RRB Technician Grade III Official Paper (Held On: 24 Dec, 2024 Shift 1) (Previous Year Paper)

Shortcut Trick

Net multiplier for successive discounts of 10% and 15% = 0.90 × 0.85 = 0.765

Selling Price = Marked Price × Net multiplier

⇒ SP = 28,000 × 0.765

⇒ SP = 21,420

∴ The correct answer is Rs. 21,420.

Alternate Method

Given:

Marked Price (MP) = Rs. 28,000

First Discount (d₁) = 10%

Second Discount (d₂) = 15%

Formula Used:

Selling Price (SP) = MP × (1 − d₁/100) × (1 − d₂/100)

Calculations:

⇒ Price after 1^st discount = 28,000 − (10% of 28,000)

⇒ Price after 1^st discount = 28,000 − 2,800 = Rs. 25,200

⇒ Selling Price = 25,200 − (15% of 25,200)

⇒ SP = 25,200 − (15/100 × 25,200)

⇒ SP = 25,200 − 3,780

⇒ SP = Rs. 21,420

∴ The correct answer is Rs. 21,420.

Additional Information

Single Equivalent Discount

For two successive discounts of x% and y%, the single equivalent discount is calculated as (x + y − xy/100)%.

Relationship between MP and SP

Selling Price = Marked Price × (100 − Discount%)/100. Discounts are always calculated on the Marked Price unless stated otherwise.

Successive Percentage Change

Final Value = Initial Value × (1 ± r₁/100) × (1 ± r₂/100), where r represents the rate of increase (+) or decrease (−).

Given:

{15 × 32 ÷ 2 × 5} ÷ 75

Formula used:

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

Calculations:

{15 × 32 ÷ 2 × 5} ÷ 75

⇒ {15 × 16 × 5} ÷ 75

⇒ {240 × 5} ÷ 75

⇒ 1200 ÷ 75

⇒ 16

∴ The correct answer is option (1).

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

According to the question, sum of the 5^th digit from the left and the 10^th digit from the right: (Left) 7 0 6 0 6 7 7 2 7 6 1 5 0 1 9 2 9 2 2 6 5 9 2 4 0 0 7 7 3 8 (Right) → 6 + 5 = 11

Hence, "Option 1" is the correct answer.

The correct answer is Three-carbon molecule.

Key Points

• Pyruvate is a three-carbon molecule produced during glycolysis as the end product of glucose metabolism.
• It is a crucial intermediate compound in cellular respiration, leading to further metabolic processes like the citric acid cycle (Krebs cycle) in aerobic conditions.
• Pyruvate can be converted into lactate in anaerobic conditions (lactic acid fermentation) or into acetyl-CoA in the presence of oxygen.
• Pyruvate plays an essential role in both energy production and metabolic pathways in cells, especially in tissues like muscles.
• It is produced from glucose, a six-carbon molecule, after a series of enzymatic reactions in the cytoplasm during glycolysis.

Additional Information

• Glycolysis
• It is a set of reactions that converts glucose to pyruvate or lactate.
• Glycolysis is the primary step of cellular respiration.
• Glycolysis is followed by the Krebs cycle during aerobic respiration.

The correct answer is New Delhi.

Key Points

• The World Heritage Committee is responsible for the implementation of the World Heritage Convention.
• The Committee defines the use of the World Heritage Fund and allocates financial assistance upon requests from States Parties.
• In July 2024, the 46^th session of the World Heritage Committee was held in New Delhi, India.
• New Delhi is the capital city of India and is known for its rich cultural heritage and significant historical landmarks.
• The hosting of the session in New Delhi highlights India's commitment to preserving and promoting its cultural and natural heritage.

 Additional Information

• Jaipur
• Jaipur, also known as the Pink City, is the capital of the Indian state of Rajasthan.
• It is famous for its palaces, forts, and vibrant culture.
• Jaipur is a major tourist destination and has been recognized as a UNESCO World Heritage Site.
• Indore
• Indore is the largest city in the Indian state of Madhya Pradesh.
• It is known for its educational institutions, commercial activity, and vibrant food culture.
• Indore has consistently ranked as one of the cleanest cities in India.
• Bengaluru
• Bengaluru (also known as Bangalore) is the capital of the Indian state of Karnataka.
• It is known as the Silicon Valley of India due to its role as the nation's leading information technology (IT) exporter.
• Bengaluru is known for its pleasant climate, parks, and nightlife.

Shortcut Trick

Find the LCM of the given time intervals: 30, 45, and 60.

LCM(30, 45, 60) = 180 seconds.

Convert 180 seconds to minutes: 180 ÷ 60 = 3 minutes.

Add the interval to the initial time: 8:30 a.m. + 3 minutes = 8:33 a.m.

∴ The correct answer is 8:33 a.m.

Alternate Method

Given: Intervals are 30 sec, 45 sec, and 60 sec. Starting time = 8:30 a.m.

Formula: Simultaneous occurrence time = LCM of individual intervals.

⇒ Prime factors of 30 = 2 × 3 × 5

⇒ Prime factors of 45 = 3² × 5

⇒ Prime factors of 60 = 2² × 3 × 5

⇒ LCM = 2² × 3² × 5 = 4 × 9 × 5 = 180 seconds

⇒ 180 seconds = 180 ÷ 60 minutes = 3 minutes

⇒ Next simultaneous time = 8:30:00 + 0:03:00 = 8:33 a.m.

∴ The correct answer is 8:33 a.m.

Additional Information

LCM Application

LCM (Least Common Multiple) is used to find the first instance when multiple periodic events with different frequencies occur at the same time.

Time Conversion

Always ensure all units are consistent. 60 seconds = 1 minute and 60 minutes = 1 hour.

Successive Occurrences

To find the nth simultaneous occurrence, use the formula: Start Time + (n × LCM).

The correct answer is Tyndall effect.

Key Points

• The Tyndall effect is the scattering of light by particles in a colloid or in a very fine suspension.
• This phenomenon is named after the 19^th-century physicist John Tyndall.
• The effect is used to distinguish between colloidal and true solutions.
• When a beam of light passes through a colloid, the particles in the colloid scatter the light, making the light beam visible. This is the Tyndall effect.
• This scattering is more pronounced when the particles are large compared to the wavelength of the light.
• Examples of the Tyndall effect include the visibility of beams of sunlight in misty or dusty air and the light scattered by the particles in a colloidal solution.

 Additional Information

• Delay in sunset
• The delay in sunset is caused by the refraction of light in the Earth's atmosphere.
• As the Sun sets, its light passes through more of the Earth's atmosphere, which bends the light and makes the Sun appear higher in the sky than it actually is.
• Twinkling of stars
• The twinkling of stars is caused by the atmospheric turbulence that refracts the light from stars in different directions.
• This phenomenon is also known as stellar scintillation.
• Rainbow
• A rainbow is caused by the dispersion of light in water droplets, resulting in a spectrum of light appearing in the sky.
• This phenomenon involves reflection, refraction, and dispersion of light.

The correct answer is New Delhi.

Key Points

• World Telecom Standardization Assembly (WTSA) is a prestigious event organized by the International Telecommunication Union (ITU).
• The WTSA event is held every four years and defines the next period of study for the ITU-T (International Telecommunication Union - Telecommunication Standardization Sector).
• New Delhi being the capital city of India, often hosts such significant international events due to its strategic importance and robust infrastructure.
• The assembly brings together experts from around the world to discuss and set telecommunication standards that will shape the future of global communications.
• The event in New Delhi underscores India's growing influence and active participation in the global telecommunications sector.
• Hosting WTSA 2024 in New Delhi aligns with India's goal to become a leader in information and communication technology (ICT).

 Additional Information

• Jaipur
• Jaipur is known as the Pink City and is a major tourist destination in India.
• It is famous for its rich cultural heritage, including historical palaces and forts.
• While Jaipur hosts various national and regional conferences, it is less likely to host major international telecommunication events compared to New Delhi.
• Chandigarh
• Chandigarh is a union territory and serves as the capital of both Punjab and Haryana.
• It is known for its modern architecture and urban planning, designed by the Swiss-French architect Le Corbusier.
• Though a significant city, it is not a common choice for hosting large-scale international events like the WTSA.
• Kolkata
• Kolkata, formerly known as Calcutta, is the capital of the Indian state of West Bengal.
• It is known for its rich cultural and literary heritage, including being the home of the famous poet Rabindranath Tagore.
• While Kolkata is a major city with significant historical importance, New Delhi's strategic position as the capital gives it an edge in hosting international events like WTSA.

Shortcut Trick

In Simple Interest, Total % Interest = Rate × Time.

Total Interest = 4% × 6 = 24%.

Amount % = Principal (100%) + Interest (24%) = 124%.

124% = ₹1,116 ⇒ 1% = 9 ⇒ 100% = ₹900.

∴ The correct answer is ₹900.

Alternate Method

Given:

Amount (A) = ₹1,116

Rate (R) = 4% per annum

Time (T) = 6 years

Formula Used:

Amount = Principal × (1 + (R × T) ÷ 100)

Calculations:

⇒ 1,116 = P × (1 + (4 × 6) ÷ 100)

⇒ 1,116 = P × (1 + 24 ÷ 100)

⇒ 1,116 = P × (124 ÷ 100)

⇒ P = (1,116 × 100) ÷ 124

⇒ P = 9 × 100

⇒ P = ₹900

∴ The correct answer is ₹900.

Additional Information

Simple Interest Formula

The basic formula for SI is (P × R × T) ÷ 100, where P is Principal, R is Rate, and T is Time.

Difference between SI and CI

In Simple Interest, interest is calculated only on the principal, whereas in Compound Interest, interest is calculated on the principal plus the accumulated interest.

Relationship between Amount and Principal

Amount (A) is always the sum of Principal (P) and Interest (I). i.e., A = P + I.

The correct answer is Bharatiya Janata Party.

Key Points

• The Bharatiya Janata Party (BJP) is one of the two major political parties in India, along with the Indian National Congress.
• The BJP's political ideology is centered around Hindutva, which seeks to promote Hindu values and culture.
• The party was founded in 1980 as the political wing of the Rashtriya Swayamsevak Sangh (RSS).
• It has been in power in various states and at the central level multiple times, with significant electoral victories in recent years.
• The BJP is known for its focus on economic reforms, national security, and infrastructure development.
• In the 2024 Assembly elections in Odisha, the BJP managed to secure a majority and formed the government.

 Additional Information

• Aam Aadmi Party (AAP)
• The Aam Aadmi Party (AAP) was founded in 2012 by Arvind Kejriwal and other social activists.
• The party emerged from the India Against Corruption movement and focuses on issues like anti-corruption, education, and healthcare.
• AAP has a significant presence in Delhi, where it has formed the government multiple times.
• Janata Dal (United)
• Janata Dal (United) is a center-left political party primarily active in the state of Bihar.
• The party was formed in 1999 through the merger of the Janata Dal factions and is led by Nitish Kumar.
• JD(U) emphasizes social justice, secularism, and regional development.
• Indian National Congress
• The Indian National Congress is one of the oldest political parties in India, founded in 1885.
• The party played a crucial role in the Indian independence movement against British rule.
• Congress has a center-left political stance, focusing on social justice, economic development, and secularism.

Shortcut Trick

Let the number be 100%.

Difference in percentages = 30% − 20% = 10%.

Given, 10% of the number = 12.

So, 100% of the number = 12 × 10 = 120.

∴ The correct answer is 120.

Alternate Method

Given:

First percentage = 30%

Second percentage = 20%

Difference value = 12

Calculation:

Let the number be x.

⇒ (30/100) × x − (20/100) × x = 12

⇒ (10/100) × x = 12

⇒ 0.1x = 12

⇒ x = 12 ÷ 0.1

⇒ x = 120

∴ The correct answer is 120.

Additional Information

Percentage Difference

When comparing two percentages of the same base, the absolute difference in value is equal to the difference in percentages multiplied by the base value (Number × (P₁% − P₂%) = Difference).

Base Value Concept

In percentage problems, the original number is always considered as 100% unless specified otherwise.

The Correct answer is Gulveer Singh.

Key Points

• Gulveer Singh is an Indian track and field athlete.
• He specializes in long-distance running.
• Gulveer Singh has shown exceptional performance in various national and international events.
• His record-breaking performance at the 2024 Portland Track Festival gained significant attention.
• The Portland Track Festival is known for featuring elite athletes and providing a competitive platform for breaking records.

 Additional Information

• Avinash Sable
• Avinash Sable is an Indian track and field athlete specializing in 3,000 meters steeplechase.
• He has represented India at various international competitions including the Olympics.
• Muhammad Anas
• Muhammad Anas is an Indian sprinter specializing in the 400 meters race.
• He has set national records and represented India in multiple international events.
• Jyoshna Sabar
• Jyoshna Sabar is an emerging Indian athlete known for her performance in middle-distance running.
• She has been a part of various national-level competitions.

Given:

Expression = 36² ÷ 9² + 4²

Formula used:

BODMAS rule (Division then Addition)

(a ÷ b)ⁿ = aⁿ ÷ bⁿ

Calculations:

36² ÷ 9² + 4²

⇒ (36 ÷ 9)² + 4²

⇒ 4² + 4²

⇒ 16 + 16

⇒ 32

∴ The correct answer is option (2).

The correct answer is Pituitary.

Key Points

• The pituitary gland is a small, pea-shaped gland located at the base of the brain.
• It is often referred to as the "master gland" because it controls several other hormone glands in the body, including the thyroid and adrenal glands.
• The pituitary gland secretes growth hormone (GH), which is crucial for growth, cell repair, and metabolism.
• Growth hormone stimulates growth in almost all tissues of the body, including bones and muscles.
• The pituitary gland is divided into two parts: the anterior pituitary and the posterior pituitary. Growth hormone is produced in the anterior pituitary.

 Additional Information

• Thyroid
• The thyroid gland is located in the neck and produces hormones like thyroxine (T4) and triiodothyronine (T3) that regulate metabolism.
• It plays a vital role in controlling the body's metabolic rate, heart and digestive functions, muscle control, brain development, and bone maintenance.
• Pancreas
• The pancreas is located behind the stomach and has both endocrine and exocrine functions.
• It produces important hormones like insulin and glucagon which regulate blood sugar levels.
• Adrenal
• The adrenal glands are located on top of each kidney.
• They produce a variety of hormones including adrenaline and cortisol which help regulate metabolism, immune response, blood pressure, and stress responses.

The correct answer is addition reaction.

Key Points

• Hydrogenation is a chemical reaction between hydrogen (H₂) and another compound or element.
• This reaction typically occurs in the presence of a catalyst such as nickel (Ni).
• In the case of vegetable oils, hydrogenation converts unsaturated fats to saturated fats by adding hydrogen atoms to the double bonds in the fatty acid chains.
• This is an addition reaction because hydrogen atoms are being added to the molecules of the vegetable oil.
• Vegetable oils typically contain unsaturated fatty acids which have one or more double bonds in their structure.
• The process of hydrogenation makes the oils more solid at room temperature and increases their shelf life.
• Hydrogenation is widely used in the food industry to produce margarines and shortenings.

 Additional Information

• Rearrangement reaction
• A rearrangement reaction involves the reorganization of the molecular structure of a compound.
• It often results in a change in the connectivity of atoms within the molecule.
• Rearrangement reactions are common in organic chemistry and are used to synthesize complex molecules.
• Elimination reaction
• An elimination reaction involves the removal of atoms or groups from a molecule, resulting in the formation of a double or triple bond.
• This type of reaction is often the opposite of an addition reaction.
• Examples include the formation of alkenes from alcohols.
• Combustion reaction
• A combustion reaction is a high-temperature exothermic redox chemical reaction between a fuel and an oxidant, producing oxidized products and releasing heat.
• Common examples include the burning of hydrocarbons in oxygen to produce carbon dioxide and water.

Shortcut Trick

Side of rhombus (a) = Perimeter ÷ 4 = 148 ÷ 4 = 37 cm.

In a rhombus, the half-diagonals (d₁/2, d₂/2) and the side (a) form a Pythagorean triplet.

Half-diagonal 1 = 24 ÷ 2 = 12 cm. Using triplet (12, 35, 37), half-diagonal 2 = 35 cm.

Area = 2 × (d₁/2 × d₂/2) = 2 × 12 × 35 = 840 cm².

∴ The correct answer is 840 cm².

Alternate Method

Given: Perimeter = 148 cm, Diagonal 1 (d₁) = 24 cm.

Formula Used: Side (a) = Perimeter ÷ 4; Area = (1/2) × d₁ × d₂; Relationship: a² = (d₁/2)² + (d₂/2)².

⇒ Side (a) = 148 ÷ 4 = 37 cm

⇒ (d₂/2)² = a² − (d₁/2)²

⇒ (d₂/2)² = 37² − 12² = 1369 − 144 = 1225

⇒ d₂/2 = √1225 = 35 cm ⇒ d₂ = 70 cm

⇒ Area = (1/2) × 24 × 70 = 12 × 70 = 840 cm²

∴ The correct answer is 840 cm².

Additional Information

Properties of Rhombus

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

Area of Rhombus

Area = (1/2) × d₁ × d₂ or Area = base × height.

Side-Diagonal Relation

4a² = d₁² + d₂², where 'a' is the side and d₁, d₂ are diagonals.

Shortcut Trick

Total work (LCM of 15, 10, 30) = 30 units.

Efficiencies: P = +2, Q = +3, R = −1. Combined (P+Q+R) = 4.

Work done in 2 hours = 4 × 2 = 8 units. Remaining = 30 − 8 = 22 units.

Time with P and Q only = 22 ÷ 5 = 4.4 hours (4 hr 24 min).

Time if R was never open = 30 ÷ 5 = 6 hours. But from t=0, P+Q take 30/5 = 6 hours. After 2 hours, they would need 4 hours. Extra time = 4 hr 24 min − 4 hr = 24 min.

∴ The correct answer is 24 min.

Alternate Method

⇒ Combined efficiency of P, Q and R = 2 + 3 − 1 = 4 units/hr

⇒ Work done in first 2 hours = 4 × 2 = 8 units

⇒ Remaining work = 30 − 8 = 22 units

⇒ After closing R, efficiency of (P + Q) = 2 + 3 = 5 units/hr

⇒ Actual time to complete remaining work = 22 ÷ 5 = 4.4 hours = 4 hours 24 minutes

⇒ Ideal time needed after 2 hours (if R was never open) = (30 − (5 × 2)) ÷ 5 = 20 ÷ 5 = 4 hours

⇒ Extra time taken = 4 hr 24 min − 4 hr = 24 minutes

∴ The correct answer is 24 min.

Additional Information

Negative Efficiency

In Pipes and Cisterns, an emptying pipe (leak) is always assigned a negative efficiency while a filling pipe is assigned a positive one.

Time and Work Relation

Efficiency × Time = Total Work. Total work is usually taken as the LCM of the individual time periods for easier calculation.

Extra Time Calculation

Extra time is the difference between the actual time taken to fill the tank and the scheduled time if no error/leak occurred.

Decoding letters:

Given: 15 A 3 B 9 D 2 C 4 = ?

After interchanging the letters,

15 A 3 B 9 D 2 C 4 = ? ⇒ 15 ÷ 3 + 9 - 2 × 4 = ?

⇒ 15 ÷ 3 + 9 - 2 × 4 = ?

⇒ 5 + 9 - 2 × 4 = ?

⇒ 5 + 9 - 8 = ?

⇒ 14 - 8 = ?

⇒ 6 = ?

Hence, "Option 3" is the correct answer.

Shortcut Trick

Mean Proportional of a and b = √(a × b)

⇒ √(25 × 36)

⇒ 5 × 6 = 30

∴ The correct answer is 30.

Alternate Method

Given:

First number (a) = 25

Second number (b) = 36

Formula Used:

If x is the mean proportional between a and b, then a : x :: x : b

⇒ x² = a × b

Calculations:

⇒ x² = 25 × 36

⇒ x = √(25 × 36)

⇒ x = √(900)

⇒ x = 30

∴ The correct answer is 30.

Additional Information

Third Proportional

For two numbers a and b, the third proportional c is such that a : b :: b : c, which gives c = b² / a.

Fourth Proportional

For three numbers a, b, and c, the fourth proportional d is such that a : b :: c : d, which gives d = (b × c) / a.

Continued Proportion

Three quantities a, b, c are in continued proportion if a/b = b/c.

The Correct answer is Only (a).

Key Points

• The principal focus of a spherical mirror is the point where rays of light parallel to the principal axis converge (in a concave mirror) or appear to diverge from (in a convex mirror) after reflection.
• For a concave mirror, the principal focus lies midway between the pole (the center of the mirror's surface) and the center of curvature (the center of the sphere of which the mirror is a part).
• The position of the principal focus does not depend on the size of the mirror. It is always at a fixed distance, which is half the radius of curvature (i.e., focal length = radius of curvature / 2).
• For a convex mirror, the principal focus is also located midway between the pole and the center of curvature but appears to be behind the mirror.

 Additional Information

• Its position depends on the size of the mirror
• This statement is incorrect because the position of the principal focus is determined by the radius of curvature and not by the size of the mirror.
• The focal length remains constant for a given mirror regardless of its size.
• It always lies at the centre of curvature
• This statement is incorrect because the principal focus is distinct from the center of curvature. The center of curvature is twice the distance from the mirror compared to the principal focus.

The logic followed here is:

Given:

(2, 8, 32)

2 × 4 = 8

8 × 4 = 32

And,

(5, 20, 80)

5 × 4 = 20

20 × 4 = 80

So, checking each option one by one:

Option 1) (9, 36, 144)

9 × 4 = 36

36 × 4 = 144

Option 2) (9, 36, 124)

9 × 4 = 36

36 × 4 = 124 ≠ 144

Option 3) (9, 36, 142)

9 × 4 = 36

36 × 4 = 142 ≠ 144

Option 4) (9, 39, 144)

9 × 4 = 36 ≠ 39

39 × 4 = 156 ≠ 144

Thus, out of all the options, '(9, 36, 144)' follows the same logic as given.

Hence, "Option 1" is the correct answer.

Shortcut Trick

For the average of first n natural numbers, the direct formula is (n + 1) ÷ 2.

Here, n = 10.

Average = (10 + 1) ÷ 2 = 11 ÷ 2 = 5.5.

∴ The correct answer is 5.5.

Alternate Method

Given: First 10 natural numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Formula Used: Average = Sum of observations ÷ Total number of observations

⇒ Sum = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

⇒ Total numbers = 10

⇒ Average = 55 ÷ 10

⇒ Average = 5.5

∴ The correct answer is 5.5.

Additional Information

Sum of First n Natural Numbers

The sum of the first n natural numbers is given by S_n = [n(n + 1)] ÷ 2.

Average of AP Series

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

Average of Even/Odd Numbers

Average of first n even numbers is (n + 1). Average of first n odd numbers is n.

Decoding symbols:

Given: S + T - U × V - W + X

S + T → S is the sister of T.

T - U → T is the husband of U.

U × V → U is the mother of V.

V - W → V is the husband of W.

W + X → W is the sister of X.

Thus, V is T's son.

Hence, the correct answer is "Option 2".

The correct answer is high pressure and low temperature.

Key Points

• Gases can be liquefied by increasing the pressure and decreasing the temperature.
• Increasing the pressure forces gas molecules closer together, promoting the formation of a liquid phase.
• Decreasing the temperature reduces the kinetic energy of the gas molecules, making it easier for intermolecular forces to hold the molecules together in a liquid state.
• These principles are based on the Ideal Gas Law and Phase Diagrams which describe the state of matter under different conditions of pressure and temperature.
• Liquefaction of gases is a fundamental process in the production and storage of liquefied natural gas (LNG), liquefied petroleum gas (LPG), and in the industrial gas industry.

 Additional Information

• Low pressure and high temperature
• Low pressure and high temperature conditions generally favor the formation of gases rather than liquids because the molecules have high kinetic energy and are far apart.
• Low pressure and low temperature
• While low temperature can support liquefaction, low pressure does not help in bringing molecules close together, making it ineffective for liquefying gases.
• High pressure and high temperature
• High pressure can promote liquefaction, but high temperature increases the kinetic energy of molecules, counteracting the effects of high pressure.

Shortcut Trick

Interior angles on the same side of a transversal (consecutive interior angles) between parallel lines are always supplementary.

Sum = 180°

∠2 = 180° − 65° = 115°

∴ The correct answer is 115°.

Alternate Method

Given:

Lines are parallel.

m∠1 = 65°

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

Formula Used:

Sum of consecutive interior angles = 180°

Calculations:

⇒ m∠1 + m∠2 = 180°

⇒ 65° + m∠2 = 180°

⇒ m∠2 = 180° − 65°

⇒ m∠2 = 115°

∴ The correct answer is 115°.

Additional Information

Alternate Interior Angles

When parallel lines are intersected by a transversal, alternate interior angles are equal in measure.

Corresponding Angles

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

Vertically Opposite Angles

When two lines intersect, the angles opposite each other at the vertex are always equal.

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

Conclusions:

(I) No door is a key → Does not follow (As some doors are locks and no lock is a key. As no direct relation is given between doors and key, therefore it is false)

(II) Some locks are doors → Follow (As some doors are locks. As some part of doors is common with locks, therefore it is true.)

∴ Here, Only conclusion II follows.​

Hence, the correct answer is "Option 1"

Shortcut Trick

Ratio of A : B : C : D = 4 : 7 : 9 : 3

Difference between C and D in ratio = 9 − 3 = 6 units

Given, 6 units = Rs. 720 ⇒ 1 unit = Rs. 120

D share = 3 units = 3 × 120 = Rs. 360

∴ The correct answer is Rs. 360.

Alternate Method

Given: Ratio of shares A : B : C : D = 4x : 7x : 9x : 3x

Difference between C share and D share = Rs. 720

⇒ 9x − 3x = 720

⇒ 6x = 720

⇒ x = 720 ÷ 6

⇒ x = 120

D share = 3x

⇒ 3 × 120 = 360

∴ The correct answer is Rs. 360.

Additional Information

Ratio and Proportion Basics

A ratio a:b represents the relative sizes of two quantities. If a total sum S is divided in ratio a:b:c, the share of the first person is (a / (a+b+c)) × S.

Difference Rule in Ratios

When the difference between two parts is given, equate the difference in ratio units to the actual value to find the value of 1 unit (x).

Total Sum Calculation

Total Sum = (Sum of all ratio parts) × Value of 1 unit. For this case: (4+7+9+3) × 120 = 23 × 120 = Rs. 2760.

The correct answer is Kulhad non-biodegradable.

Key Points

• Biodegradable materials are those that can be broken down by natural processes and decomposed by microorganisms.
• Kulhad is a traditional Indian cup made from clay, which is an eco-friendly and biodegradable material.
• Since Kulhad is made from natural clay, it easily decomposes back into the soil, contributing to environmental sustainability.
• Using Kulhad helps reduce the use of plastic and other non-biodegradable materials, thereby reducing environmental pollution.
• In contrast, materials like plastic take hundreds of years to decompose and can cause significant environmental damage.

 Additional Information

• Paper cup - biodegradable
• Paper cups are typically made from wood pulp and are biodegradable.
• They can decompose naturally and are often recyclable.
• Plastic glass - non-biodegradable
• Plastic glasses are made from synthetic polymers, which are non-biodegradable.
• They can persist in the environment for hundreds of years, causing pollution.
• Vegetable - biodegradable
• Vegetables are organic and biodegradable.
• They decompose naturally through the action of microorganisms.

The correct answer is Rings of cartilage.

Key Points

• Rings of cartilage are present in the trachea, also known as the windpipe.
• These rings are C-shaped structures that provide structural support to the trachea.
• They prevent the trachea from collapsing and ensure that the airway remains open for air to pass through.
• This structure is crucial for maintaining an unobstructed pathway for respiration.
• Cartilage is a flexible but strong connective tissue that provides necessary rigidity while allowing some flexibility.

 Additional Information

• Nostrils large hairs
• Large hairs present in the nostrils filter out dust and other particles from the air before it enters the respiratory system.
• They do not play a role in preventing the collapse of the air passage in the throat.
• Size of mouth cavity
• The size of the mouth cavity affects speech and chewing, but it does not influence the structural integrity of the air passage in the throat.
• Nostrils large pores
• The nostrils contain small pores that help in the passage of air and the filtering process, but they do not contribute to preventing the collapse of the air passage in the throat.

The correct answer is Pascal.

Key Points

• Pascal (Pa) is the SI unit of pressure.
• It is defined as one newton per square meter (N/m²).
• Named after the French mathematician and physicist Blaise Pascal.
• Commonly used to measure internal pressure, stress, Young's modulus, and ultimate tensile strength.
• In everyday applications, kilopascal (kPa) is often used, where 1 kPa = 1000 Pa.
• In meteorology, atmospheric pressure is often given in hectopascals (hPa), where 1 hPa = 100 Pa.

 Additional Information

• Kelvin
• Kelvin (K) is the SI unit of temperature.
• It is one of the seven base units in the International System of Units (SI).
• The Kelvin scale starts from absolute zero, the theoretical point where molecular motion ceases.
• Cubic metre
• Cubic metre (m³) is the SI unit of volume.
• It is the volume of a cube with edges one metre in length.
• Commonly used to measure the volume of liquids or gases.
• Newton
• Newton (N) is the SI unit of force.
• It is named after Sir Isaac Newton in recognition of his work in classical mechanics.
• Defined as the force required to accelerate a one-kilogram mass by one metre per second squared (m/s²).

The Correct answer is Pascal.

Key Points

• The Pascal (Pa) is the SI unit of pressure.
• It is defined as one newton per square meter (N/m²).
• The unit is named after the French mathematician Blaise Pascal, who made significant contributions to fluid mechanics and the study of pressure.
• It is widely used in various fields such as physics, engineering, and meteorology.
• Common multiples of the Pascal include the hectopascal (hPa) and the kilopascal (kPa).

 Additional Information

• Newton
• The Newton (N) is the SI unit of force.
• It is named after Sir Isaac Newton for his work on the laws of motion.
• It is defined as the force required to accelerate a one-kilogram mass by one meter per second squared.
• Angstrom
• The Angstrom (Å) is a unit of length used primarily to express wavelengths of light.
• One angstrom is equivalent to 10^-10 meters or 0.1 nanometers.
• It is named after the Swedish physicist Anders Jonas Ångström.

The correct answer is Only liquid.

Key Points

• Butter is an example of a colloid, specifically an emulsion.
• In a colloidal system, the dispersed phase is the phase that is distributed in the form of very small particles or droplets throughout the bulk of another phase, known as the continuous phase.
• In the case of butter, the continuous phase is solid fat.
• The dispersed phase in butter is water, making it a liquid.
• This means that the water droplets are dispersed throughout the solid fat.
• Therefore, the dispersed phase of butter is only liquid.

 Additional Information

• Only gas
• In a colloidal system, if the dispersed phase is a gas, the colloid is typically termed as a foam.
• An example of such a system is whipped cream, where air (gas) is dispersed in liquid cream.
• Only solid
• When the dispersed phase is a solid, such colloidal systems are known as sols or gels.
• An example includes gelatin, where solid particles are dispersed in water.
• Both solid and liquid
• There are colloidal systems where both solid and liquid can be dispersed phases, but butter specifically has liquid as the dispersed phase.
• An example of a system with both dispersed phases might be a complex colloid with multiple phases, but this is not the case with butter.

The correct answer is 1/3.

Key Points

• Magnification is the ratio of the height of the image to the height of the object.
• Magnification (m) = height of image (h') / height of object (h).
• In this case, the height of the object (h) is 30 cm and the height of the image (h') is 10 cm.
• Therefore, m = h' / h = 10 / 30.
• This simplifies to m = 1 / 3, which is equivalent to 0.33.
• Since this is a concave lens, the magnification will be negative.
• Therefore, the magnification is -0.33.

 Additional Information

• Concave Lens
• A concave lens is a diverging lens that spreads out light rays that have been refracted through it.
• It forms a virtual, upright, and diminished image of the object.
• These lenses are used in eyeglasses for people with myopia (nearsightedness).
• Magnification
• Magnification is a measure of how much larger or smaller the image is compared to the object.
• It is a dimensionless quantity.
• The formula for magnification in lenses and mirrors is the same: m = h' / h or m = -v / u where v is the image distance and u is the object distance.

The Correct answer is uniformly accelerated motion.

Key Points

• A freely falling body is an object that is moving under the influence of gravity alone.
• The acceleration due to gravity, denoted by 'g', is approximately 9.8 m/s² near the Earth's surface.
• This acceleration is constant and acts vertically downwards.
• As the body falls, its velocity increases uniformly because of this constant acceleration.
• Thus, the motion of a freely falling body is an example of uniformly accelerated motion.
• In uniformly accelerated motion, the velocity of the object changes at a constant rate.

 Additional Information

• Uniform velocity motion
• Uniform velocity motion refers to motion where an object moves with a constant speed in a straight line.
• In this type of motion, there is no change in the speed or direction of the object.
• Uniform speed motion
• Uniform speed motion occurs when an object covers equal distances in equal intervals of time, regardless of the direction.
• This differs from uniformly accelerated motion, where the speed changes due to acceleration.
• Non-uniformly accelerated motion
• Non-uniformly accelerated motion refers to motion where the rate of acceleration is not constant.
• In such motion, the velocity of the object changes at a varying rate over time.

The Correct answer is Evaporation.

Key Points

• Evaporation is the process where liquid water is converted into water vapor by absorbing heat.
• In summer, our bodies sweat to cool down, and the sweat evaporates, taking away heat from our body.
• Cotton clothes are preferred in summer because they are light and breathable, allowing air to circulate and sweat to evaporate more easily.
• This process of evaporation helps in maintaining the body’s natural temperature and prevents overheating.
• Cotton being a natural fiber, absorbs sweat and allows it to evaporate quickly, providing a cooling effect.

 Additional Information

• Sublimation
• Sublimation is the process where a solid changes directly into a gas without passing through the liquid state.
• This process is seen in substances like dry ice (solid carbon dioxide).
• Condensation
• Condensation is the process where water vapor turns back into liquid water.
• This process is commonly observed when water droplets form on the outside of a cold glass.
• Fusion
• Fusion, also known as melting, is the process where a solid turns into a liquid by absorbing heat.
• An example of this process is ice melting into water.

The logic followed here is:

Option 1) JN-IM

Option 2) RV-QU

Option 3) PT-OS

Option 4) MQ-LO

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

Hence, "Option 4" is the correct answer.

The Correct answer is "Decoding the Green Transition for India".

Key Points

• The theme "Decoding the Green Transition for India" focuses on understanding and implementing the strategies and policies needed for India to transition towards a sustainable and green economy.
• The conference aimed to address the challenges and opportunities that come with the green transition, including renewable energy, sustainable agriculture, and climate resilience.
• Experts and policymakers discussed the roadmap for achieving net-zero emissions and the importance of innovation and technology in driving this transition.
• The event highlighted the need for collaborative efforts from various sectors including government, private sector, and civil society.
• The focus was also on the importance of public awareness and education in fostering a culture of sustainability.

 Additional Information

• Towards a Greener Future: India's Roadmap
• This theme suggests a focus on planning India's journey towards a greener future but lacks the emphasis on decoding and implementing specific strategies.
• Innovating for Sustainable India
• While this theme highlights innovation, it does not specifically address the comprehensive approach of decoding the transition necessary for a green future.
• Empowering India's Climate Action
• This theme focuses on empowerment but does not cover the detailed aspect of transition strategies for sustainability.

The Correct answer is voluntary muscles.

Key Points

• Voluntary muscles are muscles that can be consciously controlled by the individual.
• These muscles are primarily skeletal muscles, which are attached to bones and are involved in movement.
• The term "voluntary" refers to the fact that these muscles move when we decide to move them.
• These muscles work by contracting and relaxing in response to signals from the nervous system.
• Examples of voluntary muscles include the biceps, triceps, and quadriceps.
• Voluntary muscles are also characterized by their striated appearance under a microscope.

 Additional Information

• Involuntary muscles
• Involuntary muscles are muscles that cannot be controlled consciously. They work automatically.
• These muscles are primarily found in the internal organs such as the stomach, intestines, and blood vessels.
• Involuntary muscles include smooth muscles and cardiac muscles.
• Unstriated muscles
• Unstriated muscles are another term for smooth muscles.
• These muscles lack the striations seen in voluntary muscles and are found in the walls of internal organs.
• Cardiac muscles
• Cardiac muscles are found only in the heart.
• They are involuntary and have a striated appearance similar to skeletal muscles.
• Cardiac muscles work continuously and rhythmically without conscious control.

The logic followed here is:

Given: 

ID-LG-OQ

And,

LG-OJ-RT 

So, checking each option one by one:

Option 1) MI-QL-TU

Option 2) MI-QK-TV

Option 3) NI-QL-TV

Option 4) NI-QK-TU

Thus, out of all the options 'NI-QL-TV' is the odd one out.

Hence, "Option 3" is the correct answer.

The correct answer is Conversion of copper oxide into copper.

Key Points

• Reduction reaction refers to the process in which a substance gains electrons and decreases its oxidation state.
• In the conversion of copper oxide (CuO) into copper (Cu), copper oxide is reduced to copper by gaining electrons.
• This process often involves the removal of oxygen or the addition of hydrogen.
• Copper oxide (CuO) is an inorganic compound that can be reduced to copper metal (Cu) through a reduction reaction.
• In this reaction, the oxygen is removed from copper oxide, leaving behind pure copper.

 Additional Information

• Conversion of copper into copper oxide
• This is an example of an oxidation reaction where copper (Cu) reacts with oxygen (O₂) to form copper oxide (CuO).
• Oxidation involves the loss of electrons and an increase in the oxidation state of the element.
• Conversion of carbon into carbon dioxide
• This is also an oxidation reaction where carbon (C) reacts with oxygen (O₂) to form carbon dioxide (CO₂).
• In this reaction, carbon undergoes oxidation by losing electrons and forming carbon dioxide.
• Conversion of ethanol into acetic acid
• This is an example of an oxidation reaction where ethanol (C₂H₅OH) is oxidized to acetic acid (CH₃COOH).
• Oxidation of ethanol involves the loss of hydrogen atoms and the formation of acetic acid.

The correct answer is Inertia is proportional to mass.

Key Points

• Inertia refers to the resistance of any physical object to a change in its state of motion or rest.
• The greater the mass of an object, the greater its inertia. This means it is more difficult to change the motion of an object with a larger mass.
• Newton's First Law of Motion, also known as the Law of Inertia, states that an object will remain at rest or in uniform motion unless acted upon by an external force.
• In practical terms, a heavy object (high mass) like a truck has more inertia compared to a light object like a bicycle.
• This proportional relationship means that if you double the mass of an object, its inertia will also double.

 Additional Information

• Inertia is independent of mass
• This statement is incorrect because inertia is directly related to the mass of an object. A higher mass results in greater inertia.
• Inertia is inversely proportional to mass
• This statement is also incorrect. If inertia were inversely proportional to mass, an increase in mass would result in a decrease in inertia, which contradicts the principles of physics.
• The data provided here is not adequate to draw any conclusion
• This option is incorrect because the relationship between mass and inertia is well-established in physics and does not require additional data for a conclusion.

The Correct answer is concave mirror.

Key Points

• The front side of a table spoon has a concave surface, which means it curves inward.
• When you look at the front side of a table spoon, it acts like a concave mirror.
• Concave mirrors reflect light from their inwardly curved surface, focusing light to a point.
• These mirrors form an inverted image when the object is placed beyond the focal point.
• Concave mirrors are commonly used in applications where focused light is required, such as in telescopes, headlights, and shaving mirrors.

 Additional Information

• Concave lens
• A concave lens diverges light rays that pass through it, spreading them apart.
• It is used in corrective glasses for people with myopia (nearsightedness).
• Convex mirror
• A convex mirror has an outwardly curved surface and diverges light rays, spreading them out.
• It forms a virtual, upright, and diminished image of objects.
• Convex mirrors are often used in vehicle side mirrors and security mirrors.
• Plane mirror
• A plane mirror has a flat reflective surface that forms a virtual, upright, and same-size image of the object.
• Plane mirrors are commonly used in household mirrors and periscopes.

Given: 12 × 12 ÷ 12 - 12 + 15 = ?

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

12 × 12 ÷ 12 - 12 + 15 = ? ⇒ 12 ÷ 12 × 12 + 12 - 15 = ?

⇒ 12 ÷ 12 × 12 + 12 - 15 = ?

⇒ 1 × 12 + 12 - 15 = ?

⇒ 12 + 12 - 15 = ?

⇒ 24 - 15 = ?

⇒ 9 = ?

Hence, "Option 1" is the correct answer.

Given:

Benji starts from Point A and drives 70 km towards South.

He then takes a right turn, drives 20 km, turns right and drives 35 km.

He then takes a left turn and drives 15 km.

He takes a final right turn, drives 35 km and stops at Point P. 

Thus, Benji should drive (20 km + 15 km) 35 km in the east direction in order to reach Point A again.

Hence, "Option 2" is the correct answer.

The logic followed here is:

Given: 

GL-IF-JM

And,

JO-LI-MP 

So, checking each option one by one:

Option 1) MR-OL-PS

Option 2) KP-MJ-NO 

Option 3) LQ-NK-OP

Option 4) NS-PM-QR

Thus, out of all the options 'MR-OL-PS' follows the same logic as given.

Hence, "Option 1" is the correct answer.

Shortcut Trick

Total Cost = 4800 + 800 = Rs. 5600.

CP per apple = 5600 ÷ 800 = Rs. 7.

Required Profit per apple = Rs. 10.

Selling Price (SP) per apple = CP + Profit = 7 + 10 = Rs. 17.

∴ The correct answer is Rs. 17.

Alternate Method

Given: Total apples = 800, Purchasing Price = Rs. 4800, Overhead expenses = Rs. 800, Desired profit per apple = Rs. 10.

Formulas: Total CP = Purchasing Price + Overhead Expenses | CP per unit = Total CP ÷ Total Quantity | SP per unit = CP per unit + Profit per unit.

⇒ Total Cost Price = 4800 + 800 = Rs. 5600.

⇒ Cost Price (CP) for one apple = 5600 ÷ 800 = Rs. 7.

⇒ Required Selling Price (SP) per apple = CP per apple + Profit per apple.

⇒ SP per apple = 7 + 10 = Rs. 17.

∴ The correct answer is Rs. 17.

Additional Information

Effective Cost Price

The Effective CP includes the actual price paid plus any overhead expenses like transportation, labor, or repairs.

Profit Calculation

Profit can be calculated on a per-unit basis or on the total quantity; the ratio between profit and cost remains proportional.

The Correct answer is New Delhi.

Key Points

• The 15^th edition of the annual art fair took place in New Delhi.
• This event featured over 100 exhibitors from various parts of the world.
• A special inaugural section focused on Design Initiatives, highlighting innovative design works.
• New Delhi is a significant cultural hub in India, often hosting major art and cultural events.
• The fair attracted a diverse crowd, including artists, collectors, and art enthusiasts.
• This edition of the art fair included a variety of art forms, such as paintings, sculptures, and digital art.

 Additional Information

• Kolkata
• Kolkata is known for its rich cultural heritage and vibrant arts scene.
• The city hosts many art galleries and cultural festivals throughout the year.
• Surat
• Surat is a major commercial hub, especially known for its diamond cutting and textile industries.
• It is not typically known for hosting major art fairs.
• Chennai
• Chennai is famous for its cultural events, particularly in the field of classical music and dance.
• The city is also home to several important art galleries and museums.

Shortcut Trick

For a circle circumscribing a square, the diameter of the circle is equal to the diagonal of the square.

Diagonal of square = side × √2 = 7√2 cm.

Circumference = π × diameter = (22/7) × 7√2 = 22√2 cm.

∴ The correct answer is 22√2 cm.

Alternate Method

Given: Side of square (a) = 7 cm.

Formula Used: Diameter of circumcircle (d) = a√2; Circumference = πd

⇒ Diagonal of the square = √(side² + side²)

⇒ Diagonal = √(7² + 7²) = √(49 + 49) = √98 = 7√2 cm

⇒ Since the square is inscribed, circle diameter (d) = Diagonal = 7√2 cm

⇒ Circumference = π × d

⇒ Circumference = (22/7) × 7√2

⇒ Circumference = 22√2 cm

∴ The correct answer is 22√2 cm.

Additional Information

Incircle of a Square

For a circle inscribed inside a square, the diameter of the circle is equal to the side of the square (d = a).

Area of Circumcircle

The area of the circle circumscribing a square is πr², where r = (a√2)/2. Area = πa²/2.

Ratio of Areas

The ratio of the area of the incircle to the area of the circumcircle of the same square is always 1 : 2.

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

Conclusions:

(I) Some hands are ears → Follow (As all legs are hands and some legs are ears. As some part of ears is common with legs which whole comes in hands, therefore it is true.)

(II) Some ears are legs → Follow (As some legs are ears. As some part of legs is common with ears, therefore it is true.)

∴ Here, Both conclusions I and II follow.​

Hence, the correct answer is "Option 3"

The correct answer is lower temperature than the normal body temperature.

Key Points

• The testes are located in the scrotum outside the abdominal cavity.
• This location is crucial because sperm formation requires a temperature that is lower than the normal body temperature.
• The normal body temperature is about 37 degrees Celsius, while the scrotal temperature is around 34 degrees Celsius, which is ideal for spermatogenesis.
• A lower temperature is necessary to maintain the viability and motility of sperm.
• The scrotum acts as a natural thermoregulator, ensuring that the testes remain at a temperature conducive to sperm production.

 Additional Information

• Higher body temperature
• A higher body temperature would be detrimental to sperm production as it would negatively affect the viability and motility of sperm.
• Higher temperature than the normal body temperature
• Similar to higher body temperature, a higher temperature than the normal body temperature would also impair sperm formation.
• Normal body temperature
• Sperm formation does not occur optimally at the normal body temperature; it requires a slightly cooler environment.

The correct answer is Both Potential and Kinetic.

Key Points

• When a ball is dropped from a height, it initially possesses only potential energy.
• As the ball falls, the potential energy gradually converts into kinetic energy.
• At the midpoint of the fall, the ball has fallen through half of the total distance.
• At this point, it has both potential energy (due to the height it is still above the ground) and kinetic energy (due to the velocity it has gained while falling).
• Specifically, at the midpoint, the energies are distributed such that the sum of potential energy and kinetic energy equals the total initial potential energy.
• This is a direct consequence of the law of conservation of energy, which states that the total energy in a closed system remains constant.

 Additional Information

• Potential Energy
• Potential energy is the energy stored in an object due to its position relative to some zero position.
• In this case, the zero position is the ground, and the ball has potential energy due to its height above the ground.
• Kinetic Energy
• Kinetic energy is the energy an object possesses due to its motion.
• As the ball falls, its velocity increases, and it gains kinetic energy.

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

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

Required condition: Perfect square - Odd digit - Even digit

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

Thus, there are no such odd digit which are immediately preceded by a perfect square and is immediately followed by an even digit.

Hence, "Option 1" is the correct answer.

The Correct answer is South pole to its North pole.

Key Points

• Inside a bar magnet, the direction of magnetic field lines is from its South pole to its North pole.
• Magnetic field lines are continuous loops that travel from the North pole to the South pole outside the magnet and from the South pole to the North pole inside the magnet.
• This characteristic of magnetic field lines is a fundamental property of how magnetic fields behave.
• Understanding the direction of magnetic field lines is crucial in the study of electromagnetism and the functioning of magnetic devices.

 Additional Information

• always perpendicular to the South pole
• The magnetic field lines are not always perpendicular to the South pole; they form continuous loops from the North pole to the South pole outside the magnet and vice versa inside.
• North pole to its South pole
• Outside a bar magnet, the magnetic field lines indeed travel from the North pole to the South pole.
• This is opposite to the direction inside the bar magnet.
• always perpendicular to the North pole
• The magnetic field lines are not always perpendicular to the North pole; they form continuous loops.

The correct answer is Salivary gland — trypsin.

Key Points

• Salivary glands secrete saliva, which contains the enzyme amylase (also known as ptyalin), not trypsin.
• Trypsin is an enzyme produced in the pancreas and released into the small intestine. It helps in digesting proteins.
• The main enzymes secreted by the salivary glands are amylase, which begins the digestion of carbohydrates in the mouth.
• Amylase breaks down starches into simpler sugars like maltose and dextrin.

 Additional Information

• Liver — bile juice
• The liver produces bile juice, which is stored in the gallbladder.
• Bile contains bile salts that help in the emulsification of fats, making them easier to digest.
• Bile also aids in the absorption of fat-soluble vitamins such as A, D, E, and K.
• Gastric gland — pepsin
• Gastric glands in the stomach lining secrete pepsinogen, which is converted to pepsin in the presence of hydrochloric acid (HCl).
• Pepsin is a proteolytic enzyme that breaks down proteins into peptides.
• The acidic environment in the stomach is essential for the activation and function of pepsin.
• Pancreas — pancreatic juice
• The pancreas secretes pancreatic juice, which contains several digestive enzymes.
• These enzymes include trypsin, chymotrypsin, amylase, and lipase.
• Pancreatic juice also contains bicarbonate ions that neutralize the acidic chyme entering the small intestine from the stomach.

The Correct answer is they defend plant cells from a variety of external effects.

Key Points

• Plant cells have a rigid cell wall that provides structural support and protection.
• The cell wall is composed of cellulose, hemicellulose, and pectin.
• It acts as a barrier against mechanical stress and pathogens.
• The cell wall helps in maintaining the shape of the cell and prevents excessive water intake.
• It also plays a role in the transport of substances in and out of the cell.

 Additional Information

• required for photosynthesis
• Photosynthesis primarily occurs in the chloroplasts, not the cell wall.
• do not have cytoplasm
• Plant cells do have cytoplasm, which is essential for cellular processes.
• do not have proper genetic material
• Plant cells contain a nucleus that holds their genetic material.

The Correct answer is 0 m/s.

Key Points

• Average velocity is defined as the total displacement divided by the total time taken.
• In this problem, Uma swims from one end of the pool to the other and back, covering a distance of 120 m in one minute.
• The displacement refers to the change in position from the initial point to the final point.
• Since Uma returns to her starting point, the displacement is 0 m.
• The total time taken is 1 minute (or 60 seconds).
• The formula for average velocity is: Average velocity = Total displacement / Total time.
• Given the displacement is 0 m, the average velocity is 0 m/s (0 divided by 60 seconds).

 Additional Information

• Displacement is a vector quantity that refers to the overall change in position of an object. It is different from distance, which is a scalar quantity and only measures the path length.
• In cases where the starting and ending points are the same, the displacement is always zero.
• The concept of average velocity is useful in understanding motion in physics, especially in problems involving circular or repetitive paths.

The correct answer is Zn + CuCl2 → ZnCl2 + Cu.

Key Points

• The reactivity series, also known as the activity series, is a list of elements ordered by their ability to displace other elements from compounds.
• In the reactivity series, zinc (Zn) is more reactive than copper (Cu).
• This means that zinc can displace copper from its compounds.
• The chemical reaction Zn + CuCl2 → ZnCl2 + Cu is possible because zinc is more reactive and will replace copper in the compound CuCl2.
• In this reaction, zinc chloride (ZnCl2) and copper (Cu) are formed.

 Additional Information

• 3Ag + AlCl3 → 3AgCl + Al
• In the reactivity series, aluminum (Al) is more reactive than silver (Ag).
• Therefore, silver cannot displace aluminum from AlCl3.
• 3Cu + FeCl3 → 3CuCl2 + Fe
• Iron (Fe) is more reactive than copper (Cu) in the reactivity series.
• As a result, copper cannot displace iron from FeCl3.
• Cu + ZnCl2 → CuCl2 + Zn
• In this case, zinc is more reactive than copper.
• Hence, copper cannot displace zinc from ZnCl2.

The correct answer is The male germ-cell produced by pollen grain fuses with the female gamete present in the ovule..

Key Points

• Fertilisation in plants is a crucial process that involves the fusion of male and female gametes.
• The male germ-cell, also known as the sperm cell, is produced by the pollen grain.
• The pollen grain travels from the anther to the stigma of a flower.
• Once on the stigma, the pollen grain germinates and forms a pollen tube that grows down the style towards the ovule.
• Inside the ovule, the male germ-cell fuses with the female gamete (egg cell) to form a zygote.
• This zygote eventually develops into a seed which can grow into a new plant.

 Additional Information

• The male germ-cell produced by the ovule fuses with the female gamete present in the pollen tube
• The ovule does not produce the male germ-cell; it produces the female gamete.
• The pollen tube carries the male germ-cell to the ovule, not the other way around.
• The male germ-cell produced by pollen grain fuses with the female gamete present in the stigma
• The stigma is the receptive surface of a flower where pollen lands but the actual fusion of gametes occurs in the ovule.
• The male germ-cell produced by the ovary fuses with the female gamete present in the ovule
• The ovary is the part of the flower that contains the ovules but does not produce the male germ-cell.

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

1) No one sits to the right of Y.

2) Only three people sit between Y and C.

3) Only two people sit between C and Z.

4) B sits third to the left of X.

5) L sits to the immediate right of X.

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

Thus, according to the final arrangement, three people sit between A and Z.

Hence, "Option 2" is the correct answer.

Shortcut Trick

Combine terms using Algebraic Identities: (a + b)(a² − ab + b²) = a³ + b³ and (a − b)(a² + ab + b²) = a³ − b³.

Product = (a³ + b³)(a³ − b³).

Applying (x + y)(x − y) = x² − y² ⇒ (a³)² − (b³)² = a⁶ − b⁶.

∴ The correct answer is a⁶ − b⁶.

Alternate Method

Given: Expression (a + b)(a − b)(a² − ab + b²)(a² + ab + b²)

Formula Used:

1. x³ + y³ = (x + y)(x² − xy + y²)

2. x³ − y³ = (x − y)(x² + xy + y²)

3. (x + y)(x − y) = x² − y²

Calculations:

⇒ Rearranging the terms: [(a + b)(a² − ab + b²)] × [(a − b)(a² + ab + b²)]

⇒ Using identities: (a³ + b³) × (a³ − b³)

⇒ Using (x + y)(x − y) property: (a³)² − (b³)²

⇒ a⁶ − b⁶

∴ The correct answer is a⁶ − b⁶.

Additional Information

Sum of Cubes Identity

a³ + b³ = (a + b)(a² − ab + b²). This is a fundamental factorization identity.

Difference of Cubes Identity

a³ − b³ = (a − b)(a² + ab + b²). Note the positive middle term in the quadratic factor.

Difference of Squares

(x + y)(x − y) = x² − y². It is used to simplify the product of conjugate pairs.

The Correct answer is Arjun Erigaisi.

Key Points

• Arjun Erigaisi is the second Indian chess player to breach the 2800 ELO rating barrier in classical chess as of December 2024.
• The ELO rating system is a method for calculating the relative skill levels of players in two-player games such as chess.
• He has achieved significant milestones in his chess career at a young age.
• Arjun Erigaisi has been recognized for his strategic prowess and consistent performance in various international chess tournaments.
• His achievement of crossing the 2800 ELO rating is a testament to his dedication and skill in the game of chess.

 Additional Information

• Gukesh D
• Gukesh D is a young Indian chess player known for becoming the second-youngest Grandmaster in history.
• He has shown remarkable talent and potential in the chess world with numerous victories in international competitions.
• Praggnanandhaa Rameshbabu
• Praggnanandhaa Rameshbabu is another prodigious Indian chess player who became the youngest International Master at the age of 10.
• He has also earned a reputation for his strategic gameplay and has competed successfully in various international events.
• Pentala Harikrishna
• Pentala Harikrishna is an experienced Indian Grandmaster who has been a prominent figure in the chess community for many years.
• He has represented India in numerous Chess Olympiads and has a wealth of experience in top-level chess tournaments.

Shortcut Trick

Pick the smallest three consecutive even natural numbers: 2, 4, and 6.

Product = 2 × 4 × 6 = 48.

Since this is the smallest possible product, every subsequent product of three consecutive even numbers must be divisible by this value.

∴ The correct answer is 48.

Alternate Method

Given: Three consecutive even natural numbers.

Formula: Let the numbers be 2n, 2n+2, and 2n+4, where n ≥ 1.

⇒ Product (P) = 2n × 2(n+1) × 2(n+2)

⇒ P = 8 × [n × (n+1) × (n+2)]

⇒ The term [n × (n+1) × (n+2)] represents the product of three consecutive integers.

⇒ The product of r consecutive integers is always divisible by r! (factorial r).

⇒ So, n(n+1)(n+2) is divisible by 3! = 3 × 2 × 1 = 6.

⇒ Maximum Divisor = 8 × 6 = 48.

∴ The correct answer is 48.

Additional Information

Divisibility of Consecutive Integers

The product of n consecutive integers is always divisible by n!. For example, the product of 4 consecutive integers is always divisible by 24.

Consecutive Odd Numbers

Unlike even numbers, the product of three consecutive odd natural numbers (e.g., 1×3×5=15) does not have a large fixed divisor other than 3 (if the sequence starts at specific points) or 1.

Sum of Consecutive Even Numbers

The sum of n consecutive even numbers is always divisible by n if n is odd, and follows specific arithmetic progression properties.

The correct answer is Only I is a possible reason.

Key Points

• Company A has not been profitable despite having a highly skilled workforce.
• Option I states that the company is located in a region where the cost of functioning is extremely high.
• High operational costs can impact the profitability of a company, regardless of the skill level of the workforce.
• High costs can include factors such as rent, wages, taxes, and utility expenses.
• Thus, the high cost of functioning is a plausible reason for the lack of profitability.

 Additional Information

• Company Location and Operational Costs
• Companies in regions with high operational costs need to generate significantly higher revenues to remain profitable.
• Such regions may have higher costs due to economic factors, regulatory environment, or geographical challenges.
• Philanthropy and Profitability
• Option II mentions that the CEO is a well-known philanthropist, which does not necessarily relate to company profitability.
• Philanthropy may involve donations and charitable activities, but this does not explain the financial performance of a company directly.
• While philanthropy might impact the allocation of resources, it does not inherently lead to unprofitability.

The logic followed here is:

Given: X : 38 :: 9 : Y

So, checking each option one by one:

Option 1) X = 15, Y = 48 → 15 : 38 :: 9 : 48

15 × 2 + 10 = 40 ≠ 38

9 × 2 + 10 = 28 ≠ 48

Option 2) X = 14, Y = 28 → 14 : 38 :: 9 : 28

14 × 2 + 10 = 38

9 × 2 + 10 = 28

Option 3) X = 15, Y = 28 → 15 : 38 :: 9 : 28

15 × 2 + 10 = 40 ≠ 38

9 × 2 + 10 = 28

Option 4) X = 14, Y = 30 → 14 : 38 :: 9 : 30

14 × 2 + 10 = 38

9 × 2 + 10 = 28 ≠ 30

Hence, "Option 2" is the correct answer.

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

According to the question, sum of the 12^th digit from the left and the 2^nd digit from the right: (Left) 6 3 0 4 7 5 5 6 8 3 6 6 9 6 1 1 0 8 7 8 5 0 4 0 3 2 1 3 0 6 (Right) → 6 + 0 = 6

Hence, "Option 4" is the correct answer.

Shortcut Trick

Total Simple Interest percentage for 3 years = 6% × 3 = 18%.

Total Amount percentage = 100% + 18% = 118%.

Final Amount = 118% of ₹1,232 = 1.18 × 1,232.

Calculation: 1,232 × 1 + 1,232 × 0.18 = 1,232 + 221.76 = ₹1,453.76.

∴ The correct answer is ₹1,453.76.

Alternate Method

Given:

Principal (P) = ₹1,232

Rate of Interest (R) = 6% per annum

Time (T) = 3 years

Formula Used:

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

Amount (A) = Principal (P) + Simple Interest (SI)

Calculations:

⇒ SI = (1,232 × 6 × 3) ÷ 100

⇒ SI = (1,232 × 18) ÷ 100

⇒ SI = 22,176 ÷ 100 = ₹221.76

⇒ Amount (A) = 1,232 + 221.76

⇒ Amount (A) = ₹1,453.76

∴ The correct answer is ₹1,453.76.

Additional Information

Simple Interest Definition

Simple interest is calculated only on the Principal amount of a loan or investment, ensuring the interest remains constant every year.

Compound Interest Comparison

Unlike SI, Compound Interest is calculated on the principal plus the accumulated interest of previous periods: A = P(1 + R/100)ⁿ.

Rule of 72

To find the approximate time needed to double your money at a given interest rate, divide 72 by the annual Interest Rate.

Given:

Number of apples sold by Shop A to females = 26

Number of apples sold by Shop B to females = 73

Formula used:

Difference = Number of apples sold by Shop B to females - Number of apples sold by Shop A to females

Calculation:

⇒ Difference = 73 - 26

⇒ Difference = 47

∴ The difference in the number of apples sold by shops A and B to females is 47.

The Correct answer is 6.7 × 10^-11 Nm² kg^-2.

Key Points

• The universal gravitational constant (G) is a key constant in Newton's law of gravitation.
• Newton's law of gravitation states that the force of attraction between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
• The value of G is 6.7 × 10^-11 Nm² kg^-2.
• This constant is crucial for calculations in astrophysics and cosmology, such as determining the gravitational force between celestial bodies.
• The unit of G, Nm² kg^-2, helps in balancing the equation of gravitational force, ensuring that the force is measured in Newtons (N).

 Additional Information

• 9.8 ms^-2
• This value represents the acceleration due to gravity (g) on the surface of the Earth.
• It is the acceleration experienced by an object in free fall within a vacuum near the Earth's surface.
• 1.6 × 10^-19 C
• This value is the elementary charge (e), which is the magnitude of the electric charge carried by a single proton or electron.
• It is a fundamental constant in physics and is crucial for calculations in electromagnetism and quantum mechanics.
• 9.1 × 10^-31 kg
• This value represents the mass of an electron.
• The mass of an electron is significantly smaller than that of protons and neutrons, which are approximately 1.67 × 10^-27 kg.

The Correct answer is Leaves and stem.

Key Points

• Vegetative propagation is a form of asexual reproduction in plants where new plants are produced from existing vegetative structures.
• In this method, parts like leaves, stems, and roots are used to grow new plants.
• Leaves of certain plants, such as Bryophyllum, can produce new plants from the notches on their margins.
• Stems can be used in various forms for vegetative propagation, such as runners in strawberries, tubers in potatoes, and rhizomes in ginger.
• This method is advantageous as it allows the rapid multiplication of plants that maintain the genetic makeup of the parent plant.

 Additional Information

• Fruits and leaves
• Fruits are typically involved in sexual reproduction, not vegetative propagation.
• While leaves can be used in vegetative propagation, the combination of fruits and leaves is incorrect for this purpose.
• Root and flowers
• Roots can be used for vegetative propagation, as seen in plants like sweet potatoes and dahlia.
• Flowers are involved in sexual reproduction and are not used for vegetative propagation.
• Fruits and flowers
• Both fruits and flowers are part of the sexual reproduction process in plants and are not used for vegetative propagation.

The logic followed here is:

Hence, "Option 2" is the correct answer.

The Correct answer is acidity or basicity.

Key Points

• The pH scale is a measurement of the hydrogen ion concentration in a solution.
• It ranges from 0 to 14, with 7 being neutral.
• A pH value less than 7 indicates acidity, while a pH value greater than 7 indicates basicity.
• The pH scale is logarithmic, meaning each whole number on the scale represents a tenfold difference in hydrogen ion concentration.
• pH is an important parameter in various fields such as chemistry, biology, medicine, and environmental science.

 Additional Information

• Density
• Density is a measure of the mass per unit volume of a substance.
• It is typically expressed in units like grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).
• Density is an important property in fields like material science, engineering, and fluid dynamics.
• Pollution
• Pollution refers to the introduction of harmful substances or products into the environment.
• It can affect air, water, and soil quality, posing risks to human health and ecosystems.
• Common sources of pollution include industrial activity, vehicle emissions, and agricultural runoff.
• Volume
• Volume is the amount of three-dimensional space occupied by an object or substance.
• It is measured in units such as liters (L), cubic meters (m³), and gallons.
• Volume is a fundamental property in fields like physics, chemistry, and engineering.

Given: Seven boxes A, B, C, L, X, Y and Z are kept one over the other.

1) Only B is kept above A.

2) Only four boxes are kept between A and Z.

3) Only two boxes are kept between L and Y.

4) C is kept immediately above X.

5) Y is not kept immediately above C.

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

Thus, according to the final arrangement C box is kept fourth from the top.

Hence, "Option 3" is the correct answer.

The correct answer is Reproduction.

Key Points

• The creation of a DNA copy is a fundamental event in the process of reproduction.
• During reproduction, organisms produce new individuals, and this process involves the replication of DNA to ensure that the offspring receive the correct genetic information.
• The DNA replication process ensures that each new cell or organism has the same genetic information as its parent.
• This process is critical for the continuity of genetic information from one generation to the next.
• Both sexual and asexual reproduction involve the creation of a DNA copy, ensuring genetic material is passed on.

 Additional Information

• Respiration
• Respiration is the process through which organisms convert oxygen and glucose into energy, carbon dioxide, and water.
• This process does not involve the creation of DNA copies.
• Excretion
• Excretion is the process of removing waste products and toxins from the body.
• This process involves the kidneys, liver, and skin but does not involve the replication of DNA.
• Circulation
• The circulatory system is responsible for transporting blood, nutrients, gases, and wastes to and from the cells of the body.
• It does not include the process of creating DNA copies.

The logic followed here is:

Option 1) BEH

Option 2) RUX

Option 3) FIL

Option 4) CEG

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

Hence, "Option 4" is the correct answer.

Shortcut Trick

Total distance to be covered for the 2 km gap = 56 − 2 = 54 km.

Relative speed in opposite direction = 13 + 14 = 27 kmph.

Time = Distance ÷ Relative Speed = 54 ÷ 27 = 2 hours.

∴ The correct answer is 2 hr.

Alternate Method

Given:

Total distance = 56 km

Speed 1 (S₁) = 13 km/h

Speed 2 (S₂) = 14 km/h

Desired remaining distance = 2 km

Formula Used:

Relative Speed (Opposite Direction) = S₁ + S₂

Time = (Total Distance − Remaining Distance) ÷ Relative Speed

Calculations:

⇒ Relative Speed = 13 + 14 = 27 km/h

⇒ Distance to be covered = 56 − 2 = 54 km

⇒ Time required = 54 ÷ 27

⇒ Time = 2 hours

∴ The correct answer is 2 hr.

Additional Information

Relative Speed Concept

When two objects move in opposite directions, their relative speed is the sum of their individual speeds: S_rel = S₁ + S₂.

Meeting Point vs Apart Distance

To find the meeting time, use the total distance. To find the time to be 'x' distance apart before meeting, use (Total Distance − x).

Unit Conversion

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

According to the given information,

Thus, according to the given codes the code 'ca' is for the word 'travel'.

Hence, the correct answer is "Option 1".

Shortcut Trick

Current Age Difference = 60 − 46 = 14 years.

Future Ratio is 4 : 5. Difference in ratio units = 5 − 4 = 1 unit.

Since the age difference remains constant: 1 unit = 14 years.

Age of younger person after k years = 4 units = 4 × 14 = 56 years.

Value of k = 56 − 46 = 10 years.

∴ The correct answer is 10 years.

Alternate Method

Given: Present ages are 46 and 60. Ratio after k years = 4 : 5.

⇒ (46 + k) ÷ (60 + k) = 4 ÷ 5

⇒ 5 × (46 + k) = 4 × (60 + k)

⇒ 230 + 5k = 240 + 4k

⇒ 5k − 4k = 240 − 230

⇒ k = 10

∴ The correct answer is 10 years.

Additional Information

Constant Difference Property

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

Ratio Scaling

When the difference in ratio parts does not match the actual age difference, scale the ratio by multiplying with a constant factor.

Linear Equation Approach

For problems involving "k years ago" or "k years hence", use (Age ± k) and solve the resulting proportion.

The correct answer is at the centre of curvature.

Key Points

• When an object is placed at the centre of curvature of a concave mirror, the image formed is real, inverted, and of the same size as the object.
• A concave mirror is a spherical mirror with a reflecting surface that curves inward.
• In concave mirrors, the centre of curvature (C) is the point on the mirror's principal axis where the radius of the sphere of which the mirror is a part would intersect the axis.
• This type of image formation occurs because the rays of light reflecting off the mirror converge at the point where the image is formed.
• Concave mirrors are often used in applications such as telescopes, headlights, and shaving mirrors due to their ability to focus light.

 Additional Information

• At the focus
• When an object is placed at the focus of a concave mirror, the reflected rays are parallel and the image is formed at infinity.
• The image is highly enlarged, real, and inverted.
• Between the focus and the centre of curvature
• When an object is placed between the focus and the centre of curvature, the image is formed beyond the centre of curvature.
• The image is real, inverted, and enlarged.
• Far away from the centre of curvature
• When an object is placed far away from the centre of curvature, the image formed is real, inverted, and diminished.
• The image is formed between the focus and the centre of curvature.

Shortcut Trick

For two angles whose sum (S) and difference (D) are known:

Smaller angle = (Sum − Difference) ÷ 2

Sum of complementary angles = 90° | Difference = 18°

Smaller angle = (90° − 18°) ÷ 2 = 72° ÷ 2 = 36°.

∴ The correct answer is 36°.

Alternate Method

Given:

Two angles are complementary.

Difference between them = 18°.

Formula Used:

Sum of two complementary angles = 90°.

Let the two angles be x and y, where x is the smaller angle.

⇒ y + x = 90° --- (Equation 1)

⇒ y − x = 18° --- (Equation 2)

Subtract Equation 2 from Equation 1:

⇒ (y + x) − (y − x) = 90° − 18°

⇒ 2x = 72°

⇒ x = 72° ÷ 2

⇒ x = 36°

∴ The correct answer is 36°.

Additional Information

Complementary Angles

Two angles are called complementary if their sum is exactly 90°.

Supplementary Angles

Two angles are called supplementary if their sum is exactly 180°.

Linear Pair

Adjacent angles formed by intersecting lines that sum to 180° are known as a linear pair.

The Correct answer is Dispersion.

Key Points

• Dispersion is the phenomenon where white light splits into its constituent seven colours when it passes through a glass prism.
• These seven colours are often remembered by the acronym VIBGYOR, which stands for Violet, Indigo, Blue, Green, Yellow, Orange, and Red.
• The different wavelengths of the various colours of light cause them to bend by different amounts when passing through the prism.
• This results in the separation of white light into the spectrum of colours.
• Isaac Newton was the first to demonstrate and explain this phenomenon in the year 1666.

 Additional Information

• Refraction
• Refraction is the bending of light as it passes from one medium to another with a different density.
• This bending occurs due to the change in the speed of light in different mediums.
• Diffraction
• Diffraction is the bending and spreading of waves around obstacles and openings.
• This phenomenon is significant for waves with wavelengths comparable to the size of the obstacles or openings.
• Scattering
• Scattering is the process where light or other electromagnetic radiation is forced to deviate from its path due to non-uniformities in the medium through which it passes.
• Rayleigh scattering of sunlight by the atmosphere is what makes the sky appear blue.