RRB Technician Grade III Official Paper (Held On: 26 Dec, 2024 Shift 1) (Previous Year Paper)

The correct answer is a homologous series.

Key Points

• Compounds CH2OH, C2H5OH, C3H7OH, and C4H9OH all belong to the homologous series of alcohols.
• In a homologous series, compounds have the same functional group and similar chemical properties.
• The members of a homologous series differ by a CH2 unit in their molecular formula.
• Alcohols in this series have the functional group -OH, which is responsible for their similar chemical behaviors.

Additional Information

• Homologous Series
• A series of compounds with the same functional group and similar chemical properties.
• Each successive member differs by a CH2 unit from the previous one.
• Examples include alkanes, alkenes, alkynes, and alcohols.
• Functional Group
• A specific group of atoms within a molecule responsible for the characteristic chemical reactions of that molecule.
• Common functional groups include hydroxyl (-OH), carboxyl (-COOH), and amino (-NH2).
• Alcohols
• Organic compounds containing one or more hydroxyl (-OH) groups attached to a carbon atom.
• They are classified as primary, secondary, or tertiary based on the carbon atom to which the -OH group is attached.
• Chemical Properties of Alcohols
• Alcohols generally exhibit similar reactions such as oxidation, dehydration, and substitution.
• They can form hydrogen bonds, which significantly influence their boiling points and solubility in water.

The correct answer is 32.

Key Points

• The mass number of a sulphur atom is 32.
• This mass number is derived from the most common isotope of sulphur, which is Sulphur-32 (S-32).
• Sulphur has 16 protons and 16 neutrons, making the total mass number 32.
• The atomic number of sulphur is 16, which indicates the number of protons in its nucleus.

Additional Information

• Isotopes of Sulphur
• Sulphur has several isotopes, including S-32, S-33, S-34, and S-36.
• S-32 is the most abundant isotope, making up about 95% of natural sulphur.
• Isotopes differ in the number of neutrons in the nucleus while having the same number of protons.
• Atomic Structure
• An atom consists of protons, neutrons, and electrons.
• The number of protons determines the atomic number and the element's identity.
• Neutrons contribute to the atom's mass but do not affect its chemical properties.
• Periodic Table
• Sulphur is located in group 16 of the periodic table, also known as the chalcogens.
• It is a non-metal and has similar properties to other elements in its group, such as oxygen and selenium.
• Chemical Properties of Sulphur
• Sulphur is known for its bright yellow color in its solid form.
• It is commonly found in nature as a pure element and in various minerals.
• Sulphur is essential for life as it is a component of amino acids and proteins.

The logic followed here is:

Given:

(18, 6, 24)

18 + 6 = 24

24 = 24 (LHS = RHS)

And,

(27, 9, 36)

27 + 9 = 36

36 = 36 (LHS = RHS)

So, checking each option one by one:

Option 1) (33, 11, 42)

18 + 6 = 42

24 ≠ 42 (LHS ≠ RHS)

Option 2) (31, 11, 44)

31 + 11 = 44

42 ≠ 44 (LHS ≠ RHS)

Option 3) (33, 10, 44)

33 + 10 = 44

43 ≠ 44 (LHS ≠ RHS)

Option 4) (33, 11, 44)

33 + 11 = 44

44 = 44 (LHS = RHS)

Thus, out of all the options, '(33, 11, 44)' follows the same logic as given.

Hence, "Option 4" is the correct answer.

The correct answer is Auxin, Cytokinins and Gibberellins.

Key Points

• Auxins are essential for cell elongation, root initiation, and growth in plant tissues.
• Cytokinins promote cell division, influence apical dominance, and delay leaf senescence.
• Gibberellins are crucial for stem elongation, seed germination, and flowering.
• These hormones work synergistically to regulate various physiological processes in plants.

Additional Information

• Abscisic Acid (ABA)
• Known as the stress hormone, ABA helps plants respond to stress conditions like drought.
• It plays a role in stomatal closure, thus reducing water loss.
• Ethylene
• Ethylene is a gaseous hormone involved in the ripening of fruits and the shedding of leaves.
• It helps in the senescence of flowers and leaves.
• Brassinosteroids
• These are a class of polyhydroxysteroids that promote cell expansion and elongation.
• They are also involved in vascular differentiation and stress tolerance.
• Jasmonates
• Jasmonates are lipid-based hormones that play a role in plant defense against herbivores.
• They also contribute to reproductive development and root growth.

The correct answer is July 2024.

Key Points

• The Project PARI (Public Art of India) was initiated on Mon Jul 01 2024.
• The project aims to promote public art and cultural heritage across India.
• It involves collaboration with various local and international artists to create public art installations.
• The initiative is supported by the Ministry of Culture and various state governments.
• The project also aims to engage communities in the creation and appreciation of public art.

Additional Information

• Public Art
• Public art refers to works of art that are designed to be displayed in public spaces.
• It includes sculptures, murals, installations, and other forms of art that are accessible to the public.
• Public art can enhance the aesthetic appeal of a community and promote cultural heritage.
• Ministry of Culture
• The Ministry of Culture is responsible for the preservation and promotion of art and culture in India.
• It supports various cultural projects and initiatives across the country.
• Community Engagement
• Community engagement involves the participation of local communities in the planning and execution of projects.
• It fosters a sense of ownership and pride among community members.
• Cultural Heritage
• Cultural heritage includes tangible and intangible assets that are inherited from past generations.
• It encompasses traditions, practices, places, objects, and artistic expressions.

The correct answer is 2036.

Key Points

• In November 2024, India sent a formal Letter of Intent to the International Olympic Committee (IOC) to host the Olympics and Paralympics in the year 2036.
• The Indian government expressed its ambition to bring the prestigious event to India, showcasing its readiness and infrastructure capabilities.
• The bid aligns with India's growing influence and capabilities in the international sports arena.
• The proposed host city for the 2036 Olympics and Paralympics is Ahmedabad, which is being developed as a smart city with world-class facilities.

Additional Information

• International Olympic Committee (IOC)
• The IOC is the governing body of the Olympic Movement, headquartered in Lausanne, Switzerland.
• It was founded on 23 June 1894 by Pierre de Coubertin and Demetrios Vikelas.
• The IOC is responsible for organizing the Summer and Winter Olympic Games every four years.
• It also oversees the Youth Olympic Games and other associated events.
• Olympics and Paralympics
• The Olympics are a major international multi-sport event divided into summer and winter games.
• The Paralympics are a series of international contests for athletes with disabilities, held after the Olympic Games.
• Both events promote unity, excellence, and fair play among athletes worldwide.
• The Paralympic Games are overseen by the International Paralympic Committee (IPC), which works closely with the IOC.
• Ahmedabad as a Smart City
• Ahmedabad, located in the state of Gujarat, is one of India's fastest-growing cities.
• The city has seen significant infrastructure development, making it a viable candidate for hosting large-scale international events.
• Ahmedabad is home to the Sardar Vallabhbhai Patel Stadium, one of the largest cricket stadiums in the world.
• The city's smart city initiatives include improved urban planning, transportation systems, and public services.

The correct answer is In an ionic compound, the transfer of electrons takes place from a metal to a non-metal..

Key Points

• Ionic compounds are formed through the transfer of electrons from a metal to a non-metal.
• Metals tend to lose electrons and become positively charged cations.
• Non-metals tend to gain electrons and become negatively charged anions.
• The electrostatic attraction between the oppositely charged ions results in the formation of an ionic bond.
• An example of an ionic compound is sodium chloride (NaCl), where sodium (metal) transfers an electron to chlorine (non-metal).

Additional Information

• Ionic Bond
• A type of chemical bond where atoms transfer electrons to achieve a full valence shell.
• Typically occurs between elements with a large difference in electronegativity.
• Results in the formation of ions that attract each other to form a stable compound.
• Properties of Ionic Compounds
• High melting and boiling points due to strong electrostatic forces between ions.
• Good electrical conductivity in molten or aqueous states, but not in solid form.
• Generally soluble in water but insoluble in organic solvents.
• Examples of Ionic Compounds
• Sodium chloride (NaCl)
• Magnesium oxide (MgO)
• Calcium fluoride (CaF₂)
• Formation of Ions
• Metals lose electrons to achieve a stable noble gas configuration, forming cations.
• Non-metals gain electrons to achieve a stable noble gas configuration, forming anions.
• This transfer of electrons leads to the formation of an ionic bond.

Given:

Number of oranges sold by shop A to males = 21

Number of oranges sold by shop B to males = 39

Formula used:

Difference = Number of oranges sold by shop B to males - Number of oranges sold by shop A to males

Calculation:

⇒ Difference = 39 - 21

⇒ Difference = 18

∴ The difference between the number of oranges sold by shops A and B to males is 18.

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

According to the question, sum of the 15^th digit from the left and the 11^th digit from the right

(Left) 7 6 3 9 5 4 4 8 6 4 8 8 9 6 9 2 2 6 3 1 5 5 3 5 1 5 5 0 3 4 (Right) → 9 + 1 = 10

Hence, "Option 2" is the correct answer.

Shortcut Trick

For proportion, the product of extremes equals the product of means.

7 × k = 11 × 21

k = (11 × 21) ÷ 7

k = 11 × 3 = 33

∴ The correct answer is 33.

Alternate Method

Given: Numbers 7, 11, 21, and k are in proportion.

Formula Used: If a, b, c, d are in proportion, then a/b = c/d (or ad = bc).

⇒ 7 / 11 = 21 / k

⇒ 7 × k = 11 × 21

⇒ k = (11 × 21) ÷ 7

⇒ k = 11 × 3

⇒ k = 33

∴ The correct answer is 33.

Additional Information

Fourth Proportional

If a, b, c, and x are in proportion, x is the fourth proportional to a, b, and c. It is calculated as x = (b × c) ÷ a.

Mean Proportional

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

Third Proportional

If a, b, and c are in continued proportion (a:b = b:c), then c is the third proportional, calculated as c = b² ÷ a.

Shortcut Trick

Side of a rhombus (a) = √((d₁/2)² + (d₂/2)²)

Given diagonals are 10 cm and 24 cm.

Half of diagonals are 5 cm and 12 cm.

Using Pythagorean triplet (5, 12, 13), the side is 13 cm.

∴ The correct answer is 13 cm.

Alternate Method

Given:

First diagonal (d₁) = 10 cm

Second diagonal (d₂) = 24 cm

Formula Used:

4 × (Side)² = d₁² + d₂²

Calculations:

⇒ 4 × a² = 10² + 24²

⇒ 4 × a² = 100 + 576

⇒ 4 × a² = 676

⇒ a² = 676 ÷ 4

⇒ a² = 169

⇒ a = √169

⇒ a = 13 cm

∴ The correct answer is 13 cm.

Additional Information

Properties of Rhombus

All sides are equal and diagonals bisect each other at 90°.

Area of Rhombus

The area is calculated as 1/2 × d₁ × d₂.

Perimeter of Rhombus

The perimeter is 4 × Side.

The correct answer is Inversely proportional to A.

Key Points

• Resistance (R) of a conductor is inversely proportional to its cross-sectional area (A).
• This relationship is mathematically represented as $R\propto\frac{1}{A}$
• Increasing the cross-sectional area of the conductor will decrease its resistance.
• Conversely, decreasing the cross-sectional area of the conductor will increase its resistance.

Additional Information

• Ohm's Law:
• It states that the current through a conductor between two points is directly proportional to the voltage across the two points.
• It is expressed as V = IR, where V is voltage, I is current, and R is resistance.
• Factors Affecting Resistance:
• Material of the conductor: Different materials have different resistivities.
• Length of the conductor: Resistance is directly proportional to the length of the conductor (R ∝ L).
• Temperature: Resistance usually increases with temperature for conductors.
• Resistivity (ρ):
• Resistivity is a material-specific property that affects resistance.
• It is expressed in ohm-meters (Ω·m) and is defined as the resistance of a unit length and unit cross-sectional area of the material.
• Formula for Resistance:
• The resistance of a conductor can be calculated using the formula $R=\rho\frac{l}{A}$, where ρ is resistivity, L is length, and A is cross-sectional area.

The logic followed here is:

'ARID' is coded as '9078'

'DIRE' is coded as '8095'

Thus, code for 'E' is '5'.

Hence, "Option 2" is the correct answer.

The correct answer is 3) 0.065.

Key Points

• As of October 30, 2024, the repo rate at which the Reserve Bank of India (RBI) lends to banks is 0.065.
• The repo rate is a critical tool used by the RBI to control inflation and regulate the money supply in the economy.
• This rate is determined by the RBI's Monetary Policy Committee (MPC) which meets bi-monthly to review and set the repo rate.
• The repo rate influences the interest rates offered by banks on loans and deposits, affecting borrowing and spending in the economy.
• A lower repo rate typically aims to encourage borrowing and investment, stimulating economic growth.

Additional Information

• Monetary Policy Committee (MPC)
• The MPC is a committee of the RBI responsible for formulating the monetary policy of India.
• It consists of six members: three officials from the RBI and three external members appointed by the Government of India.
• The primary objective of the MPC is to maintain price stability while keeping in mind the objective of economic growth.
• Repo Rate
• The repo rate is the rate at which the central bank of a country (RBI in India) lends money to commercial banks in the event of any shortfall of funds.
• It is used by monetary authorities to control inflation.
• A decrease in the repo rate can lead to banks reducing their lending rates, making loans cheaper and boosting consumption and investment.
• Reverse Repo Rate
• The reverse repo rate is the rate at which the RBI borrows money from commercial banks.
• It is used to control the money supply in the economy.
• A higher reverse repo rate encourages banks to park more funds with the RBI, thereby reducing the money supply in the economy.
• Inflation Control
• The RBI uses various monetary policy tools, including the repo rate, to control inflation.
• High inflation can erode purchasing power and hurt economic growth, while very low inflation can lead to deflation, where prices fall continuously.
• Maintaining a balance is crucial for a stable economic environment.

Given:

4 × 4^{(n + 5)} = 256

Formula used:

a^m × aⁿ = a^{(m + n)}

If a^x = a^y, then x = y

Calculations:

4¹ × 4^{(n + 5)} = 256

⇒ 4^{(1 + n + 5)} = 4⁴

⇒ 4^{(n + 6)} = 4⁴

⇒ n + 6 = 4

⇒ n = 4 − 6

⇒ n = −2

Now, finding the value of 5^{(n + 4)}:

⇒ 5^{(−2 + 4)}

⇒ 5²

⇒ 25

∴ The correct answer is option (1).

The correct answer is Option 2: The object moves with a constant speed..

Key Points

• An object in uniform motion travels equal distances in equal intervals of time, indicating a constant speed.
• Uniform motion implies that the velocity of the object does not change over time.
• In uniform motion, both the magnitude and direction of the object's velocity remain constant.
• The path of an object in uniform motion can be linear or circular, but the speed remains constant throughout the motion.

Additional Information

• Velocity: It is the speed of an object in a given direction. Uniform motion implies constant velocity.
• Acceleration: The rate of change of velocity. In uniform motion, the acceleration is zero since the velocity is constant.
• Displacement: The change in position of an object. In uniform motion, displacement is directly proportional to time.
• Graphical Representation: A distance-time graph of an object in uniform motion is a straight line, indicating constant speed.
• Non-Uniform Motion: When an object travels unequal distances in equal intervals of time, the motion is termed non-uniform, indicating varying speed.

Shortcut Trick

Let Total Work (LCM of 18, 12, 15) = 180 units.

Efficiencies: B = +10, C = +15, A = −12. Combined (A+B+C) = 10 + 15 − 12 = 13.

Work done in 5 hours = 13 × 5 = 65 units. Remaining = 180 − 65 = 115 units.

Time taken by B and C = 115 ÷ (10 + 15) = 115 ÷ 25 = 4.6 hours.

0.6 hours = 0.6 × 60 = 36 minutes.

∴ The correct answer is 4 hr 36 min.

Alternate Method

Given: Filling time for B = 18 hrs, C = 12 hrs. Emptying time for A = 15 hrs.

⇒ Net efficiency of (A + B + C) = 10 + 15 − 12 = 13 units/hr

⇒ Work done in first 5 hours = 13 × 5 = 65 units

⇒ Remaining work to be filled = 180 − 65 = 115 units

⇒ Efficiency of (B + C) = 10 + 15 = 25 units/hr

⇒ Time required = 115 ÷ 25 = 4.6 hours

⇒ Conversion: 4 hours + (0.6 × 60) minutes = 4 hours 36 minutes

∴ The correct answer is 4 hr 36 min.

Additional Information

Pipes and Cisterns Logic

Inlet pipes contribute positive efficiency (filling) while outlet pipes contribute negative efficiency (emptying) toward the total capacity.

Time and Work Relation

Total Work = Efficiency × Time. For fractional hours, multiply the decimal part by 60 to convert it into minutes.

The correct answer is On heating, diffusion becomes faster..

Key Points

• Diffusion is the movement of particles from a region of higher concentration to a region of lower concentration.
• On heating, the kinetic energy of the particles increases, causing them to move more rapidly.
• The increased movement of particles results in faster mixing and spreading, thus increasing the rate of diffusion.
• Diffusion is faster in gases than in liquids and solids because gas particles move more quickly and freely.

Additional Information

• Temperature
• Temperature is a measure of the average kinetic energy of the particles in a substance.
• As temperature increases, the kinetic energy of particles increases, leading to faster movement and higher diffusion rates.
• Concentration Gradient
• The concentration gradient is the difference in the concentration of particles between two regions.
• Diffusion occurs more rapidly when there is a steeper concentration gradient.
• Medium of Diffusion
• Diffusion occurs in gases, liquids, and solids, but the rate varies.
• Gases have the highest diffusion rates, followed by liquids, and then solids due to the differences in particle movement and spacing.
• Applications of Diffusion
• Diffusion is essential in various biological processes, such as gas exchange in the lungs and nutrient absorption in cells.
• It also plays a crucial role in industrial processes, including the mixing of gases and the spread of pollutants.

Shortcut Trick

The expression follows the algebraic identity a² + 2ab + b² = (a + b)².

Here, a = 75 and b = 25.

⇒ (75 + 25)² = 100² = 10000.

∴ The correct answer is 10000.

Alternate Method

Given:

Expression: 75 × 75 + 2 × 75 × 25 + 25 × 25

Formula Used:

(a + b)² = a² + 2ab + b²

Calculations:

⇒ Let a = 75 and b = 25

⇒ a² = 75 × 75

⇒ b² = 25 × 25

⇒ 2ab = 2 × 75 × 25

⇒ The given expression is a² + 2ab + b²

⇒ (75 + 25)²

⇒ (100)²

⇒ 10000

∴ The correct answer is 10000.

Additional Information

Square of a Binomial (Difference)

The formula for the square of a difference is (a − b)² = a² − 2ab + b².

Difference of Two Squares

The factorization of the difference of two squares is a² − b² = (a − b)(a + b).

Square of a Trinomial

The expansion for three terms is (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.

The correct answer is Heterogeneous mixture.

Key Points

• A suspension is a heterogeneous mixture in which the solute particles do not dissolve but remain suspended throughout the bulk of the medium.
• The particles in a suspension are larger than those found in solutions, typically being greater than 1 micrometer in size.
• Suspensions can be separated into their individual components through processes such as filtration or sedimentation.
• Over time, the particles in a suspension tend to settle out due to gravity, a property not observed in true solutions.

Additional Information

• Colloids
• Colloids are mixtures where the particle size is intermediate between those in solutions and suspensions, ranging from 1 to 1000 nanometers.
• These particles do not settle out upon standing and cannot be separated by filtration.
• An example of a colloid is milk.
• Solutions
• Solutions are homogeneous mixtures composed of two or more substances.
• The solute in a solution is completely dissolved in the solvent.
• An example of a solution is salt water.
• Emulsions
• Emulsions are a type of colloid where both phases are liquids.
• They can be stabilized by emulsifying agents.
• An example of an emulsion is mayonnaise.
• Properties of Heterogeneous Mixtures
• The components of a heterogeneous mixture can be visibly distinguished.
• They do not have a uniform composition throughout.
• Examples include salads and trail mixes.

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

Conclusions:

(I) Some cups are glasses → Does not follow (As some glasses are bowls and some bowls are cups. So it is possible but not definite.)

(II) Some bowls are plates → Does not follow (As some plates are glasses and some glasses are bowls. So it is possible but not definite.)

∴ Here, Neither conclusion (I) nor (II) follows.​

Hence, the correct answer is "Option 3"

The correct answer is United Nations Environment Programme.

Key Points

• United Nations Environment Programme (UNEP) was established in 1972 following the United Nations Conference on the Human Environment in Stockholm.
• UNEP is headquartered in Nairobi, Kenya, and serves as the leading global environmental authority that sets the global environmental agenda.
• The UNEP's mission is to provide leadership and encourage partnership in caring for the environment by inspiring, informing, and enabling nations and peoples to improve their quality of life without compromising that of future generations.
• UNEP works in seven broad thematic areas: Climate Change, Disasters and Conflicts, Ecosystem Management, Environmental Governance, Chemicals and Waste, Resource Efficiency, and Environment under Review.

Additional Information

• Montreal Protocol
• It is an international treaty designed to protect the ozone layer by phasing out the production of numerous substances that are responsible for ozone depletion.
• The treaty was agreed upon on 16 September 1987 and entered into force on 1 January 1989.
• It is considered one of the most successful environmental agreements to date, with significant reductions in the global production, consumption, and emissions of ozone-depleting substances.
• Chlorofluorocarbons (CFCs)
• CFCs are a group of chemical compounds that were once commonly used in air conditioning, refrigeration, and aerosol propellants.
• They are highly stable and can remain in the atmosphere for a long time, leading to the depletion of the ozone layer.
• The discovery of the harmful effects of CFCs on the ozone layer led to international agreements to phase them out.
• Ozone Layer
• The ozone layer is a region of Earth's stratosphere that contains a high concentration of ozone (O3) and absorbs most of the Sun's ultraviolet radiation.
• It plays a crucial role in protecting living organisms on Earth from harmful UV radiation, which can cause skin cancer, cataracts, and other health issues.
• Human activities, particularly the emission of ozone-depleting substances, have caused significant thinning of the ozone layer, leading to the creation of the ozone hole.
• Vienna Convention
• The Vienna Convention for the Protection of the Ozone Layer is a multilateral environmental agreement that provided a framework for international efforts to protect the ozone layer.
• Adopted in 1985, it aimed to promote cooperation on research, monitoring, and information exchange related to the ozone layer and ozone-depleting substances.
• The Vienna Convention laid the groundwork for the subsequent Montreal Protocol.

Shortcut Trick

For two numbers, if Sum (S) and Difference (D) are known:

Elder (Larger number) = (Sum + Difference) ÷ 2

Elder = (21 + 7) ÷ 2 = 28 ÷ 2 = 14 years

∴ The correct answer is 14 years.

Alternate Method

Given:

Let the age of the elder sibling be x and the younger sibling be y.

⇒ x − y = 7 --- (Equation 1)

⇒ x + y = 21 --- (Equation 2)

Calculations:

Adding Equation 1 and Equation 2:

⇒ (x − y) + (x + y) = 7 + 21

⇒ 2x = 28

⇒ x = 28 ÷ 2

⇒ x = 14

∴ The correct answer is 14 years.

Additional Information

Linear Equations in Two Variables

When two linear equations involve the same variables, they form a system. The Elimination method is the fastest way to solve for one variable by adding or subtracting equations.

Sum and Difference Formula

If x + y = S and x − y = D, then the larger value x = (S+D)/2 and the smaller value y = (S−D)/2.

Age Invariance Property

The difference between ages of two people always remains constant, regardless of how many years pass.

The correct answer is The nuclear membrane is absent in prokaryotic cells..

Key Points

• Prokaryotic cells, such as bacteria and archaea, lack a true nucleus and do not have a nuclear membrane.
• The genetic material in prokaryotic cells is located in a nucleoid region, which is not enclosed by a membrane.
• Eukaryotic cells, including plant, animal, and fungal cells, have a well-defined nucleus enclosed by a nuclear membrane.
• The nuclear membrane in eukaryotic cells helps regulate the exchange of materials between the nucleus and the cytoplasm.

Additional Information

• Prokaryotic Cells:
• Prokaryotic cells are unicellular organisms that lack membrane-bound organelles.
• Examples include bacteria and archaea.
• They reproduce asexually through binary fission.
• They have simpler structures compared to eukaryotic cells.
• Eukaryotic Cells:
• Eukaryotic cells have a defined nucleus and membrane-bound organelles.
• They can be unicellular or multicellular organisms, including plants, animals, and fungi.
• Eukaryotic cells reproduce through mitosis and meiosis.
• They have a more complex structure compared to prokaryotic cells.
• Nuclear Membrane:
• Also known as the nuclear envelope, it consists of two lipid bilayers.
• It separates the nucleus from the cytoplasm in eukaryotic cells.
• The nuclear membrane contains nuclear pores that regulate the passage of molecules.
• It plays a critical role in protecting the genetic material.
• Nucleoid:
• The region within a prokaryotic cell where the genetic material is located.
• It is not enclosed by a membrane.
• The nucleoid contains a single circular chromosome.
• It is involved in controlling cellular activities and reproduction.

Shortcut Trick Total CP = (25 × 4) + (35 × 4.50) = 100 + 157.50 = 257.50 Total SP = (25 + 35) × 4.25 = 60 × 4.25 = 255.00 Since CP > SP, there is a Loss. Loss = 257.50 − 255.00 = 2.50 ∴ The correct answer is Rs. 2.50, loss.

Alternate Method Given → Quantity 1 = 25 kg at Rs. 4/kg, Quantity 2 = 35 kg at Rs. 4.50/kg, Selling Price = Rs. 4.25/kg. Formulas: Total CP = (Q1 × C1) + (Q2 × C2) | Total SP = (Q1 + Q2) × Selling Price | Loss = CP − SP.

⇒ Cost Price of 25 kg wheat = 25 × 4 = Rs. 100. ⇒ Cost Price of 35 kg wheat = 35 × 4.50 = Rs. 157.50. ⇒ Total Cost Price (CP) = 100 + 157.50 = Rs. 257.50. ⇒ Total Weight of mixture = 25 + 35 = 60 kg. ⇒ Total Selling Price (SP) = 60 × 4.25 = Rs. 255. ⇒ Loss = Total CP − Total SP = 257.50 − 255 = Rs. 2.50. ∴ The correct answer is Rs. 2.50, loss.

Additional Information Profit and Loss Basics When Selling Price (SP) is greater than Cost Price (CP), it is a Profit. Profit = SP − CP. Loss Condition When Cost Price (CP) is greater than Selling Price (SP), it is a Loss. Loss = CP − SP.

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

1) P sits third to the left of E.

2) G sits to the immediate left of E.

3) Only L sits between A and P. 

4. B is not an immediate neighbour of P.

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

Thus, according to the final arrangement, B sits fourth to the left of M.

Hence, "Option 4" is the correct answer.

Shortcut Trick

When a constant value is added to every number in a set, the average of the set increases by that same constant value.

New Average = Old Average + Constant Added

New Average = 7 + 21 = 28

∴ The correct answer is 28.

Alternate Method

Given:

Total numbers (n) = 10

Initial Average = 7

Formula Used:

Sum = Average × Number of terms

New Average = New Sum ÷ Number of terms

Calculations:

⇒ Initial Sum = 7 × 10 = 70

⇒ Value added to each number = 21

⇒ Total value added to sum = 21 × 10 = 210

⇒ New Sum = 70 + 210 = 280

⇒ New Average = 280 ÷ 10

⇒ New Average = 28

∴ The correct answer is 28.

Additional Information

Effect of Operations on Average

If each observation is increased, decreased, multiplied or divided by a non-zero constant 'k', the average is also increased, decreased, multiplied or divided by 'k' respectively.

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the Combined Average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Average of Consecutive Numbers

For any Arithmetic Progression (AP), the average is always the middle term or (First Term + Last Term) ÷ 2.

The correct answer is Applying pressure and reducing temperature.

Key Points

• Liquefaction of gases is primarily achieved by applying pressure and reducing temperature.
• This process involves compressing the gas to a point where it can be cooled sufficiently to turn into a liquid.
• When the gas is compressed, the molecules are brought closer together, making it easier to condense.
• Lowering the temperature reduces the kinetic energy of the gas molecules, further aiding in the transition from gas to liquid.
• This principle is used in various industrial processes, including the production of liquefied natural gas (LNG).

Additional Information

• Critical Temperature and Pressure
• The critical temperature is the highest temperature at which a substance can exist as a liquid. Above this temperature, a gas cannot be liquefied, regardless of pressure.
• The critical pressure is the pressure required to liquefy a gas at its critical temperature.
• Boyle’s Law and Charles’s Law
• Boyle’s Law states that the pressure of a given mass of gas is inversely proportional to its volume at a constant temperature.
• Charles’s Law states that the volume of a gas is directly proportional to its temperature at constant pressure.
• Industrial Applications
• Liquefaction is used in the storage and transport of gases such as oxygen, nitrogen, and natural gas.
• Liquefied gases are easier to store and transport as they take up less space.
• Refrigeration Cycles
• The principles of gas liquefaction are applied in refrigeration cycles, where refrigerants are compressed and expanded to absorb and release heat.
• This process is used in air conditioning systems and refrigerators.

The logic followed here is:

Option 1) KHEB

Option 2) AXUR

Option 3) GDAX

Option 4) OKJH

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

Hence, "Option 4" is the correct answer.

The logic followed here is:

Given: X : 36 :: 15: Y

So, checking each option one by one:

Option 1) X = 12, Y = 50 → 12 : 36 :: 15: 50

12 × 4 = 36

48 ≠ 36 (LHS ≠ RHS)

15 × 4 = 50

60 ≠ 50 (LHS ≠ RHS)

Option 2) X = 12, Y = 60 → 12 : 36 :: 15: 60

12 × 4 = 36

48 ≠ 36 (LHS ≠ RHS)

15 × 4 = 60

60 = 60 (LHS = RHS)

Option 3) X = 9, Y = 42 → 9 : 36 :: 15: 42

9 × 4 = 36

36 = 36 (LHS = RHS)

15 × 4 = 42

60 ≠ 42 (LHS ≠ RHS)

Option 4) X = 9, Y = 60 → 9 : 36 :: 15: 60

9 × 4 = 36

36 = 36 (LHS = RHS)

15 × 4 = 60

60 = 60 (LHS = RHS)

Hence, "Option 4" is the correct answer.

Shortcut Trick

Total Weighted Average = (Price₁ × Ratio₁ + Price₂ × Ratio₂ + Price₃ × Ratio₃) / (Sum of Ratios)

Average = (15 × 2 + 7.50 × 5 + 2.50 × 13) / (2 + 5 + 13)

Average = (30 + 37.5 + 32.5) / 20 = 100 / 20 = 5

∴ The correct answer is Rs. 5.

Alternate Method

Given:

Charge on Day 1 = Rs. 15 | Attendance Ratio = 2

Charge on Day 2 = Rs. 7.50 | Attendance Ratio = 5

Charge on Day 3 = Rs. 2.50 | Attendance Ratio = 13

Formula Used:

Average Charge = (Total Revenue) ÷ (Total Number of Visitors)

Let the number of visitors on Day 1, Day 2, and Day 3 be 2x, 5x, and 13x respectively.

⇒ Total Revenue = (15 × 2x) + (7.50 × 5x) + (2.50 × 13x)

⇒ Total Revenue = 30x + 37.5x + 32.5x

⇒ Total Revenue = 100x

⇒ Total Visitors = 2x + 5x + 13x = 20x

⇒ Average Charge = 100x ÷ 20x

⇒ Average Charge = Rs. 5

∴ The correct answer is Rs. 5.

Additional Information

Weighted Average

When values have different levels of importance or frequency, the average is calculated as Σ(Value_i × Weight_i) ÷ ΣWeight_i.

Ratio Application in Averages

In problems involving ratios, actual numbers are not required; the ratio parts can be treated as the actual weights to find the average.

Revenue Calculation

Total Revenue is always the product of the rate per unit and the number of units (Revenue = Price × Quantity).

The correct answer is 3.

Key Points

• In September 2024, Prime Minister Narendra Modi launched 3 Param Rudra Super Computing Systems.
• The launch also included a High Performance Computing (HPC) system dedicated to weather and climate research.
• The Param Rudra systems are part of India's efforts to enhance computational capabilities for scientific research.
• These systems are expected to significantly improve the accuracy and efficiency of weather forecasting and climate modeling.
• The initiative aligns with the Indian government's focus on leveraging technology for sustainable development.

Additional Information

• Supercomputing in India
• India has been actively developing its supercomputing capabilities under the National Supercomputing Mission (NSM).
• The mission aims to build a network of supercomputers with a total computing capacity of 45 Petaflops.
• Supercomputers are crucial for advancing research in various fields including weather forecasting, climate science, and material science.
• High Performance Computing (HPC)
• HPC involves aggregating computing power to deliver higher performance than typical desktop computers and servers.
• It is essential for solving complex scientific, engineering, and business problems.
• HPC systems can process vast amounts of data and perform a large number of calculations at high speed.
• Weather and Climate Research
• Advanced computing systems play a pivotal role in enhancing the precision of weather predictions.
• Climate models require substantial computational power to simulate the Earth's climate and predict future changes.
• Accurate weather forecasting helps in disaster management and mitigation, saving lives and property.
• Param Supercomputers
• Param is a series of supercomputers developed by the Centre for Development of Advanced Computing (C-DAC) in India.
• The name "Param" means "supreme" in Sanskrit.
• These systems are designed to meet the growing computational demands of scientific research and industrial applications in India.

The logic followed here is:

SOTQ is related to PLQN

And,

OKPM is related to LHMJ

Similarly,

LHMJ is related to

Hence, "Option 2" is the correct answer.

Given:

Number = 8.46̅

Formula used:

For a repeating decimal of the form x.ab̅ = (xab − x) / 99

Calculations:

Let n = 8.464646...

⇒ 100n = 846.464646...

⇒ 100n − n = 846.4646... − 8.4646...

⇒ 99n = 846 − 8

⇒ 99n = 838

⇒ n = 838 / 99

∴ The correct answer is option (1).

The correct answer is Sodium hydroxide.

Key Points

• Sodium hydroxide (NaOH) is a highly caustic base and alkali that decomposes proteins at ordinary ambient temperatures and may cause severe chemical burns.
• It is a white solid ionic compound consisting of sodium cations (Na⁺) and hydroxide anions (OH⁻).
• Sodium hydroxide has a pH value of approximately 14, indicating its strong basicity.
• It is commonly used in various industrial processes, including the manufacture of paper, textiles, and detergents.

Additional Information

• Basicity: It refers to the strength of a base in a solution. Strong bases like sodium hydroxide completely dissociate in water, releasing a high concentration of hydroxide ions (OH⁻).
• pH Scale: The pH scale measures how acidic or basic a solution is, ranging from 0 to 14. A pH of 7 is neutral, below 7 is acidic, and above 7 is basic.
• Common Bases: Other common bases include potassium hydroxide (KOH), calcium hydroxide (Ca(OH)₂), and ammonia (NH₃).
• Safety Precautions: Due to its caustic nature, sodium hydroxide must be handled with care, using appropriate personal protective equipment (PPE) such as gloves and safety goggles.
• Applications: Aside from industrial uses, sodium hydroxide is also used in the food industry for processing, like peeling fruits and vegetables, and in home cleaning products.

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

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

Required condition: Perfect square - Even Number - Odd Number

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

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

Hence, "Option 2" is the correct answer.

The correct answer is ₹1 Crore.

Key Points

• The Public Examinations (Prevention of Unfair Means) Bill, 2024, is a legislative proposal aimed at curbing organized cheating in public examinations.
• It proposes a stringent penalty structure to deter individuals and groups from engaging in cheating activities.
• The bill stipulates a minimum fine of ₹1 Crore for those found guilty of organized cheating.
• This significant penalty highlights the government's commitment to maintaining the integrity and fairness of public examinations.
• The legislation is part of broader efforts to enhance the quality and credibility of the education system in India.

Additional Information

• Organized Cheating:
• Involves systematic and planned efforts to manipulate examination processes to unfairly benefit certain individuals.
• Methods can include impersonation, use of unauthorized electronic devices, and collusion with examination officials.
• Public Examinations:
• Assessments conducted by government or authorized bodies to evaluate the knowledge and skills of candidates.
• Examples include board exams, entrance tests for higher education, and recruitment exams for government jobs.
• Legislative Measures:
• Legislation is a key tool used by governments to enforce rules and maintain order within various sectors, including education.
• Effective legislation can help deter malpractice and ensure fair conduct in public services.
• Education Integrity:
• Maintaining the credibility and fairness of the education system is crucial for ensuring equal opportunities for all students.
• Integrity in education fosters trust among stakeholders, including students, parents, educators, and employers.

Given: P, Q, R, S, T, U, and V are sitting around a circular table facing the centre.

1) Only 1 person sits between P and R when counted from the left of R.

2) Q and R are both immediate neighbours of U.

3) Only 1 person sits between V and T when counted from the right of V.

4) S is not an immediate neighbour of T.

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

Thus, according to the final arrangement, P sits third to the left of U.

Hence, "Option 1" is the correct answer.

Shortcut Trick

Net Profit% = a + b + (a × b) ÷ 100, where a is markup% and b is discount% (negative).

Markup = +25% and Discount = −10%.

Gain% = 25 − 10 + (25 × −10) ÷ 100

Gain% = 15 − 250 ÷ 100 = 15 − 2.5 = 12.5%.

∴ The correct answer is 12.5%.

Alternate Method

Given: Markup = 25%, Discount = 10%. Formulas: MP = CP × (100 + Markup%) ÷ 100 | SP = MP × (100 − Discount%) ÷ 100 | Profit% = (SP − CP) ÷ CP × 100.

⇒ Let Cost Price (CP) = 100. ⇒ Marked Price (MP) = 100 + 25% of 100 = 125. ⇒ Selling Price (SP) = 125 − 10% of 125 = 125 − 12.5 = 112.5. ⇒ Gain = SP − CP = 112.5 − 100 = 12.5. ⇒ Gain% = (12.5 ÷ 100) × 100 = 12.5%.

∴ The correct answer is 12.5%.

Additional Information

Relationship between CP and MP

The ratio of CP to MP can be expressed as: CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%).

Mark-up Percentage

It is the extra price added to the CP to arrive at the MP. Mark-up% = (MP − CP) ÷ CP × 100.

Given: 16 - 2 + 5 ÷ 12 × 2 = ?

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

16 - 2 + 5 ÷ 12 × 2 = ? ⇒ 16 ÷ 2 × 5 - 12 + 2 = ?

⇒ 16 ÷ 2 × 5 - 12 + 2 = ?

⇒ 8 × 5 - 12 + 2 = ?

⇒ 40 + 2 - 12 = ?

⇒ 42 - 12 = ?

⇒ 30 = ?

Hence, "Option 1" is the correct answer.

Decoding symbols:

Given: Q × R - S + T ÷ U

Q × R → Q is the mother of R.

R - S → R is the husband of S.

S + T → S is the sister of T.

T ÷ U → T is the son of U.

Thus, Q is S's mother-in-law or husband's mother.

Hence, the correct answer is "Option 4".

The logic followed here is:

Hence, "Option 4" is the correct answer.

The logic followed here is:

Option 1) NQ-LP

Option 2) FI-DG

Option 3) IL-GJ

Option 4) DG-BE

Thus, out of all the options 'NQ-LP' is the odd one out.

Hence, "Option 1" is the correct answer.

The correct answer is Molecule.

Key Points

• A molecule is not a subatomic particle; it is a chemical structure consisting of at least two atoms bonded together.
• Subatomic particles include neutrons, electrons, and protons, which are the fundamental components of an atom.
• Molecules are formed through chemical bonds and can consist of different atoms or identical atoms.
• Examples of molecules include H₂O (water), CO₂ (carbon dioxide), and O₂ (oxygen).

Additional Information

• Neutron:
• Neutrons are subatomic particles found in the nucleus of an atom.
• They have no electric charge and a mass slightly greater than that of protons.
• Neutrons play a key role in the stability of the nucleus.
• Electron:
• Electrons are negatively charged subatomic particles.
• They orbit the nucleus of an atom in various energy levels.
• Electrons are involved in chemical bonding and electricity conduction.
• Proton:
• Protons are positively charged subatomic particles found in the nucleus of an atom.
• The number of protons determines the atomic number and the element's identity.
• Protons have a mass approximately equal to that of neutrons.
• Molecule:
• Molecules are composed of two or more atoms chemically bonded together.
• They can be simple (e.g., O₂) or complex (e.g., DNA).
• Molecules are the smallest unit of a chemical compound that retains its chemical properties.

Decoding letters:

Given: 4 C 8 D 9 A 3 B 2 = ?

After interchanging the letters,

4 C 8 D 9 A 3 B 2 = ? ⇒ 4 + 8 - 9 ÷ 3 × 2 = ?

⇒ 4 + 8 - 9 ÷ 3 × 2 = ?

⇒ 4 + 8 - 3 × 2 = ?

⇒ 4 + 8 - 6 = ?

⇒ 12 - 6 = ?

⇒ 6 = ?

Hence, "Option 1" is the correct answer.

Shortcut Trick

Let the total votes be 100%.

Losing candidate got 40% → Winning candidate got (100% − 40%) = 60%.

Difference in votes = 60% − 40% = 20%.

Given 20% = 1000 votes.

100% = 1000 ÷ 20 × 100 = 5000 votes.

∴ The correct answer is 5000 votes.

Alternate Method

Given:

Percentage of votes for loser = 40%

Vote margin (Difference) = 1000

Calculations:

⇒ Total Votes = 100%

⇒ Votes of winner = 100% − 40% = 60%

⇒ Difference in percentages = 60% − 40% = 20%

⇒ 20% of Total Votes = 1000

⇒ Total Votes = (1000 ÷ 20) × 100

⇒ Total Votes = 50 × 100 = 5000

∴ The correct answer is 5000 votes.

Additional Information

Invalid Votes Concept

If invalid votes are present, then Valid Votes = Total Polled − Invalid. The winning/losing % is then calculated on valid votes unless specified otherwise.

Voter Turnout

If some voters did not cast votes: Votes Polled = Total Registered Voters × (Turnout %). Always identify the base population for percentage calculations.

The logic followed here is:

Hence, "Option 4" is the correct answer.

The correct answer is Rhizopus.

Key Points

• Rhizopus is a genus of fungi, also known as bread molds, which are multicellular organisms.
• Unlike single-celled organisms, Rhizopus consists of multiple hyphae that form a complex mycelium structure.
• The lifecycle of Rhizopus involves both asexual and sexual reproduction, indicating its multicellular nature.
• Rhizopus species are primarily saprophytic, growing on decaying organic matter, and do not exist as single cells.

Additional Information

• Bacteria
• Bacteria are unicellular microorganisms that lack a nucleus and other membrane-bound organelles.
• They reproduce primarily through binary fission, a form of asexual reproduction.
• Bacteria can exist independently as single cells.
• Chlamydomonas
• Chlamydomonas is a genus of green algae which are single-celled eukaryotes.
• They are known for their two flagella and are often found in freshwater environments.
• Amoeba
• Amoeba refers to a group of single-celled organisms that move and feed using pseudopodia.
• They are a type of protist and can live in various environments, including soil and water.
• Single-celled organisms
• Single-celled organisms are also known as unicellular organisms.
• They include bacteria, archaea, protozoa, single-celled algae, and single-celled fungi.
• These organisms perform all necessary functions within one cell.

The correct answer is Volt.

Key Points

• The unit of electromotive force (EMF) is the volt (V).
• EMF is defined as the voltage generated by a battery or by the magnetic force according to Faraday's Law.
• The volt is named after the Italian physicist Alessandro Volta (1745-1827), who invented the voltaic pile, considered to be the first chemical battery.
• One volt is defined as the difference in electric potential between two points of a conducting wire carrying a constant current of one ampere when the power dissipated between the points is one watt.

Additional Information

• Electromotive Force (EMF)
• EMF is the energy provided by a cell or battery per coulomb of charge passing through it.
• It is often denoted by the symbol ε or E.
• EMF is responsible for driving the current in an electric circuit.
• Measurement of EMF
• EMF can be measured using a device called a voltmeter.
• In practical applications, EMF is measured under open-circuit conditions, where no current is flowing.
• Faraday's Law of Electromagnetic Induction
• This law states that the induced EMF in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit.
• It is a fundamental principle used in the operation of generators, transformers, and inductors.
• Voltage vs. EMF
• While voltage refers to the potential difference between two points in a circuit, EMF refers to the total energy per charge produced by a source.
• In an ideal battery, the voltage across the terminals is equal to the EMF; however, in real batteries, internal resistance causes the terminal voltage to be less than the EMF when current flows.

The correct answer is Bryophyllum - Spore formation.

Key Points

• Bryophyllum reproduces vegetatively through leaf buds, not through spore formation.
• Vegetative reproduction in Bryophyllum occurs when plantlets arise from the notches at the margins of its leaves.
• Each plantlet can develop into a new individual when it falls onto the soil, a process known as propagation by fragmentation.
• In contrast, spore formation is a mode of asexual reproduction seen in fungi, algae, and some non-flowering plants, but not in Bryophyllum.

Additional Information

• Binary Fission in Amoeba
• Amoeba reproduces asexually by binary fission, where the cell divides into two equal parts.
• This process involves the replication of the genetic material followed by the division of the cytoplasm.
• Budding in Hydra
• Hydra reproduces by budding, a form of asexual reproduction where a new organism develops from an outgrowth or bud on the parent.
• The bud detaches when it is mature enough to survive on its own.
• Fragmentation in Spirogyra
• Spirogyra, a filamentous green alga, reproduces through fragmentation where a filament breaks into smaller pieces, each of which can grow into a new individual.
• This method is common in simple multicellular organisms and some plants.

Given:

Expression = 3 − (5 − 6 ÷ 3)

Formula used:

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

Calculations:

3 − (5 − 6 ÷ 3)

First, solve the Division inside the bracket:

⇒ 3 − (5 − 2)

Now, solve the Subtraction inside the bracket:

⇒ 3 − 3

Final Subtraction:

⇒ 0

∴ The correct answer is option (3).

Shortcut Trick For a mean proportion x between two numbers a and b, where a : x :: x : b, the formula is x = √(a × b). Given values: a = 3.2 and b = 16.2 x = √(3.2 × 16.2) = √(32/10 × 162/10) = √(5184/100) x = 72/10 = 7.2 ∴ The correct answer is 7.2. Alternate Method

Given: 3.2 : x :: x : 16.2 and x > 0 Formula Used: If a : b :: c : d, then a/b = c/d or ad = bc. ⇒ 3.2 / x = x / 16.2 ⇒ x2 = 3.2 × 16.2 ⇒ x2 = 51.84 ⇒ x = √51.84 ⇒ x = 7.2 ∴ The correct answer is 7.2. Additional Information Mean Proportional The mean proportional between two numbers a and b is a value x such that a : x = x : b, calculated as x = √(ab). Third Proportional If a : b :: b : c, then c is called the third proportional to a and b, where c = b2 / a. Fourth Proportional If a : b :: c : d, then d is the fourth proportional to a, b, and c, calculated as d = (b × c) / a.

The correct answer is Budding, regeneration and fission.

Key Points

• Unicellular organisms primarily reproduce through a process known as binary fission, where a single cell divides into two identical daughter cells.
• Binary fission is the most common mode of reproduction in prokaryotic organisms such as bacteria.
• In eukaryotic unicellular organisms, such as amoebas and paramecia, a similar process occurs but involves mitosis followed by cytokinesis.
• Fission allows for rapid population growth under favorable environmental conditions.

Additional Information

• Budding
• Budding is a form of asexual reproduction where a new organism grows from a certain part of the parent organism.
• This method is commonly seen in yeasts (unicellular fungi) and some other organisms.
• Regeneration
• Regeneration is the process of renewal, restoration, and growth that makes genomes, cells, and organisms resilient to damage.
• While commonly seen in multicellular organisms like starfish, unicellular species utilize various asexual modes including fission and budding to ensure reproduction.
• Other Modes of Asexual Reproduction
• Apart from fission, other modes of asexual reproduction include spore formation and fragmentation.

Shortcut Trick

Side of rhombus = 100 ÷ 4 = 25 cm.

Using Pythagorean triplet in the right-angled triangle formed by half-diagonals: 25, 20, 15.

Second diagonal = 2 × 15 = 30 cm.

Area = (1/2) × 40 × 30 = 600 cm².

∴ The correct answer is 600 cm².

Alternate Method

Given: Perimeter = 100 cm, Diagonal 1 (d₁) = 40 cm.

Formula Used: Side (a) = Perimeter ÷ 4; Side² = (d₁/2)² + (d₂/2)²; Area = (1/2) × d₁ × d₂

⇒ Side (a) = 100 ÷ 4 = 25 cm

⇒ Let d₂ be the second diagonal.

⇒ 25² = (40/2)² + (d₂/2)²

⇒ 625 = 20² + (d₂/2)²

⇒ 625 − 400 = (d₂/2)²

⇒ 225 = (d₂/2)²

⇒ 15 = d₂/2 ⇒ d₂ = 30 cm

⇒ Area = (1/2) × 40 × 30

⇒ Area = 20 × 30 = 600 cm²

∴ The correct answer is 600 cm².

Additional Information

Properties of Rhombus

All four sides are equal, and diagonals bisect each other at right angles (90°).

Area and Perimeter Formula

Area = (1/2) × d₁ × d₂ and Perimeter = 4 × side.

Side-Diagonal Relationship

4 × side² = d₁² + d₂². This is derived from the Pythagoras theorem.

Shortcut Trick

Combined efficiency of (A+B+C) = 1/20 units/min.

Combined efficiency with leak = 1/(20 + 10) = 1/30 units/min.

Leak efficiency = 1/20 − 1/30 = (3 − 2)/60 = 1/60 units/min.

Time to empty = 60/1 = 60 minutes.

∴ The correct answer is 60 min.

Alternate Method

Given: Filling time = 20 min, Time with leak = 20 + 10 = 30 min.

Calculation:

⇒ Efficiency of (A + B + C) = 3 units/min

⇒ Efficiency of (A + B + C + Leak) = 2 units/min

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

⇒ Efficiency of Leak = 2 − 3 = −1 unit/min (Negative sign denotes emptying)

⇒ Time taken by Leak to empty the tank = Total Work ÷ Efficiency of Leak

⇒ Time = 60 ÷ 1 = 60 minutes

∴ The correct answer is 60 min.

Additional Information

Pipes & Cisterns Efficiency

Filling pipes have positive efficiency while emptying pipes or leaks have negative efficiency.

Net Work Formula

Total Time = 1 / (1/T₁ + 1/T₂ − 1/T_leak) where T represents individual time taken by each component.

Time and Efficiency Relationship

Efficiency is inversely proportional to the time taken to complete a specific task (Work = Efficiency × Time).

Shortcut Trick

Observe the ratio of Distance and Speed for both parts.

Part 1: 60 km ÷ 40 km/h = 1.5 hours

Part 2: 120 km ÷ 80 km/h = 1.5 hours

Since the time taken for both parts is the same, the Average Speed is simply the arithmetic mean of the speeds.

Average Speed = (40 + 80) ÷ 2 = 60 km/h.

∴ The correct answer is 60 km/h.

Alternate Method

Given:

D₁ = 60 km, S₁ = 40 km/h

D₂ = 120 km, S₂ = 80 km/h

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Time for first part (T₁) = 60 ÷ 40 = 1.5 hours

⇒ Time for second part (T₂) = 120 ÷ 80 = 1.5 hours

⇒ Total Distance = 60 + 120 = 180 km

⇒ Total Time = 1.5 + 1.5 = 3 hours

⇒ Average Speed = 180 ÷ 3 = 60 km/h

∴ The correct answer is 60 km/h.

Additional Information

Equal Time Average Speed

If a journey is divided into parts with equal time durations, the average speed is the simple Arithmetic Mean of the speeds: (v₁ + v₂ + ... + v_n) ÷ n.

Equal Distance Average Speed

If two equal distances are covered at speeds v₁ and v₂, the average speed is the Harmonic Mean: (2 × v₁ × v₂) ÷ (v₁ + v₂).

General Unit Conversion

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

The correct answer is Shri Chirag Chandrashekhar Shetty.

Key Points

• Shri Chirag Chandrashekhar Shetty is an Indian badminton player who has made significant contributions to the sport.
• In January 2024, he was honored with the Major Dhyan Chand Khel Ratna Award, India's highest sporting honor.
• This prestigious award was conferred upon him by the President of India in recognition of his outstanding achievements in badminton.
• He has been a prominent figure in Indian badminton, known for his exceptional skills and dedication to the sport.

Additional Information

• Major Dhyan Chand Khel Ratna Award
• It is the highest sporting honor in India, awarded annually by the Ministry of Youth Affairs and Sports.
• The award is named after Major Dhyan Chand, an Indian field hockey player widely regarded as one of the greatest in the history of the sport.
• The award was instituted in 1991-1992 and recognizes outstanding performance in sports.
• Recipients of this award receive a medallion, a certificate, and a cash prize.
• Chirag Shetty's Achievements
• He has achieved significant success in both national and international badminton tournaments.
• He is known for his prowess in doubles, often partnering with Satwiksairaj Rankireddy.
• Chirag Shetty has represented India in various prestigious tournaments, including the BWF World Championships and the Commonwealth Games.
• Importance of the Award
• The Major Dhyan Chand Khel Ratna Award serves as a motivation for athletes to achieve excellence in their respective sports.
• It brings recognition and encouragement to sportspersons and highlights their contributions to the nation's sports culture.
• The award also helps in promoting and nurturing young talent in the sports field.

Shortcut Trick

Passing Marks = Marks Obtained + Failing Marks = 178 + 22 = 200.

As per the question, Passing Percentage = 40%.

40% → 200

100% → (200 ÷ 40) × 100 = 5 × 100 = 500.

∴ The correct answer is 500.

Alternate Method

Given:

Marks secured by the student = 178

Marks by which the student failed = 22

Minimum passing percentage = 40%

Formula Used:

Passing Marks = Marks Obtained + Failing Marks

Maximum Marks = (Passing Marks ÷ Passing Percentage) × 100

Calculations:

⇒ Passing Marks = 178 + 22

⇒ Passing Marks = 200

⇒ Let the Maximum Marks be M.

⇒ 40% of M = 200

⇒ (40 ÷ 100) × M = 200

⇒ M = (200 × 100) ÷ 40

⇒ M = 5 × 100

⇒ M = 500

∴ The correct answer is 500.

Additional Information

Percentage Calculation

To find the total value when a percentage is known: Total = (Value ÷ Percentage) × 100.

Passing Marks Concept

Passing Marks = Obtained Marks + Failing Marks. If a student gets more than passing marks, then Passing Marks = Obtained Marks − Excess Marks.

Percentage Difference

In problems with two students, the difference in their percentage marks is equal to the difference in their absolute marks.

The correct answer is 25 g.

Key Points

• The law of conservation of mass states that mass is neither created nor destroyed in a chemical reaction.
• The total mass of reactants equals the total mass of products in a closed system.
• In the given reaction, 10 grams of substance A reacts with 15 grams of substance B.
• The total mass of the reactants is 10 g + 15 g = 25 g.
• Therefore, according to the law of conservation of mass, the total mass of the products will be 25 grams.

Additional Information

• Law of Conservation of Mass
• Formulated by Antoine Lavoisier in 1789.
• States that the mass of an isolated system remains constant over time.
• Fundamental principle in classical physics and chemistry.
• Closed System
• A physical system that does not exchange any matter with its surroundings.
• Energy can be exchanged in the form of heat or work.
• Essential for observing the law of conservation of mass.
• Chemical Reaction
• A process that leads to the transformation of one set of chemical substances to another.
• Involves breaking and forming of chemical bonds.
• Examples include combustion, oxidation, and reduction reactions.
• Reactants and Products
• Reactants are the starting substances in a chemical reaction.
• Products are the substances formed as a result of the chemical reaction.
• The mass of reactants must equal the mass of products in a closed system as per the law of conservation of mass.

The correct answer is Both protons and neutrons.

Key Points

• Nucleons are particles found in the nucleus of an atom.
• The term "nucleons" encompasses both protons and neutrons.
• Protons are positively charged particles, while neutrons are neutral, having no electrical charge.
• Both protons and neutrons contribute to the atomic mass of an element.
• Nucleons are bound together in the nucleus by the strong nuclear force, which is one of the four fundamental forces of nature.

Additional Information

• Electrons:
• Electrons are negatively charged particles that orbit the nucleus of an atom in electron shells.
• Unlike protons and neutrons, electrons do not reside in the nucleus.
• The number of electrons in an atom determines its chemical properties and reactivity.
• Atomic Number:
• The atomic number of an element is equal to the number of protons in the nucleus of its atoms.
• The atomic number defines the identity of an element and its position in the periodic table.
• Isotopes:
• Isotopes are variants of a particular chemical element that have the same number of protons but different numbers of neutrons.
• Isotopes of an element exhibit similar chemical behavior but can have different physical properties, such as different mass numbers and stability.
• Strong Nuclear Force:
• The strong nuclear force is the force that holds protons and neutrons together in the nucleus.
• It is the strongest of the four fundamental forces but operates only over very short distances, on the order of a few femtometers (1 femtometer = 10^-15 meters).
• This force is essential for the stability of atomic nuclei.

The correct answer is Atmospheric refraction.

Key Points

• The twinkling of stars is primarily caused by atmospheric refraction.
• As starlight passes through the Earth's atmosphere, it is refracted (bent) due to the varying density and temperature layers in the atmosphere.
• This refraction causes the light from stars to change direction slightly, making the stars appear to shift position and intensity, which is perceived as twinkling.
• The phenomenon is more pronounced for stars closer to the horizon because their light passes through a greater thickness of the Earth's atmosphere compared to stars overhead.
• Planets do not twinkle as much as stars because they are closer to Earth and their apparent size is larger, averaging out the effects of atmospheric refraction.

Additional Information

• Atmospheric Refraction
• It is the bending of light as it passes through the Earth's atmosphere.
• The degree of refraction depends on the temperature gradient and the density of the atmospheric layers.
• This bending causes celestial objects to appear slightly higher in the sky than their true positions.
• Atmospheric refraction also affects the apparent shape and color of the sun and moon near the horizon, causing phenomena such as the green flash at sunset or sunrise.
• Scintillation
• Scintillation refers to the rapid variation in the brightness and color of starlight due to atmospheric turbulence.
• It is responsible for the twinkling effect observed in stars.
• The phenomenon is less noticeable in planets due to their larger apparent size.
• Optical Turbulence
• Optical turbulence is the random fluctuation in the refractive index of the atmosphere.
• It is caused by the turbulent mixing of air at different temperatures and densities.
• Optical turbulence is a key factor in the twinkling of stars and the blurring of astronomical images.
• Adaptive Optics
• Adaptive optics is a technology used in telescopes to compensate for the effects of atmospheric turbulence.
• It involves real-time adjustments to the telescope's optics to correct for the blurring caused by the atmosphere.
• This technology significantly improves the resolution of ground-based astronomical observations.

The correct answer is there is an equal and opposite reaction and they act on two different bodies.

Key Points

• Newton's third law states: "For every action, there is an equal and opposite reaction."
• The action and reaction forces act on two different bodies.
• This law explains the principle of conservation of momentum in isolated systems.
• The equal and opposite forces are of the same type (e.g., both are gravitational, electromagnetic, etc.).

Additional Information

• Newton's Laws of Motion:
• First Law: An object remains at rest or in uniform motion unless acted upon by a net external force (law of inertia).
• Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma).
• Applications:
• Rocket propulsion: Exhaust gases exert a force on the rocket, and the rocket exerts an equal and opposite force on the gases.
• Walking: When you push the ground backward with your foot, the ground pushes you forward with an equal and opposite force.
• Conservation of Momentum:
• In a closed system, the total momentum before and after an event remains constant.
• Newton's third law is fundamental to the principle of conservation of momentum.
• Examples in Nature:
• Birds flying: Wings push air downwards and backwards, and air pushes wings upwards and forwards.
• Swimming: Swimmers push water backwards with their hands and feet, and water pushes them forward.

Shortcut Trick

Add kilograms and grams separately.

Total Kg = 22 + 19 = 41 kg

Total Grams = 589 + 678 = 1267 g

Since 1000 g = 1 kg, then 1267 g = 1 kg 267 g

Final sum = 41 kg + 1 kg 267 g = 42 kg 267 g

∴ The correct answer is 42 kg 267 g.

Alternate Method

Given: First weight = 22 kg 589 g, Second weight = 19 kg 678 g

Formula Used: 1 kg = 1000 g

⇒ Sum of Grams = 589 + 678 = 1267 g

⇒ Carry over to Kg = 1267 ÷ 1000 = 1 kg (remainder 267 g)

⇒ Sum of Kg = 22 + 19 + 1 (carry) = 42 kg

⇒ Result = 42 kg 267 g

∴ The correct answer is 42 kg 267 g.

Additional Information

Metric Conversion

Standard unit of mass is gram. 1 kilogram (kg) = 1000 grams (g), 1 gram = 1000 milligrams (mg).

Addition Rule for Compound Units

When adding compound units like kg and g, if the sum of lower units exceeds the conversion base (1000), carry over the quotient to the higher unit.

The correct answer is Pulling hand from the flame.

Key Points

• Reflex actions are automatic and rapid responses to a stimulus that do not require conscious thought.
• Pulling your hand away from a flame is a classic example of a reflex action, specifically a withdrawal reflex.
• This action is controlled by the spinal cord, not the brain, which allows for a much quicker response to potential danger.
• The reflex arc is the neural pathway that mediates this action, involving sensory neurons, interneurons, and motor neurons.

Additional Information

• Reflex Arc:
• The reflex arc is the neural pathway that controls a reflex action.
• It typically involves a sensory neuron, an interneuron, and a motor neuron.
• The sensory neuron detects a stimulus and sends a signal to the interneuron in the spinal cord, which then activates the motor neuron to produce a response.
• Types of Reflexes:
• Monosynaptic reflexes: Involve only one synapse between the sensory and motor neurons (e.g., knee-jerk reflex).
• Polysynaptic reflexes: Involve multiple synapses with one or more interneurons (e.g., withdrawal reflex).
• Autonomic Reflexes:
• These reflexes regulate the activity of smooth muscles, the heart, and glands.
• Examples include the regulation of blood pressure, digestion, and pupil size.
• Somatic Reflexes:
• These reflexes involve the skeletal muscles.
• Examples include the stretch reflex and withdrawal reflex.

Given:

Shakti starts from Point A and drives 22 km towards South.

He then takes a left turn, drives 20 km, turns left and drives 12 km.

He then takes a left turn and drives 17 km.

He takes a final right turn, drives 10 km and stops at Point P.

Thus, Shakti should drive (20 km - 17 km) 3 km in the west direction in order to reach Point A again.

Hence, "Option 3" is the correct answer.

The logic followed here is:

MILH is related to KGJF

And,

QMPL is related to OKNJ

Similarly,

TPSO is related to

Hence, "Option 4" is the correct answer.

Shortcut Trick

Number of marbles = (Radius of larger sphere ÷ Radius of smaller marble)³

Ratio of radii = 6 ÷ 0.2 = 30

Number of marbles = 30³ = 27000

∴ The correct answer is 27000 marbles.

Alternate Method

Given:

Radius of solid sphere (R) = 6 cm

Radius of each spherical marble (r) = 0.2 cm

Formula Used:

Volume of a sphere = (4/3) × π × radius³

Number of marbles (n) = Total Volume ÷ Volume of one marble

Calculations:

⇒ n × [(4/3) × π × r³] = (4/3) × π × R³

⇒ n = R³ ÷ r³

⇒ n = 6³ ÷ (0.2)³

⇒ n = 216 ÷ 0.008

⇒ n = 216000 ÷ 8

⇒ n = 27000

∴ The correct answer is 27000 marbles.

Additional Information

Volume of Sphere

The amount of space inside a sphere is V = (4/3)πr³, where r is the radius.

Recasting Rule

When one solid is melted and recast into multiple smaller solids, the total volume remains constant.

Surface Area of Sphere

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

The correct answer is Begusarai.

Key Points

• Begusarai has been identified as the most polluted city in 2023 according to the Sixth Annual World Air Quality Report.
• The report highlights that Begusarai has the highest concentration of PM2.5 particles in the air, which are harmful to human health.
• PM2.5 levels in Begusarai have significantly surpassed the safe limit set by the World Health Organization (WHO).
• This alarming level of air pollution is attributed to factors such as industrial emissions, vehicular pollution, and biomass burning.
• The findings call for urgent measures to control and reduce air pollution in Begusarai to protect public health.

Additional Information

• PM2.5 Particles
• PM2.5 refers to particulate matter that is less than 2.5 micrometers in diameter.
• These particles can penetrate deeply into the respiratory system and cause health issues such as respiratory infections, heart disease, and lung cancer.
• World Health Organization (WHO) Air Quality Guidelines
• The WHO sets guidelines for air quality to protect public health from the adverse effects of air pollution.
• The recommended safe limit for PM2.5 is 10 µg/m³ (annual mean).
• Sources of Air Pollution
• Common sources include industrial emissions, vehicular exhaust, construction activities, and burning of biomass and fossil fuels.
• Natural sources such as dust storms and wildfires also contribute to air pollution.
• Health Effects of Air Pollution
• Short-term exposure can cause symptoms like irritation of the eyes, nose, and throat, coughing, and shortness of breath.
• Long-term exposure can lead to chronic respiratory diseases, cardiovascular diseases, and increased mortality rates.
• Measures to Reduce Air Pollution
• Implementing stricter emission standards for industries and vehicles.
• Promoting the use of public transportation and cleaner fuels.
• Increasing green cover through afforestation and urban green spaces.
• Raising public awareness about the health impacts of air pollution and encouraging community actions.

The correct answer is 96th.

Key Points

• Transparency International's Corruption Perceptions Index (CPI) is a global measure of corruption in the public sector.
• In the 2024 CPI, India was ranked 96^th out of 180 countries.
• This ranking reflects India's ongoing struggle with corruption issues within its public sector.
• The CPI score ranges from 0 (highly corrupt) to 100 (very clean), and India's score has been relatively stable in recent years.
• India's CPI score in 2024 was 38, highlighting the need for continued efforts to combat corruption.

Additional Information

• Transparency International:
• Founded in 1993, it is an international non-governmental organization working to combat global corruption.
• It is headquartered in Berlin, Germany, and operates through more than 100 national chapters worldwide.
• Transparency International publishes the Corruption Perceptions Index annually.
• Corruption Perceptions Index (CPI):
• The CPI is a composite index that ranks countries by their perceived levels of public sector corruption.
• It is based on expert assessments and opinion surveys.
• The CPI is widely used as a key indicator of corruption globally.
• Impact of Corruption:
• Corruption undermines democracy and the rule of law.
• It leads to the misallocation of resources and hampers economic development.
• Corruption adversely affects public services and the overall quality of life.
• Efforts to Combat Corruption in India:
• The Indian government has implemented various measures such as the Lokpal and Lokayuktas Act.
• Strengthening of anti-corruption agencies like the Central Vigilance Commission (CVC) and the Central Bureau of Investigation (CBI).
• Introduction of technology-based initiatives like e-governance to reduce corruption.

The correct answer is Both cranial and spinal nerves.

Key Points

• The peripheral nervous system (PNS) consists of all the nerves that lie outside the brain and spinal cord.
• It includes 12 pairs of cranial nerves and 31 pairs of spinal nerves.
• The cranial nerves originate from the brain and primarily serve the head and neck region.
• The spinal nerves originate from the spinal cord and serve the rest of the body.
• The PNS is responsible for transmitting sensory and motor information to and from the central nervous system (CNS).

Additional Information

• Central Nervous System (CNS)
• It consists of the brain and spinal cord.
• The CNS is responsible for processing and interpreting sensory information and sending out instructions.
• Autonomic Nervous System (ANS)
• It is a part of the PNS that controls involuntary bodily functions.
• The ANS is divided into the sympathetic and parasympathetic nervous systems.
• Somatic Nervous System
• It is another part of the PNS that controls voluntary movements.
• The somatic nervous system transmits sensory and motor signals to and from the CNS.
• Neurons
• They are the basic building blocks of the nervous system.
• Neurons transmit information through electrical and chemical signals.

Shortcut Trick

Ratio of numbers → 4 : 1

Difference in ratio units → 4 − 1 = 3 units

According to question, 3 units → 54

1 unit → 54 ÷ 3 = 18

Greater number (4 units) → 4 × 18 = 72

∴ The correct answer is 72.

Alternate Method

Given:

Ratio of numbers = 4 : 1

Difference between numbers = 54

Let the numbers be 4x and 1x.

⇒ 4x − 1x = 54

⇒ 3x = 54

⇒ x = 54 ÷ 3

⇒ x = 18

Greater number = 4x

⇒ 4 × 18 = 72

∴ The correct answer is 72.

Additional Information

Ratio and Proportion

A ratio compares two quantities by division. If a : b is the ratio, the numbers can be assumed as ax and bx where x is the common multiplier.

Invertendo and Alternendo

If a/b = c/d, then b/a = d/c (Invertendo) and a/c = b/d (Alternendo).

Sum of Numbers in Ratio

If ratio is a : b and sum is S, the numbers are [a/(a+b)] × S and [b/(a+b)] × S.

Shortcut Trick

Total Interest = 2040 − 1500 = ₹540

Interest for 1 year = 6% of 1500 = ₹90

Time = Total Interest ÷ Interest per year = 540 ÷ 90 = 6 years

∴ The correct answer is 6 years.

Alternate Method

Given:

Principal (P) = ₹1,500

Amount (A) = ₹2,040

Rate (R) = 6% per annum

Formula Used:

Simple Interest (SI) = Amount − Principal

Time (T) = (SI × 100) ÷ (P × R)

Calculations:

⇒ SI = 2040 − 1500 = ₹540

⇒ T = (540 × 100) ÷ (1500 × 6)

⇒ T = 54000 ÷ 9000

⇒ T = 6 years

∴ The correct answer is 6 years.

Additional Information

Simple Interest Formula

SI = (P × R × T) ÷ 100, where P is Principal, R is Rate, and T is Time.

Amount Calculation

Total Amount (A) = P + SI = P × [1 + (R × T) ÷ 100].

SI vs CI Difference

For the first year, if interest is compounded annually, SI and CI are always equal.

The correct answer is Only (A) and (B).

Key Points

• Electric oven — Uses electricity directly to generate heat.
• Electric laundry iron — Also uses electricity directly for heating.
• Solar water heater — Primarily uses solar energy (sunlight) to heat water, not electricity.
• So, only (A) and (B) are related to practical applications of electricity in daily life.

Additional Information

• Electricity in Domestic Use
• Electricity powers a range of household appliances including refrigerators, washing machines, and air conditioners, enhancing modern living standards.
• Electric lights provide illumination, significantly extending the usable hours of the day.
• Home entertainment systems, such as televisions and computers, rely on electricity, contributing to leisure and connectivity.
• Renewable Energy Applications
• Solar panels convert sunlight into electricity, representing a clean and sustainable energy source.
• Wind turbines harness wind energy to generate electricity, contributing to renewable energy production.
• Energy Efficiency
• Energy-efficient appliances reduce electricity consumption and lower utility bills.
• Smart home systems allow for automated control of electrical devices, enhancing energy management.
• Electricity in Communication
• Electricity is critical for powering communication devices such as smartphones, routers, and servers.
• The internet and telecommunication infrastructure rely heavily on a stable electrical supply.

The correct answer is It will be doubled..

Key Points

• Ohm's Law states that the current (I) flowing through a resistor is directly proportional to the voltage (V) across it and inversely proportional to the resistance (R). The formula is I = V/R.
• If the resistance (R) is halved and the voltage (V) remains constant, the current (I) will increase.
• Mathematically, if the initial resistance is R and it is halved to R/2, the new current will be I_new = V / (R/2) = 2V/R = 2I_initial.
• Therefore, halving the resistance while keeping the voltage constant will result in the current being doubled.

Additional Information

• Ohm's Law:
• Formulated by Georg Simon Ohm in 1827.
• Defines the relationship between voltage, current, and resistance in an electrical circuit.
• Expressed as V = IR, where V is voltage, I is current, and R is resistance.
• Resistance:
• Measured in ohms (Ω).
• Determines how much a material opposes the flow of electric current.
• Factors affecting resistance include material, length, cross-sectional area, and temperature.
• Current:
• Measured in amperes (A).
• Represents the flow of electric charge in a circuit.
• Can be direct (DC) or alternating (AC).
• Voltage:
• Measured in volts (V).
• Represents the electrical potential difference between two points.
• Provides the driving force that pushes the current through the circuit.

The correct answer is an oxidising agent.

Key Points

• Bleaching powder (Calcium hypochlorite) is a strong oxidising agent, which means it can donate oxygen to other substances and oxidize them.
• It is commonly used in chemical industries for bleaching paper pulp, textiles, and disinfecting drinking water due to its ability to kill bacteria and other pathogens.
• Bleaching powder releases chlorine when exposed to air and moisture, which contributes to its oxidising properties.
• It is widely used in the textile industry to bleach cotton and linen and in the paper industry to bleach wood pulp.

Additional Information

• Oxidising Agents
• Oxidising agents are substances that can accept electrons and bring about oxidation of other substances.
• Common oxidising agents include substances like hydrogen peroxide, potassium permanganate, and chlorine.
• They are used in various industrial processes including disinfection, bleaching, and water treatment.
• Calcium Hypochlorite
• Calcium hypochlorite, commonly known as bleaching powder, is a white solid, often used for water treatment and as a bleaching agent.
• Its chemical formula is Ca(ClO)₂.
• It is more stable than sodium hypochlorite (liquid bleach) and has a longer shelf life.
• Disinfection Process
• Disinfection involves the elimination of most or all pathogenic microorganisms, except bacterial spores, from inanimate objects.
• Bleaching powder is used to disinfect drinking water and swimming pools by killing harmful microorganisms.
• Safety Measures
• When handling bleaching powder, it is important to use protective gear, such as gloves and masks, to avoid irritation and inhalation of fumes.
• It should be stored in a dry, cool place away from organic materials and acids to prevent hazardous reactions.

Shortcut Trick

Interest for 1 month → 9% of ₹700 = ₹63

Interest for 7 months → 7 × ₹63 = ₹441

∴ The correct answer is ₹441.

Alternate Method

Given:

Principal (P) = ₹700

Rate (R) = 9% per month

Time (T) = 7 months

Formula Used:

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

Calculations:

⇒ SI = (700 × 9 × 7) ÷ 100

⇒ SI = 7 × 9 × 7

⇒ SI = 63 × 7

⇒ SI = 441

∴ The correct answer is ₹441.

Additional Information

Simple Interest Consistency

Always ensure that the Rate and Time are in the same unit (both monthly or both yearly) before applying the formula.

Total Amount Formula

The total Amount (A) to be paid back is the sum of Principal and Simple Interest: A = P + SI.

Unit Conversion

To convert a monthly rate to an annual rate, multiply by 12. In this case, 9% p.m. = 108% per annum.

The correct answer is Newton.

Key Points

• The SI unit of force is called the Newton, symbolized as "N".
• One Newton is defined as the amount of force required to accelerate a 1 kilogram mass by 1 meter per second squared (1 N = 1 kg·m/s²).
• The Newton is named after Sir Isaac Newton in recognition of his work in classical mechanics, particularly Newton's Laws of Motion.
• The unit was adopted in the International System of Units (SI) in 1948 during the 9^th General Conference on Weights and Measures (CGPM).

Additional Information

• Dyne
• A dyne is a unit of force in the centimeter-gram-second (CGS) system of units.
• It is equal to 10^-5 Newtons (1 dyne = 10^-5 N).
• Newton's Laws of Motion
• There are three fundamental laws that describe the relationship between the motion of an object and the forces acting on it.
• These laws form the foundation of classical mechanics.
• Force
• In physics, force is an interaction that, when unopposed, will change the motion of an object.
• It can be described as a push or pull on an object resulting from the object's interaction with another object.
• SI Units
• The International System of Units (SI) is the modern form of the metric system.
• It is the most widely used system of measurement, established in 1960.

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

Conclusions:

I. At least some tomatoes are onions → Follow (As all onions are tomatoes. As whole onions comes in tomatoes, therefore it is true.)

II. Some onions are potatoes → Does not follow (As all onions are tomatoes and some tomatoes are potatoes. So it is possible but not definite.)

∴ Here, Only conclusion I follows.​

Hence, the correct answer is "Option 4"

The logic followed here is:

Hence, "Option 1" is the correct answer.

The correct answer is Sugar and sponge.

Key Points

• Sugar is a crystalline solid that retains its shape and volume under standard conditions.
• Sponge is a porous solid material that can compress and return to its original shape, demonstrating solid-state characteristics.
• Both sugar and sponge have a defined shape and volume, which are key characteristics of solids.
• Unlike liquids or gases, the molecules in solids such as sugar and sponge are closely packed together, providing rigidity and stability.

Additional Information

• States of Matter:
• The three primary states of matter are solid, liquid, and gas.
• Solids have a fixed shape and volume, liquids have a fixed volume but take the shape of their container, and gases neither have a fixed shape nor a fixed volume.
• Properties of Solids:
• Solids are characterized by their rigidity and resistance to changes in shape or volume.
• The particles in a solid are tightly packed in a regular pattern, which gives solids their definite shape and volume.
• Crystalline and Amorphous Solids:
• Crystalline solids, like sugar, have an orderly structure with repeating patterns.
• Amorphous solids, like sponges, do not have a long-range order and can be more flexible in shape.
• Compressibility:
• Solids generally have low compressibility compared to liquids and gases.
• Sponge is an exception due to its porous structure, allowing it to compress and expand.

The correct answer is Hormusji N Cama.

Key Points

• Hormusji N Cama is a renowned figure in the field of Literature and Education-Journalism.
• He has been honored with the prestigious Padma Bhushan award in the year 2024.
• The Padma Bhushan is the third-highest civilian award in India, recognizing distinguished service of a high order.
• Hormusji N Cama has significantly contributed to the field of journalism, particularly in promoting ethical journalism and media integrity.

Additional Information

• Padma Awards
• The Padma Awards are one of the highest civilian honors in India, instituted in 1954.
• The awards are given in three categories: Padma Vibhushan, Padma Bhushan, and Padma Shri.
• These awards are announced annually on the occasion of Republic Day.
• The Padma Vibhushan is awarded for exceptional and distinguished service, the Padma Bhushan for distinguished service of a high order, and the Padma Shri for distinguished service in any field.
• Ethical Journalism
• Ethical journalism involves maintaining integrity, impartiality, and fairness in reporting news.
• It emphasizes the importance of accuracy, verification, and accountability.
• Journalists are expected to avoid conflicts of interest and to respect the privacy and dignity of individuals.
• Promoting ethical journalism helps in building public trust and ensuring the credibility of media organizations.
• Media Integrity
• Media integrity refers to the ethical standards and professional conduct of journalists and media organizations.
• It involves transparency, unbiased reporting, and accountability to the public.
• Maintaining media integrity is crucial for preserving the democratic function of the press as a watchdog.
• Efforts to ensure media integrity include self-regulation, adherence to journalistic codes of conduct, and independent oversight bodies.