RRB Technician Grade III Official Paper (Held On: 28 Dec, 2024 Shift 2) (Previous Year Paper)

Shortcut Trick

The effective Simple Interest rate for 2 years at 8% = 8 + 8 = 16%.

The effective Compound Interest rate for 2 years = 8 + 8 + (8 × 8) ÷ 100 = 16.64%.

Given that 16% corresponds to ₹2,000.

Required Compound Interest (16.64%) = (2000 ÷ 16) × 16.64

⇒ 125 × 16.64 = ₹2080.

∴ The correct answer is ₹2080.

Alternate Method

Given:

Simple Interest (SI) = ₹2,000 | Rate (R) = 8% p.a. | Time (T) = 2 years

Formula Used:

SI = (P × R × T) ÷ 100

CI for 2 years = SI + (Interest on 1^st year SI)

Calculations:

⇒ 2000 = (P × 8 × 2) ÷ 100

⇒ 2000 = 16P ÷ 100

⇒ P = (2000 × 100) ÷ 16

⇒ P = ₹12,500

⇒ SI for 1^st year = 2000 ÷ 2 = ₹1000

⇒ Compound Interest (CI) = SI for 2 years + (8% of 1^st year SI)

⇒ CI = 2000 + (1000 × 8 ÷ 100)

⇒ CI = 2000 + 80 = ₹2080

∴ The correct answer is ₹2080.

Additional Information

Effective Rate of CI

For 2 years, the effective interest rate can be calculated using the successive percentage formula: R + R + (R × R) ÷ 100.

Difference between CI and SI

The difference (D) between CI and SI for 2 years is given by the formula: D = P × (R ÷ 100)².

General CI Formula

Amount (A) = P(1 + R ÷ 100)ⁿ, where n is the number of years. CI = A − P.

Given:

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

M is kept second from the bottom. Only three boxes are kept between M and B.

A is kept at one of the positions above B.

P is kept at one of the positions below M.

Only E is kept between B and F

Thus, 'One' box is kept between L and P.

Hence, the correct answer is "Option 3".

Shortcut Trick

To find the equivalent single discount for two successive discounts, use the formula: a + b − (a × b) ÷ 100.

Here, a = 12 and b = 15.

Equivalent discount = 12 + 15 − (12 × 15) ÷ 100.

Equivalent discount = 27 − (180 ÷ 100) = 27 − 1.8 = 25.2%.

∴ The correct answer is 25.2%.

Alternate Method

Given: First discount = 12%, Second discount = 15%.

Formula: Equivalent Discount % = [1 − (1 − d₁/100) × (1 − d₂/100)] × 100

⇒ Let the Marked Price (MP) be 100.

⇒ Price after 12% discount = 100 − 12 = 88.

⇒ Price after 15% discount on 88 = 88 − (15% of 88) = 88 − 13.2 = 74.8.

⇒ Total discount = 100 − 74.8 = 25.2.

⇒ Single Equivalent Discount % = (25.2 ÷ 100) × 100 = 25.2%.

∴ The correct answer is 25.2%.

Additional Information

Successive Discounts

When a series of discounts are applied one after another on the reducing balance, they are called successive discounts. The total discount is always less than the sum of individual percentages.

Marked Price & Discount

Discount is always calculated on the Marked Price (MP). Selling Price (SP) = Marked Price − Discount.

Shortcut Trick

For four numbers a, b, c, d in proportion, the product of means equals the product of extremes: a × d = b × c.

Here, 12 × y = 24 × 45.

Dividing by 12: y = 2 × 45 = 90.

∴ The correct answer is 90.

Alternate Method

Given: Numbers 12, 24, 45, and y are in proportion.

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

⇒ 12/24 = 45/y

⇒ 1/2 = 45/y

⇒ y = 45 × 2

⇒ y = 90

∴ The correct answer is 90.

Additional Information

Mean Proportional

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

Third Proportional

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

Fourth Proportional

If a, b, c, d are in proportion (a:b = c:d), then d is the fourth proportional and d = (b × c)/a.

The correct answer is Gujarat.

Key Points

• Punjab defeated Gujarat to win the Syed Mushtaq Ali T20 Trophy in November 2023.
• The final match took place at the IS Bindra PCA Stadium, Mohali.
• This victory marked Punjab's first win in the history of the Syed Mushtaq Ali T20 Trophy.
• The Syed Mushtaq Ali Trophy is a domestic T20 cricket championship in India, organized by the Board of Control for Cricket in India (BCCI).
• Punjab's cricket team showed remarkable performance throughout the tournament to clinch the title.

Additional Information

• Syed Mushtaq Ali Trophy
• Named after the famous Indian cricketer Syed Mushtaq Ali.
• It is a premier domestic T20 cricket championship in India.
• The tournament is administered by the BCCI and features state teams from across the country.
• It serves as a platform for players to showcase their talent and get selected for the Indian Premier League (IPL) and the national team.
• Punjab Cricket Team
• Represents the Indian state of Punjab in domestic cricket competitions.
• Home ground is the PCA Stadium in Mohali.
• Has produced several notable cricketers who have represented India internationally.
• Known for its strong performances in domestic cricket tournaments over the years.
• IS Bindra PCA Stadium
• Located in Mohali, Punjab.
• Named after former BCCI president Inderjit Singh Bindra.
• It is one of the premier cricket stadiums in India and hosts international matches.
• Known for its excellent facilities and infrastructure.

The correct answer is inertia.

Key Points

• Inertia is the property of an object to resist changes to its state of motion.
• It is a fundamental concept in Newton's First Law of Motion, which states that an object will remain at rest or in uniform motion unless acted upon by an external force.
• The concept of inertia was first introduced by Galileo Galilei and later refined by Sir Isaac Newton.
• Inertia is directly proportional to the mass of an object; the greater the mass, the greater the inertia.

Additional Information

• Newton's First Law of Motion: Often called the law of inertia, it states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced external force.
• Mass and Inertia: Mass is a measure of the amount of matter in an object and is directly related to the object's inertia. More mass means more inertia.
• Galileo's Contribution: Galileo's experiments with inclined planes helped in understanding that objects resist changes in their state of motion, laying the groundwork for the concept of inertia.
• Practical Examples: Common examples of inertia include passengers moving forward in a car when it suddenly stops, or a book remaining at rest on a table until it is pushed.

The logic followed here is:

Thus, the next term in the series will be '62'.

Hence, the correct answer is "Option 1".

Shortcut Trick

For the first n natural numbers, the average is always the middle term of the series.

Shortcut Formula: Average = (n + 1) ÷ 2

Given n = 50, Average = (50 + 1) ÷ 2 = 51 ÷ 2 = 25.5.

∴ The correct answer is 25.5.

Alternate Method

Given: First 50 natural numbers (1, 2, 3, ..., 50).

Formula Used: Average = (Sum of all observations) ÷ (Total number of observations)

Sum of first n natural numbers = [n × (n + 1)] ÷ 2

⇒ Sum of first 50 numbers = [50 × (50 + 1)] ÷ 2

⇒ Sum = [50 × 51] ÷ 2 = 25 × 51 = 1275

⇒ Average = Sum ÷ n = 1275 ÷ 50

⇒ Average = 25.5

∴ The correct answer is 25.5.

Additional Information

Average of Arithmetic Progression

For any series in AP, Average = (First term + Last term) ÷ 2.

Sum of Squares

Sum of squares of first n natural numbers = [n(n + 1)(2n + 1)] ÷ 6.

Average of First n Even Numbers

The average of the first n even natural numbers is always (n + 1).

Average of First n Odd Numbers

The average of the first n odd natural numbers is exactly n.

Given word: ARTICLE 

Now, arranging in alphabetical order:

we get, 

Here, the letter 'A' and 'I' will remain unchanged after arranged in alphabetical order.

Hence, the correct answer is "Option 2".

The correct answer is 27 u.

Key Points

• The mass number of an atom is the sum of its protons and neutrons. In this case, it has 13 protons and 14 neutrons.
• The sum of 13 protons and 14 neutrons gives a mass number of 27.
• Mass number is represented by the symbol 'A' and is a whole number.
• The unit used for mass number is atomic mass unit (u), though it is often just a whole number without units.

Additional Information

• Proton:
• A proton is a subatomic particle found in the nucleus of every atom.
• It has a positive electric charge of +1 elementary charge.
• The number of protons in an atom defines the element (e.g., 13 protons define an atom as aluminum).
• Neutron:
• A neutron is a subatomic particle, also found in the nucleus of an atom, with no electric charge.
• Neutrons contribute to the atomic mass and stability of the nucleus.
• Atomic Number (Z):
• The atomic number is the number of protons in the nucleus of an atom.
• It determines the chemical properties of an element and its place in the periodic table.
• Isotopes:
• Isotopes are variants of a particular chemical element which differ in neutron number, and consequently in nucleon number.
• All isotopes of a given element have the same number of protons but different numbers of neutrons in each atom.

Shortcut Trick

Identify two numbers whose sum is 16 and product is 48.

Factors of 48: (12, 4) → 12 + 4 = 16. (True)

Value = 12² + 4² = 144 + 16 = 160.

∴ The correct answer is 160.

Alternate Method

Given:

x + y = 16

xy = 48

Formula Used:

(x + y)² = x² + y² + 2xy

Calculations:

⇒ (16)² = x² + y² + 2 × 48

⇒ 256 = x² + y² + 96

⇒ x² + y² = 256 − 96

⇒ x² + y² = 160

∴ The correct answer is 160.

Additional Information

Algebraic Identity for Squares

The identity (a − b)² = a² + b² − 2ab can also be used if the difference is known.

Relationship between Identities

(x + y)² − (x − y)² = 4xy is a common relation used to find the difference between variables.

Given series:

(Left) 2 9 # 1 * £ & % 4 6 @ 8 $ 7 & 3 Ω 5 (Right)

Symbols are there, each of which is immediately preceded by a symbol and also immediately followed by an odd number

Symbol → Symbol → Odd Number

2 9 # 1 * £ & % 4 6 @ 8 $ 7 & 3 Ω 5

There is no such pair.

Hence, the correct answer is "Option 1".

Given:

The distance between two points on a map is 5 cm.

The scale of the map is 1 : 6,00,000.

Formula used:

Actual distance = Map distance × Scale

Calculation:

Actual distance = 5 cm × 6,00,000

⇒ Actual distance = 30,00,000 cm

Since 1 km = 1,00,000 cm

⇒ Actual distance in km = 30,00,000 cm ÷ 1,00,000

⇒ Actual distance = 30 km

∴ The correct answer is option (4).

The correct answer is The solute particles can be separated from the mixture by the process of filtration..

Key Points

• A solution is a homogeneous mixture, meaning that its composition is uniform throughout.
• Due to the very small size of the particles in a solution (less than 1 nm), they do not scatter light passing through the solution, making it appear clear.
• The solute particles in a true solution cannot be separated by filtration because they are too small to be trapped by a filter.
• In a solution, the solute is completely dissolved in the solvent, resulting in a single-phase system.

Additional Information

• Homogeneous Mixtures:
• Homogeneous mixtures have a uniform composition and appearance throughout.
• Examples include saltwater, air, and alloys.
• Particle Size:
• The particles in a true solution are smaller than 1 nm in diameter.
• Due to their small size, they cannot be seen with the naked eye.
• Filtration:
• Filtration is a method used to separate solids from liquids or gases using a filter medium that allows the fluid to pass through but retains the solid particles.
• It is not effective for separating solute particles in a true solution.
• Types of Mixtures:
• Solutions are a type of homogeneous mixture, where the solute is completely dissolved in the solvent.
• Other types of mixtures include colloids and suspensions, which have different particle sizes and properties.

The correct answer is Small intestine.

Key Points

• The small intestine is the longest part of the alimentary canal, with an average length of about 6-7 meters in adults.
• It is divided into three sections: the duodenum, jejunum, and ileum.
• The primary function of the small intestine is the absorption of nutrients and minerals from food.
• It has a large surface area due to villi and microvilli, which aid in maximizing nutrient absorption.
• The small intestine is crucial for digestion, as it continues the process begun in the stomach and receives bile and pancreatic juices to aid in breaking down food.

Additional Information

• Villi and Microvilli
• Villi are small, finger-like projections that extend into the lumen of the small intestine.
• Microvilli are tiny hair-like structures on the villi that further increase the surface area for absorption.
• Both structures significantly enhance the absorption efficiency of the small intestine.
• Duodenum
• The first section of the small intestine, immediately following the stomach.
• It receives chyme from the stomach along with bile from the liver and digestive enzymes from the pancreas.
• Jejunum and Ileum
• The jejunum is the middle section of the small intestine, primarily involved in the absorption of nutrients.
• The ileum is the final section, which absorbs vitamin B12, bile salts, and any remaining nutrients.
• Peristalsis
• Peristalsis is the series of wave-like muscle contractions that move food through the digestive tract.
• In the small intestine, peristalsis helps in mixing the chyme with digestive juices and in pushing it forward for further digestion and absorption.

Given: 16 ÷ 96 × 6 - 4 + 20 = ?

After changing the signs, the equation we get: 

16 + 96 ÷  6 ×  4 - 20 = ?

→ 16 + 96 ÷  6 ×  4 - 20

→ 16 + 16 × 4 - 20

→ 16 + 64 - 20

→ 80 - 20

→ 60

Hence, the correct answer is "Option 2".

Shortcut Trick

Difference in Price = Price of (2 Tables + 3 Chairs) − Price of (2 Tables + 1 Chair)

Price of 2 Chairs = ₹540 − ₹470 = ₹70 ⇒ Price of 1 Chair = ₹35

Combined cost (2 Tables + 2 Chairs) = (2 Tables + 1 Chair) + 1 Chair

Total Cost = ₹470 + ₹35 = ₹505

∴ The correct answer is ₹505.

Alternate Method

Given:

Cost of 2 Tables + 3 Chairs = ₹540 ... (i)

Cost of 2 Tables + 1 Chair = ₹470 ... (ii)

Calculations:

Subtracting equation (ii) from (i):

⇒ (2T + 3C) − (2T + 1C) = 540 − 470

⇒ 2 Chairs = ₹70

⇒ 1 Chair = ₹35

Substituting value of 1 Chair in equation (ii):

⇒ 2 Tables + 35 = 470

⇒ 2 Tables = 470 − 35 = ₹435

Cost of 2 Tables + 2 Chairs:

⇒ 435 + 2 × 35

⇒ 435 + 70 = ₹505

∴ The correct answer is ₹505.

Additional Information

Linear Equations in Two Variables

These problems are solved using the elimination method where one variable is removed by subtracting or adding equations.

Substitution Method

Expressing one variable in terms of the other (e.g., T in terms of C) and plugging it into the second equation to find the unit price.

Averages & Ratios

In some cases, if the coefficients are symmetrical, adding and subtracting the equations can yield the value of (x + y) or (x − y) directly.

Given code language:

Thus, 'REF' is common in both code language, then code for K is '4'.

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: 1st number + 3.8 = 2nd  number.

X : 18.8 :: 21 : Y

For, X

X : 18.8

→ X + 3.8 = 18.8

→ X = 18.8 - 3.8

→ X = 15

Now, for Y

 21 : Y

→ 21 + 3.8 = Y

→ 24.8 = Y

Thus, Value of X is 15 and Value of Y is 24.8.

Hence, the correct answer is "Option 4".

The logic followed here is:

Thus, 'PID' will be the next in the series.

Hence, the correct answer is "Option 2".

A + B - C + D × E

 → A is Mother of B,

B is husband of C,

C is mother of D,

D is sister of E,

By using the symbols in the table, we can draw the family tree:

Thus, A is Father's mother of E.

Hence, the correct answer is "Option 1".

The correct answer is C₃H₆ and C₄H₈.

Key Points

• Alkenes are hydrocarbons that contain at least one carbon-carbon double bond (C=C) and have the general formula C_nH_2n.
• The pair C₃H₆ (propylene) and C₄H₈ (butene) belong to the homologous series of alkenes, which differ by a CH2 unit.
• In homologous series, compounds have similar chemical properties and a gradual change in physical properties.
• Each successive member of an alkene series increases by one carbon atom and two hydrogen atoms (CH₂ group).

Additional Information

• Homologous Series:
• A series of compounds with the same functional group and similar chemical properties, where each successive member differs by a CH₂ unit.
• Examples include alkanes (C_nH_2n+2), alkenes (C_nH_2n), and alkynes (C_nH_2n-2).
• Functional Group:
• A group of atoms responsible for the characteristic reactions of a particular compound.
• In alkenes, the functional group is the carbon-carbon double bond (C=C).
• Isomerism in Alkenes:
• Alkenes can exhibit structural isomerism and geometrical (cis-trans) isomerism.
• Isomers have the same molecular formula but different structures or spatial arrangements.
• Chemical Properties of Alkenes:
• Alkenes typically undergo addition reactions, such as hydrogenation, halogenation, and hydrohalogenation.
• They are also known for polymerization reactions, forming long-chain polymers.

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

Key Points

• The field inside a current-carrying solenoid is uniform because the magnetic field lines are parallel and evenly spaced inside the solenoid.
• The field outside the solenoid is weak and non-uniform compared to the field inside.
• The magnetic field around a solenoid resembles that of a bar magnet, having a north and south pole, creating a similar field pattern.
• The field strength inside the solenoid is determined by the current and the number of turns per unit length of the solenoid.

Additional Information

• Solenoid
• A solenoid is a coil of wire designed to create a strong magnetic field inside the coil when an electric current passes through it.
• Solenoids are used in various applications such as electromagnets, inductors, and actuators.
• Magnetic Field
• The area around a magnet where magnetic forces can be detected is called the magnetic field.
• Magnetic fields are visualized using magnetic field lines, which show the direction and strength of the field.
• Electromagnetism
• It is the interaction between electric currents and magnetic fields.
• Electromagnetic phenomena include the behavior of solenoids and the generation of magnetic fields by electric currents.
• Bar Magnet
• A bar magnet is a permanent magnet in the shape of a bar with a magnetic field similar to that of a solenoid.
• It has two poles, north and south, and the magnetic field lines emerge from the north pole and enter the south pole.

The least possible venn diagram.

Conclusions:

(I) At least some pants are shirts → True(As, All shirts are pants, so At least some pants are shirts is definitly true)

(II) Some shirts are tie → False(As, there is no direct relation between shirts and tie)

Thus, Only conclusion I follows

Hence, the correct answer is "Option 4".

The logic followed here is:

Option 1) PRU

Option 2) JLP

Option 3) FHK

Option 4) UWZ

Thus, 'JLP' not followed the same logic.

Hence, the correct answer is "Option 2".

Shortcut Trick

When the distance is constant for two speeds x and y, Average Speed = 2xy ÷ (x + y).

Given x = 30 km/h and y = 60 km/h.

Average Speed = (2 × 30 × 60) ÷ (30 + 60)

Average Speed = 3600 ÷ 90 = 40 km/h.

∴ The correct answer is 40 km/h.

Alternate Method

Given:

Distance (one way) = 90 km

Forward speed = 30 km/h

Return speed = 60 km/h

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Total Distance = 90 + 90 = 180 km

⇒ Time 1 (Forward) = Distance ÷ Speed = 90 ÷ 30 = 3 hours

⇒ Time 2 (Return) = Distance ÷ Speed = 90 ÷ 60 = 1.5 hours

⇒ Total Time = 3 + 1.5 = 4.5 hours

⇒ Average Speed = 180 ÷ 4.5

⇒ Average Speed = 40 km/h

∴ The correct answer is 40 km/h.

Additional Information

Harmonic Mean for Average Speed

When distances are equal, average speed is the Harmonic Mean of the individual speeds: Avg Speed = 2v₁v₂ ÷ (v₁ + v₂).

Average Speed for Unequal Distances

If distances d₁, d₂ are covered with speeds v₁, v₂, then Average Speed = (d₁ + d₂) ÷ (d₁/v₁ + d₂/v₂).

Arithmetic Mean Fallacy

Average speed is NOT the simple average (x+y)/2 unless the time taken for each segment is identical.

The correct answer is ribosomes.

Key Points

• The rough endoplasmic reticulum (RER) is studded with ribosomes, which gives it a rough appearance under a microscope.
• Ribosomes are essential for protein synthesis in the cell.
• The RER is primarily involved in the production and processing of proteins that are either secreted from the cell, incorporated into the cell's plasma membrane, or used within lysosomes.
• Ribosomes are composed of ribosomal RNA (rRNA) and proteins and can be found freely floating in the cytoplasm or attached to the RER.

Additional Information

• Endoplasmic Reticulum (ER)
• The endoplasmic reticulum is a network of membranes within the cytoplasm of eukaryotic cells.
• It exists in two forms: rough ER (with ribosomes) and smooth ER (without ribosomes).
• The smooth ER is involved in lipid synthesis, metabolism of carbohydrates, and detoxification of drugs and poisons.
• Protein Synthesis
• Protein synthesis is a two-step process: transcription and translation.
• Transcription occurs in the nucleus where DNA is transcribed into mRNA.
• Translation occurs at the ribosomes where mRNA is translated into a polypeptide chain, forming proteins.
• Ribosomes
• Ribosomes can be found in both prokaryotic and eukaryotic cells.
• They are the site of protein synthesis, where amino acids are assembled into proteins based on genetic instructions.
• Ribosomes can exist as free ribosomes in the cytosol or bound ribosomes on the RER.

Shortcut Trick

For a number to be divisible by 6, it must be divisible by both 2 and 3.

The number 13z4 is even, so it is divisible by 2.

For divisibility by 3, sum of digits 1 + 3 + z + 4 = (8 + z) must be a multiple of 3.

Possible values for z are 1, 4, 7. The greatest is 7.

∴ The correct answer is 7.

Alternate Method

Given: A 4-digit number 13z4 is divisible by 6.

Formula Used: Divisibility rule of 6 = Divisibility by 2 AND Divisibility by 3.

⇒ Divisibility by 2: Last digit is 4 (even), so it is satisfied.

⇒ Divisibility by 3: Sum of digits (1 + 3 + z + 4) = (8 + z).

⇒ (8 + z) must be divisible by 3.

⇒ If z = 1, 8 + 1 = 9 (Divisible by 3)

⇒ If z = 4, 8 + 4 = 12 (Divisible by 3)

⇒ If z = 7, 8 + 7 = 15 (Divisible by 3)

⇒ The values of z are {1, 4, 7}.

⇒ Greatest value of z = 7.

∴ The correct answer is 7.

Additional Information

Divisibility Rule of 3

A number is divisible by 3 if the sum of its digits is a multiple of 3.

Divisibility Rule of 2

A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.

Composite Divisibility

If a number is divisible by two co-prime numbers a and b, then it is divisible by their product (a × b).

The correct answer is current through the coil is increased.

Key Points

• The magnetic field around a current-carrying coil is directly proportional to the current passing through the coil.
• Increasing the current results in a stronger magnetic field as per Ampere's Law, which states that the magnetic field is proportional to the current.
• The strength of the magnetic field can be calculated using the formula B = μ₀ * (n * I), where B is the magnetic field, μ₀ is the permeability of free space, n is the number of turns, and I is the current.
• This relationship is fundamental in electromagnetism and is utilized in various applications such as electromagnets, transformers, and inductors.

Additional Information

• Ampere's Law:
• Ampere's Law relates the circulating magnetic field in a closed loop to the electric current passing through the loop.
• The mathematical expression of Ampere's Law is ∮B·dl = μ₀ * I, where B is the magnetic field, dl is an infinitesimal element of the path, and I is the current enclosed by the path.
• Electromagnetism:
• Electromagnetism is the branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.
• It is the fundamental principle behind electric motors, transformers, and many other modern devices.
• Magnetic Field Strength:
• Magnetic field strength, often denoted as H, is a measure of the magnetizing force and is directly proportional to the current and inversely proportional to the distance from the current-carrying conductor.
• Permeability of Free Space (μ₀):
• Permeability of free space, also known as the magnetic constant, is a physical constant that describes the magnetic permeability in a classical vacuum.
• Its value is approximately 4π × 10⁻⁷ H/m (henries per meter).

The correct answer is only in simple body organised multicellular organisms.

Key Points

• Fragmentation is a type of asexual reproduction where an organism breaks into fragments, each capable of growing independently into a new organism.
• It primarily occurs in simple body organized multicellular organisms such as algae, fungi, and some plants like liverworts.
• This method of reproduction ensures rapid population growth and survival in stable environments.
• Examples include species like Spirogyra (a type of green algae) and certain fungi.

Additional Information

• Asexual Reproduction
• It involves a single parent and produces offspring genetically identical to the parent.
• Types include binary fission, budding, spore formation, and fragmentation.
• Binary Fission
• Common in unicellular organisms like bacteria and protozoa.
• The organism splits into two equal halves, each becoming a new individual.
• Budding
• Occurs in organisms like yeast and hydra.
• A new organism grows from a bud due to cell division at one particular site.
• Spore Formation
• Seen in fungi, algae, and some plants.
• Reproduction occurs through the release of spores, which are resistant to adverse conditions.

Shortcut Trick

Gain% = 25% = 1/4 (Ratio of Profit to False Weight).

Ratio of True Weight : False Weight = (4+1) : 4 = 5 : 4.

Given True Weight (1 kg) = 1000 gm.

5 units = 1000 gm ⇒ 1 unit = 200 gm.

4 units = 4 × 200 = 800 gm.

∴ The correct answer is 800 gm.

Alternate Method

Given: Profit percentage = 25%, True weight = 1000 gm.

Formula: Gain% = [Error ÷ (True Value − Error)] × 100

Let the False Weight used be 'x' gm.

⇒ Error = 1000 − x

⇒ 25 = [(1000 − x) ÷ x] × 100

⇒ 25/100 = (1000 − x) ÷ x

⇒ 1/4 = (1000 − x) ÷ x

⇒ x = 4000 − 4x

⇒ 5x = 4000

⇒ x = 800 gm.

∴ The correct answer is 800 gm.

Additional Information

Dishonest Dealer Concept

A dealer is dishonest if he claims to sell at Cost Price but uses a weight less than the True Weight. The profit is always calculated on the weight he actually gives to the customer.

Relationship Formula

Selling Price (Effective) / Cost Price (Effective) = True Weight / False Weight. Use this ratio method for complex problems involving multiple discounts or markups.

Shortcut Trick

Total Interest % = Rate × Time = 5% × 3 = 15%.

Total Amount % = 100% (Principal) + 15% (Interest) = 115%.

Amount = 1232 × 1.15 = ₹1416.80.

∴ The correct answer is ₹1416.80.

Alternate Method

Given: Principal (P) = ₹1232, Rate (R) = 5%, Time (T) = 3 years.

Formula Used: Simple Interest (SI) = (P × R × T) ÷ 100; Amount (A) = P + SI

⇒ SI = (1232 × 5 × 3) ÷ 100

⇒ SI = (1232 × 15) ÷ 100

⇒ SI = 18480 ÷ 100 = ₹184.80

⇒ Amount = Principal + Simple Interest

⇒ Amount = 1232 + 184.80 = ₹1416.80

∴ The correct answer is ₹1416.80.

Additional Information

Simple Interest vs Compound Interest

Simple Interest is calculated only on the Principal amount, whereas Compound Interest is calculated on the Principal plus accumulated interest.

Rate of Interest (R)

If the rate is given per annum, the time must be converted to years. R = (SI × 100) ÷ (P × T).

Amount Formula

The total Maturity Value or Amount is given by A = P(1 + RT/100).

Given:

Expression = $\frac{0.5 \times 10.6 - 0.2 \times 1.4}{0.4}$

Formula used:

BODMAS rule (Multiplication before Subtraction)

Calculation:

Expression = $\frac{0.5 \times 10.6 - 0.2 \times 1.4}{0.4}$

⇒ $\frac{5.3 - 0.28}{0.4}$

⇒ $\frac{5.02}{0.4}$

⇒ $\frac{50.2}{4}$

⇒ 12.55

∴ The correct answer is option (1).

The correct answer is Distance.

Key Points

• When a body falls freely under gravity, it is under constant acceleration due to gravity, which is approximately 9.8 m/s² near the Earth's surface.
• The mass of the falling body remains constant as it falls, as mass does not change with motion.
• The universal gravitational constant (G) is a fundamental constant of nature and does not change.
• The distance covered by the body, however, changes continuously as the body falls, increasing with time.

Additional Information

• Acceleration due to Gravity (g)

• It is the acceleration of an object due to the force of gravity alone.

• On Earth, the average value of g is approximately 9.8 m/s².

• It remains constant for objects in free fall near the Earth's surface.

• Universal Gravitational Constant (G)

• It is denoted by G and is a key quantity in Newton's law of universal gravitation.

• The value of G is approximately 6.674 × 10⁻¹¹ N(m/kg)².

• It is a constant and does not change with location or motion.

• Mass

• Mass is a measure of the amount of matter in an object.

• It remains constant regardless of an object's state of motion.

• It is typically measured in kilograms (kg).

• Distance

• Distance is a measure of how far an object has moved.

• It changes as the object moves, increasing with time as the object falls.

• In free fall, the distance covered can be calculated using kinematic equations.

• Kinematic Equations

• These equations describe the motion of objects under constant acceleration.

• They include equations for calculating velocity, distance, and time.

• For free fall, the distance covered by a body can be calculated using s=ut+12gt²s=ut+12gt²s=ut+12gt²s=ut+12gt²s=ut+12gt²s=ut+12gt²

  CodeCopy

     , where u is the initial velocity (zero for free fall), g is the acceleration due to gravity, and t is time.
  

The logic followed here is:

Thus, 'CME' will be the next in the series.

Hence, the correct answer is "Option 2".

The correct answer is Incident.

Key Points

• According to the law of refraction, the incident ray, the refracted ray, and the normal to the interface all lie in the same plane.
• This principle is derived from Snell's Law, which describes the relationship between the angles of incidence and refraction.
• The incident ray is the ray that approaches the boundary between two different media, such as air and glass.
• The refracted ray is the ray that passes into the second medium and changes direction due to the change in speed.

Additional Information

• Snell's Law
• Snell's Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media.
• This law can be mathematically expressed as n1 * sin(θ1) = n2 * sin(θ2), where n1 and n2 are the refractive indices of the media.
• Refractive Index
• The refractive index of a medium is a measure of how much the speed of light is reduced inside the medium compared to vacuum.
• It is a dimensionless number defined as n = c/v, where c is the speed of light in vacuum and v is the speed of light in the medium.
• Critical Angle
• The critical angle is the angle of incidence above which total internal reflection occurs.
• It occurs when light travels from a medium with a higher refractive index to one with a lower refractive index.
• Total Internal Reflection
• Total internal reflection happens when a ray of light completely reflects back into the original medium, with no refraction occurring.
• This phenomenon is utilized in optical fibers and some types of prisms.

The correct answer is Copper (II) chloride.

Key Points

• When hydrochloric acid (HCl) is added to copper oxide (CuO), a reaction occurs producing copper (II) chloride (CuCl₂) and water (H₂O).
• The balanced chemical equation for this reaction is: CuO + 2HCl → CuCl₂ + H₂O.
• This reaction is an example of a neutralization reaction where an acid reacts with a base (metal oxide) to produce a salt and water.
• Copper (II) chloride is a compound with copper in the +2 oxidation state, which is the most stable oxidation state for copper in aqueous solutions.

Additional Information

• Hydrochloric Acid (HCl)
• Hydrochloric acid is a strong, corrosive acid commonly used in laboratory and industrial applications.
• It is a solution of hydrogen chloride in water and is known for its pungent smell.
• HCl is widely used for cleaning metals, in the production of organic compounds, and in the food industry for processing and cleaning.
• Copper Oxide (CuO)
• Copper oxide is a black solid that is used as a pigment in ceramics and glass.
• It is a basic oxide, meaning it reacts with acids to form salts and water.
• CuO is also used in the production of copper salts and as a catalyst in chemical reactions.
• Copper (II) Chloride (CuCl₂)
• Copper (II) chloride is a yellow-brown solid that dissolves in water to form a blue-green solution.
• It is used in dyeing, printing, and in various chemical syntheses.
• CuCl₂ can also act as a catalyst in organic reactions and is used in water treatment processes.
• Neutralization Reaction
• A neutralization reaction is a chemical reaction in which an acid and a base react to form a salt and water.
• This type of reaction typically results in the neutralization of the pH of the reacting solutions.
• Neutralization reactions are fundamental in various industrial processes and in everyday life, such as in antacid tablets used to relieve heartburn.

The correct answer is Thyroid gland.

Key Points

• The thyroid gland requires iodine to produce thyroxine (T4) and triiodothyronine (T3) hormones.
• Thyroxine (T4) is the primary hormone produced by the thyroid gland.
• Iodine deficiency can lead to hypothyroidism and goiter.
• The thyroid gland is located in the neck, below the Adam's apple.
• Thyroid hormones regulate the body's metabolic rate, heart and digestive functions, muscle control, brain development, and bone maintenance.

Additional Information

• Hypothyroidism:
• A condition where the thyroid gland does not produce enough thyroid hormones.
• Symptoms include fatigue, weight gain, cold intolerance, and depression.
• Hyperthyroidism:
• A condition where the thyroid gland produces excessive amounts of thyroid hormones.
• Symptoms include weight loss, heat intolerance, increased appetite, and anxiety.
• Goiter:
• An abnormal enlargement of the thyroid gland.
• Often caused by iodine deficiency.
• Iodine:
• An essential element required for the synthesis of thyroid hormones.
• Found in foods such as seafood, dairy products, grains, and iodized salt.
• Thyroid Function Tests:
• Blood tests used to measure levels of T3, T4, and thyroid-stimulating hormone (TSH).
• Help diagnose thyroid disorders and monitor treatment efficacy.

The correct answer is force × displacement.

Key Points

• Work done is defined as the product of the force applied to an object and the displacement of the object in the direction of the force.
• The formula for work done (W) is: W = F × d, where F is the force applied and d is the displacement.
• Work is a scalar quantity and has units of Joules (J) in the International System of Units (SI).
• Work done is positive when the force and displacement are in the same direction, and negative when they are in opposite directions.

Additional Information

• Force:
• A push or pull upon an object resulting from the object's interaction with another object.
• Measured in Newtons (N) in the SI system.
• Displacement:
• The change in position of an object.
• It is a vector quantity, having both magnitude and direction.
• Energy:
• The capacity to do work.
• Measured in Joules (J) in the SI system.
• Power:
• The rate at which work is done or energy is transferred.
• Measured in Watts (W) in the SI system.

The correct answer is They turn blue litmus paper red.

Key Points

• Acids turn blue litmus paper red, which is a common test to identify acidic substances.
• Acids have a sour taste, a characteristic resulting from the presence of hydrogen ions (H⁺).
• Acids have a pH less than 7, indicating their acidic nature on the pH scale.
• Acids react with bases in a neutralization reaction to form salt and water.
• Common examples of acids include hydrochloric acid (HCl), sulfuric acid (H₂SO₄), and citric acid.

Additional Information

• Litmus Paper:
• It is a dye-imbued paper used to test the acidity or basicity of a substance.
• Blue litmus paper turns red under acidic conditions, and red litmus paper turns blue under basic conditions.
• pH Scale:
• The pH scale ranges from 0 to 14, with 7 being neutral.
• Values less than 7 indicate acidity, and values greater than 7 indicate basicity.
• Neutralization Reaction:
• A chemical reaction in which an acid and a base react to form water and a salt.
• This reaction typically results in the pH of the resulting solution being closer to neutral (pH 7).
• Common Acids in Daily Life:
• Hydrochloric Acid (HCl): Found in stomach acid, aiding digestion.
• Citric Acid: Present in citrus fruits like lemons and oranges.
• Acetic Acid: The main component of vinegar.
• Uses of Acids:
• In the food industry for flavoring and preservation.
• In the chemical industry for manufacturing fertilizers, dyes, and explosives.
• In medicine for various treatments and as disinfectants.

Cause: There has been an increase in the number of thefts of bicycles being reported in the apartments in locality X in the last 2 months.

(I) Police have instructed security guards of locality X to record details of all entries and exits and verify the phone numbers of all delivery personnel.

The cause mentions an increase in bicycle thefts. To combat this, the police instructing security guards to record entries and exits, and verify delivery personnel's phone numbers, is a direct and logical response. This measure aims to increase surveillance and identify potential suspects or patterns.

Therefore, Effect I is a possible effect.

(II) Many apartment complexes have decided to install multiple CCTV cameras inside and outside their gates.

Installing CCTV cameras is a common security measure to deter and detect crime. The increase in bicycle thefts would naturally lead apartment complexes to enhance their security. Installing CCTV cameras inside and outside the gates would increase surveillance and help identify potential thieves.

Therefore, Effect II is a possible effect.

(III) More women police constables have been appointed in the police station adjoining locality X.

While increasing police presence can deter crime in general, the specific cause is bicycle thefts. Appointing more women police constables doesn't specifically address bicycle thefts. It's a general increase in police personnel, not a targeted response to the specific issue.

Therefore, Effect III is not a direct or logical effect of the given cause.

Thus, Effects I and II are possible effects of the given cause.

Hence, the correct answer is "Option 1".

Shortcut Trick

Apply Trigonometric Identities directly to simplify the expression.

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

Using identities: (1 + tan² A) = sec² A and (cosec² A − 1) = cot² A

⇒ sec² A + cot² A − sec² A − cot² A = 0

∴ The correct answer is 0.

Alternate Method

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

Formula Used:

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

Calculations:

⇒ sec² A + (cosec² A − 1) − (1 + tan² A) − cot² A

Substitute (cosec² A − 1) with cot² A:

⇒ sec² A + cot² A − (1 + tan² A) − cot² A

The +cot² A and −cot² A cancel each other out:

⇒ sec² A − (1 + tan² A)

Substitute (1 + tan² A) with sec² A:

⇒ sec² A − sec² A

⇒ 0

∴ The correct answer is 0.

Additional Information

Pythagorean Identities

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

Reciprocal Relations

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

Value Substitution Trick

For such identity-based questions, you can substitute a standard angle like A = 45° to quickly verify the numerical result.

Shortcut Trick

Identify two consecutive integers whose product is 56, because x + x² = x(x + 1).

Factors of 56 are 7 × 8.

Comparing x(x + 1) = 7 × (7 + 1), we get x = 7.

∴ The correct answer is 7.

Alternate Method

Given: A positive number added to its square equals 56.

Formula Used: Quadratic Equation x² + bx + c = 0

⇒ Let the number be x.

⇒ x + x² = 56

⇒ x² + x − 56 = 0

⇒ x² + 8x − 7x − 56 = 0

⇒ x(x + 8) − 7(x + 8) = 0

⇒ (x − 7)(x + 8) = 0

⇒ x = 7 or x = −8

⇒ Since the question states it is a positive number, x = 7.

∴ The correct answer is 7.

Additional Information

Nature of Roots

For a quadratic equation ax² + bx + c = 0, the discriminant D = b² − 4ac determines if roots are real or imaginary.

Factorization Method

Splitting the middle term involves finding two numbers that multiply to 'ac' and add up to 'b'.

Consecutive Product Rule

The expression x² + x can always be written as the product of two consecutive integers x(x + 1).

Given:

Kevin starts from point A and drives 7 km towards the North. He then takes two simultaneous right turns and drives 2 km and 1 km, respectively.

He then takes a left turn and drives 3 km. He then takes two simultaneous right turns and drives 3 km each.

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

Thus, Kevin has to drive 2 km West  to reach Point A again.

Hence, the correct answer is "Option 1".

The correct answer is catenation.

Key Points

• Catenation is the ability of an element to form bonds with other atoms of the same element.
• Carbon atoms can form long chains and rings due to their ability to catenate.
• This property allows carbon to form a vast number of compounds, more than any other element.
• Catenation is a crucial property for the formation of organic molecules, including hydrocarbons and polymers.

Additional Information

• Tetravalency of Carbon:
• Carbon has four valence electrons, allowing it to form four covalent bonds with other atoms, including other carbon atoms.
• Hydrocarbons:
• Compounds composed solely of carbon and hydrogen. They are categorized into alkanes, alkenes, and alkynes based on the types of bonds between carbon atoms.
• Isomerism:
• Carbon compounds can exhibit isomerism, where compounds have the same molecular formula but different structural arrangements.
• Polymerization:
• Carbon compounds can undergo polymerization, where small monomer units join to form large polymers, such as plastics and biological macromolecules.

The correct answer is oxides, sulphides and carbonates.

Key Points

• Metal ores in the Earth's crust are commonly found in the form of oxides, sulphides, and carbonates.
• Oxides include minerals like hematite (Fe₂O₃) and bauxite (Al₂O₃·2H₂O).
• Sulphides include minerals such as galena (PbS) and pyrite (FeS₂).
• Carbonates include minerals like calcite (CaCO₃) and dolomite (CaMg(CO₃)₂).
• These forms are the primary sources for extracting metals in various mining processes.

Additional Information

• Oxides: These are compounds of oxygen and metals. They are typically formed through the oxidation process.
• Sulphides: These are compounds of sulfur with metals. They are generally formed in reducing environments, like hydrothermal vents.
• Carbonates: These are salts of carbonic acid containing the carbonate ion (CO₃^2-). They are usually formed in sedimentary environments.
• Mining and Extraction: The process of obtaining metals from ores involves various techniques like smelting, electrolysis, and chemical reduction.
• Economic Importance: The extraction of metals from these ores is crucial for various industries including construction, electronics, and manufacturing.

The correct answer is First, carbohydrates are utilised for energy production and the rest are stored in the form of starch.

Key Points

• Carbohydrates, primarily glucose, produced during photosynthesis are first utilized by the plant for immediate energy needs.
• Plants convert the surplus glucose into starch for storage.
• Starch serves as a long-term energy reserve that can be mobilized when the plant requires energy, particularly during times when photosynthesis is not possible (e.g., night or winter).
• This storage process ensures that plants have a steady supply of energy to maintain their metabolic activities.

Additional Information

• Photosynthesis Process:
• Photosynthesis is the process by which green plants use sunlight to synthesize nutrients from carbon dioxide and water.
• The general equation for photosynthesis is: 6CO₂ + 6H₂O + light energy → C₆H₁₂O₆ + 6O₂.
• Glucose Utilization:
• Glucose can be used immediately in cellular respiration to produce ATP, the energy currency of the cell.
• It can also be used to synthesize other organic molecules like cellulose, which is essential for plant cell walls.
• Starch Storage:
• Starch is a polysaccharide composed of glucose units linked together.
• It is stored in plastids such as chloroplasts and amyloplasts within plant cells.
• Energy Metabolism:
• During periods of low photosynthetic activity, stored starch is broken down into glucose to meet the energy demands of the plant.
• This process ensures that the plant's metabolic functions continue uninterrupted.
• Additional Storage Forms:
• In addition to starch, plants may also store energy in the form of lipids (oils) and proteins in seeds.
• These storage forms are crucial for the germination and growth of seedlings.

The correct answer is Mustard.

Key Points

• Mustard is a bisexual flower, meaning it has both male (stamens) and female (pistils) reproductive organs in the same flower.
• Bisexual flowers are also known as hermaphroditic flowers.
• In mustard flowers, the stamens and pistils are arranged in such a way that it facilitates self-pollination and cross-pollination.
• This characteristic of mustard flowers ensures a higher probability of fertilization and seed production.
• Mustard plants belong to the family Brassicaceae, which includes many other important agricultural crops.

Additional Information

• Bisexual Flowers
• Bisexual flowers have both stamens (male part) and pistils (female part) in the same flower.
• They are capable of both self-pollination and cross-pollination.
• Examples include roses, lilies, and tomatoes.
• Unisexual Flowers
• Unisexual flowers have either stamens or pistils, but not both.
• They can be either male (staminate) or female (pistillate).
• Examples include cucumbers, papayas, and watermelons.
• Pollination
• Pollination is the process of transferring pollen from the male part (anther) to the female part (stigma) of a flower.
• It can be mediated by various agents including wind, water, insects, birds, and animals.
• Successful pollination leads to fertilization and the production of seeds.
• Brassicaceae Family
• The Brassicaceae family, also known as the mustard family, includes economically important crops such as cabbage, broccoli, and radishes.
• Members of this family are known for their distinctive four-petaled flowers arranged in a cross shape.
• They are widely cultivated for their nutritional and medicinal values.

The correct answer is 51st.

Key Points

• Justice Sanjiv Khanna took over as the 51st Chief Justice of India on 11 November 2024.
• He succeeded Justice Dhananjaya Y. Chandrachud as the Chief Justice of India.
• The Chief Justice of India is the head of the judiciary in India and the Supreme Court of India.
• Justice Sanjiv Khanna was appointed by the President of India following the recommendation of the collegium of judges.

Additional Information

• Role of Chief Justice of India
• The Chief Justice of India is responsible for the allocation of cases and appointment of constitutional benches.
• The CJI also plays a crucial role in judicial appointments and administrative functions of the court.
• Supreme Court of India
• It is the highest judicial forum and final court of appeal in India.
• It was established on January 28, 1950, under the Constitution of India.
• The Supreme Court comprises the Chief Justice of India and a maximum of 34 judges.
• Judicial Appointments in India
• Judges of the Supreme Court are appointed by the President of India.
• The collegium system, which includes the Chief Justice of India and four senior-most judges, recommends appointments and transfers of judges.
• Appointments are made based on seniority and merit.
• Collegium System
• It is a system of appointment and transfer of judges that has evolved through judgments of the Supreme Court.
• The collegium is headed by the Chief Justice of India and includes the four senior-most judges of the Supreme Court.
• It plays a significant role in maintaining the independence of the judiciary.

The correct answer is Potential energy.

Key Points

• Potential energy is a form of mechanical energy.
• Mechanical energy is the sum of potential energy and kinetic energy in a system.
• Potential energy is the energy possessed by an object due to its position or state.
• Examples of potential energy include gravitational potential energy, elastic potential energy, and chemical potential energy.

Additional Information

• Kinetic Energy:
• Kinetic energy is the energy possessed by an object due to its motion.
• The formula for kinetic energy is KE = 0.5 * m * v^2, where m is mass and v is velocity.
• Both potential and kinetic energy are components of mechanical energy.
• Gravitational Potential Energy:
• It is the energy possessed by an object due to its position in a gravitational field.
• The formula is U = m * g * h, where m is mass, g is the acceleration due to gravity, and h is height.
• Elastic Potential Energy:
• It is the energy stored in elastic materials as the result of their stretching or compressing.
• Common examples include springs and rubber bands.
• Conservation of Mechanical Energy:
• In a closed system with no external forces, mechanical energy remains constant.
• This principle is known as the conservation of mechanical energy.

The correct answer is Gold and silver.

Key Points

• Gold and silver are noble metals and are known for their low reactivity, which allows them to be found in their pure, elemental forms in nature.
• These metals occur in free state because they do not easily form compounds with other elements due to their low reactivity.
• Gold is often found in its native form in quartz veins, alluvial deposits, and other geological environments.
• Silver is also found in its native form, frequently in association with gold, and in various mineral ores such as argentite.

Additional Information

• Native Metals
• Native metals are metals found in their pure, metallic form in nature, rather than combined with other elements as compounds.
• Examples include gold, silver, platinum, and copper.
• Reactivity Series
• The reactivity series is a list of elements ordered by their ability to displace other elements in chemical reactions.
• Gold and silver are at the bottom of the reactivity series, indicating their low reactivity.
• Alluvial Deposits
• Alluvial deposits are sediments deposited by rivers and streams, often containing valuable minerals such as gold and silver.
• These deposits are a common source of native gold and silver.
• Gold Mining
• Gold mining is the process of extracting gold from the earth, typically from hard rock mining, alluvial deposits, or as a by-product of other mining operations.
• Major gold producing countries include China, Australia, and Russia.

The correct answer is Amphibians.

Key Points

• Amphibians, such as frogs, toads, and salamanders, have a three-chambered heart consisting of two atria and one ventricle.
• The three-chambered heart allows for some separation of oxygenated and deoxygenated blood, which is more efficient than a two-chambered heart.
• This heart structure helps amphibians adapt to both aquatic and terrestrial environments.
• Amphibians have a double circulation system, where blood passes through the heart twice during each circulation cycle, improving oxygen delivery to tissues.

Additional Information

• Mammals:
• Mammals have a four-chambered heart, consisting of two atria and two ventricles, which allows for complete separation of oxygenated and deoxygenated blood.
• This separation is essential for maintaining a high metabolic rate and efficient oxygen supply to tissues.
• Birds:
• Birds also possess a four-chambered heart, similar to mammals, facilitating efficient oxygen delivery to support their high-energy demands for flight.
• The four-chambered heart ensures a more effective and faster circulation of blood.
• Fishes:
• Fishes have a two-chambered heart, consisting of one atrium and one ventricle, which pumps blood through a single circulation loop.
• This system is sufficient for their aquatic lifestyle but less efficient compared to the hearts of amphibians, reptiles, birds, and mammals.

The correct answer is Creating casts for supporting fractured bones.

Key Points

• Plaster of Paris (POP) is primarily used to create orthopedic casts for immobilizing fractured bones during the healing process.
• It is favored in medical applications due to its quick-setting properties and ability to conform to the shape of the body part being treated.
• POP is applied as a bandage soaked in water which then hardens to form a sturdy support structure around the injured area.
• Orthopedic casts made from POP are critical in ensuring proper alignment and stabilization of bones to facilitate effective healing.

Additional Information

• Composition of Plaster of Paris
• Plaster of Paris is chemically known as calcium sulfate hemihydrate (CaSO4·½H2O).
• It is produced by heating gypsum (CaSO4·2H2O) to about 150°C to remove water molecules.
• Other Uses of Plaster of Paris
• Besides medical applications, POP is used in art for making sculptures and decorative elements.
• It is also employed in the construction industry for creating false ceilings and coating walls.
• Handling and Safety
• POP should be handled with care, as it can cause skin irritation and respiratory issues if inhaled as dust.
• It is important to use protective gear such as gloves and masks when working with POP.
• Setting and Hardening Process
• When mixed with water, POP undergoes an exothermic reaction, causing it to set and harden quickly.
• The setting time can be adjusted by altering the temperature and the amount of water used.

The correct answer is Leh.

Key Points

• In November 2024, the Indian Space Research Organisation (ISRO) initiated the country's first analogue space mission in Leh.
• The mission aims to simulate life in an interplanetary habitat to prepare for future deep space missions.
• Leh was chosen due to its harsh terrain and extreme weather conditions, which closely mimic the Martian environment.
• This mission is part of ISRO's broader strategy to enhance its capabilities in human spaceflight and interplanetary exploration.
• It is a significant step towards understanding the complexities of living and working in space over extended periods.

Additional Information

• Analogue Space Mission:
• These are simulations conducted on Earth to mimic the conditions astronauts would face in space.
• They help in understanding the physical and psychological challenges of long-duration space missions.
• Human Spaceflight:
• It involves sending humans into space and ensuring their safe return to Earth.
• ISRO's Gaganyaan mission is an example of India's effort in human spaceflight.
• Interplanetary Exploration:
• This refers to the exploration of planets and other celestial bodies within our solar system.
• Missions like Mangalyaan (Mars Orbiter Mission) have marked ISRO's entry into interplanetary exploration.
• ISRO's Future Plans:
• ISRO is working on various projects including Chandrayaan-3 and the Aditya-L1 mission to study the Sun.
• There are plans for more advanced missions to explore outer space and possibly land on other planets.

The correct answer is 4F.

Key Points

• The gravitational force between two bodies is directly proportional to the product of their masses, as per Newton's Law of Universal Gravitation.
• If the mass of one body is increased to four times, the product of the masses also becomes four times.
• The formula used is: F = G × (m₁ × m₂) / r², where F is the gravitational force.
• Since distance (r) and gravitational constant (G) remain unchanged, the force becomes 4F.
• Hence, the new gravitational force becomes four times the original force.

Additional Information

• Newton's Law of Universal Gravitation
• Formulated by Sir Isaac Newton in the 17th century.
• States that every particle attracts every other particle with a force directly proportional to the product of their masses.
• The force is inversely proportional to the square of the distance between their centers.
• Gravitational Constant (G)
• A fundamental physical constant with a value of approximately 6.674 × 10⁻¹¹ N·m²/kg².
• It is the same everywhere in the universe and plays a key role in gravitational calculations.
• Applications of Gravitational Force
• Responsible for planetary orbits, tides, and the structure of the universe.
• Used in satellite launching and calculating planetary motion.

The correct answer is 70th National Film Awards.

Key Points

• The National Film Awards is one of the most prominent film award ceremonies in India, established in 1954.
• The awards aim to encourage the production of films of high aesthetic and technical standards and educational and cultural value.
• The 70th National Film Awards recognize the best of Indian cinema released in the year 2022.
• President Draupadi Murmu conferred these awards in October 2024, honoring outstanding contributions in various categories including Best Feature Film, Best Actor, Best Actress, and others.
• These awards are presented by the Directorate of Film Festivals, an organization set up by the Ministry of Information and Broadcasting, India.

Additional Information

• Directorate of Film Festivals (DFF)
• It was established by the Ministry of Information and Broadcasting, Government of India, to organize national and international film festivals within the country.
• DFF administers the National Film Awards and the International Film Festival of India (IFFI).
• It aims to promote good cinema and facilitate the exchange of ideas and experiences between Indian and foreign filmmakers.
• Categories of National Film Awards
• These awards include Feature Films, Non-Feature Films, and Best Writing on Cinema.
• Feature Film awards comprise several categories such as Best Feature Film, Best Direction, Best Actor, Best Actress, etc.
• Non-Feature Film awards include Best Non-Feature Film, Best Director, and various technical awards.
• Significance of National Film Awards
• They are considered the most prestigious awards in the Indian film industry, often referred to as India's equivalent to the Oscars.
• These awards help in recognizing and encouraging new talent and excellence in Indian cinema.
• The awards also highlight the diversity of Indian cinema, covering films produced in different languages and regions.
• Recent Trends in National Film Awards
• In recent years, there has been a notable increase in the number of regional films being recognized.
• There is also a growing emphasis on films with strong social messages and innovative storytelling.
• Digital and independent filmmakers are increasingly gaining recognition at these awards.

The logic followed here is:

Option 1) FMH

Option 2) RYT

Option 3) JQL

Option 4) MTP

Thus, 'MTP' not follow the same logic.

Hence, the correct answer is "Option 4".

The correct answer is Mission Nishchay.

Key Points

• Punjab police launched Mission Nishchay in collaboration with BSF and VDCs in June 2024.
• The mission aims to gather intelligence on the demand and supply of drugs in border villages.
• This initiative is part of the broader efforts to combat the drug menace in Punjab, particularly in areas close to the India-Pakistan border.
• Mission Nishchay involves active participation from local communities through Village Defence Committees (VDCs).
• Cooperation with the Border Security Force (BSF) is crucial for the successful implementation of this mission.

Additional Information

• Border Security Force (BSF)
• BSF is one of the five Central Armed Police Forces of India, tasked with guarding India's land border during peace time and preventing transnational crime.
• Established on 1 December 1965, BSF is under the administrative control of the Ministry of Home Affairs.
• It plays a critical role in counter-insurgency and counter-terrorism operations.
• BSF personnel are often involved in anti-smuggling operations, including drug interdiction.
• Village Defence Committees (VDCs)
• VDCs are community-based groups formed to assist in maintaining law and order in rural and border areas.
• They provide local intelligence and support security forces in their operations.
• VDC members are usually volunteers from the local population, enhancing community participation in security efforts.
• These committees are instrumental in bridging the gap between security forces and local communities.
• Drug Menace in Punjab
• Punjab has faced significant challenges related to drug abuse, with a high prevalence of opioid addiction among its youth.
• The state borders Pakistan, making it vulnerable to drug trafficking routes.
• Efforts to combat drug abuse include rehabilitation programs, awareness campaigns, and strict law enforcement.
• Government initiatives aim to reduce demand and supply of illegal drugs through comprehensive strategies.
• Drug Trafficking
• Drug trafficking is the illegal trade involving the cultivation, manufacture, distribution, and sale of substances subject to drug prohibition laws.
• It is a global black market economy, often linked with organized crime and terrorism.
• Efforts to combat drug trafficking include international cooperation, stringent regulations, and intelligence-sharing among nations.
• Effective border security and community involvement are critical in curbing this illegal activity.

The correct answer is length.

Key Points

• The apical meristem is a region of actively dividing cells located at the tips of roots and shoots in plants.
• It is responsible for the primary growth, which leads to an increase in the length of the stem and root.
• Primary growth enables plants to extend their reach for sunlight and nutrients.
• The apical meristem gives rise to various specialized tissues such as the epidermis, cortex, and vascular tissues in the plant.

Additional Information

• Meristematic Tissue
• Meristematic tissues are regions of undifferentiated cells in plants that can divide and form new cells.
• They are classified into apical, lateral, and intercalary meristems based on their location and function.
• Lateral Meristem
• Lateral meristems, such as the vascular cambium and cork cambium, contribute to the secondary growth of plants, increasing the girth.
• They are responsible for the thickening of stems and roots.
• Root Cap
• The root cap is a protective structure that covers the tip of the root apical meristem.
• It plays a crucial role in protecting the meristematic cells as the root pushes through the soil.
• Primary and Secondary Growth
• Primary growth is associated with the increase in length of the plant, facilitated by the apical meristem.
• Secondary growth, which involves the increase in girth, is facilitated by the lateral meristem.

The correct answer is Abishek Mukherjee.

Key Points

• Abishek Mukherjee is a well-known cricket writer and historian.
• He has written extensively on the history of cricket, particularly focusing on lesser-known stories and events.
• Mukherjee has contributed to various prominent cricket publications and websites.
• He co-authored the book 'Overthrowing Cricket's Empire: How Every Team Beat England for the First Time' which was released in July 2024.
• The book discusses the historical milestones of different cricket teams defeating England for the first time.

Additional Information

• Cricket Literature
• Cricket literature encompasses a wide range of works including biographies, histories, and statistical analyses.
• Prominent cricket writers include Gideon Haigh, Neville Cardus, and C.L.R. James.
• Books on cricket history often explore the social and cultural impact of the sport.
• The genre has a dedicated following among cricket enthusiasts who seek in-depth knowledge and historical context.
• Historical Matches
• Historical cricket matches are often remembered for their significance in the sport's development.
• First victories against established teams mark important milestones for emerging cricketing nations.
• Such matches are celebrated for showcasing the rise of new talent and strategic advancements.
• These events contribute to the rich tapestry of cricket history and its global evolution.
• Cricket Historians
• Cricket historians play a crucial role in documenting and analyzing the sport's past.
• They often uncover lesser-known stories and provide context to major events and figures.
• Their work helps preserve the heritage of cricket for future generations.
• Notable cricket historians include David Frith and Mihir Bose.

The correct answer is Transpiration.

Key Points

• Transpiration is the process through which plants lose water in the form of water vapour from their aerial parts, primarily through the stomata of leaves.
• This process is crucial for the plant as it helps in the uptake and transport of essential nutrients and minerals from the soil.
• Transpiration also aids in maintaining the plant's temperature by cooling it through the evaporation of water.
• It is estimated that about 99% of the water absorbed by plants is lost through transpiration, highlighting its significance in the water cycle.

Additional Information

• Stomata
• Stomata are small pores found on the surface of leaves and stems that facilitate gas exchange and transpiration.
• Each stoma is surrounded by a pair of guard cells that regulate its opening and closing.
• Water Cycle
• Transpiration is a key component of the water cycle, contributing to the movement of water from the soil to the atmosphere.
• It works in conjunction with evaporation, which is the process of water turning into vapor from surfaces like soil and water bodies.
• Xylem
• Xylem is the tissue responsible for the transport of water and nutrients from the roots to the rest of the plant.
• It plays a crucial role in supporting the plant structure and facilitating transpiration.
• Factors Affecting Transpiration
• Environmental factors such as temperature, humidity, wind, and light intensity can significantly influence the rate of transpiration.
• Plants can regulate their transpiration rate through physiological adjustments like closing stomata during water stress.

The logic followed here is:

Logic: (1st number × 2) + 2 = 2nd number.

X : 96 :: 53 : Y 

For value of X,

X : 96

→ (X × 2) + 2 = 96

→ (X × 2) = 96 - 2

→ X = 94 ÷ 2

→ X = 47.

Now, for value of Y

53 : Y

→ (53 × 2) + 2 

→ 106 + 2

→ 108 = Y

Thus, value of X is 47 and value of Y is 108.

Hence, the correct answer is "Option 4".

The correct answer is Anil Pradhan.

Key Points

• Anil Pradhan from Odisha won the third Rohini Nayyar Prize for his significant contributions to rural development.
• The award recognizes individuals under the age of 40 who have made outstanding contributions to rural development in India.
• Anil Pradhan is known for his innovative approaches in the field of rural education and development.
• He has been instrumental in implementing various educational initiatives aimed at empowering rural youth in Odisha.
• His efforts have led to significant improvements in the quality of education and skill development in rural areas.

Additional Information

• Rohini Nayyar Prize
• The Rohini Nayyar Prize is instituted in memory of Dr. Rohini Nayyar, a renowned economist.
• The prize aims to recognize and reward young individuals who have made significant contributions to rural development in India.
• It is awarded annually to individuals under the age of 40 who have demonstrated exceptional dedication and impact in rural development.
• The prize includes a monetary reward and a citation to honor the recipient's efforts.
• Rural Development in India
• Rural development encompasses a wide range of activities aimed at improving the quality of life and economic well-being of people living in rural areas.
• It includes initiatives in areas such as agriculture, education, healthcare, infrastructure, and employment.
• The government of India, along with various NGOs and private entities, implements numerous programs to promote rural development.
• Key programs include the Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA), National Rural Livelihood Mission (NRLM), and the Pradhan Mantri Awas Yojana (Gramin).

The correct answer is m s^-2.

Key Points

• The SI unit of acceleration is the meter per second squared (m/s²).
• Acceleration is defined as the rate of change of velocity with respect to time.
• In the SI system, it is derived from the base units of length (meter) and time (second).
• This unit is universally used in physics and engineering to quantify acceleration.

Additional Information

• Velocity and Speed
• Velocity is a vector quantity that refers to the rate at which an object changes its position.
• Speed is a scalar quantity that refers to how fast an object is moving regardless of direction.
• Newton's Second Law of Motion
• States that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F=ma).
• This law is fundamental in understanding the relationship between force, mass, and acceleration.
• Uniform and Non-uniform Acceleration
• Uniform acceleration occurs when the velocity of an object changes by an equal amount in every equal time period.
• Non-uniform acceleration occurs when the velocity changes by unequal amounts in equal time periods.
• Applications of Acceleration
• Acceleration is a key concept in various fields such as automotive engineering, aerospace, and biomechanics.
• Understanding acceleration is crucial for designing safety systems in vehicles and optimizing performance in sports.

The least possible venn diagram:

Conclusions:

(I) Some nails are apples → False(as, there is no direction relation between them)

(II) Some horses are rocks → False(as, there is no direction relation between them)

Thus, Neither conclusion (I) nor (II) follows.

Hence, the correct answer "Option 2".

The correct answer is Calcium Carbonate.

Key Points

• Calcium carbonate (CaCO₃) decomposes upon heating to produce calcium oxide (CaO) and carbon dioxide (CO₂).
• The thermal decomposition reaction of calcium carbonate is: CaCO₃ (s) → CaO (s) + CO₂ (g).
• This decomposition occurs at a temperature of about 825°C (1517°F).
• Calcium oxide (CaO), also known as quicklime, is widely used in construction and industrial processes.

Additional Information

• Thermal Decomposition:
• It is a chemical reaction where a compound breaks down into simpler compounds or elements upon heating.
• Thermal decomposition reactions are usually endothermic, meaning they absorb heat.
• Calcium Oxide (CaO):
• Also known as quicklime or burnt lime.
• Used in the manufacture of cement, steel, and paper, and in water treatment.
• Carbon Dioxide (CO₂):
• A colorless, odorless gas that is a byproduct of the respiration of living organisms and the combustion of fossil fuels.
• It is used in the production of carbonated beverages, as a refrigerant, and in fire extinguishers.
• Other Thermal Decomposition Examples:
• Calcium nitrate (Ca(NO₃)₂) decomposes to calcium oxide (CaO), nitrogen dioxide (NO₂), and oxygen (O₂).
• Calcium sulfate (CaSO₄) decomposes to calcium oxide (CaO) and sulfur trioxide (SO₃).

The logic followed here is:

JAIL - ALIJ-LIAJ

ZEAL - ELAZ-LAEZ

Similarly, same logic followed in

Option 2) BORE - OERB - EROB

Hence, the correct answer is "Option 2".

The correct answer is Na.

Key Points

• Sodium (Na) is extracted by electrolysis of molten sodium chloride (NaCl).
• The process is known as the Downs process, where molten sodium chloride is electrolyzed.
• During electrolysis, sodium ions are reduced at the cathode to form sodium metal.
• Sodium is highly reactive and cannot be extracted by simple reduction methods, necessitating the use of electrolysis.
• Electrolysis is crucial for extracting highly reactive metals like sodium from their compounds.

Additional Information

• Electrolysis Process
• Electrolysis involves passing an electric current through a molten or aqueous solution to cause a chemical change.
• It is widely used for extracting metals from their ores and purifying them.
• The process is performed in an electrolytic cell, which consists of two electrodes: an anode and a cathode.
• During electrolysis, cations move towards the cathode to gain electrons (reduction), and anions move towards the anode to lose electrons (oxidation).
• Downs Process
• This process is specifically used for the extraction of sodium metal from molten sodium chloride.
• It involves the use of a carbon anode and an iron cathode in a molten sodium chloride bath.
• Sodium is collected at the cathode, while chlorine gas is produced at the anode.
• Calcium chloride is often added to lower the melting point of sodium chloride in this process.
• Reactivity Series
• The reactivity series is a list of elements ordered by their reactivity.
• Sodium is placed high in the reactivity series, indicating its high reactivity.
• Highly reactive metals like sodium cannot be extracted by simple chemical reduction methods.
• Electrolysis is necessary for extracting these metals from their compounds.
• Applications of Sodium
• Sodium is used in various industrial processes, including the manufacture of sodium compounds and in the reduction of metals.
• It is also used in street lighting and as a heat exchanger in some nuclear reactors.
• Sodium compounds, such as sodium chloride and sodium hydroxide, have numerous applications in industries and households.

The correct answer is India.

Key Points

• India hosted the '8th International Ancient Arts Festival and Symposium' in November 2024.
• This event is a significant cultural festival that showcases ancient arts and traditions from various countries.
• The festival aims to promote cultural exchange and understanding among participating nations.
• Participants include artists, scholars, and enthusiasts from across Asia and beyond, contributing to a rich exchange of knowledge and art forms.
• The event includes performances, exhibitions, workshops, and symposiums on various ancient art forms.

Additional Information

• Ancient Indian Arts
• India has a rich heritage of ancient arts including dance forms like Bharatanatyam, Kathak, and Odissi.
• Ancient Indian art also includes traditional music forms, sculptures, and paintings like Madhubani and Warli.
• These art forms are integral to India's cultural identity and heritage.
• Cultural Festivals
• Such festivals play a crucial role in preserving and promoting traditional art forms.
• They provide a platform for artists to showcase their talents and for audiences to appreciate cultural diversity.
• Cultural festivals often include educational workshops and discussions to foster a deeper understanding of the arts.
• International Participation
• International festivals encourage cross-cultural interactions and collaborations.
• They help in building global networks among artists, scholars, and cultural enthusiasts.
• These events contribute to the global recognition and appreciation of diverse art forms.

The correct answer is opposite to the direction of motion.

Key Points

• When an object is thrown upwards, the force of gravity acts downward, opposite to the direction of the object's motion.
• The force of gravity is a constant force that always acts towards the center of the Earth.
• As the object moves upward, it slows down due to the gravitational pull acting against it.
• Once the object reaches its peak height, gravity causes it to accelerate back downwards.

Additional Information

• Gravity:
• Gravity is a natural phenomenon by which all things with mass or energy are brought towards one another, including objects ranging from atoms and photons to planets and stars.
• On Earth, gravity gives weight to physical objects and causes the ocean tides.
• It is approximately 9.8 m/s² on the surface of Earth.
• Newton's Laws of Motion:
• Newton's First Law states that an object will remain at rest or in uniform motion unless acted upon by an external force.
• Newton's Second Law states that the force acting on an object is equal to the mass of the object times its acceleration (F = ma).
• Newton's Third Law states that for every action, there is an equal and opposite reaction.
• Projectile Motion:
• Projectile motion is a form of motion experienced by an object or particle that is thrown near the Earth's surface and moves along a curved path under the action of gravity only.
• This curved path was shown by Galileo to be a parabola, but may also be more generally any type of conic section.
• Peak Height:
• The peak height in projectile motion is the highest vertical position along the object's trajectory.
• At this point, the vertical component of the velocity is zero.

The correct answer is Plasmodium divides into many daughter cells simultaneously by binary fission..

Key Points

• Plasmodium, the causative agent of malaria, primarily reproduces through a process called schizogony, not binary fission.
• In schizogony, a single cell divides to form multiple daughter cells, but this is distinct from the process of binary fission.
• Binary fission involves the division of a single organism into two parts, each with a copy of the original DNA, which is not the case in Plasmodium.
• Plasmodium undergoes multiple fission, forming numerous daughter cells at once, which is a characteristic of its asexual reproduction cycle in the human liver and red blood cells.

Additional Information

• Amoeba Reproduction
• Amoeba reproduces by binary fission, where the cell splits into two equal halves, and this can occur in any plane.
• Each daughter cell is a clone of the parent cell, possessing the same genetic material.
• Yeast Reproduction
• Yeast reproduces asexually by budding, where a small bud forms on the parent cell, grows, and eventually separates to become a new individual.
• Leishmania Reproduction
• Leishmania reproduces by binary fission, which occurs in a specific orientation along the longitudinal axis of the cell.
• This process ensures that each daughter cell receives the necessary cellular components to survive and function.
• Plasmodium Life Cycle
• Plasmodium has a complex life cycle involving both asexual (schizogony) and sexual (sporogony) reproduction stages.
• In humans, the asexual stage involves schizogony in liver cells and red blood cells, producing merozoites that infect new cells.
• The sexual stage occurs in the mosquito vector, leading to the formation of sporozoites, which are transmitted to humans during a mosquito bite.

Given that: 

After replacing the symbols with their meanings in each option.

Option 1) 96 C 12 B 2 D (42 A 6) D 3 C 20 

96 + 12 × 2 - (42 ÷ 6) - 3 + 20

→ 96 + 12 × 2 - (42 ÷ 6) - 3 + 20

→ 96 + 12 × 2 - 7 - 3 + 20

→ 96 + 24 - 7 - 3 + 20

→ 120 - 10 + 20

→ 130 ≠ 113

Option 2) 96 C 12 A 2 D (42 A 6) A 3 D 20  

96 + 12 ÷ 2 - (42 ÷ 6) ÷ 3 - 20

→ 96 + 12 ÷ 2 - (42 ÷ 6) ÷ 3 - 20

→ 96 + 6 - 7 ÷ 3 - 20

→ 96 + 6 - 2.33 - 20

→ 79.63 ≠ 113

Option 3) 96 D 12 A 2 C (42 B 6) A 3 C 20 

96 - 12 ÷ 2 + (42 × 6) ÷ 3 + 20

→ 96 - 12 ÷ 2 + (42 × 6) ÷ 3 + 20

→ 96 - 6 + 252 ÷ 3 + 20

→ 96 - 6 + 84 + 20

→ 194 ≠ 113

Option 4) 96 D 12 B 2 C(42 A 6) B 3 C 20  

96 - 12 × 2 + (42 ÷ 6) × 3 + 20

→ 96 - 12 × 2 + (42 ÷ 6) × 3 + 20

→ 96 - 12 × 2 + 7 × 3 + 20

→ 96 - 24 + 21 + 20

→ 113 = 113

Hence, the correct answer is "Option 4".

The correct answer is Virtual and erect.

Key Points

• When an object is placed between the pole and the focus point of a concave mirror, the image formed is virtual and erect.
• The image is formed on the same side of the mirror as the object.
• The image is larger than the object (magnified).
• The virtual image cannot be projected onto a screen as it is formed by the apparent divergence of rays.

Additional Information

• Concave Mirror:
• A concave mirror is a spherical mirror that curves inward, resembling a portion of the interior of a sphere.
• It is also known as a converging mirror because it can converge light rays to a point.
• Focus Point (F):
• The point on the principal axis of a concave mirror where light rays parallel to the principal axis converge after reflection.
• The distance between the focus point and the mirror's surface is called the focal length.
• Real Image:
• An image formed by actual convergence of light rays that can be projected on a screen.
• Real images are always inverted in concave mirrors.
• Virtual Image:
• An image formed by the apparent divergence of light rays from a point.
• Virtual images are always erect and cannot be projected onto a screen.

Given word: FRIENDLY 

1. Each vowel is changed to the letter immediately preceding in the English alphabetical order.

2. Each consonant is changed to the letter immediately following in the English alphabetical series.

Thus, there is no letter will appear twice in the group of letters thus formed.

Hence, the correct answer is "Option 3".

Given code language:

As, 'in' is common in both the code language.

Thus, code for 'in' is 'ws'

Hence, the correct answer is "Option 4".

Shortcut Trick

Directly apply the Empirical Relation: 3 × Median = Mode + 2 × Mean.

3 × Median = 60 + 2(42)

3 × Median = 60 + 84 = 144

Median = 144 ÷ 3 = 48

∴ The correct answer is 48.

Alternate Method

Given:

Mean = 42

Mode = 60

Formula Used:

Mode = 3 × Median − 2 × Mean

Calculations:

⇒ 60 = 3 × Median − 2 × 42

⇒ 60 = 3 × Median − 84

⇒ 3 × Median = 60 + 84

⇒ 3 × Median = 144

⇒ Median = 144 ÷ 3

⇒ Median = 48

∴ The correct answer is 48.

Additional Information

Empirical Relationship

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

Symmetric Distribution

In a perfectly symmetrical distribution, the Mean, Median, and Mode all coincide at the same point (Mean = Median = Mode).

Types of Skewness

In a positively skewed distribution, Mean > Median > Mode. In a negatively skewed distribution, Mean < Median < Mode.

The least possible venn diagram:

Conclusions:

(I) Some colleges are not schools → False (As, All schools are colleges,  then all school are colleges is possibility but not definite)

(II) Some schools may be universities → False (As, No college is a university and All schools are colleges then it cannot be possible)

Thus, Neither conclusion I nor II follows.

Hence, the correct answer is "Option 2".

Shortcut Trick

Ratio of radius (r) to height (h) = 3 : 1. Let r = 3x and h = x.

Volume = πr²h ⇒ (22/7) × (3x)² × x = 9702.

⇒ (22/7) × 9x³ = 9702 ⇒ x³ = (9702 × 7) ÷ (22 × 9) = 343 ⇒ x = 7.

Radius r = 21 cm, Height h = 7 cm.

Curved Surface Area = 2πrh = 2 × (22/7) × 21 × 7 = 924 cm².

∴ The correct answer is 924 cm².

Alternate Method

Given: Ratio r : h = 3 : 1, Volume (V) = 9702 cm³.

Formula: Volume of Cylinder = πr²h; Curved Surface Area (CSA) = 2πrh.

⇒ Let r = 3x and h = x.

⇒ (22/7) × (3x)² × x = 9702

⇒ (22/7) × 9x² × x = 9702

⇒ x³ = (9702 × 7) ÷ (22 × 9) = 343

⇒ x = √343 (cube root) = 7

⇒ r = 3 × 7 = 21 cm and h = 7 cm

⇒ CSA = 2 × (22/7) × 21 × 7

⇒ CSA = 2 × 22 × 21 = 924 cm²

∴ The correct answer is 924 cm².

Additional Information

Total Surface Area (TSA) of Cylinder

The total surface area includes the curved surface and the two circular bases: TSA = 2πr(h + r).

Divisibility Shortcut

Since the formula for CSA (2πrh) contains π, the answer must be a multiple of 11. In many exams, only one option satisfies this, helping to identify 924 cm² quickly.

Shortcut Trick

Net efficiency = Efficiency of filling pipe − Efficiency of emptying pipe.

LCM of 12 and 18 is 36 units (Total Capacity).

Filling pipe efficiency = 36 ÷ 12 = 3; Emptying pipe efficiency = 36 ÷ 18 = 2.

Net efficiency = 3 − 2 = 1 unit/hour.

Time to fill 1/3^rd tank = (1/3 × 36) ÷ 1 = 12 hours.

∴ The correct answer is 12 hours.

Alternate Method

Given: Filling time = 12 hours, Emptying time = 18 hours.

Formula Used: Total Work = Time × Efficiency

⇒ Combined efficiency of both pipes = 3 + (−2) = 1 unit/hour.

⇒ Total capacity of the tank = 36 units.

⇒ Target volume to be filled = 1/3 × Total capacity = 1/3 × 36 = 12 units.

⇒ Time taken = Target volume ÷ Combined efficiency

⇒ Time taken = 12 ÷ 1 = 12 hours.

∴ The correct answer is 12 hours.

Additional Information

Inlet and Outlet Pipes

Inlet pipes add water (positive efficiency), while outlet pipes remove water (negative efficiency). The net work done per hour is the algebraic sum of their efficiencies.

Filling and Emptying Formula

If pipe A fills in x hours and pipe B empties in y hours (y > x), net time to fill the tank is (x × y) ÷ (y − x).

Partial Filling

To find time for a fraction 'k' of the tank, multiply the total time for a full tank by the fraction 'k'.

The correct answer is New Delhi.

Key Points

• The 8th India Water Week 2024 was held in New Delhi, the capital city of India.
• India Water Week is a biennial event organized by the Ministry of Jal Shakti, Government of India.
• The event focuses on the water-related issues and aims to promote sustainable water management practices.
• The conference brings together experts, policymakers, and stakeholders from around the globe to discuss and deliberate on water conservation and management strategies.
• The theme for the 2024 event was "Water Security for Sustainable Development and Equity".

Additional Information

• Ministry of Jal Shakti
• The Ministry of Jal Shakti was formed in May 2019 by merging the Ministry of Water Resources, River Development & Ganga Rejuvenation and the Ministry of Drinking Water and Sanitation.
• It focuses on the management of water resources and sanitation across the country.
• Key initiatives include the Jal Jeevan Mission and the Namami Gange Programme.
• Jal Jeevan Mission
• Launched in 2019, it aims to provide safe and adequate drinking water through individual household tap connections by 2024 to all rural households.
• The mission emphasizes community involvement and sustainable water management.
• Namami Gange Programme
• It is an integrated conservation mission, approved as a 'Flagship Programme' by the Union Government in June 2014.
• The objective is to clean and rejuvenate the Ganga River.
• The programme involves various initiatives such as sewage treatment, river surface cleaning, and afforestation.
• Water Conservation Techniques
• Rainwater Harvesting: Collecting and storing rainwater for reuse before it reaches the aquifer.
• Drip Irrigation: An efficient irrigation method that saves water by allowing water to drip slowly to the roots of plants.
• Reuse and Recycling: Treating wastewater to make it usable again for various purposes.

The correct answer is Only (i).

Key Points

• Non-biodegradable substances do not break down by biological processes and can persist in the environment for a long time.
• These substances include plastics, metals, and chemicals that can be harmful to various components of the ecosystem, including plants, animals, and humans.
• Harmful effects include pollution, toxicity, and disruption of natural processes, which can lead to long-term environmental damage.
• Since non-biodegradable substances do not decompose, they accumulate and can cause significant ecological imbalances.

Additional Information

• Biodegradable Substances
• These are organic substances that can be broken down by natural processes involving microorganisms like bacteria and fungi.
• Examples include food waste, paper, and natural fibers.
• They decompose and return nutrients to the environment, maintaining ecological balance.
• Pollution
• Pollution is the introduction of harmful substances or products into the environment.
• It can be categorized into air pollution, water pollution, soil pollution, and noise pollution.
• Waste Management
• Waste management involves the collection, transportation, and disposal or recycling of waste.
• Proper waste management practices help reduce the impact of non-biodegradable substances on the environment.
• Environmental Protection
• Environmental protection involves policies and practices aimed at preserving the natural environment against degradation.
• It includes initiatives like reducing plastic use, recycling, and promoting sustainable practices.

The correct answer is They are very large in size..

Key Points

• Particles of matter are extremely small and are beyond the resolution of a standard microscope.
• They are in a state of continuous motion due to their kinetic energy, which varies with temperature.
• There is always space between particles of matter, which is evident from the diffusion of gases and mixing of liquids.
• Particles of matter attract each other with forces that vary depending on the type of matter.

Additional Information

• Brownian Motion:
• It is the random movement of particles suspended in a fluid, resulting from their collision with quick atoms or molecules in the gas or liquid.
• This phenomenon supports the theory that particles are in continuous motion.
• Diffusion:
• It is the process by which particles spread from an area of high concentration to an area of low concentration.
• Diffusion demonstrates that particles have space between them and are constantly moving.
• Intermolecular Forces:
• These are forces of attraction or repulsion which act between neighboring particles (atoms, molecules, or ions).
• Examples include hydrogen bonds, Van der Waals forces, and ionic bonds.
• Kinetic Theory of Matter:
• This theory states that matter is composed of a large number of small particles that are in constant motion.
• The temperature of a substance is a measure of the average kinetic energy of its particles.

The correct answer is Kala-azar.

Key Points

• Kala-azar, also known as visceral leishmaniasis, is caused by the protozoan parasite Leishmania donovani.
• The disease is transmitted to humans through the bite of infected female phlebotomine sandflies.
• Symptoms of Kala-azar include prolonged fever, weight loss, enlargement of the spleen and liver, and anemia.
• It primarily affects people in tropical and subtropical regions, including countries like India, Nepal, Bangladesh, Brazil, and Sudan.
• Without treatment, Kala-azar can be fatal, but it is treatable with antileishmanial drugs such as Amphotericin B and Miltefosine.

Additional Information

• Leishmaniasis
• Leishmaniasis is a disease caused by infection with Leishmania parasites, which are spread by the bite of infected sandflies.
• There are three main forms of leishmaniasis: visceral (Kala-azar), cutaneous, and mucocutaneous.
• Cutaneous leishmaniasis causes skin sores, while mucocutaneous leishmaniasis can lead to ulcers in the mouth, nose, and throat.
• Phlebotomine Sandflies
• These are the vectors responsible for transmitting Leishmania parasites to humans.
• They are tiny, about one-third the size of mosquitoes, and are typically active during dusk and dawn.
• Diagnosis and Treatment
• Diagnosis of Kala-azar often involves serological tests, bone marrow or spleen aspiration, and PCR testing.
• Treatment includes antileishmanial medications such as Amphotericin B, Miltefosine, and Sodium Stibogluconate.
• Prevention
• Preventive measures include vector control through insecticide spraying, use of bed nets, and reducing exposure to sandfly bites.
• Education and awareness campaigns are crucial in endemic areas to prevent the spread of the disease.

Shortcut Trick

For a sphere circumscribed by a cylinder, the height of the cylinder h = 2r and the radius is the same r.

Volume ratio = (4/3)πr³ : πr²(2r)

Volume ratio = (4/3) : 2 = 4 : 6 = 2 : 3.

∴ The correct answer is 2 : 3.

Alternate Method

Given:

A sphere is perfectly enclosed (circumscribed) by a right circular cylinder.

Radius of sphere = r

Radius of cylinder = r

Height of cylinder (h) = Diameter of sphere = 2r

Formula Used:

Volume of Sphere (V_s) = (4/3)πr³

Volume of Cylinder (V_c) = πr²h

Calculations:

⇒ V_s : V_c = [(4/3)πr³] : [πr² × (2r)]

⇒ V_s : V_c = [(4/3)πr³] : [2πr³]

⇒ Ratio = (4/3) : 2

⇒ Ratio = 4 : 6

⇒ Ratio = 2 : 3

∴ The correct answer is 2 : 3.

Additional Information

Archimedes' Discovery

Archimedes proved that both the volume and surface area of a sphere are 2/3 of the circumscribing cylinder.

Surface Area Ratio

The ratio of the surface area of a sphere to the total surface area of a circumscribing cylinder is 4πr² : 6πr² = 2 : 3.

Curved Surface Area Ratio

The surface area of the sphere is exactly equal to the curved surface area of the cylinder (4πr² : 2πr(2r) = 1 : 1).