RRB Technician Grade III Official Paper (Held On: 26 Dec, 2024 Shift 2) (Previous Year Paper)

Shortcut Trick

Relative Speed in same direction = Difference of speeds = 72 − 36 = 36 km/h.

Convert speed to m/s: 36 × (5/18) = 10 m/s.

Total Distance to cover = Sum of lengths = 200 + 300 = 500 m.

Time = Distance ÷ Relative Speed = 500 ÷ 10 = 50 seconds.

∴ The correct answer is 50 sec.

Alternate Method

Given:

Length of first train (L₁) = 200 m

Length of second train (L₂) = 300 m

Speed of first train (S₁) = 72 km/h

Speed of second train (S₂) = 36 km/h

Formula Used:

Time = (L₁ + L₂) ÷ (S₁ − S₂)

Conversion: 1 km/h = 5/18 m/s

Calculations:

⇒ Relative Speed = 72 − 36 = 36 km/h

⇒ Relative Speed in m/s = 36 × (5/18) = 10 m/s

⇒ Total distance to be covered = 200 + 300 = 500 m

⇒ Time taken = 500 ÷ 10

⇒ Time taken = 50 seconds

∴ The correct answer is 50 sec.

Additional Information

Relative Speed Concept

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

Crossing Distance

To cross each other completely, the distance covered is always the sum of the lengths of both trains, regardless of the direction.

Unit Conversion

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

Decoding symbols:

Given: M + N ÷ O × P + Q

M + N → M is the mother of N.

N ÷ O → N is the brother of O.

O × P → O is the husband of P.

P + Q → P is the mother of Q.

Thus, O is Q's father.

Hence, the correct answer is "Option 1".

The correct answer is Fragmentation.

Key Points

• Spirogyra reproduces asexually through a process called fragmentation.
• In fragmentation, the filament of Spirogyra breaks into two or more fragments, each of which grows into a new individual.
• This mode of reproduction is common in many filamentous algae like Spirogyra.
• Fragmentation allows for rapid population growth and colonization of new areas.
• Environmental factors such as water currents can aid in the process of fragmentation by physically breaking the filaments.

Additional Information

• Spirogyra
• Spirogyra is a genus of filamentous green algae found in freshwater habitats.
• It is named for its characteristic helical or spiral arrangement of chloroplasts.
• Spirogyra is often found in calm and nutrient-rich waters, forming dense mats on the water surface.
• Other Reproduction Modes
• Budding: A form of asexual reproduction where a new organism develops from an outgrowth or bud due to cell division at one particular site.
• Binary Fission: A form of asexual reproduction where a single organism divides into two equal parts, each becoming a new individual.
• Multiple Fission: A form of asexual reproduction where the parent cell divides into multiple daughter cells simultaneously.
• Asexual Reproduction in Algae
• Asexual reproduction in algae can occur through various methods such as fragmentation, spore formation, and binary fission.
• It is a quick and efficient way to increase population size and colonize new environments.
• Environmental Impact
• Fragmentation in Spirogyra can be influenced by environmental factors like water flow, temperature, and nutrient availability.
• Such factors can enhance or inhibit the process of fragmentation, affecting the growth and distribution of Spirogyra populations.

The correct answer is Sodium.

Key Points

• Sodium is a highly reactive metal that can spontaneously ignite when exposed to air due to its reaction with oxygen and moisture.
• It forms sodium oxide and sodium hydroxide when it reacts with oxygen and water vapor in the air, releasing heat.
• Because of its high reactivity, sodium is stored under oil or in an inert atmosphere to prevent accidental fires.
• In its pure form, sodium is a soft, silvery-white metal that is part of the alkali metal group in the periodic table.

Additional Information

• Reactivity Series of Metals
• The reactivity series is a list of metals ranked by their reactivity, from highest to lowest.
• Metals like potassium, sodium, lithium, and calcium are highly reactive and placed at the top of the series.
• These metals react vigorously with water and air, releasing hydrogen gas and forming hydroxides.
• Alkali Metals
• Alkali metals belong to Group 1 of the periodic table and include lithium, sodium, potassium, rubidium, cesium, and francium.
• They are characterized by having one electron in their outermost shell, making them highly reactive.
• Alkali metals react strongly with water to form alkaline hydroxides and hydrogen gas.
• Safety Precautions for Handling Sodium
• Sodium should be handled with care, using gloves and protective eyewear to avoid contact with skin and eyes.
• It should be stored in a non-reactive substance like mineral oil or kerosene to prevent exposure to air and moisture.
• In case of a sodium fire, it should not be extinguished with water; instead, use a Class D fire extinguisher designed for metal fires.

The correct answer is Four.

Key Points

• During meiosis, a single cell divides twice to produce four cells.
• These four cells are called gametes, which are sperm in males and eggs in females.
• Each of these gametes contains half the number of chromosomes of the original cell.
• This reduction in chromosome number is crucial for maintaining the species' chromosome number across generations.

Additional Information

• Phases of Meiosis:
• Meiosis consists of two stages: Meiosis I and Meiosis II.
• Meiosis I includes Prophase I, Metaphase I, Anaphase I, and Telophase I.
• Meiosis II includes Prophase II, Metaphase II, Anaphase II, and Telophase II.
• Genetic Diversity:
• Meiosis increases genetic diversity through processes like crossing over and independent assortment.
• Crossing over occurs during Prophase I, where homologous chromosomes exchange genetic material.
• Chromosome Number:
• Humans have 46 chromosomes, which are reduced to 23 chromosomes in gametes through meiosis.
• When fertilization occurs, the chromosome number is restored to 46 in the zygote.
• Errors in Meiosis:
• Errors during meiosis can lead to genetic disorders such as Down syndrome, which is caused by an extra copy of chromosome 21.
• These errors are often due to nondisjunction, where chromosomes fail to separate properly.

Shortcut Trick

Let the time taken by the third pipe (C) be x hours.

Time for second pipe (B) = x + 4 hours and first pipe (A) = (x + 4) + 5 = x + 9 hours.

Given 1/A + 1/B = 1/C, which implies x = √(a × b) where a and b are the extra times relative to C.

Since A is 9 hr more and B is 4 hr more than C, then x = √(9 × 4) = 6 hours.

Time for first pipe (A) = 6 + 9 = 15 hours.

∴ The correct answer is 15 hr.

Alternate Method

Given: Efficiency of (A + B) = Efficiency of C

⇒ 1/(x + 9) + 1/(x + 4) = 1/x

⇒ [(x + 4) + (x + 9)] / [(x + 9)(x + 4)] = 1/x

⇒ (2x + 13) × x = x² + 13x + 36

⇒ 2x² + 13x = x² + 13x + 36

⇒ x² = 36

⇒ x = 6 hours (Time for Pipe C)

⇒ Time for Pipe A = x + 9 = 6 + 9 = 15 hours

∴ The correct answer is 15 hr.

Additional Information

Combined Efficiency Rule

When two pipes A and B fill a tank in the same time as pipe C alone, then 1/t_A + 1/t_B = 1/t_C.

Time and Work Square Root Shortcut

If A takes 'a' hours more than (A+B) and B takes 'b' hours more than (A+B), then the time taken by (A+B) together is √(a × b).

Shortcut Trick

For any expression of the form a + 1/a = k, the value of a² + 1/a² is given by the formula k² − 2.

Given: a + 1/a = 4 ⇒ k = 4

Calculation: 4² − 2 = 16 − 2 = 14

∴ The correct answer is 14.

Alternate Method

Given: a + 1/a = 4

Formula Used: (x + y)² = x² + y² + 2xy

Calculations:

⇒ Square both sides of the given equation:

⇒ (a + 1/a)² = 4²

⇒ a² + (1/a)² + 2 × a × (1/a) = 16

⇒ a² + 1/a² + 2 = 16

⇒ a² + 1/a² = 16 − 2

⇒ a² + 1/a² = 14

∴ The correct answer is 14.

Additional Information

Higher Power Relation

If a + 1/a = k, then a³ + 1/a³ = k³ − 3k.

Negative Sign Variation

If a − 1/a = k, then a² + 1/a² = k² + 2 and a³ − 1/a³ = k³ + 3k.

Algebraic Identity

(a + b)² − (a − b)² = 4ab, which helps in converting between sum and difference of reciprocals.

The correct answer is Nagaland.

Key Points

• The Hornbill Festival is an annual cultural festival celebrated in Nagaland, India.
• It is organized by the Government of Nagaland to encourage inter-tribal interaction and to promote the cultural heritage of Nagaland.
• The festival was first held in the year 2000 and has since become one of the largest cultural showcases in northeastern India.
• The 25th edition of the Hornbill Festival was held in December 2024.
• The festival is named after the bird 'Hornbill', which is a significant cultural symbol for the tribes of Nagaland.

Additional Information

• Nagaland
• Nagaland is a state in northeastern India, known for its rich indigenous culture and traditions.
• The state is home to several tribes, each with its own unique customs and practices.
• Kohima is the capital of Nagaland, while Dimapur is its largest city.
• The state has a predominantly mountainous terrain, with lush green forests and scenic landscapes.
• Cultural Significance
• The Hornbill Festival is often referred to as the 'Festival of Festivals' due to its grand scale and diverse cultural displays.
• It features traditional music, dance performances, handloom and handicraft exhibitions, and indigenous games.
• Various Naga tribes showcase their traditional attire, rituals, and lifestyle during the festival.
• The festival also includes events like rock concerts, fashion shows, and adventure sports, attracting tourists from all over the world.
• Tourism Impact
• The Hornbill Festival has significantly boosted tourism in Nagaland, contributing to the state's economy.
• It provides a platform for local artisans and craftsmen to exhibit and sell their products.
• The festival promotes cross-cultural understanding and strengthens the bond between different tribes and communities.
• Visitors have the opportunity to experience the vibrant and diverse culture of Nagaland firsthand.

The correct answer is Seven.

Key Points

• In August 2024, the Government of India established seven Zonal Cultural Centres (ZCCs).
• The primary goal of these centres is to promote cultural traditions and conduct research on folk arts and songs.
• The ZCCs focus on preserving and promoting rural and tribal cultural heritage.
• Each ZCC is responsible for documenting, preserving, and promoting the unique cultural heritage of their respective zones.
• The initiative is part of India's broader strategy to support and sustain diverse cultural expressions within the country.

Additional Information

• Zonal Cultural Centres (ZCCs)
• ZCCs are cultural hubs established to promote regional arts and culture in India.
• They help in organizing cultural festivals, workshops, and exhibitions to showcase regional talents.
• ZCCs work closely with local artists and communities to preserve traditional crafts and practices.
• They also play a crucial role in educating the younger generation about their cultural heritage.
• National Mission on Cultural Mapping
• An initiative by the Ministry of Culture to map and document India's cultural assets.
• Aims to create a comprehensive database of artists, art forms, and cultural resources across the country.
• Helps in the formulation of policies and programs to support and promote cultural heritage.
• Ensures that the diverse cultural expressions of India are recognized and preserved.
• Folk Arts and Songs
• Folk arts and songs are an integral part of India's cultural heritage.
• They are often region-specific and reflect the traditions, beliefs, and lifestyles of local communities.
• Efforts are being made to document and preserve these art forms for future generations.
• Folk arts and songs play a significant role in community bonding and cultural identity.
• Tribal Cultural Heritage
• India is home to a diverse range of tribal communities with unique cultural practices.
• Tribal culture includes distinct languages, rituals, and art forms.
• There are ongoing efforts to promote and preserve tribal cultural heritage.
• Tribal festivals and cultural events are organized to showcase tribal traditions and arts.

Given: 55 × 45 + 5 - 8 ÷ 4 = ?

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

55 × 45 + 5 - 8 ÷ 4 = ? ⇒ 55 - 45 ÷ 5 × 8 + 4 = ?

⇒ 55 - 45 ÷ 5 × 8 + 4 = ?

⇒ 55 - 9 × 8 + 4 = ?

⇒ 55 + 4 - 72 = ?

⇒ 59 - 72 = ?

⇒ -13 = ?

Hence, "Option 2" is the correct answer.

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

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

Required condition: Perfect square - Even digit - Even digit

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

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

Hence, "Option 4" is the correct answer.

The correct answer is Gallium and cesium.

Key Points

• Gallium has a melting point of about 29.76°C (85.57°F), which is slightly above room temperature.
• Cesium has a melting point of about 28.5°C (83.3°F), which is also close to room temperature.
• Both metals are unique in that they can exist in liquid form at temperatures near or slightly above typical room temperature.
• Gallium is often used in electronics and semiconductors, while cesium is used in atomic clocks and various scientific applications.
• The combination of their low melting points makes them interesting for various applications in science and technology.

Additional Information

• Room Temperature Definition
• Room temperature is generally considered to be around 20-25°C (68-77°F).
• It is the temperature range within which humans feel comfortable and it is commonly used in scientific studies as a standard.
• Melting Point
• The melting point is the temperature at which a solid becomes a liquid at normal atmospheric pressure.
• It is a physical property that is specific to each substance and is used to identify and characterize materials.
• Applications of Gallium
• Used in electronics, particularly in semiconductor technology.
• Employed in the production of alloys with low melting points.
• Applications of Cesium
• Used in atomic clocks, which are the most accurate timekeeping devices.
• Applied in various scientific research fields and in the oil industry for drilling fluids.

The correct answer is Oxygen.

Key Points

• Oxygen (O₂) is a diatomic molecule, meaning it consists of two oxygen atoms.
• It is the most abundant element in the Earth's atmosphere, making up about 21% by volume.
• Oxygen is essential for respiration in most living organisms and is also crucial for combustion processes.
• In its diatomic form, oxygen is a colorless, odorless gas at room temperature.

Additional Information

• Diatomic Molecules:
• Diatomic molecules are molecules composed of only two atoms, of the same or different chemical elements.
• Common diatomic molecules include hydrogen (H₂), nitrogen (N₂), oxygen (O₂), fluorine (F₂), and chlorine (Cl₂).
• Oxygen's Role in Life:
• Oxygen is vital for cellular respiration, a process by which cells produce energy.
• It is also used in medical treatments, such as oxygen therapy for patients with respiratory issues.
• Oxygen in Industrial Use:
• Oxygen is used in various industrial processes including steelmaking, welding, and as an oxidizer in rocket fuel.
• It is also used in water treatment and chemical manufacturing.
• Isotopes of Oxygen:
• There are three stable isotopes of oxygen: O-16, O-17, and O-18, with O-16 being the most abundant.
• These isotopes are used in scientific research, including climate studies and paleoclimatology.

Shortcut Trick

Identify the first 10 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Use group addition for speed: (2 + 3 + 5) + (7 + 13) + (11 + 19) + (17 + 23) + 29

⇒ 10 + 20 + 30 + 40 + 29 = 129

∴ The correct answer is 129.

Alternate Method

Given: Need to find the sum of the first 10 prime numbers.

Prime numbers are numbers greater than 1 having only two factors (1 and the number itself).

⇒ 1^st prime number = 2

⇒ 2^nd prime number = 3

⇒ 3^rd prime number = 5

⇒ 4^th prime number = 7

⇒ 5^th prime number = 11

⇒ 6^th prime number = 13

⇒ 7^th prime number = 17

⇒ 8^th prime number = 19

⇒ 9^th prime number = 23

⇒ 10^th prime number = 29

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

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

⇒ Sum = 10 + 7 + 11 + 13 + 17 + 19 + 23 + 29

⇒ Sum = 17 + 11 + 13 + 17 + 19 + 23 + 29

⇒ Sum = 28 + 13 + 17 + 19 + 23 + 29

⇒ Sum = 41 + 17 + 19 + 23 + 29

⇒ Sum = 58 + 19 + 23 + 29

⇒ Sum = 77 + 23 + 29

⇒ Sum = 100 + 29

⇒ Sum = 129

∴ The correct answer is 129.

Additional Information

Properties of Prime Numbers

The number 2 is the only even prime number. All other prime numbers are odd.

Co-prime Numbers

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

Twin Primes

Pairs of prime numbers that have a difference of 2 are called twin primes (e.g., 3 and 5, 5 and 7).

Prime Numbers up to 100

There are exactly 25 prime numbers between 1 and 100.

The correct answer is Decreasing its area of cross-section.

Key Points

• Resistance of a conductor is inversely proportional to its cross-sectional area (A). Thus, decreasing the area increases resistance.
• The resistance (R) is given by the formula R = ρ(L/A), where ρ is resistivity, L is length, and A is cross-sectional area.
• Decreasing the cross-sectional area of a conductor leads to fewer pathways for the electrons to flow, thus increasing resistance.
• In practical applications, thin wires have higher resistance compared to thicker wires of the same material and length.
• For example, resistance heating elements (like those in electric heaters) are designed with a small cross-sectional area to increase resistance and generate heat.

Additional Information

• Resistivity (ρ)
• It is a fundamental property of materials that quantifies how strongly a given material opposes the flow of electric current.
• Materials with high resistivity are poor conductors of electricity, while those with low resistivity are good conductors.
• Temperature Dependence
• Resistance of metallic conductors typically increases with temperature due to increased atomic vibrations, which scatter electrons.
• In contrast, the resistance of semiconductors and insulators usually decreases with temperature as more charge carriers become available.
• Ohm's Law
• Ohm's Law states that the current (I) through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R), given by the equation V = IR.
• This fundamental law is used extensively in electrical engineering and electronics.
• Applications of Resistance
• Resistors are used in electronic circuits to control voltage and current, set bias points, and terminate transmission lines.
• Understanding resistance is crucial in designing electrical and electronic components like sensors, heaters, and circuit protection devices.

Shortcut Trick

Total ratio parts = 4 + 5 = 9 units.

Given total chocolates = 63.

Value of 1 unit = 63 ÷ 9 = 7.

Chocolates for B = 5 units × 7 = 35.

∴ The correct answer is 35 chocolates.

Alternate Method

Given:

Total quantity = 63 chocolates

Ratio of A : B = 4 : 5

Formula Used:

Share of B = [Ratio of B ÷ (Sum of Ratios)] × Total Quantity

Calculations:

⇒ Sum of ratio parts = 4 + 5 = 9

⇒ Share of B = (5 ÷ 9) × 63

⇒ Share of B = 5 × 7

⇒ Share of B = 35

∴ The correct answer is 35 chocolates.

Additional Information

Ratio and Proportion

A ratio indicates how many times one number contains another. If a quantity Z is divided in ratio a:b, then parts are [a/(a+b)]×Z and [b/(a+b)]×Z.

Compound Ratio

The compound ratio of two ratios a:b and c:d is (ac):(bd), calculated by multiplying the corresponding antecedents and consequents.

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

1) Only three people sit between P and E when counted from the left of P.

2) G is an immediate neighbour of A as well as E. 

3) Only three people sit between M and A when counted from the right of A.

As position of G with respect to E is not known yet therefore there are two possible positions.

Case 1)

Case 2)

4) L sits to the immediate right of M.

As there is no possible for L in case 1, therefore case 1 is eliminated.

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

Case 2)

Thus, according to the final arrangement, G sits to the second to the left of B.

Hence, "Option 4" is the correct answer.

The correct answer is NITI Aayog.

Key Points

• The SDG India Index is an annual report published by NITI Aayog to track the progress of Indian states and union territories towards achieving the Sustainable Development Goals (SDGs).
• The 2023-24 SDG India Index report was published in July 2024 by NITI Aayog.
• It provides a comprehensive assessment of the performance of states and UTs on various SDG indicators, such as poverty, health, education, and climate action.
• The index uses a set of indicators to measure the progress and ranks states and UTs based on their performance.

Additional Information

• NITI Aayog
• NITI Aayog, or the National Institution for Transforming India, is a policy think tank of the Government of India.
• It was established in 2015, replacing the Planning Commission, with the aim to foster cooperative federalism through structured support initiatives and mechanisms.
• NITI Aayog plays a crucial role in designing strategic and long-term policies and programs for the Government of India.
• It provides relevant technical advice to the Centre and States and aims to promote competitive and cooperative federalism.
• Sustainable Development Goals (SDGs)
• The SDGs are a set of 17 global goals adopted by all United Nations Member States in 2015 to end poverty, protect the planet, and ensure prosperity for all by 2030.
• Each goal has specific targets to be achieved over the next 15 years.
• The SDGs cover a broad range of social, economic, and environmental development issues.
• Countries are expected to take ownership and establish a national framework for achieving the 17 Goals.
• Indicators used in SDG India Index
• The index uses multiple indicators to measure the performance of states and UTs in areas such as health, education, gender equality, economic growth, and climate action.
• These indicators help in assessing the progress and identifying areas that need more attention and resources.
• The data is collected from various sources, including government databases and international organizations.

The correct answer is Thyroxin hormone.

Key Points

• Thyroxin hormone is crucial for regulating the body’s metabolic processes, including carbohydrate, protein, and fat metabolism.
• Iodine is essential for the synthesis of thyroxin, and its deficiency can lead to thyroid-related disorders.
• The thyroid gland absorbs iodine from the bloodstream to produce thyroxin.
• Thyroxin, also known as T4, plays a critical role in growth, development, and metabolic activities.
• A balanced level of thyroxin is necessary for maintaining overall health and homeostasis.

Additional Information

• Thyroid Gland
• The thyroid gland is located in the neck and is responsible for producing hormones that regulate metabolism.
• It produces two primary hormones: thyroxin (T4) and triiodothyronine (T3).
• The secretion of thyroid hormones is regulated by the Thyroid Stimulating Hormone (TSH) produced by the pituitary gland.
• Iodine
• Iodine is a trace element that is crucial for the synthesis of thyroid hormones.
• It is commonly obtained from dietary sources such as iodized salt, seafood, and dairy products.
• Iodine deficiency can lead to goiter and hypothyroidism.
• Metabolism
• Metabolism refers to the chemical processes that occur within a living organism to maintain life.
• It includes catabolic processes that break down molecules to produce energy and anabolic processes that build up molecules.
• Thyroid hormones play a pivotal role in regulating basal metabolic rate (BMR).
• Hypothyroidism and Hyperthyroidism
• Hypothyroidism is a condition where the thyroid gland does not produce enough thyroid hormones, leading to symptoms such as fatigue, weight gain, and depression.
• Hyperthyroidism is the overproduction of thyroid hormones, resulting in symptoms like weight loss, rapid heartbeat, and anxiety.
• Both conditions require medical intervention to restore hormonal balance.

The correct answer is Three.

Key Points

• The Indian National Trust for Art and Cultural Heritage (INTACH) Research Programme for 2025 is divided into three main categories.
• These categories are designed to cover various aspects of heritage conservation and research.
• The programme aims to encourage comprehensive studies and protection of India's rich cultural heritage.
• Research topics under these categories include architectural heritage, material culture, and intangible cultural heritage.

Additional Information

• Architectural Heritage
• This category involves the study and conservation of historical buildings and structures.
• It includes documentation, analysis, and preservation techniques to maintain architectural integrity.
• Material Culture
• This involves the study of physical objects, artifacts, and other material evidence of past societies.
• Research focuses on understanding the cultural significance and historical context of these materials.
• Intangible Cultural Heritage
• This category includes traditions, rituals, and practices that are passed down through generations.
• It emphasizes the importance of preserving non-physical aspects of cultural heritage, such as oral histories and performing arts.

Shortcut Trick

Interest for 1 year = 4000 ÷ 2 = ₹2000

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

Rate = (2000 ÷ 20000) × 100 = 10%

∴ The correct answer is 10%.

Alternate Method

Given:

Principal (P) = ₹20,000

Time (T) = 2 years

Simple Interest (SI) = ₹4,000

Formula Used:

SI = (P × R × T) ÷ 100

Calculations:

⇒ 4000 = (20000 × R × 2) ÷ 100

⇒ 4000 = 200 × R × 2

⇒ 4000 = 400 × R

⇒ R = 4000 ÷ 400

⇒ R = 10%

∴ The correct answer is 10%.

Additional Information

Simple Interest (SI)

It is the interest calculated only on the principal amount for the entire duration. Formula: SI = (P × R × T) / 100.

Total Amount (A)

The sum of the principal and the interest earned over a period. A = P + SI.

Rate of Interest (R)

The percentage of the principal charged as interest per unit time. R = (SI × 100) / (P × T).

The correct answer is Emission.

Key Points

• Emission is not a phase transition; it refers to the release of energy, often in the form of light or radiation, from a source.
• Phase transitions involve changes in the state of matter, such as from solid to liquid or liquid to gas.
• Examples of phase transitions include sublimation, condensation, and vaporization, all of which involve changing physical states.
• Emission, on the other hand, is more commonly associated with physical processes like the emission of photons or particles.

Additional Information

• Sublimation:
• Sublimation is the phase transition from a solid directly to a gas, bypassing the liquid state.
• An example of sublimation is dry ice (solid carbon dioxide) turning directly into carbon dioxide gas.
• Condensation:
• Condensation is the phase transition from gas to liquid.
• This process is commonly observed when water vapor in the air condenses to form dew on cool surfaces.
• Vaporization:
• Vaporization is the phase transition from liquid to gas.
• Boiling water turning into steam is a typical example of vaporization.
• Deposition:
• Deposition is the phase transition from a gas directly to a solid, skipping the liquid phase.
• Frost formation from water vapor is an example of deposition.

Given:

3/7 = x/−35

Formula used:

Cross-multiplication: If a/b = c/d, then a × d = b × c

Calculations:

3/7 = x/−35

⇒ 3 × (−35) = 7 × x

⇒ −105 = 7x

⇒ x = −105/7

⇒ x = −15

∴ The correct answer is option (2).

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

1) No one sits to the left of B.

2. Only four people sit between B and Y. 

3) Only three people sit to the right of Z.

4) A sits to the immediate left of L.

5) D is not an immediate neighbour of Z.

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

Thus, according to the final arrangement, D sits at the rightmost end of the line.

Hence, "Option 1" is the correct answer.

The correct answer is Saturated compounds.

Key Points

• Saturated compounds are those in which the carbon atoms are linked by single bonds only.
• These compounds are also known as alkanes in organic chemistry.
• Saturated compounds generally have the chemical formula CnH2n+2, where n is the number of carbon atoms.
• They are typically less reactive than unsaturated compounds due to the stability of the single carbon-carbon bonds.

Additional Information

• Unsaturated Compounds
• These compounds contain at least one double or triple bond between carbon atoms.
• They are more reactive than saturated compounds due to the presence of multiple bonds.
• Examples include alkenes (with double bonds) and alkynes (with triple bonds).
• Ionic Compounds
• Formed by the transfer of electrons from one atom to another, creating ions.
• These compounds are typically formed between metals and non-metals.
• They exhibit high melting and boiling points and conduct electricity in molten or dissolved states.
• Covalent Compounds
• Formed by the sharing of electron pairs between atoms.
• These compounds can be polar or non-polar based on the electronegativity difference between the atoms involved.
• They generally have lower melting and boiling points compared to ionic compounds.
• Hydrocarbons
• Organic compounds consisting entirely of hydrogen and carbon.
• They are classified into alkanes, alkenes, and alkynes based on the type of bonds present.
• Hydrocarbons are the primary components of fossil fuels like coal, petroleum, and natural gas.

The correct answer is Total mechanical energy.

Key Points

• Total mechanical energy is the sum of an object's kinetic energy and potential energy.
• Kinetic energy is the energy an object possesses due to its motion.
• Potential energy is the energy stored in an object due to its position or configuration.
• The total mechanical energy of a system remains constant if only conservative forces, such as gravity, are acting on the system.
• In the absence of non-conservative forces (like friction), the total mechanical energy (kinetic + potential) is conserved.

Additional Information

• Thermal Energy
• It is the internal energy present in a system due to its temperature.
• It is not the same as total mechanical energy.
• Chemical Energy
• It is the potential of a chemical substance to undergo a chemical reaction and transform into other substances.
• It is stored in the bonds of chemical compounds.
• Electrical Energy
• It is the energy caused by the movement of electrons.
• It is commonly used in electrical circuits and devices.
• Conservation of Mechanical Energy
• In a closed system with only conservative forces, the total mechanical energy remains constant.
• This principle is used in analyzing the motion of objects in physics.

The correct answer is tendrils.

Key Points

• Tendrils are specialized structures that allow pea plants to climb by wrapping around objects for support.
• They are sensitive to touch and can coil around nearby structures, providing stability and access to sunlight.
• Tendrils are typically modified leaves or stems that have adapted to perform this climbing function.
• In pea plants, tendrils emerge from the leaf axils and can be either simple or branched.
• These structures are vital for the plant's growth in environments where space and light are limited.

Additional Information

• Climbing Mechanisms in Plants
• Plants use various structures to climb, including tendrils, roots, and stems.
• Climbing helps plants reach sunlight in dense vegetation.
• Examples of climbing plants include grapevines, cucumbers, and ivy.
• Types of Tendrils
• Leaf Tendrils: Modified leaves or leaflets, as seen in pea plants.
• Stem Tendrils: Modified stems, common in grapevines and passionflowers.
• Branched Tendrils: Tendrils that split into multiple branches, enhancing their grip.
• Adaptive Advantages
• Climbing allows plants to avoid competition for ground space.
• Provides access to better light conditions, essential for photosynthesis.
• Helps in reducing damage from herbivores by elevating the plant.
• Other Climbing Structures
• Roots: Some plants like ivy use adhesive roots to climb surfaces.
• Thorns and Hooks: Plants like roses and bougainvillea use these to latch onto supports.
• Twining Stems: Morning glories and beans use their stems to coil around supports.

Shortcut Trick

Arrange initial 11 terms: 33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92. Median (6^th term) = 58.

Replace 92 with 99 and 41 with 43. New data: 33, 35, 43, 46, 55, 58, 64, 77, 87, 90, 99.

New Median (6^th term) = 58.

Difference = 58 − 58 = 0.

∴ The correct answer is 0.

Alternate Method

Given: Data set 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33. Total terms (n) = 11.

Formula: Median for odd n = ((n + 1)/2)^th term after sorting.

⇒ Sorted Old Data: 33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92.

⇒ Old Median = 6^th term = 58.

⇒ Sorted New Data (41→43, 92→99): 33, 35, 43, 46, 55, 58, 64, 77, 87, 90, 99.

⇒ New Median = 6^th term = 58.

⇒ Difference = 58 − 58 = 0.

∴ The correct answer is 0.

Additional Information

Median for Even Observations

If n is even, Median = Average of (n/2)^th and ((n/2) + 1)^th observations.

Effect of Outliers

The Median is less affected by extreme values (outliers) compared to the Mean.

Empirical Formula

Mode = 3 × Median − 2 × Mean.

Given:

Expression = 5 − [4 − {3 − (3 − 3 − 6)}]

Formula used:

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

Calculations:

5 − [4 − {3 − (3 − 3 − 6)}]

⇒ 5 − [4 − {3 − (−6)}]

⇒ 5 − [4 − {3 + 6}]

⇒ 5 − [4 − 9]

⇒ 5 − [−5]

⇒ 5 + 5

⇒ 10

∴ The correct answer is option (4).

The logic followed here is:

Given: 

(23, 47, 85)

23 + 47 + 15 = 85

85 = 85 (LHS = RHS)

And,

(11, 20, 46)

11 + 20 + 15 = 46

46 = 46 (LHS = RHS)

So, checking each option one by one:

Option 1) (17, 6, 38)

17 + 6 + 15 = 38

38 = 38 (LHS = RHS)

Option 2) (8, 7, 35)

8 + 7 + 15 = 35

30 ≠ 35 (LHS ≠ RHS)

Option 3) (21, 15, 50)

21 + 15 + 15 = 50

51 ≠ 50 (LHS ≠ RHS)

Option 4) (9, 16, 42)

9 + 16 + 15 = 42

40 ≠ 42 (LHS ≠ RHS)

Hence, "Option 1" is the correct answer.

The logic followed here is:

Option 1) GMS

Option 2) SDF

Option 3) IOU

Option 4) QWC

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

Hence, "Option 2" is the correct answer.

Given statement: The literacy rate in Country X is significantly lower than the global average due to a lack of access to quality education, especially in rural areas.

Given Courses of Action:

I. Construct more schools and educational facilities in rural areas of Country X to improve accessibility. → Follow

Constructing more schools in rural areas directly addresses the issue of limited access to quality education, which contributes to the low literacy rate.

II. Develop a digital education platform to provide online learning resources to students in both urban and rural areas of the country. → Follow

As a digital platform can help bridge the educational gap, providing learning opportunities to students in both urban and rural regions, especially physical infrastructure is lacking.

Thus, Both I and II follow.

Hence, "Option 1" is the correct answer.

The correct answer is aperture.

Key Points

• The diameter of the reflecting surface of a spherical mirror is called its aperture.
• The aperture determines the amount of light that can enter the mirror, affecting the brightness and clarity of the image formed.
• In optical terminology, the aperture is a crucial parameter in defining the light-gathering power of the mirror.
• A larger aperture allows more light to be collected, which is particularly important for applications like telescopes and cameras.
• The aperture is distinct from the focal length and radius of curvature, which are related to the mirror's shape and focusing properties.

Additional Information

• Focal Length
• The focal length of a spherical mirror is the distance between the mirror's surface and its focal point.
• It determines how strongly the mirror converges or diverges light.
• Radius of Curvature
• The radius of curvature is the distance between the mirror's surface and the center of curvature.
• It is twice the focal length for spherical mirrors.
• Types of Spherical Mirrors
• There are two main types: concave (converging) and convex (diverging) mirrors.
• Concave mirrors can form real or virtual images, while convex mirrors always form virtual images.
• Applications of Spherical Mirrors
• Concave mirrors are used in telescopes, shaving mirrors, and headlights.
• Convex mirrors are used for rear-view mirrors in vehicles and security mirrors.

The correct answer is West Bengal.

Key Points

• West Bengal was crowned as the team champion at the 4th National Finswimming Championship held in 2024.
• The event showcased remarkable performances by athletes from various states, but West Bengal emerged as the dominant team.
• Finswimming is a competitive sport that involves swimming with the use of fins, and it requires a combination of speed, strength, and technique.
• The championship saw participation from top finswimmers across the country, making it a highly competitive event.

Additional Information

• Finswimming
• Finswimming is an underwater sport consisting of four techniques using either monofins or bifins.
• It is governed by the Confédération Mondiale des Activités Subaquatiques (CMAS).
• Competitions can be held in swimming pools or open water, with various distances ranging from sprints to long-distance events.
• National Finswimming Championship
• The National Finswimming Championship is an annual event that brings together the best finswimmers from across India.
• The championship aims to promote the sport and identify talent at the national level.
• It serves as a platform for athletes to qualify for international competitions.
• Training and Preparation
• Finswimmers undergo rigorous training that includes strength conditioning, technique refinement, and endurance building.
• Advanced equipment such as specialized fins and snorkels are used to enhance performance.
• Coaches play a crucial role in developing strategies and ensuring athletes meet their peak performance.

Given series: (Left) 1 8 4 5 9 6 5 2 4 8 0 9 5 9 5 7 9 5 3 3 5 1 5 1 4 7 6 6 4 9 (Right)

According to the question, such odd numbers which are immediately preceded by an odd digit and also immediately followed by an even digit:

Required condition: Odd digit - Odd digit - Even digit

(Left) 1 8 4 5 9 6 5 2 4 8 0 9 5 9 5 7 9 5 3 3 5 1 5 1 4 7 6 6 4 9 (Right)

Thus, there are two such odd numbers which are immediately preceded by an odd digit and also immediately followed by an even digit.

Hence, "Option 1" is the correct answer.

According to the given information,

Thus, according to the given codes the code 'ka' is for the word 'leaves'.

Hence, the correct answer is "Option 3".

The correct answer is Adrenaline.

Key Points

• Adrenaline, also known as epinephrine, is a hormone released by the adrenal glands in response to stress or danger.
• This hormone prepares the body for a 'fight or flight' response by increasing heart rate, blood pressure, and energy supply.
• Adrenaline triggers the release of glucose from energy stores and increases blood flow to major muscle groups.
• The release of adrenaline is part of the body's acute stress response system, which helps to improve physical performance in stressful situations.

Additional Information

• Adrenal Glands:
• Small, triangular-shaped glands located on top of each kidney.
• They produce essential hormones, including adrenaline, cortisol, and aldosterone.
• Fight or Flight Response:
• A physiological reaction that occurs in response to a perceived harmful event, attack, or threat to survival.
• It is a critical survival mechanism that enables an individual to react quickly to life-threatening situations.
• Sympathetic Nervous System:
• Part of the autonomic nervous system that controls the body's rapid involuntary response to dangerous or stressful situations.
• It activates the 'fight or flight' response by triggering the release of adrenaline and noradrenaline.
• Effects of Adrenaline:
• Dilates the air passages of the lungs, allowing for better oxygen intake.
• Constricts blood vessels to redirect blood to major muscle groups and vital organs.
• Increases blood sugar levels by stimulating the liver to release glucose.

The correct answer is spore formation.

Key Points

• Spore formation is a type of asexual reproduction where an organism forms spores that can develop into new individuals.
• In Rhizopus, sporangia are structures that produce and release spores.
• These spores are typically resistant to harsh environmental conditions, aiding in the survival of the organism.
• When conditions are favorable, spores germinate and grow into new Rhizopus individuals.
• Spore formation is common in fungi, algae, and some non-flowering plants.

Additional Information

• Rhizopus
• Rhizopus is a genus of common fungi, often found on bread, fruits, and vegetables.
• It is known for its fast-growing nature and is used in industrial applications like the production of biochemicals.
• Spore
• A spore is a reproductive cell capable of developing into a new individual without fusion with another cell.
• In fungi, spores are usually produced in large numbers to increase the chances of survival.
• Asexual Reproduction
• Asexual reproduction is a mode of reproduction where offspring are produced by a single parent without the involvement of gamete fusion.
• It results in genetically identical individuals, known as clones.
• Favorable Conditions for Germination
• Favorable conditions typically include adequate moisture, suitable temperature, and the presence of nutrients.
• These conditions trigger the germination process, leading to the growth of new organisms.

Shortcut Trick

For half-yearly compounding, Effective Rate for 1 year (2 periods) = r + r + (r×r)/100.

Half-yearly rate (r) = 8% ÷ 2 = 4%.

Effective Rate = 4 + 4 + (4×4)/100 = 8.16%.

Total Amount = 108.16% of ₹15,000 = 1.0816 × 15,000 = ₹16,224.

∴ The correct answer is ₹16,224.

Alternate Method

Given:

Principal (P) = ₹15,000

Rate (R) = 8% per annum

Time (n) = 1 year

Compounding: Half-yearly

Formula Used:

Amount (A) = P[1 + (r/100)]ⁿ

Where r = R/2 and n = 2 × Time (in years)

Calculations:

⇒ New Rate (r) = 8% ÷ 2 = 4% per half-year

⇒ Number of periods (n) = 1 × 2 = 2

⇒ A = 15000 × [1 + (4/100)]²

⇒ A = 15000 × (1.04)²

⇒ A = 15000 × 1.0816

⇒ A = 16224

∴ The correct answer is ₹16,224.

Additional Information

Compound Interest Compounding Frequencies

For quarterly compounding, divide the annual rate by 4 and multiply the time in years by 4. For half-yearly, divide rate by 2 and multiply time by 2.

Effective Rate of Interest

It is the actual interest rate earned/paid due to compounding. Formula: E = [1 + (r/n)]ⁿ − 1, where r is nominal rate and n is compounding periods per year.

Difference between CI and SI

For 2 periods, the difference (CI − SI) = P(r/100)². For 1 year compounded half-yearly, r is the semi-annual rate.

The correct answer is March 2024.

Key Points

• The National Rifle Association of India (NRAI) is the governing body for the sport of shooting in India.
• The NRAI Match Book contains detailed rules and regulations for shooting competitions held in India.
• Amendments to the NRAI Match Book and other technical rules ensure the standards are up-to-date and in line with international norms.
• These amendments were approved for implementation in March 2024, reflecting the NRAI's commitment to maintaining high standards in domestic competitions.
• The changes are aimed at improving the quality and fairness of shooting competitions in India.

Additional Information

• National Rifle Association of India (NRAI)
• Founded in 1951, the NRAI is responsible for promoting the sport of shooting in India.
• It is affiliated with the International Shooting Sport Federation (ISSF) and the Asian Shooting Confederation (ASC).
• The NRAI organizes national shooting championships and selects athletes for international competitions.
• Shooting Sports
• Shooting sports include various disciplines such as rifle, pistol, and shotgun events.
• These events are governed by strict rules to ensure safety and fairness.
• Competitions are held at various levels, including state, national, and international events.
• International Shooting Sport Federation (ISSF)
• The ISSF is the global governing body for the sport of shooting.
• It sets the rules and regulations for shooting competitions worldwide.
• The ISSF organizes world championships and oversees shooting events in the Olympic Games.
• Technical Rules in Shooting
• Technical rules cover aspects such as equipment specifications, scoring methods, and competition formats.
• They ensure a level playing field for all competitors.
• Periodic updates to these rules are necessary to incorporate advancements in technology and changes in international standards.

The logic followed here is:

Option 1) MO - LP

Option 2) OQ - NS

Option 3) TV-SW

Option 4) GI - FJ

Thus, out of all the options 'OQ - NS' is the odd one out.

Hence, "Option 2" is the correct answer.

Shortcut Trick

Let Initial CP be x and Initial SP be y.

Initial Profit = y − x. New SP = 2y. New Profit = 2y − x.

According to the condition: 2y − x = 3(y − x).

2y − x = 3y − 3x ⇒ 2x = y.

Initial Profit = 2x − x = x. Profit% = (x ÷ x) × 100 = 100%.

∴ The correct answer is 100%.

Alternate Method

Given: New Profit = 3 × Old Profit, New SP = 2 × Old SP.

Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100.

Step 1: Let CP = C and Initial SP = S.

Step 2: Initial Profit (P) = S − C. ⇒ (1)

Step 3: New SP = 2S. New Profit = 3P. ⇒ 2S − C = 3P.

Step 4: Substitute (1) into Step 3: 2S − C = 3(S − C).

Step 5: 2S − C = 3S − 3C ⇒ 2C = S.

Step 6: Profit% = [(S − C) ÷ C] × 100 = [(2C − C) ÷ C] × 100 = 100%.

∴ The correct answer is 100%.

Additional Information

Profit and Loss Basics

Profit occurs when Selling Price (SP) is greater than Cost Price (CP). Profit = SP − CP.

Profit Percentage Calculation

Profit percentage is always calculated on the Cost Price unless stated otherwise. Formula: (Profit ÷ CP) × 100.

The correct answer is in the liquid state, particles move freely and have greater space between each other.

Key Points

• In liquids, particles have more freedom to move compared to solids, leading to a higher rate of diffusion.
• The intermolecular spaces in liquids are larger than those in solids, facilitating easier and faster movement of particles.
• Liquids have a definite volume but no fixed shape, allowing particles to move past each other more freely.
• The kinetic energy of particles in a liquid state is higher than in a solid state, contributing to increased diffusion rates.
• Diffusion in liquids is driven by the random movement of particles from an area of higher concentration to an area of lower concentration.

Additional Information

• Diffusion:
• It is the process by which particles spread from an area of high concentration to an area of low concentration.
• Diffusion is a passive process driven by the kinetic energy of particles.
• Kinetic Theory of Matter:
• States that matter is composed of particles (atoms or molecules) that are in constant motion.
• Describes how the energy of particles varies between different states of matter (solid, liquid, gas).
• Intermolecular Forces:
• Forces of attraction or repulsion between particles within a substance.
• Stronger in solids, moderate in liquids, and weakest in gases.
• States of Matter:
• Solid: Particles are closely packed in a fixed arrangement.
• Liquid: Particles are close but can move past one another.
• Gas: Particles are far apart and move freely.

The logic followed here is:

Hence, "Option 1" is the correct answer.

​

The correct answer is Calcium.

Key Points

• Isobars are atoms of different chemical elements that have the same number of nucleons (protons + neutrons).
• Argon has an atomic number of 18 and a common isotope with a mass number of 40 (Argon-40).
• Calcium has an atomic number of 20 and a common isotope with a mass number of 40 (Calcium-40).
• Since both Argon-40 and Calcium-40 have the same mass number, they are isobars.
• Isobars of different elements differ in chemical properties but have similar atomic masses.

Additional Information

• Isotopes vs. Isobars:
• Isotopes are atoms of the same element with different numbers of neutrons and different mass numbers.
• Isobars are atoms of different elements with the same mass number but different atomic numbers.
• Importance of Isobars:
• Isobars are used in various scientific fields, including nuclear physics and chemistry, to study nuclear reactions and stability.
• Examples of Isobars:
• Argon-40 and Calcium-40 are examples of isobars.
• Other examples include Carbon-14 and Nitrogen-14.
• Applications of Isobars:
• Isobars are used in medical applications, such as in radiopharmaceuticals for imaging and treatment.
• They are also used in geological dating and tracing environmental changes.

The correct answer is independent of m.

Key Points

• The acceleration due to gravity (g) near the surface of the Earth is approximately 9.81 m/s² and is considered a constant.
• It is determined by the Earth's mass and radius, and not by the mass of the object experiencing the acceleration.
• The formula for gravitational force is F = G(m1*m2)/r², where G is the gravitational constant, m1 and m2 are the masses, and r is the distance between their centers.
• When calculating acceleration due to gravity (g), the mass of the object (m) cancels out, showing that g is independent of m.

Additional Information

• Gravitational Constant (G)
• The gravitational constant (G) is a fundamental physical constant denoted by G.
• Its value is approximately 6.674 × 10^-11 N(m/kg)².
• This constant is crucial in the calculation of gravitational forces in Newton's law of universal gravitation.
• Newton's Law of Universal Gravitation
• Proposed by Sir Isaac Newton in 1687, it states that every mass attracts every other mass with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
• The formula is F = G(m1*m2)/r².
• Earth's Radius and Mass
• The average radius of the Earth is about 6,371 kilometers.
• The mass of the Earth is approximately 5.972 × 10^24 kilograms.
• Free Fall
• In free fall, the only force acting on an object is gravity.
• All objects in free fall near the Earth's surface accelerate at the same rate, regardless of their mass.

Shortcut Trick

Successive discount formula = a + b − (ab ÷ 100)

Given a = 7% and b = 2%.

Single discount = 7 + 2 − (7 × 2 ÷ 100)

Single discount = 9 − 0.14 = 8.86%

∴ The correct answer is 8.86%.

Alternate Method

Given: First discount = 7%, Second discount = 2%. Formulas: Net Selling Price = MP × (100 − d₁)% × (100 − d₂)% | Equivalent Discount% = (MP − SP) ÷ MP × 100

⇒ Let Marked Price (MP) be 100. ⇒ After 7% discount, price = 100 − 7 = 93. ⇒ After 2% discount on 93, Selling Price (SP) = 93 × (98 ÷ 100) = 91.14. ⇒ Single equivalent discount = 100 − 91.14 = 8.86%.

∴ The correct answer is 8.86%.

Additional Information

Successive Discounts

When two or more discounts are applied one after another on the reducing balance of the marked price, they are called successive discounts.

Effective Discount Formula

For three successive discounts a%, b%, and c%, the single equivalent discount is found by applying the formula a + b − ab/100 twice or using the ratio method.

The correct answer is fragmentation.

Key Points

• Fragmentation is a form of asexual reproduction where an organism splits into fragments, and each fragment develops into a mature, fully grown individual.
• In Spirogyra, a multicellular filamentous green alga, fragmentation occurs when filaments break into smaller pieces.
• Each fragment, also known as a fragment or segment, grows into a new individual through mitotic cell divisions.
• This method of reproduction ensures rapid population growth in favorable conditions, especially in aquatic environments.
• Fragmentation is a common reproductive strategy in many algae, fungi, and some invertebrate animals.

Additional Information

• Asexual Reproduction:
• A mode of reproduction where offspring arise from a single organism, inheriting the genes of that parent only.
• It does not involve the fusion of gametes and almost never changes the number of chromosomes.
• Common methods include binary fission, budding, fragmentation, and spore formation.
• Regeneration:
• The process of renewal, restoration, and growth that makes genomes, cells, organisms, and ecosystems resilient to natural fluctuations or events that cause disturbance or damage.
• Examples include the regrowth of limbs in starfish and tissues in humans.
• Binary Fission:
• A form of asexual reproduction and cell division used by all prokaryotes and some organelles within eukaryotic organisms.
• An organism duplicates its DNA and divides into two parts, with each new organism receiving one copy of DNA.
• Budding:
• An asexual reproduction method where a new organism develops from an outgrowth or bud due to cell division at one particular site.
• The new organism remains attached as it grows, separating from the parent organism only when it is mature.
• Budding is common in some invertebrates such as hydras and yeasts.

The correct answer is NewSpace India Limited (NSIL).

Key Points

• NewSpace India Limited (NSIL) is a Public Sector Enterprise established in March 2019 under the administrative control of the Department of Space (DoS).
• NSIL is responsible for enhancing the industry participation in Indian space programmes.
• The GSAT-20 is a Ka-band high throughput communication satellite launched by NSIL.
• GSAT-20 aims to provide broadband connectivity in the Ka-band over the Indian region, supporting Digital India initiatives.
• NSIL's role includes satellite building, launching, and providing space-based services on demand.

Additional Information

• Ka-band Frequency
• The Ka-band refers to the frequency range from 26.5 to 40 GHz, used primarily for satellite communications.
• It offers higher bandwidth compared to other bands, enabling faster data transmission rates.
• High Throughput Satellites (HTS)
• HTS are advanced satellites that provide more bandwidth and higher data rates compared to traditional satellites.
• They use multiple spot beams to increase capacity and improve coverage, especially in underserved regions.
• Digital India Initiative
• An initiative by the Government of India aimed at ensuring the availability of government services electronically, improving online infrastructure, and increasing internet connectivity.
• It aims to empower citizens with digital literacy and bridge the digital divide.
• Department of Space (DoS)
• DoS is responsible for the development of space technology and the application of satellite communications and meteorology in India.
• It oversees organizations like ISRO and NSIL.

The correct answer is Myopia - near-sightedness and Hypermetropia - far-sightedness.

Key Points

• Myopia is a refractive error where close objects are seen clearly, but distant objects appear blurry.
• Hypermetropia is a refractive error where distant objects are seen clearly, but close objects appear blurry.
• Myopia is commonly known as near-sightedness or short-sightedness.
• Hypermetropia is commonly known as far-sightedness or long-sightedness.
• Both conditions can be corrected using glasses, contact lenses, or refractive surgery.

Additional Information

• Astigmatism
• It is a common refractive error caused by an irregularly shaped cornea or lens.
• Both near and distant objects can appear blurry or distorted.
• Astigmatism can occur in combination with myopia or hypermetropia.
• It is typically corrected with glasses, contact lenses, or refractive surgery.
• Presbyopia
• Aging-related condition where the eye's lens loses flexibility, affecting the ability to focus on close objects.
• Commonly occurs in people over the age of 40.
• It is corrected using reading glasses or bifocals.
• Corrective Lenses
• Glasses and contact lenses are the most common methods for correcting refractive errors.
• They work by altering the path of light entering the eye to ensure it focuses correctly on the retina.
• Refractive Surgery
• Procedures like LASIK and PRK reshape the cornea to correct refractive errors.
• They provide a permanent solution but involve surgical risks and costs.

Given:

Pranit starts from Point A and drives 27 km towards West.

He then takes a left turn, drives 17 km, turns left and drives 14 km.

He then takes a left turn and drives 10 km.

He takes a final right turn, drives 13 km and stops at Point P. 

Thus, Pranit should drive (17 km - 10 km) 7 km in the north direction in order to reach Point A again.

Hence, "Option 2" is the correct answer.

The logic followed here is:

Hence, "Option 2" is the correct answer.

Shortcut Trick

Total Capacity (LCM of 2, 3, 6) = 6 units.

Net efficiency = S + T − U = (6/2) + (6/3) − (6/6) = 3 + 2 − 1 = 4 units/hour.

Time taken = Total Capacity ÷ Net efficiency = 6/4 = 1.5 hours.

Time = 9:00 a.m. + 1 hour 30 minutes = 10:30 a.m.

∴ The correct answer is 10:30 a.m.

Alternate Method

Given: Tap S fills in 2 hours, Tap T fills in 3 hours, Tap U (outlet) empties in 6 hours.

Formula Used: Total Work = Time × Efficiency; Net Efficiency = Σ Efficiency (Filling − Emptying).

⇒ Total efficiency when all taps are open = 3 + 2 − 1 = 4 units/hour.

⇒ Total time required = 6 ÷ 4 = 1.5 hours.

⇒ 1.5 hours = 1 hour 30 minutes.

⇒ Start time = 9:00 a.m. Final time = 9:00 a.m. + 1:30 = 10:30 a.m.

∴ The correct answer is 10:30 a.m.

Additional Information

Pipes & Cisterns Efficiency

Filling pipes have positive efficiency, while emptying/outlet pipes have negative efficiency. Net rate = Rate_in − Rate_out.

Combined Time Formula

For two filling pipes A and B and one outlet C, the time taken (T) is given by 1/T = 1/A + 1/B − 1/C.

Work & Wages

Wages are always distributed in the ratio of the efficiency or the actual work done by each pipe/tap.

The correct answer is When the force is opposite to the direction of displacement.

Key Points

• Work done is negative when the force applied on an object is opposite to the direction of the object's displacement.
• In this scenario, the angle between the force and displacement is 180 degrees, resulting in a negative value for the work done.
• Negative work indicates that the force is acting in the opposite direction to the motion, thereby reducing the object's kinetic energy.
• Examples of negative work include frictional forces or any form of resistance that opposes the motion of an object.

Additional Information

• Work and Energy Relationship:
• Work done on an object results in a change in its energy. Positive work increases energy, while negative work decreases it.
• Formula for Work:
• Work (W) is calculated as the dot product of force (F) and displacement (d), represented as W = F * d * cos(θ).
• θ is the angle between the force and the direction of displacement.
• Frictional Force:
• Friction is a force that opposes the motion of an object and does negative work because it acts opposite to the direction of displacement.
• Kinetic Energy:
• Kinetic energy is the energy an object possesses due to its motion. When negative work is done, kinetic energy decreases.

The correct answer is the dividing tissue, also known as meristematic tissue, is located only at these regions.

Key Points

• Meristematic tissue is composed of cells that have the ability to divide and form new cells, which is essential for plant growth.
• These tissues are found in specific regions such as the tips of roots and shoots, and in the cambium layer of stems.
• Meristematic cells are undifferentiated and retain the ability to undergo mitosis continuously.
• The growth in length (primary growth) and thickness (secondary growth) of plants is attributed to the activity of meristematic tissue.
• Examples of meristematic tissues include apical meristems, intercalary meristems, and lateral meristems.

Additional Information

• Apical Meristems:
• Located at the tips of roots and shoots.
• Responsible for primary growth in plants, resulting in an increase in length.
• Intercalary Meristems:
• Found at the base of leaves or internodes (stem regions between the places where leaves attach).
• Facilitate regrowth of grasses and other monocots after cutting or grazing.
• Lateral Meristems:
• Located along the sides of stems and roots.
• Responsible for secondary growth, which increases the girth of the plant.
• Examples include the vascular cambium and cork cambium.
• Permanent Tissue:
• Consists of differentiated cells that have lost the ability to divide.
• Includes tissues such as xylem, phloem, and epidermis.
• Plant Growth:
• Involves both cell division and cell enlargement.
• Regulated by plant hormones such as auxins, gibberellins, and cytokinins.

The correct answer is parallel straight lines.

Key Points

• Inside a current-carrying solenoid, the magnetic field lines are parallel straight lines indicating a uniform magnetic field.
• The uniform magnetic field inside the solenoid is directed along the axis of the solenoid.
• This uniformity is due to the symmetrical and continuous winding of the wire that constitutes the solenoid.
• The strength of the magnetic field inside the solenoid is proportional to the number of turns per unit length and the current passing through the solenoid.

Additional Information

• Solenoid:
• A solenoid is a coil of wire designed to create a uniform magnetic field in its interior when an electric current passes through it.
• It is commonly used in electromagnets, inductors, and many types of electrical devices.
• Magnetic Field:
• A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.
• It is characterized by field lines that indicate the direction and strength of the magnetic force.
• Electromagnetism:
• Electromagnetism is the study of the interaction between electric currents and magnetic fields.
• It is one of the four fundamental forces of nature and is described by Maxwell's equations.
• Applications of Solenoids:
• Solenoids are used in various applications such as switches, relays, and as components in electromechanical devices like door locks and valves.
• They are also used in medical devices like MRI machines to create strong, uniform magnetic fields.

Given: Six boxes G, H, I, J, K and L are kept one over the other

1) G is kept third from the bottom. 

2) Only two boxes are kept between G and H.

3) J is kept immediately above G.

4) Only three boxes are kept between H and I.

5) K is kept immediately below I.

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

Thus, according to the final arrangement zero boxes are kept between H and L.

Hence, "Option 4" is the correct answer.

Given:

Number of cars sold by Dealer A in 2021 = 45

Number of cars sold by Dealer B in 2022 = 75

Formula used:

Absolute Difference = |Value 1 - Value 2|

Calculation:

⇒ Absolute Difference = |45 - 75|

⇒ Absolute Difference = | -30 |

⇒ Absolute Difference = 30

∴ The absolute difference is 30.

The logic followed here is:

Hence, "Option 4" is the correct answer.

The logic followed here is:

OTRP is related to UZXV

And,

HMKI is related to NSQO

Similarly,

MRPN is related to

Hence, "Option 3" is the correct answer.

The correct answer is Potential energy and kinetic energy.

Key Points

• Mechanical energy is the sum of potential energy and kinetic energy present in the components of a mechanical system.
• Potential energy is the energy stored in an object due to its position or configuration.
• Kinetic energy is the energy an object possesses due to its motion.
• Mechanical energy is conserved in a closed system where no external forces like friction act.
• Examples include a swinging pendulum, a coiled spring, and a moving vehicle.

Additional Information

• Potential Energy
• Includes gravitational potential energy and elastic potential energy.
• Gravitational potential energy depends on the height and mass of an object.
• Elastic potential energy is stored when materials stretch or compress.
• Kinetic Energy
• Depends on the mass and velocity of an object.
• Formula: K.E. = 0.5 * mass * velocity^2.
• Law of Conservation of Energy
• States that energy cannot be created or destroyed, only transformed from one form to another.
• In a frictionless system, mechanical energy remains constant.
• Mechanical Systems
• Include any system where potential and kinetic energy are present and interact.
• Examples: roller coasters, pendulums, and engines.

The correct answer is vegetative propagation.

Key Points

• Vegetative propagation is a form of asexual reproduction in which new plants grow from parts of the parent plant, such as leaves, stems, and roots.
• In Bryophyllum, buds produced in the notches along the leaf margin fall on the soil and develop into new plants.
• This method allows for the rapid multiplication and reproduction of plants without the need for seeds.
• Vegetative propagation is commonly used in horticulture and agriculture to propagate plants with desirable traits.

Additional Information

• Budding:
• A form of asexual reproduction where a new organism develops from an outgrowth or bud due to cell division at one particular site.
• Commonly seen in yeast and some invertebrates like hydra.
• Fragmentation:
• A form of asexual reproduction where an organism splits into fragments, and each fragment develops into a new organism.
• Common in algae, fungi, and some plants.
• Regeneration:
• The process of renewal, restoration, and growth that makes genomes, cells, organisms, and ecosystems resilient to natural fluctuations or events that cause disturbance or damage.
• Seen in organisms like starfish, which can regrow lost arms.
• Other Examples of Vegetative Propagation:
• Examples include the propagation of potatoes through tubers and strawberries through runners.
• This method is also used to propagate plants like sugarcane, ginger, and garlic.

Shortcut Trick

Weight of a sphere is directly proportional to its volume (W ∝ V).

Volume of a solid sphere ∝ r³ and Volume of a hollow sphere ∝ (R³ − r³).

Ratio of Volumes = 3³ : (9³ − 6³) = 27 : (729 − 216) = 27 : 513.

Given, 27 units = 6 kg ⇒ 1 unit = 6 ÷ 27 kg.

Weight of hollow sphere = 513 × (6 ÷ 27) = 19 × 6 = 114 kg.

∴ The correct answer is 114 kg.

Alternate Method

Given:

Diameter of solid rubber sphere (D₁) = 6 cm ⇒ radius (r₁) = 3 cm

Weight of solid sphere (W₁) = 6 kg

Outer diameter of hollow sphere (D₂) = 18 cm ⇒ outer radius (R) = 9 cm

Inner diameter of hollow sphere (d₂) = 12 cm ⇒ inner radius (r) = 6 cm

Formula Used:

Volume of solid sphere = 4/3 × π × r³

Volume of hollow sphere = 4/3 × π × (R³ − r³)

Weight (W) = Density × Volume

Calculations:

⇒ Volume of solid sphere (V₁) = 4/3 × π × 3³ = 36π cm³

⇒ Volume of material in hollow sphere (V₂) = 4/3 × π × (9³ − 6³)

⇒ V₂ = 4/3 × π × (729 − 216) = 4/3 × π × 513

⇒ V₂ = 4 × π × 171 = 684π cm³

⇒ Weight per unit volume = W₁ ÷ V₁ = 6 ÷ 36π = 1 ÷ 6π kg/cm³

⇒ Weight of hollow sphere = V₂ × (Weight per unit volume)

⇒ Weight = 684π × (1 ÷ 6π)

⇒ Weight = 684 ÷ 6 = 114 kg

∴ The correct answer is 114 kg.

Additional Information

Volume of a Sphere

The total space occupied by a solid sphere is given by V = 4/3 × π × r³, where r is the radius.

Volume of a Hollow Sphere

The volume of the material in a hollow sphere is V = 4/3 × π × (R³ − r³), where R is the outer radius and r is the inner radius.

Density and Weight Relationship

For objects made of the same material, weight is directly proportional to the volume: W₁/V₁ = W₂/V₂.

Shortcut Trick

Present Ratio (Woman : Daughter) = 4 : 1 (Difference = 3 units)

Ratio after 6 years = 3 : 1 (Difference = 2 units)

Equalize differences: Present (8 : 2) and Future (9 : 3). Ratio increase = 1 unit = 6 years.

Sum of present ratios = 8 + 2 = 10 units ⇒ 10 × 6 = 60 years.

∴ The correct answer is 60 years.

Alternate Method

Given: Woman age = 4 × Daughter age. After 6 years, Woman = 3 × Daughter.

Let the present age of the daughter be x and woman be 4x.

⇒ (4x + 6) = 3(x + 6)

⇒ 4x + 6 = 3x + 18

⇒ 4x − 3x = 18 − 6

⇒ x = 12 years

⇒ Woman present age = 4 × 12 = 48 years

⇒ Sum of present ages = 48 + 12 = 60 years

∴ The correct answer is 60 years.

Additional Information

Ratio Difference Constant

The age difference between two people remains constant throughout their lives. Always multiply ratios to keep the difference parts equal.

Age Sum Property

When calculating the sum after 'n' years for 'k' people, the total sum increases by n × k years.

Shortcut Trick

For parallel lines intersected by a transversal, the sum of consecutive interior angles (interior angles on the same side) is always 180°.

Measure of ∠2 = 180° − Measure of ∠1

⇒ ∠2 = 180° − 125° = 55°

∴ The correct answer is 55°.

Alternate Method

Given:

Lines are parallel.

∠1 and ∠2 are interior angles on the same side of the transversal.

m∠1 = 125°

Formula Used:

When two parallel lines are cut by a transversal, the consecutive interior angles are supplementary.

m∠1 + m∠2 = 180°

Calculations:

⇒ 125° + m∠2 = 180°

⇒ m∠2 = 180° − 125°

⇒ m∠2 = 55°

∴ The correct answer is 55°.

Additional Information

Corresponding Angles

Angles in the same relative position at each intersection where a straight line crosses two others. If the lines are parallel, corresponding angles are equal.

Alternate Interior Angles

Angles between the parallel lines on opposite sides of the transversal. These angles are always equal when lines are parallel.

Supplementary Angles

Two angles whose measures sum up to 180° are called supplementary angles.

Given series: (Left) 6 8 9 4 4 8 6 5 3 5 1 7 5 8 6 5 8 9 7 3 4 7 0 1 6 8 7 4 5 4 (Right)

According to the question, such even digits which are immediately preceded by an odd digit and also immediately followed by an even digit:

Required condition: Odd digit - Even digit - Even digit

(Left) 6 8 9 4 4 8 6 5 3 5 1 7 5 8 6 5 8 9 7 3 4 7 0 1 6 8 7 4 5 4 (Right)

Thus, there are three such even digits which are immediately preceded by an odd digit and also immediately followed by an even digit.

Hence, "Option 4" is the correct answer.

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

Conclusions:

(I) Some lakes are ponds → Does not follow (As some lakes are rivers and some rivers are ponds. So it is possible but not definite.)

(II) Some ponds are not rivers → Does not follow (As no statement restricts some ponds from being rivers, therefore it is false.)

∴ Here, Neither conclusion I nor II follows.​

Hence, the correct answer is "Option 1".

The correct answer is Maharashtra.

Key Points

• Maharashtra became the first state in India to provide a Unified Pension Scheme to its employees in August 2024.
• The scheme aims to integrate various pension schemes into a single, unified system for better management and benefits.
• It covers employees from different sectors, ensuring a streamlined process for pension disbursement.
• The Unified Pension Scheme is expected to enhance transparency and reduce administrative overheads.
• The scheme is a significant step towards securing the financial future of state employees.

Additional Information

• Unified Pension Scheme (UPS)
• The UPS is designed to combine multiple pension schemes into a single framework.
• It aims to provide a consistent and reliable pension system for government employees.
• This scheme is expected to simplify the pension management process and ensure timely disbursements.
• Pension Fund Regulatory and Development Authority (PFRDA)
• PFRDA is the regulatory body for pension schemes in India.
• It aims to promote old age income security by establishing, developing, and regulating pension funds.
• National Pension System (NPS)
• NPS is a voluntary, defined contribution retirement savings scheme designed to enable systematic savings during the working life of individuals.
• It is regulated by PFRDA and provides retirement income to citizens.
• Employee Provident Fund (EPF)
• EPF is a savings scheme for employees, providing retirement benefits.
• Employees contribute a portion of their salary towards the fund, with a matching contribution from the employer.
• Gratuity
• Gratuity is a lump sum payment made to employees as a token of gratitude for their service.
• It is typically paid upon retirement or resignation after a certain period of service.

Shortcut Trick

HCF is the difference of the numbers or a factor of the difference.

Difference = 2456 − 1248 = 1208

Check options for the highest divisor of both: 1248 ÷ 8 = 156 and 2456 ÷ 8 = 307.

Since 307 is a prime number, no higher common factor exists.

∴ The correct answer is 8.

Alternate Method

Given: Numbers are 1248 and 2456.

Formula Used: Prime Factorization Method for HCF (Highest Common Factor).

⇒ Prime factors of 1248:

⇒ 1248 = 2 × 624 = 2² × 312 = 2³ × 156 = 2⁴ × 78 = 2⁵ × 39 = 2⁵ × 3 × 13

⇒ Prime factors of 2456:

⇒ 2456 = 2 × 1228 = 2² × 614 = 2³ × 307

⇒ Common prime factors = 2³

⇒ HCF = 8

∴ The correct answer is 8.

Additional Information

HCF (Highest Common Factor)

The greatest number that divides two or more numbers without leaving a remainder. Also known as GCD (Greatest Common Divisor).

Relation between HCF and LCM

For two numbers a and b, Product of numbers (a × b) = HCF × LCM.

Division Method

Successive division where the remainder becomes the new divisor until the remainder is zero; the last divisor is the HCF.

Shortcut Trick

Given Diameter = 6 cm → Radius (r) = 3 cm.

Volume of Sphere = (4/3) × π × r³

Volume = (4/3) × π × 3 × 3 × 3 = 4 × π × 9 = 36π cm³.

∴ The correct answer is 36π cm³.

Alternate Method

Given:

Diameter (d) of the sphere = 6 cm

Formula Used:

Radius (r) = d ÷ 2

Volume of Sphere (V) = (4/3)πr³

Calculations:

⇒ Radius (r) = 6 ÷ 2 = 3 cm

⇒ Volume = (4/3) × π × (3)³

⇒ Volume = (4/3) × π × 27

⇒ Volume = 4 × π × 9

⇒ Volume = 36π cm³

∴ The correct answer is 36π cm³.

Additional Information

Surface Area of Sphere

The total surface area of a sphere is given by the formula: A = 4πr².

Volume of Hemisphere

A hemisphere is exactly half of a sphere; its volume is: V = (2/3)πr³.

Total Surface Area of Hemisphere

Includes the curved surface and the flat base area: TSA = 3πr².

The Correct answer is increases.

Key Points

• The kinetic energy of particles is directly proportional to the temperature of the matter. As temperature increases, the particles of matter gain more energy and move faster.
• Increased temperature leads to an increase in the vibrational, rotational, and translational motion of particles, which directly contributes to higher kinetic energy.
• This principle is derived from the Kinetic Molecular Theory, which states that the temperature of a substance is a measure of the average kinetic energy of its particles.
• For example, when water is heated, the molecules move faster, transitioning from a liquid to a gaseous state as the temperature increases.
• Temperature increases also cause a change of state (solid to liquid, liquid to gas) due to the higher energy levels of particles overcoming their intermolecular forces.
• This concept is fundamental in understanding phenomena such as thermal expansion, phase changes, and heat transfer.

Additional Information

• Becomes zero
• The kinetic energy of particles becomes zero only at absolute zero temperature (0 Kelvin or -273.15°C), which is theoretically the lowest possible temperature where all molecular motion ceases.
• This concept is based on the laws of thermodynamics and is practically unattainable.
• Decreases
• The kinetic energy of particles decreases only when the temperature of a substance is lowered.
• This happens during processes such as cooling or freezing, where the particles lose energy and move more slowly.
• Remains the same
• The kinetic energy of particles remains the same only when the temperature of the system is constant, i.e., there is no heat transfer or energy exchange.

The correct answer is Gibberellins: Help in the growth of the stem, Cytokinins: Promote cell division, Abscisic acid: Inhibits growth.

Key Points

• Gibberellins: These hormones significantly contribute to the elongation of stems and the growth of the plant.
• Cytokinins: They are essential for promoting cell division, especially in roots and shoots, leading to plant growth.
• Abscisic acid: This hormone primarily acts as a growth inhibitor and plays a crucial role in plant response to stress conditions like drought.
• Accurate knowledge of these hormones is vital for understanding plant physiology and improving agricultural practices.

Additional Information

• Auxins: A group of hormones that regulate various growth processes in plants, such as cell elongation, root formation, and differentiation.
• Ethylene: A gaseous hormone involved in the ripening of fruits, leaf abscission, and response to mechanical stress.
• Brassinosteroids: These hormones promote cell expansion and division, seed germination, and resistance to stress.
• Jasmonates: Involved in plant defense mechanisms against herbivores and pathogens, and also in regulating growth and development.
• Salicylic acid: Plays a crucial role in plant immunity, particularly in the systemic acquired resistance against pathogens.

Source Code:

The correct answer is Change in the directions that plant parts grow in.

Key Points

• Plants exhibit a phenomenon called tropism, which is their growth response to environmental stimuli such as light (phototropism) and gravity (gravitropism).
• Phototropism is the growth of plant parts in the direction of light. For example, stems usually grow towards light to maximize photosynthesis.
• Gravitropism (or geotropism) is the growth of plant parts in response to gravity. Roots typically grow downward (positive gravitropism) while stems grow upward (negative gravitropism).
• These directional growth changes help plants optimize their exposure to essential resources like light and water, crucial for their survival and growth.
• Hormones such as auxins play a key role in regulating these growth responses by influencing cell elongation in different parts of the plant.

Additional Information

• Thigmotropism
• It is the growth response of plants to touch or physical contact with solid objects. For example, tendrils of climbing plants wrapping around a support.
• Hydrotropism
• It is the growth response of plant roots towards moisture or water. This helps in maximizing water uptake.
• Auxins
• These are plant hormones that regulate growth by promoting cell elongation, especially in response to light and gravity.
• Auxins are primarily produced in the shoot tips and play a crucial role in phototropism and gravitropism.
• Photoperiodism
• It is the physiological reaction of organisms to the length of day or night. In plants, it affects processes like flowering and seed germination.
• Plant Hormones
• Besides auxins, other plant hormones like gibberellins, cytokinins, ethylene, and abscisic acid also influence various growth and developmental processes.

The correct answer is 32.

Key Points

• The molecular mass of oxygen (O₂) is calculated by adding the atomic masses of two oxygen atoms.
• The atomic mass of one oxygen atom is approximately 16 atomic mass units (amu).
• Therefore, the molecular mass of O₂ is 16 amu + 16 amu = 32 amu.
• This value is based on the atomic mass unit scale, where 1 amu is defined as one-twelfth the mass of a carbon-12 atom.

Additional Information

• Molecular Mass
• Molecular mass is the sum of the masses of all the atoms in a molecule.
• It is commonly measured in atomic mass units (amu) or Daltons (Da).
• Oxygen Gas (O₂)
• Oxygen is a diatomic molecule, meaning it consists of two oxygen atoms bonded together.
• It is essential for respiration in most living organisms and is used in various industrial processes.
• Atomic Mass Unit (amu)
• 1 atomic mass unit is defined as one-twelfth the mass of a carbon-12 atom, approximately 1.66053906660 × 10^-27 kg.
• This unit is used to express the mass of atoms and molecules.
• Avogadro's Number
• Avogadro's number (6.02214076 × 10²³) is the number of atoms, ions, or molecules in one mole of a substance.
• It is used to convert between atomic mass units and grams.

The correct answer is a constant greater than 1.

Key Points

• When light travels from a rarer medium to a denser medium, the speed of light decreases.
• The ratio of the sine of the angle of incidence to the sine of the angle of refraction is known as the refractive index.
• This ratio, or the refractive index, is always greater than 1 when light travels from a rarer to a denser medium.
• This relationship is described by Snell's Law: n = sin(i) / sin(r), where n is the refractive index, i is the angle of incidence, and r is the angle of refraction.

Additional Information

• Snell's Law:
• It defines the relationship between the angles of incidence and refraction when light passes through different media.
• Mathematically, it is expressed as n₁ * sin(i) = n₂ * sin(r), where n₁ and n₂ are the refractive indices of the two media.
• Refractive Index:
• A measure of how much the speed of light is reduced inside a medium.
• It is dimensionless and typically greater than 1 for most media.
• Angle of Incidence:
• The angle between the incident ray and the normal to the surface at the point of incidence.
• Angle of Refraction:
• The angle between the refracted ray and the normal to the surface at the point of refraction.

The Correct answer is 10 A.

Key Points

• To determine the current flowing through the resistor, we use the formula for power, which is derived from Ohm's law: P = I²R, where P is power, I is current, and R is resistance.
• Given in the question:
• Power (P): 400 J/s (since power is the rate of heat production).
• Resistance (R): 4 Ω.
• Rearranging the formula to find current: I = √(P/R).
• Substituting the values into the formula:
• I = √(400 / 4).
• I = √100.
• I = 10 A.
• Thus, the current flowing through the resistor is 10 A.
• This calculation is based on the relationship between power, current, and resistance, which is a fundamental concept in electric circuits.

Additional Information

• Importance of Ohm's Law:
• Ohm's Law is fundamental in understanding the relationship between voltage, current, and resistance.
• It is widely applied in designing and analyzing electrical circuits.
• Power Calculation:
• Power in an electric circuit can be calculated using different formulas, such as P = VI (voltage × current) or P = I²R.
• This is critical for determining the energy consumption and ensuring components are not overloaded.

Given:

(6 + 4) ÷ 2 − 2 + 6 × 4

Formula used:

BODMAS rule: Bracket, Of, Division, Multiplication, Addition, Subtraction.

Calculations:

(6 + 4) ÷ 2 − 2 + 6 × 4

⇒ 10 ÷ 2 − 2 + 6 × 4

⇒ 5 − 2 + 6 × 4

⇒ 5 − 2 + 24

⇒ 29 − 2

⇒ 27

∴ The correct answer is option (3).

The logic followed here is:

Given: 

(8, 4, 12)

8 + 4 = 12

12 = 12 (LHS = RHS)

And,

(18, 9, 27)

18 + 9 = 27

27 = 27 (LHS = RHS)

So, checking each option one by one:

Option 1) (24, 14, 36)

24 + 14 = 36

38 ≠ 36 (LHS ≠ RHS)

Option 2) (24, 12, 34)

24 + 12 = 34

36 ≠ 34 (LHS ≠ RHS)

Option 3) (20, 12, 36)

20 + 12 = 36

32 ≠ 36 (LHS ≠ RHS)

Option 4) (24, 12, 36)

24 + 12 = 36

36 = 36 (LHS = RHS)

Hence, "Option 4" is the correct answer.

The correct answer is Nitrogen dioxide gas.

Key Points

• During the thermal decomposition of lead nitrate (Pb(NO₃)₂), brown fumes are observed due to the formation of nitrogen dioxide gas (NO₂).
• The reaction can be represented as: 2Pb(NO₃)₂ (s) → 2PbO (s) + 4NO₂ (g) + O₂ (g).
• Nitrogen dioxide is a reddish-brown gas and is one of the several nitrogen oxides.
• This gas is a significant air pollutant and has a sharp, biting odor.

Additional Information

• Lead Nitrate Decomposition
• Lead nitrate decomposes upon heating to produce lead oxide (PbO), nitrogen dioxide (NO₂), and oxygen (O₂).
• This is an example of a thermal decomposition reaction, where a compound breaks down into simpler substances when heated.
• Nitrogen Dioxide (NO₂)
• Nitrogen dioxide is a toxic gas and a prominent air pollutant.
• It is primarily produced from combustion processes, including vehicle emissions and industrial activities.
• Prolonged exposure to high levels of NO₂ can cause respiratory problems and other health issues.
• Thermal Decomposition
• Thermal decomposition is a chemical reaction in which a compound breaks down into two or more products upon heating.
• It is an endothermic process, meaning it requires the absorption of heat.
• Air Pollution
• Air pollution refers to the presence of harmful substances in the atmosphere, including gases like nitrogen dioxide, sulfur dioxide, and particulate matter.
• It can have significant adverse effects on human health, the environment, and the climate.

The correct answer is Helps the cells to grow longer.

Key Points

• Auxins are a group of plant hormones that play a crucial role in the elongation of plant cells in the shoot system.
• They are primarily produced in the apical meristems of the plant and move downwards to stimulate cell elongation.
• Auxins help in the regulation of phototropism and gravitropism, allowing plants to grow towards light and against gravity.
• They also aid in the differentiation of vascular tissues, which is essential for the transport of water and nutrients throughout the plant.
• Another key function of auxins is to promote root initiation and development, which is vital for plant stability and nutrient uptake.

Additional Information

• Phototropism
• It is the growth of an organism in response to a light stimulus.
• Auxins accumulate on the shaded side of the plant, causing cells on that side to elongate more and the plant to bend towards the light.
• Gravitropism
• It is the orientation of a plant or other organism in response to gravity.
• Roots exhibit positive gravitropism (growing downward), while shoots exhibit negative gravitropism (growing upward).
• Apical Dominance
• It is the phenomenon where the main, central stem of the plant is dominant over other side stems.
• Auxins produced in the apical bud suppress the growth of lateral buds, thus maintaining apical dominance.
• Root Initiation
• Auxins play a pivotal role in the formation of roots from cuttings and other vegetative parts of the plant.
• They stimulate the cells in the stem to differentiate into root cells, aiding in plant propagation.

Shortcut Trick

If tan θ + cot θ = k, then tan² θ + cot² θ = k² − 2.

Given k = 21, so tan² θ + cot² θ = 21² − 2 = 441 − 2 = 439.

Value required = 6 × (tan² θ + cot² θ) = 6 × 439.

⇒ 2634.

∴ The correct answer is 2634.

Alternate Method

Given: tan θ + cot θ = 21

Formula Used: (a + b)² = a² + b² + 2ab and tan θ × cot θ = 1

⇒ (tan θ + cot θ)² = 21²

⇒ tan² θ + cot² θ + 2(tan θ × cot θ) = 441

⇒ tan² θ + cot² θ + 2(1) = 441

⇒ tan² θ + cot² θ = 441 − 2 = 439

⇒ Required value = 6(tan² θ + cot² θ)

⇒ 6 × 439 = 2634

∴ The correct answer is 2634.

Additional Information

Reciprocal Identities

tan θ and cot θ are reciprocals of each other, hence tan θ × cot θ = 1.

Pythagorean Identities

sec² θ − tan² θ = 1 and cosec² θ − cot² θ = 1.

Algebraic Shortcut

If x + 1/x = n, then x² + 1/x² = n² − 2 and x³ + 1/x³ = n³ − 3n.

The correct answer is 1 J/C.

Key Points

• 1 Volt is defined as the difference in electric potential between two points when 1 joule of energy is used to move 1 coulomb of charge between those points.
• The unit of voltage, the volt (V), is equivalent to 1 joule per coulomb (J/C).
• In the International System of Units (SI), voltage is a derived unit expressed in joules per coulomb.
• This definition is consistent with the equation $V=\frac{W}{Q}$, where V is voltage, W is work (in joules), and is charge (in coulombs).

Additional Information

• Ohm's Law: Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points, given by the formula $V=IR$, where V is voltage, I is current, and R is resistance.
• Electric Potential: Electric potential is the amount of electric potential energy per unit charge at a certain position in an electric field.
• Energy Conversion: Voltage is a measure of the energy conversion per unit charge, which is vital in understanding how electrical energy is converted to other forms of energy in circuits.
• Coulomb: The coulomb (C) is the unit of electric charge in the International System of Units (SI), and it represents the quantity of electricity transported in one second by a current of one ampere.
• Joule: The joule (J) is the SI unit of work or energy, defined as the amount of work done when a force of one newton displaces a mass over one meter.

The correct answer is Two.

Key Points

• On 3rd October 2024, the Union Cabinet decided to merge all Central schemes in the agriculture sector into two new schemes.
• This decision aims to streamline and enhance the efficiency of the agricultural support provided by the government.
• The two new schemes are designed to cover various aspects of agricultural development, including input support, marketing, and infrastructure development.
• By merging the schemes, the government seeks to reduce redundancy and improve resource allocation within the agriculture sector.
• The merger is part of a broader strategy to boost agricultural productivity and ensure sustainable development in rural areas.

Additional Information

• Pradhan Mantri Kisan Samman Nidhi (PM-KISAN)
• PM-KISAN is a central sector scheme with 100% funding from the Government of India.
• Under the scheme, income support of Rs. 6,000 per year is provided to all landholding farmer families in three equal installments.
• This scheme aims to supplement the financial needs of farmers in procuring various inputs to ensure proper crop health and appropriate yields.
• The amount is directly transferred to the bank accounts of the beneficiaries.
• Pradhan Mantri Fasal Bima Yojana (PMFBY)
• Launched in 2016, PMFBY provides a comprehensive insurance cover against failure of the crop, thus helping in stabilizing the income of farmers.
• It aims to reduce the premium burden on farmers and ensure early settlement of crop insurance claims.
• The scheme covers all food & oilseed crops and annual commercial/horticultural crops for which past yield data is available.
• Farmers pay a nominal premium, and the remaining part of the actuarial premium is borne equally by the central and state governments.
• Pradhan Mantri Krishi Sinchai Yojana (PMKSY)
• PMKSY was launched with the vision to ensure access to some means of protective irrigation to all agricultural farms in the country.
• It aims to enhance the physical access of water on the farm and expand cultivable areas under assured irrigation.
• The scheme promotes precision irrigation technologies and practices.
• It integrates water source, distribution, and efficient farm-level application.

The correct answer is Only (i).

Key Points

• Kidneys in human beings are located in the abdominal region, specifically between the levels of the last thoracic and third lumbar vertebrae, not in the thoracic region.
• Urine produced by the kidneys is stored in the urinary bladder until it is excreted from the body.
• Carbon dioxide (CO2) is indeed removed from the blood into the lungs and is then exhaled out of the body.
• The thoracic region refers to the part of the body where the ribs are located, and it primarily houses the heart and lungs.

Additional Information

• Kidneys
• The kidneys are a pair of bean-shaped organs located in the back of the abdominal cavity, one on each side of the spine.
• They perform the crucial function of filtering waste products from the blood and excreting them in the form of urine.
• They also regulate electrolyte balance and blood pressure and produce hormones that are vital for bodily functions.
• Urinary Bladder
• The urinary bladder is a muscular sac in the pelvis that stores urine until it is ready to be expelled from the body.
• The bladder can hold between 300-500 ml of urine in a healthy adult.
• Exhalation of CO2
• Carbon dioxide, a waste product of cellular respiration, is transported in the blood to the lungs.
• In the lungs, CO2 diffuses from the blood into the alveoli and is exhaled during the process of breathing out.
• Thoracic Region
• The thoracic region of the body is the part that lies between the neck and the abdomen, housing organs such as the heart and lungs.
• This region is protected by the rib cage and thoracic spine.

Given:

Expression = 25% of 30% of 45% of 1

Formula used:

x% of y = (x ÷ 100) × y

Calculations:

Result = (25 ÷ 100) × (30 ÷ 100) × (45 ÷ 100) × 1

⇒ Result = 0.25 × 0.30 × 0.45 × 1

⇒ Result = (25 × 30 × 45) ÷ (100 × 100 × 100)

⇒ Result = 33750 ÷ 1000000

⇒ Result = 0.03375

∴ The correct answer is option (4).