RRC Group D Previous Year Paper 63 (Held On: 10 Oct 2018 Shift 1)

The correct answer is to decrease in height.

Key Points

• The value of 'g' increases with a decrease in height.
• The formula relating gravity and altitude is as follows:
• $g=\frac{1}{R^2}$
• In the given statement 'g' refers to the gravitation.
  

As per the concept, the force of gravitation is inversely proportional to the altitude.

• It means that the value of g decreases when the value of altitude increases, whereas increases when the value of altitude decreases.​​

Concept:

• Variation of 'g' above the surface of earth: As we go above the surface of the earth, the value of 'g' decreases.

O Consider a body of mass m at a height 'h' above the surface of the earth. Thus, the gravitational force on the body is $F = \frac{{G{M_e}m}}{{{{\left( {{R_e} + h} \right)}^2}}}$.

If 'g' is the value of gravity at a height 'h' above the surface of the earth, then, 

$mg' = \frac{{G{M_e}m}}{{{{\left( {{R_e} + h} \right)}^2}}}$ or $g' = \frac{{G{M_e}}}{{{{\left( {{R_e} + h} \right)}^2}}} = \frac{{{g_e}R_e^2}}{{{{\left( {{R_e} + h} \right)}^2}}} = \frac{{{g_e}}}{{{{\left( {1 + \frac{h}{{{R_e}}}} \right)}^2}}} = {g_e}{\left[ {1 + \frac{h}{{{R_e}}}} \right]^{ - 2}}$.

where R_e is the radius of earth and M_e is the mass of earth, if h << R_e, then expanding binomially and neglecting higher powers of $\frac{h}{{{R_e}}}$, we get -

$g = {g_e}\left( {1 - \frac{{2h}}{{{R_e}}}} \right)$.

∴ The decrease in the value of g on going up a height 'h' above the surface of earth. 

$\Delta {g_e} = \frac{{2{g_e}h}}{{{R_e}}}$.

• According to the question statement, the typing error has led to the provision of extra marks for those who have attempted the erroneous question. Thus, it can be concluded that such grace marks are provided when the management makes errors in the question paper.
• The statement uses the words 'those who' which implies that grace marks are being provided to the students who have attempted the question. By definition of an exam, no mark is allotted for a question that is not attempted. Thus, we can conclude that those who haven't attempted will not be getting extra marks

Hence the correct answer is option 3.

The correct answer is Lewis Hamilton.

Key Points

• Lewis Hamilton has won the German Grand Prix 2018.
• The 2018 German Grand Prix (formally known as the Formula 1 Emirates Grosser Preis von Deutschland 2018) was a Formula One motor race held on 22 July 2018 at the Hockenheimring in Germany.
• The race was the 11th round of the 2018 Formula One World Championship and marked the 77th running of the German Grand Prix, and the 63rd time the race had been run as a World Championship event since the inaugural season in 1950.
• Lewis Hamilton won the Grand Prix from 14th on the grid, leading a Mercedes 1–2 ahead of teammate Valtteri Bottas after race leader and pole sitter Sebastian Vettel crashed out in light rain conditions.

Additional Information

• Kevin Jan Magnussen (born 5 October 1992) is a Danish racing driver competing in the 2021 WeatherTech SportsCar Championship driving for Chip Ganassi Racing.
• He will also be competing in the World Endurance Championship, in 2022, racing for Peugeot Sport.
• Kimi-Matias Raikkonen, nicknamed "The Iceman", is a Finnish racing driver who competed in Formula One between 2001 and 2021 for Sauber, McLaren, Ferrari, Lotus, and Alfa Romeo.
• Raikonnen won the 2007 Formula One World Championship driving for Scuderia Ferrari, their latest World Drivers' Championship to date.
• Sebastian Vettel is a German racing driver who competes in Formula One for Aston Martin, having previously driven for BMW Sauber, Toro Rosso, Red Bull, and Ferrari.
• Vettel has won four World Drivers' Championship titles, which he won consecutively from 2010 to 2013.

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

Hence, "option 2" is the correct answer.

The logic followed here is:-

1) 

 rotate 180° from the first block to the second block, then rotate clockwise direction 90° from the second block to the third block and then rotate 180° from the third block to the fourth block.

Hence, "option 3" is the correct answer.

The family tree is given below:-

The girl is the niece of Ankita's father.

Hence, "option 1" is the correct answer.

Calculation:

Total numbers of tires manufactured in India during 2017 = 1,80,000

Number of tires manufactured by company A = 25%

According to the question

⇒ (1,80,000 × 25/100)

⇒ (1800 × 25)

⇒ 45,000

∴ Numbers of tires manufactured by company A is 45,000

The logic followed here is:-

Day, year, and month are the part of calendar.

So, calendar is different from others.

Hence, "option 4" is the correct answer.

Given that:-

9 - 4 + 14 × 7 ÷ 6

9 × 4 - 14 ÷ 7 + 6

Applying BODMAS rule:-

= 9 × 4 - 2 + 6

= 36 - 2 + 6

= 42 - 2

= 40

Hence, "option 2" is the correct answer.

Shortcut Trick

Diagonal properties of a Rhombus: Side² = (d₁/2)² + (d₂/2)²

Given: Side = 26 cm and half of first diagonal (d₁/2) = 48/2 = 24 cm.

Using Pythagorean triplet (10, 24, 26): Half of second diagonal = 10 cm.

Full second diagonal = 10 × 2 = 20 cm.

∴ The correct answer is 20 cm.

Alternate Method

Given: Side (a) = 26 cm, Diagonal 1 (d₁) = 48 cm.

Formula Used: 4a² = d₁² + d₂²

⇒ In a rhombus, diagonals bisect each other at 90°.

⇒ Let half of the second diagonal be x.

⇒ 26² = 24² + x²

⇒ 676 = 576 + x²

⇒ x² = 676 − 576 = 100

⇒ x = √100 = 10 cm

⇒ Length of second diagonal (d₂) = 2 × x = 2 × 10 = 20 cm.

∴ The correct answer is 20 cm.

Additional Information

Area of Rhombus

The area of a rhombus is calculated as 1/2 × d₁ × d₂, where d₁ and d₂ are the lengths of the diagonals.

Perimeter of Rhombus

Since all sides of a rhombus are equal, the perimeter is 4 × side.

Diagonals Property

Diagonals of a rhombus are not necessarily equal, but they always bisect each other at right angles (90°).

The correct answer is Bharat Net Project.

Key Points

• Bharat Net Project is the basis of the Digital India campaign.
• BharatNet is an initiative of the Government of India to provide broadband services at 100 Mbps to around 2.5 lakh gram panchayats of the country.
• It aims to provide around 2 to 20 Mbps broadband connectivity to all the households of India especially in rural areas.
• It is the world s largest rural connectivity scheme to be connected by the Optical Fibre network.
• BharatNet forms the main pillar behind the union government's Digital India initiative.
• The project was originally started in 2011 as National Optical Fibre Network (NOFN).
• It was renamed as BharatNet in 2015.
• The project is being implemented by Bharat Broadband Network Limited (BBNL) through a Special Purpose Vehicle (SPV).

Additional Information

• The Union Government has launched e-Rashtriya Kisan Agri Mandi (e-RaKAM) portal to provide a platform for farmers to sell agricultural produce.
• e-RaKAM is a first-of-its-kind initiative that leverages technology to connect farmers from the smallest villages to the biggest markets of the world through the internet.
• The Ministry of Civil Aviation has released the Policy on biometric-based digital processing of passengers at Airports called "Digi Yatra".
• DigiYatra envisages a connected ecosystem enhancing the seamless travel experience for the passengers and simultaneously improving the security.

The logic followed here is:-

L, T, and V are the consonant while A is the vowel.

So, A is different from others.

Hence, "option 3" is the correct answer.

Alternate Method

The pattern followed here is:

So, A is different from other images.

Hence, the correct answer is "A"

Calculation:

According to the question

The personal computers were sold by company XYZ in the year 2008 = 50

∴ Required number of personal computers is 50

The correct answer is Ashok Das.

Key Points

• Ashok Das has been appointed as the next Ambassador of India to the Federal Republic of Brazil.
• Senior Indian Foreign Service (IFS) officer Ashok Das has been appointed as the new Indian Ambassador to Brazil.
• Das is the first Odia IFS officer to hold such a crucial assignment in South America.
• He presently is Additional Secretary (Latin America & Caribbean).
• Earlier, he was Ambassador to the Republic of Iceland.

Additional Information

• Gautam Bambawale is an Indian diplomat and served as the Indian Ambassador to China from 2017 to 2018.
• He had previously served as the Indian High Commissioner to Pakistan.
• Manjeev Singh Puri is an Indian civil servant of the Indian Foreign Service cadre and the former Ambassador of India to Nepal.
• Vikram Mistri is Indian ambassador to China.

The correct answer is Potential energy.

Key Points

• When you stretch a rubber band, the energy transferred is stored in the form of potential energy.
• When elastic is stretched, it's loaded with potential energy, when released there is a shift to kinetic energy.
• This is especially true if the elastic is transporting another object, such as with a rock being flung from a slingshot.
• Potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.

Additional Information

• Muscular energy is the conscious movement of energy along the lines of the body, drawing muscle to bone and connecting limbs to joints as the energy moves ever inward to the body's core.
• Mechanical energy, the sum of the kinetic energy, or energy of motion, and the potential energy, or energy stored in a system by reason of the position of its parts.
• Neglecting friction at the pivot and air resistance, the sum of the kinetic and potential energies of the pendulum, or its mechanical energy, is constant.
• Kinetic energy is a form of energy that an object or a particle has by reason of its motion.
• Kinetic energy is a property of a moving object or particle and depends not only on its motion but also on its mass.

The correct answer is More.

Key Points

• For an applied force, if the area is less then the pressure will be more.
• Pressure is inversely proportional to area, if the area is less then the pressure will be more.
• $P ={ F \over{A}}$
• If the area is more then the pressure will be less.
• Pressure is directly proportional to force, if the force increases then the pressure also increases vice versa.

Additional Information

• Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
• Gauge pressure is the pressure relative to the ambient pressure. Various units are used to express pressure.
• Air pressure can be called atmospheric pressure.
• The air around us has weight, and it presses against everything it touches.
• That pressure is called atmospheric pressure, or air pressure.
• It is the force exerted on a surface by the air above it as gravity pulls it to Earth.

Shortcut Trick

To check if a number N is prime, test divisibility by primes up to √N.

For 553, √553 ≈ 23.5. Primes to check: 2, 3, 5, 7, 11, 13, 17, 19, 23.

Sum of digits 5+5+3 = 13 (not div by 3). Ends in 3 (not div by 2, 5).

Check 7: 553 ÷ 7 = 79. Since it is divisible by 7, it is a composite number.

∴ The correct answer is 553.

Alternate Method

Given: Numbers 853, 953, 553, 653.

Formula: A prime number has only two factors: 1 and itself. A composite number has more than two factors.

⇒ Testing 553:

⇒ 553 ÷ 7 = 79

⇒ Factors of 553 are 1, 7, 79, 553.

⇒ Testing 853: Not divisible by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. It is prime.

⇒ Testing 953: Not divisible by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31. It is prime.

⇒ Testing 653: Not divisible by 2, 3, 5, 7, 11, 13, 17, 19, 23. It is prime.

∴ The correct answer is 553.

Additional Information

Prime Number Definition

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

Divisibility Rule of 7

Double the last digit and subtract it from the rest of the number. If the result is divisible by 7, the original number is too. (e.g., for 553: 55 − (3×2) = 49, which is 7×7).

Composite Number

A positive integer greater than 1 that has at least one divisor other than 1 and itself.

The correct answer is NH3, CH4 and H2S.

Key Points

• The atmosphere of the early Earth was mainly composed of NH3, CH4 and H2S.
• Earth’s original atmosphere was rich in methane, ammonia, water vapour, and the noble gas neon, but it lacked free oxygen.
• Its early atmosphere was probably formed from the gases given out by volcanoes.

​

Additional Information

• Atmospheric pressure is commonly measured with a barometer.
• In a barometer, a column of mercury in a glass tube rises or falls as the weight of the atmosphere changes.
• An atmosphere (atm) is a unit of measurement equal to the average air pressure at sea level at a temperature of 15 degrees Celsius (59 degrees Fahrenheit).
• One atmosphere is 1,013 millibars or 760 millimetres (29.92 inches) of mercury.
• Condensation is the process where water vapour becomes liquid.
• It is the reverse of evaporation, where liquid water becomes a vapour.
• Condensation happens one of two ways:
• Either the air is cooled to its dew point or it becomes so saturated with water vapour that it cannot hold any more water or it becomes so saturated with water vapour that it cannot hold any more water.

Shortcut Trick

If the price of an item increases by r%, the reduction in consumption required to keep the expenditure constant is given by: [r / (100 + r)] × 100%.

Required reduction = [10 / (100 + 10)] × 100% = [10 / 110] × 100% = 100 / 11%.

100 / 11% = 9 (1/11)%.

∴ The correct answer is 9 (1/11)%.

Alternate Method

Let the initial price of petrol be ₹100 and initial consumption be 100 units.

⇒ Initial Expenditure = Price × Consumption = 100 × 100 = ₹10,000.

⇒ New Price = 100 + 10% of 100 = ₹110.

⇒ To keep expenditure constant at ₹10,000, New Consumption = 10,000 ÷ 110 = 1000 / 11 units.

⇒ Reduction in Consumption = 100 − (1000 / 11) = (1100 − 1000) / 11 = 100 / 11 units.

⇒ Percentage Reduction = (Reduction / Original Consumption) × 100 = (100 / 11 ÷ 100) × 100 = 100 / 11% = 9 (1/11)%.

∴ The correct answer is 9 (1/11)%.

Additional Information

Price-Consumption Relationship

Since Expenditure = Price × Consumption, if Expenditure is constant, Price is inversely proportional to Consumption.

Percentage Decrease Formula

If price decreases by r%, the increase in consumption required is [r / (100 − r)] × 100%.

Successive Percentage Change

Net change = a + b + (ab / 100). For constant expenditure, net change must be 0%.

Concept Used:   

Follow the BODMAS rule according to the table given below:

Calculation:

$\frac{1}{5} + (\frac{999 + 494}{495}) × 99 - 6 = ?$

⇒ 1/5 + 1493/495 × 99 – 6 = ?

⇒ 1/5 + 1493/5 – 6 = ?

⇒ (1 + 1493)/5 – 6 = ?

⇒ 1494/5 – 6 = ?

⇒ (1494 – 30)/5 = ?

⇒ 1464/5 = ?

⇒ 292.8 = ?

∴ The value of ? is 292.8

The correct answer is Sulfur.

Key Points

• Sulphur is a polyatomic element.
• The elements which exist as single atoms are called monoatomic elements.
• But sulphur exists as S₈ and hence it is polyatomic.

Additional Information

• A polyatomic ion, also known as a molecular ion, is a covalently bonded set of two or more atoms, or of a metal complex, that can be considered to behave as a single unit and that has a net charge that is not zero.
• Unlike a molecule, which has a net charge of zero, this chemical species is an ion.
• Phosphorus is considered tetratomic because it has 4 atoms in its molecule.
• Chlorine is a diatomic molecule and argon is a monatomic molecule.

The correct answer is Prashant Ranganathan.

Key Points

• An Indian boy has won the world's largest pre-college science competition The Intel International Science and Engineering Fair (Intel ISEF) in the US in the environmental engineering category for his project on biodegradation of pesticides.
• Prashant Ranganathan, a 12th grader from Jamshedpur, along with over 20 high school students from various parts of India, participated in the Intel International Science and Engineering Fair.
• Prashant bagged the coveted award for his innovation for fighting against pesticides and getting rid of its side effects through biodegradable use.

Additional Information

• The topmost Gordon E Moore Award of USD 75,000 went to Ivo Zell, 18, of Germany for designing and constructing a remote-control prototype of a new flying wing, almost all participants of the Indian delegation returned from the annual competition with one award or the other.
• India really boasts really extraordinary mathematics, science, physics, education,
• Maya Ajmera president and CEO of the Society for Science and Public told the news agency in an interview. In fact, every section of the award ceremony had budding Indian scientists on the stage.

The correct answer is Esters.

Key Points

• Easters reacts in the presence of an acid or base to give back alcohol and carboxylic acid.
• Esterification is the process of combining an organic acid (RCOOH) with an alcohol (ROH) to form an ester (RCOOR) and water; or a chemical reaction resulting in the formation of at least one ester product.
• Ester is obtained by an esterification reaction of an alcohol and a carboxylic acid.

Additional Information

• Properties of Esters
• The name of an ester is derived from its carboxylic acid that takes part in the esterification reaction.
• They have a pleasant smell.
• They have a wide application in the perfume and food industries.
• Esters are organic compounds found in oils and fats.
• Uses of Esters
• ​Esters that have fragrances are used in perfumes, food flavourings, and cosmetics.
• Used as an organic solvent.
• Nitroglycerin is known and famous for its explosive properties.
• In the manufacturing of surfactants like detergents and soaps.
• Natural occurring esters are present in pheromones
• The backbone of DNA molecules is formed by phosphoric esters.
• Polyesters are used in the production of plastics

The statement emphasizes on taking advice from retired professors for improvement.

• The statement does not talk about its employees, so action I does not follow the statement.
• Action II follows the statement as it suggests the same thing, to involve retired i.e. experienced people for development.

Hence the correct answer is option 1.

Additional Information

• Some rules to solve Statements and Course of action questions must be kept in mind while solving it.

Rule 1. Have an unbiased and neutral mind frame. Individual perception must not be used to judge the course of action to be taken.

Rule 2. The first step should be to identify the root cause of the problem. Once the problem is solved, a logical mindset should be employed to figure out the course of action.

Rule 3. There must be no extremity involved in the course of action.

Rule 4. A course of action must be able to solve, reduce, or minimize the problem given in the situation.

Rule 5. The course of action can be said to solve/reduce the problem when it is an established fact, when it is logically possible and when it is known from experience.

The correct answer is West Bengal.

Key Points

• West Bengal won the Santosh Trophy, 2017 related to football.
• West Bengal lifted the Santosh Trophy for the 32nd time after Manvir Singh struck in the 119th minute for a 1-0 win over Goa, extending their domination in the premier domestic football tournament.

Additional Information

• The Senior National Football Championship or Santosh Trophy is a football knock-out competition contested by the regional state associations and government institutions under the All India Football Federation (AIFF), the sport's governing body in India.
• Before the starting of the first national club league, the National Football League in 1996, the Santosh Trophy was considered the top domestic championship in India.
• Many players who have represented India internationally played and gained accolades while playing in the Santosh Trophy.
• The tournament is held every year with 31 teams who are divided into groups and who must qualify for the tournament proper through the preliminary round.
• The current champions are Services, who won their 6th title during the 2018–19 edition.​

The correct answer is If desires are not relieved, then misery can be avoided.

Key Points

• The Four Noble Truths comprise the essence of Buddha's teachings, though they leave much left unexplained.
• They are the truth of suffering (dukkha), the truth of the cause of suffering (samudaya), the truth of the end of suffering (nirhodha), and the truth of the path that leads to the end of suffering (magga)​.
• If desires are not relieved, then misery can be avoided is not among the Four Noble Truths of Lord Buddha.

Additional Information

• Buddhism is a widespread Asian religion or philosophical tradition based on a series of original teachings attributed to Gautama Buddha.
• It originated in ancient India as a Sramana tradition sometime between the 6th and 4th centuries BCE, spreading through much of Asia.
• The Eightfold Path consists of eight practices: right view, right resolve, right speech, right conduct, right livelihood, right effort, right mindfulness, and right samadhi ('meditative absorption or union').
• The Noble Eightfold Path is one of the principal teachings of Buddhism, taught to lead to Arhatship.

The correct answer is 125 J.

Concept:

• Kinetic energy (K.E): The energy possessed by a body by the virtue of its motion is called kinetic energy.

The expression for kinetic energy is given by:

$KE = \frac{1}{2}m{v^2}$

Where m = mass of the body and v = velocity of the body

• Momentum (p): The product of mass and velocity is called momentum.

Momentum (p) = mass (m) × velocity (v)

Key Points

• Given that
• Mass of the body (m) = 10 kg
• Velocity of the body (v) = 5 m/s
• $Kinetic Energy (KE) of the body = {1\over{2}}* m* (v)^2$
• $Kinetic Energy (KE) of the body = {1\over{2}}* 10* (5)^2$
• $Kinetic Energy (KE) of the body = {125 J}$
• So Kinetic energy of the body will be 125 J.

Shortcut Trick

Ratio 5 years ago (Man : Son) = 7 : 1 (Difference = 6 units)

Ratio 5 years hence (Man : Son) = 3 : 1 (Difference = 2 units)

Equate difference: Multiply second ratio by 3 → 9 : 3. Gap (9−7) = 2 units corresponds to (5+5) = 10 years.

1 unit = 5 years. Ages 5 years ago: Man = 35, Son = 5. Ages 2 years ago (add 3): 38 and 8.

∴ The correct answer is 38 years and 8 years.

Alternate Method

Let Son's age 5 years ago be x and Man's age be 7x.

⇒ Present ages: Man = 7x + 5, Son = x + 5.

⇒ Ages after 5 years: Man = 7x + 10, Son = x + 10.

⇒ According to question: (7x + 10) = 3 × (x + 10)

⇒ 7x + 10 = 3x + 30

⇒ 4x = 20 ⇒ x = 5.

⇒ Man's age 5 years ago = 7 × 5 = 35 years.

⇒ Son's age 5 years ago = 5 years.

⇒ Ages 2 years ago = (35 + 3) and (5 + 3) = 38 years and 8 years.

∴ The correct answer is 38 years and 8 years.

Additional Information

Age Difference Property

The difference between the ages of two persons remains constant throughout their lives, regardless of how many years pass.

Ratio Balancing Method

If the age difference in two ratios is not same, multiply the ratios by the difference of the other ratio to balance them.

Group 13 is called the boron group, and boron is the only metalloid in this group.

The other group of 13 elements are metaThe correct answer is 2, 8, 3.

Additional Information

• 2, 8, 3  is the electronic configuration of the metal.

• The element with the electronic configuration (2, 8, 3) is aluminium as it has the atomic number 13.

• It has been placed in group 13 of the periodic table along with Boron, Gallium, Indium, and Thallium.

• Group 13 is called the boron group, and boron is the only metalloid in this group.

• The other group of 13 elements are metals.

Additional Information

• The electron configuration of an element describes how electrons are distributed in their atomic orbitals.
• Electron configurations of atoms follow a standard notation in which all electron-containing atomic subshells (with the number of electrons they hold written in superscript) are placed in a sequence.
• The atomic number or proton number (symbol Z) of a chemical element is the number of protons found in the nucleus of every atom of that element.
• The atomic number uniquely identifies a chemical element.
• It is identical to the charge number of the nucleus.

The mirror image of the given figure is:-

Hence, "option 4" is the correct answer.

Additional Information

1. The reflection of an object into the water is its water image. It appears by inverting an object vertically i.e. upside down.
2. The water image of the figure looks like the mirror image of the figure in case the mirror is horizontally at the bottom of the figure.
3. Water image is just a reflection where top and bottom part of the images changed where left and right side of the image remain same.
4. In Mirror image left side and right side changed vice-versa where top and bottom remain same.

The logic followed here is:-

Figure A is the water image of the given letter:-

Figure B is the water image of the given letter:-

Figure C is not the water image of the given letter:-

Figure D is the water image of the given letter:-

Figure C is different from others.

Hence, "option 1" is the correct answer.

The correct answer is High melting point and boiling point​.

Key Points

• When two non-metals react with each other they form a covalent compound.
• The covalent compound has low melting and boiling point.

Additional Information

• Covalent compounds do not conduct electricity, they have lower enthalpies of vaporization and fusion, contain energy of about 80kCal per mole, and are very powerful bonds that exist between atoms.
• Water is a polar solvent, but covalent compounds are nonpolar.
• This implies that covalent compounds don't dissolve in water and make a separate layer on the surface of the water.
• Hence we can say that covalent compounds are insoluble in water.
• A covalent bond is a chemical bond that involves the sharing of electron pairs between atoms.
• These electron pairs are known as shared pairs or bonding pairs, and the stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding.

The logic followed here is:-

Given that:-

PICTURE is coded as 6.

Total number of letter of word - 1 = 7 - 1 = 6,

And 

STUDIO is coded as 5.

Total number of letter of word - 1 = 6 - 1 = 5

Similarly,

TELEVISION is coded as:-

Total number of letter of word - 1 = 10 - 1 = 9

Hence, "option 2" is the correct answer.

Shortcut Trick

Let the present age be P.

Equation: P + 12 = 3 × (P − 4)

P + 12 = 3P − 12

2P = 24 ⇒ P = 12

∴ The correct answer is 12 Years.

Alternate Method

Given:

Time into the future = 12 years

Time in the past = 4 years

Ratio of future age to past age = 3 : 1

Let age 4 years ago be x.

Age 12 years later = 3x

The difference between these two points in time = 12 + 4 = 16 years.

⇒ 3x − x = 16

⇒ 2x = 16

⇒ x = 8 years (Age 4 years ago)

⇒ Present Age = 8 + 4 = 12 years

∴ The correct answer is 12 Years.

Additional Information

Age Ratio Concepts

If the ratio of ages of two people is a:b, then after 'n' years, the ratio becomes (a+n):(b+n). The difference between ages always remains constant.

Future and Past Ages

If present age is 'x', age 'n' years ago is (x − n) and age 'm' years hence is (x + m). The total gap between these two periods is (n + m) years.

Shortcut Trick

Total Work (LCM of 13, 39) = 39 units.

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

Work done in 18 days (9 pairs) = 9 × 4 = 36 units.

Remaining work = 3 units, which A completes on the 19^th day.

∴ The correct answer is 19 days.

Alternate Method

Given: Time taken by A = 13 days, Time taken by B = 39 days.

Calculations:

⇒ Work done in a 2-day cycle (A + B) = 3 + 1 = 4 units.

⇒ Total work to be completed = 39 units.

⇒ Number of complete cycles = 39 ÷ 4 = 9 cycles (with remainder).

⇒ Days in 9 cycles = 9 × 2 = 18 days.

⇒ Work completed in 18 days = 9 × 4 = 36 units.

⇒ Remaining work = 39 − 36 = 3 units.

⇒ On the 19^th day, it is A's turn. Time taken by A = 3 ÷ 3 = 1 day.

⇒ Total days = 18 + 1 = 19 days.

∴ The correct answer is 19 days.

Additional Information

Alternate Day Work

When people work on alternate days, calculate the work done in one full cycle (sum of individual efficiencies) and multiply to reach close to the total work.

Efficiency and Time Relationship

Efficiency is inversely proportional to time. Efficiency = Total Work ÷ Time.

Pipes & Cisterns Analogy

The same logic applies to pipes filling a tank alternately, where outlet pipes have negative efficiency.

The correct answer is Porifera.

 Key Points

• The invertebrates, or Invertebrata, are animals that do not contain bony structures such as the cranium and vertebrae.
• The simplest of all the invertebrates are the Parazoans, which include only the phylum Porifera.
• The animals of Porifera are non-movable.
• Phylum Porifera are popularly known as sponges.
• Sponge larvae are able to swim.

Additional Information 

• The flatworms, flatworms, Platyhelminthes, or platyhelminths are a phylum of relatively simple bilaterian, unsegmented, soft-bodied invertebrates.
• Unlike other bilaterians, they are acoelomates (having no body cavity), and have no specialized circulatory and respiratory organs,
• The nematodes or roundworms constitute the phylum Nematoda (also called Nemathelminthes),]with plant-parasitic nematodes also known as eelworms.
• They are a diverse animal phylum inhabiting a broad range of environments.

Shortcut Trick

Breadth = Area ÷ Length

Breadth = 12.46 ÷ 3.5

Breadth = 3.56 m

∴ The correct answer is 3.56 m.

Alternate Method

Given:

Area of the rectangle = 12.46 m²

Length of the rectangle = 3.5 m

Formula Used:

Area of rectangle = Length × Breadth

Calculations:

⇒ 12.46 = 3.5 × Breadth

⇒ Breadth = 12.46 ÷ 3.5

⇒ Breadth = 124.6 ÷ 35

⇒ Breadth = 3.56 m

∴ The correct answer is 3.56 m.

Additional Information

Perimeter of Rectangle

The total boundary length of a rectangle is given by P = 2 × (Length + Breadth).

Diagonal of Rectangle

The distance between opposite corners is Calculated as d = √(Length² + Breadth²).

Area conversion

To convert m² to cm², multiply the value by 10,000 (10⁴).

The correct answer is Two.

Key Points

• Two pairs of contrasting traits are found in a dihybrid cross. The pairs of contrasting traits act independently, each pair assorts independently.
• Dihybrid cross is the cross between two different genes that differ in two observed traits.

Additional Information

• A dihybrid cross is a breeding experiment between two organisms that are identical hybrids for two traits.
• In other words, a dihybrid cross is a cross between two organisms, with both being heterozygous for two different traits.
• The individuals in this type of trait are homozygous for a specific trait.
• These traits are determined by DNA segments called genes.
• In a dihybrid cross, the parents carry different pairs of alleles for each trait.
• One parent carries a homozygous dominant allele, while the other one carries a homozygous recessive allele.
• The offspring produced after the crosses in the F1 generation are all heterozygous for specific traits.

Shortcut Trick

Salary = ₹6,00,000

Total Lease (5 years) = 50% of Salary = ₹3,00,000

Lease per year = ₹3,00,000 ÷ 5 = ₹60,000

Total Annual Income = Salary + Yearly Lease = ₹6,00,000 + ₹60,000 = ₹6,60,000

∴ The correct answer is ₹6,60,000.

Alternate Method

Given:

Annual Salary of Suman = ₹6,00,000

Lease Duration = 5 years

Total Lease Income (5 years) = 50% of Annual Salary

Calculations:

⇒ Total Income from Agricultural Land (5 years) = 50% × 6,00,000

⇒ Total Lease Income = (50/100) × 6,00,000 = ₹3,00,000

⇒ Annual Income from Lease = 3,00,000 ÷ 5

⇒ Annual Lease Income = ₹60,000

⇒ Total Annual Income = Annual Salary + Annual Lease Income

⇒ Total Annual Income = 6,00,000 + 60,000 = ₹6,60,000

∴ The correct answer is ₹6,60,000.

Additional Information

Percentage Calculation

To find x% of a value V, use the formula: (x ÷ 100) × V.

Annual Average

When a total sum is earned over n years, the annual income is calculated by dividing the total sum by n.

Total Income

Total Income is the sum of all individual revenue streams like Salary, Rent, and Interest within a specific timeframe.

Shortcut Trick

Relative Speed when moving in opposite directions = 24 + 30 = 54 km/h.

Meeting Time = Total Distance ÷ Relative Speed.

Time = 86.4 ÷ 54 = 1.6 hours.

∴ The correct answer is 1.6 hr.

Alternate Method

Given:

Speed of Car 1 (S₁) = 24 km/h

Speed of Car 2 (S₂) = 30 km/h

Total Distance (D) = 86.4 km

Formula Used:

Relative Speed (Opposite Direction) = S₁ + S₂

Time = Distance ÷ Relative Speed

Calculations:

⇒ Relative Speed = 24 km/h + 30 km/h = 54 km/h

⇒ Meeting Time = 86.4 ÷ 54

⇒ Meeting Time = 1.6 hr

∴ The correct answer is 1.6 hr.

Additional Information

Relative Speed Concept

When two objects move in opposite directions, their relative speed is the sum of their individual speeds (S₁ + S₂). If they move in the same direction, it is the difference (|S₁ − S₂|).

Conversion of Units

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

Time and Distance Relation

Distance is directly proportional to time when speed is constant (D = S × T).

Calculation:

According to the question

The two farms which have the same number of sheeps is

⇒ Farm 3 and Farm 5

∴ The required answer is farm 3 and farm 5

The correct answer is Three times.

Key Points​

• The force of attraction between two bodies is 1/9 F.
• $F= {GMm\over r^2}$
• where F is the Force of attraction between two bodies
• G is gravitational constant
• m is mass
• r is distance between two bodies
• Hence, 
• F is inversely proportional to ${1\over r^2}$
• r is inversely proportional to ${1\over \sqrt{f}}$
• Thereforce r will be ${1\over \sqrt{1\over9}}$
• r will be $\sqrt{9}$
• r will be 3 times
• So, the distance between these two bodies will be Three times.

Shortcut Trick

Average Speed = Total Distance ÷ Total Time

Total Distance = 20 + 30 = 50 m

Total Time = 6 + 4 = 10 s

Average Speed = 50 ÷ 10 = 5 ms⁻¹

∴ The correct answer is 5 ms⁻¹.

Alternate Method

Given:

First distance (d₁) = 20 m, Time (t₁) = 6 s

Second distance (d₂) = 30 m, Time (t₂) = 4 s

Formula Used:

Average Speed = (Total Distance Covered) / (Total Time Taken)

Calculations:

⇒ Total Distance = d₁ + d₂ = 20 m + 30 m = 50 m

⇒ Total Time = t₁ + t₂ = 6 s + 4 s = 10 s

⇒ Average Speed = 50 m ÷ 10 s

⇒ Average Speed = 5 ms⁻¹

∴ The correct answer is 5 ms⁻¹.

Additional Information

Average Speed vs Average Velocity

Average speed is total distance/total time (scalar), while average velocity is total displacement/total time (vector).

Uniform Motion

When an object covers equal distances in equal intervals of time, it is said to be in uniform motion; its speed remains constant.

Unit Conversion

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

Shortcut Trick

Since the length of line PQ is equal to the radius r, and CP = CQ = r, triangle CPQ is an equilateral triangle.

In an equilateral triangle, all internal angles are 60°, so ∠CPQ = 60°.

The tangent to a circle at any point is perpendicular to the radius at that point, so the angle between the tangent and radius CP is 90°.

The acute angle between the tangent and line PQ = 90° − 60° = 30°.

Converting to radians: 30° × (π / 180°) = π/6.

∴ The correct answer is π/6.

Alternate Method

Given:

Center of the circle = C

Points on the circle = P and Q

Length of line PQ = Radius (r)

Formula Used:

1. In a circle, the tangent is perpendicular to the radius at the point of contact.
2. Angle in Radians = (Angle in Degrees × π) ÷ 180

Calcul

The correct answer is Carl Linnaeus.

Key Points

• Carl Linnaeus is known as the Father of Taxonomy.
• Carl Linnaeus, also known after his ennoblement as Carl von Linné, was a Swedish botanist, zoologist, taxonomist, and physician who formalized binomial nomenclature, the modern system of naming organisms.
• He is known as the "father of modern taxonomy".
• Many of his writings were in Latin, and his name is rendered in Latin as **Carolus Linnaeus.**​

Additional Information

• Dr. B.R Ambedkar is recognized as the Father of the Constitution of India.
• He was appointed as the Chairman of the Constitution Drafting Committee and was appointed by the Assembly to write India's new Constitution on 29th August.
• Charles Babbage is considered to be the ‘Father of Modern Digital Computer’.

The correct answer is 73rd.

Key Points

• The Constitution (73rd Amendment) Act, 1992 has added a new part IX consisting of 16 Articles and the Eleventh Schedule to the Constitution.
• The amendment provides for a three-tier Panchayat Raj System at the village, intermediate, and district levels.
• Compulsory provisions of the act are as follows:-
• Direct election to all the seats of the Panchayats. Indirect election to the post of Chairman at the intermediate and district level.
• The minimum age to contest a Panchayat election is decided to be 21 years.
• The tenure of the Panchayats has been fixed for five years.

Additional Information

• The system of Municipalities or Urban Local Governments was constitutionalized through the 74th Constitutional Amendment Act of 1992.
• The provisions in this amendment are included in Part IXA which came into force on June 1, 1993.
• The Ninety-second Amendment of the Constitution of India, officially known as The Constitution (Ninety-second Amendment) Act, 2003, amended the Eighth Schedule to the Constitution so as to include Bodo, Dogri, Maithili, and Santali languages, thereby raising the total number of languages listed in the schedule to 22.
• The Constitution (53rd Amendment) Act, 1986
• It confers Statehood on Mizoram and ensures against unnecessary interference by the Central Government with the laws relating to spheres of social relationship and community conduct applicable to Mizoram.

The logic followed here is:

• In the statement, the man says that he finds it difficult to understand the difference between astronomy and astrology. It implies that the man is not well-versed or familiar with the two concepts.
• Thus, both the assumptions are implicit from the given statement.

Hence the correct answer is option 4.

Additional Information

1. Read the statement with an approach that the assumptions would be true about the statement.
2. Do not go too logical with the statements. Analyze the given information and the assumption must only be made based on the information in the statement. Do not over-complicate it.
3. Common assumptions can always be followed but other than that do not align the statement with General Knowledge or other facts
4. Use the elimination method if you are unable to apprehend the answer. Read the statement and then the assumptions given in the options, you shall notice that a few of them will most definitely not follow. Eliminate them and then choosing from lesser options may prove to be more convenient
5. One thing to note is that the assumption is something that the author believes to be true, so while choosing the correct option, keep this thought in mind. If any option contradicts the statement, then that assumption will not follow.

The correct answer is WBC.

Key Points

• The white blood cells or leukocytes help provide immunity by destroying or killing foreign pathogens and antigens and thereby provide protection from diseases and infections.
• They are therefore called the soldiers of our body.
• They all work together to protect you from germs and help you get better when you're sick.
• The main parts of the immune system are white blood cells: serving as an army against harmful bacteria and viruses, white blood cells search for, attack, and destroy germs to keep you healthy.

Additional Information

• The abdomen (commonly called the belly) is the body space between the thorax (chest) and pelvis.
• The abdomen contains all the digestive organs, including the stomach, small and large intestines, pancreas, liver, and gallbladder.
• The heart is a muscular organ about the size of a fist, located just behind and slightly left of the breastbone.
• The heart pumps blood through the network of arteries and veins called the cardiovascular system.
• Red blood cells also referred to as red cells, red blood corpuscles, haematids, erythroid cells or erythrocytes, are the most common type of blood cell and the vertebrate's principal means of delivering oxygen to the body tissues.

Given:

Number of people sitting = 4/7

Number of chairs available = 7/12

Number of empty chairs = 20

Calculation:

Let the number of people be x and chairs be y respectively

Number of available chairs = y × 7/12 = 7y/12

Number of empty chair = y – (7y/12)

⇒ 5y/12

According to the question

⇒ 5y/12 = 20

⇒ y = 48

Total numbers of chairs = 48

Numbers of chairs in which people are sitting = (48 – 20) = 28

Number of people who are sit = x × (4/7) = 4x/7

Again,

⇒ 4x/7 = 28

⇒ x = 49

Total number of people = 49

Now,

Number of people standing in the hall = (49 – 28)

⇒ 21

∴ Required people standing in the hall is 21

The correct answer is Height.

Key Points

• The potential energy of an object increases with its height.
• Because the equation for potential energy is $mgh$.
• So as height increases potential energy also increases thus the total energy of an object increases.

Additional Information

• Potential energy, stored energy that depends upon the relative position of various parts of a system. 
• The gravitational potential energy at large distances is directly proportional to the masses and inversely proportional to the distance between them.
• The gravitational potential energy increases as r increases.
• The total energy of the object = mgh.
• As it falls, its potential energy will change into kinetic energy.
• If v is the velocity of the object at a given instant, the $KE = {1\over{2}}mv^2$
• As the fall of the object continues, the potential energy would decrease while the kinetic energy would increase.

The logic Venn diagram is given below:-

Conclusion:

1. Some keys are locks. → False (All keys are metal, some metals are locks, there is no direct relation between keys and locks so some keys are locks it can be possible but not definite, hence, false)
2. Some metals are keys. → True (All keys are metal, so some metals are also keys, it is definitely true)

Hence, "Option 4" is the correct answer.

Additional Information

The correct answer is Bihar.

Key Points

• The alliance of political parties called the Grand Alliance before the 2015 assembly elections and which broke up in 2017, belongs to the state of Bihar.
• Mahagathbandhan also known as Grand Alliance, is a coalition of political parties in the Eastern state of Bihar in India, formed ahead of the upcoming 2020 Vidhan Sabha elections in Bihar.
• The alliance consists of Rashtriya Janata Dal (RJD), Indian National Congress (INC), and several Left parties including the Communist Party of India (CPI), Communist Party of India (Marxist–Leninist) Liberation-CPIML(Liberation), and Communist Party of India (Marxist) (CPIM), with Tejashwi Yadav as the proposed Chief Minister candidate.​ 

The correct answer is 0.29 A.

Key Points​

• Given,
• Resistance(R)= 750 ohm
• Voltage( V) = 220V
• According to Ohm's Law,
• $V = IR$
• $I = {V\over{R}}$
• $I = {220\over{750}}$
• => 0.2933 = 0.29 A
• So the current through the coil will be 0.29 A.

The correct answer is 77%.

Key Points

• US retail giant Walmart has signed a definitive agreement to acquire a 77 percent stake in India's largest e-commerce marketplace Flipkart with an investment of around $16 billion, making it the largest transaction in the history of the online retail space globally.

Additional Information

The correct answer is Raipur.

Key Points

• The country's first 'Garbage Festival' was organized recently in Raipur.
• The Raipur Municipal Corporation in Chhattisgarh organised the three-day Kachra Mahotsav 2018, India's first Garbage Festival.
• The festival aimed to increase awareness, use the waste generated in the city creatively, and to showcase multiple techniques for reusing things that are labelled as garbage.
• The event had workshops, talks, and performances.

Additional Information

• Raipur is the capital city of Chhattisgarh state in central India.
• In the center, the ancient Dudhadhari Math temple is a sacred monument dedicated to Lord Rama, decorated with scenes from the epic poem “Ramayana.” Nearby, a statue of the Hindu monk Swami Vivekananda towers over Vivekananda Sarovar lake.
• Southeast, Purkhouti Muktangan is an open-air museum featuring landscaped grounds, statues and tribal artifacts

The correct answer is Both A and B are true.

Key Points

• The mass per unit volume of a substance is called density (density = mass/volume).
• The SI unit of density is $kg\over{m^3}$.
• So A is true.
• Kinetic energy is the energy an object has because of its motion, transferred to the object, and the object will be moving with a new constant speed.
• So B is true.

Additional Information

• Mechanical energy, sum of the kinetic energy, or energy of motion, and the potential energy, or energy stored in a system by reason of the position of its parts.
• Neglecting friction at the pivot and air resistance, the sum of the kinetic and potential energy.
• Kinetic energy is a form of energy that an object or a particle has by reason of its motion. 
• Kinetic energy is a property of a moving object or particle and depends not only on its motion but also on its mass.
• In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.

The correct answer is Concave mirror.

Key Points

• A concave mirror is called a converging mirror because it converges the Ray of light incident parallels to the mirror into a point called the focus.
• A convex mirror is called a diverging mirror as it diverges the Ray incident parallel to the mirror that appears to Meet at a point called the focus.

Additional Information

• A convex mirror or diverging mirror is a curved mirror in which the reflective surface bulges towards the light source.
• Convex mirrors reflect light outwards, therefore they are not used to focus light.
• The image is smaller than the object but gets larger as the object approaches the mirror.
• A plane mirror is a mirror with a flat reflective surface.
• For light rays striking a plane mirror, the angle of reflection equals the angle of incidence.
• The angle of the incidence is the angle between the incident ray and the surface normal.
• The image formed by a plane mirror is always virtual and erect.​
• The image formed by the plane mirror is virtual and erect i.e. image cannot be projected or focused on a screen.
• The distance of the image 'behind' the mirror is the same as the distance of the object in front of the mirror.
• The size of the image formed is the same as the size of the object.

The logic followed here is:-

Hence, "option 2" is the correct answer.

The correct answer is Bal Gangadhar Tilak.

Key Points

• Bal Gangadhar Tilak founded the Marathi newspaper 'Kesari'.
• Kesari is a Marathi newspaper that was founded on 4 January 1881 by Lokmanya Bal Gangadhar Tilak, a prominent leader of the Indian Independence movement.
• The newspaper was used as a spokes piece for the Indian national freedom movement and continues to be published by the Kesari Maratha Trust and Tilak's descendants.
• Bal Gangadhar Tilak used to run his two newspapers, Kesari, in Marathi and Mahratta in English from Kesari Wada, Narayan Peth, Pune.
• The newspapers were originally started as a co-operative by Chiplunkar, Agarkar, and Tilak.

Additional Information

• The first English Newspaper was started by Irishman James Augustus Hicky in 1779.
• It was founded in Calcutta.
• The name of the First English Newspaper is Hicky's Bengal Gazette.
• In 1811 started ‘Calcutta Chronicle’ and the editor was James Silk Buckingham.
• He had introduced a new approach to Journalism in India.
• He initiated clear journalistic practices and covered the problems of local people and their lives.
• "The Hindu" was started in the English language in 1878, which was mainly distributed in Tamil Nadu and Kerala.
• News agency services became available on a regular basis with the Press Trust of India which was started in 1946.
• Raja Ram Mohan Roy a social reformer recognized the power of newspapers and started a Bengali newspaper ‘Sambad Kaumudi’ in 1822 and a Persian paper ‘Mirat-ul-Akhbar’ in 1822.
• Fardaonji Murzban in 1822 started ‘Bombay Samachar’, he was a pioneer of the Vernacular Press in Bombay.

The correct answer is A.P.J Abdul Kalam.

Key Points

• Wings of Fire: An Autobiography of APJ Abdul Kalam (1999), former President of India.
• It was written by Dr. Abdul Kalam and Arun Tiwari.
• Here he expresses one event, which happened in his school days, "Rameswaram Sastry, a new teacher of his school he could not stomach a Hindu Priest's son sitting with a Muslim boy.
• In accordance with our social ranking as the new teacher saw it, I was asked to go and sit on the backbench.

Additional Information

• Kocheril Raman Narayanan was an Indian statesman, diplomat, academician, and politician who served as the tenth President of India and ninth vice president of India.
• Pranab Kumar Mukherjee; 11 December 1935 – 31 August 2020 was an Indian statesman who served as the 13th president of India from 2012 until 2017.
• Inder Kumar Gujral was an Indian diplomat, politician, and freedom activist who served as the 12th prime minister of India from April 1997 to March 1998.
• Born in Punjab, he was influenced by nationalistic ideas as a student and joined the All India Students Federation and the Communist Party of India.

The logic followed here is:-

Hence, "option 4" is the correct answer.

The correct answer is Safeena Husain.

Key Points

• Safeena Husain is a social worker and founder of Educate Girls – a non-profit organization that is headquartered in Mumbai, India.
• Safeena Husain is the founder and executive director of 'Educate Girls', an NPO working for the education of girls in the most educationally backward districts of India.
• It focusses on mobilising communities for girls’ education in India’s rural and educationally backward areas.
• Under her leadership, Educate Girls’ launched world’s first Development Impact Bond in education which on its completion in 2018 surpassed both its target outcomes.

Additional Information

• Educate Girls’ is a non-profit organization in India, established in 2007, founded by Safeena Husain, that works towards girls' education in India's rural and educationally backward areas by mobilizing communities.
• It cu rrently operates in over 13,000 villages in Rajasthan and Madhya Pradesh.
• Founded: 2007
• Founder: Safeena Husain
• Headquarters location: Mumbai
• Area se rved: India

The correct answer is Earth.

Key Points

• Apart from Neptune, Earth is also known as 'Blue Planet'.
• The Earth is 23 ½ degrees tilted on its axis and thus makes 66 ½ degrees angle.
• It is known as a watery planet or blue planet due to the presence of huge amounts of water in it.

Additional Information

• Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter.
• It is a gas giant with an average radius of about nine and a half times that of Earth.
• It only has one-eighth the average density of Earth; however, with its larger volume, Saturn is over 95 times more massive.
• Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, being larger than only Mercury.
• In English, Mars carries the name of the Roman god of war and is often referred to as the "Red Planet".
• Pluto is a dwarf planet in the Kuiper belt, a ring of bodies beyond the orbit of Neptune.
• It was the first and the largest Kuiper belt object to be discovered.
• After Pluto was discovered in 1930, it was declared to be the ninth planet from the Sun.

Shortcut Trick

Factorize each expression to find the Highest Common Factor and LCM.

Expression 1: 2(x³ − 8) → 2(x − 2)(x² + 2x + 4)

Expression 2: 3(x + 5)(x − 2)

Expression 3: x(x² + 2x − 8) → x(x + 4)(x − 2)

LCM is the product of highest powers of all factors: 2 × 3 × x × (x − 2) × (x + 5) × (x + 4) × (x² + 2x + 4).

∴ The correct answer is 6x(x − 2)(x + 4)(x + 5)(x² + 2x + 4).

Alternate Method

Given Expressions:

E₁ = 2x³ − 16

E₂ = 3(x² + 3x − 10)

E₃ = x³ + 2x² − 8x

Factorization:

⇒ E₁ = 2(x³ − 2³) = 2(x − 2)(x² + 2x + 4) [Using a³ − b³ formula]

⇒ E₂ = 3(x² + 5x − 2x − 10) = 3[x(x + 5) − 2(x + 5)] = 3(x − 2)(x + 5)

⇒ E₃ = x(x² + 2x − 8) = x(x² + 4x − 2x − 8) = x[x(x + 4) − 2(x + 4)] = x(x − 2)(x + 4)

Calculation of LCM:

⇒ Numerical part = LCM of (2, 3, 1) = 6

⇒ Variable part = x

⇒ Common factors = (x − 2)

⇒ Remaining factors = (x + 5), (x + 4), (x² + 2x + 4)

⇒ LCM = 6 × x × (x − 2) × (x + 5) × (x + 4) × (x² + 2x + 4)

∴ The correct answer is 6x(x − 2)(x + 4)(x + 5)(x² + 2x + 4).

Additional Information

Difference of Cubes Formula

The identity for a³ − b³ is (a − b)(a² + ab + b²).

LCM of Polynomials

The Least Common Multiple (LCM) is the product of the highest power of each factor present in the given expressions.

HCF of Polynomials

The Highest Common Factor (HCF) is the product of the lowest power of the common factors only. For this problem, HCF = (x − 2).

Shortcut Trick

Assume the Total Distance is a value divisible by 4 (LCM of denominators 4 and 2), say 60 km.

Time 1 (1/4th distance at 15 km/hr) → 15/15 = 1 hr.

Time 2 (1/2 distance at 30 km/hr) → 30/30 = 1 hr.

Time 3 (Rest 1/4th distance at 5 km/hr) → 15/5 = 3 hr.

Average Speed = Total Distance ÷ Total Time = 60 ÷ (1 + 1 + 3) = 60 ÷ 5 = 12 km/hr.

∴ The correct answer is 12 km/h.

Alternate Method

Given: Total Time = 2 hours. Distance fractions are 1/4, 1/2, and (1 − 1/4 − 1/2) = 1/4.

Formula Used: Average Speed = Total Distance ÷ Total Time

⇒ Let total distance be D km.

⇒ Total Time = Time₁ + Time₂ + Time₃

⇒ 2 = (D/4 ÷ 15) + (D/2 ÷ 30) + (D/4 ÷ 5)

⇒ 2 = D/60 + D/60 + D/20

⇒ 2 = (D + D + 3D) ÷ 60

⇒ 2 = 5D ÷ 60

⇒ D = (2 × 60) ÷ 5 = 24 km

⇒ Average Speed = 24 km ÷ 2 hours = 12 km/h

∴ The correct answer is 12 km/h.

Additional Information

Average Speed for Equal Distances

If a person covers two equal distances at speeds x and y, Average Speed = 2xy ÷ (x + y).

General Average Speed

Always calculated as (Total Distance Covered) ÷ (Total Time Taken), regardless of varying speeds or stops.

Unit Conversion

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

Shortcut Trick

Let the original price of the car be 100.

Dealer bought it at 30% discount ⇒ CP = 100 − 30 = 70.

He added 40% profit margin to his purchase price ⇒ New Base = 70 × (140 ÷ 100) = 98.

He sold it at 25% discount on this base ⇒ SP = 98 × (75 ÷ 100) = 73.5.

Overall Profit% = (SP − CP) ÷ CP × 100 = (73.5 − 70) ÷ 70 × 100 = 3.5 ÷ 70 × 100 = 5%.

∴ The correct answer is 5% profit.

Alternate Method

Given: Discount on purchase = 30%, Profit margin added = 40%, Selling discount = 25%.

Formulas: SP = CP × (100 + P%) ÷ 100 | Profit% = (Net Change ÷ Initial Value) × 100

⇒ Let the original list price = 100.

⇒ Dealer's Cost Price (CP) = 100 − (30% of 100) = 70.

⇒ Dealer marks up his price by 40%: 70 + (40% of 70) = 70 + 28 = 98.

⇒ Dealer gives 25% discount on this price: 98 − (25% of 98) = 98 − 24.5 = 73.5.

⇒ Selling Price (SP) = 73.5.

⇒ Net Profit = SP − CP = 73.5 − 70 = 3.5.

⇒ Profit % = (3.5 ÷ 70) × 100 = 5%.

∴ The correct answer is 5% profit.

Additional Information

Successive Percentage Change

When a value is changed by a% and then by b%, the net change is given by [a + b + (a × b ÷ 100)]%.

Profit and Loss on CP

Always remember that the overall profit or loss for the dealer is calculated based on the price the dealer actually paid (his CP), not the original list price.

Shortcut Trick

Sum of two numbers × Difference of two numbers = Difference of their squares

Sum of numbers × 6 = 240

Sum of numbers = 240 ÷ 6 = 40

∴ The correct answer is 40.

Alternate Method

Given:

Difference between numbers (x − y) = 6

Difference of squares (x² − y²) = 240

Formula Used:

Standard Algebraic Identity: a² − b² = (a − b)(a + b)

Calculations:

⇒ x² − y² = 240

⇒ (x − y)(x + y) = 240

⇒ 6 × (x + y) = 240

⇒ x + y = 240 ÷ 6

⇒ x + y = 40

∴ The correct answer is 40.

Additional Information

Algebraic Identities of Squares

The square of a sum is (a + b)² = a² + 2ab + b², and the square of a difference is (a − b)² = a² − 2ab + b².

Relationship between Sum and Difference

The difference between the square of the sum and the square of the difference is (a + b)² − (a − b)² = 4ab.

Sum of Squares Identity

The sum of squares can be expressed as a² + b² = (a + b)² − 2ab or a² + b² = (a − b)² + 2ab.

Shortcut Trick

Rate of 5% as a fraction = 1/20.

For 2 years, the Principal to Amount ratio = (20 : 21)² = 400 : 441.

Given Principal (400 units) = ₹8000 → 1 unit = ₹20.

Total Amount (441 units) = 441 × 20 = ₹8820.

∴ The correct answer is ₹8820.

Alternate Method

Given:

Principal (P) = ₹8000

Rate (R) = 5% per annum

Time (n) = 2 years

Formula Used:

Amount (A) = P(1 + R/100)ⁿ

⇒ A = 8000 × (1 + 5/100)²

⇒ A = 8000 × (1 + 1/20)²

⇒ A = 8000 × (21/20) × (21/20)

⇒ A = 8000 × (441 / 400)

⇒ A = 20 × 441

⇒ A = ₹8820

∴ The correct answer is ₹8820.

Additional Information

Compound Interest Formula

The formula for total amount is A = P(1 + r/n)^nt, where n is the number of times interest is compounded per year.

CI vs SI Difference for 2 Years

The difference (D) between Compound Interest and Simple Interest for 2 years is given by D = P(R/100)².

Effective Annual Rate

For a rate of x% compounded annually for 2 years, the effective rate is [x + x + (x × x)/100]%.

The advertisement only states that the company will provide travelling allowance to outsiders.

• Nothing is stated about the selection of the candidates. and use of the word "Only". So argument I does not follow.
• The advertisement does not specify any train, thus argument II does not follow.
• Thus, neither of the arguments follow.

Hence the correct answer is option 2.

Additional Information

1. The agreement which is the reconstruing part of the statement is a strong agreement.
2. The argument should not be imagined.
3. The relationship of the agreement should be direct from the statement.
4. The argument should be simple and clear.
5. The agreement should be based on scientific facts.
6. The statement in the argument should receive a logical answer.

The logic followed here is:-

Dark to light from the first box to the second box and light to dark from the second to the third box and so on.

• From the first box to the second box five circles reduce to four circles and the second box to the third box four circles reduce to three circles and so on.

• The cross line inside the circle convert into dark circle in each step alternatively.

Hence, "option 4" is the correct answer.

Confusion PointsThese option A and C both are different.

Shortcut Trick

Present ratio S : A = 5 : 4 (difference 1 unit) and ratio after 3 years = 11 : 9 (difference 2 units).

To equate differences, multiply present ratio by 2 → 10 : 8.

Increase in units (11 − 10) = 1 unit, which represents 3 years.

Present age of S = 10 units = 10 × 3 = 30 years.

∴ The correct answer is 30 years.

Alternate Method

Given: Present ratio of S and A = 5 : 4. Ratio after 3 years = 11 : 9.

Formula Used: Age after n years = (Present age + n).

⇒ Let the present ages of S and A be 5x and 4x respectively.

⇒ According to question: (5x + 3) / (4x + 3) = 11 / 9

⇒ 9 × (5x + 3) = 11 × (4x + 3)

⇒ 45x + 27 = 44x + 33

⇒ 45x − 44x = 33 − 27

⇒ x = 6

⇒ Present age of S = 5x = 5 × 6 = 30 years.

∴ The correct answer is 30 years.

Additional Information

Ratio Difference Method

If the age difference between two people is constant, the difference between their ratio parts must be equal for different time periods.

Concept of Uniform Growth

When n years are added to the ages of two individuals, the numerical increase in their respective ratio units represents the same time value n.

The correct answer is 30 J. 

Key Points

• Given that
• Charge (Q) = 3 C
• Potential difference (V) = 10 V
• $Work done (W) = V * Q$
• = 10 * 3
• =  30 J
• So the work that has to be done is 30 J.

Shortcut Trick

Each corner cut creates a hypotenuse of length √(0.5² + 0.5²) = 0.5√2 cm.

Perimeter = 4 × (Side − 2 × Cut) + 4 × Hypotenuse = 4 × (3 − 1) + 4 × 0.5√2 = 8 + 2√2 cm.

Area = Area of Square − 4 × Area of small Corner Triangle = 3² − 4 × (0.5 × 0.5 × 0.5) = 9 − 0.5 = 8.5 cm².

∴ The correct answer is (8 + 2√2) cm and 8.5 cm².

Alternate Method

Given: Side of square = 3 cm, Length cut from each corner = 0.5 cm.

Calculations for Perimeter:

⇒ Straight side of octagon = 3 − (0.5 + 0.5) = 2 cm.

⇒ Length of slanted edge (hypotenuse) = √(0.5² + 0.5²) = √0.5 = 0.5√2 cm.

⇒ Total Perimeter = (4 × 2) + (4 × 0.5√2) = 8 + 2√2 cm.

Calculations for Area:

⇒ Area of original square = 3 × 3 = 9 cm².

⇒ Area of one corner triangle = 1/2 × Base × Height = 0.5 × 0.5 × 0.5 = 0.125 cm².

⇒ Area of 4 corner triangles = 4 × 0.125 = 0.5 cm².

⇒ Area of octagon = 9 − 0.5 = 8.5 cm².

∴ The correct answer is (8 + 2√2) cm and 8.5 cm².

Additional Information

Regular Octagon Properties

A regular octagon has all sides equal. Area = 2(1 + √2)s² where s is the side length.

Pythagoras Theorem

In a right-angled triangle, Hypotenuse = √(Base² + Perpendicular²). For isosceles right triangles, H = side√2.

Polygon Perimeter

The perimeter of any polygon is the sum of the lengths of all its exterior boundaries.

Concept Used:    

Follow the BODMAS rule according to the table given below:

Calculation:

257 – [ 153 + {308 ÷ (24 – 10)}]

⇒ 257 – [153 + (308 ÷ 14)]

⇒ 257 – (153 + 22)

⇒ 257 – 175

⇒ 82

∴ The required value is 82

The logic followed here is:-

Both symbols

 rotate of one place in the clockwise direction in each step.

Both symbols 

 rotate of one place in the clockwise direction in each step.

Both symbols 

 rotate of one place in the clockwise direction in each step.

Both symbols 

 rotate of one place in the clockwise direction in each step.

The final figure is:-

Hence, "option 2" is the correct answer.

The correct answer is Laterite.

Key Points

• Lateritic Soils
• ‘Laterite’ means brick in Latin.
• They harden greatly on losing moisture.
• Laterite soils are red in colour due to little clay and more gravel of red sand-stones.
• Distribution of Laterite – Lateritic Soils
• A continuous stretch of laterite soil is found on the summits of Western Ghats at 1000 to 1500 m above mean sea level, Eastern Ghats, the Rajmahal Hills, Vindhyan, Satpuras, and Malwa Plateau.
• Bauxite is widely distributed in Ranchi, Jamnagar, Jabalpur, Kolhapur, and Shevroy Hills as surface deposits occur in these areas, where laterite soil is found.
• High-grade bauxite is found in abundance in India.
• Bauxite is widely distributed as surface deposits in those areas where laterite soil is found
• This mineral is the ore of aluminum metal that is used largely in the manufacture of special alloys, aluminum powder, utensils, and electric cables.
• Aluminum alloys are used in the manufacture of automobile engines because of their light and tough.
• Bauxite is used in the manufacture of cement and chemicals.

Additional Information

• Black soils are derivatives of trap lava and are spread mostly across interior Gujarat, Maharashtra, Karnataka, and Madhya Pradesh on the Deccan lava plateau and the Malwa Plateau, where there is both moderate rainfall and underlying basaltic rock.
• Soils developed at steep or very steep slopes of the hilly regions are susceptible to erosion (including landslips on some soils).
• ​Crops in Laterite – Lateritic Soils
• Laterite soils lack fertility due to intensive leaching.
• When manured and irrigated, some laterites are suitable for growing plantation crops like tea, coffee, rubber, cinchona, coconut, areca nut, etc.
• Red Soils
• Red soils along with their minor groups form the largest soil group of India.
• The main parent rocks are crystalline and metamorphic rocks like acid granites, gneisses, and quartzites.

The correct answer is CaO.

Key Points

• CaO+H₂O→Ca(OH)₂
• When slaked lime is added to water it turns into a suspension which is called “milk of lime”.
• Also, from above it is clear that calcium oxide and water react to form 'calcium hydroxide or slaked lime.
• Calcium hydroxide, also called slaked lime, Ca(OH)₂, is obtained by the action of water on calcium oxide.
• When mixed with water, a small proportion of it dissolves, forming a solution known as limewater, the rest remaining as a suspension called milk of lime.

Additional Information

• Ca(OH)₂ reacts vigorously with water to form slaked lime.
• Calcium hydroxide, also called slaked lime, Ca(OH)2, is obtained by the action of water on calcium oxide.
• When mixed with water, a small proportion of it dissolves, forming a solution known as limewater, the rest remaining as a suspension called milk of lime(Calcium hydroxide).
• Calcium hydroxide (traditionally called slaked lime) is an inorganic compound with the chemical formula Ca(OH)2.
• It is a colorless crystal or white powder and is produced when quicklime (calcium oxide) is mixed or slaked with water.
• It has many names including hydrated lime, caustic lime, builders' lime, slaked lime, cal, and pickling lime.
• Calcium hydroxide is used in many applications, including food preparation.
• Limewater, also called milk of lime, is the common name for a saturated solution of calcium hydroxide.

The figure is given below:-

Sunny faces east direction then move 45° clockwise direction and the move 135° anticlockwise direction. Now Sunny faces north direction.

Hence, "option 2" is the correct answer.

Shortcut Trick

Arrange the 12 scores in ascending order: 6, 8, 9, 9, 10, 11, 12, 15, 16, 16, 17, 21.

Since the number of observations is even (n = 12), the median is the average of the 6^th and 7^th terms.

Median = (11 + 12) ÷ 2 = 11.5.

∴ The correct answer is 11.5.

Alternate Method

Given: Points scored by 12 people = 6, 17, 8, 9, 16, 10, 15, 21, 9, 11, 12, 16.

Formula Used: For an even number of observations (n), Median = [(n/2)^th term + (n/2 + 1)^th term] ÷ 2.

⇒ Arrange the data in ascending order: 6,

Shortcut Trick

For n standard dice thrown simultaneously, the total number of outcomes in the sample space is given by 6ⁿ.

Here, the number of dice n = 4.

Total outcomes = 6⁴ = 6 × 6 × 6 × 6 = 1296.

∴ The correct answer is 1296.

Alternate Method

Given:

Number of dice thrown simultaneously = 4

Each die has 6 possible outcomes {1, 2, 3, 4, 5, 6}.

Formula Used:

Total outcomes in sample space = (Number of outcomes for one die)^{Number of dice}

Calculations:

⇒ Total outcomes = 6 × 6 × 6 × 6

⇒ Total outcomes = 36 × 36

⇒ Total outcomes = 1296

∴ The correct answer is 1296.

Additional Information

Fundamental Principle of Counting

If an event can occur in m ways and another independent event can occur in n ways, the total number of ways both can occur is m × n.

Coin Tossing Sample Space

For n coins tossed simultaneously, the total number of outcomes is 2ⁿ.

Sum of outcomes for 2 dice

When 2 dice are thrown, the total outcomes are 36, and the sum ranges from 2 to 12.

The correct answer is Neerja.

Key Points

• Neerja film won the Best Film award at the IIFA Awards ceremony in 2017.
• The film won two awards at the 64th ceremony of India's National Film Awards—Best Feature Film in Hindi and Special Mention for Kapoor.
• At the 62nd Filmfare Awards, Neerja won five awards, including Best Film (Critics) and Best Actress (Critics); the film was also nominated for Best Director and Best Film.

Additional Information

• The International Indian Film Academy Awards are a set of awards presented annually.
• It was created by Wizcraft International Entertainment Pvt. Ltd., which is an International Event Management Company.
• The awards are voted by fans online for the Indian film industry.
• Udta Punjab is a 2016 Indian crime film co-written and directed by Abhishek Chaubey.
• It is loosely based on and revolves around the drug abuse by the youth population in the Indian state of Punjab and the various conspiracies surrounding it.
• Pink is a 2016 Indian Hindi-language legal thriller film directed by Aniruddha Roy Chowdhury and written by Shoojit Sircar, Ritesh Shah, and Aniruddha Roy.
• Sultan ( transl. King) is a 2016 Indian Hindi-language sports drama film directed by Ali Abbas Zafar.
• Produced by Aditya Chopra under the Yash Raj Films.