RRB Technician Grade III Official Paper (Held On: 28 Dec, 2024 Shift 1) (Previous Year Paper)

The correct answer is Gas to Liquid: Sublimation.

Key Points

• Sublimation is the process where a substance transitions directly from a solid to a gas without passing through the liquid phase.
• The correct term for the transition from gas to liquid is condensation.
• Deposition is the process where a gas turns directly into a solid without passing through the liquid state.
• Evaporation refers to the process where a liquid changes into a gas, typically at a temperature below its boiling point.

Additional Information

• Condensation
• Condensation is the process by which water vapor in the air is changed into liquid water. It is crucial for the water cycle as it is responsible for cloud formation.
• Condensation occurs when the temperature of the vapor decreases to its dew point or when the air becomes saturated with vapor.
• This process releases latent heat, which can affect local weather conditions.
• Freezing and Melting
• Freezing is the process where a liquid turns into a solid when its temperature is lowered below its freezing point.
• Melting is the transition from solid to liquid when a substance is heated above its melting point.
• Both processes are essential for understanding phase transitions in materials.
• Boiling
• Boiling is the rapid vaporization of a liquid, which occurs when a liquid is heated to its boiling point, the temperature at which the vapor pressure of the liquid equals the pressure surrounding the liquid.
• During boiling, bubbles of vapor form within the liquid and rise to the surface to escape into the air.

The correct answer is Freezing point.

Key Points

• The freezing point is the temperature at which a liquid turns into a solid.
• During the freezing process, the molecules of the liquid lose energy and move closer together to form a solid structure.
• For water, the freezing point is 0°C (32°F) under normal atmospheric pressure.
• The freezing point can be affected by pressure and the presence of other substances (impurities) in the liquid.

Additional Information

• Melting Point
• The melting point is the temperature at which a solid becomes a liquid.
• It is the same temperature as the freezing point but in the opposite direction of phase change.
• For pure substances, the melting point is a precise and specific temperature.
• Condensation Point
• The condensation point is the temperature at which a gas turns into a liquid.
• This phase change occurs when the gas loses energy and the molecules come closer together.
• The condensation point is the same as the boiling point but in the reverse phase change.
• Boiling Point
• The boiling point is the temperature at which a liquid turns into a gas.
• At this temperature, the vapor pressure of the liquid equals the atmospheric pressure surrounding the liquid.
• For water, the boiling point is 100°C (212°F) at standard atmospheric pressure.
• Factors Affecting Freezing Point
• Pressure: Increased pressure generally raises the freezing point.
• Impurities: The presence of impurities, such as salt in water, lowers the freezing point, a phenomenon known as freezing point depression.
• Pure substances have a specific and sharp freezing point, while mixtures freeze over a range of temperatures.

Shortcut Trick

Price Ratio (Original : New) = 100 : 80 = 5 : 4

Quantity Ratio (Original : New) = 4 : 5 (Inverse of Price ratio)

Difference in Quantity = 5 − 4 = 1 unit → 10 kg

Original Quantity = 4 units × 10 = 40 kg

Original Price = Total Expenditure ÷ Original Quantity = 100 ÷ 40 = ₹2.50

∴ The correct answer is ₹2.50.

Alternate Method

Given:

Total Expenditure = ₹100

Reduction in Price = 20%

Extra Rice purchased = 10 kg

Formula Used:

Reduced Price = (Expenditure × % Reduction) ÷ (Extra Quantity × 100)

Original Price = (Reduced Price × 100) ÷ (100 − % Reduction)

⇒ Reduced Price = (100 × 20) ÷ (10 × 100)

⇒ Reduced Price = 2000 ÷ 1000 = ₹2 per kg

⇒ Original Price = (2 × 100) ÷ (100 − 20)

⇒ Original Price = 200 ÷ 80

⇒ Original Price = ₹2.50 per kg

∴ The correct answer is ₹2.50.

Additional Information

Constant Expenditure Rule

If the price of a commodity decreases by r%, the increase in consumption so as not to decrease the expenditure is [r / (100 − r)] × 100%.

Price and Consumption Relationship

When the total expenditure remains constant, the Price is inversely proportional to the Consumption (Quantity). If Price ratio is x : y, then Quantity ratio is y : x.

Direct Formula for Original Price

Original Price = (Expenditure × % Change) ÷ [Extra Quantity × (100 ± % Change)]. Use − for decrease and + for increase.

The correct answer is Bryophyllum.

Key Points

• Bryophyllum is a plant known for its ability to reproduce asexually through vegetative propagation.
• The buds produced in the notches along the leaf margins of Bryophyllum can fall on the soil and develop into new plants.
• This method of reproduction allows Bryophyllum to spread efficiently and colonize new areas.
• Each bud can grow into a complete plant, which has the same genetic makeup as the parent plant.
• This unique characteristic makes Bryophyllum an interesting subject of study in plant biology and horticulture.

Additional Information

• Vegetative Propagation
• It is a form of asexual reproduction in plants where new plants grow from parts of the parent plant such as leaves, stems, or roots.
• This method is commonly used in horticulture to propagate plants with desirable traits.
• Examples of vegetative propagation include tubers in potatoes, runners in strawberries, and leaf buds in Bryophyllum.
• Advantages of Asexual Reproduction in Plants
• It allows for rapid multiplication of plants.
• Plants produced are genetically identical to the parent, ensuring uniformity of traits.
• It is a reliable method for reproducing plants that do not produce viable seeds.
• Disadvantages of Asexual Reproduction
• Lack of genetic diversity makes plants more susceptible to diseases and adverse environmental conditions.
• Over time, asexual reproduction can lead to the accumulation of genetic mutations.
• Bryophyllum in Traditional Medicine
• Bryophyllum leaves are used in traditional medicine for their anti-inflammatory and wound-healing properties.
• Extracts from Bryophyllum are believed to have antimicrobial activity and are used in treating infections.

The correct answer is 'A' is correct and 'B' is incorrect..

Key Points

• In a parallel circuit, the potential difference (voltage) across each resistor is the same.
• This is because all the resistors are connected directly across the same two points.
• The current flowing through each resistor in a parallel circuit is different, depending on the resistance of each resistor.
• Ohm's Law (V = IR) applies individually to each resistor in the parallel network.
• Therefore, statement 'A' is correct and statement 'B' is incorrect.

Additional Information

• Parallel Circuit
• In a parallel circuit, components are connected across common points or junctions, providing multiple paths for the current.
• Voltage is the same across each component in the parallel circuit.
• If one component fails, the overall circuit is not broken and current can still flow through other paths.
• Current in Parallel Circuits
• The total current flowing in the circuit is the sum of the currents through each parallel branch.
• The current through each resistor is inversely proportional to its resistance.
• The effective resistance in a parallel circuit is always less than the smallest resistance in the circuit.
• Ohm's Law
• Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
• The formula is represented as V = IR, where V is voltage, I is current, and R is resistance.
• This law is fundamental in analyzing electrical circuits.
• Resistors in Parallel
• Resistors in parallel have the same voltage across them but different currents.
• The equivalent resistance (R_eq) of resistors in parallel is given by the reciprocal of the sum of the reciprocals of the individual resistances: 1/R_eq = 1/R1 + 1/R2 + ...
• This configuration is used to achieve a desired resistance value that is lower than that of the individual resistances.

Shortcut Trick Ratio of Selling Prices is equivalent to the ratio of (100 − Loss%) to (100 + Gain%). SP1 : SP2 = (100 − 30) : (100 + 5) = 70 : 105. Simplified ratio = 2 : 3. Given 2 units = Rs. 1,148, then 1 unit = 1,148 ÷ 2 = Rs. 574. Required SP (3 units) = 574 × 3 = Rs. 1,722. ∴ The correct answer is Rs. 1,722.

Alternate Method Given: First Selling Price (SP1) = Rs. 1,148, Loss = 30%, Target Gain = 5%. Formulas: CP = SP × 100 ÷ (100 − Loss%) | SP = CP × (100 + Gain%) ÷ 100

⇒ Step 1: Find Cost Price (CP) of the blanket. ⇒ CP = 1,148 × 100 ÷ (100 − 30) = 1,148 × 100 ÷ 70 = 16.4 × 100 = Rs. 1,640. ⇒ Step 2: Find the New Selling Price (SP2) for 5% gain. ⇒ SP2 = 1,640 × (100 + 5) ÷ 100 = 1,640 × 1.05 = Rs. 1,722. ∴ The correct answer is Rs. 1,722.

Additional Information Cost Price vs Selling Price If SP > CP, it is a profit; if SP < CP, it is a loss. CP is always considered 100% for base calculations. Direct Multiplication Factor To find a new price directly: New SP = Old SP × (Required Percentage ÷ Given Percentage). Here: 1148 × (105 ÷ 70) = 1722.

The correct answer is evaporation.

Key Points

• Evaporation is the process by which water changes from a liquid to a gas or vapor at temperatures below its boiling point.
• This process occurs at the surface of the liquid where molecules with sufficient energy escape into the air.
• Evaporation is a critical component of the water cycle, contributing to the formation of clouds and precipitation.
• Factors affecting evaporation include temperature, surface area, air movement, and humidity.

Additional Information

• Sublimation
• Sublimation is the transition of a substance directly from the solid to the gas phase without passing through the liquid phase.
• Common examples include dry ice (solid carbon dioxide) and mothballs (naphthalene).
• Deposition
• Deposition is the direct solidification of a vapor by cooling; the reverse of sublimation.
• An example is the formation of frost on cold surfaces from water vapor in the air.
• Fusion
• Fusion is the process of a substance changing from a solid to a liquid state, also known as melting.
• It occurs when a substance absorbs heat and reaches its melting point.
• Boiling
• Boiling is the rapid vaporization of a liquid, which occurs when it is heated to its boiling point.
• At this temperature, the vapor pressure of the liquid equals the pressure exerted on the liquid by the surrounding environment.

According to the given information,

Thus, according to the given codes the code 'ti' is for the word 'chess'.

Hence, the correct answer is "Option 4".

The logic followed here is:

JMHK is related to NQLO

And,

MPKN is related to QTOR

Similarly,

PSNQ is related to

Hence, "Option 4" is the correct answer.

Given: B, C, D, E, F, G and K are sitting around a circular table, facing the centre.

1) Only two people sit between E and F when counted from the left of F.

2) C sits second to the left of E.

3) C sits to the immediate right of K.

4) G sits third to the left of K.

5. B is not an immediate neighbour of G.

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

Thus, according to the final arrangement, D sits third to the right of B.

Hence, "Option 1" is the correct answer.

Shortcut Trick

For a number to be divisible by 11, the difference between the sum of digits at odd places and the sum of digits at even places must be 0 or a multiple of 11.

Sum of digits at odd places: 8 + 3 + 5 + 6 = 22

Sum of digits at even places: 6 + 2 + k = 8 + k

Difference: 22 − (8 + k) = 14 − k

For divisibility by 11, 14 − k = 11 ⇒ k = 3.

∴ The correct answer is 3.

Alternate Method

Given: The 7-digit number is 86325k6.

Formula Used: Divisibility rule of 11 states that the difference between the sum of digits at odd positions and even positions must be either 0 or divisible by 11.

Let the positions of the digits from left to right be:

1^st digit (odd position) = 8

2^nd digit (even position) = 6

3^rd digit (odd position) = 3

4^th digit (even position) = 2

5^th digit (odd position) = 5

6^th digit (even position) = k

7^th digit (odd position) = 6

⇒ Sum of digits at odd positions (S_odd) = 8 + 3 + 5 + 6 = 22

⇒ Sum of digits at even positions (S_even) = 6 + 2 + k = 8 + k

⇒ Difference (D) = S_odd − S_even = 22 − (8 + k) = 14 − k

⇒ Since k is a single digit (0 ≤ k ≤ 9), the only value of k that makes 14 − k a multiple of 11 (which is 11) is:

⇒ 14 − k = 11

⇒ k = 14 − 11

⇒ k = 3

∴ The correct answer is 3.

Additional Information

Divisibility Rule of 11

A number is completely divisible by 11 if the difference of the alternating sum of its digits is a multiple of 11 (including 0, 11, 22, etc.).

Single Digit Constraint

Since k represents a single digit in the place value of a number, its value must lie in the integer range [0, 9].

Shortcut Trick

Expression is of the form (x/y) + (y/x) where x = cos 50° and y = 1 + sin 50°.

Sum = (x² + y²) / (xy) = (cos² 50° + (1 + sin 50°)²) / (cos 50°(1 + sin 50°)).

Numerator = cos² 50° + 1 + sin² 50° + 2 sin 50° = 1 + 1 + 2 sin 50° = 2(1 + sin 50°).

Value = 2(1 + sin 50°) / [cos 50°(1 + sin 50°)] = 2 / cos 50° = 2 sec 50°.

∴ The correct answer is 2 sec 50°.

Alternate Method

Given: [cos 50° / (1 + sin 50°)] + [(1 + sin 50°) / cos 50°]

Formula Used: sin²θ + cos²θ = 1 and secθ = 1/cosθ

⇒ Take LCM of denominators: cos 50°(1 + sin 50°)

⇒ Numerator becomes: (cos 50° × cos 50°) + (1 + sin 50°) × (1 + sin 50°)

⇒ cos² 50° + (1 + sin² 50° + 2 sin 50°)

⇒ (cos² 50° + sin² 50°) + 1 + 2 sin 50°

⇒ 1 + 1 + 2 sin 50° = 2 + 2 sin 50° = 2(1 + sin 50°)

⇒ Expression = [2(1 + sin 50°)] / [cos 50°(1 + sin 50°)]

⇒ Expression = 2 / cos 50°

⇒ Expression = 2 sec 50°

∴ The correct answer is 2 sec 50°.

Additional Information

Trigonometric Identities

Fundamental identity: sin²θ + cos²θ = 1. Also, 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ.

Reciprocal Relations

secθ = 1/cosθ, cosecθ = 1/sinθ, and cotθ = 1/tanθ.

Complementary Angles

sin(90° − θ) = cosθ and cos(90° − θ) = sinθ.

The correct answer is International Institute of Sports Management (IISM).

Key Points

• The International Institute of Sports Management (IISM) is the first institution in India to launch a book on sports psychology.
• The book aims to provide insights into the mental aspects of sports and athletic performance.
• It covers various psychological techniques and strategies that athletes can use to enhance their performance.
• The book is targeted at athletes, coaches, sports managers, and students pursuing sports management courses.

Additional Information

• Sports Psychology:
• Sports psychology is the study of how psychological factors affect performance and how participation in sports and exercise affect psychological and physical factors.
• It involves the application of psychological principles to improve athletic performance and well-being.
• Common topics include motivation, performance anxiety, and the psychological benefits of sports.
• Importance of Mental Training in Sports:
• Mental training helps athletes to stay focused, manage anxiety, and maintain a positive attitude.
• Techniques such as visualization, goal setting, and self-talk are often used.
• Mental resilience can be a determining factor in high-pressure situations and competitions.
• Role of Sports Psychologists:
• Sports psychologists work with athletes to enhance performance, cope with pressure, and recover from injuries.
• They may provide individual counseling and mental skills training.
• They also work with coaches and teams to improve communication and team dynamics.
• Applications Beyond Sports:
• The principles of sports psychology can be applied to other areas of life, such as business and education.
• Skills like goal setting, focus, and resilience are valuable in many fields.
• Sports psychology techniques can also be used to improve overall mental health and well-being.

The correct answer is Leishmania.

Key Points

• Leishmania is a genus of protozoan parasites that has a whip-like structure called a flagellum at one end of the cell.
• These flagella are crucial for the motility of the organism, aiding in its movement and infection processes.
• Binary fission in Leishmania occurs in a specific orientation, ensuring that the division is coordinated with the position of the flagellum.
• The presence of flagella and orientation-specific binary fission are key characteristics that distinguish Leishmania from other unicellular organisms.

Additional Information

• Flagellum
• A flagellum is a long, whip-like structure that protrudes from the cell body and is used for locomotion and sensory functions.
• In many protozoa, flagella are vital for movement, allowing them to swim through liquid environments.
• Binary Fission
• Binary fission is an asexual mode of reproduction common among unicellular organisms.
• During binary fission, the parent cell divides into two equal-sized daughter cells.
• Leishmaniasis
• Leishmaniasis is a disease caused by infection with Leishmania parasites, which are spread by the bite of infected sandflies.
• It can cause skin sores, fever, and damage to the spleen and liver.
• Protozoa
• Protozoa are a diverse group of unicellular eukaryotic organisms.
• They can be free-living or parasitic and are found in various aquatic environments and soil.

Shortcut Trick

Ratio of equal sides to base = 3 : 3 : 4.

Total units for perimeter = 3 + 3 + 4 = 10 units.

10 units = 20 cm ⇒ 1 unit = 2 cm.

Sides are 6 cm, 6 cm and 8 cm. Base = 8 cm, Half-base = 4 cm.

Altitude = √(6² − 4²) = √(36 − 16) = √20 = 2√5 cm.

∴ The correct answer is 2√5 cm.

Alternate Method

Given: Perimeter = 20 cm, Ratio of equal side to base = 3 : 4.

Formula Used: Perimeter = sum of all sides; Altitude (h) of isosceles triangle = √(side² − (base/2)²).

Let the equal sides be 3x and the base be 4x.

⇒ 3x + 3x + 4x = 20

⇒ 10x = 20

⇒ x = 2 cm

⇒ Equal sides = 3 × 2 = 6 cm

⇒ Base = 4 × 2 = 8 cm

⇒ Altitude AD bisects the base BC, so BD = 8/2 = 4 cm.

⇒ In right ▵ABD: AD² + BD² = AB²

⇒ h² + 4² = 6²

⇒ h² = 36 − 16 = 20

⇒ h = √20 = 2√5 cm

∴ The correct answer is 2√5 cm.

Additional Information

Isosceles Triangle Properties

Two sides are equal, and the angles opposite to these sides are also equal. The altitude to the base bisects the base at a 90° angle.

Area of Isosceles Triangle

Area = (1/2) × base × altitude = (b/4) × √(4a² − b²), where 'a' is the equal side and 'b' is the base.

Pythagoras Theorem

In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a² + b² = c².

The correct answer is Maharatna CPSE.

Key Points

• Hindustan Aeronautics Limited (HAL) has been upgraded to the status of Maharatna Central Public Sector Enterprise (CPSE) by the Ministry of Finance in 2024.
• The Maharatna status is one of the highest recognitions given to Central Public Sector Enterprises (CPSEs) in India.
• This status provides HAL with greater autonomy and financial powers, enabling it to undertake larger investments and enhance its operational efficiency.
• HAL is a premier aerospace and defense company in India, playing a crucial role in the design, manufacture, and maintenance of aircraft and helicopters.
• With Maharatna status, HAL can now invest up to 15% of its net worth in a single project without government approval.

Additional Information

• Maharatna CPSE
• The Maharatna status is granted to select CPSEs to enhance their financial and operational autonomy.
• To qualify for Maharatna status, a CPSE must have a minimum annual turnover of Rs. 25,000 crore, net worth of Rs. 15,000 crore, and net profit of Rs. 5,000 crore for three consecutive years.
• Maharatna companies can form joint ventures and subsidiaries, and enter into technology collaborations without government approval.
• Navratna CPSE
• Navratna status is a recognition given to CPSEs that show operational efficiency and profitability.
• Navratna companies have greater operational autonomy compared to Mini Ratna companies, but less than Maharatna companies.
• Navratna companies can invest up to Rs. 1,000 crore without government approval.
• Mini Ratna CPSE
• Mini Ratna status is granted to relatively smaller CPSEs that have shown consistent profitability and operational efficiency.
• There are two categories of Mini Ratna: Category I and Category II, with Category I having higher financial autonomy.
• Mini Ratna companies can invest up to Rs. 500 crore or an amount equal to their net worth, whichever is lower, without government approval.
• Hindustan Aeronautics Limited (HAL)
• HAL was established in 1940 and is headquartered in Bangalore, India.
• The company is involved in the design, manufacture, and maintenance of aircraft, helicopters, and their engines.
• HAL plays a crucial role in India's defense sector and has partnerships with several international aerospace companies.

Shortcut Trick

Recall the standard count of prime numbers in different ranges: 1 to 50 contains exactly 15 prime numbers.

For the range 1 to 30, the prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Counting these gives a total of exactly 10 prime numbers.

∴ The correct answer is 10.

Alternate Method

Given: Range of numbers from 1 to 30.

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

Let us write down all the numbers from 1 to 30 and identify the prime numbers:

⇒ Numbers to check: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.

⇒ 1 is neither prime nor composite.

⇒ Prime numbers in the unit place/first decade (1-10): 2, 3, 5, 7 (4 primes)

⇒ Prime numbers in the second decade (11-20): 11, 13, 17, 19 (4 primes)

⇒ Prime numbers in the third decade (21-30): 23, 29 (2 primes)

⇒ Total prime numbers = 4 + 4 + 2 = 10 primes.

∴ The correct answer is 10.

Additional Information

Definition of Prime and Composite Numbers

A prime number has exactly two distinct factors: 1 and itself. A composite number has more than two factors. The number 1 is unique as it has only one factor.

Standard Prime Counts

Prime numbers between 1 and 50 = 15. Prime numbers between 1 and 100 = 25.

Properties of 2

The number 2 is the smallest prime number and the only even prime number.

The correct answer is Scattering of light.

Key Points

• The Tyndall effect is a phenomenon where light is scattered by particles in a colloid or in a very fine suspension.
• It is named after the 19th-century physicist John Tyndall, who first studied the effect.
• The scattering of light by the particles causes the light beam to become visible, which is why we can see the path of a beam of sunlight entering a dusty room.
• This effect is most often observed when the diameter of the particles is in the range of 40 to 900 nanometers.

Additional Information

• Colloids
• A colloid is a mixture where one substance of microscopically dispersed insoluble particles is suspended throughout another substance.
• Examples include fog, milk, and jelly.
• Rayleigh Scattering
• It is a phenomenon where particles much smaller than the wavelength of light cause the light to scatter.
• It explains why the sky appears blue; shorter wavelengths (blue) are scattered more than longer wavelengths (red).
• Mie Scattering
• This scattering occurs when the particles causing the scattering are of a size comparable to the wavelength of light being scattered.
• Mie scattering explains the white appearance of clouds, where water droplets scatter all wavelengths of light equally.
• Applications of Tyndall Effect
• Used in determining the size and density of particles in aerosols.
• Applied in medical diagnostics, such as in detecting the presence of proteins in urine.

The logic followed here is:

Hence, "Option 4" is the correct answer.

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

According to the question, such symbols which are immediately preceded by a number and is immediately followed by another number:

Required condition: Number - Symbols - Number

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

Thus, there are two such such symbols which are immediately preceded by a number and is immediately followed by another number.

Hence, "Option 1" is the correct answer.

The correct answer is It has a fixed shape..

Key Points

• Gases do not have a fixed shape; they take the shape of the container they are in.
• The particles in a gas are in constant, random motion and are very loosely packed.
• Gases are highly compressible compared to solids and liquids.
• The rate of diffusion in gases is very high due to the large spaces between particles.

Additional Information

• Diffusion:
• Diffusion is the process by which molecules spread from areas of high concentration to areas of low concentration.
• In gases, diffusion occurs rapidly due to the high kinetic energy of gas particles.
• Compressibility:
• Compressibility refers to the ability of a substance to decrease in volume under pressure.
• Gases are highly compressible because their particles are far apart and can be brought closer together.
• Kinetic Theory of Gases:
• This theory explains the behavior of gases, stating that gas particles are in constant, random motion.
• The theory assumes that collisions between gas particles and with the walls of the container are perfectly elastic.
• Boyle's Law:
• This law states that the pressure of a given mass of gas is inversely proportional to its volume, provided the temperature remains constant.
• It demonstrates the compressibility of gases.

The correct answer is Atmospheric refraction of starlight towards the normal.

Key Points

• Atmospheric refraction is the bending of light as it passes through Earth's atmosphere, causing the apparent position of the star to change.
• This refraction occurs because the atmosphere's density varies with altitude, causing a change in the speed of light.
• When starlight enters the Earth's atmosphere at a shallow angle near the horizon, it bends more significantly towards the normal (the perpendicular to the surface at the point of incidence).
• This bending makes the star appear higher in the sky than its true geometric position.
• Atmospheric refraction is more pronounced near the horizon compared to when a star is overhead due to the increased thickness of the atmosphere the light passes through.

Additional Information

• Refraction:
• Refraction is the change in direction of a wave passing from one medium to another caused by its change in speed.
• In the context of atmospheric refraction, the medium changes from the vacuum of space to the Earth's atmosphere.
• Snell's Law:
• Snell's Law describes how the angle of incidence and the angle of refraction are related for a wave crossing the interface between two media with different refractive indices.
• It is given by the formula: n1 * sin(θ1) = n2 * sin(θ2), where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively.
• Apparent Position:
• The apparent position of an object is where it appears to be located, which can differ from its true position due to effects such as refraction.
• For stars near the horizon, their apparent position is higher than their true position due to atmospheric refraction.
• Atmospheric Layers:
• The Earth's atmosphere is composed of several layers, each with different densities and temperatures, affecting the refraction of light.
• The main layers include the troposphere, stratosphere, mesosphere, and thermosphere, with the majority of atmospheric refraction occurring in the troposphere.
• Mirage:
• A mirage is another optical phenomenon caused by the refraction of light through layers of air at different temperatures.
• It often occurs in deserts or on hot roads, where light bends to create the illusion of water or other images.

The correct answer is 40 g J.

Key Points

• The formula to calculate potential energy (PE) is PE = mgh, where m is mass, g is acceleration due to gravity, and h is height.
• Given: Mass (m) = 8 kg, Height (h) = 5 m, and g (acceleration due to gravity) = 9.8 m/s².
• Substituting the values: PE = 8 * g * 5 .
• Potential Energy = 40 g J.
• Since g is represented as a factor, the potential energy in terms of g is 40 g J (where g = 9.8 m/s²).

Additional Information

• Potential Energy (PE):
• Potential energy is the energy held by an object due to its position relative to other objects.
• In the context of gravity, it's the energy possessed by an object due to its height above the ground.
• Gravitational Potential Energy:
• It is a form of potential energy related to an object's height and the force of gravity acting on it.
• Expressed as PE = mgh, where m is mass, g is the acceleration due to gravity, and h is the height above the reference point.
• Acceleration due to Gravity (g):
• It is the acceleration that is imparted to objects due to the gravitational force of Earth.
• Standard value of g is approximately 9.8 m/s² near the Earth's surface.
• SI Units:
• The International System of Units (SI) is the modern form of the metric system.
• In this context, mass is measured in kilograms (kg), height in meters (m), and potential energy in joules (J).

Mistake Points 

Since options are in g J (where g = acceleration due to gravity) So we will not put the value of 'g' while solving potential energy. 40 gJ is the correct answer.

Given: 17 + 13 × 3 ÷ 12 - 4 = ?

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

17 + 13 × 3 ÷ 12 - 4 = ? ⇒ 17 × 13 + 3 - 12 ÷ 4 = ?

⇒ 17 × 13 + 3 - 12 ÷ 4 = ?

⇒ 17 × 13 + 3 - 3 = ?

⇒ 221 + 3 - 3 = ?

⇒ 224 - 3 = ?

⇒ 221 = ?

Hence, "Option 2" is the correct answer.

Given statement: Even though sugar is added in most of the food items cooked, it is not good for health.

Given reasons:

I. Sugar adds more taste into any food being cooked. → Not Possible 

Reason I is logically incorrect due to the absolute term 'any food' and fails to explain the health concern.

II. Sugar is the most consumed material in the country → Not Possible 

Reason II is a general fact that doesn't explain the statement's causality.

Thus, Neither I nor II is a possible reason.

Hence, "Option 1" is the correct answer.

Shortcut Trick

Recognize the Pythagorean Triplet: 6, 8, 10.

Since the hypotenuse is 10 and one side is 8, the other side (height) must be 6 units.

Area = (1/2) × base × height = (1/2) × 8 × 6 = 24 sq. units.

∴ The correct answer is 24 sq. units.

Alternate Method

Given: Hypotenuse (c) = 10 units, Side (a) = 8 units.

Formula Used: Pythagoras Theorem: a² + b² = c²; Area = (1/2) × base × height.

⇒ 8² + b² = 10²

⇒ 64 + b² = 100

⇒ b² = 100 − 64 = 36

⇒ b = √36 = 6 units

⇒ Area = (1/2) × 8 × 6

⇒ Area = 4 × 6 = 24 sq. units

∴ The correct answer is 24 sq. units.

Additional Information

Pythagorean Triplets

Sets of three integers that satisfy a² + b² = c², such as (3, 4, 5), (5, 12, 13), and (8, 15, 17).

Area of Right-Angled Triangle

Always calculated as half the product of the two sides forming the 90° angle: Area = 0.5 × base × height.

Circumradius of Right Triangle

The circumradius (R) of a right-angled triangle is always half of the hypotenuse: R = Hypotenuse ÷ 2.

Given:

Expression = 36 − [12 + (3 × 10 ÷ 2)]

Formula used:

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

Calculations:

36 − [12 + (3 × 10 ÷ 2)]

⇒ 36 − [12 + (3 × 5)]

⇒ 36 − [12 + 15]

⇒ 36 − 27

⇒ 9

∴ The correct answer is option (3).

The correct answer is A solenoid of finite length carrying current.

Key Points

• A solenoid of finite length carrying current generates a magnetic field similar to that of a bar magnet with distinct north and south poles.
• The magnetic field inside a solenoid is uniform and parallel to the axis of the solenoid, resembling the internal field of a bar magnet.
• Outside the solenoid, the field lines spread out from one end and curve around to enter the other end, similar to a bar magnet's external magnetic field.
• When current flows through a solenoid, it creates a magnetic field due to the alignment of magnetic dipoles, akin to the magnetization in a bar magnet.

Additional Information

• Magnetic Field Lines:
• Magnetic field lines are imaginary lines used to represent the strength and direction of a magnetic field.
• They emerge from the north pole and enter the south pole of a magnet, forming closed loops.
• Electromagnetism:
• Electromagnetism refers to the interaction between electric currents and magnetic fields.
• It is one of the fundamental forces of nature, described by Maxwell's equations.
• Applications of Solenoids:
• Solenoids are used in various applications such as electromagnetic relays, inductors, and electric bells.
• They are also used in MRI machines and as actuators in automotive systems.
• Bar Magnet:
• A bar magnet is a permanent magnet with a north and a south pole.
• It creates a magnetic field in the surrounding space, which can attract or repel other magnetic materials.

The correct answer is Formation of iron sulphate from copper sulphate and iron.

Key Points

• The reaction between copper sulphate and iron is a displacement reaction, not a combination reaction.
• In this reaction, iron displaces copper from copper sulphate solution, forming iron sulphate and copper.
• Displacement reactions are characterized by one element being displaced by another in a compound.
• The general form of a displacement reaction is A + BC → AC + B, where element A displaces B in compound BC to form AC.

Additional Information

• Combination Reaction
• A combination reaction is a chemical reaction where two or more substances combine to form a single product.
• The general form of a combination reaction is A + B → AB.
• Examples include the formation of water (H₂ + O₂ → H₂O) and the formation of slaked lime from quick lime (CaO + H₂O → Ca(OH)₂).
• Displacement Reaction
• A displacement reaction involves an element reacting with a compound, displacing an element from it.
• These reactions are typically observed in solutions of metals and salts.
• Example: Fe + CuSO₄ → FeSO₄ + Cu.
• Types of Chemical Reactions
• Synthesis Reaction: Two or more simple substances combine to form a more complex product.
• Decomposition Reaction: A compound breaks down into two or more simpler substances.
• Single Displacement Reaction: One element displaces another in a compound.
• Double Displacement Reaction: The ions of two compounds exchange places in an aqueous solution to form two new compounds.
• Real-life Applications
• Combination reactions are essential in various industrial processes, such as the manufacturing of ammonia.
• Displacement reactions are utilized in metal extraction and corrosion prevention.

The correct answer is DNA.

Key Points

• Chromatin is a complex of DNA and protein found in eukaryotic cells.
• In a non-dividing cell, chromatin material is present in a diffuse, less condensed form.
• Chromatin's primary function is to package DNA into a more compact, denser shape.
• This compact structure allows for efficient regulation of gene expression and DNA replication.
• Chromatin is essential for maintaining the integrity of DNA and ensuring proper function during the cell cycle.

Additional Information

• Histones:
• Histones are proteins that help in the organization of DNA into structural units called nucleosomes.
• They play a crucial role in the compaction and regulation of chromatin.
• Nucleosomes:
• Nucleosomes are the basic unit of DNA packaging in eukaryotes, consisting of a segment of DNA wound around a core of histone proteins.
• They help in folding DNA into higher-order structures.
• Chromosomes:
• During cell division, chromatin condenses to form chromosomes.
• Chromosomes ensure accurate distribution of genetic material to daughter cells.
• Epigenetics:
• Epigenetic modifications, such as DNA methylation and histone modification, influence chromatin structure and gene expression.
• These modifications do not change the DNA sequence but can affect gene activity and phenotype.

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

Conclusions:

(I) Some rulers are sketch pens → Does not follow (As some erasers are rulers and all sketch pens are erasers. So it is possible but not definite.)

(II) Some erasers are pens → Follow (As some pens are sketch pens, all sketch pens are erasers and some erasers are rulers. As some part of pens is common with sketch pens which whole comes in erasers, therefore it is true.)

∴ Here, Only conclusion (II) follows.​

Hence, the correct answer is "Option 4"

The correct answer is Wed Sep 18 2024 00:00:00 GMT+0530 (India Standard Time).

Key Points

• The National Pension System Vatsalya (NPS Vatsalya) is a government-initiated pension scheme.
• It was launched on Wed Sep 18 2024.
• The scheme aims to provide a secure and regular income post-retirement to its subscribers.
• NPS Vatsalya is targeted at individuals seeking a financially stable retirement plan.
• The scheme allows contributions from both the subscriber and the government to build a retirement corpus.

Additional Information

• National Pension System (NPS)
• It is a voluntary, defined contribution retirement savings scheme.
• NPS is designed to enable systematic savings during the subscriber's working life.
• It is regulated by the Pension Fund Regulatory and Development Authority (PFRDA).
• The scheme is open to all Indian citizens aged 18-65 years.
• Upon retirement, a part of the corpus can be withdrawn, and the remaining amount is used to purchase an annuity for regular income.
• Pension Fund Regulatory and Development Authority (PFRDA)
• It is a statutory body established by the Government of India.
• PFRDA is responsible for regulating and developing the pension sector in India.
• It ensures the orderly growth and development of the pension market.
• The authority also aims to protect the interests of subscribers to pension schemes.
• Retirement Planning
• It involves setting retirement income goals and the actions and decisions necessary to achieve those goals.
• It includes identifying sources of income, estimating expenses, implementing a savings program, and managing assets and risk.
• Effective retirement planning ensures a secure and comfortable post-retirement life.
• It is crucial to start planning early to build a sufficient retirement corpus.
• Annuity
• An annuity is a financial product that provides a steady income stream, typically used as part of retirement planning.
• It involves making a lump sum payment or series of payments to an insurance company in exchange for regular disbursements.
• Annuities can be fixed or variable, immediate or deferred, depending on the terms of the contract.
• They help mitigate the risk of outliving one's savings by ensuring a continuous income.

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

1) Only five people sit between B and L.

2) Z sits to the immediate left of L.

3) Only one person sits between Z and C.

4) A sits at some place to the left of Y but at some place to the right of X.

Thus, according to the final arrangement, A sits third from the left end of the line.

Hence, "Option 4" is the correct answer.

Given:

Expression: $\rm \left(\frac{(-2)}{5}\right)^{-2} \times \left(\frac{(-4)}{5}\right)^4$

Formula used:

(a/b)⁻ⁿ = (b/a)ⁿ

(a/b)ⁿ = aⁿ/bⁿ

Calculations:

$\rm \left(\frac{-2}{5}\right)^{-2} \times \left(\frac{-4}{5}\right)^4$

⇒ $\rm \left(\frac{5}{-2}\right)^2 \times \frac{(-4)^4}{5^4}$

⇒ $\rm \frac{5^2}{(-2)^2} \times \frac{256}{625}$

⇒ $\rm \frac{25}{4} \times \frac{256}{625}$

⇒ $\rm \frac{1}{1} \times \frac{64}{25}$

⇒ 64/25

∴ The correct answer is option (1).

The correct answer is Satyaki Roy.

Key Points

• Satyaki Roy is a well-known economist and author.
• He specializes in the study of India's political economy and social disparities.
• Roy's work often explores the intersections of economic policy and social justice.
• His book, "INDIA'S ECONOMY 2024: Disparities in Fractured Democracy," delves into the challenges and prospects of India's economic landscape.

Additional Information

• Political Economy
• Political economy is the study of production and trade and their links with government policy and law.
• It examines how political institutions, the political environment, and the economic system influence each other.
• Social Disparities
• Social disparities refer to inequalities that exist within a society, often related to economic status, education, and access to resources.
• These disparities can impact the overall development and cohesion of a country.
• Economic Policy in India
• Economic policy in India includes government actions to influence the economy, such as tax policies, monetary policies, and regulations.
• These policies aim to promote economic growth, reduce poverty, and improve living standards.
• India's Economic Growth
• India has seen significant economic growth over the past few decades, becoming one of the world's largest economies.
• However, this growth has been accompanied by challenges such as income inequality and regional disparities.

The correct answer is Snail.

Key Points

• Snails are hermaphrodites, meaning each individual possesses both male and female reproductive organs.
• During mating, snails can both exchange sperm and fertilize each other's eggs.
• This characteristic allows snails to reproduce more flexibly, especially in environments where mates are scarce.
• Snails do not have genetically predetermined sexes like many other animals; instead, they can assume either role in reproduction.

Additional Information

• Hermaphroditism
• Hermaphroditism is a condition in which an individual has both male and female reproductive organs.
• It is common in many invertebrates, such as snails, earthworms, and some fish species.
• This reproductive strategy can be advantageous in environments where finding a mate is challenging.
• Reproductive Adaptations
• Some animals have developed unique reproductive adaptations to ensure survival and reproduction in various environments.
• Examples include the ability of some fish to change sex in response to environmental conditions or social structure.
• Genetically Determined Sex
• In contrast to hermaphroditic species, many organisms have genetically predetermined sexes, determined by specific sex chromosomes.
• Humans, for example, have XY (male) and XX (female) sex chromosomes.
• Sexual Dimorphism
• Sexual dimorphism refers to the differences in appearance between males and females of the same species.
• These differences can include size, color, and the presence of specific physical traits used in mating displays or competition.

The correct answer is Xanthium and Urena.

Key Points

• Xanthium and Urena are plants known for their spiny seeds with hooks that attach to the fur of animals.
• These hooked seeds are adapted for epizoochory—a type of seed dispersal by animals.
• As animals move, the seeds are carried to new locations where they can germinate and grow.
• This method of seed dispersal helps in the wide distribution of the plant species.
• The hooks on the seeds ensure that they remain attached to the animal's body until they are dislodged at a different location.

Additional Information

• Epizoochory: Seed dispersal method where seeds are transported on the outside of animals.
• Seed Dispersal: The movement or transport of seeds away from the parent plant to reduce competition and spread the species.
• Adaptation: Traits like hooks or spines on seeds that help in attachment to animal fur are examples of adaptation for survival and reproduction.
• Germination: The process by which a seed develops into a new plant under suitable conditions.
• Biodiversity: Effective seed dispersal contributes to plant diversity and ecosystem health by enabling plants to colonize new areas.

The correct answer is a concave lens of suitable power.

Key Points

• Myopia, also known as nearsightedness, is a common vision condition where distant objects appear blurry.
• This condition occurs when the eyeball is too long or the cornea is too curved, causing light rays to focus in front of the retina.
• Myopia can be corrected by using a concave lens, which diverges light rays before they enter the eye, allowing them to focus on the retina.
• Concave lenses are specified with a negative diopter value, indicating their ability to correct nearsightedness.

Additional Information

• Hyperopia (Farsightedness)
• Hyperopia is a condition where distant objects are seen more clearly than near objects.
• This condition occurs when the eyeball is too short or the cornea is not curved enough, causing light to focus behind the retina.
• Hyperopia can be corrected by using convex lenses, which converge light rays before they enter the eye.
• Astigmatism
• Astigmatism is a common vision condition that causes blurred vision due to an irregularly shaped cornea or lens.
• This irregular shape prevents light from focusing properly on the retina, leading to distorted or blurred vision at all distances.
• Astigmatism can be corrected using cylindrical lenses that compensate for the irregular curvature of the cornea or lens.
• Presbyopia
• Presbyopia is an age-related condition where the eye gradually loses the ability to focus on near objects.
• This condition typically becomes noticeable in the early to mid-40s and continues to worsen with age.
• It can be corrected using reading glasses, bifocals, or progressive lenses.
• Refractive Errors
• Refractive errors occur when the shape of the eye prevents light from focusing directly on the retina.
• Common refractive errors include myopia, hyperopia, astigmatism, and presbyopia.
• These errors can be corrected with the use of prescription lenses, contact lenses, or refractive surgery.

The correct answer is Project PARI.

Key Points

• Project PARI is an initiative by the Ministry of Culture, Government of India.
• It is being executed by Lalit Kala Akademi and the National Gallery of Modern Art.
• The project is set to commence in July 2024.
• PARI stands for Project for Art and Regional Integration, focusing on promoting regional art forms.
• The initiative aims to preserve and promote India's rich cultural heritage and diverse art forms.

Additional Information

• Lalit Kala Akademi
• Established in 1954, it is the National Academy of Art under the Ministry of Culture.
• It aims to promote and propagate understanding of Indian art, both within and outside the country.
• It organizes various national and international exhibitions, art camps, and workshops.
• National Gallery of Modern Art (NGMA)
• Founded in 1954, NGMA is a premier institution for modern and contemporary Indian art.
• It houses a vast collection of paintings, sculptures, and other works of art from prominent Indian artists.
• NGMA organizes exhibitions, educational programs, and workshops to promote art awareness.
• Ministry of Culture, Government of India
• The ministry is responsible for the preservation and promotion of Indian cultural heritage.
• It oversees various cultural institutions, festivals, and initiatives across the country.
• It aims to foster cultural integration and appreciation among the diverse population of India.
• Art and Regional Integration
• Focuses on promoting regional art forms and cultural practices across India.
• Aims to create a platform for artists from different regions to showcase their talent.
• Encourages cultural exchange and appreciation among various communities and states.

The correct answer is 2.

Key Points

• Manu Bhaker is an accomplished Indian sport shooter, known for her impressive performances in international events.
• At the 2024 Paris Olympics, she made history by becoming the first Indian woman to win an Olympic shooting medal.
• She also became the first Indian to win a total of 4 medals in shooting events at a single edition of the Olympics.
• Her achievement has set a new benchmark for Indian shooting sports and brought significant recognition to the country.
• Bhaker's success is attributed to her dedication, rigorous training, and support from national sports bodies.

Additional Information

• Olympic Shooting Events
• Shooting sports at the Olympics include events for rifles, pistols, and shotguns.
• Disciplines include 10m Air Rifle, 10m Air Pistol, 25m Pistol, 50m Rifle Three Positions, and Skeet, among others.
• Competitors aim for precision and accuracy in hitting targets to score points.
• Training and Preparation
• Top-level shooters undergo rigorous training, including mental conditioning, physical fitness, and technical drills.
• Consistency and focus are crucial for success in competitive shooting.
• India’s Performance in Shooting
• India has a growing reputation in shooting sports, with several athletes winning medals in international competitions.
• The country invests in training facilities and support systems to nurture talent in this field.
• Manu Bhaker’s Career Highlights
• Bhaker has won multiple medals in Youth Olympics, ISSF World Cup, and Commonwealth Games.
• Her determination and success have inspired many young athletes in India.

The correct answer is ₹20 lakh.

Key Points

• The Union Budget 2024-25 increased the limit for Mudra loans under the 'Tarun' category to ₹20 lakh.
• This enhancement is aimed at providing greater financial assistance to entrepreneurs who have successfully repaid their previous loans.
• Mudra loans are part of the Pradhan Mantri Mudra Yojana (PMMY), which was launched in April 2015.
• The 'Tarun' category is for loans above ₹10 lakh and up to ₹20 lakh.
• This initiative is expected to boost the growth of small businesses and startups in India.

Additional Information

• Pradhan Mantri Mudra Yojana (PMMY)
• Launched by the Government of India in April 2015 to provide loans to small and micro enterprises.
• MUDRA stands for Micro Units Development and Refinance Agency Ltd.
• The scheme offers loans under three categories: Shishu (up to ₹50,000), Kishore (₹50,000 to ₹5 lakh), and Tarun (₹5 lakh to ₹20 lakh).
• It aims to promote entrepreneurship among individuals and small businesses.
• The loans are provided by Commercial Banks, RRBs, Small Finance Banks, Cooperative Banks, MFIs, and NBFCs.
• Credit Guarantee Scheme (CGS)
• Launched to strengthen the credit delivery system and facilitate the flow of credit to the MSE sector.
• Provides credit guarantee for loans up to ₹2 crore.
• Helps small and micro enterprises in obtaining credit without the need for collateral security.
• Implemented by the Credit Guarantee Fund Trust for Micro and Small Enterprises (CGTMSE).
• Startup India Initiative
• Launched by the Government of India on January 16, 2016.
• Aims to build a strong ecosystem for nurturing innovation and startups in the country.
• Offers benefits such as tax exemptions, simplified compliance, and fast-tracking of patent applications.
• Provides funding support through the Fund of Funds for Startups (FFS) with a corpus of ₹10,000 crore.
• Stand-Up India Scheme
• Launched on April 5, 2016, to promote entrepreneurship among women and SC/ST communities.
• Provides bank loans between ₹10 lakh and ₹1 crore for setting up a greenfield enterprise.
• The scheme covers all branches of Scheduled Commercial Banks.
• Aims to facilitate at least two such projects per bank branch.

Shortcut Trick

Let Total Work (LCM of 7, 10, 14) = 70 units.

Efficiencies: A = 10, B = 7, C = −5. Combined (A+B+C) = 10 + 7 − 5 = 12 units/hr.

Work done in 4.5 hours = 12 × 4.5 = 54 units.

Remaining work = 70 − 54 = 16 units. Combined (B+C) = 7 − 5 = 2 units/hr.

Remaining time = 16 ÷ 2 = 8 hours.

∴ The correct answer is 8 hours.

Alternate Method

Given: Pipe A fills in 7 hrs, Pipe B in 10 hrs, Pipe C empties in 14 hrs. A is closed after 4.5 hrs.

Formula Used: Efficiency = Total Work ÷ Time

⇒ Efficiency of (A + B + C) = 10 + 7 − 5 = 12 units/hr

⇒ Tank filled in 4.5 hours = 12 × 4.5 = 54 units

⇒ Remaining Work = 70 − 54 = 16 units

⇒ Efficiency of (B + C) = 7 − 5 = 2 units/hr

⇒ Remaining Time = 16 ÷ 2 = 8 hours

∴ The correct answer is 8 hours.

Additional Information

Pipes & Cisterns Sign Convention

Inlet pipes (filling) are taken as positive efficiency, while outlet pipes (emptying/leakage) are taken as negative efficiency.

Work done by multiple pipes

Total part filled in 1 hour = (1/A) + (1/B) − (1/C), where A and B are inlet and C is an outlet pipe.

Total Time Calculation

If the question asks for total time, add the initial 4.5 hours to the remaining 8 hours (Total = 12.5 hours).

Shortcut Trick

Net discount = a + b − (a × b) ÷ 100 ⇒ 20 + 20 − (20 × 20) ÷ 100 = 36%.

Selling Price (SP) = 100% − 36% = 64%.

Given 64% = ₹16,000.

MRP (100%) = (16,000 ÷ 64) × 100 = 250 × 100 = ₹25,000.

∴ The correct answer is ₹25,000.

Alternate Method

Given: SP = ₹16,000, First Discount (d₁) = 20%, Second Discount (d₂) = 20%.

Formula: SP = MRP × (100 − d₁)% × (100 − d₂)%

⇒ 16,000 = MRP × (80 ÷ 100) × (80 ÷ 100)

⇒ 16,000 = MRP × (4 ÷ 5) × (4 ÷ 5)

⇒ 16,000 = MRP × (16 ÷ 25)

⇒ MRP = (16,000 × 25) ÷ 16

⇒ MRP = 1,000 × 25 = ₹25,000.

∴ The correct answer is ₹25,000.

Additional Information

Successive Discounts

When two or more discounts are applied one after another, the net discount is calculated on the reducing balance or by using the formula x + y − xy/100.

Marked Price (MRP)

It is the price printed on an article. Discounts are always calculated on the Marked Price to reach the Selling Price.

Given:

Total number of cars sold in India in the year 2022 = 15,00,000

The percentage of cars sold by Mafindre = 18%

Concept Used:

Number of cars sold by a company = (Percentage of sales by the company / 100) × Total number of cars sold

Calculation:

Number of cars sold by Mafindre = (18 / 100) × 15,00,000

⇒ Number of cars sold by Mafindre = 2,70,000

∴ The number of cars sold by Mafindre in India in 2022 is 2,70,000.

According to the given information,

Thus, according to the given codes the code 'Su' is for the word 'We'.

Hence, the correct answer is "Option 2".

The correct answer is Both A and C.

Key Points

• Gonorrhoea is a sexually transmitted bacterial infection caused by the bacterium Neisseria gonorrhoeae.
• Syphilis is another sexually transmitted infection caused by the bacterium Treponema pallidum.
• Both infections are primarily transmitted through sexual contact, including vaginal, anal, and oral sex.
• Early detection and treatment with antibiotics are crucial to prevent long-term complications and transmission to sexual partners.

Additional Information

• AIDS (Acquired Immunodeficiency Syndrome) is caused by the Human Immunodeficiency Virus (HIV) and is not a bacterial infection but a viral infection.
• Neisseria gonorrhoeae can infect the genital tract, mouth, and rectum, leading to symptoms such as painful urination and discharge.
• Treponema pallidum causes syphilis, which progresses in stages: primary, secondary, latent, and tertiary, each presenting different symptoms.
• Sexually transmitted infections (STIs) can be prevented through the use of condoms, regular screening, and maintaining a mutually monogamous relationship with an uninfected partner.
• Public health initiatives emphasize education, testing, and treatment to reduce the spread of STIs and protect community health.

Shortcut Trick

Given a − b = 1 and a³ − b³ = 61.

Test values for a and b with difference 1: Let a = 5 and b = 4.

Check: 5³ − 4³ = 125 − 64 = 61. Condition satisfied.

Value of ab = 5 × 4 = 20.

∴ The correct answer is 20.

Alternate Method

Given: a − b = 1, a³ − b³ = 61

Formula Used: a³ − b³ = (a − b)³ + 3ab(a − b)

⇒ 61 = (1)³ + 3 × ab × (1)

⇒ 61 = 1 + 3ab

⇒ 61 − 1 = 3ab

⇒ 60 = 3ab

⇒ ab = 60 ÷ 3

⇒ ab = 20

∴ The correct answer is 20.

Additional Information

Algebraic Identities

(a − b)³ = a³ − b³ − 3ab(a − b)

Difference of Cubes

a³ − b³ = (a − b)(a² + ab + b²)

Sum of Cubes

a³ + b³ = (a + b)(a² − ab + b²) = (a + b)³ − 3ab(a + b)

The correct answer is Earth's gravitational force.

Key Points

• Gravitational force is a natural phenomenon by which all things with mass or energy are brought toward one another, including objects falling toward Earth.
• This force causes an acceleration of approximately 9.8 m/s² near the surface of the Earth, known as gravitational acceleration.
• Gravitational force was first described by Sir Isaac Newton in his law of universal gravitation.
• Every object with mass exerts a gravitational pull on every other mass; however, due to Earth's large mass, its gravitational force is the dominant one affecting objects near its surface.

Additional Information

• Law of Universal Gravitation
• Formulated by Sir Isaac Newton, it states that every point mass attracts every other point mass by a force acting along the line intersecting both points.
• The formula is F = G * (m₁*m₂) / r², where F is the force between the masses, G is the gravitational constant, m₁ and m₂ are the masses of the objects, and r is the distance between the centers of the masses.
• Gravitational Constant (G)
• A fundamental constant, G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻², which quantifies the strength of the gravitational force in the law of universal gravitation.
• Free Fall
• The motion of a body where gravity is the only force acting upon it.
• In a vacuum, all objects fall at the same rate regardless of their mass due to the absence of air resistance.
• Acceleration due to Gravity (g)
• Denoted as 'g', it is approximately 9.8 m/s² on the surface of Earth.
• This value can vary slightly depending on altitude and geographical location.

The correct answer is 71.

Key Points

• The SDG India Index 2023-24 is prepared by NITI Aayog, the policy think tank of the Government of India.
• India's composite score in the SDG India Index 2023-24 is 71.
• The index measures the progress of all states and union territories towards achieving the Sustainable Development Goals (SDGs).
• The composite score is derived from the performance of the country across various SDG indicators.
• This index helps in identifying gaps and areas that need improvement to meet the SDG targets by 2030.

Additional Information

• Sustainable Development Goals (SDGs)
• The SDGs are a set of 17 global goals established by the United Nations in 2015.
• They aim to address global challenges including poverty, inequality, climate change, environmental degradation, peace, and justice.
• Each goal has specific targets to be achieved by 2030.
• The goals are interconnected and balance the three dimensions of sustainable development: economic, social, and environmental.
• NITI Aayog
• NITI Aayog stands for National Institution for Transforming India.
• It was established in 2015, replacing the Planning Commission.
• It aims to foster cooperative federalism through structured support initiatives and mechanisms with the states on a continuous basis.
• NITI Aayog provides relevant strategic and technical advice across the spectrum of key policies and programs.
• India's Performance in SDGs
• India's performance on the SDGs is tracked annually by the SDG India Index.
• The index assesses the progress made by states and union territories on various SDG indicators.
• The index helps in identifying best practices and the key challenges faced by different regions.
• It serves as a valuable tool for policy-makers to prioritize actions for achieving the SDGs by 2030.
• Composite Score
• The composite score is a summary measure of performance across various indicators.
• It is calculated by aggregating the scores of individual indicators, which are weighted according to their importance.
• A higher composite score indicates better performance towards achieving the SDGs.
• This score helps in benchmarking and tracking progress over time.

The correct answer is The sum of the individual resistances..

Key Points

• When resistors are connected in series, the equivalent resistance is the sum of all individual resistances.
• This is because the current has only one path to take, and it flows through each resistor sequentially.
• The formula for the equivalent resistance R_eq in a series circuit is $R_{eq} = R_1 + R_2 + R_3 + .......+ R_n$.
• In a series circuit, the total resistance increases with the addition of more resistors.
• This principle is essential for designing electrical circuits to control the total resistance and current flow.

Additional Information

• Ohm's Law:
• Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
• The formula is $V=IR$, where V is voltage, I is current and R is Resistance.
• Series Circuit Characteristics:
• In a series circuit, the same current flows through all components.
• The total voltage across the circuit is the sum of the voltages across each component.
• If one component fails, the entire circuit is broken.
• Parallel Circuit:
• In contrast to a series circuit, a parallel circuit has multiple paths for current to flow.
• The equivalent resistance of parallel resistors is less than the smallest individual resistor.
• The formula for the equivalent resistance R_p in a parallel circuit is $\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+.......+\frac{1}{R_n}$
• Applications of Series Circuits:
• Series circuits are used in applications where the current must be the same through all components, such as in string lights.
• They are also used in voltage divider circuits, which are used to create reference voltages.

Shortcut Trick

Interest for 3 years (5 − 2) = ₹2,000 − ₹1,250 = ₹750

Interest for 1 year = ₹750 ÷ 3 = ₹250

Principal (P) = Amount after 2 years − Interest for 2 years = ₹1,250 − (2 × ₹250) = ₹750

Rate % = (Interest per year ÷ Principal) × 100 = (250 ÷ 750) × 100 = 33.33%

∴ The correct answer is 33.33%.

Alternate Method

Given: Amount (A₁) = ₹1,250 at T₁ = 2 years; Amount (A₂) = ₹2,000 at T₂ = 5 years.

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

⇒ Interest for 3 years = A₂ − A₁ = 2,000 − 1,250 = ₹750

⇒ Simple Interest for 1 year = 750 ÷ 3 = ₹250

⇒ Simple Interest for 2 years = 250 × 2 = ₹500

⇒ Principal (P) = A₁ − SI for 2 years = 1,250 − 500 = ₹750

⇒ Rate (R) = (SI_1yr × 100) ÷ P = (250 × 100) ÷ 750

⇒ Rate (R) = 100 ÷ 3 = 33.333...%

∴ The correct answer is 33.33%.

Additional Information

Simple Interest Constant Property

In Simple Interest, the interest earned remains the same every year because it is always calculated on the original Principal.

Rate of Interest Formula

The annual rate of interest can be calculated as R = (SI for 1 year ÷ Principal) × 100. This is the standard unitary method approach.

Relation between Amount and Time

Since Interest is linear, the difference in amounts for two different time periods gives the Simple Interest for the difference in those time periods.

Decoding symbols:

Given: X - Y × Z + A × B ÷ C

X - Y → X is the husband of Y.

Y × Z → Y is the mother of Z.

Z + A → Z is the sister of A.

A × B → A is the mother of B.

B ÷ C → B is the son of C.

Thus, Z is C's wife's sister or sister-in-law.

Hence, the correct answer is "Option 2".

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

Conclusions:

(I) All buds are insects → Does not follow (As all buds are flowers and all insects are flowers. So it is possible but not definite.)

(II) All flowers are buds → Does not follow (As all buds are flowers. So it is possible but not definite.)

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

Hence, the correct answer is "Option 3"

The correct answer is Cuscuta.

Key Points

• Cuscuta is a genus of parasitic plants, commonly known as dodder.
• It lacks chlorophyll and cannot perform photosynthesis, relying on host plants for nutrients.
• Cuscuta attaches to host plants using specialized structures called haustoria, which penetrate the host's vascular system.
• This parasitic relationship allows Cuscuta to extract water and essential nutrients from the host plant.
• Cuscuta can significantly affect the growth and productivity of its host plants, often leading to decreased yields in agricultural settings.

Additional Information

• Parasitic Plants:
• Plants that derive some or all of their nutritional requirements from another living plant.
• They can be obligate (completely dependent on the host) or facultative (can survive without the host).
• Haustoria:
• Specialized structures used by parasitic plants to connect with the host plant's vascular system.
• They facilitate the transfer of water, minerals, and nutrients from the host to the parasite.
• Photosynthesis:
• A process used by plants and other organisms to convert light energy into chemical energy that can be used to fuel the organism's activities.
• Parasitic plants like Cuscuta lack chlorophyll and are unable to perform photosynthesis.
• Impact on Agriculture:
• Parasitic plants can cause significant damage to crops, leading to reduced yields and economic losses.
• Effective management strategies are essential to control the spread and impact of parasitic plants in agricultural fields.

The logic followed here is:

Given: X : 54 :: 8 : Y

So, checking each option one by one:

Option 1) X = 10, Y = 39 → 10 : 54 :: 8 : 39

10 × 5 - 1 = 54

50 - 1 = 54

49 ≠ 54 (LHS ≠ RHS)

8 × 5 - 1 = 39

40 - 1 = 39

39 ≠ 39 (LHS ≠ RHS)

Option 2) X = 10, Y = 59 → 10 : 54 :: 8 : 59

10 × 5 - 1 = 54

50 - 1 = 54

49 ≠ 54 (LHS ≠ RHS)

8 × 5 - 1 = 59

40 - 1 = 59

39 ≠ 59 (LHS ≠ RHS)

Option 3) X = 11, Y = 36 → 11 : 54 :: 8 : 36

11 × 5 - 1 = 54

55 - 1 = 54

54 ≠ 54 (LHS ≠ RHS)

8 × 5 - 1 = 36

40 - 1 = 36

39 ≠ 36 (LHS ≠ RHS)

Option 4) X = 11, Y = 39 → 11 : 54 :: 8 : 39

11 × 5 - 1 = 54

55 - 1 = 54

54 = 54 (LHS = RHS)

8 × 5 - 1 = 39

40 - 1 = 39

39 = 39 (LHS = RHS)

Hence, "Option 4" is the correct answer.

The correct answer is The particles of a suspension can be seen by the naked eye..

Key Points

• A suspension is a heterogeneous mixture in which solid particles do not dissolve in a liquid solution.
• The particles in a suspension are large enough to be seen with the naked eye.
• When left undisturbed, the particles in a suspension will eventually settle to the bottom due to gravity.
• The particles in a suspension can be separated from the liquid by filtration or decantation.

Additional Information

• Colloid:
• A colloid is a mixture where very small particles of one substance are distributed evenly throughout another substance.
• Unlike suspensions, colloids do not settle out upon standing, and the particles cannot be seen with the naked eye.
• Solution:
• A solution is a homogeneous mixture of two or more substances.
• The solute is the substance that is dissolved, and the solvent is the substance in which the solute is dissolved.
• Solutions are transparent and do not scatter light.
• Emulsion:
• An emulsion is a type of colloid formed by combining two liquids that normally don't mix.
• Common examples include milk and mayonnaise.
• Decantation:
• Decantation is a process for the separation of mixtures by removing a liquid layer that is free of precipitate.
• This method is commonly used to separate suspensions.

The correct answer is Orange juice with pulp.

Key Points

• A homogeneous mixture is one that has a uniform composition and appearance throughout.
• Orange juice with pulp is a heterogeneous mixture because the pulp is not uniformly distributed throughout the liquid.
• In a heterogeneous mixture, the different components are visibly distinguishable.
• Other examples provided, such as pure air, sugar solution, and vinegar, are homogeneous mixtures where components are evenly distributed.

Additional Information

• Homogeneous Mixture
• A mixture in which the composition is uniform throughout the mixture.
• Examples: Salt water, air, and vinegar.
• These mixtures have the same phase and properties throughout.
• Heterogeneous Mixture
• A mixture in which the composition is not uniform throughout the mixture.
• Examples: Salad, sand and water, and orange juice with pulp.
• Different phases and properties can be observed in different parts of the mixture.
• Solution
• A type of homogeneous mixture composed of two or more substances.
• The solute is the substance that is dissolved, and the solvent is the substance that does the dissolving.
• Examples: Sugar in water, salt in water.
• Colloid
• A mixture where very small particles of one substance are evenly distributed throughout another substance.
• Examples: Milk, mayonnaise, and jelly.
• Particles do not settle and cannot be separated out by ordinary filtering or centrifuging like those in a suspension.

Given: Six boxes P, Q, R, S, T and U are kept one over the other

1) P is kept third from the bottom.

2) Only two boxes are kept between P and Q.

3) Only three boxes are kept between Q and R.

4) T is kept immediately below Q.

5) S is kept immediately below R.

After positioning S only one position is left which will be occupied by the only box left i.e. U. 

Thus, according to the final arrangement two boxes are kept between U and S.

Hence, "Option 2" is the correct answer.

The correct answer is One.

Key Points

• Each ovary typically releases one egg per month during the menstrual cycle.
• The process of releasing an egg from the ovary is called ovulation.
• Ovulation generally occurs around the middle of the menstrual cycle, which is usually about 14 days before the start of the next menstrual period.
• The menstrual cycle is controlled by a complex interaction of hormones, primarily estrogen and progesterone.

Additional Information

• Ovaries are the female reproductive organs responsible for producing eggs and hormones.
• Follicles in the ovaries mature during the first half of the menstrual cycle in response to the follicle-stimulating hormone (FSH).
• Once a follicle is mature, a surge in luteinizing hormone (LH) triggers ovulation, releasing the egg.
• If the egg is not fertilized, the corpus luteum degenerates, leading to a decrease in progesterone and the onset of menstruation.
• Conditions such as polycystic ovary syndrome (PCOS) can affect ovulation and menstrual cycles.

Shortcut Trick

First 10 odd prime numbers: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31

Sum = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 = 158

Average = Sum ÷ Count = 158 ÷ 10 = 15.8

∴ The correct answer is 15.8.

Alternate Method

Given: First 10 odd prime numbers.

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

3, 5, 7, 11, 13, 17, 19, 23, 29, 31 First 10 Odd Prime Numbers Total Count = 10 Sum = 158

⇒ Prime numbers are numbers greater than 1 with exactly two factors (1 and itself).

⇒ The list of prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37...

⇒ Excluding 2 (even prime), the first 10 odd prime numbers are: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31.

⇒ Sum = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 = 158

⇒ Average = 158 ÷ 10

⇒ Average = 15.8

∴ The correct answer is 15.8.

Additional Information

Prime Numbers

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. 2 is the only even prime number.

Odd Prime Numbers

Except for 2, all prime numbers are odd. The sequence begins with 3, 5, 7, 11, 13, 17, ...

Average of Observations

Average = Sum of terms ÷ Number of terms. For consecutive odd integers, the average is the middle term, but this does not apply to primes as they are not evenly spaced.

The correct answer is Cuscuta.

Key Points

• Cuscuta is a genus of parasitic plants, commonly known as dodder.
• It belongs to the family Convolvulaceae.
• Cuscuta lacks chlorophyll and relies on host plants for nutrients.
• It attaches to host plants using structures called haustoria to extract water and nutrients.
• Cuscuta is found worldwide and can parasitize a wide range of host plants, including agricultural crops.

Additional Information

• Parasitic Plants:
• Parasitic plants derive some or all of their nutritional requirements from another living plant.
• They are categorized as either hemiparasites (partially parasitic, can photosynthesize) or holoparasites (completely parasitic, cannot photosynthesize).
• Examples include mistletoe (hemiparasitic) and Rafflesia (holoparasitic).
• Haustoria:
• Specialized structures used by parasitic plants to attach to and penetrate host plants.
• Haustoria facilitate the transfer of water, minerals, and nutrients from the host to the parasite.
• Impact on Agriculture:
• Parasitic plants like Cuscuta can cause significant damage to crops, leading to reduced yields.
• Management practices include crop rotation, resistant varieties, and chemical treatments.
• Convolvulaceae Family:
• Commonly known as the bindweed or morning glory family.
• Includes both parasitic and non-parasitic plants.
• Notable members include sweet potato (Ipomoea batatas) and field bindweed (Convolvulus arvensis).

The logic followed here is:

Given:

QL-GK-ON

And,

MH-CG-KJ

So, checking each option one by one:

Option 1) PJ-EI-ML

Option 2) OJ-EI-ML

Option 3) PJ-EI-MK

Option 4) OJ-EH-MK

Thus, out of all the options 'OJ-EI-ML' follows the same logic as given.

Hence, "Option 2" is the correct answer.

The correct answer is all types of reflecting surfaces including spherical surfaces.

Key Points

• The laws of reflection are universally applicable to all types of reflecting surfaces, whether they are plane, spherical, or curved.
• These laws state that the angle of incidence is equal to the angle of reflection, and the incident ray, the reflected ray, and the normal to the surface all lie in the same plane.
• For spherical surfaces, the laws of reflection apply at each point on the surface where the ray intersects.
• This universality ensures that the behavior of light on different surfaces can be predicted using the same fundamental principles.

Additional Information

• Reflection of Light
• Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated.
• There are two types of reflection: specular (mirror-like) and diffuse (scattering).
• Specular reflection occurs on smooth surfaces, while diffuse reflection occurs on rough surfaces.
• Spherical Mirrors
• Spherical mirrors are mirrors with surfaces that form part of a sphere.
• They can be concave (inward curved) or convex (outward curved).
• These mirrors focus light to a point or spread it out depending on the curvature.
• Plane Mirrors
• Plane mirrors have a flat reflective surface.
• They produce images that are virtual, upright, and of the same size as the object.
• They are commonly used in everyday life, such as in household mirrors.
• Curved Mirrors
• Curved mirrors bend inward (concave) or outward (convex).
• Concave mirrors can produce real or virtual images depending on the object's position relative to the focal point.
• Convex mirrors always produce virtual, diminished, and upright images.

The correct answer is 10^-10 m.

Key Points

• The radius of a hydrogen atom is approximately 0.53 Ångström (Å), which is equivalent to 0.53 x 10^-10 meters.
• This value is based on the Bohr radius, which is a fundamental physical constant.
• The Bohr radius is derived from the basic principles of quantum mechanics and is crucial for understanding atomic structure.
• Hydrogen, being the simplest atom with one proton and one electron, has its electron orbit at this average distance.

Additional Information

• Bohr Radius:
• The Bohr radius is a physical constant approximately equal to 0.529 x 10^-10 meters.
• It represents the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state.
• Ångström (Å):
• An Ångström is a unit of length equal to 10^-10 meters or 0.1 nanometers.
• It is commonly used to express atomic and molecular dimensions.
• Quantum Mechanics:
• Quantum mechanics is the fundamental theory in physics describing the behavior of matter and energy on atomic and subatomic scales.
• It underpins the calculation of atomic structures, including the hydrogen atom.
• Hydrogen Atom:
• The hydrogen atom is the simplest atom, consisting of one proton and one electron.
• Its simplicity makes it a fundamental model for studying atomic physics and quantum mechanics.

Shortcut Trick

Net percentage change in Curved Surface Area is given by: [a + b + (a × b)/100]

Here, increase in radius (a) = +20% and decrease in height (b) = −30%.

Net % Change = 20 − 30 + [20 × (−30)]/100 = −10 − 6 = −16%.

The negative sign indicates a decrease of 16%.

∴ The correct answer is 16%.

Alternate Method

Given: Increase in radius = 20%, Decrease in height = 30%.

Formula Used: Curved Surface Area (CSA) of cylinder = 2πrh

⇒ Initial CSA₁ = 2 × π × r × h

⇒ New Radius (r') = r + 0.2r = 1.2r

⇒ New Height (h') = h − 0.3h = 0.7h

⇒ New CSA₂ = 2 × π × (1.2r) × (0.7h) = 0.84 × (2πrh)

⇒ Percentage Change = [(CSA₂ − CSA₁) / CSA₁] × 100

⇒ Percentage Change = [(0.84 − 1) / 1] × 100 = −0.16 × 100 = −16%

∴ The correct answer is 16%.

Additional Information

Successive Percentage Change

When a quantity depends on the product of two variables (like CSA = 2πrh), the net percentage change can be calculated using the successive formula: a + b + (ab/100).

Cylinder Surface Area Formulas

Total Surface Area = 2πrh + 2πr² = 2πr(h + r). Area of each base = πr².

Volume Change Property

Volume of cylinder = πr²h. If radius changes by x% and height by y%, Volume change = [(1 + x/100)²(1 + y/100) − 1] × 100.

The correct answer is New Delhi.

Key Points

• The first Project PARI (Public Art of India) was launched in New Delhi in July 2024.
• Project PARI is an initiative by the Ministry of Culture, Government of India.
• The project aims to promote public art and create a platform for artists across India to showcase their work.
• It includes various forms of art installations, murals, and sculptures in public spaces to enhance the cultural landscape of the city.

Additional Information

• Ministry of Culture
• The Ministry of Culture is responsible for the preservation and promotion of art and culture in India.
• It oversees various cultural institutions, museums, and galleries across the country.
• The ministry also organizes cultural events, festivals, and exhibitions to promote India's rich heritage.
• Public Art
• Public art refers to artworks that are created for public spaces and are accessible to everyone.
• It includes sculptures, murals, installations, and performances.
• Public art plays a significant role in enhancing the aesthetic appeal of urban areas and promoting cultural expression.
• Art Installations
• Art installations are large-scale, three-dimensional works designed to transform the perception of a space.
• They can be temporary or permanent and often interact with the environment and audience.
• Installations are a popular form of public art used to convey social, political, and cultural messages.
• Murals
• Murals are large paintings or artworks applied directly to walls, ceilings, or other permanent surfaces.
• They are often used to depict historical events, cultural stories, or social issues.
• Murals can transform public spaces and contribute to the visual identity of a community.

Shortcut Trick

Required percentage = (Marks of B ÷ Marks of A) × 100

⇒ (60 ÷ 75) × 100 = (4 ÷ 5) × 100

⇒ 4 × 20% = 80%

∴ The correct answer is 80%.

Alternate Method

Given:

Marks obtained by A = 75

Marks obtained by B = 60

Formula Used:

Percentage = (Value ÷ Base Value) × 100

Calculations:

⇒ Required Percentage = (60 ÷ 75) × 100

⇒ Required Percentage = (4 ÷ 5) × 100

⇒ Required Percentage = 0.8 × 100

⇒ Required Percentage = 80%

∴ The correct answer is 80%.

Additional Information

Percentage Comparison

When comparing two values, the value following the word 'of' or 'than' is always taken as the Base Value in the denominator.

Fraction to Percentage Conversion

Standard fractions simplify calculations: 1/5 = 20%, 2/5 = 40%, 3/5 = 60%, 4/5 = 80%.

Given: 3 + 13 × 26 ÷ 8 - 4 = ?

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

3 + 13 × 26 ÷ 8 - 4 = ? ⇒ 3 × 13 + 26 - 8 ÷ 4 = ?

⇒ 3 × 13 + 26 - 8 ÷ 4 = ?

⇒ 3 × 13 + 26 - 2 = ?

⇒ 39 + 26 - 2 = ?

⇒ 65 - 2 = ?

⇒ 63 = ?

Hence, "Option 1" is the correct answer.

The correct answer is Newton's third law of motion.

Key Points

• Newton's third law of motion states that for every action, there is an equal and opposite reaction.
• When a sailor jumps out of a rowing boat, he exerts a force on the boat in the forward direction.
• As a reaction, the boat exerts an equal force on the sailor in the opposite direction, causing the boat to move backward.
• This law demonstrates the interaction between two bodies and the forces they exert on each other.

Additional Information

• Newton's First Law of Motion: Also known as the law of inertia, it states that an object will remain at rest or in uniform motion unless acted upon by an external force.
• Newton's Second Law of Motion: This law 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).
• Inertia: The tendency of an object to resist changes in its state of motion.
• Action and Reaction Forces: According to Newton's third law, action and reaction forces act on different bodies, not on the same body.
• Applications: Newton's third law is fundamental in understanding the mechanics of various phenomena, such as rocket propulsion and walking.

The correct answer is membrane.

Key Points

• The cell membrane, also known as the plasma membrane, is a biological membrane that separates and protects the interior of all cells from the outside environment.
• The membrane is selectively permeable, allowing certain substances to pass through while blocking others, maintaining the cell's internal environment.
• It is composed primarily of a lipid bilayer, with embedded proteins that perform various functions such as transport, signaling, and structural support.
• The fluid mosaic model describes the cell membrane as a dynamic structure with lipids and proteins moving laterally within the layer, providing flexibility and functionality.

Additional Information

• Lipid Bilayer
• The lipid bilayer forms the basic structure of the cell membrane, with hydrophobic tails facing inward and hydrophilic heads facing outward, creating a barrier to most water-soluble substances.
• It provides fluidity and flexibility to the membrane, allowing for cell movement and growth.
• Membrane Proteins
• Membrane proteins are integral or peripheral proteins that assist in various functions such as transporting molecules, acting as enzymes, or serving as receptors.
• These proteins are crucial for communication between the cell and its environment.
• Selective Permeability
• The selective permeability of the cell membrane allows the cell to maintain homeostasis by regulating the entry and exit of substances.
• It ensures that essential molecules such as nutrients and ions can enter the cell while waste products are removed.
• Fluid Mosaic Model
• Proposed by S.J. Singer and G.L. Nicolson in 1972, this model describes the cell membrane as a fluid, dynamic structure with proteins embedded in or attached to a fluid lipid bilayer.
• The model emphasizes the flexibility and varied functions of the membrane components.

The correct answer is Sieve tubes and companion cells.

Key Points

• Sieve tubes are elongated cells in the phloem of flowering plants which are responsible for transporting sugars and other nutrients.
• Companion cells are associated with sieve tube elements and help in the maintenance of the sieve tubes and assist in the transport of photosynthetic products.
• Sieve tubes and companion cells are crucial for the long-distance translocation of organic substances in plants.
• The phloem tissue in plants primarily consists of sieve tubes, companion cells, phloem fibers, and phloem parenchyma.

Additional Information

• Phloem is one of the two types of vascular tissues in plants, the other being xylem.
• Xylem is responsible for the transport of water and minerals from roots to other parts of the plant.
• Sieve plates are the porous end walls that facilitate the flow of materials between sieve tube elements.
• Phloem transport is an active process requiring energy in the form of ATP.
• Source-sink relationship in plants refers to the movement of photosynthates from a source (e.g., leaves) to a sink (e.g., roots, fruits).

The logic followed here is:

Option 1) UOI

Option 2) PKI

Option 3) BVP

 

Option 4) KEY

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

Hence, "Option 2" is the correct answer.

The correct answer is P = (V^2)/R.

Key Points

• The relation P = (V^2)/R is derived from Ohm's Law and the power formula in electrical circuits.
• Ohm's Law states that V = IR, where V is voltage, I is current, and R is resistance.
• Power (P) in an electrical circuit is given by P = VI, where V is voltage and I is current.
• Substituting I from Ohm's Law into the power formula, we get P = V(V/R) which simplifies to P = (V^2)/R.
• This formula is particularly useful in calculating power dissipation in resistive elements of electrical circuits.

Additional Information

• Ohm's Law
• Formulated by Georg Simon Ohm, it defines the relationship between voltage, current, and resistance in an electrical circuit.
• Expressed as V = IR, it is a fundamental principle in the study of electrical engineering and physics.
• Power in Electrical Circuits
• Power (P) is the rate at which electrical energy is transferred by an electric circuit.
• Measured in watts (W), it is calculated as P = VI, where V is voltage and I is current.
• Resistance (R)
• Resistance is a measure of the opposition to current flow in an electrical circuit.
• Measured in ohms (Ω), it determines how much current will flow for a given voltage.
• Voltage (V)
• Voltage, also known as electric potential difference, is the force that pushes electric current through a conductor.
• Measured in volts (V), it is a key parameter in designing and analyzing electrical circuits.

The logic followed here is:

Hence, "Option 1" is the correct answer.

The correct answer is It has a small amount of solute dissolved in a large amount of solvent..

Key Points

• A dilute solution is characterized by a small amount of solute in a large amount of solvent.
• The concentration of solute in a dilute solution is much lower compared to the solvent.
• Such solutions are typically homogeneous, meaning the solute is evenly distributed throughout the solvent.
• Examples include a small amount of salt in water or a tiny quantity of sugar in tea.

Additional Information

• Concentration
• Refers to the amount of solute present in a given quantity of solvent or solution.
• It can be expressed in various units, such as molarity, molality, or percentage.
• Solute
• The substance that is dissolved in a solvent to form a solution.
• It can be a solid, liquid, or gas.
• Solvent
• The substance in which the solute is dissolved.
• Water is known as the "universal solvent" because it can dissolve a wide variety of substances.
• Homogeneous Mixture
• A mixture where the components are evenly distributed and not easily distinguishable.
• Solutions are a type of homogeneous mixture.

Shortcut Trick

Total interest percentage = Rate × Time

Interest % = 7% × 9 = 63%

Simple Interest = 63% of ₹700 = 0.63 × 700 = ₹441

∴ The correct answer is ₹441.

Alternate Method

Given:

Principal (P) = ₹700

Rate (R) = 7% per month

Time (T) = 9 months

Formula Used:

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

Calculations:

⇒ SI = (700 × 7 × 9) ÷ 100

⇒ SI = 7 × 7 × 9

⇒ SI = 49 × 9

⇒ SI = ₹441

∴ The correct answer is ₹441.

Additional Information

Total Amount Formula

The total amount (A) is the sum of Principal and Simple Interest: A = P + SI = P(1 + RT/100).

Rate and Time Units

Always ensure the Rate and Time are in the same unit (e.g., both per month or both per year) before calculation.

Simple Interest Characteristic

Unlike Compound Interest, Simple Interest remains constant for every equal time interval as it is always calculated on the original Principal.

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

According to the question, such symbols which are immediately preceded by a symbols and is immediately followed by another symbol:

Required condition: Symbol - Symbols - Symbol

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

Thus, there is one such such symbols which are immediately preceded by a symbols and is immediately followed by another symbol.

Hence, "Option 4" is the correct answer.

The correct answer is Refraction of light.

Key Points

• The wavy appearance of objects seen through a turbulent stream of hot air is caused by the refraction of light.
• Refraction occurs when light passes through mediums of different densities, causing a change in its speed and direction.
• In a turbulent stream of hot air, the varying temperatures create regions of different air densities, resulting in continuous changes in the light's path.
• This effect is especially noticeable when looking at objects through the hot air above surfaces like roads or rooftops on a sunny day.
• The phenomenon is similar to the mirage effect observed in deserts or over hot pavements.

Additional Information

• Refraction
• Refraction is the bending of light as it passes from one medium to another with different densities.
• It is governed by Snell's Law, which relates the angles of incidence and refraction to the indices of refraction of the two media.
• Common examples of refraction include the bending of light in water and the formation of rainbows.
• Mirage
• A mirage is an optical phenomenon that creates the illusion of water or a distorted image of distant objects.
• It is caused by the refraction of light through layers of air at different temperatures.
• Mirages are commonly seen on hot roads or deserts where the ground heats the air above it.
• Diffraction
• Diffraction is the bending of light around obstacles or through small openings.
• It leads to the formation of patterns of light and dark bands or fringes.
• This phenomenon is different from refraction and is observed in wave-like behavior of light.
• Interference
• Interference is the phenomenon where two waves superimpose to form a resultant wave of greater, lower, or the same amplitude.
• It can be constructive (amplifying) or destructive (diminishing) based on the phase relationship of the waves.
• Interference is a fundamental concept in wave optics and is responsible for various optical effects like thin-film interference seen in soap bubbles.

Shortcut Trick

Arrange in ascending order: 4, 4, 6, 7, 8, 9, 9, 11, 12, 14.

Number of observations (n) = 10 (even).

Median = Average of 5^th and 6^th terms.

Median = (8 + 9) ÷ 2 = 8.5.

∴ The correct answer is 8.5.

Alternate Method

Given: Observations = 4, 14, 11, 9, 7, 8, 9, 12, 4, 6

Formula Used: If n is even, Median = [(n/2)^th term + (n/2 + 1)^th term] ÷ 2

⇒ Arrange observations in ascending order: 4, 4, 6, 7, 8, 9, 9, 11, 12, 14

⇒ Count of observations n = 10

⇒ Median = [(10/2)^th term + (10/2 + 1)^th term] ÷ 2

⇒ Median = [5^th term + 6^th term] ÷ 2

⇒ 5^th term = 8, 6^th term = 9

⇒ Median = (8 + 9) ÷ 2 = 17 ÷ 2

⇒ Median = 8.5

∴ The correct answer is 8.5.

Additional Information

Median for Odd Number of Terms

If the number of observations n is odd, the median is simply the ((n + 1)/2)^th term after sorting.

Relation between Mean, Median, and Mode

For a moderately skewed distribution, the empirical formula is: Mode = 3 × Median − 2 × Mean.

Range of Data

Range = Maximum Value − Minimum Value. In this set, Range = 14 − 4 = 10.

Shortcut Trick

Ratio of Length (L) to Breadth (B) = 3 : 1

Sum of ratio parts for perimeter = 2 × (3 + 1) = 8 units

8 units = 48 cm ⇒ 1 unit (Breadth) = 6 cm & 3 units (Length) = 18 cm

Area = L × B = 18 × 6 = 108 cm²

∴ The correct answer is 108 cm².

Alternate Method

Given: Perimeter = 48 cm, Length (L) = 3 × Breadth (B)

Formula Used: Perimeter = 2(L + B) | Area = L × B

⇒ Let Breadth = x, then Length = 3x

⇒ 2(3x + x) = 48

⇒ 2(4x) = 48

⇒ 8x = 48

⇒ x = 6 cm

⇒ Length = 3 × 6 = 18 cm

⇒ Area = 18 × 6 = 108 cm²

∴ The correct answer is 108 cm².

Additional Information

Properties of a Rectangle

A rectangle is a quadrilateral with opposite sides equal and all interior angles equal to 90°.

Diagonal of a Rectangle

The length of the diagonal (d) is calculated using Pythagoras theorem: d = √(L² + B²).

Relation between Area and Perimeter

For a given perimeter, the area is maximum when the rectangle is a square (L = B).

Shortcut Trick

When the distance covered is equal for both parts of the journey, the Average Speed is given by the formula: [2 × s₁ × s₂] ÷ (s₁ + s₂).

Average Speed = [2 × 4 × 20] ÷ (4 + 20)

Average Speed = 160 ÷ 24 = 20/3 km/h

∴ The correct answer is 20/3 km/h.

Alternate Method

Given: Speed while walking (s₁) = 4 km/h, Speed on scooter (s₂) = 20 km/h.

Formula Used: Average Speed = Total Distance ÷ Total Time

⇒ Let the distance from Home to School be 'd' km.

⇒ Time taken to walk (t₁) = d ÷ 4

⇒ Time taken to return (t₂) = d ÷ 20

⇒ Total Distance = d + d = 2d km

⇒ Total Time = (d/4) + (d/20) = (5d + d)/20 = 6d/20 = 3d/10 hours

⇒ Average Speed = 2d ÷ (3d/10) = (2d × 10) ÷ 3d

⇒ Average Speed = 20/3 km/h

∴ The correct answer is 20/3 km/h.

Additional Information

Harmonic Mean for Average Speed

When distances are constant, the average speed is the harmonic mean of the individual speeds: Average Speed = n ÷ [ (1/s₁) + (1/s₂) + ... + (1/s_n) ].

Average Speed for Constant Time

If a person travels at different speeds for equal time intervals, the average speed is the arithmetic mean: Average Speed = (s₁ + s₂) ÷ 2.

Unit Conversion

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

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

Key Points

• Pyruvate is converted into ethanol and carbon dioxide in yeast during fermentation: This anaerobic process is known as alcoholic fermentation and occurs in yeast cells.
• In muscle cells, pyruvate is converted into lactic acid: This process is known as lactic acid fermentation and occurs under anaerobic conditions in muscle cells.
• During anaerobic respiration, the complete breakdown of glucose does not occur, which leads to the formation of by-products such as ethanol, carbon dioxide, and lactic acid.
• These processes allow cells to generate energy (ATP) without the presence of oxygen, although less efficiently than aerobic respiration.

Additional Information

• Chloroplast: The organelle in plant cells where photosynthesis occurs. It is not involved in the breakdown of pyruvate using oxygen.
• Aerobic Respiration: A metabolic process in which pyruvate is fully broken down to carbon dioxide and water in the presence of oxygen, primarily occurring in the mitochondria.
• Fermentation: A metabolic process that converts sugar to acids, gases, or alcohol in the absence of oxygen. It includes alcoholic fermentation in yeast and lactic acid fermentation in muscle cells.
• ATP (Adenosine Triphosphate): The energy currency of the cell, produced during both aerobic and anaerobic respiration.
• Mitochondria: The powerhouse of the cell where aerobic respiration and energy (ATP) production take place.