RRB Technician Grade III Official Paper (Held On: 28 Dec, 2024 Shift 3) (Previous Year Paper)

The Correct answer is peripheral nervous system.

Key Points

• The peripheral nervous system (PNS) consists of all the nerves that lie outside the brain and spinal cord.
• It includes cranial nerves (arising directly from the brain) and spinal nerves (arising from the spinal cord).
• The PNS is responsible for connecting the central nervous system (CNS) to the organs, limbs, and skin, enabling communication between the brain and the rest of the body.
• It is divided into two main components: the somatic nervous system and the autonomic nervous system.
• The somatic nervous system controls voluntary movements of skeletal muscles.
• The autonomic nervous system regulates involuntary functions such as heart rate, digestion, and respiratory rate.
• Cranial nerves like the optic nerve and olfactory nerve perform critical sensory and motor functions.
• Spinal nerves are categorized into cervical, thoracic, lumbar, sacral, and coccygeal nerves based on their location in the spinal column.

 Additional Information

• Central Nervous System
• The central nervous system (CNS) includes the brain and spinal cord.
• It is responsible for processing and interpreting sensory information and sending out instructions.
• The CNS is protected by the skull and vertebral column, as well as cerebrospinal fluid.
• Autonomic Nervous System
• The autonomic nervous system is a division of the PNS that controls involuntary functions such as heartbeat, breathing, and digestion.
• It is further divided into the sympathetic and parasympathetic systems, which work together to maintain balance in the body's functions.
• Endocrine System
• The endocrine system is not part of the nervous system but works closely with it.
• It consists of glands that secrete hormones into the bloodstream to regulate processes like metabolism, growth, and reproduction.
• Examples of endocrine glands include the pituitary gland, thyroid gland, and adrenal glands.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

(I) All lilies are roses → Does not follow (As all roses are lilies. So it is possible but not definite.)

(II) No rose is a marigold → Follow (As all roses are lilies and no lily is a marigold. As whole roses comes in lilies which cannot be marigold, therefore it is true)

∴ Here, Only conclusion II follows.​

Hence, the correct answer is "Option 4"

The correct answer is Gold.

Key Points

• Gold is the most ductile metal known to mankind, meaning it can be drawn into extremely thin wires without breaking.
• It is possible to draw a single gram of gold into a wire with a length of approximately 2.4 kilometers.
• The exceptional ductility of gold is due to its metallic bonding, where electrons are free to move, allowing atoms to slide past each other without breaking the structure.
• Gold is widely used in electrical wiring, jewelry, and decorative items due to its ductility and other properties such as resistance to corrosion and excellent conductivity.
• Its ability to be shaped into intricate designs makes it invaluable in industries such as electronics and aerospace.
• Gold is also highly valued for its economic and cultural significance across the globe, often symbolizing wealth and prosperity.

 Additional Information

• Sodium
• Sodium is a highly reactive alkali metal and is not known for its ductility.
• It is soft and can be cut with a knife, but its low melting point and reactivity make it unsuitable for applications requiring ductility.
• Sodium is primarily used in chemical industries and in the production of sodium compounds like sodium hydroxide and table salt.
• Lithium
• Lithium is the lightest metal and is moderately ductile, but it does not compare to gold in terms of ductility.
• It is widely used in batteries, especially in lithium-ion batteries, due to its high energy density.
• Other applications include ceramics, glass manufacturing, and as a mood-stabilizing drug in medicine.
• Lead
• Lead is a soft and malleable metal, but it is far less ductile than gold.
• It is primarily used in batteries (lead-acid batteries), radiation shielding, and in the production of alloys and pipes.
• Lead has a high density and is toxic, limiting its use in certain industries.

The Correct answer is Haryana.

Key Points

• Haryana emerged as the champion of the Khelo India Para Games 2023, showcasing outstanding performances by its athletes.
• The event was held in New Delhi in December 2023 and aimed to promote inclusivity and provide a platform for para-athletes to display their talent.
• Haryana is known for its strong emphasis on sports and has consistently produced top athletes in various disciplines, including para-sports.
• The state's para-athletes excelled in multiple events, contributing significantly to Haryana's overall medal tally.
• The Khelo India Para Games is a part of the larger Khelo India initiative, launched by the Government of India to promote sports at the grassroots level and nurture young talent.
• The event featured a variety of sports tailored to the abilities of para-athletes, including athletics, swimming, badminton, and wheelchair basketball.
• Haryana's victory highlights the state's commitment to fostering sports infrastructure and providing support to athletes with disabilities.

 Additional Information

• Gujarat
• Gujarat is known for its initiatives in promoting sports, including hosting major events like the National Games of India 2022.
• However, it did not secure the top position in the Khelo India Para Games 2023.
• Uttar Pradesh
• Uttar Pradesh has been actively working to enhance its sports infrastructure and has produced many talented athletes over the years.
• While the state performed well, it could not surpass Haryana in the medal tally at the Khelo India Para Games 2023.
• Tamil Nadu
• Tamil Nadu has a rich history of supporting para-athletes and promoting inclusivity in sports.
• Despite its efforts and participation, the state did not achieve the top spot in this edition of the games.

Shortcut Trick

Total Simple Interest for 10 years is ₹650.

Interest for 1 year = 650 ÷ 10 = ₹65.

Rate % = (Interest for 1 year ÷ Principal) × 100

Rate % = (65 ÷ 1300) × 100 = 5%.

∴ The correct answer is 5%.

Alternate Method

Given:

Principal (P) = ₹1,300

Simple Interest (SI) = ₹650

Time (T) = 10 years

Formula Used:

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

Calculations:

⇒ 650 = (1300 × R × 10) ÷ 100

⇒ 650 = 130 × R

⇒ R = 650 ÷ 130

⇒ R = 5%

∴ The correct answer is 5%.

Additional Information

Simple Interest Basics

Interest remains constant every year in Simple Interest. Total Amount = Principal + SI.

Effective Rate of Interest

Effective Rate for the entire period is R × T %. Here, 5% × 10 = 50%, which matches ₹650 being 50% of ₹1,300.

Relationship with Compound Interest

For the first year (or first compounding period), Simple Interest and Compound Interest are always equal.

The Correct answer is Carbon dioxide.

Key Points

• Carbon dioxide (CO₂) is primarily produced during the burning of coke because coke is primarily composed of carbon.
• When coke burns in the presence of oxygen, it undergoes a chemical reaction known as combustion, which releases carbon dioxide and energy.
• The chemical reaction for the combustion of coke is: C + O₂ → CO₂.
• This process is widely used in industrial applications, such as in steel manufacturing, where coke serves as a reducing agent in the extraction of iron from its ore.
• Carbon dioxide is a significant greenhouse gas, and its release into the atmosphere contributes to global warming and climate change.
• Coke is derived from coal and primarily consists of carbon with minimal impurities, making it efficient for high-temperature processes.
• The burning of coke is also associated with energy production due to the exothermic nature of the combustion reaction.

 Additional Information

• Nitrogen dioxide
• Nitrogen dioxide (NO₂) is a toxic gas that is produced during the combustion of fossil fuels, but it is not a major product of coke burning.
• It is commonly associated with vehicle emissions and industrial processes.
• NO₂ contributes to air pollution and forms part of the group of gases known as nitrogen oxides (NOx).
• It plays a role in the formation of acid rain and photochemical smog.
• Oxygen
• Oxygen (O₂) is not a product of coke burning but rather a reactant that is essential for the combustion process.
• It is a vital element for all combustion reactions and is present in the atmosphere.
• Oxygen supports the burning of fuels, including coke, by facilitating the release of energy through oxidation.
• Sulphur dioxide
• Sulphur dioxide (SO₂) is produced when fuels containing sulphur are burned, but coke typically has a low sulphur content.
• SO₂ contributes to acid rain and can harm the environment and human health.
• It is primarily emitted from the combustion of sulphur-rich coal and oil.

The Correct answer is zygotes.

Key Points

• Asexual reproduction does not involve the formation of zygotes, as it is a process that occurs without the fusion of gametes.
• In asexual reproduction, a single parent reproduces offspring that are genetically identical, as there is no mixing of genetic material.
• Zygote formation is characteristic of sexual reproduction, where male and female gametes fuse to form a diploid cell.
• Examples of organisms that reproduce asexually include amoeba, bacteria, hydra, and certain plants like bryophytes.
• Methods of asexual reproduction include budding, binary fission, fragmentation, spore formation, and vegetative propagation.
• Asexual reproduction is advantageous as it enables rapid reproduction in stable environments and ensures the perpetuation of successful genetic traits.

 Additional Information

• Buds
• Budding is a type of asexual reproduction where a new organism develops from an outgrowth or bud due to cell division at one particular site.
• Examples include hydra and yeast, where the bud eventually detaches to become an independent organism.
• Spore
• Spore formation is another mode of asexual reproduction, commonly seen in fungi, algae, and some non-flowering plants like mosses and ferns.
• It involves the production of spores, which are reproductive units capable of developing into a new organism under favorable conditions.
• Leaves
• In certain plants, asexual reproduction can occur through vegetative propagation, where new plants grow from leaves.
• For instance, the plant Bryophyllum reproduces asexually when plantlets grow along the edges of its leaves.

The logic followed here is:

Given:

(6, 12, 48)

6 × 6 + 12 = 48

36 + 12 = 48

48 = 48 (LHS = RHS)

And,

(8, 16, 64)

8 × 6 + 16 = 64

48 + 16 = 64

64 = 64 (LHS = RHS)

So, checking each option one by one:

Option 1) (15, 30, 130)

15 × 6 + 30 = 130

90 + 30 = 130

120 ≠ 130 (LHS ≠ RHS)

Option 2) (15, 40, 120)

15 × 6 + 40 = 120

90 + 40 = 120

130 ≠ 120 (LHS ≠ RHS)

Option 3) (5, 30, 120)

5 × 6 + 30 = 120

30 + 30 = 120

60 ≠ 120 (LHS ≠ RHS)

Option 4) (15, 30, 120)

15 × 6 + 30 = 120

90 + 30 = 120

120 = 120 (LHS = RHS)

Thus, out of all the options, '(15, 30, 120)' follows the same logic as given.

Hence, "Option 4" is the correct answer.

Shortcut Trick

Direct formula application: (a + b + c)² = a² + b² + c² + 2(ab + bc + ca).

Substitute the given values: 9² = a² + b² + c² + 2 × 23.

⇒ 81 = a² + b² + c² + 46.

⇒ a² + b² + c² = 81 − 46 = 35.

∴ The correct answer is 35.

Alternate Method

Given:

a + b + c = 9

ab + bc + ca = 23

Formula Used:

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Calculations:

⇒ (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

⇒ (9)² = a² + b² + c² + 2(23)

⇒ 81 = a² + b² + c² + 46

⇒ a² + b² + c² = 81 − 46

⇒ a² + b² + c² = 35

∴ The correct answer is 35.

Additional Information

Algebraic Identity: Cubic Expansion

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

Special Case: Sum of Squares

If a + b + c = 0, then a³ + b³ + c³ = 3abc.

Alternative Square Form

a² + b² + c² − ab − bc − ca = 1/2 [(a − b)² + (b − c)² + (c − a)²].

The Correct answer is Negative.

Key Points

• When a stone is thrown upward, the direction of motion is opposite to the direction of gravitational force.
• The acceleration due to gravity (g) always acts in the downward direction, i.e., towards the center of the Earth.
• In this scenario, since the upward motion of the stone is opposite to the direction of gravity, the value of g becomes negative.
• The negative sign indicates the opposing direction of the gravitational force relative to the motion of the object.
• As the stone rises, its velocity decreases due to the negative acceleration until it reaches the highest point, where the velocity becomes zero.
• Once the stone starts to fall back down, the acceleration due to gravity acts in the same direction as its motion, and the value of g becomes positive.
• This principle is based on the laws of motion and Newton’s universal law of gravitation.
• Understanding the sign convention of g is crucial for solving various problems in physics, such as projectile motion, free fall, and other kinematic calculations.

 Additional Information

• Infinite
• The term infinite is not applicable in this context as the acceleration due to gravity (g) has a fixed value near the Earth's surface, approximately 9.8 m/s².
• Infinity generally refers to an unbounded or limitless value, which does not describe gravitational acceleration.
• Zero
• The value of g cannot be zero as long as the object is within the influence of Earth's gravity.
• Zero gravitational acceleration would only occur in deep space, far away from any massive object exerting a gravitational pull.
• Positive
• The value of g is considered positive when the motion of the object is in the same direction as the gravitational force.
• In this case, when the stone is falling back down, the acceleration due to gravity becomes positive.

The logic followed here is:

Option 1) TZ—YC

Option 2) BH-GK

Option 3) WC -BF

Option 4) AD-YW

Thus, out of all the options 'AD-YW' is the odd one out.

Hence, "Option 4" is the correct answer.

The Correct answer is Soap.

Key Points

• Soap is a substance that has a dual nature - a hydrophilic (water-attracting) end and a hydrophobic (water-repelling) end.
• The hydrophilic end of soap is attracted to water molecules, making it soluble in water.
• The hydrophobic end is attracted to oil, grease, and dirt, helping to remove these substances from surfaces.
• When soap is mixed with water, it forms structures called micelles, where the hydrophobic ends trap grease and dirt, while the hydrophilic ends remain in water, helping to wash away impurities.
• Soap is widely used in cleaning, personal hygiene, and industrial processes due to its amphiphilic properties.
• Soap is made through a process called saponification, where fats or oils are reacted with an alkali, such as sodium hydroxide or potassium hydroxide.
• Examples of soap products include bar soap, liquid soap, and detergent powders.

 Additional Information

• Water
• Water is a universal solvent but does not have amphiphilic properties like soap.
• It is composed of hydrogen and oxygen (H₂O) and forms hydrogen bonds with other water molecules.
• It is essential for life and is used in drinking, agriculture, industry, and sanitation.
• Perfume
• Perfume is a mixture of fragrant essential oils or aroma compounds, solvents, and fixatives used to create a pleasant smell.
• It does not have hydrophilic or hydrophobic ends and is insoluble in water.
• Perfumes are primarily used in personal care products and for aromatherapy.
• Cream
• Cream is an emulsion of water and fat and is used in cosmetics, skincare, and food products.
• While it contains both water and oil, it does not exhibit the dual hydrophilic and hydrophobic properties of soap.
• Cream products are used for hydration, moisturization, and cooking.

The logic followed here is:

Given: 

HE-JG-LN

And,

MJ-OL-QS 

So, checking each option one by one:

Option 1) RO-TQ-VW

Option 2) QN-SP-UW 

Option 3) PM-RO-TU

Option 4) OL-QN-ST

Thus, out of all the options 'QN-SP-UW ' follows the same logic as given.

Hence, "Option 2" is the correct answer.

The Correct answer is (1/v) + (1/u) = (1/f).

Key Points

• This equation is known as the Mirror Formula, which establishes a relationship between the object distance (u), image distance (v), and focal length (f) for a spherical mirror.
• The formula is applicable for both concave and convex mirrors.
• In the equation, all distances are measured from the pole of the mirror, and the sign convention must be followed to determine the nature of the distances (positive or negative).
• Concave mirrors form real and inverted images for objects placed beyond the focal point and virtual images when the object is within the focal length.
• Convex mirrors, however, always produce virtual, erect, and diminished images regardless of the object’s position.
• The formula is derived from the geometry of the mirror and is used in various applications, including optics, imaging systems, and physics experiments.
• The equation ensures the quantitative analysis of image formation, allowing scientists and engineers to calculate the exact position and size of the image.

Given cause: Heavy rains and flash floods have inundated many low lying areas of City X.

Given effects:

(I) The State Government has appointed a new head for the municipality of City X. → Not possible

As mismanagement during the flood could lead to a leadership change but this is not an immediate or guaranteed effect of the disaster itself. 

(II) The State Government has evacuated over 5500 people stranded in low lying areas of City X. → Possible

When floods occur, authorities often evacuate people from affected areas for safety. The given cause mentions that low lying areas were inundated, making evacuation necessary.

(III) Food and water is being distributed at multiple locations to help citizens who have been evacuated from City X. → Possible

After being displaced, people require basic necessities such as food and water. Disaster relief efforts typically involve such measures, making this a possible and reasonable effect.

Thus, Both II and III can be the possible effects.

Hence, "Option 1" is the correct answer.

The Correct answer is Colloids.

Key Points

• The Tyndall effect refers to the scattering of light by particles in a medium, making the path of light visible.
• Colloids are mixtures where the particle size ranges between 1 nm to 1000 nm, large enough to scatter light.
• When a beam of light passes through a colloidal solution, the light is scattered, and this phenomenon is called the Tyndall effect.
• Examples of colloids include fog, milk, smoke, and gelatin solutions.
• The particles in a colloid are dispersed in a continuous medium and are not visible to the naked eye, but their effect on light is noticeable.
• The visibility of the light beam in colloids demonstrates the presence of dispersed particles, proving the heterogeneous nature of colloids.

 Additional Information

• Solutions
• Solutions are homogeneous mixtures where the particle size is smaller than 1 nm.
• Due to their small particle size, they do not scatter light and hence do not show the Tyndall effect.
• Examples of solutions include sugar water, salt water, and vinegar.
• Metals
• Metals are solid substances with a characteristic luster and high electrical and thermal conductivity.
• They are not mixtures or dispersions and do not exhibit the Tyndall effect.
• Examples of metals include iron, gold, silver, and copper.
• Gases
• Gases are composed of particles that are widely spaced and move freely.
• Pure gases do not exhibit the Tyndall effect as their particles are too small to scatter light significantly.
• Examples of gases include oxygen, nitrogen, and carbon dioxide.

The Correct answer is Concave Mirror.

Key Points

• A concave mirror is a spherical mirror whose reflecting surface faces towards the centre of the sphere.
• It is also known as a converging mirror because it reflects light inward toward a focal point.
• The principal applications of concave mirrors include their use in telescopes, headlights, shaving mirrors, and dental mirrors, where a magnified image is required.
• Concave mirrors are capable of forming both real and virtual images depending on the position of the object.
• The focal length of a concave mirror is half the radius of curvature, denoted mathematically as f = R/2.
• They are widely used in scientific instruments due to their ability to focus light accurately.
• Concave mirrors are also used in solar concentrators to focus sunlight for generating heat or energy.

 Additional Information

• Plano-convex Mirror
• Plano-convex mirrors have a flat surface on one side and a convex surface on the other.
• They are not spherical mirrors but are typically used in optical systems for focusing or collimating light.
• These mirrors are mainly used in lasers, imaging systems, and optical instruments.
• Plane Mirror
• A plane mirror has a flat reflecting surface.
• It reflects light to form a virtual image that is upright and of the same size as the object.
• Plane mirrors are commonly used in bathrooms, dressing tables, and optical setups.
• They do not have the capability to converge or diverge light.
• Convex Mirror
• A convex mirror is a spherical mirror whose reflecting surface bulges outward.
• It is also known as a diverging mirror because it spreads light outward.
• Convex mirrors always form a virtual, upright, and diminished image.
• They are widely used in vehicle rearview mirrors, surveillance systems, and blind spot detection.

The Correct answer is IBM.

Key Points

• L&T Semiconductor Technologies (SiLT) signed a partnership agreement with IBM in September 2024.
• This collaboration aims to co-develop advanced processors for edge devices, hybrid cloud systems, and areas like mobility, industrial, energy, and servers.
• IBM is a globally renowned technology company that specializes in hardware, software, and cutting-edge technology solutions, such as AI, cloud computing, and quantum computing.
• The focus of the partnership is to leverage IBM's expertise in processor development and SiLT's capabilities in semiconductor technology to address the growing demand for innovative solutions in these sectors.
• This collaboration is expected to foster technological advancements and boost India's semiconductor industry, aligning with the country's ambition to become a global hub for semiconductor manufacturing.
• Edge devices are critical components in modern computing systems, enabling real-time data processing closer to the source, thereby reducing latency and improving efficiency.

 Additional Information

• Nvidia
• Nvidia is a leading company in graphics processing units (GPUs) and AI hardware.
• Nvidia is known for its contributions to gaming technology and its role in advancing AI development through platforms like CUDA.
• Although Nvidia is a key player in the technology sector, it is not directly involved in this specific collaboration with L&T Semiconductor Technologies.
• Intel
• Intel is one of the largest semiconductor chip manufacturers globally, known for its processors and innovations in computing technology.
• Intel specializes in developing processors for personal computers, servers, and mobile devices.
• While Intel plays a significant role in the semiconductor industry, it is not the company collaborating with SiLT in this case.
• Dell
• Dell is a multinational computer technology company known for its hardware solutions like laptops, desktops, and servers.
• Although Dell is a major player in the technology industry, its expertise lies more in hardware manufacturing rather than semiconductor or processor development.

The Correct answer is Milk is not a colloidal solution.

Key Points

• Milk is, in fact, a colloidal solution, not a non-colloidal solution as mentioned in the question.
• A colloidal solution is a heterogeneous mixture where one substance is dispersed evenly throughout another.
• In milk, fat globules are dispersed in water, making it an example of an emulsion, which is a type of colloidal solution.
• The particles in colloidal solutions, such as milk, are so small that they do not settle down and cannot be separated by ordinary filtration methods.
• Milk exhibits the Tyndall effect, which is a characteristic property of colloids, where light is scattered by the dispersed particles.
• Examples of colloidal solutions like milk are common in daily life and include substances such as fog, whipped cream, and jelly.

 Additional Information

• Colloidal solutions are a heterogeneous mixture
• A heterogeneous mixture is one where the composition is not uniform throughout the solution.
• In a colloidal solution, the dispersed phase (small particles) and the dispersion medium (substance in which particles are dispersed) remain separate, making it heterogeneous.
• Examples of colloidal solutions include fog, smoke, and milk.
• Components cannot be separated by the process of filtration
• The particles in a colloidal solution are very small, typically in the range of 1-1000 nanometers.
• Due to their small size, they pass through ordinary filter paper, and hence, filtration cannot separate them.
• Specialized methods like ultrafiltration are required to separate colloidal particles.
• Fog is an example of a colloidal solution
• Fog is an example of an aerosol, which is a type of colloidal solution where tiny liquid droplets are dispersed in air.
• The particles in fog scatter light, making it another example of the Tyndall effect.
• This dispersion of water droplets in air is why fog reduces visibility significantly.

The logic followed here is:

‘POEM’ is coded as ‘7591'

‘MINT’ is coded as '6728'

Thus, code for ‘M’ is '7'.

Hence, "Option 1" is the correct answer.

Shortcut Trick

In a rhombus, diagonals bisect each other at 90°. Half of the given diagonal is 15 cm.

Using the Pythagorean triplet (15, 20, 25), where 25 is the hypotenuse (side of rhombus), the other half-diagonal must be 20 cm.

Full length of the second diagonal d₂ = 20 × 2 = 40 cm.

Area = (1/2) × d₁ × d₂ = (1/2) × 30 × 40 = 600 cm².

∴ The correct answer is 600 sq cm.

Alternate Method

Given: Side (a) = 25 cm, Diagonal 1 (d₁) = 30 cm.

Formula Used: 4 × a² = d₁² + d₂² and Area = (1/2) × d₁ × d₂.

⇒ 4 × (25)² = (30)² + d₂²

⇒ 4 × 625 = 900 + d₂²

⇒ 2500 − 900 = d₂²

⇒ d₂² = 1600

⇒ d₂ = 40 cm

⇒ Area = (1/2) × 30 × 40 = 600 cm²

∴ The correct answer is 600 sq cm.

Additional Information

Properties of a Rhombus

All sides are equal and opposite angles are equal. Diagonals bisect each other at right angles (90°).

Perimeter of Rhombus

The perimeter is given by the formula P = 4 × side.

Relation between Side and Diagonals

Side (a) = (1/2) √(d₁² + d₂²).

The Correct answer is Cytoplasm.

Key Points

• Glucose is converted into pyruvate through a process known as glycolysis.
• Glycolysis is an anaerobic process, meaning it does not require oxygen to occur.
• This process occurs in the cytoplasm of the cell, which is the gel-like substance that surrounds the cell organelles.
• During glycolysis, one molecule of glucose (6-carbon molecule) is broken down into two molecules of pyruvate (3-carbon molecule).
• This process generates a small amount of energy in the form of ATP (Adenosine Triphosphate) and NADH (Nicotinamide Adenine Dinucleotide).
• The pyruvate produced in the cytoplasm can then enter the mitochondria for further energy production through processes such as the Krebs cycle and oxidative phosphorylation, if oxygen is available.
• Glycolysis is the first step of cellular respiration and is essential for energy production in both prokaryotic and eukaryotic organisms.

 Additional Information

• Ribosome
• The ribosome is the site of protein synthesis in the cell.
• It is not involved in the process of glycolysis or the conversion of glucose into pyruvate.
• Ribosomes are found either floating freely in the cytoplasm or attached to the endoplasmic reticulum.
• Golgi-complex
• The Golgi apparatus, also known as the Golgi-complex, is responsible for modifying, sorting, and packaging proteins and lipids for secretion or use within the cell.
• It has no role in the metabolic pathway of glycolysis.
• Mitochondria
• The mitochondria are known as the powerhouse of the cell and are the site of aerobic respiration.
• The pyruvate generated in the cytoplasm during glycolysis is transported to the mitochondria for further breakdown in the Krebs cycle and electron transport chain to produce a larger amount of ATP.
• However, glycolysis itself does not occur in the mitochondria.

Given:

Divit starts from point A and drives 4 km towards the East.

He then takes two simultaneous right turns and drives 2 km and 4 km, respectively.

He takes another right turn and drives 5 km.

He then takes a left turn and drives 3 km.

He takes a final left turn and drives 3 km to reach point B.

Thus, Divit should drive (5 km - 2 km) 3 km in the east direction in order to reach Point A again.

Hence, "Option 3" is the correct answer.

The Correct answer is less than the resistance of the individual resistors.

Key Points

• The effective resistance of a parallel combination of resistors is always less than the resistance of the smallest individual resistor in the circuit.
• In a parallel circuit, the total current through the circuit is the sum of the currents through each resistor.
• As more paths are provided for the current to flow, the overall resistance decreases.
• The formula to calculate the effective resistance for two resistors connected in parallel is:
  

1/R_effective = 1/R₁ + 1/R₂.

• This relationship ensures that the effective resistance is always less than any of the individual resistances.
• For example, if two resistors with resistances of 10 Ω and 20 Ω are connected in parallel, the effective resistance will be around 6.67 Ω, which is less than both 10 Ω and 20 Ω.
• Parallel resistors are commonly used in circuits to reduce resistance and allow more current to flow.

The Correct answer is 10 Coulombs.

Key Points

• The relationship between current (I), charge (Q), and time (t) is given by the formula: I = Q / t.
• Rearranging the formula to calculate charge, we get: Q = I × t.
• Here, the current (I) is 1 A (ampere) and the time (t) is 10 seconds.
• Substituting the values into the formula: Q = 1 × 10 = 10 Coulombs.
• Charge is measured in the unit of coulombs, which represents the quantity of electricity transported.
• This means that a current of 1 ampere flowing for 10 seconds results in a total charge flow of 10 coulombs.
• This calculation is based on the fundamental relationship in electricity and magnetism, forming the basis for understanding current flow in circuits.

 Additional Information

• Concept of Current:
• Current (I) is the rate at which charge flows through a conductor.
• It is measured in amperes (A), where 1 ampere represents the flow of 1 coulomb of charge per second.
• Charge (Q):
• Charge is a fundamental property of matter associated with the presence of electrons or protons.
• It is measured in coulombs (C).
• The charge of a single electron is approximately -1.6 × 10⁻¹⁹ coulombs.
• Practical Application of Formula:
• This formula is used in various fields such as electronics, electrical engineering, and physics to calculate the flow of charge in circuits.
• It helps in determining the amount of energy transferred in a circuit over a given time.

The correct answer is greater at the poles than at the equator.

Key Points

• The acceleration due to gravity (g) is not uniform across the Earth's surface due to its non-spherical shape and rotational motion.
• The Earth is an oblate spheroid, meaning it is flattened at the poles and bulges at the equator.
• At the poles, the distance between the Earth's center and the surface is shorter compared to the equator. Since gravity is inversely proportional to the square of the distance, g is greater at the poles.
• The Earth's rotational motion creates a centrifugal force, which is maximum at the equator and reduces the net gravitational pull. This centrifugal force is negligible at the poles, resulting in a higher value of g.
• Mathematically, the relationship between gravity and distance can be expressed as g ∝ 1/r², where r is the radius of the Earth at a given location.
• Thus, the combination of the Earth's shape and rotation explains why gravity is greater at the poles than at the equator.

The Correct answer is If an object is in motion, applied force is directly proportional to the acceleration.

Key Points

• Newton's second law of motion states that the force applied to an object is directly proportional to the rate of change of momentum, and for a constant mass, it is directly proportional to the acceleration of the object. Mathematically, it is expressed as: F = ma, where F is the force, m is the mass, and a is the acceleration.
• It explains the relationship between the force applied on an object, its mass, and the resulting acceleration. This law is fundamental in understanding motion in physics.
• The second law is crucial for calculating forces in various applications such as engineering, mechanics, and aerospace sciences.
• This principle is applied in real-life scenarios like vehicle acceleration, the motion of projectiles, and the study of gravitational forces.
• It helps determine how much force is required to move or stop an object, which is important in designing machines and ensuring safety measures.

Shortcut Trick

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

Speed in m/s = 36 × (5/18)

Speed in m/s = 2 × 5 = 10 m/s

∴ The correct answer is 10 m/s.

Alternate Method

Given: Speed = 36 km/h

Formula Used: 1 km = 1000 m and 1 hour = 3600 seconds

⇒ Speed = 36 × (1000 m / 3600 s)

⇒ Speed = 36 × (10 / 36) m/s

⇒ Speed = 1 × 10 m/s

⇒ Speed = 10 m/s

∴ The correct answer is 10 m/s.

Additional Information

Unit Conversion Factor

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

Average Speed

Average Speed = Total Distance ÷ Total Time. For two equal distances at speeds a and b, Average Speed = 2ab/(a+b).

Relative Speed

In the same direction, subtract speeds (S₁ − S₂). In opposite directions, add speeds (S₁ + S₂).

The Correct answer is Both a) and b).

Key Points

• Waste can be classified into two main categories: biodegradable and non-biodegradable.
• Biodegradable waste includes organic materials like food scraps, paper, and plant debris that decompose naturally.
• Non-biodegradable waste includes plastics, metals, and glass that do not decompose easily and may harm the environment.
• It is essential to separate dry waste (like plastics, metals, glass) and wet waste (organic waste) for proper disposal and recycling.
• Segregation of waste aids in the efficient recycling process and minimizes environmental hazards.
• Biodegradable waste can be turned into compost, which is beneficial for agriculture, while non-biodegradable waste can be recycled to reduce pollution.
• Proper waste segregation practices align with global efforts to promote sustainable waste management.

Shortcut Trick

Subtract the milliliters first by borrowing 1 ltr (1000 ml) from the total capacity.

1000 ml − 225 ml = 775 ml

299 ltr − 87 ltr = 212 ltr

Result: 212 ltr 775 ml

∴ The correct answer is 212 ltr 775 ml.

Alternate Method

Given:

Initial quantity of water in tank = 300 ltr

Quantity of water used = 87 ltr 225 ml

Formula Used:

Water left = Total water − Used water

1 liter = 1000 milliliters

Calculations:

⇒ Total water = 300.000 ltr

⇒ Used water = 87.225 ltr

⇒ Water left = 300.000 − 87.225

⇒ Water left = 212.775 ltr

⇒ 212.775 ltr = 212 ltr 775 ml

∴ The correct answer is 212 ltr 775 ml.

Additional Information

Metric Conversion

Standard unit of volume is liters. 1 Liter (L) = 1000 Milliliters (ml). To convert L to ml, multiply by 1000.

Subtraction with Units

When subtracting mixed units, subtract the smaller units first. If the upper value is smaller, borrow 1 unit from the larger category (e.g., borrow 1 ltr to get 1000 ml).

The correct answer is Sustainable development of fisheries.

Key Points

• The central budget for 2024-25 focused on nine priority areas aimed at creating opportunities for all. These areas were aligned with the government's vision of inclusive growth and economic development.
• While critical sectors like employment, skills, energy security, and manufacturing and services were emphasized, “Sustainable development of fisheries” was not explicitly mentioned as one of the budget’s highlighted priority areas.
• The nine priority areas generally focused on infrastructure, digital transformation, green energy, and human capital development, leaving out fisheries as a distinct focus area in this context.
• However, fisheries and allied sectors may still be part of broader schemes or programs under the government’s agricultural and rural development initiatives.
• The omission of fisheries as a specific priority does not undermine its importance but reflects a strategic focus on other sectors driving macroeconomic growth.

 Additional Information

• Employment and Skill Training
• The budget emphasized employment generation through skill development programs, particularly focusing on youth and women.
• Programs like PM Kaushal Vikas Yojana and initiatives for skilling in emerging technologies (e.g., AI, IoT) were highlighted.
• Energy Security
• Energy security was a prominent priority area in the budget, focusing on renewable energy projects and reducing dependency on fossil fuels.
• Significant investments were allocated for green hydrogen, solar energy parks, and energy transition initiatives.
• Manufacturing and Services
• The budget aimed to boost the manufacturing sector through Production Linked Incentive (PLI) schemes and promote services such as IT, tourism, and finance.
• This focus was intended to enhance India's global competitiveness and contribute to the goal of Aatmanirbhar Bharat.

The Correct answer is Marimuthu Yoganathan.

Key Points

• Marimuthu Yoganathan is a bus conductor from the state of Tamil Nadu, India, who has dedicated his life to environmental conservation.
• He is widely recognized for his remarkable achievement of planting over 3 lakh saplings over a span of 30 years.
• He has been actively involved in eco-activism while simultaneously working as a bus conductor in the Tamil Nadu State Transport Corporation (TNSTC).
• Marimuthu Yoganathan's efforts have earned him several awards and accolades for his contributions to environmental sustainability.
• He is also known for educating the public, especially students, about the importance of tree plantation and environmental protection.
• Despite his modest background, he has made a significant impact by using his personal resources and time for this noble cause.
• His initiative has inspired many others to take up environmental conservation as a personal responsibility.

 Additional Information

• MS Swaminathan
• MS Swaminathan is known as the Father of the Indian Green Revolution.
• He played a key role in developing and introducing high-yielding varieties (HYVs) of crops in India, leading to increased agricultural productivity.
• His work primarily focused on food security and sustainable agriculture.
• Vijay Kumar
• The name Vijay Kumar does not directly relate to notable environmental or eco-activism contributions in the context of this question.
• Sundar Pichai
• Sundar Pichai is the CEO of Alphabet Inc. and Google.
• He is a well-known figure in the technology and innovation sector, not directly associated with environmental activism.
• He was born in Chennai, Tamil Nadu, India, and has had a significant impact on global technology advancements.

The Correct answer is 20 N.

Key Points

• Pressure is defined as the force exerted per unit area of a surface.
• The formula for calculating pressure is Pressure = Force/Area.
• In this case, the pressure is given as 10 N/m² and the area of the body is 2 m².
• To find the thrust (or force) acting on the body, we use the formula Thrust = Pressure × Area.
• Substituting the values into the formula: Thrust = 10 × 2 = 20 N.
• The thrust acting on the body is therefore 20 N, which corresponds to the correct option.
• Thrust is a term used to describe the total force exerted perpendicular to a surface.
• This concept is important in mechanics and fluid dynamics to understand the interaction between forces and surfaces.

 Additional Information

• Pressure
• Pressure is measured in units of Newton per square meter (N/m²), also known as Pascals (Pa).
• It is widely used in areas such as engineering, physics, fluid mechanics, and material science.
• Pressure is a scalar quantity, meaning it has magnitude but no direction.
• Thrust
• Thrust is a term used to describe the perpendicular force exerted by a body on a surface.
• It is commonly discussed in the context of aerodynamics, fluid dynamics, and propulsion systems.
• Thrust is measured in units of Newton (N), which is the standard unit for force in the International System of Units (SI).
• Area
• Area is a measure of the surface covered by a shape or object.
• It is expressed in square units such as m² in the SI system.
• Understanding area is essential for calculations involving pressure, thrust, and energy distribution.

The Correct answer is Nephron.

Key Points

• The nephron is the basic structural and functional unit of the kidney.
• It is responsible for the filtration, reabsorption, secretion, and excretion of waste products and excess substances from the blood.
• Each kidney contains millions of nephrons, which contribute to maintaining the body's fluid and electrolyte balance.
• The nephron consists of the following parts:
• Bowman's Capsule: Encapsulates the glomerulus and facilitates filtration.
• Glomerulus: A cluster of capillaries that filters blood to remove waste.
• Proximal Convoluted Tubule: Reabsorbs essential nutrients like glucose, amino acids, and ions.
• Loop of Henle: Concentrates urine by reabsorbing water and salts.
• Distal Convoluted Tubule: Adjusts the composition of filtrate by secreting ions and reabsorbing water.
• Collecting Duct: Finalizes urine composition and transports it to the renal pelvis.
• Nephrons play a critical role in regulating blood pressure through mechanisms like the Renin-Angiotensin-Aldosterone System (RAAS).
• They also help maintain the body's acid-base balance by excreting hydrogen ions and reabsorbing bicarbonate ions.
• The health of nephrons is essential for preventing conditions like chronic kidney disease (CKD) and acute kidney injury (AKI).

 Additional Information

• Neuron
• A neuron is the basic unit of the nervous system, responsible for transmitting nerve impulses.
• It consists of three main parts: cell body, dendrites, and axon.
• Neurons are not involved in filtration processes; their function is in communication between the brain and other parts of the body.
• Seminiferous tubule
• Seminiferous tubules are located in the testes and are involved in the production of sperm cells.
• They are not related to the kidney or filtration functions.
• Sperm
• Sperm is the male reproductive cell, produced in the testes.
• It has no role in kidney filtration or the excretion of waste products.

The Correct answer is Variation.

Key Points

• Variation is essential for the survival of species over time as it helps organisms adapt to changing environments.
• It occurs due to genetic differences among individuals within a species.
• Variations can arise through processes like mutation, recombination during reproduction, and environmental factors.
• These differences may provide certain individuals with a survival advantage, especially when environmental conditions change.
• This mechanism leads to natural selection, which ensures that favorable traits are passed on to future generations.
• For example, the development of antibiotic resistance in bacteria is an outcome of genetic variation and selection pressure.
• It contributes to the evolution of species, ensuring long-term survival and adaptability.
• Without variation, species would be unable to cope with new challenges like diseases, predators, or climate changes, leading to extinction.

 Additional Information

• Reproduction
• Reproduction is the biological process by which new individual organisms are produced.
• It ensures the continuity of species but does not directly aid in the survival of species in changing environments.
• There are two types of reproduction: sexual reproduction (involving two parents and genetic variation) and asexual reproduction (involving one parent and no variation).
• Budding
• Budding is a type of asexual reproduction commonly seen in organisms like yeast and hydra.
• It involves the formation of a new organism from a small projection or bud on the parent organism.
• Since it is a type of asexual reproduction, it does not lead to genetic variation.
• Population
• A population refers to the group of individuals of the same species living in a particular area.
• While the size and density of a population are important, they do not directly ensure the survival of species in changing environments.

Given word: DREAMS

According to the question,

Thus, the new formed letter cluster → B E F N S T

So, fourth from the right in the group of letters thus formed: (Left end) B E F N S T (Right end) → F

Hence, "Option 4" is the correct answer.

The Correct answer is chromosomes.

Key Points

• Chromosomes are thread-like structures made up of DNA and associated proteins found in the nucleus of most living cells.
• They carry genetic information in the form of genes, which determine the characteristics of an organism.
• Each chromosome contains a tightly packed DNA molecule, which is organized into functional units called genes.
• Genes are responsible for controlling heredity and traits like eye color, height, and certain diseases.
• In humans, there are 46 chromosomes (23 pairs), with one set inherited from each parent.
• Chromosomes are visible under a microscope during the cell division process (mitosis and meiosis).
• The DNA within chromosomes carries instructions for the development, functioning, growth, and reproduction of all living organisms and many viruses.
• The study of chromosomes and genes is crucial in the field of genetics and has numerous applications in medicine, agriculture, and evolutionary biology.

 Additional Information

• Vacuoles
• Vacuoles are membrane-bound organelles found in both plant and animal cells, but they are much larger in plants.
• In plant cells, vacuoles help in storing water, nutrients, and waste products and play a role in maintaining turgor pressure to provide structural support.
• In animal cells, vacuoles are smaller and are involved in processes like endocytosis and exocytosis.
• Endoplasmic Reticulum (ER)
• The endoplasmic reticulum (ER) is a network of membrane-bound tubules and sacs in the cytoplasm of eukaryotic cells.
• It is divided into two types: rough ER (studded with ribosomes) and smooth ER (lacking ribosomes).
• The rough ER is involved in protein synthesis, while the smooth ER plays a role in lipid synthesis, detoxification, and calcium storage.
• Lysosome
• Lysosomes are membrane-bound organelles containing digestive enzymes.
• They are responsible for breaking down cellular waste, damaged organelles, and macromolecules, a process known as autophagy.
• Lysosomes are often referred to as the "suicidal bags" of the cell because they can digest the cell itself under certain conditions.

The Correct answer is 180 days.

Key Points

• The Indian Government has introduced a new rule in June 2024, granting maternity leave for both the surrogate mother and the commissioning mother in surrogacy cases.
• As per this rule, 180 days of maternity leave can now be availed by government employees in these roles.
• The decision was taken to recognize the physical, emotional, and mental demands of motherhood, irrespective of whether it is through natural birth or surrogacy.
• This measure ensures gender equality and supports the concept of work-life balance for women in government service.
• It is a step in alignment with India's commitment to maternal health and the rights of women as highlighted in Sustainable Development Goals (SDGs).
• The rule acknowledges that both the surrogate and commissioning mothers play crucial roles in the childbirth process, requiring adequate rest and recovery time.
• The provision applies specifically to government servants, reflecting progressive steps toward inclusive maternity benefits in the workplace.

Shortcut Trick

Mode is the value that appears most frequently in a given data set.

By observation, the frequencies of the wickets taken are:

0 → 1 time, 1 → 1 time, 3 → 2 times, 4 → 1 time, 5 → 1 time, 6 → 1 time, and 2 → 3 times.

Since 2 has the highest frequency (occurs 3 times), the mode is 2.

∴ The correct answer is 2.

Alternate Method

Given:

Data set of wickets taken: 2, 6, 4, 5, 0, 2, 1, 3, 2, 3

Formula Used:

Mode = Value with the maximum frequency in the observation set.

Calculations:

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

⇒ Number of times 0 occurs = 1

⇒ Number of times 1 occurs = 1

⇒ Number of times 2 occurs = 3

⇒ Number of times 3 occurs = 2

⇒ Number of times 4 occurs = 1

⇒ Number of times 5 occurs = 1

⇒ Number of times 6 occurs = 1

⇒ The observation with the highest frequency is 2 with a frequency of 3.

⇒ Mode = 2

∴ The correct answer is 2.

Additional Information

Empirical Relationship

For a moderately skewed distribution, the relationship between mean, median, and mode is given by: Mode = 3 × Median − 2 × Mean.

Bimodal and Multimodal Data

If two or more values share the same maximum frequency, the data set can have more than one mode (bimodal or multimodal).

Shortcut Trick

Net Discount % = 20 + 15 − (20 × 15)/100 = 35 − 3 = 32%

Selling Price % = 100% − 32% = 68%

Given: 68% of Marked Price = 571.20

Marked Price = (571.20 ÷ 68) × 100 = 8.4 × 100 = 840

∴ The correct answer is 840.

Alternate Method

Given: Selling Price (SP) = Rs. 571.20, Discount 1 (d₁) = 20%, Discount 2 (d₂) = 15%

Formula Used: SP = MP × (100 − d₁)/100 × (100 − d₂)/100

MP (x) −20%

Price 1 −15%

SP = 571.20 MP = 571.20 ÷ (0.80 × 0.85)

⇒ 571.20 = MP × (100 − 20)/100 × (100 − 15)/100

⇒ 571.20 = MP × (80/100) × (85/100)

⇒ 571.20 = MP × (4/5) × (17/20)

⇒ 571.20 = MP × (68/100)

⇒ MP = (571.20 × 100) ÷ 68

⇒ MP = 57120 ÷ 68

⇒ MP = 840

∴ The correct answer is 840.

Additional Information

Successive Discount Formula

Total Discount % = d₁ + d₂ − (d₁ × d₂)/100. This is used for two successive discounts.

Relationship between SP and MP

Selling Price = Marked Price × (100 − Discount%)/100. If multiple discounts exist, multiply the factors successively.

Discount Value

Discount = Marked Price − Selling Price. It is always calculated on the Marked Price unless stated otherwise.

The Correct answer is 100ºC (212ºF).

Key Points

• Water transforms into steam at a temperature of 100ºC (212ºF) under normal atmospheric pressure, which is approximately 1 atm (101.325 kPa).
• This process is called boiling, and it occurs when the vapor pressure of water equals the atmospheric pressure.
• At the boiling point, water molecules gain enough kinetic energy to overcome intermolecular forces and transition from the liquid phase to the gaseous phase.
• The boiling point of water can vary depending on altitude and pressure. At higher altitudes where pressure is lower, water boils at a temperature below 100ºC.
• This temperature is widely used in science, cooking, and industrial applications to measure and control heat processes.
• The boiling point of water is a crucial reference point in the Celsius temperature scale, where it is defined as 100ºC.

 Additional Information

• 50ºC (122ºF)
• This temperature is far below the boiling point of water under normal atmospheric pressure.
• At 50ºC, water remains in the liquid state and is often considered warm but not hot enough for steam formation.
• This temperature is commonly used in applications like heating water for bathing or other domestic uses.
• 80ºC (176ºF)
• 80ºC is still below the boiling point of water.
• Water at this temperature is considered hot and is often used in cooking or beverage preparation, like making tea or coffee.
• At this temperature, water may begin to exhibit signs of evaporation, but it does not boil or turn into steam under normal atmospheric pressure.
• 0ºC (32ºF)
• This is the freezing point of water under normal atmospheric pressure, not the boiling point.
• At 0ºC, water transitions from a liquid to a solid, forming ice.
• This temperature is a key reference in the Celsius and Fahrenheit scales.

Shortcut Trick

For Point B to lie on the line segment AC, the sum of segments AB and BC must be exactly equal to AC.

AB + BC = AC

(k + 3) + (2k) = 4k − 5

3k + 3 = 4k − 5

k = 8

∴ The correct answer is 8.

Alternate Method

Given:

Length of AB = k + 3

Length of BC = 2k

Length of AC = 4k − 5

Property used:

If three points A, B, and C are collinear and B lies between A and C, then by the Segment Addition Postulate, the total distance AC is the sum of the parts AB and BC.

Calculations:

⇒ AB + BC = AC

⇒ (k + 3) + 2k = 4k − 5

⇒ 3k + 3 = 4k − 5

⇒ 3 + 5 = 4k − 3k

⇒ 8 = k

∴ The correct answer is 8.

Additional Information

Collinearity of Points

Three points are collinear if they lie on the same straight line. For points A, B, and C, if AB + BC = AC, then B lies between A and C.

Triangle Inequality Theorem

In any triangle, the sum of any two sides must be greater than the third side (AB + BC > AC). If AB + BC = AC, the "triangle" degenerates into a straight line.

Distance Formula

In coordinate geometry, the distance between (x₁, y₁) and (x₂, y₂) is given by √((x₂−x₁)² + (y₂−y₁)²).

Given: 24 × 6 ÷ 3 - 11 + 13 = ?

According to the question, after ‘+’ and ‘-’ are interchanged and ‘×’ and ‘÷’ are interchanged:

24 × 6 ÷ 3 - 11 + 13 = ? ⇒ 24 ÷ 6 × 3 + 11 - 13 = ?

⇒ 24 ÷ 6 × 3 + 11 - 13 = ?

⇒ 4 × 3 + 11 - 13 = ?

⇒ 12 + 11 - 13 = ?

⇒ 23 - 13 = ?

⇒ 10 = ?

Hence, "Option 2" is the correct answer.

Given:

y³ = 0.008

Formula used:

If yⁿ = a, then y = a^1/n

Calculations:

y³ = 0.008

⇒ y³ = (0.2)³

⇒ y = 0.2

Now, finding the value of y⁵:

⇒ y⁵ = (0.2)⁵

⇒ y⁵ = 0.2 × 0.2 × 0.2 × 0.2 × 0.2

⇒ y⁵ = 0.00032

∴ The correct answer is option (2).

The logic followed here is:

Given:

(7,28,56)

7 × 4 + 28 = 56

28 + 28 = 56

56 = 56 (LHS = RHS)

And,

(9,36,72)

9 × 4 + 36 = 72

36 + 36 = 72

36 = 72 (LHS = RHS)

So, checking each option one by one:

Option 1) (13, 52, 94)

13 × 4 + 52 = 94

52 + 52 = 94

104 ≠ 94 (LHS ≠ RHS)

Option 2) (11, 52, 104)

11 × 4 + 52 = 104

44 + 52 = 104

96 ≠ 104 (LHS ≠ RHS)

Option 3) (13, 50, 104)

13 × 4 + 50 = 104

52 + 50 = 104

102 ≠ 104 (LHS ≠ RHS)

Option 4) (13, 52, 104)

13 × 4 + 52 = 104 

52 + 52 = 104 

104  = 104 (LHS = RHS)

Thus, out of all the options, '(13, 52, 104)' follows the same logic as given.

Hence, "Option 4" is the correct answer.

Shortcut Trick

Let the total work be the LCM of 5, 20, and 2 = 20 units.

Efficiency of A = 20 ÷ 5 = 4 units/day.

Efficiency of B = 20 ÷ 20 = 1 unit/day.

Combined efficiency of A + B + C = 20 ÷ 2 = 10 units/day.

Efficiency of C = 10 − (4 + 1) = 5 units/day.

Time taken by C alone = 20 ÷ 5 = 4 days.

∴ The correct answer is 4 days.

Alternate Method

Given:

Time taken by A = 5 days

Time taken by B = 20 days

Time taken by A + B + C = 2 days

Formula Used:

1/A + 1/B + 1/C = 1/Total Time

Calculations:

⇒ Efficiency of C = Efficiency of (A + B + C) − Efficiency of A − Efficiency of B

⇒ Efficiency of C = 10 − 4 − 1 = 5 units/day

⇒ Time taken by C alone = Total Work ÷ Efficiency of C

⇒ Time taken by C alone = 20 ÷ 5 = 4 days

∴ The correct answer is 4 days.

Additional Information

LCM Method for Time and Work

Total Work is assumed as the Least Common Multiple (LCM) of individual days. This avoids working with fractions and simplifies calculations.

Work and Efficiency Relation

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

The logic followed here is:

'PAIN" is coded as '9315'

'LIFT' is coded as '4256'

Thus, code for ‘I’ is '5'.

Hence, "Option 3" is the correct answer.

The Correct answer is Ovary.

Key Points

• The ovary is the part of a flower that develops into a fruit after fertilization.
• It is located at the base of the pistil, which is the female reproductive structure of the flower.
• Inside the ovary, there are one or more ovules, which contain the egg cells.
• After pollination, the pollen grains fertilize the ovules, leading to the formation of seeds.
• Once fertilization occurs, the ovary undergoes changes and ripens into a fruit, which helps in seed dispersal.
• The fruit can be fleshy or dry, depending on the type of plant.
• Examples of fruits formed from ripened ovaries include apples, mangoes, and tomatoes.
• This process is essential for the reproduction and propagation of flowering plants.

 Additional Information

• Petal
• Petals are the colorful parts of a flower that attract pollinators such as bees, butterflies, and birds.
• They do not play a direct role in the formation of fruits but are crucial for pollination.
• Petals are part of the flower's corolla and act as a protective layer for the reproductive organs of the flower.
• Pollen Tube
• The pollen tube is a structure that forms after a pollen grain lands on the stigma of a flower.
• It facilitates the transfer of male gametes from the pollen grain to the ovule.
• While it is essential for fertilization, it does not ripen or develop into a fruit.
• Anther
• The anther is the part of the flower's male reproductive system where pollen grains are produced.
• It is located at the tip of the stamen and is responsible for dispersing pollen.
• Anthers do not contribute to the formation of fruits; their primary role is in pollination.

The Correct answer is Yellow Flame.

Key Points

• When unsaturated compounds such as alkenes and alkynes undergo combustion, they generally produce a yellow flame.
• The yellow flame is caused by the incomplete combustion of hydrocarbons, which leads to the formation of soot particles.
• Unsaturated hydrocarbons contain double or triple bonds between carbon atoms, which require more oxygen for complete combustion compared to saturated hydrocarbons.
• Due to insufficient oxygen supply during burning, the combustion is incomplete, resulting in the release of carbon particles that glow yellow when heated.
• Examples of unsaturated hydrocarbons include ethylene (C₂H₄) and acetylene (C₂H₂).
• The yellow flame is often observed in laboratory experiments when burning hydrocarbons with limited oxygen availability.

 Additional Information

• Green Flame
• A green flame is not typically produced by the combustion of hydrocarbons. It is usually observed when certain elements like copper or boron compounds burn, as these elements emit green light due to their specific emission spectra.
• For example, the combustion of copper salts in a flame produces a green color.
• Red Flame
• A red flame is associated with the combustion of certain elements like strontium or lithium compounds.
• It is not related to the burning of hydrocarbons, whether saturated or unsaturated.
• Clean Flame
• A clean flame is typically produced by the complete combustion of saturated hydrocarbons like methane or propane.
• Complete combustion occurs when there is a sufficient supply of oxygen, resulting in no soot and the production of carbon dioxide and water vapor.

The Correct answer is Union Ministry of Culture.

Key Points

• Project PARI (Public Art for Resilient India) is an initiative launched by the Union Ministry of Culture to celebrate and enhance the public art scene in India.
• The project aims to promote public engagement with art and provide a platform for local and contemporary artists to showcase their creativity in public spaces.
• The initiative is part of the government's larger effort to integrate art and culture into everyday life, thereby fostering a sense of pride and ownership among citizens.
• It emphasizes the preservation and promotion of India's rich cultural heritage while also embracing modern and innovative art forms.
• Through Project PARI, the Ministry seeks to transform urban and rural landscapes by installing public artworks that reflect the diversity and dynamism of Indian culture.
• The initiative aligns with the 'Ek Bharat Shreshtha Bharat' program, which aims to strengthen cultural unity and collaboration across the country.

 Additional Information

• Lalit Kala Akademi
• The Lalit Kala Akademi, also known as the National Academy of Art, is an autonomous organization under the Ministry of Culture.
• It was established in 1954 to promote and propagate understanding of Indian visual arts, such as painting, sculpture, and graphics.
• It organizes art exhibitions, workshops, and camps and also provides scholarships and awards to artists.
• However, it is not directly involved in public art initiatives like Project PARI.
• Centre for Cultural Resources and Training (CCRT)
• The CCRT is an autonomous organization under the Ministry of Culture, established in 1979.
• Its primary objective is to promote the integration of culture and education by providing training to school teachers and students in cultural heritage.
• It is not directly involved in public art projects but focuses on educational and cultural enrichment programs.
• Sahitya Akademi
• The Sahitya Akademi, also known as the National Academy of Letters, is dedicated to the promotion of literature in India.
• Established in 1954, it recognizes and awards excellence in Indian literature across various languages.
• It primarily focuses on literary works and activities, not public art or visual arts.

The Correct answer is Its state of motion remains unchanged.

Key Points

• Balanced forces are forces that are equal in magnitude but act in opposite directions.
• When balanced forces act on an object, the net force becomes zero.
• An object remains in its current state of motion (either at rest or in uniform motion) when no net force acts on it, as per Newton's First Law of Motion.
• This phenomenon is often referred to as the law of inertia, which states that an object will continue in its existing state unless acted upon by an unbalanced force.
• For example, if a book is lying on a table and balanced forces act on it (gravity and the table's upward force), the book remains stationary.
• Similarly, if an object is moving in a straight line with constant speed and balanced forces act on it, its motion remains unchanged.
• Balanced forces do not cause any acceleration, change in direction, or deformation of the object.

 Additional Information

• It changes its direction of motion.
• Forces can change the direction of motion, but this happens only when the forces are unbalanced, not balanced.
• Unbalanced forces produce a net force that can alter the trajectory of the object.
• It speeds up.
• An object speeds up when unbalanced forces act on it, causing acceleration.
• Balanced forces do not lead to any change in the speed or velocity of an object.
• It slows down.
• Slowing down or deceleration occurs due to unbalanced forces, such as friction or resistance.
• Balanced forces cannot decrease an object's speed because there is no net force acting on it.

Shortcut Trick

Put θ = 0° to simplify the expression quickly.

When θ = 0°, cos 0° = 1 and sin 0° = 0.

Expression = (1 / (1 − 0)) + ((1 − 0) / 1) = 1 + 1 = 2.

Check options: 2 sec 0° = 2 × 1 = 2.

∴ The correct answer is 2 sec θ.

Alternate Method

Given: $\frac{\cos \theta}{1-\sin \theta}+\frac{1-\sin \theta}{\cos \theta}$

Formula Used: sin² θ + cos² θ = 1; sec θ = 1/cos θ

⇒ Taking LCM: [cos² θ + (1 − sin θ)²] / [cos θ(1 − sin θ)]

⇒ Expanding (1 − sin θ)²: [cos² θ + 1 + sin² θ − 2 sin θ] / [cos θ(1 − sin θ)]

⇒ Using Identity (sin² θ + cos² θ = 1): [1 + 1 − 2 sin θ] / [cos θ(1 − sin θ)]

⇒ [2 − 2 sin θ] / [cos θ(1 − sin θ)]

⇒ [2(1 − sin θ)] / [cos θ(1 − sin θ)]

⇒ 2 / cos θ = 2 sec θ

∴ The correct answer is 2 sec θ.

Additional Information

Trigonometric Identities

Primary identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Reciprocal Relations

sec θ = 1/cos θ, cosec θ = 1/sin θ, and cot θ = 1/tan θ.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

(I) All perfumes are watches → Does not follow (As all watches are perfumes. So it is possible but not definite.)

(II) No perfume is a tie → Does not follow (As all watches are perfumes and no watch is a tie. As no direct relation is given between perfumes and tie, therefore it is false)

∴ Here, Neither conclusion I nor II follows.​

Hence, the correct answer is "Option 2"

The Correct answer is Upgrading the Sukhoi-30MKI fleet with new avionics.

Key Points

• The Sukhoi-30MKI, a multirole fighter aircraft, serves as the backbone of the Indian Air Force.
• The upgrade in 2024 focused on equipping the Sukhoi-30MKI fleet with advanced avionics systems, enhancing its combat readiness and operational capabilities.
• The new avionics include radar systems, electronic warfare suites, and advanced communication systems, which make the aircraft more effective in modern warfare scenarios.
• This upgrade ensures better integration with indigenous weapon systems, such as the BrahMos supersonic missile, making the aircraft a formidable platform for strategic missions.
• The project aligns with the government's ‘Make in India’ initiative, as many components of the upgrade are manufactured indigenously.
• The upgrade enhances the ability to counter aerial threats, undertake long-range missions, and perform precision strikes.
• The modernization of the Sukhoi-30MKI fleet represents a critical step toward strengthening India's air superiority and addressing emerging challenges in the region.
• The Indian Air Force has partnered with Hindustan Aeronautics Limited (HAL) to implement these upgrades efficiently.

 Additional Information

• Acquisition of advanced drones for surveillance
• Drones are unmanned aerial vehicles (UAVs) used for a variety of purposes, including surveillance, reconnaissance, and combat missions.
• While the IAF is indeed expanding its drone capabilities, the focus in 2024 was more on upgrading existing platforms like the Sukhoi-30MKI.
• India has made significant advancements in indigenous drone development, such as the DRDO's Rustom series and other UAV projects.
• Expansion of the cyber defense unit
• Cyber defense is critical in modern warfare to protect sensitive data and operational systems from cyber-attacks.
• The IAF has been working on strengthening its cybersecurity infrastructure, but this was not the primary focus in 2024.
• Cyber defense involves deploying firewalls, encryption systems, and AI-driven monitoring tools to safeguard communication networks.
• Development of indigenously produced submarines
• Submarine development is primarily the responsibility of the Indian Navy, not the Indian Air Force.
• India has been working on its indigenous submarine programs, such as the INS Arihant, under the Strategic Forces Command.
• Submarines are crucial for maritime security, underwater reconnaissance, and nuclear deterrence capabilities.

The correct answer is Zero.

Key Points

• Work done is determined by the formula: W = F × d × cos(θ), where:
• W is the work done,
• F is the magnitude of the force applied,
• d is the displacement of the object,
• θ is the angle between the force and displacement.
• When the displacement is perpendicular to the direction of the force, the angle θ becomes 90 degrees.
• The cosine of 90 degrees is equal to 0. Hence, the work done (W) becomes 0, regardless of the magnitude of force or displacement.
• This is because there is no component of force acting in the direction of the displacement when the two are perpendicular.
• Examples of such cases include:
• Carrying a bag horizontally while walking forward – the force exerted (vertically upward) by the arms is perpendicular to the horizontal displacement.
• Motion of a satellite in a circular orbit – the force (gravitational) is perpendicular to the displacement.

 Additional Information

• Infinite
• The term infinite work is not applicable in real-world physics as it defies the laws of energy conservation.
• Work is always a finite quantity, based on the force applied and the displacement.
• Positive
• Work is considered positive when the force and displacement are in the same direction.
• For example, pushing a box forward applies a force in the direction of displacement, resulting in positive work.
• Negative
• Work is considered negative when the force and displacement are in opposite directions.
• For instance, when braking a car, the frictional force acts in the opposite direction to the car's displacement, resulting in negative work.

The Correct answer is prokaryotes.

Key Points

• Prokaryotes are organisms whose cells lack a well-defined nuclear membrane, meaning their genetic material is not enclosed within a nucleus.
• Their genetic material, usually in the form of a single circular DNA molecule, floats freely in a region called the nucleoid.
• Prokaryotic cells are simpler in structure and lack membrane-bound organelles such as the nucleus, mitochondria, and Golgi apparatus.
• Examples of prokaryotic organisms include bacteria (e.g., Escherichia coli) and archaea (e.g., Halobacterium).
• The absence of a nuclear membrane allows prokaryotes to carry out cellular processes efficiently as their genetic material is easily accessible for replication and transcription.
• Prokaryotes are generally smaller in size (usually ranging from 0.1 to 5 micrometers) compared to eukaryotic cells.
• They reproduce primarily through an asexual process called binary fission.

 Additional Information

• Eukaryotes
• Eukaryotic cells possess a well-defined nucleus enclosed by a nuclear membrane.
• They contain membrane-bound organelles such as mitochondria, chloroplasts, and the endoplasmic reticulum.
• Examples of eukaryotic organisms include plants, animals, fungi, and protists.
• Eukaryotic cells are generally larger in size, ranging from 10 to 100 micrometers.
• Cytoplasm
• The cytoplasm is the gel-like substance inside the cell where various cellular components and organelles are suspended.
• It plays a crucial role in facilitating cellular processes such as growth, metabolism, and replication.
• Chromatin
• Chromatin is the complex of DNA and proteins found in the nucleus of eukaryotic cells.
• It condenses to form chromosomes during cell division.

Shortcut Trick

For a number to be divisible by 4, its last two digits must be divisible by 4.

The last two digits of 12z4 are z4.

Possible values for z (where z4 is divisible by 4): 0, 2, 4, 6, 8.

The greatest possible value among these is 8.

∴ The correct answer is 8.

Alternate Method

Given: 4-digit number = 12z4, Divisor = 4.

Formula Used: Divisibility rule of 4 → Last two digits of the number must be a multiple of 4.

⇒ Last two digits = z4 (representing 10z + 4)

⇒ For z = 9: 94 ÷ 4 = 23.5 (No)

⇒ For z = 8: 84 ÷ 4 = 21 (Yes)

⇒ Since 8 is the largest single-digit integer satisfying the condition, z = 8.

∴ The correct answer is 8.

Additional Information

Divisibility by 2ⁿ

For 2¹ (2), last 1 digit must be even. For 2² (4), last 2 digits must be divisible by 4. For 2³ (8), last 3 digits must be divisible by 8.

Divisibility by 3 and 9

A number is divisible by 3 or 9 if the sum of its digits is divisible by 3 or 9 respectively.

The Correct answer is Condom — Mechanical barrier.

Key Points

• Condoms act as a mechanical barrier by physically preventing the sperm from reaching the egg, thereby avoiding fertilization.
• They are made of materials such as latex, polyurethane, or lambskin, which provide an effective barrier to sperm and sexually transmitted infections (STIs).
• Condoms are one of the most widely used contraceptive methods and are effective in preventing unintended pregnancies and reducing the risk of HIV/AIDS and other STIs.
• They are easy to use, widely available, and do not require a prescription, making them a popular choice worldwide.
• Both male and female condoms are available, but male condoms are more commonly used.
• Condoms do not involve hormones, which makes them suitable for individuals who cannot or do not want to use hormonal contraceptives.

 Additional Information

• Contraceptive pills — Uterine device
• This is incorrect because contraceptive pills do not act as uterine devices. Instead, they contain hormones (estrogen and progestin) that prevent ovulation, thicken cervical mucus, and thin the uterine lining to avoid pregnancy.
• Contraceptive pills are an example of hormonal contraception, not a physical device.
• Copper T — Hormonal imbalance
• This is incorrect because Copper T is a type of intrauterine device (IUD) that works by releasing copper ions, which are toxic to sperm. It does not cause hormonal imbalance.
• Copper IUDs are non-hormonal and function as a long-term reversible contraceptive method.
• Tubectomy — Chemical barrier
• This is incorrect because tubectomy is a form of permanent surgical sterilization in females. It involves blocking or cutting the fallopian tubes to prevent the egg from reaching the uterus.
• It is not a chemical barrier but a surgical procedure.

The Correct answer is Germination.

Key Points

• Germination is the process by which a seed develops into a new plant or seedling under suitable conditions.
• The seed contains an embryo, which is the future plant, along with stored nutrients that support its initial growth.
• During germination, the seed absorbs water in a process called imbibition, which activates the enzymes needed for growth.
• After water absorption, the seed swells, and the radicle (embryonic root) emerges first, anchoring the plant to the soil.
• Next, the plumule (embryonic shoot) emerges and begins growing upward toward the light.
• The process requires specific conditions such as adequate water, oxygen, and a suitable temperature range to take place.
• Germination is critical for plant reproduction and helps ensure the continuation of plant species.
• Examples of seeds undergoing germination are those of wheat, rice, and beans.

 Additional Information

• Regeneration
• Regeneration refers to the process by which organisms regrow lost or damaged tissues, organs, or limbs.
• This is observed in some animals like starfish, lizards, and planarians, but not in plants as a primary growth process.
• In plants, regeneration can occur in tissues during vegetative propagation, but it is distinct from germination.
• Fermentation
• Fermentation is a metabolic process where microorganisms like bacteria or yeast convert sugars into alcohol, gases, or acids.
• It is commonly used in the production of alcoholic beverages, bread, and yogurt.
• This process is unrelated to the growth of plants from seeds.
• Plantation
• Plantation refers to the act of planting trees or crops over a large area.
• It is a method of cultivation for crops like tea, coffee, and rubber, rather than a natural growth process like germination.

The Correct answer is New Delhi.

Key Points

• The Ministry of Coal inaugurated its first-ever coal gallery titled 'Black Diamond: Unveiling the Depths' in New Delhi in October 2024.
• This gallery showcases the rich history, importance, and significance of coal mining in India.
• New Delhi, as the capital city, is a hub for major government initiatives, exhibitions, and cultural events, making it a suitable location for this gallery.
• The exhibition is aimed at educating people about the role of coal in India's energy sector and its impact on the nation's economy.
• It also highlights advancements in coal mining technologies and measures for sustainable mining practices.
• The Ministry of Coal's efforts in creating this gallery align with its initiative to promote awareness and innovation in the coal sector.

 Additional Information

• Dhanbad
• Dhanbad is referred to as the 'Coal Capital of India' due to its extensive coal mining activities.
• It is home to major coalfields such as the Jharia and Raniganj coalfields.
• The city hosts the Indian School of Mines, a premier institute focusing on mining education.
• Ranchi
• Ranchi is the capital of Jharkhand, a state rich in mineral resources including coal.
• The city is a major administrative center for coal-related industries and is close to major coal mining areas.
• Raipur
• Raipur is the capital of Chhattisgarh, another state with significant coal reserves.
• It is known for its industrial importance and proximity to coal mining regions like Korba.

Given word: PLASTID

According to the question,

Thus, the new formed letter cluster → S R O K J C B

So, third from the left in the group of letters thus formed: (Left end) S R O K J C B (Right end) → O

Hence, "Option 4" is the correct answer.

Shortcut Trick

For the same remainder, the required greatest number is the HCF of the absolute differences between the numbers.

Numbers: 57, 95, 211

Differences: (95 − 57) = 38; (211 − 95) = 116; (211 − 57) = 154

HCF(38, 116, 154): 38 = 2 × 19; 116 = 2 × 58; 154 = 2 × 77

The only common factor is 2.

∴ The correct answer is 2.

Alternate Method

Given: Numbers are 57, 95, and 211.

Formula Used: Required Number = HCF(|x − y|, |y − z|, |z − x|)

⇒ First difference = 95 − 57 = 38

⇒ Second difference = 211 − 95 = 116

⇒ Third difference = 211 − 57 = 154

⇒ Factors of 38 = 1, 2, 19, 38

⇒ Factors of 116 = 1, 2, 4, 29, 58, 116

⇒ Factors of 154 = 1, 2, 7, 11, 14, 22, 77, 154

⇒ Highest Common Factor (HCF) = 2

∴ The correct answer is 2.

Additional Information

HCF with same remainder

When the remainder is the same but unknown, calculate the HCF of the differences between the given numbers: HCF(|a−b|, |b−c|, |c−a|).

HCF with different remainders

To find the greatest number that divides a, b, c leaving remainders r₁, r₂, r₃, calculate HCF(a−r₁, b−r₂, c−r₃).

LCM Property

LCM is the smallest number exactly divisible by all given numbers. For a remainder 'r' in each case, the number is LCM(a, b, c) + r.

Shortcut Trick

Ratio of present ages of Amit and Amita = 7 : 5

Difference in ratio parts (7 − 5) = 2 units

As per condition: (7 units − 5) = (5 units + 5) ⇒ 2 units = 10 years

Sum of present ages (7 + 5) = 12 units

If 2 units = 10 years, then 12 units = 10 × 6 = 60 years

∴ The correct answer is 60 years.

Alternate Method

Given:

Ratio of present ages of Amit and Amita = 7 : 5

Let Amit present age = 7x and Amita present age = 5x

Calculations:

⇒ (Amit age 5 years ago) / (Amita age 5 years hence) = 1 / 1

⇒ (7x − 5) / (5x + 5) = 1 / 1

⇒ 7x − 5 = 5x + 5

⇒ 7x − 5x = 5 + 5

⇒ 2x = 10

⇒ x = 5

⇒ Sum of present ages = 7x + 5x = 12x

⇒ Sum = 12 × 5 = 60 years

∴ The correct answer is 60 years.

Additional Information

Ratio and Proportions in Ages

When a constant number of years is added or subtracted, the absolute difference between two people's ages remains constant.

Cross-Multiplication Method

Useful for solving age problems where two different ratios at two different time points are provided: (a/b) → (c/d) over 'n' years.

The Correct answer is BaSO4(s) + 2NaCl (aq).

Key Points

• The reaction between sodium sulfate (Na2SO4) and barium chloride (BaCl2) is a classic example of a double displacement reaction.
• In this reaction, the sulfate ion (SO4²⁻) from sodium sulfate reacts with the barium ion (Ba²⁺) from barium chloride to form an insoluble compound, barium sulfate (BaSO4), which precipitates as a solid.
• The balanced equation for the reaction is: Na2SO4(aq) + BaCl2(aq) → BaSO4(s) + 2NaCl(aq).
• Barium sulfate (BaSO4) is a white precipitate, and its formation is used as an analytical test for the presence of sulfate ions.
• The other product, sodium chloride (NaCl), remains in the solution as an aqueous compound.
• This reaction demonstrates the principle of precipitation reactions, where an insoluble substance (precipitate) is formed when two aqueous solutions are mixed.

 Additional Information

• BaSO4(s) + 2NaCl2 (aq)
• This option is incorrect because the formula "NaCl2" is not valid. Sodium chloride (NaCl) is a simple ionic compound, and sodium does not form NaCl2.
• BaSO2(s) + NaCl (aq) + O2(g)
• This option is incorrect because BaSO2 is not a product of this reaction. Moreover, no gas like O2 is released in this double displacement reaction.
• BaSO2(s) + NaCl (aq) + 2O2(g)
• This option is incorrect for the same reasons as the previous one. The compound BaSO2 does not form, and oxygen gas is not evolved in this reaction.

The Correct answer is K, L, M, N, O...

Key Points

• Niels Bohr, in his atomic model, represented different electron orbits or energy levels using the symbols K, L, M, N, O....
• These orbits correspond to the principal quantum numbers (n = 1, 2, 3, 4, 5...) and represent specific energy levels around the nucleus.
• Each orbit is associated with a specific energy state, with the K-shell (n=1) being the closest to the nucleus and having the lowest energy.
• This representation helped in understanding the distribution of electrons in an atom and their arrangement across various energy levels.
• The concept of energy levels (or shells) is crucial in explaining the chemical properties of elements and the formation of bonds.
• The naming convention (K, L, M, N...) was adopted to avoid confusion with the alphabetical representation of other atomic properties like subshells (s, p, d, f).
• This model laid the foundation for the modern quantum mechanical model of the atom.

Decoding signs:

Given: 27 ÷ 66 × 11 - 7 + 10 = ?

After interchanging the letters,

27 ÷ 66 × 11 - 7 + 10 = ? ⇒ 27 + 66 ÷ 11 × 7 - 10 = ?

⇒ 27 + 66 ÷ 11 × 7 - 10 = ?

⇒ 27 + 6 × 7 - 10 = ?

⇒ 27 + 42 - 10 = ?

⇒ 69 - 10 = ?

⇒ 59 = ?

Hence, "Option 2" is the correct answer.

The Correct answer is Gautam Gambhir.

Key Points

• Gautam Gambhir is a former Indian cricketer and one of the most celebrated batsmen in Indian cricket history.
• He played a crucial role in India's triumphs in both the 2007 ICC T20 World Cup and the 2011 ICC Cricket World Cup, making significant contributions in the finals.
• Gambhir is known for his determined batting style and ability to perform under pressure.
• Post-retirement, he has been actively involved in cricket commentary, analysis, and mentoring young cricketers.
• His appointment as the Head Coach of the Indian men's cricket team in July 2024 highlights his deep understanding of the game and leadership qualities.
• Gautam Gambhir has also been involved in politics, representing Bharatiya Janata Party (BJP) and serving as a Member of Parliament from East Delhi Constituency.
• His dual experience in sports and leadership roles makes him a capable figure to guide the Indian cricket team.

 Additional Information

• Rahul Dravid
• Rahul Dravid is the current head coach of the Indian team as of 2023 and a legendary cricketer known as "The Wall" for his solid batting.
• He has previously served as the coach for India’s Under-19 team, guiding them to win the 2018 ICC Under-19 World Cup.
• Dravid is an iconic figure in Indian cricket and has played a significant role in mentoring young talent.
• VVS Laxman
• VVS Laxman is another former Indian cricketer known for his elegant batting style and exceptional performances, especially in Test cricket.
• He serves as the Head of the National Cricket Academy (NCA) in Bengaluru and has contributed to nurturing upcoming players.
• Laxman’s mentorship has been instrumental in shaping the next generation of Indian cricketers.
• MS Dhoni
• MS Dhoni is one of India’s most successful cricket captains, known for his calm demeanor and finishing abilities.
• He led India to victory in the 2007 ICC T20 World Cup, 2011 ICC Cricket World Cup, and the 2013 ICC Champions Trophy.
• Dhoni retired from international cricket in 2020 but continues to play in the Indian Premier League (IPL) for the Chennai Super Kings.

The Correct answer is Ca(OH)₂.

Key Points

• Calcium hydroxide has the chemical formula Ca(OH)₂. It consists of one calcium atom (Ca) bonded to two hydroxide ions (OH).
• It is commonly known as slaked lime and is widely used in various industries, including construction, agriculture, and water treatment.
• Calcium hydroxide is produced when calcium oxide (quicklime) reacts with water in an exothermic reaction.
• The compound is slightly soluble in water and forms a solution known as lime water, which is often used to test for the presence of carbon dioxide.
• Ca(OH)₂ is a strong base and reacts with acids to form salts and water, making it useful in neutralizing acidic solutions.
• It is also used in the preparation of mortars and plasters due to its ability to set and harden when exposed to carbon dioxide.

 Additional Information

• Mg(OH)₂
• Magnesium hydroxide has the chemical formula Mg(OH)₂ and is commonly known as milk of magnesia.
• It is used as an antacid to relieve indigestion and heartburn and as a laxative for treating constipation.
• Magnesium hydroxide is less soluble in water compared to calcium hydroxide.
• KOH
• Potassium hydroxide is a strong base with the chemical formula KOH.
• It is used in the production of soaps, detergents, and fertilizers.
• KOH is highly soluble in water and forms a strongly alkaline solution.
• NaOH
• Sodium hydroxide, also known as caustic soda, has the chemical formula NaOH.
• It is widely used in industries such as paper, textiles, and cleaning agents.
• NaOH is highly corrosive and is a strong base.

Given series: (Left) 7 2 5 5 2 1 9 2 4 1 2 2 6 9 5 5 5 3 8 5 5 3 1 1 6 3 3 (Right)

According to the question, such even digit which are immediately preceded by a perfect square and is immediately followed by an even digit:

Required condition: Perfect square - Even digit - Even digit

(Left) 7 2 5 5 2 1 9 2 4 1 2 2 6 9 5 5 5 3 8 5 5 3 1 1 6 3 3 (Right)

Thus, there are two such even digit which are immediately preceded by a perfect square and is immediately followed by an even digit.

Hence, "Option 2" is the correct answer.

The Correct answer is CO.

Key Points

• The molecular formula CO represents Carbon Monoxide, a compound composed of one carbon atom and one oxygen atom.
• Carbon Monoxide is a colorless, odorless, and tasteless gas that is highly toxic to humans and animals when inhaled.
• This gas is produced by the incomplete combustion of fossil fuels such as coal, natural gas, and gasoline.
• Its chemical structure consists of a triple bond between the carbon and oxygen atoms, making it a very stable molecule.
• Applications: Carbon Monoxide is used in various industrial processes such as the production of methanol and as a reducing agent in metallurgy.
• Health Hazards: Prolonged exposure to Carbon Monoxide can lead to carbon monoxide poisoning, which can be fatal due to its ability to bind with hemoglobin and prevent oxygen transport in the blood.

 Additional Information

• CO3
• CO3 does not exist as a stable compound. It is often mistaken for the carbonate ion (CO₃²⁻), which is a polyatomic ion composed of one carbon atom bonded to three oxygen atoms and carries a negative charge.
• The carbonate ion is common in compounds such as calcium carbonate (CaCO₃), which is found in limestone and chalk.
• CO2
• CO2, or Carbon Dioxide, is another molecular compound of carbon and oxygen, consisting of one carbon atom double-bonded to two oxygen atoms.
• It is a naturally occurring gas in the Earth's atmosphere and is produced during respiration, combustion, and volcanic activity.
• Applications: Carbon Dioxide is widely used in industries for carbonated beverages, fire extinguishers, and as a refrigerant.
• C2O
• C2O does not represent a commonly known or stable molecule. It may be a misrepresentation or an incorrect formula.

Shortcut Trick

Let the sum of money become 2ⁿ times in n × T years, where T is the time to double.

Here, the sum doubles in 10 years, so T = 10 years.

We need the sum to become 16 times, and 16 = 2⁴.

Total time for 16 times = 4 × 10 = 40 years.

Additional years required = 40 − 10 = 30 years.

∴ The correct answer is 30 years.

Alternate Method

Given:

Time to double (P → 2P) = 10 years

Target amount = 16 times (16P)

Calculations:

⇒ Amount (A) = P(1 + r/100)ⁿ

⇒ For doubling: 2P = P(1 + r/100)¹⁰ ⇒ 2 = (1 + r/100)¹⁰

⇒ For 16 times: 16P = P(1 + r/100)^T ⇒ 16 = (1 + r/100)^T

⇒ (2)⁴ = [(1 + r/100)¹⁰]⁴

⇒ (1 + r/100)^T = (1 + r/100)⁴⁰

⇒ Total time (T) = 40 years

⇒ More years needed = Total time − Initial time = 40 − 10 = 30 years

∴ The correct answer is 30 years.

Additional Information

Compound Interest Growth

In Compound Interest, if a sum becomes x times in t years, it will become xⁿ times in n × t years.

Simple Interest vs CI Growth

In Simple Interest, if a sum doubles (becomes 2P) in 10 years, it means it adds P interest every 10 years. To become 16P, it needs 15P interest, taking 15 × 10 = 150 years.

Shortcut Trick

Let the average expenditure of all 9 men be x.

The 9^th man spent the average plus ₹2 (x + 2). This extra ₹2 is distributed among the other 8 men.

Extra per person for 8 men = 2 ÷ 8 = ₹0.25.

Average (x) = Individual spend of 8 men + Extra share = 3 + 0.25 = ₹3.25.

Total Expenditure = Average × Number of men = 3.25 × 9 = ₹29.25.

∴ The correct answer is ₹29.25.

Alternate Method

Given: Number of men = 9. Spending of 8 men = ₹3 each. 9^th man spent ₹2 more than the total average.

Formula Used: Total Expenditure = Average × Number of items.

⇒ Let the average expenditure be x.

⇒ Total expenditure = 9 × x = 9x.

⇒ Total expenditure = (8 × 3) + (x + 2).

⇒ 9x = 24 + x + 2.

⇒ 9x − x = 26.

⇒ 8x = 26.

⇒ x = 26 ÷ 8 = 3.25.

⇒ Total money spent = 9 × 3.25 = ₹29.25.

∴ The correct answer is ₹29.25.

Additional Information

Average Concept

Average is the sum of all observations divided by the total number of observations. Formula: Average = Sum ÷ Count.

Deviation Method

In problems where one person spends more than the average, that extra amount is equally contributed to the remaining members to find the true average.

Weighted Average

When groups have different averages, the combined average is (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

The Correct answer is image is real.

Key Points

• The negative sign in the magnification of spherical mirrors indicates that the image formed is inverted.
• In the case of mirrors, an inverted image is always a real image.
• A real image is formed when the reflected rays actually meet at a point.
• Convex mirrors always produce virtual, erect, and diminished images, but concave mirrors can produce real or virtual images depending on the object’s position.
• When the object is placed beyond the focal point of a concave mirror, the image formed is real and inverted, leading to a negative magnification.
• The magnification formula is: m = -v/u, where v is the image distance, u is the object distance, and the negative sign denotes the inverted (real) image.
• This concept is crucial in applications such as optical instruments, telescopes, and projectors, which utilize real images.

 Additional Information

• Image is diminished
• A diminished image is smaller than the object.
• It is typically formed by convex mirrors and some specific cases of concave mirrors.
• Diminished images are usually virtual, although real images can also be diminished in specific setups.
• Image is enlarged
• An enlarged image is larger than the object.
• It is often formed by a concave mirror when the object is placed between the focal point and the mirror.
• Such images are usually virtual, although real images can also be enlarged in particular cases.
• Image is virtual
• A virtual image is formed when the reflected rays do not actually meet but appear to meet when extended backward.
• Virtual images are always erect and are commonly produced by plane mirrors, convex mirrors, and concave mirrors under specific conditions.
• Virtual images cannot be projected onto a screen.

The Correct answer is 8.

Key Points

• In the 2024 Lok Sabha elections, the Indian National Congress secured 8 seats in Rajasthan.
• Rajasthan has a total of 25 Lok Sabha constituencies, making it a significant state in national elections.
• The Congress party's performance in Rajasthan reflects its ability to maintain a foothold in this politically diverse state despite electoral challenges.
• Rajasthan has historically alternated between the two major political parties, Indian National Congress and Bharatiya Janata Party (BJP), in Lok Sabha elections.
• The Congress party's campaign in Rajasthan focused on issues such as farmer welfare, unemployment, and social justice to resonate with the voters.
• Rajasthan is known for its political dynamics, where factors like caste equations, rural-urban divide, and regional issues play a crucial role in determining electoral outcomes.
• The Congress party's performance in Rajasthan was part of a broader strategy to reclaim its influence in northern India.

Given: A, B, E, F, P, Q and R are sitting around a circular table facing the centre. 

1) A sits fourth to the right of F. 

2) Only two people sit between A and Q. 

3) Only two people sit between R and Q.

4) P sits to the immediate left of B.

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

Thus, according to the final arrangement, two people sit between P and E when counted from the right of E.

Hence, "Option 3" is the correct answer.

Shortcut Trick

Let the third number be 100.

First number = 120 and Second number = 125.

Required percentage = (First number ÷ Second number) × 100.

⇒ (120 ÷ 125) × 100 = 24 × 4 = 96%.

∴ The correct answer is 96%.

Alternate Method

Given:

First number = 20% more than third number.

Second number = 25% more than third number.

Formula Used:

Percentage = (Value ÷ Base Value) × 100

Calculations:

Let the third number be x.

⇒ First number = x + 20% of x = 1.20x

⇒ Second number = x + 25% of x = 1.25x

⇒ Required Percentage = (1.20x ÷ 1.25x) × 100

⇒ Required Percentage = (120 ÷ 125) × 100

⇒ Required Percentage = 0.96 × 100 = 96%

∴ The correct answer is 96%.

Additional Information

Base Change Rule

Always identify the value after the word 'than' or 'of' as the base (denominator) for percentage calculations.

Percentage Increase

If a number is increased by R%, the new number is (100 + R)/100 × original number.

Fraction to Percentage Conversion

4/5 = 80%, 24/25 = 96%, 1/4 = 25%. Knowing these common fractions helps in fast calculation.

Given: Seven boxes, A, B, E, F, L, M and P, are kept one over.

1) Only A is kept above E. 

2) Only P is kept below M.

3) Only two boxes are kept between E and F.

4) B is not kept immediately above F.

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