RRC Group D Previous Year Paper 57 (Held On: 29 Oct 2018 Shift 3)

The statement talks about the place Kashmir and describes it as heaven.

• Thus, it is logical to conclude that Kashmir is the most beautiful place, since it is compared to heaven.
• The statement does not talk about the Kashmiri people or describe them. So, we cannot conclude anything about the Kashmiri people. So conclusion 2 is not logical.

Hence the correct answer is option 1.

After rotating the given figure in clockwise direction, we obtain which is given below:-

Hence, "option 1" is the correct answer.

The correct answer is 10 kg.

Key Points

• Given that
• Momentum of the body = 50 kgms^-1
• Velocity of the body = 5 ms^-1
• $Mass = { Momentum \over Velocity }$
• = ${ 50 \over 5 }$
• = 10 Kg
• Hence the mass of a body is 10 kg.

Additional Information

• Momentum, the product of the mass of a particle and its velocity.
• Momentum is a vector quantity; i.e., it has both magnitude and direction.
• Isaac Newton's second law of motion states that the time rate of change of momentum is equal to the force acting on the particle.
• Newton’s third law states that when two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction.
• The third law is also known as the law of action and reaction.

The correct answer is Girija Devi.

Key Points

• Girija Devi was known as the queen of thumri, a common genre of semi-classical Indian music.
• Girija Devi, one of the brightest stars of the Seniya and Banaras gharanas, took the thumri to a whole new level of greatness.
• Girija Devi, one of the last exponents of the Benaras Gharana of thumri, died on 24 October at the BM Birla Heart Research Centre in Kolkata.
• She was 88.

Additional Information

• Thumri is a vocal genre or style of Indian music.
• The text is romantic or devotional in nature, the lyrics are usually in Uttar Pradesh dialects of Hindi called Awadhi and Brij Bhasha.
• Thumri is characterized by its sensuality, and by a greater flexibility with the raga.
• Madurai Shanmukhavadivu Subbulakshmi was an Indian Carnatic singer from Madurai, Tamil Nadu.
• She was the first musician ever to be awarded the Bharat Ratna, India's highest civilian honour.
• Kesarbai Kerkar was an Indian classical vocalist of the Jaipur-Atrauli gharana.
• A protege of Ustad Alladiya Khan, the founder of the gharana, from age sixteen, she went on to become one of the most noted khayal singers of the second half of the 20th century.

The least possible Venn diagram is given below:-

Conclusion :

1. Some silver are trinket. → True (Some trinkets are silver, then some silver are trinket is definitely correct.)
2. Some metals are trinkets. → True (Some trinkets are silver, all silver are metals, then some metals are trinkets is definitely correct.)

Hence, "option 4" is the correct answer.

Additional Information

Shortcut Trick

Total Work (LCM of 10, 30) = 30 units.

Efficiency: A = 3, B = 1. Total efficiency in 2 days (A+B) = 4 units.

In 14 days (7 pairs): 7 × 4 = 28 units. Remaining = 30 − 28 = 2 units.

On 15th day, A can do 3 units, but only 2 units are left. Time taken = 2/3 day.

Total time = 14 + 2/3 = 14 2/3 days.

∴ The correct answer is 14 2/3 days.

Alternate Method

Given: Time taken by A = 10 days, Time taken by B = 30 days.

Formula Used: Total Work = Efficiency × Time; Work done in alternate shifts.

⇒ Work done in a cycle of 2 days (A then B) = 3 + 1 = 4 units.

⇒ Number of complete cycles = 30 ÷ 4 = 7 cycles (covering 28 units).

⇒ Days elapsed in 7 cycles = 7 × 2 = 14 days.

⇒ Remaining work = 30 − 28 = 2 units.

⇒ Turn on 15th day = A (Efficiency = 3).

⇒ Time taken by A to finish 2 units = 2/3 day.

⇒ Total time = 14 + 2/3 = 14 2/3 days.

∴ The correct answer is 14 2/3 days.

Additional Information

Alternate Day Work

In alternate work, tasks are solved by finding the work done in one complete cycle of rotations and then calculating remaining work for the next individual turn.

LCM Method

Assuming the Total Work as the Least Common Multiple (LCM) of individual time durations simplifies calculations by providing integer values for efficiency.

Efficiency Ratio

Efficiency is inversely proportional to time. If A is thrice as fast as B, A will take 1/3 of the time B takes to complete the same work.

The logic followed is:

In the question given that does watching mobile too much cause headaches, we can say that by looking at the mobile, tension arises in the eyes, due to which the pituitary gland gets excited and headache is caused by excessive stimulation of the pituitary gland.

So, statements 1 and 2 together are enough.

Hence, "option 4" is the correct answer.

Additional Information

• If there are two or more sentences that are used to frame a statement, then, the sentences must be interrelated, and mutual contradiction should be there.
• Do not look for truthful notions. The information provided in the statement is the only requirement for a student to answer the question. No assumptions must be made.
• Read the statement carefully and look for keywords that are common between the statement and the conclusions.
• If there is more than one conclusion that is applicable to the statement, students must ensure that the conclusions they opt for have some relation with each other.

Statement 1:-

A is older than D and B.

A > D and B

Here, there is no information given about C and we can't decide who is youngest.

Therefore, statement 1 alone is not sufficient.

Statement​ 2:-

C is older than A.

C > A

No information is given about B and D and we can't decide who is youngest. Therefore, statement 2 alone is not sufficient.

From statements 1 and 2 together then:-

C > A > D/B > B/D

So, either B or D is the youngest person which is no definite position.

Both the statements are not sufficient.

Hence, "option 1" is the correct answer.

The correct answer is Japan.

 Key Points

• Shinzo Abe is the Prime Minister of Japan, who visited India in the month of September 2017. 
• In his first stint in 2006-07, Abe visited India and addressed Parliament.
• During his second stint, he visited India thrice (January 2014, December 2015, September 2017) — the most visits by any Japanese PM.
• He was the first Japanese PM to be Chief Guest at the Republic Day parade in 2014.

Additional Information

• Shinzo Abe is a Japanese politician who served as Prime Minister of Japan and President of the Liberal Democratic Party from 2006 to 2007 and again from 2012 to 2020.
• He is the longest-serving prime minister in Japanese history.
• Prime Minister Narendra Modi's official visit from 13 November to 5 November 2019 was to Brazil.
• Purpose of the visit
• To attend the 11th BRICS Summit.
• This was the second visit of PM Narendra Modi to Brazil.
• Bilateral talks with counterparts from China, Brazil, and Russia.
• This was the sixth time that Modi Ji participated in the BRICS Summit.
• Fortaleza in Brazil 2014 was his first BRICS summit.

The family tree is given below:-

Swati's only son is the grandson of Vani.

Hence, "option 3" is the correct answer.

The correct answer is 0°C.

Key Points

• Water exists in both liquid and solid-state at 0 degrees Celcius.
• Zero degree Celsius is also known as the triple point of water.
• At this temperature, water is in the process of changing from a solid state into the liquid phase or vice versa.
• Molecules in the liquid phase can lose a bit of energy and solidify whilst solid water (ice) can gain some energy and melt.
• So both the liquid and solid-state exist at 0-degree Celsius.

Additional Information

• Water is a liquid between 0 degrees Celsius and 100 degrees celsius.
• The single combination of pressure and temperature at which liquid water, solid ice, and water vapor can coexist in a stable equilibrium occurs at exactly 273.1600 K (0.0100 °C; 32.0180 °F) and partial vapor pressure of 611.657 pascals.

​

​

The correct answer is Pawan Kumar Chamling.

Key Points

• As of August 2018, Pawan Kumar Chamling was the Chief Minister of Sikkim.
• Pawan Kumar Chamling (born 22 September 1949) is an Indian politician and the former Chief Minister of Sikkim.
• Chamling is the Founder and President of the Sikkim Democratic Front, which governed the state for five successive terms since 1994.
• Chamling's 24.4-year stint (December 1994 to May 2019) is the longest ever by a chief minister of any Indian state, surpassing Jyoti Basu's 23 years in West Bengal.
• Prior to establishing the Sikkim Democratic Front, Chamling served as Minister for Industries, Information, and Public Relations from 1989 to 1992 in Nar Bahadur Bhandari's cabinet

Additional Information

• Sikkim is a state in northeast India, bordered by Bhutan, Tibet, and Nepal.

• Part of the Himalayas, the area has a dramatic landscape that includes India’s highest mountain, 8,586m Kangchenjunga.

• Sikkim is also home to glaciers, alpine meadows, and thousands of varieties of wildflowers.

• Pema Khandu Thungan was sworn in as the 9th Chief Minister of Arunachal Pradesh.

• Shri Pema Khandu has been sworn in as the Chief Minister of Arunachal Pradesh in a magnificent function at the Dorjee Khandu Convention Centre, Itanagar on 29th May 2019.

• Nongthombam Biren Singh (born 1 January 1961) is an Indian politician and former footballer and journalist.

• He is the current Chief Minister of Manipur.

Shortcut Trick

In any triangle ABC, the sum of internal angles is A + B + C = 180°.

Divide by 2: (A + B + C)/2 = 90° ⇒ (B + C)/2 = 90° − A/2.

Apply cosine: cos((B + C)/2) = cos(90° − A/2).

Using complementary angle identity: cos(90° − θ) = sin θ.

∴ The correct answer is Sin A/2.

Alternate Method

Given: A triangle ΔABC.

Formula Used: Angle Sum Property (A + B + C = 180°) and Trigonometric Identities.

⇒ A + B + C = 180°

⇒ B + C = 180° − A

⇒ (B + C)/2 = (180° − A)/2

⇒ (B + C)/2 = 90° − A/2

Taking cosine on both sides:

⇒ cos((B + C)/2) = cos(90° − A/2)

⇒ Since cos(90° − θ) = sin θ,

⇒ cos((B + C)/2) = sin A/2

∴ The correct answer is Sin A/2.

Additional Information

Complementary Angle Identities

Trigonometric ratios of (90° − θ): sin(90° − θ) = cos θ, tan(90° − θ) = cot θ, and sec(90° − θ) = cosec θ.

Triangle Angle Sum Property

In any Euclidean triangle, the sum of all internal angles is always equal to 180° or π radians.

Related Half-Angle Identities

Similarly, sin((B + C)/2) = cos A/2 and tan((B + C)/2) = cot A/2 for any triangle ABC.

The logic followed here is:-

Figures A Dollar ($), figure B Euro (€), and figure C Yen (¥) are the currency symbol but figure D plus(+) is the mathematical operator.

Figure D is different from others.

Hence, "option 3" is the correct answer.

Shortcut Trick

Total pens = 100

Defective pens = 8

Non-defective pens = 100 − 8 = 92

Probability (Not defective) = 92/100 = 23/25

∴ The correct answer is 23/25.

Alternate Method

Given:

Total number of pens (Sample Space n(S)) = 100

Number of defective pens = 8

Formula Used:

P(E) = n(E) / n(S)

P(Not Defective) = 1 − P(Defective)

Calculations:

⇒ Number of favorable outcomes (Not defective) = Total − Defective

⇒ n(E) = 100 − 8 = 92

⇒ Probability P(E) = 92 / 100

⇒ P(E) = (92 ÷ 4) / (100 ÷ 4)

⇒ P(E) = 23 / 25

∴ The correct answer is 23/25.

Additional Information

Complementary Events

The sum of the probability of an event and its complement is always 1: P(E) + P(E') = 1.

Range of Probability

The probability of any event always lies between 0 and 1 inclusive: 0 ≤ P(E) ≤ 1.

Sure and Impossible Events

A sure event has a probability of 1, while an impossible event has a probability of 0.

The correct answer is Feather, coin and brick all will reach the bottom together.

Key Points

• A coin, feather, and brick are dropped simultaneously in a vacuum, then feather, coin, and brick all will reach the bottom together.
• It is first further to be assumed that both are dropped from the same height and both heat the same ground.
• As this is being carried out in a vacuum, no force other than that due to gravity is acting on them.
• Therefore they will hit the ground at the same time.
• The mass has no role here.
• The distance (height) they are over is the same = $h= ut+{1\over{2}}gt^2$.
• Hence no mass was involved.

Additional Information

• The original question is about Galileo’s experiment performed in a vacuum.
• Galileo’s original experiment was performed using an inclined plane to slow the motion enough to measure the elapsed time using a water clock.
• The acceleration by which the earth attracts any object is always equal for any type of object.
• Acceleration due to gravity may refer to
• Gravitational acceleration, the acceleration caused by the gravitational attraction of massive bodies in general
• The gravity of Earth, the acceleration caused by the combination of gravitational attraction and centrifugal force of the Earth
• Standard gravity, or g, the standard value of gravitational acceleration at sea level on Earth

The alphabet table is given below:-

The logic followed here is:-

Hence, "option 1" is the correct answer.

The correct answer is Football.

Key Points

• The recently concluded Begum Hazrat Mahal Cup is related to the sports of football.
• Cups & Trophies Associated with Football
• Begum Hazrat Mahal Cup:
• BILT Cup
• Bordoloi Trophy
• Colombo Cup
• Confederation Cup
• DCM Trophy
• Durand Cup
• Rovers Cup
• B.C. Raj Trophy (National Championship)
• FIFA world Cup
• Kalinga Cup
• Santosh Trophy (National Championship)
• IFA Shield
• Scissor Cup
• Subroto Mukherjee Cup
• Sir Ashutosh Mukherjee Trophy
• Todd Memorial Trophy
• Vittal Trophy.

Additional Information

• Football is also known as Soccer.
• Federation of International Football Association (FIFA) organizes the World Cup (Men & Women) every four years of interval.
• The headquarter of FIFA is situated in Zurich in Switzerland.
• On June 12, 2020, the FIFA ranking was released.
• Indian team retained its 108th position as the international football for the year 2020 has been suspended since March. 
• Belgium remained at the top spot and was ahead of France and Brazil.
• England and Uruguay continued to remain at fourth and fifth position.

The correct answer is Indian journalist and news anchor.

Key Points

• Shereen Bhan (born 20 August 1976) is an Indian journalist and news anchor.
• She is the Managing Editor of CNBC-TV18. Shereen took over as managing editor of CNBC-TV18 from 1 September 2013 after Udayan Mukherjee decided to step aside.
• Over the course of her 14-year tryst with business journalism, Shereen has been the recipient of the 'Best Business Talk Show' award at the News Television awards for two years consecutively.
• Bhan anchors and produces several shows like Young Turks, India Business Hour, The Nation's Business and Power Turks.

The alphabet table is given below:-

The logic followed here is:-

Hence, "option 3" is the correct answer.

The given question asks whether distance education be banned, and to answer that the justification should have a solid reason in favor of or against distance education.

• Argument 1 gives a strong justification by highlighting that distance education does not provide one of the major personality building factors i.e teacher-student interaction. So, Argument 1 is strong.
• Argument 2 highlights the perks of distance education by stating that it is more affordable as compared to regular education. Thus, it makes a strong argument to not abolish distance education.

Hence, both the arguments are strong. The correct answer is option 3.

The correct answer is Metallic property decreases from left to right in a period but increases from top to bottom in a group.

Key Points​

• The metallic property of an element in modern periodic table  decreases from left to right in a period but increases from top to bottom in a group.
• Due to a decrease in the ability of an element to lose valence electrons from left to right across a period, metallic character decreases across a period from left to right. -
• As we move down the group from top to bottom atomic size increases as new electrons get added to the new shell.
• Atomic size gradually decreases from left to right across a period of elements.
• This is because, within a period or family of elements, all electrons are added to the same shell.

Additional Information

• Elements of the same group in the modern periodic table have the same valence electrons.
• The atomic mass of an element is the average mass of the atoms of an element measured in the atomic mass unit (AMU, also known as daltons, D).
• The atomic mass is a weighted average of all of the isotopes of that element, in which the mass of each isotope is multiplied by the abundance of that particular isotope.
• The atomic radius of a chemical element is a measure of the size of its atoms, usually the mean or typical distance from the center of the nucleus to the boundary of the surrounding shells of electrons.

Shortcut Trick

For a period of 2 years, the difference between Compound Interest (CI) and Simple Interest (SI) is given by the formula: Difference (D) = P × (R/100)².

Given Rate (R) = 5% and Difference (D) = ₹2.

2 = P × (5/100)² ⇒ 2 = P × (1/20)²

2 = P ÷ 400 ⇒ P = 2 × 400 = ₹800.

∴ The correct answer is ₹800.

Alternate Method

Given: Difference between CI and SI (D) = ₹2, Rate (R) = 5%, Time (T) = 2 years.

Formula Used: SI = (P × R × T) ÷ 100 and CI = P[(1 + R/100)^T − 1].

⇒ SI = (P × 5 × 2) ÷ 100 = 0.1P

⇒ CI = P[(1 + 5/100)² − 1] = P[(21/20)² − 1]

⇒ CI = P[441/400 − 1] = P[41/400] = 0.1025P

⇒ CI − SI = 0.1025P − 0.1P = 0.0025P

⇒ 0.0025P = 2

⇒ P = 2 ÷ 0.0025 = 800

∴ The correct answer is ₹800.

Additional Information

Difference for 3 Years

The difference between CI and SI for 3 years is given by D = P(R/100)² × (3 + R/100).

Effective Rate Method

For 2 years at R%, SI effective rate is 2R% and CI effective rate is [2R + (R²/100)]%.

Interest Compounded Half-Yearly

If interest is compounded half-yearly, the rate becomes R/2% and the time period becomes 2n.

Shortcut Trick To find the maximum value of the perimeter, we need the maximum possible values for the length and breadth that round to the given integers. Max length = 35.5 m (as any value < 35.5 rounds to 35) and Max breadth = 25.5 m (as any value < 25.5 rounds to 25). Max Perimeter = 2 × (35.5 + 25.5) = 2 × 61 = 122 m. ∴ The correct answer is 122 m.

Alternate Method Given: Length (L) rounded to nearest integer = 35 m Breadth (B) rounded to nearest integer = 25 m Formula Used: Perimeter (P) = 2 × (L + B)

For a number to be rounded to 35, the actual value must be in the range [34.5, 35.5). ⇒ Maximum possible length (Lmax) ≈ 35.5 m For a number to be rounded to 25, the actual value must be in the range [24.5, 25.5). ⇒ Maximum possible breadth (Bmax) ≈ 25.5 m ⇒ Maximum Perimeter = 2 × (35.5 + 25.5) ⇒ Maximum Perimeter = 2 × 61 ⇒ Maximum Perimeter = 122 m ∴ The correct answer is 122 m.

Additional Information Rounding Off Rule When rounding to the nearest integer, values with a decimal part of 0.5 or more are rounded up, while values less than 0.5 are rounded down. Minimum Perimeter To find the minimum perimeter, use the lowest values in the range: 2 × (34.5 + 24.5) = 2 × 59 = 118 m. Perimeter of Rectangle The total distance around the outside of a rectangle, calculated as 2 × (length + width).

The correct answer is Forebrain.

Key Points 

• The forebrain is the main thinking part of the brain.
• The cerebrum (a major part of the forebrain) is the main thinking part of the brain.
• It has sensory, motor, and association areas.

Additional Information

• The human brain is the central organ of the human nervous system, and the spinal cord makes up the central nervous system.
• The brain consists of the cerebrum, the brainstem, and the cerebellum.
• The cerebrum, the largest part of the human brain, consists of two cerebral hemispheres.
• Forebrain (also known as the prosencephalon), midbrain (mesencephalon), and hindbrain (rhombencephalon).

Shortcut Trick

For finding the HCF of fractions, use the direct formula:

HCF = HCF of Numerators ÷ LCM of Denominators

Numerators: 3, 9, 6 → HCF is 3

Denominators: 5, 10, 25 → LCM is 50

∴ The correct answer is 3/50.

Alternate Method

Given Fractions: 3/5, 9/10, and 6/25

Formula: HCF of fractions = [HCF of (3, 9, 6)] ÷ [LCM of (5, 10, 25)]

Step 1: Find HCF of Numerators (3, 9, 6)

⇒ Factors of 3: 1 × 3

⇒ Factors of 9: 1 × 3 × 3

⇒ Factors of 6: 1 × 2 × 3

⇒ Common highest factor = 3

Step 2: Find LCM of Denominators (5, 10, 25)

⇒ 5 = 5¹

⇒ 10 = 2¹ × 5¹

⇒ 25 = 5²

⇒ LCM = 2¹ × 5² = 2 × 25 = 50

Step 3: Calculate final HCF

⇒ HCF = 3/50

∴ The correct answer is 3/50.

Additional Information

LCM of Fractions

LCM of fractions is calculated as (LCM of Numerators) ÷ (HCF of Denominators).

Simplification Rule

Before finding HCF or LCM, ensure all fractions are in their simplest/lowest form to avoid calculation errors.

Relation between HCF and LCM

For any two numbers A and B: A × B = HCF(A,B) × LCM(A,B).

The correct answer is Light Density.

Key Points

• The ability of a medium to refract light is also expressed in terms of its optical or Light density.
• Optical density is not the same as mass density.
• Denser medium means Optically denser medium and Rarer medium means Optically rarer medium.

Additional Information

• The phenomenon of bending of a ray of light towards normal while entering from rarer medium to denser medium and vice versa is called the Refraction of Light.
• When light enters from a rare medium, say air to a denser medium say water, it bends towards normal and when enters from a denser medium to a rarer medium, say from water to air, it goes away from normal.
• When light passes from a denser to a less dense substance, (for example passing from water into the air), the light is refracted (or bent) away from the normal.
• The bending occurs because light travels more slowly in a denser medium

The pattern followed here is:

In Figures A, B, and D there are four circles inside the square but in figure C only three circles are inside the square.

Figure C is different from others.

Hence, "option 3" is the correct answer.

The family tree is given below:-

Y is the sister-in-law of Z.

Hence, "option 2" is the correct answer.

The correct answer is Itanagar.

Key Points

• The city of Itanagar is included in the batch of 9 new cities selected for Smart Cities Mission in January 2018.
• The nine cities include three from Uttar Pradesh – Moradabad, Bareilly and Saharanpur, Bihar Sharif (Bihar), Silvassa (Dadra and Nagar Haveli), Erode (Tamil Nadu), Daman and Diu, Itanagar (Arunachal Pradesh), and Kavaratti (Lakshadweep).

Additional Information

• National Smart Cities Mission is an urban renewal and retrofitting program by the Government of India with the mission to develop smart cities across the country, making them citizen-friendly and sustainable.
• The Union Ministry of Urban Development is responsible for implementing the mission in collaboration with the state governments of the respective cities.
• The mission initially included 100 cities, with the deadline for completion of the projects set between 2019 and 2023.
• The effective combined completion of all projects as of 2019 is at 11%.
• Smart Cities Mission envisions developing an area within the cities in the country as model areas based on an area development plan, which is expected to have a rub-off effect on other parts of the city,and nearby cities and towns.

Shortcut Trick

For numbers a, b, c, d to be in proportion after adding x, the shortcut formula is:

x = (ad − bc) ÷ ((a + d) − (b + c))

Given numbers: 4, 8, 12, 22

⇒ x = (4 × 22 − 8 × 12) ÷ ((4 + 22) − (8 + 12))

⇒ x = (88 − 96) ÷ (26 − 20) = −8 ÷ 6 = −4/3

Since we need the magnitude of the value to be added: 4/3

∴ The correct answer is 4/3.

Alternate Method

Given: Numbers are 4, 8, 12, 22.

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

Let the number to be added be x.

⇒ (4 + x) ÷ (8 + x) = (12 + x) ÷ (22 + x)

⇒ (4 + x)(22 + x) = (12 + x)(8 + x)

⇒ 88 + 4x + 22x + x² = 96 + 12x + 8x + x²

⇒ 88 + 26x = 96 + 20x

⇒ 26x − 20x = 96 − 88

⇒ 6x = 8

⇒ x = 8/6 = 4/3

∴ The correct answer is 4/3.

Additional Information

Mean Proportional

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

Third Proportional

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

Fourth Proportional

For three numbers a, b, c, the fourth proportional d is such that a/b = c/d, which means d = (bc)/a.

The correct answer is 2 kgm–3.

Key Points

• Given that
• Mass of the object = 300 kg
• The volume of the object = 150 m³
• $Density = {Mass \over {Volume}}$
• = ${300 \over {150}}$
• = $2 kgm^{-3}$
• So the density of the object will be $2 kgm^{-3}$.

Additional Information

• The density of a substance is its mass per unit volume.
• The symbol most often used for density is ρ although the Latin letter D can also be used.
• Specific gravity:
• It is defined as the density of material with respect to the density of water at 4°C.
• $Specific:gravity:of:material$  = $\left ( \frac{Density:of :substance}{Density:of :water } \right )$
• It can be defined as the ratio of mass or weight of substance with respect to mass or weight of water at 4º C
• $Specific:gravity:of:material=\left ( \frac{Mass :of :substance}{Mass:of :water} \right )or\left ( \frac{Weight:of:substance}{Weight:of:water } \right )$

The logic followed here is:-

Violinist, Singer, and Dancer all are related to music. Whereas swimmer is related to olympic.

The swimmer is different from others.

Hence, "option 1" is the correct answer.

Given that:-

28N5L50P5M4

28 × 5 + 50 ÷ 5 - 4

Apply BODMAS rule:-

= 28 × 5 + 10 - 4

= 140 + 10 - 4

= 150 - 4

= 146

Hence, "option 2" is the correct answer.

Shortcut Trick

Total Volume = Volume of Cone + Volume of Cylinder − Volume of Hemisphere

V = (1/3)πr²h₁ + πr²h₂ − (2/3)πr³

V = π × 3² × [(1/3) × 3 + 10 − (2/3) × 3]

V = 9π × [1 + 10 − 2] = 9π × 9 = 81π

∴ The correct answer is 81π m³.

Alternate Method

Given:

Radius (r) of all parts = 3 m

Height of Cone (h₁) = 3 m

Height of Cylinder (h₂) = 10 m

Formula Used:

Volume of Cone = (1/3)πr²h

Volume of Cylinder = πr²h

Volume of Hemisphere = (2/3)πr³

⇒ Volume of Cone = (1/3) × π × 3² × 3 = 9π m³

⇒ Volume of Cylinder = π × 3² × 10 = 90π m³

⇒ Volume of Semicircular/Hemispherical Cut = (2/3) × π × 3³ = 18π m³

⇒ Total Volume = 9π + 90π − 18π

⇒ Total Volume = 81π m³

∴ The correct answer is 81π m³.

Additional Information

Right Circular Cone

Slant height l = √(r² + h²) and Total Surface Area = πr(l + r).

Cylinder Properties

Curved Surface Area = 2πrh and Total Surface Area = 2πr(h + r).

Hemisphere

Volume = (2/3)πr³ and Curved Surface Area = 2πr².

The correct answer is Mahindra & Mahindra.

Key Points

• Mahindra and Mahindra is the indigenous MNC that was awarded the title of Innovator of the Year 2017 at the Times India Awards.
• Mahindra & Mahindra Ltd (M&M Ltd.), a part of the Mahindra Group, a global diversified federation of companies headquartered in India, received the prestigious 'Innovator for the Year' award at the second annual TIME India Awards 2017.
• The winners were selected from among 18 finalists, who were shortlisted from a pool of approximately 15,000 manufacturing companies after an extensive evaluation of qualitative and quantitative parameters by McKinsey & Co., the knowledge partner for the awards.
• The finalists were announced at the World Economic Forum in Davos, Switzerland.

Additional Information

• Mahindra & Mahindra Limited is an Indian multinational automotive manufacturing corporation headquartered in Mumbai, Maharashtra, India.
• It was established in 1945 as Muhammad & Mahindra and later renamed as Mahindra and Mahindra.
• It is one of the largest vehicle manufacturers by production in India.
• M&M Ltd. was selected as a winner for being one of India's most versatile automotive majors with a portfolio built on a bedrock of technological prowess.
• The company stood out for its unrivaled ability to constantly innovate in both its products and processes, in an industry that is on the cusp of major disruption.

The correct answer is Abhinav Bindra.

Key Points

• In the 2008 Summer Olympic Games, Abhinav Bindra was the first Indian to win an individual gold medal.
• At the 2008 Beijing Olympics, Abhinav Bindra won gold in the Men's 10-meter air rifle event becoming the first Indian to win an individual gold medal at the Olympic Games.
• He is the first and one of only 2 Indians to win an individual Olympic Gold Medal.

Additional Information

• Lieutenant Colonel Abhinav Apjit Bindra is an Indian Olympic gold medallist, retired sport shooter, and businessman.
• He is the first Indian to have held concurrently the world and Olympic titles for the men's 10-meter air rifle event, having earned those honors at the 2008 Summer Olympics and the 2006 ISSF World Shooting Championships.
• Bindra has also won seven medals at the Commonwealth Games and three medals at the Asian Games.
• The Summer Olympic Games, also known as the Games of the Olympiad, are a major international multi-sport event normally held once every four years.
• The inaugural Games took place in 1896 in Athens, Greece, and most recently the postponed 2020 Summer Olympics were celebrated in 2021 in Tokyo, Japan.

Shortcut Trick

Total ratio parts = 4 + 5 + 6 = 15 units.

Value of 15 units = ₹900 → 1 unit = ₹60.

Difference between X and Z = 6 − 4 = 2 units.

Required difference = 2 × 60 = ₹120.

∴ The correct answer is ₹120.

Alternate Method

Given:

Total Amount = ₹900

Ratio of X : Y : Z = 4 : 5 : 6

Calculations:

⇒ Let the amounts be 4k, 5k, and 6k.

⇒ 4k + 5k + 6k = 900

⇒ 15k = 900

⇒ k = 900 ÷ 15 = 60

⇒ Amount of X = 4 × 60 = ₹240

⇒ Amount of Z = 6 × 60 = ₹360

⇒ Difference = 360 − 240 = ₹120

∴ The correct answer is ₹120.

Additional Information

Ratio Distribution Rule

To find the value of a specific part in a ratio a:b:c, use (part ÷ sum of parts) × Total Value.

Compound Ratio

The compound ratio of two ratios a:b and c:d is calculated as (ac):(bd).

Proportion

If four quantities a, b, c, d are in proportion, then a × d = b × c (Product of extremes = Product of means).

Shortcut Trick

Identify two-digit positive integers ≤ 29: {10, 11, 12, ..., 29}.

Check the count of factors for the number 24 (a common high-factor candidate): 1, 2, 3, 4, 6, 8, 12, 24.

Number of factors of 24 is 8.

Since no number ≤ 29 has more than 8 factors (e.g., 28 has 6, 20 has 6, 12 has 6), the maximum is 8.

∴ The correct answer is 8.

Alternate Method

Given: A two-digit positive integer n such that 10 ≤ n ≤ 29.

Formula Used: If prime factorization is p₁^a × p₂^b, then number of factors = (a + 1)(b + 1).

⇒ Possible candidates for maximum factors: 12, 16, 18, 20, 24, 28.

⇒ Factors of 12: 1, 2, 3, 4, 6, 12 (Total = 6)

⇒ Factors of 18: 1, 2, 3, 6, 9, 18 (Total = 6)

⇒ Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 (Total = 8)

⇒ Factors of 28: 1, 2, 4, 7, 14, 28 (Total = 6)

⇒ Comparing all values between 10 and 29, the maximum count of factors is 8.

∴ The correct answer is 8.

Additional Information

Prime Factorization Rule

To find the total factors of N = p₁^a × p₂^b × p₃^c..., multiply the increments of exponents: (a+1)(b+1)(c+1)...

Highly Composite Numbers

Numbers that have more factors than any smaller positive integer are called highly composite numbers (e.g., 1, 2, 4, 6, 12, 24, 36).

Perfect Squares

Only perfect squares (like 16 or 25) have an odd number of factors.

Shortcut Trick

Substitute standard values: sin(π/4) = 1/√2, sin(π/3) = √3/2, and sin(π/6) = 1/2.

Expression = (1/√2)⁴ + 4 × (1/√2)⁴ × (√3/2)⁴ + (1/2)⁴

Expression = 1/4 + 4 × (1/4) × (9/16) + 1/16

Expression = 1/4 + 9/16 + 1/16 = 4/16 + 9/16 + 1/16 = 14/16 = 7/8

∴ The correct answer is 7/8.

Alternate Method

Given: sin⁴ $\frac{\pi}{4}$ + 4sin⁴ $\frac{\pi}{4}$ sin⁴ $\frac{\pi}{3}$ + sin⁴ $\frac{\pi}{6}$

Standard Values:

⇒ sin(π/4) = 1/√2 ⇒ sin⁴(π/4) = (1/2)² = 1/4

⇒ sin(π/3) = √3/2 ⇒ sin⁴(π/3) = (3/4)² = 9/16

⇒ sin(π/6) = 1/2 ⇒ sin⁴(π/6) = (1/2)⁴ = 1/16

Calculation:

⇒ Value = 1/4 + 4 × (1/4) × (9/16) + 1/16

⇒ Value = 1/4 + 9/16 + 1/16

⇒ Value = (4 + 9 + 1) / 16

⇒ Value = 14 / 16 = 7 / 8

∴ The correct answer is 7/8.

Additional Information

Trigonometric Ratios of standard angles

Standard values in radians: π/6 = 30°, π/4 = 45°, π/3 = 60°, π/2 = 90°.

Power of Trigonometric Functions

sinⁿθ is equivalent to (sinθ)ⁿ. For sin⁴(45°), calculate sin 45° then raise it to power 4.

The correct answer is Power.

Key Points

• A more powerful engine can do more work in less time.
• For example, an airplane covers a greater distance in less time than a car, so an airplane is more powerful than a car.
• It is an example of power.

Additional Information

• In physics, power is the amount of energy transferred or converted per unit of time.
• In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, power is sometimes called activity.
• Power is a scalar quantity.
• $Power = {work \over{ time} }$
• The standard metric unit of power is the watt.
• As is implied by the equation for power, a unit of power is equivalent to a unit of work divided by a unit of time.
• Thus, a Watt is equivalent to a Joule/second.
• One horsepower is equivalent to approximately 750 Watts.

Shortcut Trick

Let Hanit's present age be H and Ankur's be A.

Given: A = 2H − 5 and after 10 years A + 10 = 1.5 × (H + 10).

Substitute A: (2H − 5) + 10 = 1.5H + 15 ⇒ 2H + 5 = 1.5H + 15.

0.5H = 10 ⇒ H = 20 years.

Present age of Ankur = 2 × 20 − 5 = 35 years.

∴ The correct answer is 35 years.

Alternate Method

Given:

Present age of Ankur = A, Present age of Hanit = H.

Equation 1: A = 2H − 5

Equation 2: (A + 10) = 150% of (H + 10)

Calculations:

⇒ A + 10 = 1.5 × (H + 10)

⇒ A + 10 = 1.5H + 15

⇒ A − 1.5H = 5

Substitute A = 2H − 5 in the above equation:

⇒ (2H − 5) − 1.5H = 5

⇒ 0.5H = 10

⇒ H = 20

Now, find Ankur's present age:

⇒ A = 2 × 20 − 5 = 40 − 5 = 35

∴ The correct answer is 35 years.

Additional Information

Age Ratio Method

If the ratio of ages is given at two different times, use the constant difference property to find the multiplier.

Percentage to Fraction

150% is equivalent to 1.5 or 3/2. Always use fractions for faster calculation in age-related problems.

Linear Equations in Ages

If 'n' years ago/hence is mentioned, always add or subtract 'n' from the present age for all individuals involved.

Given:

2 - 5 + 7 × 8 + (9 + 11) ÷ 2

Concept used:

Calculation:

2 - 5 + 7 × 8 + (9 + 11) ÷ 2

⇒ 2 - 5 + 7 × 8 + 20 ÷ 2

⇒ 2 - 5 + 7 × 8 + 10

⇒ 2 - 5 + 56 + 10

⇒ 68 - 5

⇒ 63

∴ Required answer is 63

Shortcut Trick

Total buying at least one = (Individual sums) − (Sum of those buying exactly two) − 2 × (Sum of those buying all three)

Given: All three = 2. At least two = 5. Therefore, Exactly two = 5 − 2 = 3.

Total = (10 + 20 + 15) − 3 − 2 × 2 = 45 − 3 − 4 = 38.

∴ The correct answer is 38.

Alternate Method

Given:

n(Okra) = 10, n(Onion) = 20, n(Bitter Gourd) = 15

n(All three) = 2

n(At least two) = 5 ⇒ n(Exactly two) + n(All three) = 5

⇒ n(Exactly two) = 5 − 2 = 3

Formula Used:

Total (At least one) = ∑n(A) − ∑n(A ∩ B) + n(A ∩ B ∩ C)

Note: ∑n(A ∩ B) = n(Exactly two) + 3 × n(All three)

Calculations:

⇒ ∑n(A ∩ B) = 3 + 3 × 2 = 9

⇒ Total = (10 + 20 + 15) − 9 + 2

⇒ Total = 45 − 9 + 2 = 38

∴ The correct answer is 38.

Additional Information

Venn Diagram for Three Sets

For three sets A, B, and C, the number of elements in at least one set is n(A∪B∪C) = n(A) + n(B) + n(C) − [n(A∩B) + n(B∩C) + n(C∩A)] + n(A∩B∩C).

Exactly vs At Least

Number of people buying at least two = (Exactly two) + (Exactly three). Always distinguish between these to avoid double counting.

The family tree is given below:-

Z's sister is the aunt of X.

Hence, "option 3" is the correct answer.

Shortcut Trick

Sum of all pairs = 127 + 153 + 160 = 440.

Sum of individuals (R + S + A) = 440 ÷ 2 = 220.

Raveena's share = (R + S + A) − (Suniti + Avinash) = 220 − 153 = 67.

∴ The correct answer is Rs. 67.

Alternate Method

Given:

Raveena (R) + Suniti (S) = Rs. 127 ---(i)

Suniti (S) + Avinash (A) = Rs. 153 ---(ii)

Avinash (A) + Raveena (R) = Rs. 160 ---(iii)

Adding equations (i), (ii), and (iii):

⇒ 2 × (R + S + A) = 127 + 153 + 160

⇒ 2 × (R + S + A) = 440

⇒ R + S + A = 220 ---(iv)

To find Raveena's money (R), subtract equation (ii) from (iv):

⇒ R = (R + S + A) − (S + A)

⇒ R = 220 − 153

⇒ R = 67

∴ The correct answer is Rs. 67.

Additional Information

Sum of Cyclic Pairs

When sums of pairs like (A+B), (B+C), and (C+A) are given, the individual sum (A+B+C) is always half the total sum of those pairs.

Ratio & Proportion application

Similar logic is used in Time and Work when two people work in pairs. Efficiency of (A+B+C) = (Sum of efficiencies of pairs) ÷ 2.

The correct answer is Two.

Key Points

• The leaves of angiosperm plants have two types of venation.
• The arrangement of veins and veinlets on the lamina of a leaf is called venation.
• There are two types of venation, reticulate and parallel venation.
• Reticulate venation: In some leaves, the veins and veinlets are irregularly distributed over the entire lamina, forming a network. Such leaves are said to have reticulated venation.
• Parallel venation: In some leaves, the veins and veinlets run parallel to each other. Such leaves are said to have parallel venation.

Additional Information

• Leaves initially arise from cell divisions in the shoot apical meristem.
• A slight bulge (a leaf buttress) is produced, which in eudicots continues to grow and elongate to form a leaf primordium.
• Marginal and submarginal meristems on opposite flanks of the primordium initiate leaf-blade formation.
• Differences in the local activity of marginal meristems cause the lobed shapes of simple leaves and the leaflets in compound leaves.
• An increase in width and in the number of cell layers is brought about by marginal meristems.
• Subsequent expansion and increase in length are achieved by cell division and the general enlargement of cells throughout the blade.

The mirror image of the given figure is given below:-

Hence, "option 4" is the correct answer.

The correct answer is Both A and B are true.

Key Points

• The speed of sound in helium at 0°C is about 972 m/s, compared to 331 m/s in air.
• ​Hence statement A is false.
• This is consistent with the general relationship for sound speed in gases since the density of helium is so much less than that of air.
• The speed of sound in hydrogen at NTP is 1270 ms⁻¹.
• Hence statement B is false.​

Additional Information

• The speed of sound depends on the type and properties of the medium through which it is travelling.
• The speed of sound in a particular medium depends on the temperature and pressure of that medium.
• The speed of sound decreases when it passes from the solid to the gaseous state of a given medium.
• In any medium, if the temperature increases, the speed of sound also increases and vice versa.

Mistake PointsHere the question says Km/s and not m/s. So neither A nor B is correct

https://ncert.nic.in/ncerts/l/iesc112.pdf

The correct answer is 1949.

Key Points

• RBI was nationalized in 1949.
• The Reserve Bank of India was nationalised with effect from 1st January, 1949 on the basis of the Reserve Bank of India (Transfer to Public Ownership) Act, 1948.
• All shares in the capital of the Bank were deemed transferred to the Central Government on payment of a suitable compensation.

Additional Information

• The Reserve Bank of India (RBI) is India's central bank and regulatory body and is responsible for the issue and supply of the Indian rupee and the regulation of the Indian banking system.
• It also manages the country's main payment systems and works to promote its economic development.
• Bharatiya Reserve Bank Note Mudran is one of the specialised divisions of RBI through which it mints Indian bank notes and coins.
• RBI established the National Payment Corporation of India as one of its specialised division to regulate the payment and settlement systems in India.
• Deposit Insurance and Credit Guarantee Corporation was established by RBI as one of its specialised division for the purpose of providing insurance of deposits and guaranteeing of credit facilities to all Indian banks.
• Nationalization is the process of taking privately-controlled companies, industries, or assets and putting them under the control of the government.

Important Points

• Shaktikanta Das : 
• Currently, Shaktikanta Das serving as the 25th governor of the Reserve Bank of India (RBI).
• He was appointed Governor of the Reserve Bank of India by the ACC on 11 December 2018 for three years, replacing Urjit Patel who had resigned the day before.
• He has also served as India’s Alternate Governor in the World Bank, ADB, NDB & AIIB.
• He has represented India in various international forums like the IMF, G20, BRICS, SAARC, etc.
• He was earlier a member of the Fifteenth Finance Commission and India's Sherpa to the G20.
• Raghuram Rajan :
• On 6 August 2013, Raghuram Rajan was announced as the Governor of the Reserve Bank of India for a term of 3 years.
• He was serving as the 23rd governor of RBI.
• In 2016, he was named by Time in its list of the '100 Most Influential People in the World'.
• In 2015, during his tenure at the RBI, he became the Vice-Chairman of the Bank for International Settlements.
• Awards: Financial Times and McKinsey Business Book of the Year Award.

Shortcut Trick

Selling Price (SP) can be calculated directly using the multiplier method.

SP = CP × (100 + Profit%) ÷ 100

SP = 65 × (116 ÷ 100) = 65 × 1.16

65 × 1.16 = 75.40

∴ The correct answer is Rs. 75.40.

Alternate Method

Given: Cost Price (CP) = Rs. 65, Profit Percentage = 16%

Formulas: Profit = (Profit% ÷ 100) × CP | SP = CP + Profit

⇒ Profit = (16 ÷ 100) × 65

⇒ Profit = 0.16 × 65 = 10.40

⇒ Selling Price (SP) = CP + Profit

⇒ SP = 65 + 10.40 = 75.40

∴ The correct answer is Rs. 75.40.

Additional Information

Cost Price & Selling Price

The Cost Price is the price at which an item is purchased, and Selling Price is the price at which it is sold to a customer.

Profit and Loss Percentage

Profit or loss is always calculated on the Cost Price (CP) unless stated otherwise. Formula: Profit% = (Profit ÷ CP) × 100.

The correct answer is Gujarat.

Key Points

• Ankleshwar: The first major oil find came in 1958 with the discovery of Ankleshwar field located about 80 km south of Vadodara and nearly 160 km south of Khambhat.
• Ankleshwar anticline is about 20 km long and 4 km wide. Oil is available at depths varying from 1,000 to 1,200 meters.
• It has a capacity of 2.8 million tonnes per annum. It is estimated that 25 lakh tonnes per year of oil can be obtained from this field.
• Oil from this field is sent to refineries at Trombay and Koyali.
• Khambhat or Lunej field: The oil and Natural Gas Commission drilled test wells in 1958 at Lunej near Ahmadabad and confirmed the occurrence of a commercially exploitable oil field.
• The annual production is 15 lakh tonnes of oil and 8-10 lakh cubic meters of gas.
• The total reserves are estimated at 3 crore tonnes
• Ahmedabad and Kalol field: It lies about 25 km northwest of Ahmedabad.
• This field and a part of the Khambhat basin contain ‘pools’ of heavy crude trapped in chunks of coal. Nawgam, Kosamba, Mehsana, Sanand, Kathana, etc. are important producers.​

Additional Information

• The major oilfields in north-eastern India are those of Brahmaputra valley of north-east India and its neighboring areas including Arunachal Pradesh, Nagaland, Tripura, Manipur, Mizoram, and Meghalaya.
• Assam: It is the oldest oil-producing state in India
• The Digboi field: It is the oldest oil field in India. Most oil is sent to the refinery at Digboi.
• The Naharkatiya field: Oil from this area is sent to oil refineries at Noonamati in Assam and Barauni in Bihar through the pipeline.
• It was discovered in 1953.
• Arunachal Pradesh: Oil reserves are found in Manabhaum, Kharsang and Charai.
• Tripura: Oil reserves are found at Manmumbhanga, Manu, Ampi Bazar.

Each day of the week is repeated after 7 days.

Today is Monday.

After 63 days = 63 / 7 = 0 odd day

So, after 63 days will be the same day (because it is multiple of 7) i.e. Monday.

Hence, "option 1" is the correct answer.

The statement asks if loud and heavy music be banned at night in residential areas, so the argument to this statement should justify why the music be banned or allowed.

• Argument 1 reasons that loud music creates pollution and affects the vulnerable population. Thus, it is making a strong point in favor of banning the music.
• Argument 2 claims that banning the music is not a solution, however from argument 1 it can already be seen that if the music is banned, the problems are solved. Thus, argument 2 is not strong.

Hence the correct answer is option 2.

Shortcut Trick

Biggest 6-digit number is 999999.

Required value = 999,999 − 135,642

Subtracting last digits: 9 − 2 = 7 (Unit digit must be 7).

Subtracting whole: 999999 − 135642 = 864357.

∴ The correct answer is 864357.

Alternate Method

Given:

Current number = 135642

Target number = Biggest 6-digit number

Formula Used:

Required Addend = Target Number − Given Number

Calculations:

⇒ The biggest 6-digit number is formed by writing 9 six times.

⇒ Target Number = 999999

⇒ Required value = 999999 − 135642

⇒ 999999 − 135642 = 864357

∴ The correct answer is 864357.

Additional Information

Largest n-digit number

The largest n-digit number is always represented by 'n' nines (e.g., largest 4-digit is 9999).

Smallest n-digit number

The smallest n-digit number is 1 followed by (n−1) zeros (e.g., smallest 6-digit is 100000).

Successor and Predecessor

The successor of the largest n-digit number is the smallest (n+1)-digit number.

The number of triangles is:-

Total number of triangles is 13.

Hence, "option 4" is the correct answer.

The logic followed here is:-

In figures A, B, and C there are four dots in the square but in figure D only two dots in the square.

Hence, "option 2" is the correct answer.

The correct answer is Cinema.

 Key Points

• 'Godavari Gaurav Puraskar' is given for excellence in the field of cinema.
• The award carries a prize of Rs 21,000 and a memento.
• Well-known actor Nana Patekar will get the 'Godavari Gaurav' award, instituted by city-based 'Kusumagraj Prathishthan'.
• Noted actor Amol Palekar was honored with the 'Godavari Gaurav' award in March 2018.

Additional Information

• The Nana Patekar is known for his performance in movies like Gol Maal, Choti Si Baat, Chitchor among others.
• The award has been instituted by Nashik-based ‘Kusumagraj Prathishthan’.
• The award carries a prize of Rs 21,000 and a memento. The award was given by noted Marathi writer Madhu Mangesh Karnik, who is the chairperson the Prathishthan.
• Classical singer Pandit Satyasheel Deshpande also received the ‘Godavari Gaurav’ award.

The correct answer is 6.022 × 1023.

Key Points

• The number of atoms in 1g of oxygen is $6.022 × 10^{23}$.
• For one gram atomic weight of oxygen with atomic weight of 16 grams, one mole of oxygen also contains $6.022 × 10^{23}$ oxygen atoms.

Additional Information

• The definition of Avogadro's number of $6.022 × 10^{23}$/mole is the number of atoms or molecules per one gram atomic weight.
• The word ‘mole’ has been adopted to represent the Avogadro number of atoms of an element, that is, the relative atomic mass of an element.
• When applied to molecules, one mole of molecules is the relative molecular mass of that molecule, which is the summation of the individual relative atomic masses of the constituent atoms.

Shortcut Trick

Composite numbers have more than 2 factors.

List between 1 and 20: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18.

Total items = 10.

Sum = 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 = 112.

Average = 112 ÷ 10 = 11.2.

∴ The correct answer is 11.2.

Alternate Method

Given: The range is from 1 to 20 (exclusive of boundaries for 'between').

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

⇒ Composite numbers between 1 and 20 (excluding 1 and 20): 4, 6, 8, 9, 10, 12, 14, 15, 16, 18

⇒ Number of observations (n) = 10

⇒ Sum = 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 = 112

⇒ Average = Sum ÷ n

⇒ Average = 112 ÷ 10 = 11.2

∴ The correct answer is 11.2.

Additional Information

Composite and Prime Definitions

A composite number is a positive integer greater than 1 that has at least one divisor other than 1 and itself. A prime number has exactly two factors: 1 and itself.

Smallest Composite Number

The smallest composite number is 4. The number 1 is unique as it is neither prime nor composite.

Average Formula

Average = (x₁ + x₂ + ... + x_n) ÷ n. For consecutive numbers or specific patterns, specialized shortcuts like (first + last) ÷ 2 can be applied only if the common difference is constant.

Shortcut Trick

Restore base value = [Rate / (100 + Rate)] × 100

Required Reduction = [25 / (100 + 25)] × 100

Required Reduction = [25 / 125] × 100 = 1/5 × 100 = 20%

∴ The correct answer is 20%.

Alternate Method

Given:

Initial Basic Pay = 100

Percentage Increase = 25%

Calculations:

⇒ New Pay = 100 + 25% of 100 = 125

⇒ Amount to be reduced to restore basic pay = 125 − 100 = 25

⇒ Required Percentage Reduction = (Reduction / New Pay) × 100

⇒ Required Percentage = (25 / 125) × 100

⇒ Required Percentage = 1/5 × 100 = 20%

∴ The correct answer is 20%.

Additional Information

Percentage Increase-Decrease Relationship

If a value is increased by x%, then it must be decreased by [x / (100 + x)] × 100% to return to the original value.

Base Change Property

When the reference point (base) changes, the absolute difference remains the same but the percentage value changes inversely to the base value.

Fraction Conversion

An increase of 1/n requires a decrease of 1/(n+1) to restore the original value (e.g., 1/4 increase → 1/5 decrease).

The correct answer is Sanjeev Gupta.

Key Points

• Sanjeev Gupta is the British billionaire of Indian origin, who is currently challenging Tesla, the market leader in making the world's largest lithium-ion battery.
• He is the CEO and chairman of GFG Alliance, an international conglomerate that operates primarily in the steel and mining industries.
• The HRH Prince of Wales appointed Gupta as an official HRH Ambassador for Industrial Cadets in March 2018.

Additional Information

• Elon Musk last year soon resulted in the world’s highest output lithium-ion battery plant by Tesla in Australia.
• Now, both Elon Musk and Tesla have a reputation for achieving a lot of ‘firsts’ in the world so we weren’t shocked with the world’s most powerful battery plant.
• the stake to the throne is being made by an Indian-born British businessman Sanjeev Gupta.
• His challenge to Tesla’s Australian plant will fructify in Australia.
• Tesla’s battery plant presently has a peak storage capacity of 100MW/129MWH, which is quite a lot in literal terms.

Shortcut Trick

To rationalize the denominator of 1/(a + √b), multiply numerator and denominator by the conjugate (a − √b).

New Denominator = a² − (√b)² = a² − b

For 1/(5 + √3), Denominator = 5² − 3 = 25 − 3 = 22.

The rationalized form is (5 − √3)/22.

∴ The correct answer is (5 − √3)/22.

Alternate Method

Given: Fraction = 1/(5 + √3)

Formula Used: (a + b)(a − b) = a² − b²

⇒ Multiply numerator and denominator by (5 − √3):

⇒ [1 × (5 − √3)] / [(5 + √3) × (5 − √3)]

⇒ (5 − √3) / [5² − (√3)²]

⇒ (5 − √3) / (25 − 3)

⇒ (5 − √3) / 22

∴ The correct answer is (5 − √3)/22.

Additional Information

Rationalization

Process of moving a root or imaginary number from the bottom of a fraction to the top by multiplying by its conjugate.

Conjugate Pair

For a term (a + √b), the conjugate is (a − √b). Their product always results in a rational number: a² − b.

Difference of Squares

The identity (x + y)(x − y) = x² − y² is the fundamental principle used in simplifying surds in denominators.

The correct answer is Papaya.

Key Points

• Papaya is a unisexual flower.
• Papaya flowers are called unisexual because the flowers only contain one of the two reproductive parts of the plant and never both.
• Therefore, the flowers of papaya either consist of the male reproductive part, the stamens, or the female reproductive part, the carpels.

Additional Information

• A flower that contains both male and female reproductive organs is called a bisexual flower.
• The male reproductive organ is called the androecium and the female reproductive organ is called the gynoecium.
• **Example: Mustard,Hibiscus,Sunflower.

The logic followed here is:-

The stick, blade, spoon are made up of different elements. Whereas Glass (Pb) is an element. Glass is different from others.

Hence, "option 1" is the correct answer.

 Alternate Method

The logic followed here is:

All options except glass are the name of utensils, which is used in the kitchen but glass is used in tableware, housing and buildings etc.

Glass is different from others.

Hence, "option 1" is the correct answer.

The family tree is given below:-

Sadhan's mother's brother is maternal uncle of Samarth.

Hence, "option 3" is the correct answer.

Shortcut Trick

When the perimeter of a circle and a square are equal, the ratio of their areas is always 14 : 11.

Let Perimeter = 44 units ⇒ Circle radius (r) = 7, Square side (a) = 11.

Area of Circle = 154, Area of Square = 121.

Ratio = 154 : 121 = 14 : 11.

∴ The correct answer is 14 : 11.

Alternate Method

Given: Perimeter of Circle = Perimeter of Square

Formula Used: Perimeter of Circle = 2πr; Perimeter of Square = 4a; Area of Circle = πr²; Area of Square = a²

⇒ 2πr = 4a

⇒ πr = 2a

⇒ a = πr / 2

⇒ Ratio of Areas = Area of Circle / Area of Square

⇒ Ratio = πr² / a²

⇒ Ratio = πr² / (πr / 2)²

⇒ Ratio = πr² / (π²r² / 4)

⇒ Ratio = 4 / π

⇒ Ratio = 4 / (22/7) = (4 × 7) / 22

⇒ Ratio = 28 / 22 = 14 / 11

∴ The correct answer is 14 : 11.

Additional Information

Area comparison for fixed perimeter

For a given perimeter, a circle encloses the maximum area compared to any polygon.

Circle Properties

The ratio of circumference to diameter is always π ≈ 22/7.

Square Properties

The diagonal of a square is side × √2 and its area can also be written as (diagonal²)/2.

The logic followed here is:-

Both arrows rotate of one place in the clockwise direction in each step and the arrow direction change in each step.

Both symbols (€Ω) rotate of one place in the clockwise direction in each step and both symbols interchange their position in each step.

Symbols (±^±) rotate of one place in the clockwise direction in each step and symbol ±^± changes to symbol ± in each step.

The symbol “±” rotate one place in the clockwise direction in each step.

So, the next image of the given series is:-

Hence, "option 1" is the correct answer.

The correct answer is Evaporation.

Key Points

• Acetone is highly sublimable.
• It converts into vapour at a fast rate which increases the liquid molecules around it in the vapour phase.
• Thus when poured on the palm, it absorbs the heat in our palm and evaporates quickly leaving a cool sensation.
• Hence when we pour some acetone on our palm, it feels cold.
• During evaporation, particles of the liquid absorb energy from the surrounding or the surface of the palm to compensate for the loss of energy, making the surroundings cool.

Additional Information

• Acetone, petrol, perfume, etc., being volatile, evaporates very fast when exposed to larger surfaces.
• When we put some acetone or petrol or perfume on our palms, it evaporates.
• During evaporation, particles of the liquid absorb energy from the surface of the palm to compensate for the loss of energy, making the surroundings cool.
• The acetone, petrol, or perfume take this latent heat of vaporisation from our palm.
• The palm loses heat and feels cold.
• Latent heat of vaporization is the heat consumed or discharged when matter disintegrates, changing stage from fluid to gas stage at a consistent temperature.

The correct answer is 307.5 W.

Key Points

• Given mass of body (m) = 50 kg
• h = 41×15 = 615 cm = 6.15 m
• t=10 s, g = 10 ms–2
• Potential energy = mgh
• = 50 × 10 × 6.15
• = 3075
• $Power = {Work done \over time}$
• $= { 3075\over 10}$
• = 307.5 W

Additional Information

• Potential Energy:
• It is the energy possessed by a body by virtue of its position.
• PE of a body in the gravitational field of the earth is mgh.
• where m = mass, g = acceleration due to gravity, h = height of the body from the surface of the earth.
• When a body is falling downwards, then its potential energy goes on changing to kinetic energy.

The correct answer is Plasmodium.

Key Points

• Through multiple fission, plasmodium divides into many daughter cells simultaneously.
• Plasmodium after feeding on red blood cells in humans undergoes asexual reproduction which is called schizogony or multiple fission.
• In multiple fission, Plasmodium divides into many cells.

Additional Information

• MULTIPLE FISSION: In this type of fission parental body divides into many cells during unfavorable conditions.
• In this, a protective-resistant cyst is formed.
• Inside the cyst, the nucleus divides repeatedly to form several daughter nuclei.
• Some algae, some protozoans, and the true slime molds (Myxomycetes) are regularly divided by multiple fission.
• In such cases the nucleus undergoes several mitotic divisions, producing a number of nuclei.
• After the nuclear divisions are complete, the cytoplasm separates, and each nucleus becomes encased in its own membrane to form an individual cell.

The correct answer is Natural gas.

Key Points

• Natural gas is an example of a conventional source of energy.
• Conventional sources of energy are non-renewable sources of energy so natural gas is an example of a conventional source of energy.
• Natural gas is a non-renewable hydrocarbon used as a source of energy for heating, cooking, and electricity generation.
• Natural gas can be efficiently burned to generate heat and electricity, emitting less waste and toxins at the point of use relative to other fossil and biomass fuels.
• Coal, fossil fuels, petroleum, and, natural gas, are examples of conventional sources of energy.
• Conventional energy sources such as natural gas, oil, coal, or nuclear are finite but still hold the majority of the energy market.
• However, renewable energy sources like wind, fuel cells, solar, biogas/biomass, tidal, geothermal, etc. are clean and abundantly available in nature and hence are competing with conventional energy sources.

Additional Information

• Conventional sources of energy can be described as non-renewable sources of energy that have been used for a long time.
• Conventional sources of energy are used extensively by mankind and the magnitude of usage is so high that the reserves have got depleted to a great extent.
• Example: Coal, petroleum, natural gas.
• Nuclear energy is one of the most environmentally friendly conventional sources of energy as it produces fewer greenhouse gas emissions during the production of electricity in comparison to sources like coal power plants.
• Energy generated by using wind, solar, small hydro, tides, geothermal heat, and biomass is known as non-conventional energy.
• Non-conventional energy resources are renewable.
• These resources are available in an unlimited quantity.
• Non-conventional energy sources are eco-friendly in nature.

The correct answer is Switzerland.

Key Points

• The World Trade Organization is an intergovernmental organization that regulates and facilitates international trade between nations.
• Governments use the organization to establish, revise, and enforce the rules that govern international trade.
• Headquarters: Geneva, Switzerland
• Founded: 1 January 1995

Additional Information

• The World Health Organization is a specialized agency of the United Nations responsible for international public health. 
• The WHO was established on 7 April 1948.
• The WHO has played a leading role in several public health achievements, most notably the eradication of smallpox, the near-eradication of polio, and the development of an Ebola vaccine.
• It has six regional offices and 150 field offices worldwide.
• Headquartered - Geneva, Switzerland

The question simply asks whether hunting of lions should be banned.

• Argument 1 states that hunting of lions should be banned because it requires a lot of money. It is not logically correct, because it cannot be determined if the fact is true and more importantly, it is not a fair justification to ban hunting. Thus, argument 1 is not strong.
• Argument 2 does not give a reason as to why hunting of lions should not be banned. Thus, it is not making any point to be strong.

Hence the correct answer is option 4.

The correct answer is v = u + at.

Key Points

• $v=u+at$ is the first equation of motion.

• It is the equation of motion-time relation.

• In this $v=u+at$ equation,

• u is the initial velocity

• v is the final velocity

• a is acceleration

• t is the time period

• The given equation is derived from the acceleration point of view. (It can also be derived from velocity and time graph)

• We know that acceleration is defined as the rate of change of velocity

• So, Rearranging the terms in the above equation, we get,$a= v-ut$

• $v=u+at$

• The equations of motion are also used in the calculation of optical properties.

The correct answer is Basic.

Key Points

• Magnesium oxide is a simple basic oxide because it contains oxide ions.
• It reacts with water to form magnesium hydroxide which is a base.
• Metal oxides on the left side of the periodic table produce basic solutions in water (e.g. Na₂O and MgO).
• Non-metal oxides on the right side of the periodic table produce acidic solutions (e.g. Cl2O, SO2, P4O10).
• A basic solution is an aqueous solution containing more OH-ions than H+ions.
• Examples of common basic solutions include soap or detergent dissolved in water or solutions of sodium hydroxide, potassium hydroxide, or sodium carbonate.

Additional Information

• A solution with a pH less than 7 is considered acidic, and a solution with a pH greater than 7 is considered basic, or alkaline.
• Strong acids have a higher concentration of hydrogen ions, and they are assigned values closer to 0.
• An amphoteric solution is a substance that can chemically react as either acid or base. However, it is also possible for oxide to be neither acidic nor basic, but is a neutral oxide.
• Examples of amphoteric substances include water, amino acids, proteins, and many metal oxides and hydroxides. Oxides and hydroxides of aluminium, antimony, arsenic, antimony, bismuth, beryllium, chromium, cobalt.
• Neutral solutions are the solutions in which the concentration of hydrogen ions and hydroxide ions are equal Sodium chloride solution or a sugar solution is an example of a neutral solution.
• A neutral solution has a pH equal to 7.
• Water is another common substance that is neutral on the pH scale.

The correct answer is 1028.

Key Points

• There are 1028 mantras in the Rigveda which include the unpromising Valakhilia hymns.
• The Rig Veda consists of 1028 hymns, organised into ten books known as maṇḍalas.
• They were composed in an archaic language named Vedic that gradually evolved into classical Sanskrit.
• Each maṇḍala has sūktas (hymns) formed by individual strophes.
• The Rig Veda is the earliest of the four Vedas and one of the most important texts of the Hindu tradition.
• It is a large collection of hymns in praise of the gods, which are chanted in various rituals.

Additional Information

• Samaveda
• There are 1549 verses (except 75 verses, all have been taken from Rigveda)
• There are two Upanishads embedded in Samaveda – Chandogya Upanishad and Kena Upanishad
• The Samaveda is considered the root of Indian classical music and dance
• It is considered as the storehouse of the melodious chants
• Though it has lesser verses than Rigveda, however, its texts are larger
• There are three recensions of the text of the Samaveda – Kauthuma, Raṇayaniya and Jaimaniya
• Yajurveda
• Stands to mean ‘Worship Knowledge’, Yajurveda dates back to 1100-800 BCE; corresponding with Samaveda.
• It compiles ritual-offering mantras/chants.
• These chants were offered by the priest alongside a person who used to perform a ritual (in most cases yajna fire).
• Atharvaveda
• Stands to mean a tatpurusha compound of Atharvan, an ancient sage, and knowledge (atharvan+knowledge), it dates back to 1000-800 BCE.

Shortcut Trick

A rectangle is a parallelogram with all angles equal to 90°.

Property check: Diagonals of a rectangle are equal but not perpendicular.

Perpendicular diagonals are a property of a Rhombus or a Square.

∴ The correct answer is Its diagonals are perpendicular to each other.

Alternate Method

Given: A rectangle with length 'l' and breadth 'b'.

Evaluating the options based on geometric properties:

⇒ Opposite sides are parallel: This is True for all parallelograms, including rectangles.

⇒ Adjacent sides are not equal: This is True for a general rectangle (if they were equal, it would be a square).

⇒ Diagonals are equal: This is True. Length of each diagonal = √(l² + b²).

⇒ Diagonals are perpendicular: This is False. Diagonals bisect each other but meet at 90° only in a Rhombus or Square.

∴ The correct answer is Its diagonals are perpendicular to each other.

Additional Information

Properties of a Rectangle

All four interior angles are 90°. The diagonals are equal in length and bisect each other.

Rhombus vs Rectangle

In a Rhombus, diagonals are perpendicular bisectors of each other but are generally not equal.

Square Property

A Square is a special rectangle where adjacent sides are equal and diagonals are both equal and perpendicular.

The alphabet table is given below:-

The logic followed here is:-

Hence, "option 3" is the correct answer.

Given:

25 – 2 + [3 {(10 – 4)2 – 19 × 2}]

Concept used:

Calculation:

25 – 2 + [3 {(10 – 4)2 – 19 × 2}]

⇒ 25 – 2 + [3 {36 – 19 × 2}]

⇒ 25 – 2 + [3 {36 – 38}]

⇒ 25 – 2 + [3 × – 2]

⇒ 25 – 2 – 6

⇒ 25 – 8

⇒ 17

∴ Required answer is 17

The correct answer is Malayalam.

Key Points

• Malayalam is a Dravidian language spoken in the Indian state of Kerala and the union territories of Lakshadweep and Puducherry by the Malayali people.
• It is a member of the South Dravidian subgroup of the Dravidian language family.
• It is the official language of the state of Kerala and the union territory of Lakshadweep.
• It is one of 22 scheduled languages of India and is spoken by 2.88% of Indians.

Additional Information

• Kerala is a state on the Malabar Coast of India.
• It was formed on 1 November 1956, following the passage of the States Reorganisation Act, by combining Malayalam-speaking regions of the erstwhile regions of Cochin, Malabar, South Canara, and Travancore.
• It is bordered by Karnataka to the north and northeast, Tamil Nadu to the east and south, and the Lakshadweep Sea to the west.
• Marathi is an Indo-Aryan language predominantly spoken by Marathi people in the Indian state of Maharashtra.
• It is the official language of Maharashtra, and a co-official language in Goa and the union territory of Dadra and Nagar Haveli and Daman and Diu.
• Tamil is a Dravidian language.
• It is spoken in the Tamil Nadu and Puducherry states of India and parts of Sri Lanka.
• Many people in Singapore and Malaysia .