27 = 54

⇒ (11 × 3)/54 − (7 × 2)/54

⇒ 33/54 − 14/54

⇒ (33 − 14) / 54

⇒ 19/54

∴ The correct answer is option (2).

The correct answer is Alkyne, alkene, and alkane hydrocarbons, respectively.

Key Points

• C2H2 is known as acetylene and is classified as an alkyne hydrocarbon.
• C2H4 is known as ethylene and is classified as an alkene hydrocarbon.
• C2H6 is known as ethane and is classified as an alkane hydrocarbon.
• Alkynes have a triple bond between carbon atoms, alkenes have a double bond, and alkanes have single bonds only.
• These classifications are based on the type of carbon-carbon bonds present in the molecule.

Additional Information

• Hydrocarbon Types:
• Alkanes: Saturated hydrocarbons with only single bonds between carbon atoms (e.g., methane, ethane).
• Alkenes: Unsaturated hydrocarbons with at least one double bond between carbon atoms (e.g., ethylene, propylene).
• Alkynes: Unsaturated hydrocarbons with at least one triple bond between carbon atoms (e.g., acetylene, propyne).
• Bond Characteristics:
• Single bonds (sigma bonds) allow for free rotation around the bond axis.
• Double bonds (one sigma and one pi bond) restrict rotation and create a planar structure.
• Triple bonds (one sigma and two pi bonds) are linear and the shortest and strongest among the three types.
• Uses of Hydrocarbons:
• Alkanes are primarily used as fuels and lubricants.
• Alkenes are used in the production of polymers and as intermediates in chemical reactions.
• Alkynes are used in welding and as precursors to other chemicals.
• Isomerism:
• Hydrocarbons can exhibit structural isomerism, where compounds have the same molecular formula but different structures.
• Geometric isomerism is seen in alkenes due to the restricted rotation around the double bond.

The correct answer is body design of the organisms.

Key Points

• The mode of reproduction in organisms is significantly influenced by their body structure and design.
• Organisms with simpler body designs, such as single-celled organisms, typically reproduce asexually through processes like binary fission or budding.
• More complex organisms, including most animals and plants, often reproduce sexually, involving specialized reproductive organs and processes.
• The body design can determine the feasibility and efficiency of different reproductive strategies, ensuring the survival and adaptation of species.

Additional Information

• Asexual Reproduction
• Involves a single parent and produces offspring identical to the parent.
• Common methods include binary fission, budding, fragmentation, and spore formation.
• Examples include bacteria (binary fission) and yeast (budding).
• Sexual Reproduction
• Involves the combination of genetic material from two parents to produce genetically diverse offspring.
• Involves specialized reproductive cells called gametes (sperm and egg).
• Common in animals, plants, and many other organisms.
• Reproductive Strategies
• Reproductive strategies can be influenced by environmental factors, availability of mates, and evolutionary pressures.
• Some organisms can switch between asexual and sexual reproduction based on environmental conditions.
• Adaptation and Survival
• Reproductive modes are crucial for the adaptation and survival of species in changing environments.
• Genetic diversity from sexual reproduction can enhance the resilience of populations to diseases and environmental changes.

The correct answer is ((Mass of solute)/(Mass of solution)) × 100.

Key Points

• The mass by mass percentage of a solution is calculated by dividing the mass of the solute by the mass of the solution and then multiplying by 100.
• This formula is used to express the concentration of a solution, indicating the amount of solute present in a given mass of the solution.
• The mass of the solution is the total mass of both the solute and the solvent combined.
• Mass by mass percentage is often used in chemistry and industry to prepare solutions with precise concentrations.

Additional Information

• Solution:
• A homogeneous mixture composed of two or more substances.
• In a solution, the solute is uniformly distributed within the solvent.
• Solute:
• The substance that is dissolved in a solution.
• For example, in a saltwater solution, salt is the solute.
• Solvent:
• The substance that dissolves the solute to form a solution.
• Water is known as the "universal solvent" because it can dissolve many substances.
• Concentration:
• The amount of a substance (solute) present in a certain volume or mass of the solution or solvent.
• It can be expressed in various ways, including mass by mass percentage, volume by volume percentage, and molarity.

The correct answer is Ductility.

Key Points

• Ductility is the property of a material that allows it to be drawn into thin wires.
• This property is most commonly observed in metals such as gold, silver, copper, and aluminum.
• Gold is known to be one of the most ductile metals, capable of being drawn into very fine wires.
• The measure of ductility is typically expressed as a percentage of elongation or the reduction of area in a tensile test.
• Ductility is essential for manufacturing processes like wire drawing and tube making.

Additional Information

• Malleability
• Malleability is the ability of a material to be hammered or rolled into thin sheets without breaking.
• Like ductility, malleability is a property of metals, allowing them to be shaped and formed.
• Gold and silver are also highly malleable, making them useful for various industrial and jewelry applications.
• Tensile Strength
• Tensile strength is the maximum amount of tensile stress that a material can withstand before failure.
• It is an important property for materials that are used in structures and machines.
• High tensile strength materials are often also ductile, but this is not always the case.
• Brittleness
• Brittleness is the tendency of a material to break or shatter without significant deformation when under stress.
• Brittle materials, like glass, ceramics, and some polymers, have low ductility and malleability.
• These materials are often used where high hardness and low deformability are required.
• Plasticity
• Plasticity is the ability of a material to undergo permanent deformation without breaking.
• This property is crucial for processes such as forging, molding, and stamping.
• Metals and polymers typically exhibit high plasticity.

The correct answer is Option 1.

Key Points

• The kinetic energy of an object is the energy it possesses due to its motion, not its position.
• Kinetic energy increases with the mass of the object; the formula is KE = 0.5 * m * v^2, where m is mass and v is velocity.
• Kinetic energy also increases with the square of the object's velocity.
• Potential energy, not kinetic energy, is related to the position of an object in a force field, such as gravity.

Additional Information

• Kinetic Energy (KE)
• Defined as the energy that an object possesses due to its motion.
• The SI unit of kinetic energy is the Joule (J).
• Kinetic energy is a scalar quantity; it has magnitude but no direction.
• Examples of kinetic energy include a moving car, a flying airplane, and flowing water.
• Potential Energy (PE)
• Energy possessed by an object due to its position or state.
• Examples include gravitational potential energy, elastic potential energy, and chemical potential energy.
• Potential energy can be converted into kinetic energy and vice versa.
• Work-Energy Theorem
• The work done on an object is equal to the change in its kinetic energy.
• Mathematically, W = ΔKE, where W is work done and ΔKE is the change in kinetic energy.
• Law of Conservation of Energy
• States that energy cannot be created or destroyed but can only be transformed from one form to another.
• In a closed system, the total energy remains constant.

Shortcut Trick

Loss of 15% means SP₁ = 100% − 15% = 85%.

Gain of 15% means SP₂ = 100% + 15% = 115%.

According to the question, 85% = ₹ 18,700.

Unitary method: 1% = 18,700 ÷ 85 = ₹ 220.

Therefore, 115% = 220 × 115 = ₹ 25,300.

∴ The correct answer is ₹ 25,300.

Alternate Method

Given: First Selling Price (SP₁) = ₹ 18,700, Loss% = 15%, Required Profit% = 15%.

Formulas: CP = SP × 100 ÷ (100 − Loss%) | SP = CP × (100 + Gain%) ÷ 100

⇒ Cost Price (CP) = 18,700 × 100 ÷ (100 − 15) = 18,700 × 100 ÷ 85 = ₹ 22,000.

⇒ New Selling Price (SP₂) = 22,000 × (100 + 15) ÷ 100 = 22,000 × 115 ÷ 100.

⇒ SP₂ = 220 × 115 = ₹ 25,300.

∴ The correct answer is ₹ 25,300.

Additional Information

Cost Price (CP)

The price at which an article is purchased. It is always considered as 100% in percentage calculations of profit or loss.

Selling Price (SP)

The price at which an article is sold. SP = CP + Profit OR SP = CP − Loss.

Shortcut Trick

Empirical relationship: (Mode − Mean) = 3 × (Median − Mean)

Also, (Mode − Median) = 2/3 × (Mode − Mean)

⇒ Required value = 2/3 × 16.2

⇒ Required value = 2 × 5.4 = 10.8

∴ The correct answer is 10.8.

Alternate Method

Given:

Mode − Mean = 16.2

Formula Used:

The Empirical Relationship between measures of central tendency is:

Mode = 3 × Median − 2 × Mean

Calculations:

⇒ Mode = 3 × Median − 2 × Mean

⇒ Mode + 2 × Mean = 3 × Median

⇒ Subtract 3 × Median from both sides and rearrange to find Mode − Median:

⇒ Mode − Mean = 16.2 (Equation 1)

⇒ Mean = Mode − 16.2

⇒ Substitute Mean in Empirical formula: Mode = 3 × Median − 2 × (Mode − 16.2)

⇒ Mode = 3 × Median − 2 × Mode + 32.4

⇒ 3 × Mode − 32.4 = 3 × Median

⇒ Divide by 3: Mode − 10.8 = Median

⇒ Mode − Median = 10.8

∴ The correct answer is 10.8.

Additional Information

Empirical Formula

For a moderately skewed distribution, the relationship is Mode = 3 Median − 2 Mean.

Symmetrical Distribution

In a perfectly symmetrical distribution (like the Normal Distribution), Mean = Median = Mode.

Measures of Central Tendency

Mean is the average, Median is the middle value, and Mode is the most frequent value in a data set.

The correct answer is 24 cm.

Key Points

• The radius of curvature (R) of a spherical mirror is twice the focal length (f).
• Given the focal length (f) is 12 cm, the formula R = 2f can be applied.
• By substituting f = 12 cm into the formula, we get R = 2 * 12 cm.
• Thus, the radius of curvature (R) is 24 cm.
• This relationship holds true for both concave and convex mirrors.

Additional Information

• Spherical Mirrors:
• Spherical mirrors are mirrors with a consistent curvature, such as concave and convex mirrors.
• Concave mirrors curve inward, focusing light to a point, and are used in applications like telescopes.
• Convex mirrors curve outward, spreading light out, and are used for wide-angle viewing like in vehicle side mirrors.
• Focal Length (f):
• The focal length is the distance between the mirror's surface and its focal point, where parallel rays of light either converge or appear to diverge.
• In concave mirrors, the focal point is in front of the mirror; in convex mirrors, it is behind the mirror.
• Radius of Curvature (R):
• The radius of curvature is the radius of the sphere from which the spherical mirror is a segment.
• The center of this sphere is called the center of curvature, and the radius connects it to any point on the mirror.
• Mirror Equation:
• The mirror equation relates the object distance (u), image distance (v), and the focal length (f): 1/f = 1/u + 1/v.
• This equation is essential for understanding image formation by spherical mirrors.

Given: Seven boxes, A, B, C, D, E, F and G, are kept one over the other but not necessarily in the same order.

Only C is kept above D. Only two boxes are kept between D and F.

Only G is kept below A. B is not kept immediately above F. 

Final arrangement,

Thus, E is the box is kept fourth from the top.

Hence, the correct answer is "Option 1".

Shortcut Trick

Use Value Substitution: Let A = 45°.

tan 45° + 1/tan 45° = 1 + 1/1 = 2.

Check options: (2) cosec 45° × sec 45° = √2 × √2 = 2. Match found.

∴ The correct answer is cosec A sec A.

Alternate Method

Given: tan A + 1/tan A

Formula Used: tan A = sin A/cos A and sin²A + cos²A = 1

⇒ tan A + 1/tan A = tan A + cot A

⇒ (sin A / cos A) + (cos A / sin A)

⇒ (sin²A + cos²A) / (sin A cos A)

⇒ 1 / (sin A cos A)

⇒ (1 / sin A) × (1 / cos A)

⇒ cosec A sec A

∴ The correct answer is cosec A sec A.

Additional Information

Reciprocal Identities

cosec A = 1/sin A, sec A = 1/cos A, and cot A = 1/tan A are the primary reciprocal ratios.

Pythagorean Identities

sin²A + cos²A = 1, 1 + tan²A = sec²A, and 1 + cot²A = cosec²A.

Common Result

The expression tan A + cot A is frequently encountered and simplifies directly to sec A cosec A.

Statement:

The bee population in the region has been steadily declining due to the widespread use of pesticides in agriculture.

Courses of Action:

I. Introduce regulations that restrict the use of certain pesticides during peak pollination seasons - Follows(Regulating pesticide use during peak pollination seasons can help reduce harm to bees, allowing them to thrive and continue their ecological role in pollination).

II. Establish urban beekeeping programmes to artificially boost the bee population and pollination efforts - Follows(Urban beekeeping can help counteract the decline in bee populations by providing safe habitats, though it does not directly address the root cause (pesticides).

Thus, Both Course of Action I and II follow.

Course I directly addresses the root cause, while Course II provides an alternative solution to sustain the bee population.

Hence, the correct answer is "Option 4".

Shortcut Trick

For a sum to double itself, the Simple Interest must be equal to the Principal (100%).

Shortcut Formula: Rate (R) = 100 ÷ Time (T)

⇒ R = 100 ÷ 8

⇒ R = 12.5%

∴ The correct answer is 12.5%.

Alternate Method

Given:

Time (T) = 8 years

Let Principal (P) = 100

Amount (A) = 2 × 100 = 200 (as it doubles)

Formula Used:

Simple Interest (SI) = A − P

SI = (P × R × T) ÷ 100

Calculations:

⇒ SI = 200 − 100 = 100

⇒ 100 = (100 × R × 8) ÷ 100

⇒ 100 = 8R

⇒ R = 100 ÷ 8

⇒ R = 12.5%

∴ The correct answer is 12.5%.

Additional Information

General Formula for n-times growth

If a sum becomes 'n' times in 'T' years, then Rate R = [(n − 1) × 100] ÷ T.

Simple Interest vs Amount

Simple Interest is calculated only on the Principal, while Amount is the sum of Principal and Interest (A = P + SI).

Constant Nature of SI

In Simple Interest, the interest earned remains the same every year if the rate and principal are constant.

The correct answer is 0.2 joule.

Key Points

• Kinetic energy is the energy that an object possesses due to its motion.
• The formula for calculating kinetic energy (KE) is: $K.E=\frac{1}{2}mv^2$
• In this problem, the mass (m) of the object is 0.1 kg.
• The velocity (v) of the object is 2 m/s.
• Using the formula:
• KE = 1/2mv² = 1/2 × 0.1 × (2)² = 1/2 × 0.1 × 4 = 0.2 J

Additional Information

• Energy:
• Energy is the capacity to do work and is measured in joules (J) in the International System of Units (SI).
• Different forms of energy include kinetic energy, potential energy, thermal energy, chemical energy, and more.
• Mass:
• Mass is a measure of the amount of matter in an object and is measured in kilograms (kg) in the SI unit.
• It is an intrinsic property of an object and does not change with its location.
• Velocity:
• Velocity is the speed of an object in a specific direction and is measured in meters per second (m/s) in the SI unit.
• It is a vector quantity, meaning it has both magnitude and direction.
• Work:
• Work is done when a force applied to an object moves it through a distance.
• It is calculated as the product of the force and the distance moved in the direction of the force, measured in joules (J).

The correct answer is unbalanced force.

Key Points

• An unbalanced force is necessary to change the state of motion of an object, as per Newton's First Law of Motion.
• Applying an unbalanced force to an object on a horizontal table overcomes the frictional force between the object and the table surface.
• When the forces acting on an object are unbalanced, they cause a change in the object's velocity, resulting in acceleration.
• The direction of the unbalanced force determines the direction in which the object will move.
• An unbalanced force implies that the net force acting on the object is not zero, leading to motion.

Additional Information

• Newton's First Law of Motion (Law of Inertia)
• States that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external unbalanced force.
• Highlights the concept of inertia, which is the tendency of objects to resist changes in their state of motion.
• Friction
• A force that opposes the relative motion or tendency of such motion of two surfaces in contact.
• Can be reduced by applying lubricants or by using smoother surfaces.
• Balanced Forces
• When two forces acting on an object are equal in size but opposite in direction, they are balanced forces.
• Balanced forces do not cause a change in the motion of an object.
• Net Force
• The overall force acting on an object when all the individual forces acting on it are combined.
• If the net force is not zero, the forces are unbalanced, leading to a change in the object's motion.

The correct answer is Compressed Natural Gas and Liquefied Petroleum Gas.

Key Points

• Compressed Natural Gas (CNG) is a fuel gas mainly composed of methane, compressed to less than 1% of its volume at standard atmospheric pressure.
• Liquefied Petroleum Gas (LPG) consists mainly of propane, butane, or a mixture of these gases, and is stored in liquid form under moderate pressure.
• CNG is primarily used as an alternative to gasoline, diesel, and propane fuel in vehicles.
• LPG is commonly used for heating, cooking, and as a fuel for certain vehicles and equipment.
• Both CNG and LPG are considered cleaner alternatives to other fossil fuels, emitting lower levels of pollutants.

Additional Information

• Methane (CH₄)
• Methane is a colorless, odorless, and highly flammable gas, which is the main component of natural gas.
• It is used as a fuel and is a major greenhouse gas, contributing to global warming.
• CNG is primarily composed of methane, making it a cleaner burning fuel compared to gasoline and diesel.
• Propane (C₃H₈)
• Propane is a three-carbon alkane gas, normally compressed and stored as a liquid.
• It is widely used in heating, cooking, and as a fuel for engines.
• Propane is a major component of LPG.
• Butane (C₄H₁₀)
• Butane is a four-carbon alkane gas, usually found mixed with propane in LPG.
• It is used in lighters, portable stoves, and as a propellant in aerosol sprays.
• Butane is another key component of LPG.
• Environmental Impact
• CNG vehicles produce lower emissions of carbon monoxide, nitrogen oxides, and particulate matter compared to gasoline and diesel vehicles.
• LPG burns more cleanly than many other fossil fuels, resulting in fewer greenhouse gases and pollutants.
• Both CNG and LPG contribute to reducing the carbon footprint when used as alternative fuels.

The correct answer is 1, 2 and 3.

Key Points

• A mixture has a variable composition, meaning the proportions of its components can vary.
• In compounds, the composition of each new substance is always fixed, with elements combined in definite ratios.
• A mixture exhibits the properties of the substances that make it up, without chemical bonding between the components.
• Mixtures can be separated into their individual components by physical means such as filtration, distillation, or evaporation.
• Examples of mixtures include air, which is a mixture of gases, and saltwater, which is a mixture of salt and water.

Additional Information

• Homogeneous Mixtures
• These mixtures have a uniform composition throughout. Examples include solutions like sugar in water.
• The different components of a homogeneous mixture cannot be easily distinguished.
• Heterogeneous Mixtures
• These mixtures have a non-uniform composition. Examples include mixtures like sand in water.
• The different components of a heterogeneous mixture can be easily distinguished.
• Physical Separation Techniques
• Filtration: Used to separate solids from liquids in a heterogeneous mixture.
• Distillation: Used to separate liquids based on differences in boiling points.
• Evaporation: Used to separate a dissolved solid from a liquid.
• Compounds vs. Mixtures
• Compounds are substances formed when two or more elements are chemically bonded together, with fixed composition.
• Mixtures involve physical blending of two or more substances without chemical bonding.

Shortcut Trick

Apply the Difference of Squares formula (a − b)(a + b) = a² − b² repeatedly.

(x − y)(x + y) → x² − y²

(x² − y²)(x² + y²) → x⁴ − y⁴

(x⁴ − y⁴)(x⁴ + y⁴) → x⁸ − y⁸

∴ The correct answer is x⁸ − y⁸.

Alternate Method

Given: (x − y) (x + y) (x² + y²) (x⁴ + y⁴)

Formula Used: (a − b)(a + b) = a² − b²

⇒ Step 1: Multiply the first two terms

⇒ (x − y)(x + y) = x² − y²

⇒ Step 2: Multiply the result with the third term

⇒ (x² − y²)(x² + y²) = (x²)² − (y²)² = x⁴ − y⁴

⇒ Step 3: Multiply the result with the fourth term

⇒ (x⁴ − y⁴)(x⁴ + y⁴) = (x⁴)² − (y⁴)² = x⁸ − y⁸