RRB Technician Grade III Official Paper (Held On: 20 Dec, 2024 Shift 2) (Previous Year Paper)

Given:

Numbers: 4⁵⁰, 2¹⁰⁰, 16²⁵

Formula used:

(a^m)ⁿ = a^{m × n}

Calculations:

Expressing all numbers with base 2:

First number = 4⁵⁰

⇒ (2²)⁵⁰ = 2^{2 × 50} = 2¹⁰⁰

Second number = 2¹⁰⁰

Third number = 16²⁵

⇒ (2⁴)²⁵ = 2^{4 × 25} = 2¹⁰⁰

Comparing the results:

⇒ 2¹⁰⁰ = 2¹⁰⁰ = 2¹⁰⁰

∴ The correct answer is option (1).

The correct answer is Both 'A' and 'B' are correct.

Key Points

• Weight (Statement A):
• Weight is indeed a force. Specifically, it's the force of gravity acting on an object's mass.
• This force is always directed towards the center of the Earth, hence "vertically downward."
• Weight is measured in Newtons (N), just like any other force.
• The magnitude of weight is calculated using the formula: Weight (W) = mass (m) × acceleration due to gravity (g).
• On Earth, the acceleration due to gravity (g) is approximately 9.8 m/s².
• Therefore, a heavier object experiences a greater gravitational force.
• Weight is a vector quantity, meaning it has both magnitude and direction.
• It is important to remember that weight is not the same as mass. Mass is the amount of matter in an object, while weight is the force of gravity on that mass.
• The weight of an object will change depending on the gravity of the location, while the mass will remain constant.
• For example, an object on the moon will have a lower weight than on earth, due to the moons lower gravity.
• Weight is a fundamental force that governs the motion of celestial bodies and the behavior of objects on Earth.

Additional Information

• Thrust (Statement B):
• Thrust is a type of force that acts perpendicular to a surface.
• It's often associated with fluids (liquids or gases) exerting pressure on a surface.
• For instance, the force exerted by water on the bottom of a container is thrust.
• In aerodynamics, thrust is the force generated by an aircraft's engines that propels it forward.
• In that case the thrust force is pushing air backwards, and the reaction force is pushing the aircraft forward.
• The direction of the thrust force is always perpendicular to the surface it acts upon.
• Thrust is also a vector quantity.
• The concept of thrust is crucial in understanding buoyancy, where the upward thrust of a fluid supports an object.
• Thrust can be generated by many things, including fluids, solid objects, and even electromagnetic fields.
• The amount of thrust generated is dependent on the amount of pressure exerted on the surface, and the area of the surface.
• Thrust is also measured in Newtons (N).
• The pressure exerted by the fluid is the force exerted per unit area.
• When an object is submerged in a fluid, the thrust force is equal to the weight of the fluid displaced by the object.

Shortcut Trick

Use the algebraic identity a² − b² = (a + b)(a − b).

10000x = (9982 + 18) × (9982 − 18)

10000x = 10000 × 9964

∴ The correct answer is 9964.

Alternate Method

Given: 10000x = (9982)² − (18)²

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

⇒ 10000x = (9982 + 18)(9982 − 18)

⇒ 10000x = (10000) × (9964)

⇒ x = (10000 × 9964) ÷ 10000

⇒ x = 9964

∴ The correct answer is 9964.

Additional Information

Difference of Two Squares

The identity a² − b² = (a − b)(a + b) is used to simplify calculations involving the subtraction of two squared numbers.

Square of Sum and Difference

Related identities include (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

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

The 10th digit from the left end is: 9

and the 4th digit from the right end is: 0

So, the sum of the 10th digit from the left end and the 4th digit from the right end of the series will be 9 + 0 = 9.

Hence, the correct answer is "Option 1".

The correct answer is Centrifugation.

Key Points

• Centrifugation:
• Centrifugation is a technique that uses centrifugal force to separate particles based on their size, shape, and density.
• Colloidal particles are very small and do not settle under normal gravitational forces.
• A centrifuge spins a mixture at high speeds, creating a strong centrifugal force that pushes denser particles outward.
• This force causes the colloidal particles to sediment or settle at the bottom of the centrifuge tube, forming a pellet.
• The liquid above the pellet, called the supernatant, can then be separated from the sediment.
• This technique is highly effective for separating colloidal particles because it provides a much greater force than gravity.
• Different types of centrifuges exist, including ultracentrifuges, which can generate extremely high centrifugal forces.
• Centrifugation is widely used in various fields, including biology, chemistry, and medicine, for separating cells, proteins, and other colloidal particles.
• The speed of centrifugation is measured in revolutions per minute (RPM) or relative centrifugal force (RCF).

Additional Information

• Distillation:
• Distillation is a process used to separate liquids with different boiling points.
• It involves heating a liquid mixture to vaporize the component with the lower boiling point.
• The vapor is then cooled and condensed back into a liquid, which is collected separately.
• Distillation is effective for separating homogeneous liquid mixtures, such as alcohol and water.
• However, it is not suitable for separating colloidal particles, as they are dispersed throughout a liquid rather than being dissolved.
• Distillation relies on the vaporization and condensation of liquids, which is not applicable to separating dispersed solid particles.
• Colloidal particles do not change their state of matter in a typical distillation process.
• Therefore, distillation would not result in the separation of colloids.
• Distillation is used in the purification of water, and the separation of crude oil into usable products.
• Filtration:
• Filtration is a process used to separate solid particles from a liquid or gas by passing the mixture through a filter.
• The filter allows the liquid or gas to pass through while trapping the solid particles.
• Traditional filtration is effective for separating relatively large solid particles from a liquid.
• However, colloidal particles are too small to be effectively trapped by most standard filters.
• While ultrafiltration uses very fine filters, and can separate some larger colloidal particles, standard filtration is ineffective.
• Colloidal dispersions have particles that are so small that they will pass through normal filter paper.
• The particle size of colloids ranges from 1 nanometer to 1 micrometer.
• Thus, normal filtration is not a correct method for colloid separation.
• Filtration is used in water treatment, and air purification.
• Evaporation:
• Evaporation is the process of a liquid changing into a gas.
• It occurs when the liquid is heated or exposed to air, causing its molecules to gain enough energy to escape into the atmosphere.
• Evaporation can be used to separate a dissolved solid from a liquid solvent.
• However, it is not effective for separating colloidal particles, as they remain dispersed throughout the liquid even after the solvent has evaporated.
• Evaporation removes the liquid portion of the mixture, leaving behind any dissolved solids.
• Colloidal particles will remain in the solid residue after evaporation.
• Evaporation does not separate the dispersed colloidal particles from each other.
• Evaporation is used in the production of salt from seawater, and in drying wet clothes.

The correct answer is Collenchyma.

Key Points

• Collenchyma:
• Collenchyma tissue provides mechanical support and flexibility to young stems, petioles, and leaves.
• It consists of elongated living cells with thickened primary cell walls, particularly at the corners.
• These thickenings are due to the deposition of cellulose, hemicellulose, and pectin.
• The uneven thickening of the cell walls allows for flexibility and tensile strength, enabling the plant to bend without breaking.
• Collenchyma is commonly found in the peripheral regions of stems and leaf petioles, where flexibility is most needed.
• This tissue is what allows climbers and other plants to bend, and twist around objects.
• Because the cells are living, they can continue to grow, and provide support to growing plant parts.
• Collenchyma is typically found below the epidermis.

Additional Information

• Chlorenchyma:
• Chlorenchyma is a type of parenchyma tissue that contains chloroplasts.
• Its primary function is photosynthesis, the process of converting light energy into chemical energy.
• Chlorenchyma is found in the leaves and green stems of plants, where sunlight is readily available.
• It is responsible for the green color of plants due to the presence of chlorophyll in the chloroplasts.
• While it contributes to the overall structure of the plant, it does not provide the flexibility needed for bending.
• Chlorenchyma is a modified form of parenchyma.
• This tissue is very important for food production in plants.
• Aerenchyma:
• Aerenchyma is a specialized type of parenchyma tissue with large air spaces.
• It is found in aquatic plants and those growing in waterlogged soils.
• Aerenchyma provides buoyancy and facilitates gas exchange in these environments.
• The air spaces allow for the diffusion of oxygen to submerged plant parts.
• It does not contribute to the flexibility of plant stems or tendrils.
• Aerenchyma is modified to help plants with gas exchange in low oxygen environments.
• The large air spaces reduce the density of the plant tissue.
• Parenchyma:
• Parenchyma is the most abundant and versatile type of plant tissue.
• It consists of thin-walled, living cells that perform various functions, including storage, photosynthesis, and secretion.
• Parenchyma cells are loosely packed, allowing for intercellular spaces that facilitate gas exchange and nutrient transport.
• While parenchyma provides structural support, it does not offer the specialized flexibility provided by collenchyma.
• Parenchyma is found in many plant parts, including the cortex, pith, and mesophyll.
• Parenchyma cells can also help in the process of repair and regeneration.
• Parenchyma cells can also store food.

Shortcut Trick

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

Time (T) = 100 ÷ Rate of Interest (R)

T = 100 ÷ 20 = 5 years

∴ The correct answer is 5 years.

Alternate Method

Given:

Let the Principal (P) = ₹100

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

Simple Interest (SI) = A − P = 200 − 100 = ₹100

Rate of Interest (R) = 20%

Formula Used:

SI = (P × R × T) ÷ 100

Calculations:

⇒ 100 = (100 × 20 × T) ÷ 100

⇒ 100 = 20 × T

⇒ T = 100 ÷ 20

⇒ T = 5 years

∴ The correct answer is 5 years.

Additional Information

Multiplier Method for Simple Interest

If a sum becomes 'n' times in 'T' years, the relation is (n − 1) = (R × T) ÷ 100.

Simple Interest vs Compound Interest

In Simple Interest, the interest is always calculated on the original principal, whereas in Compound Interest, it is calculated on the accumulated amount.

Effective Rate of Interest

The total percentage of interest earned over 'T' years at 'R%' rate is simply R × T %.

Given Equation: 18 C 6 D 18 A 6 B 18 = ?

BODMAS Rule:

Decoding the given information:

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

⇒ 18 ÷ 6 × 18 + 6 - 18

⇒ 3 × 18 + 6 - 18

⇒ 54 + 6 - 18

⇒ 60 - 18

⇒ 42

Hence, the correct option is "Option 2".

The correct answer is Vanilla essence.

Key Points

• Vanilla essence:
• Vanilla essence is an olfactory indicator, meaning it uses changes in odor to detect acidic or basic substances.
• In acidic solutions, vanilla essence retains its characteristic sweet smell.
• In basic solutions, the smell of vanilla essence diminishes or disappears.
• Olfactory indicators are particularly useful for visually impaired individuals.
• The change in odor is due to the reaction of the basic substance with the compounds responsible for the vanilla scent.
• This is a qualitative test, and not a quantitative test.

Additional Information

• Phenolphthalein:
• Phenolphthalein is a chemical indicator that changes color depending on the pH of a solution.
• It is colorless in acidic solutions and pink in basic solutions.
• Phenolphthalein is commonly used in titrations to determine the endpoint of acid-base reactions.
• It is a visual indicator, not an olfactory indicator.
• The color change happens due to the change in the phenolphthalein molecule structure, due to changes in the pH.
• Red litmus:
• Red litmus paper is a pH indicator that changes color in the presence of basic solutions.
• It remains red in acidic solutions and turns blue in basic solutions.
• Litmus paper is used to determine whether a solution is acidic or basic.
• It is a visual indicator, not an olfactory indicator.
• Litmus paper is a natural dye derived from lichens.
• Methyl orange:
• Methyl orange is a pH indicator that changes color depending on the acidity of a solution.
• It is red in strongly acidic solutions, orange in moderately acidic solutions, and yellow in neutral or basic solutions.
• Methyl orange is commonly used in titrations.
• It is a visual indicator, not an olfactory indicator.
• The color change happens due to the change in the methyl orange molecule structure, due to changes in the pH.

According to the given information,

Here, we can see that the code for 'File' is 'Zi'.

Hence, the correct answer is "Zi".

According to the given information,

Here, we can see that the code for 'hurt' is 'ja'.

Hence, the correct answer is "ja".

Given series:

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

Condition to be checked:

perfect square → odd digits → even digit

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

Thus there are two such patterns (1 7 6, 1 7 8) that are following the above conditions.

Hence,"2" is the correct answer.

Mistake Point

Immediately preceded by means immediately before or to come just before.

Immediately followed by means immediately after or to come just after.

Given:

Expression = 6 + 6 × 6 − 6

Formula used:

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

Calculations:

6 + 6 × 6 − 6

⇒ 6 + 36 − 6

⇒ 42 − 6

⇒ 36

∴ The correct answer is option (4).

The correct answer is The iron rod would float on water surface.

Key Points

• Two primary forces are at play: the downward force of gravity (weight) and the upward force of upthrust (buoyant force).

• The weight of the iron rod is due to its mass and the acceleration due to gravity (W = mg).

• Upthrust is the upward force exerted by a fluid on an immersed or partially immersed object.

• Upthrust is equal to the weight of the fluid displaced by the object (Archimedes' principle).

• The Scenario:

• The question states that the upthrust of the water on the iron rod is greater than the downward force (weight).

• This means the upward force is stronger than the downward force.

• Resultant Force:

• When upthrust is greater than weight, the resultant force on the iron rod is upward.

• This upward force will cause the iron rod to accelerate upward.

• Floating:

• If the iron rod is initially at rest on the water's surface, the excess upthrust will lift it.

• The rod will continue to rise until it reaches a point where the upthrust equals its weight.

• At this point, the rod will float on the water's surface.

• The object will reach an equilibrium point where the weight of the water it displaces is equal to the weight of the object.

• The density of the iron, and the volume of water displaced are the main factors in determining the upthrust.

• If the iron rod was a hollow shape, it would displace more water, thus increasing the upthrust.

• The shape of an object greatly affects its ability to float.

• A solid iron rod has a high density, and therefore it normally sinks.

• For an object to float, the upthrust must be equal to or greater than the objects weight.

• The buoyant force is directly proportional to the density of the fluid.

• The buoyant force is also directly proportional to the volume of the displaced fluid.

• If the water was replaced with a denser fluid, the upthrust would increase.

• The weight of the object is a constant, unless the mass of the object changes.

• The upthrust force is a variable, dependent on the fluid and the volume displaced.

• The concept of upthrust is essential in naval architecture and the design of ships.

The logic followed here is:

Hence, "Option 2" is the correct answer.

The correct answer is Endoplasmic reticulum.

Key Points

• Endoplasmic reticulum (ER):
• The endoplasmic reticulum is a network of membranous tubules and sacs found within the cytoplasm of eukaryotic cells.
• It functions as a passageway for the transport of materials within the cell, particularly proteins.
• There are two main types of ER: rough ER (RER) and smooth ER (SER).
• RER is studded with ribosomes, making it a site for protein synthesis and modification.
• SER lacks ribosomes and is involved in lipid synthesis, detoxification, and calcium storage.
• The ER is a major part of the cells internal transport system.
• The ER plays a critical role in the folding of newly synthesized proteins.

Additional Information

• Plastids:
• Plastids are membrane-bound organelles found in plant cells and some algae.
• They are involved in various functions, including photosynthesis (chloroplasts), storage of starch (amyloplasts), and pigment storage (chromoplasts).
• Plastids do not function as a general intracellular transport system.
• They are primarily focused on the production and storage of specific molecules.
• Plastids have their own DNA.
• Plastids are able to replicate independently of the cell.
• Mitochondria:
• Mitochondria are the "powerhouses" of the cell, responsible for cellular respiration.
• They generate ATP (adenosine triphosphate), the cell's primary energy currency.
• Mitochondria have their own DNA and are involved in various cellular processes, but not in general intracellular transport as a main function.
• Mitochondria have a double membrane.
• Mitochondria are found in nearly all eukaryotic cells.
• The inner membrane of the mitochondria is folded into cristae, which increase the surface area for cellular respiration.
• Ribosome:
• Ribosomes are cellular structures responsible for protein synthesis.
• They can be found freely floating in the cytoplasm or attached to the rough endoplasmic reticulum.
• Ribosomes read messenger RNA (mRNA) and assemble amino acids into polypeptide chains.
• While they are crucial for protein production, they do not function as a general transport network.
• Ribosomes are made of ribosomal RNA (rRNA) and proteins.
• Ribosomes are essential for all living cells.
• Ribosomes are not membrane bound organelles.

Shortcut Trick

Compare the ratios of the coefficients: a₁/a₂, b₁/b₂, and c₁/c₂.

a₁/a₂ = 3 ÷ (−6) = −1/2

b₁/b₂ = (−5) ÷ 10 = −1/2

c₁/c₂ = 7 ÷ 7 = 1

Since a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the lines are parallel.

∴ The correct answer is no solution.

Alternate Method

Given:

Equation 1: 3x − 5y = 7

Equation 2: −6x + 10y = 7

Formula Used:

For a pair of linear equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂:

If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the system has no solution.

Calculations:

⇒ a₁ = 3, b₁ = −5, c₁ = 7

⇒ a₂ = −6, b₂ = 10, c₂ = 7

⇒ a₁/a₂ = 3 / (−6) = −1/2

⇒ b₁/b₂ = (−5) / 10 = −1/2

⇒ c₁/c₂ = 7 / 7 = 1

⇒ Here, a₁/a₂ = b₁/b₂ ≠ c₁/c₂

⇒ The lines are parallel and do not intersect.

∴ The correct answer is no solution.

Additional Information

Unique Solution (Intersecting Lines)

If a₁/a₂ ≠ b₁/b₂, the system of linear equations is consistent and has exactly one solution.

Infinitely Many Solutions (Coincident Lines)

If a₁/a₂ = b₁/b₂ = c₁/c₂, the system is consistent (dependent) and has infinite solutions.

No Solution (Parallel Lines)

If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the system is inconsistent and has no solution.

The least possible Venn diagram:

Conclusion:

I. All machines are cushions → False (because all cushions are machines So, all machines are cushions it may be possible but not defined)

II. Some bells are machines → True (because some cushions are bells and all cushions are machines So, some bells are also machines)

So, Only conclusion (II) follows.

Hence, the correct answer is "Option 4".

Shortcut Trick

Common person Amita appears on both sides of the age sum comparison.

The difference in sums is directly equal to the difference between the unique persons.

(Amit + Amita) − (Amita + Amrita) = 15 years.

Amit − Amrita = 15 years.

∴ The correct answer is 15 years.

Alternate Method

Given: Sum of Amit and Amita = (Sum of Amita and Amrita) + 15

Calculations:

⇒ Let Amit's age be A, Amita's age be B, and Amrita's age be C.

⇒ A + B = (B + C) + 15

⇒ A + B − B − C = 15

⇒ A − C = 15

∴ The correct answer is 15 years.

Additional Information

Linear Equations in Ages

When a common variable exists on both sides of an addition-based equation, it cancels out, leaving the difference between the remaining variables.

Age Difference Invariance

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

The correct answer is Wayanad.

Key Points

• Reports indicate that extremely heavy rainfall in late July 2024 caused catastrophic landslides and flooding, particularly affecting Wayanad district in Kerala.
• There are reports of heavy rainfall also affecting Idukki district, and also red alerts being issued for Idukki.
• Specifically the Wayanad landslide was very severe, with many deaths and much distruction.
• The landslides in Wayanad occurred in areas including Punjirimattom, Mundakkai, Chooralmala, and Vellarimala villages in Meppadi panchayat, Vythiri taluk.
• The heavy rains triggered flash floods and multiple landslides on the steep slopes in these areas.
• The scale of the disaster in Wayanad led to significant rescue and relief efforts, involving various agencies.
• The event resulted in substantial loss of life, property damage, and displacement of residents.
• The geographical terrain of Wayanad, characterized by steep slopes and heavy rainfall, makes it vulnerable to landslides.
• Heavy rain fall through out the western ghats, causes many land slides, that is why many districts were placed on red alert.
• The heavy rainfall caused the collapse of hillsides, leading to the destruction of villages below.
• Rescue operations were hindered by damaged roads and bridges, making access to affected areas difficult.
• The disaster prompted the deployment of personnel from the National Disaster Response Force (NDRF), Army, Air Force, Navy, and other emergency services.
• The Kerala government provided relief camps for displaced residents.
• Financial assistance and rehabilitation efforts were initiated for the affected communities.
• The event highlighted the vulnerability of the region to climate-related disasters.
• The landslides caused significant damage to infrastructure, including roads, bridges, and buildings.
• Agricultural lands were also heavily impacted by the landslides.
• The disaster resulted in the loss of livestock and wildlife.
• The event underscored the need for improved disaster preparedness and mitigation measures.
• The impact of the landslide was widely reported in national and international media.
• There were great efforts made to provide medical assistance to those injured.

Shortcut Trick

For a continued proportion a : b :: b : c, the mean proportional logic is b² = a × c.

Given 40 : 35 :: 35 : k ⇒ k = (35 × 35) ÷ 40.

k = 1225 ÷ 40 = 245/8.

Value of k − 1 = 245/8 − 1 = 237/8.

∴ The correct answer is 237/8.

Alternate Method

Given: 40 : 35 :: 35 : k

Formula Used: If a, b, c are in continued proportion, then a/b = b/c

⇒ 40 / 35 = 35 / k

⇒ k = (35 × 35) / 40

⇒ k = 1225 / 40

⇒ k = 245 / 8

To find: k − 1

⇒ k − 1 = 245/8 − 1

⇒ k − 1 = (245 − 8) / 8

⇒ k − 1 = 237 / 8

∴ The correct answer is 237/8.

Additional Information

Fourth Proportional

In a proportion a : b :: c : d, the term d is called the fourth proportional, calculated as d = (b × c) / a.

Third Proportional

In a continued proportion a : b :: b : c, the term c is the third proportional, where c = b² / a.

Mean Proportional

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

The correct answer is Milk of magnesia.

Key Points

• Milk of magnesia:
• Milk of magnesia is a colloidal dispersion of magnesium hydroxide in water.
• It is a sol, which is a type of colloid where solid particles are dispersed in a liquid medium.
• The magnesium hydroxide particles are very small and remain suspended in the water, giving it a milky appearance.
• It is commonly used as an antacid and laxative.
• The particles in milk of magnesia do not settle easily due to their small size and the presence of stabilizing agents.
• The particle size of the suspended Mg(OH)2 is within the colloidal range.

Additional Information

• Face cream:
• Face cream is an emulsion, which is a mixture of two or more immiscible liquids (typically oil and water).
• Emulsions are different from sols, as they involve the dispersion of liquids in liquids.
• Face creams contain emulsifiers that stabilize the mixture and prevent the liquids from separating.
• They are designed to provide moisture and other beneficial ingredients to the skin.
• Face cream is a complex mixture of many different substances.
• The consistency of face cream is due to the emulsifiers present.
• Foam:
• Foam is a colloidal dispersion where gas bubbles are trapped within a liquid or solid.
• It is a type of dispersion known as a foam, not a sol.
• Examples of foams include whipped cream and shaving cream.
• Foams are characterized by their light and airy texture.
• The stability of a foam is dependent on the surface tension of the liquid.
• Foams can be either liquid or solid.
• Rubber:
• Rubber, in its raw form, can be a latex, which is a colloidal dispersion, but processed rubber is a solid polymer.
• Processed rubber is not a sol.
• Raw latex is a colloidal dispersion of polymer particles in a water based liquid.
• Vulcanized rubber is a solid material.
• Rubber is an elastic polymer.
• The properties of rubber are due to its long chain polymer structure.

Given: 

Shahid starts from Point A and drives 20 km towards West.

He then takes a left turn, drives 20 km, turns left and drives 15 km.

He then takes a left turn and drives 12 km.

He takes a final right turn, drives 5 km and stops at Point P. 

It then turns 90° to its right.

So, 8 km towards the direction he should drive to reach Point A again.

Hence, the correct answer is "Option 1".

The correct answer is Change in velocity per unit time - Acceleration.

Key Points

• 2) Change in velocity per unit time - Acceleration:
• Acceleration is defined as the rate of change of velocity with respect to time.
• This means that acceleration measures how quickly the velocity of an object is changing.
• It is a vector quantity, possessing both magnitude and direction.
• The units of acceleration are meters per second squared (m/s²).
• If the velocity increases, the acceleration is positive; if the velocity decreases, the acceleration is negative (deceleration or retardation).
• An object that speeds up, or slows down, or changes direction, is accelerating.

Additional Information

• 1) Motion of a freely falling body - Non-uniform acceleration:
• A freely falling body experiences uniform acceleration due to gravity.
• The acceleration due to gravity is approximately 9.8 m/s² near the Earth's surface, and it is considered constant.
• Therefore, the motion of a freely falling body is an example of uniform acceleration, not non-uniform acceleration.
• Air resistance can change the acceleration, but in a vacuum, the acceleration is constant.
• The velocity of a freely falling object increases at a constant rate.
• 3) Velocity does not change with time - Non-uniform motion:
• If the velocity of an object does not change with time, it means the object is moving with uniform velocity.
• Uniform velocity implies uniform motion, not non-uniform motion.
• Non-uniform motion is when velocity changes with time.
• An object with a constant velocity has zero acceleration.
• Uniform motion is motion in a straight line with constant speed.
• 4) Velocity varies with time - Uniform motion:
• If the velocity of an object varies with time, it means the object is undergoing non-uniform motion.
• Uniform motion implies that the velocity remains constant.
• Uniform motion has constant velocity, and zero acceleration.
• If velocity varies, then acceleration is present.
• Non-uniform motion can have varying degrees of acceleration.

The correct answer is Mouth - Oesophagus - Stomach.

Key Points

• Mouth (Oral Cavity):
• The digestive process initiates in the mouth, serving as the entry point for food.
• Mechanical digestion occurs through mastication (chewing), breaking down food into smaller particles, increasing surface area.
• Salivary glands, located in the mouth, secrete saliva, which contains enzymes like salivary amylase.
• Salivary amylase begins the chemical digestion of carbohydrates, specifically starch, into simpler sugars.
• The tongue manipulates food, forming a bolus, a rounded mass of chewed food.
• The tongue also plays a role in taste perception, detecting flavors through taste buds.
• The process of swallowing begins when the bolus is pushed towards the pharynx.
• The mouth prepares the food for further digestion by adding moisture and enzymes.
• The teeth are essential for the mechanical breakdown of food.
• The oral cavity is lined with mucous membrane, which helps lubricate food.
• Oesophagus (Esophagus):
• The oesophagus is a muscular tube approximately 25 centimeters long in adults.
• It connects the pharynx to the stomach, acting as a conduit for food passage.
• Peristalsis, a series of rhythmic muscle contractions, propels the bolus downward.
• These wave-like muscle movements ensure unidirectional movement of food towards the stomach.
• The lower esophageal sphincter, a muscular ring at the junction of the oesophagus and stomach, prevents the backflow of stomach acid.
• The oesophagus is lined with a mucous membrane that aids in the smooth passage of food.
• The walls of the oesophagus contain both circular and longitudinal muscle layers.
• The movement of the bolus is largely involuntary.
• The oesophagus passes through the diaphragm.
• The oesophagus is essential for transporting the bolus from the oral cavity to the stomach.
• Stomach:
• The stomach is a muscular, J-shaped organ that acts as a temporary storage and digestion site.
• It secretes gastric juices, including hydrochloric acid (HCl), pepsinogen, and mucus.
• HCl creates an acidic environment (pH 1.5-3.5), which activates pepsinogen to pepsin.
• Pepsin, a protease enzyme, breaks down proteins into smaller peptides.
• The stomach's muscular walls churn and mix the food with gastric juices, forming chyme.
• Mucus protects the stomach lining from the corrosive effects of HCl.
• The stomach's capacity is approximately 1 liter, allowing for the storage of ingested food.
• The stomach also absorbs some substances, such as water, alcohol, and certain medications.
• The stomach has folds called rugae, which allow it to expand.
• The stomach has three muscle layers: longitudinal, circular, and oblique.

The correct answer is Mitochondria.

Key Points

• Mitochondria:
• Mitochondria are often referred to as the "powerhouses of the cell" because they are the primary sites of cellular respiration.
• Cellular respiration is the process by which glucose and other organic molecules are broken down to produce ATP (adenosine triphosphate), the cell's primary energy currency.
• Mitochondria have a double membrane structure: an outer membrane and a highly folded inner membrane called cristae.
• The cristae increase the surface area for the chemical reactions of cellular respiration.
• Mitochondria contain their own DNA and ribosomes, allowing them to produce some of their own proteins and replicate independently.

Additional Information

• Endoplasmic reticulum (ER):
• The endoplasmic reticulum is a network of membranous tubules and sacs found within the cytoplasm of eukaryotic cells.
• There are two types of ER: rough ER (RER), which is studded with ribosomes, and smooth ER (SER), which lacks ribosomes.
• The RER is involved in protein synthesis and modification, particularly for proteins destined for secretion or insertion into membranes.
• The SER plays roles in lipid synthesis, detoxification, and calcium storage.
• The ER is a major site of membrane biosynthesis in the cell.
• Plastids:
• Plastids are organelles found in plant cells and algae, responsible for various functions, including photosynthesis and storage.
• Chloroplasts are a type of plastid containing chlorophyll, the pigment that absorbs light energy for photosynthesis.
• Chromoplasts are plastids that contain pigments other than chlorophyll, giving fruits and flowers their colors.
• Leucoplasts are colorless plastids that store substances like starch, lipids, or proteins.
• Plastids, like mitochondria, have their own DNA.
• Vacuoles:
• Vacuoles are membrane-bound sacs found in the cytoplasm of plant, fungal, and some animal cells.
• In plant cells, a large central vacuole occupies a significant portion of the cell volume, maintaining cell turgor pressure.
• Vacuoles store water, ions, nutrients, and waste products.
• They can also play roles in detoxification and the breakdown of cellular debris.
• Vacuoles are enclosed by a membrane known as the tonoplast.

The correct answer is In the nucleus.

Key Points

• Rutherford's model, also known as the nuclear model, was developed based on the results of his gold foil experiment.
• In the gold foil experiment, alpha particles (positively charged particles) were directed at a thin sheet of gold foil.
• Most of the alpha particles passed straight through the foil, indicating that atoms are mostly empty space.
• However, a small fraction of alpha particles were deflected at large angles, and some even bounced back.
• This unexpected result suggested the presence of a dense, positively charged region in the center of the atom.
• Rutherford concluded that this central region, which he named the nucleus, contains most of the atom's mass.
• The nucleus is extremely small compared to the overall size of the atom.
• The nucleus contains protons, which are positively charged particles, and neutrons, which are neutral particles.
• Protons and neutrons are much heavier than electrons, which are negatively charged particles.
• Electrons orbit the nucleus at relatively large distances, occupying most of the atom's volume.
• The electrons contribute very little to the atom's overall mass.
• The concentration of mass in the nucleus explains why alpha particles were deflected when they came close to it.
• The positive charge of the nucleus repelled the positively charged alpha particles, causing them to change direction.
• The strong deflection of some alpha particles indicated that the nucleus is very dense and compact.
• Rutherford's model replaced the earlier plum pudding model, which proposed that atoms were uniformly filled with positive charge and electrons.
• The nuclear model provided a more accurate description of the atom's structure.
• The gold foil experiment was a pivotal moment in the development of atomic theory.
• Rutherford's model established the concept of a nucleus as the central component of the atom.
• The discovery of the nucleus revolutionized our understanding of atomic structure.
• The nucleus is responsible for the majority of the atomic weight.
• The dense nucleus is the reason for the deflection of the alpha particles.

The correct answer is tracheid.

Key Points

• Tracheid:
• Tracheids are elongated, tubular cells found in the xylem of vascular plants.
• They are primarily responsible for the transport of water and minerals throughout the plant.
• Tracheids have thick, lignified cell walls that provide structural support to the plant.
• They are a component of vascular tissue, which is a plant tissue, not connective tissue.
• Tracheids are dead at maturity, leaving only their cell walls to function in transport.

Additional Information

• Bone:
• Bone is a specialized connective tissue that forms the skeletal framework in vertebrates.
• It consists of a hard, mineralized matrix containing calcium phosphate and collagen fibers.
• Bone provides structural support, protects internal organs, and serves as a site for mineral storage.
• It also contains bone marrow, which is involved in blood cell production.
• Bone is a living tissue that is constantly being remodeled.
• Blood:
• Blood is a fluid connective tissue that circulates throughout the body.
• It consists of plasma, red blood cells, white blood cells, and platelets.
• Blood transports oxygen, nutrients, hormones, and waste products.
• It also plays a crucial role in immune response and blood clotting.
• Blood is vital for maintaining homeostasis.
• Cartilage:
• Cartilage is a flexible connective tissue that provides support and cushioning to joints and other structures.
• It consists of chondrocytes embedded in a matrix of collagen and elastic fibers.
• Cartilage lacks blood vessels, which results in slow healing.
• It is found in various locations, including the ears, nose, and joints.
• Cartilage provides a smooth surface for joint movement.

The logic follows here:

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

The correct answer is KTCT Higher Secondary School.

Key Points KTCT Higher Secondary School:

• KTCT Higher Secondary School, located in Thiruvananthapuram, Kerala, made history by introducing "Iris," India's first AI-powered teacher.
• Iris is a humanoid robot designed to enhance the educational experience for students.
• The development of Iris was a collaborative effort with Makerlabs Edutech.
• Iris is equipped with an in-built voice assistant, enabling interactive learning.
• It is powered by an Intel chipset, providing the necessary processing power.
• Iris is designed to answer complex questions across various subjects.
• It offers personalized voice assistance, catering to individual student needs.
• The robot is designed to facilitate engaging and interactive learning experiences.
• Iris is equipped with wheels, allowing for mobility within the classroom.
• It was built under the Atal Tinkering Lab (ATL) project, an initiative by NITI Aayog.
• The ATL project aims to foster extracurricular activities and innovation in schools.
• Iris represents a significant step forward in integrating AI into the Indian education system.
• The robot's capabilities include multilingual communication, broadening its accessibility.
• It is designed to understand and address complex problems across diverse subjects.
• The introduction of Iris has generated considerable excitement and attention.
• The developers intend for Iris to support and complement traditional teaching methods.
• Iris is a representation of the growing role of AI in personalizing education.
• The AI teacher is intended to make learning more engaging and effective for students.
• The development of Iris highlights the evolving landscape of educational technology in India.
• Iris is designed to interact with students, creating a more dynamic learning environment.

The correct answer is Angle of prism.

Key Points

• Angle of prism:
• The angle of prism, also known as the refracting angle, is the angle between the two refracting surfaces (lateral faces) of a prism.
• This angle is a fixed characteristic of a particular prism.
• It plays a crucial role in determining how light refracts as it passes through the prism.
• The angle of the prism is a key factor in the dispersion of white light into its constituent colors.
• The angle of prism is generally measured in degrees.

Additional Information

• Base angle:
• Base angles are typically associated with triangles, particularly isosceles triangles, and refer to the angles at the base of the triangle.
• In the context of a prism, the base is usually considered the face opposite the refracting angle.
• The base angles of the triangular faces that form the prism are related to the shape of the prism, but are not the angle between the refracting faces.
• Base angles are not the angle that defines the optical properties of the prism.
• Base angles deal with the shape of the triangular faces, and not the relation between the lateral faces.
• Angle of deviation:
• The angle of deviation is the angle between the incident ray and the emergent ray of light passing through a prism.
• It depends on the angle of incidence, the angle of prism, and the refractive index of the prism material.
• The angle of deviation varies with the angle of incidence.
• This angle is the measure of how much the light has been bent by the prism.
• The angle of deviation is an effect of the angle of prism.
• Inclination angle:
• Inclination angle generally refers to the angle of a slope or a tilt.
• While the lateral faces of a prism are inclined, the specific angle between them is referred to as the angle of prism.
• Inclination angle is a broad term, and not a specific term related to prisms in this way.
• Inclination angles can be used in many contexts, like the angle of a ramp, or the tilt of a surface.
• In the context of the prism, the angle of prism is the correct terminology.

Shortcut Trick

Uniform motion implies Distance is directly proportional to Time.

Ratio of Time = 5 : 3

Distance for 5 s = 25 m → (1 unit = 5 m)

Distance for 3 s = 3 × 5 = 15 m

∴ The correct answer is 15 m.

Alternate Method

Given:

Distance₁ = 25 m, Time₁ = 5 s, Time₂ = 3 s

Formula Used:

Speed = Distance ÷ Time

Distance = Speed × Time

Calculations:

⇒ Speed of Rambabu = 25 ÷ 5

⇒ Speed = 5 m/s

⇒ Distance covered in 3 s = Speed × Time₂

⇒ Distance = 5 × 3

⇒ Distance = 15 m

∴ The correct answer is 15 m.

Additional Information

Uniform Motion

An object is said to be in uniform motion if it covers equal distances in equal intervals of time, meaning its speed remains constant.

Average Speed

For any journey, Average Speed = Total Distance ÷ Total Time. In uniform motion, instantaneous speed equals average speed.

Unit Conversion

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

Shortcut Trick

Passing Marks = 780

Marks Obtained = 728

Marks Deficiency = 780 − 728 = 52

Given 5% deficiency = 52 marks

100% (Maximum Marks) = (52 ÷ 5) × 100 = 1040

∴ The correct answer is 1040 marks.

Alternate Method

Given:

Required Passing Marks = 780

Sonal's Marks = 728

Fail Percentage = 5%

Calculations:

⇒ Difference in Marks = Passing Marks − Obtained Marks

⇒ Difference = 780 − 728 = 52 marks

⇒ According to the question, this 52 marks represents 5% of the maximum aggregate marks.

⇒ Let Maximum Marks be M.

⇒ 5% of M = 52

⇒ (5 ÷ 100) × M = 52

⇒ M = (52 × 100) ÷ 5

⇒ M = 52 × 20 = 1040

∴ The correct answer is 1040 marks.

Additional Information

Percentage Base Change

To find the total value when a percentage of it is known, use the formula: Total Value = (Known Value ÷ Percentage) × 100.

Passing Percentage Calculation

Passing Percentage = (Passing Marks ÷ Maximum Marks) × 100. In this case, (780 ÷ 1040) × 100 = 75%.

Unitary Method in Percentage

If x% equals y, then 1% equals y/x, and 100% equals (y/x) × 100.

The logic followed here is:

Option 1) MOQ

Option 2) QSU

Option 3) AGH

Option 4) ZBD

Thus, out of all the options 'AGH' is the odd one out.

Hence, "Option 3" is the correct answer

The correct answer is Menstrual cycle.

Key Points Ovaries and the Menstrual Cycle:

• Ovaries are female reproductive organs that play a central role in the menstrual cycle.
• They produce and release eggs (ova) during ovulation, a key event in the menstrual cycle.
• Ovaries secrete hormones, primarily estrogen and progesterone, which regulate the menstrual cycle.
• Estrogen is responsible for the development and maintenance of female secondary sexual characteristics.
• Progesterone prepares the uterus for implantation of a fertilized egg.
• The menstrual cycle involves the thickening and shedding of the uterine lining (endometrium).
• Estrogen stimulates the growth of the endometrium in the first half of the cycle.
• Progesterone maintains the thickened endometrium in the second half of the cycle.
• If fertilization does not occur, progesterone levels drop, leading to menstruation (shedding of the endometrium).
• The ovaries' hormonal output directly influences the duration and regularity of the menstrual cycle.
• Follicle-stimulating hormone (FSH) and luteinizing hormone (LH) from the pituitary gland control ovarian function.
• Ovarian hormones, in turn, provide feedback to the pituitary gland, regulating FSH and LH secretion.
• The ovaries are the primary source of female sex hormones, which are essential for reproductive health.
• The menstrual cycle is a complex interplay of hormones and physiological changes.
• The ovaries are essential for female fertility.
• The ovarian hormones have impacts on bone density, and cardiovascular health.
• The ovaries contain follicles, which are sacs that contain the developing eggs.
• The process of ovulation is the release of a mature egg from a follicle.
• The corpus luteum, which forms after ovulation, secretes progesterone.
• The ovaries are vital for the proper functioning of the female reproductive system

Shortcut Trick

The relationship between Cost Price (CP) and Marked Price (MP) is given by the ratio: CP : MP = (100 − Discount%) : (100 + Profit%).

Ratio CP : MP = (100 − 15) : (100 + 20) = 85 : 120.

Simplify the ratio by dividing by 5: 17 : 24.

Given CP = 17 units = Rs. 153. Multiplier = 153 ÷ 17 = 9.

MP = 24 units × 9 = Rs. 216.

∴ The correct answer is Rs. 216.

Alternate Method

Given → Cost Price (CP) = Rs. 153, Profit% = 20%, Discount% = 15%. Formulas: SP = CP × (100 + Profit%) ÷ 100 | MP = SP × 100 ÷ (100 − Discount%)

⇒ First, calculate Selling Price (SP): SP = 153 × (120 ÷ 100) = 153 × 1.2 = Rs. 183.6. ⇒ Now, calculate Marked Price (MP): 183.6 = MP × (100 − 15) ÷ 100. ⇒ 183.6 = MP × (85 ÷ 100) ⇒ MP = (183.6 × 100) ÷ 85. ⇒ MP = 18360 ÷ 85 = Rs. 216.

∴ The correct answer is Rs. 216.

Additional Information

Marked Price & Discount

Marked Price is the price printed on the label. Discount is always calculated on the Marked Price to reach the Selling Price.

Markup Percentage

It is the percentage by which the Marked Price is higher than the Cost Price. Formula: Markup% = [(MP − CP) ÷ CP] × 100.

The correct answer is Only C.

Key Points Ecosystem Components:

• An ecosystem consists of two main components: biotic (living) and abiotic (non-living).
• Biotic components include all living organisms, such as plants, animals, fungi, and bacteria.
• Abiotic components include non-living factors, such as soil, water, air, minerals, and sunlight.
• These components interact with each other, creating a complex and dynamic system.
• The flow of energy and the cycling of nutrients are essential processes in an ecosystem.
• Biotic factors are influenced by abiotic factors, and vice versa.
• For example, plants (biotic) rely on sunlight, water, and minerals (abiotic) for growth.
• Animals (biotic) depend on plants (biotic) and water (abiotic) for survival.
• Soil (abiotic) is a crucial component that supports plant growth and provides habitat for various organisms (biotic).
• Soil contains many minerals.
• Minerals are inorganic substances that are essential for the growth and development of living organisms.
• Minerals in the soil are absorbed by plants and then passed on to animals through the food chain.
• The availability of minerals can significantly affect the health and productivity of an ecosystem.
• Water (abiotic) is essential for all living organisms and plays a vital role in nutrient transport and other biological processes.
• Air (abiotic) provides oxygen for respiration and carbon dioxide for photosynthesis.
• Sunlight (abiotic) is the primary source of energy for most ecosystems.
• The interactions between biotic and abiotic components determine the structure and function of an ecosystem.
• Ecosystems are constantly changing due to natural and human-induced factors.
• The balance between biotic and abiotic factors is crucial for maintaining ecosystem stability.
• Therefore, minerals are correctly classified as an abiotic component of an ecosystem.
• Living organisms are correctly classified as a biotic component.
• Soil is correctly classified as an abiotic component, although it contains biotic organisms.

Shortcut Trick

Area of Regular Hexagon = 6 × Area of one Equilateral Triangle

Area = 6 × (√3 ÷ 4) × side²

Area = 1.5 × √3 × 6²

Area = 1.5 × √3 × 36

Area = 54√3 cm²

∴ The correct answer is 54√3 cm².

Alternate Method

Given: side (a) = 6 cm

Formula Used: Area of Regular Hexagon = [3√3 ÷ 2] × a²

⇒ Area = [3 × √3 ÷ 2] × (6)²

⇒ Area = [3 × √3 ÷ 2] × 36

⇒ Area = 3 × √3 × 18

⇒ Area = 54√3 cm²

∴ The correct answer is 54√3 cm².

Additional Information

Interior Angles of Hexagon

Each interior angle of a regular hexagon is 120° and the sum of all interior angles is 720°.

Perimeter of Regular Hexagon

The perimeter is calculated as P = 6 × a, where a is the side length.

Inradius and Circumradius

For side a, the circumradius (R) = a and the inradius (r) = (√3 ÷ 2) × a.

The correct answer is Alpha particles.

Key Points 

• Alpha particles:
• Alpha particles are composed of two protons and two neutrons, making them identical to the nucleus of a helium atom.
• This composition results in a double positive charge (He²⁺).
• They are emitted during the radioactive decay of some heavy atomic nuclei.
• Alpha particles have relatively low penetration power and can be stopped by a sheet of paper.
• They have a relatively high ionizing power, meaning they can easily knock electrons out of atoms.

Additional Information

• Gamma particles:
• Gamma rays are high-energy electromagnetic radiation.
• They have no mass or charge.
• Gamma rays are emitted from atomic nuclei during radioactive decay.
• They have high penetration power and can pass through thick materials.
• Gamma rays are highly ionizing.
• X-rays:
• X-rays are also electromagnetic radiation, but they have lower energy than gamma rays.
• They are produced when electrons are decelerated or when inner-shell electrons transition to lower energy levels.
• X-rays have varying penetration power depending on their energy.
• They are used in medical imaging and industrial applications.
• X-rays are ionizing radiation.
• Beta particles:
• Beta particles are high-speed electrons or positrons emitted during radioactive decay.
• They have a single negative or positive charge.
• Beta particles have greater penetration power than alpha particles but less than gamma rays.
• They are involved in beta decay, a type of radioactive transformation.
• Beta particles are ionizing radiation.

Shortcut Trick

Check divisibility of each number by prime numbers up to √n.

For 373: √373 ≈ 19.3. Check 2, 3, 5, 7, 11, 13, 17, 19. None divide 373.

For 221: 13 × 17 = 221 (Not prime).

For 437: 19 × 23 = 437 (Not prime).

For 161: 7 × 23 = 161 (Not prime).

∴ The correct answer is 373.

Alternate Method

Given Numbers: 373, 221, 437, 161

Method: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

⇒ 161: 161 ÷ 7 = 23. So, 161 is composite.

⇒ 221: 221 ÷ 13 = 17. So, 221 is composite.

⇒ 437: 437 ÷ 19 = 23. So, 437 is composite.

⇒ 373: Testing primes 2, 3, 5, 7, 11, 13, 17, 19... None divide 373 exactly.

⇒ Since 373 has no factors other than 1 and 373, it is a prime number.

∴ The correct answer is 373.

Additional Information

Prime Number Definition

Numbers having exactly two factors (1 and itself). 2 is the only even prime number.

Test for Primality

To check if 'n' is prime, test divisibility by all primes less than or equal to √n.

Co-prime Numbers

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

The correct answer is Amoeba.

Key Points

• Amoeba:
• Amoeba reproduces asexually through binary fission.
• During binary fission in Amoeba, the nucleus divides first, followed by the cytoplasm.
• Because Amoeba lacks a fixed shape, the division can occur in any plane.
• This flexibility in division plane is a characteristic feature of Amoeba's reproduction.
• The resulting daughter Amoebae are genetically identical to the parent.

Additional Information

• Plasmodium:
• Plasmodium reproduces asexually through multiple fission, also known as schizogony.
• This process involves the nucleus dividing multiple times before the cytoplasm splits, producing many daughter cells.
• Plasmodium is an intracellular parasite that causes malaria.
• Its reproduction is complex and involves both asexual and sexual stages in different hosts.
• The multiple fission is a very specific type of reproduction, and not a random splitting of two cells in any plane.
• Leishmania:
• Leishmania reproduces asexually through binary fission.
• However, Leishmania has a flagellum and a defined cellular structure, meaning that the binary fission occurs in a specific, longitudinal plane.
• Leishmania is a protozoan parasite that causes leishmaniasis.
• Their reproduction is more ordered than that of the Amoeba.
• Leishmania is a single celled organism that requires a specific orientation during division.
• Hydra:
• Hydra reproduces asexually through budding.
• Budding involves the outgrowth of a bud from the parent's body, which eventually detaches to form a new individual.
• Hydra is a multicellular organism, not a protozoan.
• Hydra also reproduces sexually.
• Hydra is a fresh water organism that has specialized cells.

The correct answer is President of India, Smt. Droupadi Murmu.

Key Points Sangeet Natak Akademi Awards:

• The Sangeet Natak Akademi Awards, also known as the Akademi Puraskar, are prestigious national honors bestowed upon eminent artists in the fields of performing arts.
• These awards recognize outstanding contributions to music, dance, theatre, traditional folk arts, and puppetry.
• The awards are presented by the Sangeet Natak Akademi, India's national academy for music, dance, and drama.
• The awards are a symbol of excellence and recognition in the performing arts.
• The Sangeet Natak Akademi is an autonomous body under the Ministry of Culture, Government of India.
• The awards aim to preserve and promote the rich cultural heritage of India.
• The awards are given annually, but in this case, the awards for two years were given at the same ceremony.
• The 94 eminent artists were selected for their significant contributions to their respective fields.
• The awards are presented in a formal ceremony, highlighting the importance of the arts in Indian culture.
• The President of India, Smt. Droupadi Murmu, conferred the awards, emphasizing the national significance of the event.
• The award ceremony serves as a platform to celebrate the diverse and vibrant artistic traditions of India.
• The Sangeet Natak Akademi plays a crucial role in fostering artistic talent and promoting cultural exchange.
• The awards contribute to the preservation of traditional art forms that are integral to India's cultural identity.
• The awards provide encouragement and recognition to artists who have dedicated their lives to the performing arts.
• The Sangeet Natak Akademi awards are one of the most respected awards given to artists in India.
• The awards cover a wide range of artistic disciplines, reflecting the diversity of Indian performing arts.
• The ceremony highlights the importance of cultural preservation.
• The President of India's participation underscores the government's commitment to supporting the arts.
• The awards are a testament to the dedication and talent of Indian artists.

The logic followed here is:

TPVS is related to LHNK

WSYV is related to OKQN.

Similarly, RNTQ will be related:

Hence, the correct answer is "JFLI".

Shortcut Trick

For any circular motion, the total distance covered in one complete lap is the circumference of the circle.

Circumference = 2πr

Speed (v) = Distance ÷ Time = 2πr / t

∴ The correct answer is v = 2πr/t.

Alternate Method

Given:

Radius of the circular path = r

Time taken for one revolution = t

Formula Used:

Speed (v) = Total Distance / Total Time

Calculations:

⇒ Distance covered in one round = Circumference of the circle

⇒ Distance = 2 × π × r = 2πr

⇒ Speed (v) = Distance / Time

⇒ v = 2πr / t

∴ The correct answer is v = 2πr/t.

Additional Information

Uniform Circular Motion

When an object moves in a circular path with constant speed, its motion is called uniform circular motion. Even if speed is constant, velocity changes due to direction change.

Angular Velocity (ω)

The rate of change of angular displacement. Relation with linear speed is v = rω, where ω = 2π/t.

Displacement vs Distance

After one full revolution, the displacement is 0 (since the athlete returns to the start), but the distance is the full circumference 2πr.

Shortcut Trick

Total Simple Interest % = Rate × Time = 7.5% × 4 = 30%.

Total Amount % = 100% (Principal) + 30% (Interest) = 130%.

Amount = 130% of ₹85,000 = 1.3 × 85,000 = ₹1,10,500.

∴ The correct answer is ₹1,10,500.

Alternate Method

Given:

Principal (P) = ₹85,000

Rate (R) = 7.5% per annum

Time (T) = 4 years

Formula Used:

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

Amount (A) = Principal (P) + Simple Interest (SI)

Calculations:

⇒ SI = (85,000 × 7.5 × 4) ÷ 100

⇒ SI = (85,000 × 30) ÷ 100

⇒ SI = 850 × 30 = ₹25,500

⇒ Amount = 85,000 + 25,500

⇒ Amount = ₹1,10,500

∴ The correct answer is ₹1,10,500.

Additional Information

Simple Interest Formula

SI remains constant every year on the same principal. SI = (P × R × T) ÷ 100.

Total Amount

The sum of Principal and Interest. A = P(1 + RT/100).

Rate and Time Relation

If the rate is R% per annum and time is T years, the total interest is (R × T)% of the principal.

The correct answer is Sweating causes rapid evaporation, which absorbs heat from the body surface and cools the body.

Key Points Evaporative Cooling:

• Sweating is a physiological response to elevated body temperature.
• When the body gets hot, sweat glands release sweat onto the skin's surface.
• Sweat is primarily composed of water, with small amounts of salts and other substances.
• The process of evaporation requires energy, specifically heat energy.
• When sweat evaporates, it absorbs heat energy from the surrounding skin.
• This heat absorption cools the skin's surface, lowering the body's overall temperature.
• Evaporation is a highly effective cooling mechanism, especially in dry environments.
• The rate of evaporation is influenced by factors such as humidity and air movement.
• In humid conditions, evaporation occurs more slowly, reducing the cooling effect.
• In dry conditions, evaporation occurs more rapidly, providing a greater cooling effect.
• The body's thermoregulatory system controls sweating to maintain a stable internal temperature.
• Sweating is a crucial mechanism for preventing overheating and heatstroke.
• The hypothalamus in the brain monitors body temperature and triggers sweating when necessary.
• The process of evaporation is a physical change, where liquid sweat transforms into water vapor.
• This phase change requires the input of latent heat of vaporization.
• The body uses this process to regulate its temperature, and maintain homeostasis.
• The cooling effect of sweating is based on the principles of thermodynamics.
• The bodies blood vessels also dilate during times of heat, bringing warm blood closer to the surface of the skin, increasing the rate of evaporation.
• The bodies nervous system regulates the sweat glands.
• This is an example of negative feedback, where the body works to return to a set point.

The correct answer is Pollen grain and ovule.

Key Points 

• Pollen grain and ovule:
• Pollen grains contain the male gametes (sperm cells) of a plant.
• Ovules contain the female gametes (egg cells) of a plant.
• Fertilization occurs when a male gamete from a pollen grain fuses with a female gamete inside an ovule.
• This fusion results in the formation of a zygote, which develops into an embryo.
• Therefore, pollen grains and ovules are essential for sexual reproduction and fertilization in plants.

Additional Information

• Thalamus:
• The thalamus is the part of a flower's receptacle that supports the other floral organs.
• It is the base of the flower to which sepals, petals, stamens, and pistils are attached.
• While it is structurally important, it does not directly participate in fertilization.
• The thalamus primary function is to support the other floral parts.
• The thalamus can, in some plants, develop into part of the fruit.
• Petals:
• Petals are the colorful, often showy parts of a flower.
• Their primary function is to attract pollinators, such as insects or birds.
• While they aid in the process leading to fertilization by attracting pollinators, they are not directly involved in the fusion of gametes.
• Petals can also protect some of the inner flower parts.
• Petal color and shape vary widely among plant species.
• Sepal:
• Sepals are the outermost whorl of floral parts, typically green and leaf-like.
• Their primary function is to protect the developing flower bud.
• They play no direct role in the process of fertilization.
• Sepals can also provide some level of photosynthetic activity.
• After the bud opens, sepals can remain, or fall off.

Shortcut Trick

Numbers divisible by 5 between 12 and 39 form an Arithmetic Progression (AP): 15, 20, 25, 30, 35.

For any Arithmetic Progression, the Average is simply (First term + Last term) ÷ 2.

Average = (15 + 35) ÷ 2 = 50 ÷ 2 = 25.

∴ The correct answer is 25.

Alternate Method

Given: Range between 12 and 39.

Formula Used: Average = Sum of observations ÷ Total number of observations

Calculations:

⇒ Natural numbers divisible by 5 between 12 and 39 are: 15, 20, 25, 30, and 35.

⇒ Number of terms (n) = 5

⇒ Sum = 15 + 20 + 25 + 30 + 35 = 125

⇒ Average = 125 ÷ 5 = 25

∴ The correct answer is 25.

Additional Information

Arithmetic Progression (AP) Average

The average of any sequence in AP is always the middle term (if n is odd) or the mean of the two middle terms (if n is even).

Sum of Multiples

The sum of an AP is given by S_n = (n/2) × (a + l), where a is the first term and l is the last term.

Shortcut Trick

The sum of the first 10 prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23, 29) is 129.

Average = Total Sum ÷ Total Count = 129 ÷ 10 = 12.9.

∴ The correct answer is 12.9.

Alternate Method

Given: First 10 prime numbers.

Formula Used: Average = Sum of observations ÷ Number of observations

⇒ First 10 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

⇒ Sum = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29

⇒ Sum = 129

⇒ Number of elements = 10

⇒ Average = 129 ÷ 10 = 12.9

∴ The correct answer is 12.9.

Additional Information

Prime Numbers

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The number 2 is the only even prime number.

Average of Numbers

The average (arithmetic mean) is calculated by dividing the sum of all values in a dataset by the total number of values.

The logic followed here is:

Hence, "Option 3" is the correct answer.

Shortcut Trick

Ratio of sides = 1 : 4. Sum of ratio parts = 1 + 4 = 5.

Perimeter = 2 × (Sum of sides) ⇒ 50 = 2 × (5 units) ⇒ 10 units = 50 ⇒ 1 unit = 5 cm.

Sides of rectangle are 5 cm and 20 cm. Area = 5 × 20 = 100 cm².

For a square with area 100 cm², side = √100 = 10 cm. Perimeter = 4 × 10 = 40 cm.

∴ The correct answer is 40 cm.

Alternate Method

Given: Perimeter of rectangle = 50 cm, Ratio of sides (l : b) = 4 : 1.

Formula: Perimeter of rectangle = 2(l + b); Area = l × b; Perimeter of square = 4a.

⇒ Let length = 4x and breadth = x.

⇒ 2(4x + x) = 50

⇒ 10x = 50 ⇒ x = 5 cm.

⇒ Sides of rectangle: Length = 20 cm, Breadth = 5 cm.

⇒ Area of rectangle = 20 × 5 = 100 cm².

⇒ Area of square = a² = 100 cm².

⇒ Side of square (a) = √100 = 10 cm.

⇒ Perimeter of square = 4 × 10 = 40 cm.

∴ The correct answer is 40 cm.

Additional Information

Rectangle Properties

Area = length × width; Diagonal = √(l² + b²). All internal angles are 90°.

Square Properties

Area = side²; Perimeter = 4 × side; Diagonal = side × √2. A square is a special rectangle with all sides equal.

Ratio and Proportions

If a quantity is divided in ratio a:b, the parts are a/(a+b) and b/(a+b) of the total sum.

The correct answer is Hypothalamus.

Key Points

• Hypothalamus
• The hypothalamus is a region in the brain that plays a crucial role in regulating hormone release.
• When growth hormone levels are low, the hypothalamus releases growth hormone-releasing hormone (GHRH).
• GHRH then stimulates the pituitary gland to secrete growth hormone (GH).
• This process is part of the feedback mechanism that maintains hormonal balance in the body.
• The hypothalamus also releases somatostatin, which inhibits GH release when levels are sufficient.

Additional Information

• Thyroid Gland:
• The thyroid gland produces hormones like thyroxine (T4) and triiodothyronine (T3), which regulate metabolism.
• It does not directly influence the release of growth hormone or growth hormone-releasing factor.
• The thyroid gland is regulated by the thyroid-stimulating hormone (TSH) from the pituitary gland.
• Dysfunction in the thyroid gland can affect growth indirectly by altering metabolic rates.
• However, it is not involved in the direct release of growth hormone-releasing factor.
• Adrenal Gland:
• The adrenal glands produce hormones like cortisol, adrenaline, and aldosterone.
• These hormones are involved in stress response, blood pressure regulation, and electrolyte balance.
• The adrenal glands do not produce or regulate growth hormone-releasing factor.
• They are regulated by the adrenocorticotropic hormone (ACTH) from the pituitary gland.
• While cortisol can influence growth indirectly, it is not part of the growth hormone release mechanism.
• Pancreas:
• The pancreas is primarily responsible for producing insulin and glucagon, which regulate blood sugar levels.
• It does not play a role in the release of growth hormone or growth hormone-releasing factor.
• The pancreas is part of the endocrine and digestive systems but is not involved in the hypothalamic-pituitary axis.
• Insulin-like growth factors (IGFs) are influenced by growth hormone but are not produced by the pancreas.
• The pancreas has no direct connection to the regulation of growth hormone release

The correct answer is It has fixed volume but not fixed shape.

Key Points Liquids and Their Characteristics:

• Liquids are one of the three primary states of matter, along with solids and gases.
• A key characteristic of liquids is that they have a definite volume.
• This means that a given amount of liquid will always occupy the same amount of space.
• However, liquids do not have a fixed shape.
• They take the shape of the container they occupy.
• This is because the particles in a liquid are able to move past each other, unlike the particles in a solid, which are fixed in place.
• Liquids are generally incompressible, or only very slightly compressible.
• This is due to the close proximity of the particles within the liquid.
• The forces between liquid particles are strong enough to maintain a fixed volume, but weak enough to allow them to flow.
• Liquids exhibit the property of fluidity, which means they can flow.
• This fluidity is due to the ability of the particles to slide past each other.
• The surface of a liquid at rest is generally horizontal.
• Liquids can exhibit surface tension, which is a force that causes the surface of a liquid to behave like a stretched elastic membrane.
• Viscosity is another characteristic of liquids, which is a measure of their resistance to flow.
• Liquids have a density that is typically between that of solids and gases.
• Liquids can evaporate, which is the process of a liquid changing into a gas.
• Liquids can also condense, which is the process of a gas changing into a liquid.
• The temperature of a liquid affects its properties, such as viscosity and density.
• The particles in a liquid have kinetic energy, which increases with temperature.
• Liquids can dissolve various substances, forming solutions.
• Liquids are essential for numerous biological and industrial processes.
• The intermolecular forces in liquids are stronger than in gasses, but weaker than in solids.
• The ability of the particles to move freely within the liquid allows it to take the shape of its container.

The correct answer is 51st

Key Points

current Chief Justice of India (CJI), Justice Sanjiv Khanna (as of December 2024).

• Justice Sanjiv Khanna took oath as the 51st Chief Justice of India on November 11, 2024.
• His tenure is short and will end on May 13, 2025, upon reaching the retirement age of 65 years.
• Before being elevated to the Supreme Court in 2019, he served as a judge of the Delhi High Court.
• He has been part of significant rulings, including cases related to electoral reforms and the constitutional status of Article 370.
• He is the nephew of Justice H.R. Khanna, known for his historic dissent during the Emergency in the ADM Jabalpur case.

Given: 

It moves 15 m to the right from point 'A' and then moves 15 m to the opposite direction

So, 0 m displacement is needed to reach the same point, 'A'.

Hence, the correct answer is "Option 3".

Shortcut Trick

Speed in m/s = 90 × (5/18) = 25 m/s.

Length of train = Speed × Time.

Length = 25 × 5 = 125 m.

∴ The correct answer is 125 m.

Alternate Method

Given:

Speed of train = 90 km/h

Time taken to cross the pole = 5 sec

Formula Used:

Distance = Speed × Time

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

Calculations:

⇒ Speed in m/s = 90 × (5/18) m/s

⇒ Speed = 5 × 5 = 25 m/s

⇒ Length of train (Distance) = 25 m/s × 5 sec

⇒ Length = 125 m

∴ The correct answer is 125 m.

Additional Information

Unit Conversion

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

Crossing a Stationary Object

When a train crosses a pole or a standing man, the distance covered is equal to the length of the train.

Crossing a Platform

When a train crosses a platform or bridge of length P, total distance = Length of train + P.

Shortcut Trick

Combined filling time (without leak) = (21 × 24) ÷ (21 + 24) = 504 ÷ 45 = 11.2 hours = 11 hours 12 minutes.

Time with leak = 11 hours 12 minutes + 48 minutes = 12 hours.

Leakage efficiency = (1/11.2) − (1/12) = (12 − 11.2) ÷ (11.2 × 12) = 0.8 ÷ 134.4 = 1/168.

Leakage time = 168 hours.

∴ The correct answer is 168 hr.

Alternate Method

Given: Filling time of Pipe X = 21 hours, Pipe Y = 24 hours. Extra time due to leakage = 48 minutes.

⇒ Combined Efficiency (X + Y) = 8 + 7 = 15 units/hour.

⇒ Ideal Time to fill = 168 ÷ 15 = 11.2 hours.

⇒ Actual Time (with leak) = 11.2 + (48/60) = 11.2 + 0.8 = 12 hours.

⇒ Net Efficiency (X + Y − Leak) = 168 ÷ 12 = 14 units/hour.

⇒ Leak Efficiency = (X + Y) − (X + Y − Leak) = 15 − 14 = 1 unit/hour.

⇒ Time for leak to empty = 168 ÷ 1 = 168 hours.

∴ The correct answer is 168 hr.

Additional Information

Pipes & Cisterns Efficiency

Filling pipes have positive efficiency while leakage or emptying pipes have negative efficiency. Total Work = Time × Net Efficiency.

Time and Work Relation

If a pipe fills a tank in 'x' hours and another empties it in 'y' hours, net work in 1 hour = (1/x) − (1/y).

Conversion Rule

To convert minutes into hours, divide by 60. Example: 48 minutes = 48/60 = 0.8 hours.

Shortcut Trick

Efficiency Ratio (Nayan : Tarun) = 100 : 125 = 4 : 5

Since Time is inversely proportional to Efficiency, the Time Ratio = 5 : 4

Given Nayan's time (5 units) = 25 days ⇒ 1 unit = 5 days

Tarun's time (4 units) = 4 × 5 = 20 days

∴ The correct answer is 20 days.

Alternate Method

Given: Time taken by Nayan = 25 days. Tarun's efficiency is 25% more than Nayan's.

Formula Used: Total Work = Efficiency × Time

⇒ Let Nayan's efficiency be 4 units/day (calculated from LCM or assumed).

⇒ Total Work = 4 units/day × 25 days = 100 units.

⇒ Tarun's efficiency = 125% of 4 = 1.25 × 4 = 5 units/day.

⇒ Days taken by Tarun = Total Work ÷ Tarun's Efficiency

⇒ Days = 100 ÷ 5 = 20 days.

∴ The correct answer is 20 days.

Additional Information

Inverse Relation of Time and Efficiency

If the efficiency of two people is in the ratio a : b, then the time taken by them to complete the same work is in the ratio b : a.

Work Constant Principle

When the amount of work is constant, E₁ × T₁ = E₂ × T₂. This allows for direct comparison between different workers.

Given:

Total marks scored by Student A = 260

Percentage of marks in Physics = 25%

Percentage of marks in English = 10%

Formula used:

Marks in a subject = (Total marks × Percentage in subject) / 100

Calculation:

Marks in Physics = (260 × 25) / 100

⇒ Marks in Physics = 65

Marks in English = (260 × 10) / 100

⇒ Marks in English = 26

Total marks in Physics and English = Marks in Physics + Marks in English

⇒ Total marks in Physics and English = 65 + 26 = 91

∴ The correct answer is option 1.

The correct answer is non-uniform acceleration.

Key Points

• Non-uniform acceleration:
• Non-uniform acceleration occurs when the velocity of an object changes by unequal amounts in equal intervals of time.
• This means the rate of change of velocity is not constant.
• In simpler terms, the car is speeding up or slowing down at a changing rate.
• This is common in real-world scenarios, such as driving in traffic or on a winding road.
• The acceleration can be increasing, decreasing, or even changing direction.

Additional Information

• Uniform velocity:
• Uniform velocity implies that an object is moving at a constant speed in a straight line.
• This means there is no change in either the speed or the direction of motion.
• If the speed increases by unequal amounts, the velocity is not uniform.
• Uniform velocity would mean zero acceleration.
• This is rarely found in real world driving situations.
• Uniform speed:
• Uniform speed means that an object is moving at a constant speed, but it does not specify the direction.
• While the speed is constant, the direction could change, resulting in acceleration.
• If the speed is increasing by unequal amounts, the speed is not uniform.
• Uniform speed does not mean uniform velocity.
• Uniform speed means the magnitude of the velocity is constant.
• Uniform acceleration:
• Uniform acceleration occurs when the velocity of an object changes by equal amounts in equal intervals of time.
• This means the rate of change of velocity is constant.
• In simpler terms, the car is speeding up or slowing down at a constant rate.
• An example of this is a freely falling object.
• This situation is not what is described in the provided question.

The correct answer is Double displacement reaction.

Key Points

Double displacement reaction:

• A double displacement reaction involves the exchange of ions between two reactants, resulting in the formation of

two new products

• • In the given reaction, potassium ions (K⁺) exchange places with barium ions (Ba²⁺).
• This results in the formation of potassium iodide (KI) and barium bromide (BaBr₂).
• One of the products, barium bromide, is formed as a solid precipitate, indicating a double displacement (precipitation) reaction.
• The general form of a double displacement reaction is AB + CD → AD + CB.

Additional Information

• Displacement reaction:

• A displacement reaction involves one element replacing another element in a compound.

• This typically occurs when a more reactive element displaces a less reactive element.

• The given reaction involves an exchange of ions between two compounds, not the replacement of an element within a compound.

• A single element would have to replace another element in a compound for it to be a displacement reaction.

• Displacement reactions usually involve a single element and a compound.

• Combination reaction:

• A combination reaction, also known as a synthesis reaction, involves two or more reactants combining to form a single product.

• The given reaction involves two reactants forming two products, not a single product.

• Combination reactions are also known as synthesis reactions.

• A+B = AB is the general form of a combination reaction.

• Combination reactions form one product.

• Decomposition reaction:

• A decomposition reaction involves a single reactant breaking down into two or more products.

• The given reaction involves two reactants, not a single reactant.

• Decomposition reactions are the opposite of combination reactions.

• AB = A+B is the general form of a decomposition reaction.

• Decomposition reactions break one reactant into multiple products.

The correct answer is The magnitude of the magnetic field outside but close to the solenoid is extremely large.

Key Points Solenoid and its Magnetic Field:

• A solenoid is a coil of wire wound into a tightly packed helix.
• When an electric current flows through the solenoid, it produces a magnetic field.
• The magnetic field inside a long solenoid is nearly uniform and strong.
• This uniform field is one of the key characteristics of a solenoid.
• The magnetic field lines inside the solenoid are parallel to the axis of the solenoid.
• The magnetic field outside the solenoid is relatively weak and spreads out.
• The magnetic field lines form closed loops, entering the solenoid at one end and exiting at the other.
• The solenoid behaves similarly to a bar magnet, with distinct north and south poles.
• The strength of the magnetic field inside the solenoid is directly proportional to the current flowing through it.
• The strength of the magnetic field is also directly proportional to the number of turns of wire per unit length.
• Increasing the number of turns increases the magnetic field strength.
• The magnetic field near the center of a long solenoid is nearly constant, meaning it has the same strength at different points along the axis.
• The magnetic field outside the solenoid, especially at a distance, diminishes rapidly.
• The magnetic field lines outside the solenoid form loops that close back to the solenoid.
• The magnetic field outside but close to the solenoid is not extremely large; it is relatively weak compared to the inside.
• The strength of the magnetic field drops off rapidly as you move away from the solenoid.
• The end faces of the solenoid act as magnetic poles.
• Solenoids are used in many electrical components, such as relays and electromagnets.
• The magnetic field inside of the solenoid is uniform, where as the field outside is non-uniform.
• The direction of the magnetic field can be determined by the right-hand rule

Shortcut Trick

Convert total quantity to milliliters: (8 × 1000) + 785 = 8785 ml.

Divide by the number of people: 8785 ÷ 35.

8785 ÷ 35 = 251 ml.

∴ The correct answer is 251 ml.

Alternate Method

Given:

Total quantity of soup = 8 ltr 785 ml

Number of people = 35

Formula Used:

Quantity per person = Total Quantity ÷ Number of People

Calculations:

⇒ 1 liter = 1000 ml

⇒ 8 ltr 785 ml = (8 × 1000) + 785 = 8785 ml

⇒ Soup per person = 8785 ÷ 35

⇒ Soup per person = 251 ml

∴ The correct answer is 251 ml.

Additional Information

Unit Conversion

Always convert larger units to smaller units (Liters to Milliliters) for easier calculation by multiplying by 1000.

Equal Distribution

The term 'distributed equally' always implies the mathematical operation of division.

Given: Seven people, A, B, D, L, X, Y and Z, are sitting in a row, facing north

Only Z sits to the right of D. Only three people sit to the left of A.

Only three people sit between D and L.

Y sits at some place to the left of X but at some place to the right of B.

So, 'Three' people sit between B and X.

Hence, the correct answer is "Option 2".

Shortcut Trick

To find Gain Percentage, equate the quantity by cross-multiplying cost and selling prices.

Quantity × Rate: 6 pencils for Rs. 5 (CP) and 5 pencils for Rs. 6 (SP).

Cross-multiply: CP = 5 × 5 = 25 and SP = 6 × 6 = 36.

Profit = 36 − 25 = 11.

Gain % = (11 ÷ 25) × 100 = 44%.

∴ The correct answer is 44%.

Alternate Method

Given → CP of 6 pencils = Rs. 5 | SP of 5 pencils = Rs. 6. Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100.

⇒ Let total pencils be LCM of 6 and 5 = 30 pencils. ⇒ CP of 30 pencils = (5 ÷ 6) × 30 = Rs. 25. ⇒ SP of 30 pencils = (6 ÷ 5) × 30 = Rs. 36. ⇒ Profit = 36 − 25 = 11. ⇒ Profit % = (11 ÷ 25) × 100 = 44%.

∴ The correct answer is 44%.

Additional Information

Unitary Method in Profit and Loss

Calculating the price of a single unit helps compare CP and SP easily. CP of 1 pencil = 5/6; SP of 1 pencil = 6/5.

LCM Method

Assume a total quantity equal to the Lowest Common Multiple of quantities to avoid fractions during calculation.

Shortcut Trick

Each exterior angle = 180° − 165° = 15°.

Number of sides (n) = 360° ÷ Exterior Angle.

⇒ n = 360° ÷ 15° = 24.

∴ The correct answer is 24 sides.

Alternate Method

Given: Each interior angle of a regular polygon = 165°.

Formula Used: Interior angle of a regular polygon = [(n − 2) × 180°] ÷ n, where n is the number of sides.

Calculations:

⇒ 165° = [(n − 2) × 180°] ÷ n

⇒ 165n = 180n − 360

⇒ 180n − 165n = 360

⇒ 15n = 360

⇒ n = 360 ÷ 15

⇒ n = 24

∴ The correct answer is 24 sides.

Additional Information

Sum of Interior Angles

The sum of all interior angles of a polygon with n sides is always (n − 2) × 180°.

Sum of Exterior Angles

For any convex polygon, the sum of all exterior angles (one at each vertex) is always 360°.

Regular Polygon Property

In a regular polygon, all sides and all interior angles are equal. The exterior angle = 360° ÷ n.

The correct answer is To empower the creative economy and cultural industries of Tamil Nadu.

Key Points British Council and Guidance Tamil Nadu Partnership:

• The partnership between the British Council and Guidance Tamil Nadu focuses on strengthening the creative economy and cultural industries within the state.
• The primary objective is to develop and enhance the creative sector, which includes arts, culture, design, and media.
• This collaboration aims to provide opportunities for artists, creators, and cultural entrepreneurs in Tamil Nadu.
• The initiative seeks to build capacity and provide training to individuals and organizations involved in the creative industries.
• It aims to foster innovation and entrepreneurship within the cultural sector.
• The partnership supports the development of sustainable business models for creative enterprises.
• It seeks to promote cultural exchange and collaboration between Tamil Nadu and the United Kingdom.
• The collaboration will facilitate access to international networks and resources for Tamil Nadu's creative professionals.
• The partnership intends to enhance the skills and employability of individuals working in the creative industries.
• It aims to contribute to the economic growth of Tamil Nadu through the development of its creative sector.
• The partnership will support the development of cultural infrastructure and facilities.
• It will promote the use of digital technologies in the creative industries.
• The project will seek to preserve and promote Tamil Nadu's rich cultural heritage.
• It aims to create opportunities for young people to participate in the creative economy.
• The partnership will support the development of cultural tourism in Tamil Nadu.
• It will provide platforms for showcasing the work of Tamil Nadu's artists and creators.
• The collaboration will foster greater understanding and appreciation of Tamil Nadu's cultural diversity.
• It aims to build stronger cultural ties between Tamil Nadu and the UK.
• The partnership shows the British council's commitment to the cultural and creative industries within India.
• Guidance Tamil Nadu is the nodal agency for investment promotion and facilitation in Tamil Nadu, and this partnership shows the states commitment to developing these industries.

The correct answer is Chlorofluorocarbons.

Key Points

• Chlorofluorocarbons (CFCs):
• CFCs are synthetic chemicals that were widely used as refrigerants, propellants in aerosol cans, and in various industrial applications.
• When CFCs are released into the atmosphere, they eventually reach the stratosphere, where the ozone layer is located.
• In the stratosphere, ultraviolet (UV) radiation from the sun breaks down CFC molecules, releasing chlorine atoms.
• Chlorine atoms act as catalysts, destroying ozone molecules in a chain reaction.
• This process led to a significant depletion of the ozone layer, particularly the formation of the "ozone hole" over Antarctica in the 1980s.
• CFCs are very stable molecules, which means they can remain in the atmosphere for long periods of time.

Additional Information

• Chloroiodocarbons:
• While iodine can also contribute to ozone depletion, chloroiodocarbons were not as widely used as CFCs.
• The primary driver of ozone depletion in the 1980s was the widespread use of CFCs.
• Iodine compounds tend to be less stable in the lower atmosphere, and therefore less likely to reach the stratosphere.
• The primary chemical of concern was chlorine.
• Iodine containing chemicals have different reactions than chlorine containing chemicals.
• Iodobromocarbons:
• Similar to chloroiodocarbons, iodobromocarbons were not the primary cause of the ozone depletion observed in the 1980s.
• Bromine, like chlorine, can also destroy ozone, but CFCs were the dominant ozone-depleting substances.
• Bromine is also a very efficient destroyer of ozone.
• The concentration of bromine containing chemicals was not as high as Chlorine containing chemicals.
• The Montreal protocol addressed bromine containing chemicals as well as chlorine containing chemicals.
• Iodofluorocarbons:
• While these compounds exist, they were not the main culprits behind the ozone depletion of the 1980s.
• The stability and widespread use of CFCs made them the primary concern.
• Fluorine itself does not directly destroy ozone in the same way that chlorine and bromine do.
• Iodine compounds are less stable in the atmosphere.
• The combination of Chlorine and Fluorine in the CFC molecule created a very stable compound that was very damaging to the ozone layer.

Decoding the Symbols:

 

Given: P × Q ÷ R - S × T

It means: P is the father of Q, Q is the sister of R, R is the wife of S and S is the father of T.

So,  P is the 'Mother's father' of T.

Hence, the correct answer is "Option 1".

Given:

A, B, E, G, P, L and M are sitting around a circular table facing the centre.

1. Only two people sit between A and M when counted from the right of A.

2. M sits to the immediate right of L.

3. Only three people sit between P and L when counted from the right of L.

4. E sits to the immediate right of G. 

So, 'E' sits fourth to the right of B.

Hence, the correct answer is "Option (1)".

Shortcut Trick

Ratio of A : B : C : D = 4 : 7 : 9 : 3

Difference between C and B in units = 9 − 7 = 2 units

Given 2 units = ₹800 ⇒ 1 unit = ₹400

Amount for D = 3 units = 3 × 400 = ₹1200

∴ The correct answer is ₹1200.

Alternate Method

Given:

Ratio of shares A : B : C : D = 4 : 7 : 9 : 3

Difference between C's share and B's share = ₹800

Formula Used:

Value of a part = (Total Difference) ÷ (Difference in ratio parts)

Calculations:

⇒ Let the shares be 4x, 7x, 9x, and 3x.

⇒ According to the question, C − B = 800

⇒ 9x − 7x = 800

⇒ 2x = 800

⇒ x = 400

⇒ Amount received by D = 3x

⇒ D = 3 × 400 = 1200

∴ The correct answer is ₹1200.

Additional Information

Concept of Proportionality

If a total amount T is divided in the ratio a:b:c, then the share of the first person is [a / (a+b+c)] × T.

Ratio Difference Method

When the absolute difference between two shares is known, divide that value by the difference in their ratio parts to find the value of 1 unit.

Total Sum Calculation

The total sum in this problem would be (4+7+9+3) × 400 = 23 × 400 = ₹9200.

The correct answer is Plasmolysis.

Key Points

• Plasmolysis:
• Plasmolysis is the process where a plant cell loses water due to osmosis and the protoplasm shrinks away from the cell wall.
• This occurs when the cell is placed in a hypertonic solution, meaning the concentration of solutes is higher outside the cell than inside.
• Water moves out of the cell, causing the cell membrane to detach from the rigid cell wall.
• The cell becomes flaccid, and if severe enough, can lead to cell death.
• Plasmolysis is a visible demonstration of osmosis in plant cells.

Additional Information

• Diffusion:
• Diffusion is the movement of molecules from an area of higher concentration to an area of lower concentration.
• It is a passive process, meaning it does not require energy input.
• Diffusion occurs until equilibrium is reached, where the concentration of molecules is uniform throughout the space.
• While water movement in osmosis is a type of diffusion, plasmolysis is the specific result of water loss in plant cells due to a hypertonic environment.
• Diffusion occurs in gasses, liquids, and solids.
• Active Transport:
• Active transport is the movement of molecules across a cell membrane against their concentration gradient.
• This process requires energy input, usually in the form of ATP (adenosine triphosphate).
• Active transport is essential for moving substances that cannot diffuse across the membrane due to concentration differences or size.
• Active transport is not related to the water loss and shrinkage seen in plasmolysis.
• Active transport uses transport proteins.
• Passive Transport:
• Passive transport is the movement of molecules across a cell membrane without requiring energy input.
• It includes processes like diffusion, facilitated diffusion, and osmosis.
• While osmosis is a form of passive transport, plasmolysis is the specific outcome of water loss in plant cells due to osmosis in a hypertonic environment.
• Passive transport moves with the concentration gradient.
• Osmosis, a type of passive transport, is the movement of water across a semipermeable membrane

The correct answer is pure metal.

Key Points

• Pure metal:
• In electrolytic refining, the cathode is made of a thin strip or rod of the pure metal that is to be refined.
• During electrolysis, metal ions from the electrolyte solution are attracted to the cathode.
• These ions gain electrons and are deposited as pure metal atoms onto the cathode.
• The cathode thus grows in size as pure metal accumulates on it.
• This process allows for the production of highly pure metals.

Additional Information

• Impure metal:
• The impure metal is used as the anode in electrolytic refining.
• At the anode, the impure metal undergoes oxidation, releasing metal ions into the electrolyte solution.
• Impurities that are more reactive than the metal being refined dissolve in the electrolyte.
• Impurities that are less reactive fall to the bottom as "anode mud."
• Therefore, the impure metal is used at the anode, not the cathode.
• Alloy metal:
• Alloy metals are mixtures of two or more metals.
• Alloys are not used as the cathode in electrolytic refining because the goal is to obtain a pure metal.
• Using an alloy would defeat the purpose of the refining process.
• Alloys are often the starting material for metals that need to be refined.
• An alloy is not a pure substance.
• Metal salt:
• A metal salt is used as the electrolyte in electrolytic refining.
• The electrolyte solution contains ions of the metal that is to be refined.
• The metal ions in the electrolyte are reduced at the cathode, forming pure metal.
• The metal salt provides the necessary ions for the electrolytic process.
• The metal salt is not the material that the cathode is made from.

The correct answer is Integrated Test Range (ITR), Chandipur, Odisha.

Key Points

• Integrated Test Range (ITR), Chandipur, Odisha:
• The Integrated Test Range (ITR) in Chandipur, Odisha, is a major missile testing facility of the Defence Research and Development Organisation (DRDO).
• It is a well-established location for conducting flight tests of various missiles developed by DRDO.
• The ITR provides the necessary infrastructure and tracking systems for conducting complex missile tests.
• It is strategically located to allow for safe and controlled testing over the Bay of Bengal.
• The ITR is a crucial asset for India's missile development program.

Additional Information

• Missile Test Facility, Bengaluru:
• While Bengaluru is a hub for DRDO and other defense-related activities, it does not have a dedicated open-air test range like ITR Chandipur.
• Bengaluru is more focused on the design, development, and integration of missile systems.
• Many electronic and software components of missiles are developed in Bengaluru.
• Bengaluru is a hub for aerospace industries, but not for large scale open air missile testing.
• Testing in Bengaluru would be limited to component testing.
• Indian Space Research Centre, Thiruvananthapuram:
• The Indian Space Research Centre (ISRO) in Thiruvananthapuram primarily focuses on space-related activities, such as satellite launches and space exploration.
• While ISRO and DRDO collaborate on various projects, missile testing is primarily conducted at DRDO's dedicated facilities.
• ISRO focuses on space launch vehicles, and satellites.
• ISRO and DRDO are seperate organizations.
• ISRO specializes in orbital mechanics, and space based systems.
• Defence Research Facility, Hyderabad:
• Hyderabad is another important center for DRDO, with various laboratories and research facilities.
• However, the large-scale flight testing of long-range missiles is typically conducted at the ITR in Chandipur.
• Hyderabad is a location for development of missile technology.
• Many electronic systems are designed and built in Hyderabad.
• Hyderabad is home to important DRDO labs, but not the primary long range test range.

The correct answer is parallel and equidistant straight lines.

Key Points

• Uniform Magnetic Field Representation:
• A uniform magnetic field is a region where the magnetic field strength and direction are the same at all points.
• This means that the magnetic field lines must be parallel to each other.
• Additionally, the magnetic field lines must be equidistant, meaning they are equally spaced.
• Parallel and equidistant straight lines are the standard representation of a uniform magnetic field.
• This representation accurately depicts the constant strength and direction of the field.
• This type of field is created inside a long solenoid, or between the poles of a strong magnet.
• The uniformity of the field is crucial for many scientific and technological applications.
• For example, uniform magnetic fields are used in particle accelerators and magnetic resonance imaging (MRI).
• The magnetic field lines are imaginary lines that represent the direction and strength of the magnetic field.
• The density of the lines indicates the strength of the field.
• In a uniform field, the density of the lines remains constant.
• The direction of the lines indicates the direction of the magnetic force that a north pole would experience.
• A uniform magnetic field implies that the magnetic force on a moving charged particle is the same at all points in the region.
• This is essential for controlling and manipulating charged particles in various experiments and devices.
• The concept of a uniform magnetic field is a fundamental principle in electromagnetism.
• The representation of a uniform field simplifies calculations and analysis of magnetic phenomena.
• Non-uniform magnetic fields, on the other hand, have varying strength and direction.
• Those non-uniform fields are represented by lines that are not parallel or equidistant.
• The magnetic field between two flat parallel magnets is considered to be uniform.
• The ideal uniform field is a theoretical concept, as real fields will have slight variations.
• The visual representation of parallel and equidistant lines is a very useful tool in understanding magnetic fields.

Additional Information

• Concentric circular lines:
• Concentric circular lines represent the magnetic field around a straight current-carrying wire.
• This field is not uniform because the strength of the field decreases with distance from the wire.
• The direction of the field also changes as you move around the wire.
• This is a non-uniform field.
• Parallel but irregular straight lines:
• While parallel lines indicate a consistent direction, irregular spacing indicates a varying field strength.
• Therefore, parallel but irregular straight lines do not represent a uniform magnetic field.
• This would indicate a field that is constant in direction, but not in magnitude.
• Elliptical lines:
• Elliptical lines do not represent a uniform magnetic field.
• Elliptical lines would represent a non-uniform field with a changing direction and strength.
• Elliptical lines are not a standard way to represent magnetic fields.
• Magnetic field lines always form closed loops, and while they can be curved, they are not typically elliptical.

The correct answer is Bank of Baroda.

Key Points

• AI-Powered Virtual Relationship Manager – Launched in September 2024, 'Aditi' is a GenAI-powered chatbot designed to enhance customer service digitally.
• Multilingual & 24x7 Availability – Provides support via chat, audio, and video in multiple languages, improving accessibility for a diverse customer base.
• Enhances Customer Experience – Offers conversational banking services, helping users with transactions, queries, and banking assistance.
• Part of AI Initiatives – Alongside 'Aditi', BoB introduced 'GyanSahay.AI', an AI-driven knowledge platform for employees to improve efficiency.

Additional Information

• State Bank of India:
• While SBI is also investing in digital transformation, the specific launch of "Aditi" is associated with HDFC Bank.
• SBI has its own digital platforms and customer service initiatives.
• SBI has been working on various digital banking solutions.
• SBI has large scale digital banking infrastructure.
• SBI is the largest public sector bank in India.
• Canara Bank:
• Canara Bank is another major public sector bank that is focusing on digital banking.
• However, the "Aditi" GenAI initiative is specifically an HDFC Bank project.
• Canara Bank is also working on improving digital customer interactions.
• Canara bank has a wide network of branches.
• Canara bank is involved in many digital banking programs.

The correct answer is Mumbai.

Key Points

• The Ranji Trophy is India's premier domestic first-class cricket championship.
• The 2023-2024 season marked the 42nd edition of this prestigious tournament.
• Mumbai and Vidarbha competed in the final match to determine the winner.
• Mumbai emerged victorious, securing their 42nd Ranji Trophy title.
• The Ranji Trophy is named after Kumar Shri Ranjitsinhji, a legendary Indian cricketer.
• The tournament features teams representing various state associations and union territories in India.
• The format of the Ranji Trophy involves a league stage followed by knockout rounds.
• Mumbai has a historically dominant record in the Ranji Trophy, having won the title more times than any other team.
• The Ranji Trophy serves as a crucial platform for Indian cricketers to showcase their talent.
• It plays a significant role in the selection process for the Indian national cricket team.
• The tournament is organized by the Board of Control for Cricket in India (BCCI).
• The final match of the 2023-2024 season was highly anticipated by cricket enthusiasts across the country.
• The Ranji Trophy contributes to the development of first-class cricket in India.
• The competition provides valuable experience for young cricketers.
• The Ranji trophy is a very important part of the Indian domestic cricket season.
• The win was a very celebrated victory for Mumbai.
• The tournament has a very long and storied history.
• The matches are played over multiple days, testing the players stamina and skill.
• The Ranji trophy is a symbol of cricketing excellence in India.
• The win in 2024, adds to Mumbai's already impressive Ranji trophy record.

The logic followed here is:

PLSO is related to VRYU

MIPL is related to SOVR.

Similarly, IELH will be related:

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

The correct answer is 234.

Key Points

• The Multidimensional Poverty Index (MPI) is a measure of poverty that goes beyond income, considering various aspects of deprivation.
• The 2024 MPI report by the United Nations Development Programme (UNDP) and the Oxford Poverty and Human Development Initiative (OPHDI) provides a global overview of multidimensional poverty.
• India has the highest number of people living in multidimensional poverty worldwide, according to the report.
• The report indicates that approximately 230 million people in India are affected by multidimensional poverty.
• Multidimensional poverty includes deprivations in health, education, and living standards.
• The MPI assesses factors such as nutrition, child mortality, years of schooling, school attendance, cooking fuel, sanitation, drinking water, electricity, housing, and assets.
• The report highlights that while India has made progress in reducing poverty, significant challenges remain.
• The 230 million figure underscores the scale of poverty in India, despite its economic growth.
• The MPI provides a more comprehensive understanding of poverty than traditional income-based measures.
• The data from the MPI can be used to inform policy decisions and target interventions to reduce poverty.
• The report emphasizes the importance of addressing multiple dimensions of poverty simultaneously.
• The report also shows that children are disproportionately affected by multidimensional poverty.
• The MPI report provides insights into the regional disparities in poverty within India.
• The report also highlights the importance of data collection and analysis in monitoring poverty trends.
• The index is designed to give policy makers and global organizations the best data to help alleviate poverty.
• The MPI is a valuable tool for tracking progress towards the Sustainable Development Goals (SDGs), particularly SDG 1 (No Poverty).
• The report emphasizes the need for targeted interventions to address the specific deprivations faced by different populations.
• The 2024 MPI report provides a comprehensive picture of global multidimensional poverty, with a strong focus on India.
• The report serves as a call to action for governments, organizations, and individuals to work together to reduce poverty in all its forms.
• The MPI is an important tool for understanding the complexity of poverty.

The correct answer is anode mud.

Key Points

• Anode mud:
• In electrolytic refining, the impure metal is used as the anode.
• During electrolysis, the impure metal dissolves, releasing metal ions into the electrolyte.
• Impurities that are less reactive than the metal being refined do not dissolve.
• These undissolved impurities settle down at the bottom of the anode.
• This accumulated residue of impurities is known as "anode mud."
• The composition of anode mud varies depending on the impure metal being refined.

Additional Information

• Cathode mud:
• "Cathode mud" is not a standard term used in electrolytic refining.
• The cathode is where the pure metal is deposited, not where impurities settle.
• The cathode increases in mass as the pure metal is deposited.
• The cathode is made of pure metal.
• Impurities do not collect at the cathode.
• Electrolytic mud:
• While the term "electrolytic mud" might seem plausible, "anode mud" is the specific and correct term.
• "Electrolytic mud" is not a standard scientific term.
• The term anode mud is used to specifically describe the sludge from the anode.
• The electrolyte itself is a solution, not mud.
• Gangue:
• Gangue refers to the unwanted rock and mineral matter associated with valuable minerals in an ore.
• It is a term used in mining and ore processing, not specifically in electrolytic refining.
• Gangue is removed before the electrolytic refining process.
• Gangue is associated with raw ore.
• Gangue is not related to the electrolytic process itself.

Possible diagram is:

Conclusions:

I. No jeans are pants → True (because all pants are ties and no ties are jeans So, no jeans are pants)

II. All pants are shirts → False (because all shirts are pants so, all pants are shirts is possible but not defined)

So, Only conclusion (I) follows.

Hence, the correct answer is "Option (4)".

The correct answer is The autotrophs or the producers are at the first trophic level.

Key Points

Trophic Levels in a Food Chain:

• Trophic levels represent the position of an organism in a food chain or food web.
• The first trophic level always consists of autotrophs, also known as producers.
• Autotrophs are organisms that can produce their own food using sunlight (photosynthesis) or chemical energy (chemosynthesis).
• Examples of autotrophs include plants, algae, and some bacteria.
• These organisms form the base of the food chain, providing energy for all other trophic levels.
• The second trophic level consists of herbivores or primary consumers.
• Herbivores are heterotrophs that consume producers (autotrophs).
• Examples of herbivores include cows, deer, and rabbits.
• The third trophic level consists of carnivores or secondary consumers.
• Secondary consumers are heterotrophs that eat herbivores.
• Examples of secondary consumers include snakes, frogs, and some birds.
• The fourth trophic level, or higher, consists of larger carnivores or tertiary consumers.
• Tertiary consumers are heterotrophs that eat secondary consumers.
• Examples of tertiary consumers include hawks, lions, and sharks.
• Energy flows through the food chain from the producers to the consumers.
• At each trophic level, a significant amount of energy is lost as heat, limiting the number of trophic levels in a food chain.
• Typically, only about 10% of the energy from one trophic level is transferred to the next.
• This energy loss is explained by the second law of thermodynamics.
• The flow of energy is unidirectional, starting with the sun and ending with the top predators.
• Food chains and food webs are essential for maintaining the balance of ecosystems.
• The concept of trophic levels helps us understand the relationships between organisms in an ecosystem.
• Disruptions at any trophic level can have cascading effects on the entire ecosystem.
• The study of trophic levels is crucial for understanding ecosystem dynamics and conservation.
• Decomposers (bacteria and fungi) also play a vital role by breaking down dead organic matter, returning nutrients to the ecosystem.
• Trophic levels are a fundamental concept in ecology.

The correct answer is Advance sunrise and delayed sunset.

Key Points

Atmospheric Refraction and Sunrise/Sunset:

• Atmospheric refraction is the bending of light as it passes through the Earth's atmosphere.
• The atmosphere's density increases as you get closer to the Earth's surface.
• This varying density causes light to bend as it travels through the atmosphere.
• During sunrise and sunset, sunlight has to travel through a greater portion of the atmosphere.
• As the sunlight enters the atmosphere at a shallow angle, it is refracted, or bent.
• This bending causes the apparent position of the sun to be slightly higher than its actual position.
• As a result, we see the sun before it has physically risen above the horizon (advance sunrise).
• Similarly, we continue to see the sun for a short time after it has physically set below the horizon (delayed sunset).
• This effect extends the duration of daylight by a few minutes each morning and evening.
• The amount of refraction depends on the temperature and density of the air.
• Refraction is more pronounced near the horizon because light travels through a denser layer of air.
• The phenomenon is also responsible for the oval shape of the sun near the horizon.
• Atmospheric refraction also causes the twinkling of stars.
• The bending of light is a continuous process as the atmosphere's density changes.
• The refractive index of air increases with its density.
• The refraction of light is a consequence of the change in the speed of light in different mediums.
• The effect is most easily seen when looking at objects very close to the horizon.
• The amount of advance sunrise and delayed sunset varies depending on the latitude and time of year.
• Atmospheric refraction is a common optical phenomenon.
• The effect is most noticable when the sun is very close to the horizon.
• The atmosphere acts like a series of prisms bending the light.
• The effect of atmospheric refraction is a daily occurrence.

Given: 

Shreya's rank from the left end = 11th

Ravi's rank from the left end = 12th

Ravi is exactly between Shreya and Rahul.

Rahul's rank from the right end = 15th

To find Rahul's rank from the left end:

Ravi's position is exactly between Shreya and Rahul, so the difference in their positions is equal on both sides of Ravi.

Ravi's rank from the left end - Shreya's rank from the left end = Rahul's rank from the left end - Ravi's rank from the left end

12 - 11 = Rahul's rank from the left end - 12

1 = Rahul's rank from the left end - 12

Rahul's rank from the left end = 13

Total number of people in the row = Rahul's rank from the left end + Rahul's rank from the right end - 1

13 + 15 - 1 = 27

Hence, the total number of people in the row is "27".

The correct answer is 10 m/s.

Key Points

• Initial velocity (u) = 0 m/s (since the car starts from rest)
• Acceleration (a) = 0.5 m/s²
• Time (t) = 20 s
• v = u + at
• v = 0 + (0.5 m/s² * 20 s)
• v = 10 m/s

The logic followed here is:

Option 1) GD - FI

Option 2) JG - IM

Option 3) NK - MP

Option 4) DA - CF

Thus, out of all the options 'JG - IM' is the odd one out.

Hence, "Option 2" is the correct answer

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

The 1st digit from the left end is: 2

The 15th digit from the right end is: 1

So, the sum of the 1st digit from the left and the 15th digit from the right is: 2 + 1 = 3

Hence, the correct answer is "Option 1".

Given Equation: 8 + 7 ÷ 36 × 9 - 12 = ?

BODMAS Rule:

Decoding the given information:

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

⇒ 8 + 7 × 36 ÷ 9 - 12 = ?

⇒ 8 + 7 × 4 - 12 = ?

⇒ 8 + 28 - 12 = ?

⇒ 36 - 12 = ?

⇒ 24

Hence, the correct option is "Option 2".

The correct answer is backwards.

Key Points Inertia and Newton's First Law:

• The tendency to fall backward is explained by Newton's first law of motion, also known as the law of inertia.
• Inertia is the tendency of an object to resist changes in  its state of motion.
• When the bus is at rest, your body is also at rest.
• When the bus suddenly accelerates forward, your feet, which are in contact with the bus floor, move forward with the bus.
• However, the upper part of your body tends to remain at rest due to inertia.
• This difference in motion between your feet and upper body causes you to lean backward.
• Your feet are experiencing the force of the bus's acceleration, while your upper body resists this force.
• The upper part of your body tries to maintain its original state of rest.
• The muscles in your body work to counteract this effect and maintain your balance.
• The sudden change in motion creates an imbalance, leading to the backward lean.
• The faster the acceleration of the bus, the greater the tendency to fall backward.
• This phenomenon is a common experience and a direct result of inertia.
• The effect is more pronounced when the bus accelerates rapidly.
• The concept of inertia applies to all objects, not just human bodies.
• This is an example of how forces and motion interact in everyday situations.
• The backward lean is a temporary effect, as your body eventually adjusts to the new motion.
• If you were holding onto a railing or seat, the effect would be less pronounced.
• The force of friction between your feet and the bus floor also plays a role in your movement.
• The center of mass of your body also influences your stability during this movement.
• The human body's balancing mechanisms are designed to counteract such forces.
• This situation demonstrates the fundamental principle that objects resist changes to their current state of motion.
• This is a real world example of how inertia effects the human body.

The correct answer is Chalk powder in water.

Key Points

Suspension:

• A suspension is a heterogeneous mixture in which solid particles are dispersed in a liquid.
• The particles in a suspension are large enough to be seen with the naked eye.
• These particles do not dissolve in the liquid but remain suspended throughout it.
• Over time, the particles in a suspension will settle down due to gravity.
• Chalk powder in water is a classic example of a suspension.
• The chalk particles are insoluble in water and remain dispersed.
• If left undisturbed, the chalk powder will settle at the bottom of the container.
• Suspensions are unstable mixtures.
• Suspensions can be separated by filtration.
• Suspensions are often cloudy or opaque.
• The size of the particles in a suspension is typically greater than 1000 nanometers.
• Suspensions scatter light, making them appear turbid.
• Suspensions are different from solutions, where the solute dissolves completely in the solvent.
• Suspensions are also different from colloids, where the particles are smaller and do not settle easily.
• The particles in a suspension are large enough to be separated by sedimentation.
• Examples of other suspensions include mud, sand in water, and some medicinal preparations.
• Suspensions are not homogeneous mixtures.
• Suspensions are a common type of mixture.
• The particles in a suspension are visible to the naked eye.
• Suspensions are an important part of many industrial processes.

The logic followed here is:

Logic: 1st number × 13 = 2nd number.

For, X : 117

⇒ X × 13 = 117

⇒ X = 117 ÷ 13 = 9.

Similarly, 

For, 15 : Y

⇒ 15 × 13 = 195.

Hence, the correct answer is "Option 4".

Shortcut Trick

Substitute a standard value for the angle, such as A = 45°, into the expression.

sec² 45° + (cosec² 45° − 1) + (1 + tan² 45°) − cot² 45°

⇒ (√2)² + ((√2)² − 1) + (1 + 1²) − 1²

⇒ 2 + (2 − 1) + (1 + 1) − 1 = 2 + 1 + 2 − 1 = 4

Now check the options: 2 sec² 45° = 2 × (√2)² = 2 × 2 = 4.

∴ The correct answer is 2 sec² A.

Alternate Method

Given: sec² A + (cosec² A − 1) + (1 + tan² A) − cot² A

Formulas Used:

1. cosec² A − 1 = cot² A
2. 1 + tan² A = sec² A

⇒ The given expression is: sec² A + (cosec² A − 1) + (1 + tan² A) − cot² A

⇒ Substituting the trigonometric identities:

⇒ sec² A + cot² A + sec² A − cot² A

⇒ Grouping the terms: (sec² A + sec² A) + (cot² A − cot² A)

⇒ 2 sec² A + 0

⇒ 2 sec² A

∴ The correct answer is 2 sec² A.

Additional Information

Pythagorean Identities

There are three fundamental identities: sin² A + cos² A = 1, 1 + tan² A = sec² A, and 1 + cot² A = cosec² A.

Reciprocal Identities

Secant and cosecant are reciprocals of cosine and sine: sec A = 1/cos A and cosec A = 1/sin A.

Standard Values

At A = 45°, sin A = cos A = 1/√2, tan A = cot A = 1, and sec A = cosec A = √2.

The correct answer is Rishav Ray.

Key Points

Rishav Ray and "A Game of Two Halves":

• Rishav Ray is the author of "A Game of Two Halves: The Story of the Golden Era of Indian Club Football."
• The book delves into the rich history of Indian club football, particularly focusing on its golden era.
• It explores the period when Indian club football was at its peak, highlighting the achievements and stories of various clubs and players.
• The book provides insights into the social and cultural context of Indian football during that era.
• It documents the rivalries, triumphs, and challenges faced by Indian football clubs.
• The book serves as a valuable historical record of Indian football's past.
• It aims to revive interest in the history of Indian club football.
• The book has been met with critical acclaim by sports enthusiasts.
• It is a well-researched work that provides a comprehensive overview of the golden era.
• The book highlights the importance of club football in the development of Indian football.
• It narrates the stories of legendary players and clubs that shaped the landscape of Indian football.
• The book provides a nostalgic look back at a time when Indian club football was a major force.
• Rishav Ray's work contributes to the preservation of Indian football's heritage.
• The book is a must-read for anyone interested in the history of Indian sports.
• The work discusses the impact that the clubs had on their local communities.
• The book is a result of extensive research, and interviews.
• The author has attempted to capture the essence of the time period.
• The book has helped to generate renewed interest in the history of Indian football.
• The book provides a narrative of a time when Indian football was very popular.

Given:

Expression: $\frac{9}{10}\div \left(\frac{4}{5}+\frac{1}{10} \right)$

Formula used:

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

Calculations:

First, solve the expression inside the bracket:

$\frac{4}{5} + \frac{1}{10}$

⇒ $\frac{4\times2 + 1}{10}$

⇒ $\frac{8 + 1}{10} = \frac{9}{10}$

Now, substitute this value back into the main expression:

$\frac{9}{10}\div \frac{9}{10}$

⇒ $\frac{9}{10} \times \frac{10}{9}$

⇒ 1

∴ The correct answer is option (2).

The correct answer is Water.

Key Points

• Water:
• The hydrophilic end of a soap molecule is the polar end.
• This end is attracted to water molecules because water is also a polar molecule.
• "Hydrophilic" literally means "water-loving."
• The hydrophilic end of the soap molecule contains a negatively charged carboxylate group (COO-) or a similar ionic group.
• This charged end interacts strongly with the polar water molecules through ion-dipole interactions and hydrogen bonding.
• This interaction allows soap to dissolve in water.

Additional Information

• Hydrocarbon:
• Hydrocarbons are non-polar molecules.
• The hydrophobic end of a soap molecule, which is the long hydrocarbon chain, interacts with hydrocarbons.
• This non-polar end is repelled by water.
• Hydrocarbons are oil based molecules.
• The hydrocarbon chain is what allows soaps to interact with grease and oil.
• Oil:
• The hydrophobic end of a soap molecule interacts with oil.
• This end is non-polar and is repelled by water.
• The hydrophobic end is the long hydrocarbon chain.
• This is how soap removes oils and greases.
• The oil is surrounded by the hydrophobic ends, and the hydrophilic ends interact with the water, allowing the oil to be washed away.

Given:

Expression = X − 90% of X

Formula used:

Percentage value = (Rate/100) × Number

Calculations:

According to the question:

⇒ Result = X − (90/100) × X

⇒ Result = X − 0.9 × X

⇒ Result = X(1 − 0.9)

⇒ Result = 0.1 × X

Comparing with multiplying X by a factor:

⇒ Result = 0.1 × X

∴ The correct answer is option (4).

The logic followed here is:

Logic: 1st number × 11 = 2nd number.

For, X : 88

⇒ X × 11 = 88

⇒ X = 88 ÷ 11 = 8

Similarly, 

For, 12 : Y

⇒ 12 × 11 = 132.

Hence, the correct answer is "Option 3".

The correct answer is It stimulates growth in all organs.

Key Points

Growth Hormone (GH) Function:

• Growth hormone, also known as somatotropin, is a peptide hormone produced by the anterior pituitary gland.
• Its primary function is to stimulate growth, cell reproduction, and cell regeneration.
• GH affects virtually all tissues of the body, promoting growth in bones, muscles, and organs.
• It plays a crucial role in childhood and adolescence, when rapid growth occurs.
• GH stimulates the liver to produce insulin-like growth factor 1 (IGF-1), which mediates many of its growth-promoting effects.
• IGF-1 stimulates cell growth and proliferation, particularly in cartilage and bone.
• GH also has metabolic effects, including increasing protein synthesis and fat breakdown.
• It helps regulate body composition by increasing lean muscle mass and reducing fat mass.
• GH influences carbohydrate metabolism, often leading to increased blood glucose levels.
• It plays a role in maintaining bone density and strength.
• GH is essential for proper development and maturation of various tissues and organs.
• The secretion of GH is regulated by the hypothalamus, which releases growth hormone-releasing hormone (GHRH) and somatostatin.
• GHRH stimulates GH release, while somatostatin inhibits it.
• GH secretion is influenced by factors such as sleep, exercise, stress, and nutrition.
• GH levels are typically highest during childhood and adolescence and decline with age.
• Deficiencies in GH can lead to growth disorders, such as dwarfism in children.
• Excess GH can result in gigantism in children and acromegaly in adults.
• GH is involved in the repair and regeneration of tissues after injury.
• GH has impacts on the immune system as well.
• The hormone plays a part in the regulation of sleep.

Given statement: Even though Company X is the biggest exporter of wheat in the country, it is not among one of the biggest profit earning companies in the Country.

Reasons:

I. Trading in other materials other than wheat, like iron, is much more profitable

II. Company X has heavy miscellaneous expenditure

To determine which of the reasons explains the statement:

Reason I suggests that other materials are more profitable, which might imply that despite being the biggest exporter of wheat, wheat trade itself is not as profitable as other trades. This could be a valid reason.

Reason II suggests that Company X has heavy miscellaneous expenditures, which could also be a valid reason for not being among the biggest profit-earning companies despite being the biggest exporter of wheat.

Therefore, both reasons I and II could explain why Company X is not among the biggest profit-earning companies.

Hence, the correct answer is "Option 2".

The correct answer is The number of atoms of each element in a molecule.

Key Points

Subscripts in Chemical Formulas:

• A subscript in a chemical formula is a number written below and to the right of an element's symbol.
• It indicates the number of atoms of that specific element present in a molecule or formula unit of the compound.
• For example, in the formula H₂O, the subscript "2" indicates that there are two hydrogen atoms.
• The absence of a subscript implies that there is only one atom of that element.
• Subscripts are used to accurately represent the composition of chemical compounds.
• They are essential for writing balanced chemical equations.
• Subscripts are integral to understanding the stoichiometry of chemical reactions.
• They provide crucial information about the molecular structure of compounds.
• Subscripts are used in ionic compounds to show the ratio of ions in the formula unit.
• They are also used in covalent compounds to show the actual number of atoms in a molecule.
• Subscripts are a fundamental part of chemical notation.
• They allow scientists to communicate the exact composition of substances.
• The subscript is always a whole number.
• Subscripts are used in empirical and molecular formulas.
• They help to distinguish between different compounds with similar elements.
• Subscripts provide the quantitative information about elements in a compound.
• They are vital for calculating molar masses and performing other stoichiometric calculations.
• Subscripts are used to denote the number of atoms present in a polyatomic ion, when that ion is included multiple times in a compound.
• Subscripts are used to show the ratio of elements in a compound.
• Subscripts are a vital part of chemical shorthand.