RRB Technician Grade III Official Paper (Held On: 27 Dec, 2024 Shift 3) (Previous Year Paper)

The correct answer is NaOH + H2 + Cl2.

Key Points

• The chlor-alkali process involves the electrolysis of an aqueous sodium chloride (NaCl) solution, also known as brine.
• When electricity is passed through the brine, it decomposes into three main products: sodium hydroxide (NaOH), chlorine gas (Cl2), and hydrogen gas (H2).
• The reactions occurring at the electrodes are:
• Cathode (Reduction): 2H₂O + 2e^- → H₂ + 2OH^-
• Anode (Oxidation): 2Cl^- → Cl₂ + 2e^-
• The sodium ions (Na⁺) in the solution combine with the hydroxide ions (OH^-) to form sodium hydroxide (NaOH).
• The products NaOH, H2, and Cl2 are commercially valuable. Sodium hydroxide is used in the manufacture of paper, soap, and detergents. Chlorine is used for disinfecting water, in the production of PVC, and in the manufacture of various chemicals. Hydrogen is used in hydrogenation processes and as a fuel.

 Additional Information

• NaCl + H2
• This option is incorrect because sodium chloride (NaCl) is the reactant, not the product, in the chlor-alkali process.
• Hydrogen gas (H2) is indeed produced, but not sodium chloride.
• NaHCO3 + Cl2
• This option is incorrect because sodium bicarbonate (NaHCO3) is not produced in the chlor-alkali process.
• Chlorine gas (Cl2) is produced, but not sodium bicarbonate.
• H2 + O2
• This option is incorrect because oxygen gas (O2) is not produced in the chlor-alkali process.
• Hydrogen gas (H2) is produced, but not oxygen.

The correct answer is homologous series.

Key Points

• A homologous series is a group of organic compounds that have a similar general formula and possess similar chemical properties.
• In a homologous series, each successive member differs by a -CH2- unit.
• The members of a homologous series are called homologues.
• Homologous series exhibit a gradual change in physical properties such as boiling point, melting point, and density.
• Examples of homologous series include alkanes, alkenes, and alkynes.
• One notable characteristic is that the functional group remains the same throughout the series.
• Homologous series are important in organic chemistry because they help in the systematic study and prediction of properties of organic compounds.

 Additional Information

• Isomers
• Isomers are compounds that have the same molecular formula but different structural arrangements.
• Isomers can be classified into structural isomers and stereoisomers.
• Structural isomers have different connectivity of atoms, while stereoisomers have the same connectivity but differ in spatial arrangement.
• Isochores
• Isochores are regions of DNA with a high degree of uniformity in base composition.
• They are significant in the field of genetics and genomics.
• Isobars
• Isobars are atoms of different chemical elements that have the same number of nucleons.
• Isobars differ in chemical properties because they have different atomic numbers.

Shortcut Trick

Effective Rate of Interest for 2 years at 4% = x + y + (xy/100)

⇒ 4 + 4 + (4 × 4)/100 = 8.16%

Compound Interest = 8.16% of ₹13,000

⇒ 130 × 8.16 = ₹1060.80

∴ The correct answer is ₹1060.80.

Alternate Method

Given: Principal (P) = ₹13,000, Rate (R) = 4%, Time (n) = 2 years

Formula Used: Amount (A) = P(1 + R/100)ⁿ; CI = A − P

⇒ A = 13000(1 + 4/100)²

⇒ A = 13000(104/100) × (104/100)

⇒ A = 130 × 1.04 × 104 = 14060.80

⇒ CI = 14060.80 − 13000

⇒ CI = ₹1060.80

∴ The correct answer is ₹1060.80.

Additional Information

Successive Percentage Method

Compound interest is essentially the result of successive percentage increases on the principal amount.

Difference between SI and CI

For 2 years, the difference between CI and SI is given by the formula: D = P(R/100)².

Compounding Half-Yearly

If interest is compounded half-yearly, the rate is halved (R/2) and the time is doubled (2n).

Shortcut Trick

Net difference between Monday and Friday = Number of days × (Difference in averages)

⇒ Monday − Friday = 4 × (48 − 46) = 4 × 2 = 8°C

⇒ 42 − Friday = 8

⇒ Friday = 42 − 8 = 34°C

∴ The correct answer is 34°C.

Alternate Method

Given:

Average (Mon, Tue, Wed, Thu) = 48°C

Average (Tue, Wed, Thu, Fri) = 46°C

Temperature on Monday = 42°C

Formula Used:

Sum of observations = Average × Number of observations

Calculations:

⇒ Sum(Mon + Tue + Wed + Thu) = 48 × 4 = 192°C

⇒ Sum(Tue + Wed + Thu + Fri) = 46 × 4 = 184°C

⇒ (Mon + Tue + Wed + Thu) − (Tue + Wed + Thu + Fri) = 192 − 184

⇒ Mon − Fri = 8°C

⇒ 42 − Fri = 8

⇒ Fri = 42 − 8 = 34°C

∴ The correct answer is 34°C.

Additional Information

Average of a Group

Average = (Sum of all observations) ÷ (Total number of observations).

Deviation Method

If one member is replaced, the change in sum = (Number of members) × (Change in Average).

Temperature Problems

In overlapping day series, common days cancel out when subtracting the total sums of the two sets.

The correct answer is Magnetic field lines are not closed curves..

Key Points

• Magnetic field lines are indeed closed curves. They start from the north pole of a magnet and end at the south pole, forming continuous loops inside and outside the magnet.
• No two field lines are found to cross each other. If they did, it would mean that the magnetic field has two directions at that point, which is not possible.
• Inside the magnet, the direction of field lines is from its south pole to its north pole. This is part of the continuous loop of the magnetic field lines.
• The relative strength of the magnetic field is shown by the degree of closeness of the field lines. The closer the lines, the stronger the magnetic field in that region.

 Additional Information

• No two field lines cross each other
• If two magnetic field lines crossed, it would imply that the magnetic field has two different directions at the same point, which is impossible.
• Inside the magnet, the direction of field lines is from south to north
• This indicates that magnetic field lines form closed loops, going from north to south outside the magnet and from south to north inside the magnet.
• The relative strength of the magnetic field
• The closeness of magnetic field lines indicates the strength of the magnetic field; closer lines mean a stronger field.

Shortcut Trick

Total Votes = 7500

Valid Votes = 80% of 7500 = 6000

Winner gets 55%, so Other Candidate gets 45% of valid votes.

Other Candidate = 45% of 6000 = 0.45 × 6000 = 2700

∴ The correct answer is 2700 votes.

Alternate Method

Given:

Total votes = 7500

Invalid votes = 20%

Winner candidate share = 55% of valid votes

Calculations:

⇒ Total Valid votes = 7500 × (100 − 20)%

⇒ Total Valid votes = 7500 × 80/100 = 6000

⇒ Other candidate share = 100% − 55% = 45% of valid votes

⇒ Votes for other candidate = 45/100 × 6000

⇒ Votes for other candidate = 45 × 60 = 2700

∴ The correct answer is 2700 votes.

Additional Information

Percentage Base Change

Always identify the correct base for percentages. In elections, candidate percentages are usually calculated on Valid Votes, not Total Votes, unless specified otherwise.

Successive Percentage Shortcut

Result = Total × (Valid % / 100) × (Candidate % / 100). Here, 7500 × 0.80 × 0.45 = 2700.

Shortcut Trick

Growth rate = 5% → Multiplying factor = 1 + 5/100 = 1.05

Successive increase for 2 years = (1.05)² = 1.1025

New Population = 1,76,400 × 1.1025 = 1,94,481

∴ The correct answer is 1,94,481.

Alternate Method

Given:

Present Population (P) = 1,76,400

Rate of Increase (R) = 5%

Time period (n) = 2 years

Formula Used:

Population after n years = P × (1 + R/100)ⁿ

Calculations:

⇒ Population = 1,76,400 × (1 + 5/100)²

⇒ Population = 1,76,400 × (105/100) × (105/100)

⇒ Population = 1,76,400 × (21/20) × (21/20)

⇒ Population = 1,76,400 × (441/400)

⇒ Population = 441 × 441

⇒ Population = 1,94,481

∴ The correct answer is 1,94,481.

Additional Information

Population Decrease

If the population decreases at rate R, the formula becomes: P × (1 − R/100)ⁿ.

Successive Percentage Method

For two years, the net percentage change can be calculated as x + y + (xy/100). Here, 5 + 5 + (25/100) = 10.25%.

Finding Previous Population

To find the population n years ago, the formula is: Population / (1 + R/100)ⁿ.

Given:

(24 ÷ 3) × 2

Formula used:

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

Calculations:

(24 ÷ 3) × 2

⇒ 8 × 2

⇒ 16

∴ The correct answer is option (3).

Shortcut Trick

Using the price-quantity-percentage relation: (Price₁) ÷ (Quantity₁ × Selling%₁) = (Price₂) ÷ (Quantity₂ × Selling%₂)

Here, Selling%₁ = 100% − Loss% = 100% − 20% = 80%

And, Selling%₂ = 100% + Gain% = 100% + 20% = 120%

Let the required quantity of oranges be x.

⇒ 40 ÷ (8 × 80) = 30 ÷ (x × 120)

⇒ 40 ÷ 640 = 30 ÷ (120x) ⇒ 1 ÷ 16 = 1 ÷ (4x) ⇒ 4x = 16 ⇒ x = 4

∴ The correct answer is 4.

Alternate Method

Given:

Selling Price (SP₁) of 8 oranges = ₹40

Loss percentage = 20%

Desired Gain percentage = 20%

New Total Selling Price (SP₂) = ₹30

Formulas:

Cost Price (CP) = SP × 100 ÷ (100 − Loss%)

New Selling Price (SP) = CP × (100 + Gain%) ÷ 100

Steps:

⇒ SP of 1 orange in first case = 40 ÷ 8 = ₹5

⇒ Since there is a 20% loss, CP of 1 orange = 5 × 100 ÷ (100 − 20) = 5 × 100 ÷ 80 = ₹6.25

⇒ CP of 8 oranges = 8 × 6.25 = ₹50

⇒ To gain 20%, SP of 8 oranges should be = 50 × (100 + 20) ÷ 100 = 50 × 1.2 = ₹60

⇒ If 8 oranges are sold for ₹60 to get 20% gain, then the number of oranges to be sold for ₹30 is:

⇒ Quantity for ₹30 = (8 ÷ 60) × 30 = 4 oranges

∴ The correct answer is 4.

Additional Information

Unitary Method in Price and Quantity

For a constant total value, the quantity sold is inversely proportional to the price per unit. When the required profit increases, the selling price per unit increases, which means fewer items must be sold for the same amount of money.

The correct answer is either positive or negative.

Key Points

• The work done by a constant force on a body depends on the direction of the force relative to the direction of the displacement of the body.
• If the force is in the same direction as the displacement, the work done is positive.
• If the force is in the opposite direction to the displacement, the work done is negative.
• When the force and displacement are perpendicular to each other, the work done is zero.
• Therefore, the work done by a constant force can be positive, negative, or zero.

 Additional Information

• always zero
• This option is incorrect because the work done by a constant force is not always zero.
• Work done can be zero only if the force is perpendicular to the displacement.
• always positive
• This option is incorrect because the work done by a constant force is not always positive.
• Work done is positive only if the force is in the same direction as the displacement.
• always negative
• This option is incorrect because the work done by a constant force is not always negative.
• Work done is negative only if the force is in the opposite direction to the displacement.

The correct answer is Samir Kumar Sinha.

Key Points

• Samir Kumar Sinha took over as the new Director General (Acquisition) in the Defence Ministry in January 2024.
• The position of Director General (Acquisition) plays a crucial role in overseeing and managing the procurement of defense equipment and services for the Indian Armed Forces.
• Prior to this appointment, Samir Kumar Sinha has held various significant positions within the defense sector.
• The role is vital for ensuring that the defense acquisition process is streamlined, transparent, and efficient.
• The appointment comes at a time when the Indian government is focusing on modernizing its defense forces and enhancing self-reliance in defense production.

The Correct answer is kinetic energy.

Key Points

• Kinetic energy is the energy possessed by a body due to its motion.
• It is calculated using the formula: KE = 1/2 mv², where m is the mass of the object and v is its velocity.
• All moving objects have kinetic energy, regardless of their direction of motion.
• Examples include a moving car, a flying airplane, a flowing river, and even the particles in a gas or liquid.
• Conversion of energy: Kinetic energy can be converted into other forms of energy, such as potential energy, thermal energy, etc.
• It is a scalar quantity and always has a positive value.
• The SI unit of kinetic energy is the joule (J).

 Additional Information

• Electromagnetic energy
• Electromagnetic energy is a form of energy that is reflected or emitted in the form of electrical and magnetic waves that can travel through space.
• Examples include light, radio waves, and X-rays.
• Nuclear energy
• Nuclear energy is the energy released during nuclear reactions, such as fission or fusion.
• It is used in nuclear power plants and nuclear weapons.
• Potential energy
• Potential energy is the energy possessed by an object due to its position or configuration.
• Examples include a stretched spring or an object held at a height.

Given: 

Town I is to the east of Town X.

Town L is to the west of Town X.

Town N is to the north of Town L.

Town P is to the north-east of Town L.

Town P is to the east of Town N.

Town I is to the south-west of Town P. 

So, Town P is in 'North-east' direction with respect to Town X

Hence, the correct answer is "Option 1".

Shortcut Trick

An identity must hold true for all values of the variables involved.

Test option 3 with a = 1, b = 1:

LHS = (1 + 1)² = 2² = 4 | RHS = 1² + 1² = 2

Since 4 ≠ 2, the equation is not an identity.

∴ The correct answer is (a + b)² = a² + b².

Alternate Method

Given: Four mathematical expressions to identify which is not an identity.

Concept: An identity is an equality that remains true regardless of the values chosen for its variables. An equation that is true only for specific values is not an identity.

⇒ Option 1: (a + b)² = a² + b² + 2ab (Standard Algebraic Identity)

⇒ Option 2: (a + 1)(a + 2) = a × a + a × 2 + 1 × a + 1 × 2 = a² + 3a + 2 (True for all 'a')

⇒ Option 4: (a − b)² = a² + b² − 2ab (Standard Algebraic Identity)

⇒ Option 3: (a + b)² = a² + b²

⇒ Expanding LHS: a² + b² + 2ab

⇒ Comparing with RHS: a² + b² + 2ab ≠ a² + b² (unless a × b = 0)

∴ The correct answer is (a + b)² = a² + b².

Additional Information

Algebraic Identity

An equality relation A = B, such that A and B contain some variables and A and B produce the same value as each other regardless of what values are substituted for the variables.

Difference of Squares

A very common identity used in simplification is (a + b)(a − b) = a² − b².

Conditional Equations

Equations like x + 2 = 5 are only true for x = 3, hence they are not identities.

The Correct answer is Only statement I is correct.

Key Points

• Saturated carbon compounds are hydrocarbons where carbon atoms are connected by single covalent bonds.
• These compounds are typically alkanes.
• Unsaturated carbon compounds are hydrocarbons where carbon atoms are connected by double or triple covalent bonds.
• These compounds include alkenes (with double bonds) and alkynes (with triple bonds).
• Statement I correctly describes saturated carbon compounds.
• Statement II incorrectly describes unsaturated carbon compounds as having single covalent bonds, which is characteristic of saturated compounds.

 Additional Information

• Saturated hydrocarbons
• These are aliphatic hydrocarbons like methane, ethane, and propane.
• They are generally less reactive than unsaturated hydrocarbons.
• Unsaturated hydrocarbons
• These compounds include ethene (ethylene) and ethyne (acetylene).
• They are more reactive due to the presence of multiple bonds.

The correct answer is Both I and II are possible reasons.

Key Points

• Migration refers to the movement of a person or people from one country, locality, or place of residence to settle in another.
• Reason I explains that migration occurs due to various factors such as the search for work, economic opportunities, joining family, or studying. Additionally, people may migrate to escape conflict, persecution, terrorism, or human rights violations.
• Reason II highlights that migration can also be driven by environmental factors such as the adverse effects of climate change, natural disasters, or other environmental challenges.
• Both reasons are valid and encompass a wide range of factors that contribute to migration.

 Additional Information

• Reason I
• People often migrate for economic opportunities such as better job prospects and higher wages.
• Family reunification is another important factor where people move to join family members already settled in another region.
• Many students migrate to pursue higher education and enhance their skills.
• Migration also occurs as a means to escape conflict, persecution, or human rights violations, ensuring personal safety and security.
• Reason II
• Climate change has led to environmental degradation, prompting people to move to safer areas.
• Natural disasters such as earthquakes, floods, and hurricanes can cause significant displacement.
• Other environmental factors like desertification and rising sea levels also contribute to migration.

The correct answer is Kulhad — non-biodegradable.

Key Points

• Kulhad is a traditional clay cup commonly used in India for serving tea or other beverages.
• It is made from natural clay and is therefore biodegradable.
• Being biodegradable, kulhads can decompose naturally over time and do not harm the environment.
• This makes kulhads environmentally friendly compared to plastic or other non-biodegradable materials.

 Additional Information

• Vegetable — biodegradable
• Vegetables are organic matter and decompose naturally.
• They are classified as biodegradable because they break down through natural processes.
• This decomposition enriches the soil with nutrients.
• Plastic glass — non-biodegradable
• Plastic glass is made from synthetic materials.
• It is classified as non-biodegradable because it does not decompose naturally.
• Improper disposal can lead to environmental pollution.
• Paper cup — biodegradable
• Paper cups are made from paper, which is a natural material.
• They are generally biodegradable and can decompose naturally.
• However, if coated with plastic, they may not be fully biodegradable.

Shortcut Trick

Since ∠Q = ∠R, Δ PQR is an Isosceles triangle with PQ = PR = 10 cm.

In an isosceles triangle, the altitude PS bisects the base QR → QS = SR = 12 ÷ 2 = 6 cm.

Using Pythagorean triplet (6, 8, 10) in right-angled Δ PSQ: PS² + 6² = 10².

PS = √(100 − 36) = √64 = 8 cm.

∴ The correct answer is 8 cm.

Alternate Method

Given: QR = 12 cm, PR = 10 cm, ∠Q = ∠R.

Formula Used: Pythagoras Theorem: Hypotenuse² = Base² + Perpendicular².

⇒ In Δ PQR, as ∠Q = ∠R, sides opposite to equal angles are equal ∴ PQ = PR = 10 cm.

⇒ PS is the altitude to the base QR of an isosceles triangle, so it bisects QR.

⇒ QS = SR = QR ÷ 2 = 12 ÷ 2 = 6 cm.

⇒ In right Δ PSQ, PQ² = PS² + QS².

⇒ 10² = PS² + 6²

⇒ 100 = PS² + 36

⇒ PS² = 64

⇒ PS = 8 cm.

∴ The correct answer is 8 cm.

Additional Information

Isosceles Triangle Properties

The altitude from the vertex between equal sides to the base bisects the base and the vertex angle.

Pythagorean Triplets

Common triplets like (3, 4, 5), (6, 8, 10), and (5, 12, 13) help solve right-triangle problems instantly.

Area of Triangle

Area = 1/2 × Base × Height. For this triangle, Area = 1/2 × 12 × 8 = 48 cm².

The correct answer is NaHCO3.

Key Points

• NaHCO3 is commonly known as sodium bicarbonate or baking soda.
• In a soda-acid fire extinguisher, sodium bicarbonate reacts with sulfuric acid to produce carbon dioxide gas.
• The carbon dioxide gas produced helps to smother the fire by cutting off the oxygen supply.
• This reaction also produces water, which helps in cooling the fire.
• Sodium bicarbonate is preferred due to its easy availability, cost-effectiveness, and non-toxic nature.

 Additional Information

• Na2CO3
• Sodium carbonate, also known as soda ash or washing soda, is not used in fire extinguishers.
• It is primarily used in glass manufacturing and as a cleaning agent.
• H2CO3
• Carbonic acid is a weak acid formed when carbon dioxide dissolves in water.
• It is not used in fire extinguishers and is primarily found in carbonated beverages.
• Ca(OH)2
• Calcium hydroxide, also known as slaked lime or hydrated lime, is not suitable for fire extinguishers.
• It is commonly used in construction, water treatment, and agriculture.

The Correct answer is 9 J.

Key Points

• The formula to calculate kinetic energy (KE) is KE = 1/2 * m * v², where m is the mass and v is the velocity.
• Given, mass (m) = 0.5 kg and velocity (v) = 6 m/s.
• Substituting the values in the formula: KE = 1/2 * 0.5 kg * (6 m/s)².
• Calculating the velocity squared: (6 m/s)² = 36 m²/s².
• Now, KE = 1/2 * 0.5 kg * 36 m²/s² = 0.25 kg * 36 m²/s².
• Finally, KE = 9 J.
• Therefore, the kinetic energy of the ball is 9 J.

Shortcut Trick

Equate work: (6M + 8B) × 10 = (26M + 48B) × 2

⇒ 60M + 80B = 52M + 96B ⇒ 8M = 16B ⇒ 1M = 2B

Total Work = (6M + 8B) × 10 = (12B + 8B) × 10 = 200B

Required Efficiency (40M + 20B) = (80B + 20B) = 100B

Time = 200B ÷ 100B = 2 days

∴ The correct answer is 2 days.

Alternate Method

Given:

Case 1: 6 men and 8 boys in 10 days

Case 2: 26 men and 48 boys in 2 days

Formula Used:

M₁D₁ = M₂D₂ (where M is the total efficiency and D is time)

Calculations:

⇒ (6M + 8B) × 10 = (26M + 48B) × 2

⇒ 30M + 40B = 26M + 48B

⇒ 4M = 8B ⇒ 1M = 2B

⇒ Total Work = (6 × 2B + 8B) × 10 = 20B × 10 = 200B units

⇒ Efficiency of 40 men + 20 boys = (40 × 2B + 20B) = 100B units/day

⇒ Time taken = 200B ÷ 100B = 2 days

∴ The correct answer is 2 days.

Additional Information

Man-Day Concept

The amount of work done is proportional to the number of persons and the time taken: W = M × D × H.

Efficiency Ratio

If 1 man = 2 boys, the efficiency ratio of Man to Boy is 2 : 1. Always convert all entities into a single unit (either all Men or all Boys).

Work and Wages

Wages are always distributed in the ratio of the actual work done or the ratio of efficiencies if they work for the same duration.

The logic followed here is:

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

For, X : 163

⇒ (X × 2) + 1 = 163

⇒ X = (163 - 1) ÷ 2 = 162 ÷ 2 = 81

Similarly, 

For, 74 : Y

⇒ (74 × 2) + 1 = Y

⇒ 148 + 1 = 149

Hence, the correct answer is "Option 1".

The logic follows here is,

Given:

SALT-ALST-TLAS

And, HOLE -OLHE - ELOH

Similarly, in option (3): VIBE - IBVE - EBIV

Hence the correct answer is "Option 1"

The correct answer is Urethra - a pair.

Key Points

• The urethra is a tube that carries urine from the urinary bladder to the outside of the body.
• In males, the urethra also carries semen during ejaculation.
• Humans have a single urethra, which is unpaired.
• The female urethra is approximately 4 cm long, while the male urethra is about 20 cm long.
• The urethra opens at the external urethral orifice, which is located at the tip of the penis in males and above the vaginal opening in females.

 Additional Information

• Ureter
• The ureters are a pair of tubes that carry urine from the kidneys to the urinary bladder.
• Each human body has a pair of ureters, one attached to each kidney.
• The ureters are approximately 25-30 cm long.
• They enter the urinary bladder at an oblique angle to prevent the backflow of urine.
• Kidney
• Humans have a pair of kidneys, which are vital organs for filtering blood and producing urine.
• Each kidney is located on either side of the spine, just below the rib cage.
• Kidneys help in removing waste products and excess substances from the blood.
• They also regulate electrolyte balance and blood pressure.
• Urinary bladder
• The urinary bladder is a hollow, muscular organ that stores urine until it is excreted.
• It is located in the pelvis, just above and behind the pubic bone.
• The bladder can hold between 300-500 mL of urine.
• When it is full, stretch receptors in the bladder signal the brain to initiate the urge to urinate.

The Correct answer is Chlorine gas.

Key Points

• Bleaching powder is chemically known as calcium hypochlorite (Ca(OCl)₂).
• It is produced by the action of chlorine gas on dry slaked lime (calcium hydroxide).
• The chemical reaction involved is: Ca(OH)₂ + Cl₂ → Ca(OCl)₂ + H₂O.
• Bleaching powder is widely used for disinfecting drinking water and in the textile industry for bleaching fabrics.
• It is also utilized in the paper industry for bleaching wood pulp.
• The process of making bleaching powder involves solid-phase reactions where chlorine gas is passed over dry slaked lime.

 Additional Information

• Hydrogen gas
• Hydrogen gas is the lightest and most abundant element in the universe.
• It is commonly used in industrial processes such as ammonia production and hydrogenation of fats and oils.
• Hydrogen is also being explored as a clean fuel alternative in fuel cells and hydrogen-powered vehicles.
• Carbon dioxide gas
• Carbon dioxide (CO₂) is a colorless, odorless gas found in Earth's atmosphere.
• It is used in various industries, including the beverage industry for carbonation and the food industry for refrigeration and preservation.
• CO₂ is also a significant greenhouse gas contributing to global warming.
• Water
• Water (H₂O) is a universal solvent and essential for all known forms of life.
• It is used in a wide range of applications including drinking, agriculture, industrial processes, and sanitation.
• Water is chemically neutral and does not react with slaked lime to produce bleaching powder.

The logic followed here is:

Option 1) LP-MQ

Option 2) FJ-GI

Option 3) IM-JL

Option 4) QU-RT

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

Hence, "Option 1" is the correct answer

The correct answer is Decrease in the amount of ozone in the atmosphere is due to chlorofluorocarbons (CFC)..

Key Points

• Ozone is a molecule composed of three oxygen atoms (O₃).
• Ozone depletion refers to the thinning of the ozone layer in the Earth's stratosphere.
• Chlorofluorocarbons (CFCs) are the primary cause of ozone layer depletion. CFCs are man-made chemical compounds used in air conditioning, refrigeration, and aerosol propellants.
• When CFCs are released into the atmosphere, they eventually rise to the stratosphere, where they are broken down by UV radiation, releasing chlorine atoms.
• The chlorine atoms react with ozone molecules, causing the ozone to break down into oxygen molecules, thus depleting the ozone layer.
• The Montreal Protocol was established in 1987 to phase out the production and use of substances that deplete the ozone layer, including CFCs.

 Additional Information

• It is not poisonous.
• Ozone at ground level is harmful and can cause respiratory problems and other health issues. While in the stratosphere, it is essential for blocking harmful UV radiation.
• It is formed by combining only two atoms of oxygen.
• Ozone is actually formed by combining three oxygen atoms (O₃), not two. The molecule of two oxygen atoms is regular oxygen (O₂).
• It causes blood cancer.
• There is no direct evidence linking ozone to blood cancer. However, exposure to high levels of ground-level ozone can cause respiratory problems and other health issues.

Given:

x = 3² × 2³

Formula used:

(a^m × bⁿ)^p = a^m×p × b^n×p

Calculations:

We need to find the value of x⁴

⇒ x⁴ = (3² × 2³)⁴

⇒ x⁴ = 3^2×4 × 2^3×4

⇒ x⁴ = 3⁸ × 2¹²

∴ The correct answer is option (4).

Shortcut Trick

For a ratio a : b : c, the inverse ratio is (b×c) : (a×c) : (a×b).

Given ratio → 1 : 2 : 3

Inverse parts → (2×3) : (1×3) : (1×2)

⇒ 6 : 3 : 2

∴ The correct answer is 6 : 3 : 2.

Alternate Method

Given: Ratio = 1 : 2 : 3

Formula Used: Inverse ratio of a : b : c is 1/a : 1/b : 1/c

Calculations:

⇒ Inverse ratio = 1/1 : 1/2 : 1/3

⇒ To convert to whole numbers, multiply each term by the LCM of denominators (1, 2, 3) = 6

⇒ (1/1 × 6) : (1/2 × 6) : (1/3 × 6)

⇒ 6 : 3 : 2

∴ The correct answer is 6 : 3 : 2.

Additional Information

Inverse Ratio Property

The inverse ratio (or reciprocal ratio) of a : b is 1/a : 1/b, which simplifies to b : a.

Compound Ratio

The compound ratio of (a : b) and (c : d) is (a×c) : (b×d).

Duplicate and Sub-duplicate Ratio

Duplicate ratio of a : b is a² : b², and sub-duplicate ratio is √a : √b.

The correct answer is Helps the cells to grow longer.

Key Points

• Auxins are a class of plant hormones that play a crucial role in the growth and development of plants.
• They are primarily involved in the elongation of cells in the shoots and roots.
• Auxins stimulate cell elongation by loosening the cell walls, which allows the cells to take up more water and expand.
• They are also involved in various other plant growth processes such as apical dominance, root initiation, and fruit development.
• Auxins are produced in the apical meristems (growth regions at the tips of roots and shoots) and are transported to other parts of the plant where they exert their effects.
• One of the most well-known auxins is Indole-3-acetic acid (IAA), which is naturally occurring in plants.

 Additional Information

• Make plants insect resistant
• This function is not related to auxins. Instead, plant resistance to insects is often achieved through genetic modifications or breeding techniques that increase the plant’s natural defenses.
• Increases stem width
• Increasing stem width is primarily influenced by another class of plant hormones called gibberellins and cytokinins.
• Induce flowering
• While auxins are involved in many growth processes, the induction of flowering is mainly regulated by florigen and other specific flowering hormones.

The Correct answer is Photosynthesis.

Key Points

• Photosynthesis is an endothermic reaction, meaning it absorbs energy.
• In this process, plants use sunlight to convert carbon dioxide and water into glucose and oxygen.
• It requires the input of light energy from the sun, which is absorbed by chlorophyll.
• Since it absorbs energy rather than releasing it, photosynthesis is not exothermic.
• This process is crucial for producing organic compounds and maintaining the oxygen levels in the atmosphere.

 Additional Information

• Dilution of a strong acid
• This is an exothermic reaction as it releases heat when the strong acid is diluted with water.
• Respiration
• Respiration is an exothermic process because it releases energy by breaking down glucose in the presence of oxygen.
• Burning of natural gas
• The burning of natural gas is a highly exothermic reaction, releasing a significant amount of heat and light energy.
• Natural gas primarily consists of methane which combusts to produce carbon dioxide and water.

The Correct answer is Nutrition.

Key Points

• Nutrition is the process by which organisms obtain and assimilate food.
• It involves the intake of nutrients from the environment and their incorporation into the body.
• This process is essential for providing the energy and materials required for growth, reproduction, and maintenance of the organism.
• Nutrition includes different modes such as autotrophic (self-feeding) and heterotrophic (feeding on others).
• In humans and animals, nutrition involves the consumption of food, its digestion, and the absorption of nutrients into the bloodstream.

 Additional Information

• Metabolism
• Metabolism refers to the biochemical processes that occur within a living organism to maintain life.
• These processes include the conversion of food to energy, the building of cellular structures, and the elimination of waste products.
• Transportation
• Transportation in biology refers to the movement of substances such as nutrients, gases, and wastes within an organism.
• In plants, it involves the movement of water and nutrients through the xylem and phloem.
• Translocation
• Translocation is a specific type of transportation process in plants.
• It refers to the movement of organic compounds, especially sucrose, from sources (where they are synthesized) to sinks (where they are used or stored).

The logic followed here is:

JGOK is related to HEMI

TQYU is related to ROWS

Similarly, NKSO will be related:

Hence, the correct answer is "LIQM".

The correct answer is Manganese (Mn).

Key Points

• Manganese (Mn) reacts with very dilute nitric acid to evolve hydrogen gas.
• When dilute nitric acid is used, it acts as a typical acid releasing hydrogen gas.
• Manganese is a transition metal with the atomic number 25.
• Unlike other metals, when reacted with very dilute nitric acid, manganese releases hydrogen gas instead of producing nitrogen oxides.
• In most cases, nitric acid acts as a strong oxidizing agent, but in its dilute form, it can facilitate the release of hydrogen gas with certain metals.

 Additional Information

• Aluminium (Al)
• Aluminium reacts with nitric acid to form a passive oxide layer, preventing the release of hydrogen gas.
• This passive layer makes aluminium resistant to further reaction with nitric acid.
• Iron (Fe)
• Iron reacts with nitric acid, but instead of releasing hydrogen gas, it typically forms iron nitrate (Fe(NO₃)₃) and nitrogen oxides (NO or NO₂).
• Iron does not release hydrogen gas when reacted with nitric acid due to the oxidizing nature of nitric acid.
• Zinc (Zn)
• Zinc reacts with nitric acid to form zinc nitrate (Zn(NO₃)₂) and nitrogen oxides (NO or NO₂), rather than releasing hydrogen gas.
• Like iron, the reaction of zinc with nitric acid results in the formation of nitrogen oxides due to the strong oxidizing properties of nitric acid.

The correct answer is Convex mirror.

Key Points

• A convex mirror is used in the rear-view mirrors of cars.
• Convex mirrors are chosen because they provide a wider field of view compared to flat or concave mirrors.
• This wider field of view allows drivers to see more of the area behind them, which helps in preventing accidents.
• Convex mirrors also produce smaller and upright images, which makes it easier for drivers to judge the distance and speed of vehicles approaching from behind.
• These mirrors are also known as diverging mirrors because they spread out light rays that strike their surface.
• The use of convex mirrors in vehicles is a safety feature mandated by many automobile safety regulations.

 Additional Information

• Plano-convex lens
• A plano-convex lens is a type of lens with one flat surface and one convex surface.
• These lenses are commonly used in optical instruments such as magnifying glasses, cameras, and projectors.
• They are not suitable for rear-view mirrors because they do not provide a wide field of view.
• Concave mirror
• A concave mirror has an inward-curved reflecting surface and is also known as a converging mirror.
• These mirrors are used in applications where focused light is needed, such as in torches, headlights, and shaving mirrors.
• Concave mirrors produce a limited field of view, making them unsuitable for use as rear-view mirrors in vehicles.
• Biconvex lens
• A biconvex lens has two outward-curved surfaces.
• They are commonly used in microscopes and telescopes to focus light and form clear images.
• Biconvex lenses are not used in rear-view mirrors because they do not offer a wide field of view and can distort the image.

Shortcut Trick

Mode is the value that appears most frequently in a data set.

List frequencies: 23(1), 25(1), 30(1), 31(1), 32(1), 35(1), 41(1), 42(1), 43(1), and 20(5).

Since 20 repeats 5 times (more than any other number), it is the mode.

∴ The correct answer is 20.

Alternate Method

Given: Observations = 20, 23, 25, 30, 20, 31, 32, 35, 20, 41, 42, 43, 20, 20

Formula Used: Mode = Most frequent observation in the series.

Calculations:

⇒ Arranging the data in ascending order: 20, 20, 20, 20, 20, 23, 25, 30, 31, 32, 35, 41, 42, 43

⇒ Frequency of 20 = 5

⇒ Frequency of other terms = 1 each

⇒ Maximum frequency is associated with the term 20.

⇒ Mode = 20

∴ The correct answer is 20.

Additional Information

Empirical Formula

The relationship between Mean, Median, and Mode is given by: Mode = 3 × Median − 2 × Mean.

Bimodal and Multimodal

If two or more values have the same maximum frequency, the distribution is called bimodal or multimodal.

Central Tendency

Mode is one of the three measures of central tendency, primarily used for categorical data to find the most popular item.

Decoding the Symbols:

Given: M ÷ N × O + K × L - R

It means: P is the brother of N, N is the wife of O, O is the father of L, L is the son of R.

So,  K is the 'Son's wife' of R.

Hence, the correct answer is "Option 4".

The correct answer is less than the weight on the earth.

Key Points

• An object’s weight is the force exerted on it due to gravity.
• The Moon's gravitational force is about 1/6^th of the Earth's gravitational force.
• Thus, an object on the Moon weighs less than it does on Earth.
• This is because the mass of the Moon is much smaller compared to Earth, leading to a weaker gravitational pull.
• For example, an object that weighs 60 kg on Earth would weigh only around 10 kg on the Moon.

 Additional Information

• May be greater than or less than depending on the density of the object
• This option is incorrect because the weight of an object is determined by the gravitational force, not its density.
• Weight is a force and is affected by gravity, whereas density is a property of matter and does not change with location.
• Greater than the weight on the Earth
• This is incorrect because the Moon's gravitational force is weaker than Earth's.
• An object cannot weigh more on the Moon compared to Earth due to the lower gravitational pull.
• Equal to the weight on the Earth
• This is incorrect as the gravitational force on the Moon is not the same as on Earth.
• The weight of an object changes with the change in gravitational force.

The correct answer is kg m s^-1.

Key Points

• Momentum is a fundamental concept in physics that describes the quantity of motion an object has.
• It is a vector quantity, meaning it has both magnitude and direction.
• The formula for momentum (p) is given by p = m × v, where m is the mass of the object and v is its velocity.
• The SI unit (International System of Units) for mass is kilogram (kg) and for velocity is meters per second (m/s).
• Therefore, the SI unit of momentum is derived from these two units, resulting in kg m s^-1.
• Understanding momentum is crucial in various fields of physics and engineering, such as in the study of collisions and conservation laws.

 Additional Information

• kg m^-1 s^-1
• This unit is used in the context of viscosity in fluid dynamics, specifically the dynamic viscosity.
• Dynamic viscosity is a measure of a fluid's resistance to flow.
• kg m
• This combination of units does not correspond to a standard physical quantity in the SI system.
• kg m s
• This unit is incorrect because it does not account for the squared time unit required for velocity.

Shortcut Trick

In a continued proportion a : b :: b : c, the product of extremes equals the product of means.

Given 3 : 6 :: 6 : a

Product of extremes = 3 × a

Product of means = 6 × 6 = 36

a = 36 ÷ 3 = 12

∴ The correct answer is 12.

Alternate Method

Given: 3 : 6 :: 6 : a

Formula Used: If w : x :: y : z, then w/x = y/z.

⇒ 3 / 6 = 6 / a

⇒ 1 / 2 = 6 / a

⇒ a = 6 × 2

⇒ a = 12

∴ The correct answer is 12.

Additional Information

Mean Proportional

If a, b, c are in continued proportion, then b is the mean proportional between a and c, where b² = ac or b = √(ac).

Third Proportional

In the proportion a : b :: b : c, the term c is called the third proportional to a and b, calculated as c = b² ÷ a.

Fourth Proportional

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

Given:

0.0488 ÷ 0.002

Formula used:

Division of decimals

Calculations:

? = 0.0488 ÷ 0.002

⇒ ? = 48.8 ÷ 2

⇒ ? = 24.4

∴ The correct answer is option (3).

The least possible Venn diagram:

Conclusion:

I. Some fans are bulbs → False (because no direct relationship given between fans and bulbs so it may be possible not defined)

II. All bulbs are fans → False (because no direct relationship given between fans and bulbs so it may be possible not defined)

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

Hence, the correct answer is "Option 1".

The correct answer is Blood.

Key Points

• Blood is a type of connective tissue.
• It consists of cells suspended in a liquid matrix called plasma.
• Blood performs various essential functions such as transporting oxygen and nutrients to the cells and removing waste products.
• It also plays a crucial role in the immune system and in regulating body temperature.
• Components of blood include red blood cells, white blood cells, platelets, and plasma.
• Red blood cells (RBCs) are responsible for carrying oxygen from the lungs to the rest of the body.
• White blood cells (WBCs) are involved in protecting the body against infections.
• Platelets help in blood clotting and wound healing.

 Additional Information

• Cuboidal Epithelium
• Cuboidal epithelium is a type of epithelial tissue that consists of cube-shaped cells.
• It is found in various organs such as the kidney tubules and glands.
• The primary function of cuboidal epithelium is secretion and absorption.
• Muscle
• Muscle tissue is responsible for movement in the body.
• There are three types of muscle tissues: skeletal, cardiac, and smooth muscle.
• Skeletal muscles are involved in voluntary movements, while cardiac and smooth muscles control involuntary functions.
• Columnar Epithelium
• Columnar epithelium consists of elongated cells that are taller than they are wide.
• This type of epithelium is found in the digestive tract and is specialized for absorption and secretion.
• It often contains goblet cells which secrete mucus.

Shortcut Trick

Curved Surface Area of Cylinder = 2πrh = πdh

Surface Area of Sphere = 4πR²

Given: 4πR² = π × 12 × 12

4R² = 144 ⇒ R² = 36 ⇒ R = 6 cm

∴ The correct answer is 6 cm.

Alternate Method

Given:

Height of cylinder (h) = 12 cm

Diameter of cylinder (d) = 12 cm ⇒ Radius (r) = 6 cm

Formula Used:

Surface Area of Sphere = 4πR²

Curved Surface Area of Cylinder = 2πrh

Calculations:

⇒ Surface Area of Sphere = Curved Surface Area of Cylinder

⇒ 4 × π × R² = 2 × π × 6 × 12

⇒ 4R² = 144

⇒ R² = 144 ÷ 4

⇒ R² = 36

⇒ R = √36 = 6 cm

∴ The correct answer is 6 cm.

Additional Information

Total Surface Area of Cylinder

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

Volume of Sphere and Cylinder

Volume of Sphere = (4/3)πR³ and Volume of Cylinder = πr²h.

Hemisphere Properties

CSA of Hemisphere = 2πR² and TSA of Hemisphere = 3πR².

The Correct answer is Both Zn and CO

Key Points

• When zinc oxide reacts with carbon, the process is called reduction. Zinc oxide (ZnO) is reduced by carbon (C) to form zinc (Zn) and carbon monoxide (CO).
• The chemical reaction can be written as: ZnO + C → Zn + CO
• This reaction involves the removal of oxygen from zinc oxide, leaving zinc metal and producing carbon monoxide as a byproduct.
• This reaction occurs at high temperatures, typically in a furnace or reactor, where the carbon acts as a reducing agent, converting zinc oxide into zinc metal while releasing CO gas.

Additional Information

Types of Chemical Reactions-The The basis for different types of reactions is the product formed, the changes that occur, the reactants involved, and so on. Different types of reactions are

• Combustion reaction
• Decomposition reaction
• Neutralization reaction
• Precipitation or Double-Displacement Reaction

Combustion Reaction-

• It is a reaction with a combustible material with an oxidizer to give an oxidized product.
• An oxidizer is a chemical a fuel requires to burn, generally oxygen.
• For an example of the combustion of magnesium metal.2Mg + O2→2MgO + Heat Here, 2 magnesium atoms react with a molecule of oxygen-producing 2 molecules of the compound magnesium oxide-releasing some heat in the process.

Decomposition Reaction-

• It is a reaction in which a single component breaks down into multiple products.
• Certain changes in energy in the environment have to be made like heat, light, or electricity breaking bonds of the compound. for example of the decomposition of calcium carbonate giving out CaO (Quick Lime) which is a major component of cement. CaCO3(s)→CaO(s)+CO2(g) Here, the compound Calcium carbonate when heated breaks down into Calcium Oxide and Carbon Dioxide.

Neutralization Reaction-

• It is basically the reaction between an acid and a base giving salt and water as the products.
• The water molecule formed is by the combination of OH- ions and H+ ions. The overall pH of the products when a strong acid and a strong base undergo a neutralization reaction will be 7.
• Consider the example of the neutralization reaction between Hydrochloric acid and Sodium Hydroxide giving out sodium chloride(Common Salt) and water. HCl + NaOH → NaCl + H2O Here, an acid and a base, Hydrochloric acid and Sodium Hydroxide react in a neutralization reaction to produce Sodium Chloride(Common Salt) and Water as the by-products.

Given:

Seven people, A, B, E, F, P. Q and R, are sitting in a row, facing north.

Only two people sit to the left of B. Only three people sit between B and R.

P sits second to the right of B.

Only two people sit between P and A.

F sits at some place to the right of E but at some place to the left of Q.

So, 'Three' people sit to the right of F.

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

The correct answer is Only statement I is correct.

Key Points

• Atomic number is a fundamental property of an element that determines its identity.
• Statement I is correct because the atomic number of an element represents the number of protons present in the nucleus of an atom.
• Protons carry a positive charge, and the number of protons defines the chemical properties of the element.
• The atomic number is unique to each element and is used to distinguish one element from another in the periodic table.

 Additional Information

• Statement II is incorrect because the number of neutrons in an atom's nucleus is not represented by the atomic number but rather contributes to the atomic mass along with the protons.
• The number of neutrons can vary among atoms of the same element, leading to different isotopes of that element.
• The atomic number is denoted by the symbol Z and is always a whole number.
• For example, the atomic number of hydrogen is 1, meaning it has one proton, while the atomic number of carbon is 6, meaning it has six protons.

The correct answer is plant cells.

Key Points

• Vacuoles are membrane-bound organelles found in cells.
• They are primarily present in plant cells and are usually large and central.
• The main function of vacuoles in plant cells is to maintain turgor pressure, which keeps the plant rigid and upright.
• Vacuoles store nutrients, waste products, and other substances essential for the cell's survival.
• In plant cells, the vacuole can occupy up to 90% of the cell's volume.
• The membrane that surrounds a vacuole is called the tonoplast.
• Vacuoles also play a role in cell growth by absorbing water and enlarging, which helps the cell to expand.

 Additional Information

• Bacteria
• Bacteria are prokaryotic microorganisms that do not have membrane-bound organelles such as vacuoles.
• They have simpler structures compared to eukaryotic cells and rely on other mechanisms for storage and waste management.
• Both plant cells and animal cells
• While both plant and animal cells have vacuoles, they are more prominent and larger in plant cells.
• In animal cells, vacuoles are smaller and more numerous, serving different functions such as storage and transport.
• Animal cells
• Animal cells do have vacuoles, but they are typically smaller and serve different roles compared to those in plant cells.
• Animal cell vacuoles are involved in processes like sequestering waste products and helping in intracellular digestion.

Shortcut Trick

Efficiency of B = Combined efficiency − A's efficiency.

If (A + B) takes 2 days and A takes 4 days, then B's efficiency is 1/2 − 1/4 = 1/4.

B alone takes 4 days for 1 unit of work.

For 21-times the work, B will take 4 × 21 = 84 days.

∴ The correct answer is 84 days.

Alternate Method

Given: Time taken by (A + B) = 2 days, Time taken by A = 4 days.

Formula Used: Total Work = LCM of days; Efficiency = Total Work ÷ Time.

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

⇒ Efficiency of B = 2 − 1 = 1 unit/day

⇒ New Work = 21 × 4 = 84 units

⇒ Time taken by B = New Work ÷ B's Efficiency = 84 ÷ 1 = 84 days

∴ The correct answer is 84 days.

Additional Information

Combined Work Formula

If A takes 'x' days and B takes 'y' days, together they take (x × y) ÷ (x + y) days.

Work & Time Relationship

Time is directly proportional to the amount of work done when efficiency remains constant (T₁/W₁ = T₂/W₂).

Given Equation: 85 A 17 C 82 D 11 B 2 = ?

BODMAS Rule:

Decoding the given information:

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

⇒ 85 ÷ 17 + 82 - 11 × 2

⇒ 5 + 82 - 11 × 2

⇒ 5 + 82 - 22

⇒ 87 - 22

⇒ 65

Hence, the correct option is "Option 1".

The correct answer is Magnesium.

Key Points

• Magnesium is a metal that does not react with cold water.
• It only reacts with hot water or steam to produce magnesium hydroxide and hydrogen gas.
• The reaction of magnesium with water is much slower compared to other metals like potassium, sodium, and calcium.
• Magnesium forms a protective layer of magnesium hydroxide on its surface, which prevents further reaction with water.
• This characteristic makes magnesium less reactive with cold water.

 Additional Information

• Potassium
• Potassium reacts very vigorously with cold water, producing potassium hydroxide and hydrogen gas.
• The reaction is exothermic and can ignite the hydrogen gas produced.
• Sodium
• Sodium also reacts vigorously with cold water, forming sodium hydroxide and hydrogen gas.
• Similar to potassium, the reaction is exothermic and can ignite the hydrogen gas.
• Calcium
• Calcium reacts with cold water to produce calcium hydroxide and hydrogen gas, but the reaction is less vigorous compared to potassium and sodium.

The Correct answer is Raigad Fort.

Key Points

• Raigad Fort is located in the Raigad district of Maharashtra.
• This fort is historically significant as it was the site of the coronation of Chhatrapati Shivaji Maharaj, the founder of the Maratha Empire, in 1674.
• The fort is situated at an altitude of 2,700 feet above sea level, offering a strategic vantage point.
• Raigad Fort was originally known as Rairi and was renamed by Shivaji Maharaj.
• The fort is known for its impressive architecture and includes features such as the Queen's quarters, public Durbar, watchtowers, and several gateways.
• It played a crucial role in the history of the Maratha Empire and is considered a symbol of Maratha pride and heritage.

 Additional Information

• Karnala Fort
• Karnala Fort is located in the Raigad district of Maharashtra.
• This fort is also known as the Funnel Hill and is a popular trekking destination.
• Karnala Fort is situated within the Karnala Bird Sanctuary and offers a habitat for various bird species.
• Korigad Fort
• Korigad Fort is situated near Lonavala in Maharashtra.
• The fort is known for its scenic views and has a large plateau with two lakes at the top.
• Korigad Fort was incorporated into the kingdom of Chhatrapati Shivaji Maharaj in 1657.
• Mangi-Tungi Fort
• Mangi-Tungi is a prominent twin-pinnacle peak located in the Nashik district of Maharashtra.
• This site is a significant Jain pilgrimage destination and is known for its ancient temples and sculptures.
• The fort is situated at an elevation of 4,343 feet above sea level.

The logic followed here is:

Logic: 1^st number + 52 = 2^nd number.

For, X : 75

⇒ X + 52 = 75

⇒ X = 75 - 52 = 23.

Similarly, 

For, 29 : Y

⇒ 29 + 52 = 81.

Hence, the correct answer is "Option 1".

The correct answer is Anirudha Bhattacharjee.

Key Points

• Anirudha Bhattacharjee is a well-known author and film historian.
• He co-authored the book 'Kishore Kumar: The Ultimate Biography' with Parthiv Dhar.
• The book provides a comprehensive look at the life and career of Kishore Kumar, one of India's most beloved playback singers and actors.
• The Ministry of Information & Broadcasting of India announced the award in October 2024.
• The book was awarded the Best Book on Cinema for its in-depth research and engaging narrative.
• Anirudha Bhattacharjee has previously co-authored other significant works on Indian cinema, including books on R.D. Burman and S.D. Burman.

The correct answer is Lactic acid.

Key Points

• Lactic acid accumulates in muscles during intense exercise or sudden activity.
• This happens because of anaerobic respiration, where glucose is broken down without oxygen to produce energy.
• The buildup of lactic acid leads to a condition known as muscle acidosis, causing cramps and fatigue.
• This process is typically a temporary response to high-intensity exercise.
• The body usually clears out lactic acid through the bloodstream once the activity level decreases and oxygen becomes available.

 Additional Information

• Sucrose
• Sucrose is a common sugar found in many plants and is used as a sweetener in foods and beverages.
• It does not accumulate in muscles nor cause cramps during physical activity.
• Glucose
• Glucose is the primary source of energy for the body's cells.
• During exercise, glucose is broken down to produce energy, but it does not directly cause cramps.
• Pyruvic acid
• Pyruvic acid is an intermediate product in the breakdown of glucose during cellular respiration.
• It does not accumulate in muscles during exercise; instead, it is converted to lactic acid under anaerobic conditions.

Given:

The 7-digit number is 451k603.

Formula Used:

A number is divisible by 9 if the sum of its digits is divisible by 9.

Calculation:

Sum of the digits of 451k603 = 4 + 5 + 1 + k + 6 + 0 + 3

Sum = 19 + k

For 451k603 to be divisible by 9, 19 + k must be divisible by 9.

Find the smallest value of k that makes 19 + k divisible by 9:

19 + k = 27

⇒ k = 27 - 19

⇒ k = 8

The correct answer is option 1.

The correct answer is Kolkata.

Key Points

• Prime Minister Narendra Modi inaugurated the PARAM Rudra Supercomputer in September 2024.
• The event took place in Kolkata, a major city in the eastern part of India.
• The PARAM Rudra is part of the National Supercomputing Mission, which aims to enhance India's computational capabilities.
• This supercomputer is expected to significantly boost research and development in various fields such as climate modeling, computational biology, and material science.
• PARAM is a series of supercomputers developed by the Centre for Development of Advanced Computing (C-DAC).
• The name PARAM signifies supreme in Sanskrit.
• Kolkata is known as the cultural capital of India and has been a center for education, science, and technology.

 Additional Information

• Hyderabad
• Hyderabad is known for its Information Technology industry and is often referred to as Cyberabad.
• The city is home to major IT firms and the Hyderabad Information Technology and Engineering Consultancy City (HITEC City).
• It is the capital city of the Indian state of Telangana.
• Chennai
• Chennai is the capital of the Indian state of Tamil Nadu.
• It is known for its strong automobile industry and is often referred to as the Detroit of India.
• Chennai is also a major center for education and healthcare in South India.
• Bengaluru
• Bengaluru is known as the Silicon Valley of India due to its role as the nation's leading information technology (IT) exporter.
• It is the capital of the Indian state of Karnataka.
• The city is also known for its green spaces and pleasant climate.

The correct answer is Muscular tissue.

Key Points

• Muscular tissue is responsible for the movement in our body.
• There are three types of muscular tissue: skeletal, smooth, and cardiac muscles.
• Skeletal muscles are attached to bones and are responsible for voluntary movements.
• Smooth muscles are found in the walls of internal organs and help in involuntary movements such as digestion.
• Cardiac muscles are found in the heart and are responsible for pumping blood throughout the body.
• Muscular tissues can contract and relax, which allows them to produce movement.

 Additional Information

• Epithelial tissue
• Epithelial tissue covers the outer surfaces of organs and blood vessels throughout the body, as well as the inner surfaces of cavities in many internal organs.
• It acts as a barrier to protect the body from outside invaders and helps in absorption, secretion, and sensation.
• Cartilage
• Cartilage is a flexible connective tissue found in various parts of the body including joints, ear, nose, and bronchial tubes.
• It provides support and cushioning in the joints and reduces friction between bones.
• Areolar tissue
• Areolar tissue is a type of connective tissue that holds organs in place and attaches epithelial tissue to underlying tissues.
• It also serves as a reservoir of water and salts for surrounding tissues.

Shortcut Trick

For a cuboid, if the areas of three adjacent faces are x, y, and z, then the Volume (V) is given by √(x × y × z).

Given areas: x = 66, y = 192, z = 198

V = √(66 × 192 × 198) = √(66 × 192 × (66 × 3)) = 66 × √(192 × 3) = 66 × √576 = 66 × 24

V = 1584 cm³

∴ The correct answer is 1584 cm³.

Alternate Method

Given:

Area of face 1 (lb) = 66 cm²

Area of face 2 (bh) = 192 cm²

Area of face 3 (lh) = 198 cm²

Formula Used:

Volume of cuboid (V) = length (l) × breadth (b) × height (h)

Calculations:

⇒ (lb) × (bh) × (lh) = 66 × 192 × 198

⇒ l²b²h² = 66 × 192 × 198

⇒ (lbh)² = 66 × 192 × (66 × 3)

⇒ V² = 66² × (192 × 3)

⇒ V² = 66² × 576

⇒ V = √(66² × 24²)

⇒ V = 66 × 24 = 1584 cm³

∴ The correct answer is 1584 cm³.

Additional Information

Total Surface Area of Cuboid

The total surface area is given by the formula 2(lb + bh + lh), where l, b, and h are length, breadth, and height.

Diagonal of a Cuboid

The length of the longest rod that can be placed in a cuboid is the diagonal, given by √(l² + b² + h²).

Volume and Product of Face Areas

If A₁, A₂, and A₃ are areas of three adjacent faces, then Volume V = √(A₁ × A₂ × A₃).

The Correct answer is Union Bank.

Key Points

• The Finance Minister launched the Nari Shakti branches of Union Bank to empower women entrepreneurs in November 2024.
• The initiative aims to provide financial services and support to women-led businesses.
• These branches are designed to cater specifically to the needs of women entrepreneurs, offering tailored financial products and services.
• The launch of these branches is part of a broader effort to encourage and support women in the business sector.
• Union Bank of India is one of the largest government-owned banks in India, with a significant focus on inclusive banking.

 Additional Information

• HDFC Bank
• HDFC Bank is one of India's leading private sector banks.
• It is known for its extensive range of financial products and services.
• While it supports various initiatives, the Nari Shakti branches were not launched under this bank.
• PNB
• Punjab National Bank (PNB) is one of the oldest and largest government-owned banks in India.
• It offers a wide range of banking services but was not the bank associated with the Nari Shakti initiative.
• SBI
• State Bank of India (SBI) is the largest bank in India and a public sector banking and financial services company.
• Although SBI has numerous initiatives for women, the specific Nari Shakti branches were not launched by this bank.

The correct answer is White.

Key Points

• When magnesium burns in air, it produces a bright white flame.
• This white flame is due to the formation of magnesium oxide (MgO).
• Magnesium has a high affinity for oxygen, leading to a highly exothermic reaction.
• The bright white light produced is so intense that it can cause temporary blindness if viewed directly.
• Because of this intense white light, magnesium is often used in pyrotechnics and photographic flashbulbs.

 Additional Information

• Pink
• Pink flames are not typically associated with the burning of metals like magnesium.
• In the context of flames, pink could be indicative of the presence of lithium compounds.
• Green
• Green flames are usually produced by the presence of copper compounds.
• For example, copper chloride can produce a green flame.
• Red
• Red flames are often produced by the presence of strontium compounds.
• Strontium chloride is known to give a bright red flame.

The correct answer is 10 N.

Key Points

• The thrust acting on the table surface is equal to the weight of the metal box.
• The weight of an object can be calculated using the formula Weight (W) = mass (m) x acceleration due to gravity (g).
• Here, the mass (m) of the metal box is 1 kg.
• The acceleration due to gravity (g) is given as 10 m/sec².
• Therefore, the weight (W) = 1 kg x 10 m/sec² = 10 N.
• Hence, the thrust acting on the table surface is 10 N.

 Additional Information

• Thrust
• Thrust is the force exerted by an object perpendicular to the surface it is in contact with.
• In the context of weight, it is the gravitational force acting downward due to the object's mass.
• Weight
• Weight is a measure of the force exerted by gravity on an object.
• It is dependent on both the mass of the object and the local gravitational field strength.

The correct answer is Heart.

Key Points

• The heart is a muscular organ located in the chest cavity.
• It is responsible for pumping blood throughout the body via the circulatory system.
• The heart ensures the continuous supply of oxygen and nutrients to tissues and organs.
• The heart operates through a series of rhythmic contractions, regulated by electrical impulses.
• It consists of four chambers: the right atrium, right ventricle, left atrium, and left ventricle.
• The heart's activity is vital for maintaining homeostasis and supporting life.

 Additional Information

• Pancreas
• The pancreas is a gland located behind the stomach.
• It plays a crucial role in digestive and endocrine functions.
• The pancreas produces digestive enzymes and hormones such as insulin.
• Stomach
• The stomach is a muscular organ involved in the digestion of food.
• It secretes gastric juices that aid in breaking down food.
• The stomach's environment is highly acidic, which helps in killing harmful bacteria.
• Liver
• The liver is a vital organ located in the upper right quadrant of the abdomen.
• It performs various functions including detoxification, protein synthesis, and production of bile.
• The liver also plays a role in metabolism and regulation of blood sugar levels.

Given:

(-5/3) × (9/25) + (1/5 − 3)

Formula used:

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

Calculations:

Solving the expression step by step:

⇒ [(-5/3) × (9/25)] + (1/5 − 3)

First, calculate the multiplication part:

⇒ [(-1/1) × (3/5)] + (1/5 − 3)

⇒ (-3/5) + (1/5 − 3)

Now, solve the bracket part:

⇒ (-3/5) + [(1 − 15)/5]

⇒ (-3/5) + (-14/5)

Combine the fractions:

⇒ (-3 − 14)/5

⇒ -17/5

∴ The correct answer is option (4).

The Correct answer is Snow leopard.

Key Points

• The Snow leopard is a large cat native to the mountain ranges of Central and South Asia.
• It has been listed as Vulnerable on the IUCN Red List because the global population is estimated to number fewer than 10,000 mature individuals and continues to decline.
• Snow leopards are well adapted to their cold environment with thick fur, small rounded ears, and wide, fur-covered paws that act as natural snowshoes.
• The species is distributed across 12 countries including China, India, Mongolia, and Russia.
• In India, they are found in the states of Jammu and Kashmir, Himachal Pradesh, Uttarakhand, Sikkim, and Arunachal Pradesh.
• The snow leopard is an apex predator in its habitat, playing a crucial role in maintaining the balance of the ecosystem.

 Additional Information

• Yak
• The Yak is a long-haired domesticated bovid found throughout the Himalayan region of the Indian subcontinent, the Tibetan Plateau, and as far north as Mongolia and Russia.
• Yaks are used for a variety of purposes including transportation, milk production, and meat.
• Sheep
• Sheep are domesticated ruminant mammals typically kept as livestock. They are raised for their wool, meat, and milk.
• There are numerous breeds of sheep adapted to various climates around the world.
• Snow bear
• Snow bears, or more commonly known as Polar bears, are native to the Arctic region.
• They are classified as marine mammals because they spend most of their lives on the sea ice of the Arctic Ocean.
• Polar bears are apex predators in their ecosystem, primarily feeding on seals.

The Correct answer is HCL Technologies.

Key Points

• HCL Technologies is an Indian multinational information technology (IT) services and consulting company.
• The founder and chairman of HCL Technologies is Shiv Nadar.
• Shiv Nadar has topped the EdelGive-Hurun India Philanthropy List 2024, recognizing his significant contributions to philanthropy.
• HCL Technologies is headquartered in Noida, India.
• The company operates in over 50 countries and has a worldwide network of R&D, innovation labs, and delivery centers.
• HCL Technologies provides services including software development, business process outsourcing (BPO), and IT infrastructure management.
• The company is one of the top IT services companies in India and is known for its innovation and customer-centric approach.

 Additional Information

• Reliance Industries
• Reliance Industries is an Indian multinational conglomerate company headquartered in Mumbai, India.
• The company is involved in businesses across sectors such as petrochemicals, refining, oil, telecommunications, and retail.
• It is one of the largest companies in India in terms of market capitalization and revenue.
• WIPRO
• WIPRO Limited is an Indian multinational corporation that provides information technology, consulting, and business process services.
• Headquartered in Bengaluru, India, WIPRO is one of the largest IT services companies in India.
• It was founded by Mohamed Premji in 1945.
• TCS
• Tata Consultancy Services (TCS) is an Indian multinational information technology services and consulting company.
• It is headquartered in Mumbai, India, and operates in 46 countries.
• TCS is a part of the Tata Group, one of India's largest and oldest industrial conglomerates.

Shortcut Trick

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

MP ÷ 120 = (100 + 10) ÷ (100 − 4)

MP ÷ 120 = 110 ÷ 96

MP = (110 × 120) ÷ 96

MP = 13200 ÷ 96 = 137.50

∴ The correct answer is ₹137.50.

Alternate Method

Given: CP = ₹120, Profit% = 10%, Discount% = 4%.

Formulas: SP = CP × (100 + P%) ÷ 100 | MP = (SP × 100) ÷ (100 − D%)

⇒ Selling Price (SP) = 120 × (110 ÷ 100) = 132

⇒ Marked Price (MP) × (100 − 4) ÷ 100 = 132

⇒ MP × 0.96 = 132

⇒ MP = 132 ÷ 0.96 = 137.50

∴ The correct answer is ₹137.50.

Additional Information

Marked Price and Discount

The Marked Price is the price printed on the label, and Discount is always calculated on the MP to arrive at the Selling Price.

MP-CP Ratio Formula

The direct ratio MP/CP = (100 + P%)/(100 - D%) is the most efficient way to solve problems involving both discount and profit.

Given series:

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

Condition to be checked:

Perfect square → Odd digits → Even digit

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

Thus there is one such pattern (4 3 2) that is following the above conditions.

Hence, "1" is the correct answer.

Mistake Points

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

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

The logic follows here:

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

Given Equation: (14 B 4) A 2 C (15 A 5) B 9 D 34 C (48 A 6) B 2 = ?

BODMAS Rule:

Decoding the given information:

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

⇒ (14 × 4) ÷ 2 + (15 ÷ 5) × 9 - 34 + (48 ÷ 6) × 2

⇒ 56 ÷ 2 + 3 × 9 - 34 + 8 × 2

⇒ 28 + 3 × 9 - 34 + 8 × 2

⇒ 28 + 27 - 34 + 16

⇒ 71 - 34

⇒ 37

Hence, the correct option is "Option 1".

Given series:

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

If all the symbols are dropped from the series, the remaining series will be:

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

Counting from the right, the seventh element is:

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

Seventh from the right: 2

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

Shortcut Trick

Effective Rate of Interest for 3 years = 16% × 3 = 48%.

Given, 48% of Principal = ₹960.

1% = 960 ÷ 48 = 20.

100% (Principal) = 20 × 100 = ₹2000.

∴ The correct answer is ₹2000.

Alternate Method

Given:

Simple Interest (SI) = ₹960

Time (T) = 3 years

Rate (R) = 16% per annum

Formula Used:

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

Calculations:

⇒ 960 = (P × 16 × 3) ÷ 100

⇒ 960 = (P × 48) ÷ 100

⇒ 48 × P = 960 × 100

⇒ P = 96000 ÷ 48

⇒ P = ₹2000

∴ The correct answer is ₹2000.

Additional Information

Definition of Simple Interest

It is the interest calculated only on the original principal amount for every period. SI = (P × R × T) ÷ 100.

Total Amount Formula

The total Amount (A) after T years is the sum of Principal and Simple Interest. A = P + SI = P[1 + (RT/100)].

Relationship between SI and Rate

For a constant principal and time, Simple Interest is directly proportional to the Rate of Interest.

Shortcut Trick

Total length = (24 carriages + 1 engine) × 60 m + 1.5 km = 25 × 60 + 1500 = 3000 m.

Speed = 50 km/h = 50 × (5/18) m/s.

Time = Distance ÷ Speed = 3000 ÷ (250/18) = 12 × 18 = 216 seconds.

Time in minutes = 216 ÷ 60 = 3.6 min.

∴ The correct answer is 3.6 min.

Alternate Method

Given:

Number of carriages = 24, Number of engines = 1

Length of each unit = 60 m, Length of bridge = 1.5 km = 1500 m

Speed of train = 50 km/h

Calculations:

⇒ Total length of train = (24 + 1) × 60 = 25 × 60 = 1500 m

⇒ Total distance to cover = Length of train + Length of bridge = 1500 + 1500 = 3000 m

⇒ Speed in m/s = 50 × (5/18) = 250/18 m/s

⇒ Time taken (seconds) = 3000 ÷ (250/18) = (3000 × 18) ÷ 250 = 12 × 18 = 216 sec

⇒ Time in minutes = 216 ÷ 60 = 3.6 min

∴ The correct answer is 3.6 min.

Additional Information

Unit Conversion

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

Crossing Distance Rule

When a train crosses a platform, bridge, or another train, the total distance is the sum of the lengths of the train and the object.

Relative Speed

For two objects moving in the same direction, relative speed = S₁ − S₂. In opposite directions, relative speed = S₁ + S₂.

Given word: 'FRIENDLY'

After applying the specified transformations:

So, common letter is: I and J

Hence, the correct answer is "Option 4".

The Correct answer is Undigested food.

Key Points

• Plasma is the liquid component of blood that holds the blood cells in whole blood in suspension.
• It is composed mainly of water (about 90-92%) and contains various substances including salts, proteins, hormones, and waste products.
• Salts in plasma help in maintaining osmotic balance, pH, and various other functions crucial for homeostasis.
• Proteins in plasma include albumins, globulins, and fibrinogen, which play essential roles in maintaining osmotic balance, immune response, and blood clotting.
• Hormones are also found in plasma and are vital for regulating physiological activities and maintaining homeostasis.
• However, undigested food is not present in the plasma as it is usually processed and absorbed in the digestive system, and only nutrients absorbed from the food enter the bloodstream.

 Additional Information

• Salts
• Salts such as sodium, potassium, calcium, and magnesium are crucial for various cellular functions including nerve transmission and muscle contraction.
• They help to maintain the osmotic balance and pH levels in the blood.
• Proteins
• Proteins in plasma serve multiple functions including transport, immune defense, and blood clotting.
• Albumins maintain osmotic pressure, globulins are involved in the immune response, and fibrinogen is essential for the clotting process.
• Hormones
• Hormones are chemical messengers that regulate physiological processes including growth, metabolism, and reproductive functions.
• They are secreted by various endocrine glands and transported via plasma to target organs.

The correct answer is Hydra.

Key Points

• Hydra is a genus of small, freshwater organisms of the phylum Cnidaria and class Hydrozoa.
• Hydra reproduces asexually through a process known as budding.
• In budding, a small bud develops on the body of the parent organism, grows by acquiring cells from the parent, and eventually detaches to form a new, genetically identical individual.
• This process involves the use of regenerative cells, which allow Hydra to regenerate and form new buds.
• Hydra's remarkable ability to regenerate is due to the presence of stem cells that can differentiate into any cell type needed for growth and repair.

 Additional Information

• Planaria
• Planaria are flatworms known for their ability to regenerate lost body parts, but they reproduce primarily through fission rather than budding.
• They belong to the class Turbellaria in the phylum Platyhelminthes.
• Amoeba
• An Amoeba is a single-celled organism that primarily reproduces through a process called binary fission, not budding.
• It belongs to the phylum Amoebozoa.
• Spirogyra
• Spirogyra is a filamentous green alga that reproduces through fragmentation and sexual reproduction, not budding.
• It belongs to the class Zygnematophyceae in the phylum Chlorophyta.

The correct answer is 12 u.

Key Points

• Carbon-12 is the most common isotope of carbon, consisting of 6 protons and 6 neutrons.
• The atomic mass unit (u) is a standard unit of mass that quantifies mass on an atomic or molecular scale (atomic mass).
• The atomic mass of an atom is defined relative to the atomic mass of Carbon-12, which is set at 12 u.
• This standardization helps in comparing the masses of different atoms.
• The mass of Carbon-12 is exactly 12 u because it is the reference from which atomic masses are calculated.

 Additional Information

• 14 u
• This value is closer to the atomic mass of the isotope Carbon-14, which has 6 protons and 8 neutrons.
• Carbon-14 is used in radiocarbon dating to determine the age of ancient objects.
• 6 u
• This is incorrect as it does not match the atomic mass of any naturally occurring carbon isotope.
• 16 u
• This value is closer to the atomic mass of the isotope Oxygen-16, which has 8 protons and 8 neutrons.
• Oxygen-16 is the most abundant isotope of oxygen.

The Correct answer is Varanasi.

Key Points

• The Krishi Sakhi Convergence Programme (KSCP) is an initiative under the Lakhpati Didi programme.
• This programme was launched by Prime Minister Narendra Modi in June 2024.
• It was launched from the ancient city of Varanasi, which is also known for its rich cultural and historical heritage.
• The aim of the KSCP is to empower rural women by providing them with skills and resources in agriculture and allied activities.
• The programme seeks to improve the livelihood of rural women and make them lakhpatis (earning more than one lakh rupees annually).

 Additional Information

• Lucknow
• Lucknow is the capital city of the Indian state of Uttar Pradesh.
• It is known for its rich history, culture, and heritage, including landmarks such as the Bara Imambara and Chota Imambara.
• Lucknow is also famous for its unique style of Chikankari embroidery.
• Ahmedabad
• Ahmedabad is the largest city in the Indian state of Gujarat.
• It is an important economic and industrial hub, known for its textile industry.
• The city is home to the Sardar Vallabhbhai Patel International Airport and the Indian Institute of Management Ahmedabad (IIM-A).
• Nagpur
• Nagpur is a major city in the central part of India, located in the state of Maharashtra.
• It is known as the Orange City due to its famous Nagpur oranges.
• Nagpur is also the geographical center of India and houses the Zero Mile Stone.

The correct answer is F = G(M × m)/(d^2).

Key Points

• The formula F = G(M × m)/(d^2) represents Newton's Law of Universal Gravitation.
• According to this law, the force of attraction between two objects is directly proportional to the product of their masses (M and m).
• The force is also inversely proportional to the square of the distance (d) between the two objects.
• G is the universal gravitational constant, which has a value of approximately 6.674 × 10^-11 N(m/kg)^2.
• This formula is crucial in understanding the gravitational interactions between objects, from small particles to astronomical bodies.

 Additional Information

• Incorrect Options
• F = G(M)/(d^2): This formula is incorrect because it does not include the mass of object B (m).
• F = G(1)/(d^2): This formula is incorrect because it does not include the masses of either object.
• F = G(M × m)/(d): This formula is incorrect because the force is inversely proportional to the square of the distance (d^2), not just the distance (d).
• Important Points
• Newton's Law of Universal Gravitation is fundamental in physics and astronomy.
• This law helps in calculating the gravitational forces between celestial bodies, which is essential for understanding their orbits and movements.
• The universal gravitational constant (G) was first measured by Henry Cavendish in 1798.