RRC Group D Previous Year Paper 72 (Held On: 5 Nov 2018 Shift 2)

Shortcut Trick

In a 30°-60°-90° triangle, the ratio of sides opposite to these angles is 1 : √3 : 2.

The side adjacent to 60° (base) is 1 unit = 58 m.

The side opposite to 60° (height) is √3 units = 58√3 m.

∴ The correct answer is 58√3 m.

Alternate Method

Given:

Distance between tower and building (Base) = 58 m

Angle of depression = 60° ⇒ Angle of elevation from base to top = 60°

Formula Used:

tan(θ) = Perpendicular / Base

Calculations:

⇒ tan(60°) = Height / 58

⇒ √3 = Height / 58

⇒ Height = 58 × √3

⇒ Height = 58√3 m

∴ The correct answer is 58√3 m.

Additional Information

Angle of Depression

It is the angle formed between the horizontal line and the line of sight when looking down at an object. It is numerically equal to the angle of elevation due to alternate interior angles.

Trigonometric Ratios

For standard angles: tan 30° = 1/√3, tan 45° = 1, and tan 60° = √3. These are essential for solving Height and Distance problems.

The statement highlights that due to a shortage of water, people were asked to reduce water consumption.

• Thus, it is safe to assume that most people can reduce the consumption of water since the government wouldn't have issued an order in that regard if they would feel that consumption cannot be reduced. So, assumption 1 is implicit.
• From the data given in the statement, it cannot be assumed whether most people can or cannot protest against the order. The statement does not suggest any dissatisfaction of the people. Thus, assumption 2 is not implicit.

Hence the correct answer is option 2.

Shortcut Trick

Ratio of Speeds (Forward : Backward) = 8 : 6 = 4 : 3

Ratio of Time (Forward : Backward) = 3 : 4 (Inverse of speed ratio)

Total Time units = 3 + 4 = 7 units → 24.5 hours

1 unit = 3.5 hours → Time taken at 8 km/hr = 3 × 3.5 = 10.5 hours

Distance = Speed × Time = 8 × 10.5 = 84 km

∴ The correct answer is 84 km.

Alternate Method

Given: Forward Speed = 8 km/hr, Return Speed = 6 km/hr, Total Time = 24.5 hours

Formula: Distance (D) = [ (S₁ × S₂) ÷ (S₁ + S₂) ] × Total Time

⇒ Total Time = 24½ = 49/2 hours

⇒ D = [ (8 × 6) ÷ (8 + 6) ] × (49 / 2)

⇒ D = (48 ÷ 14) × 24.5

⇒ D = (24 ÷ 7) × 24.5

⇒ D = 24 × 3.5

⇒ D = 84 km

∴ The correct answer is 84 km.

Additional Information

Average Speed

When the distance is the same for both journeys, Average Speed = (2 × S₁ × S₂) ÷ (S₁ + S₂).

Relation between Speed and Time

For a constant distance, Speed is inversely proportional to Time (S₁/S₂ = T₂/T₁).

Relative Speed

If two objects move in opposite directions, relative speed is S₁ + S₂; if same direction, it is |S₁ − S₂|.

Shortcut Trick

Total items Nilanjani has = 10 items.

Items in Basket 1 (from S1) = 3 items.

Items in Basket 3 (from S2) = 5 items.

Items in Basket 2 = Total − (Basket 1 + Basket 3) = 10 − 8 = 2 items.

Both statements together are required to find the missing value of the second basket.

∴ The correct answer is Statements 1 and 2 both are sufficient.

Alternate Method

Given:

Total number of items = 10

Total number of baskets = 3 (Basket₁, Basket₂, Basket₃)

Formula Used:

Total items = Sum of items in all individual baskets

Total items = Items in (Basket₁ + Basket₂ + Basket₃)

Calculations:

⇒ Let the items in Basket 1, Basket 2, and Basket 3 be x, y, and z respectively.

⇒ x + y + z = 10

⇒ From Statement 1: x = 3 (3 packets of noodles)

⇒ From Statement 2: z = 5 (5 canisters)

⇒ Substitute values from both statements: 3 + y + 5 = 10

⇒ 8 + y = 10

⇒ y = 10 − 8 = 2

⇒ Since we used both statements to find y, both are necessary.

∴ The correct answer is Statements 1 and 2 both are sufficient.

Additional Information

Data Sufficiency Logic

In Data Sufficiency, a statement is sufficient if it uniquely determines the answer. If two variables are unknown, two independent equations or values are generally required.

Sum of Components

When a total is divided into 'n' parts, if 'n−1' parts are known, the 'nth' part can always be calculated using: Part_n = Total − (Sum of all other parts).

Independent Statements

Always check each statement individually first. If neither is sufficient alone, then combine them to see if they collectively provide the solution.

The correct answer is 30th

Key Points

• India is ranked 30th on a global manufacturing index, behind China in fifth place but ahead of other BRICS countries such as Brazil, Russia, and South Africa.
• In the WEF's first 'Readiness for the Future of Production' assessment, Japan was determined to have the best production structure, followed by South Korea, Germany, Switzerland, China, the Czech Republic, the United States, Sweden, Austria, and Ireland in the top ten.

Important Points

• World Economic Forum:
• Formation: January 1971
• Founder: Klaus Schwab
• Headquarters: Cologny, Switzerland

The logic followed here is:-

• In figures A, B, and C, mirror images are given.
• Figure D contains a water image of the mirror image of P.
• So, figure D is different from others.

Hence, "option 1" is the correct answer.

The logic followed here is:-

• The wrist is the ending joint of the arm whereas the shoulder is the beginning joint of the arm

Similarly,

• The ankle is the ending joint of the leg whereas the hip is the beginning joint of the leg

Hence, "option 1" is the correct answer.

Additional InformationJoints:

• Joints are where two bones meet.
• They make the skeleton flexible — without them, movement would be impossible.

Joints allow our bodies to move in many ways.

• Some joints open and close like a hinge (such as knees and elbows),
• whereas others allow for more complicated movement — a shoulder or hip joint, for example, allows for backward, forward, sideways, and rotating movement.

Joints are classified by their range of movement:

• Immovable, or fibrous, joints don't move.
• Partially movable, or cartilaginous (pronounced: kar-tuh-LAH-juh-nus), joints move a little.
• Freely movable, or synovial (pronounced: sih-NO-vee-ul), joints move in many directions.

Shortcut Trick

Saving in time = 2 hours = 4/5 of Train Time.

⇒ 4/5 × T_train = 2 hours ⇒ T_train = 2.5 hours.

Total time = 4 hours ∴ T_plane = 4 − 2.5 = 1.5 hours.

Entire journey by Plane takes 4 − 2 = 2 hours for 360 km → V_plane = 180 kmph.

Distance by Plane = 1.5 × 180 = 270 km.

Distance by Train = 360 − 270 = 90 km.

∴ The correct answer is 90 km.

Alternate Method

Given: Total Distance = 360 km, Total Time = 4 hours, Time saved by Plane = 2 hours.

Formula Used: Distance = Speed × Time; Time Saved = T_train − T_{equivalent plane time}

⇒ Let time spent on Train be T_t and Plane be T_p.

⇒ T_t + T_p = 4 hours.

⇒ Time saved = 4/5 × T_t = 2 hours.

⇒ T_t = (2 × 5) ÷ 4 = 2.5 hours.

⇒ T_p = 4 − 2.5 = 1.5 hours.

⇒ If entire 360 km is covered by Plane, time = 4 − 2 = 2 hours.

⇒ Speed of Plane (V_p) = 360 ÷ 2 = 180 kmph.

⇒ Distance by Plane = V_p × T_p = 180 × 1.5 = 270 km.

⇒ Distance by Train = Total Distance − Distance by Plane = 360 − 270 = 90 km.

∴ The correct answer is 90 km.

Additional Information

Average Speed

Average Speed = Total Distance ÷ Total Time. In this case, 360 ÷ 4 = 90 kmph.

Relative Speed

When moving in the same direction, relative speed is V₁ − V₂; in opposite directions, it is V₁ + V₂.

Speed-Time Inverse Relation

For a constant distance, speed is inversely proportional to time (V₁/V₂ = T₂/T₁).

The correct answer is 3.33 N.

Key Points

• Given:
• The object weighs on the surface of earth = 20 N
• Solution:
• The object on earth weighs = 20 N
• Weight = m x g
• where, m = mass of the object, g = acceleration due to gravity,
• Acceleration due to gravity on Earth = 6 x Acceleration due to gravity on the moon
• Hence,
• The object weighs on the moon = 20×1/6
• The object weighs on the moon = 10/3
• Therefore, Object weighs on moon = 3.33333 N

The direction diagram will be as follows:

• At point H, Mr. X is facing south.

Hence, "option 1" is the correct answer.

The correct answer is Inflation.

Key Points

• Inflation is defined as the rate at which prices rise over time. Inflation is usually defined as a wide measure of price increases or increases in the cost of living in a country.
• For some things, such as food, or services, like a haircut, it may be calculated more precisely.
• Inflation refers to how much a specific set of goods and/or services has become more expensive during a specific time period, most commonly a year.

Important Points

• Stagflation, often known as recession-inflation, occurs when inflation is high, economic growth slows, and unemployment is persistently high.
• The lack of excessive macroeconomic swings is defined as economic stability.
• Economic stability is defined as an economy with relatively consistent output growth and low and stable inflation.
• A drop in the overall price level of products and services is referred to as deflation. When the inflation rate goes below 0%, it is called deflation.

The correct answer is Sulfide.

Key Points

• The basis of froth flotation is based on the difference in wetting qualities of ore and gangue particles with water and oil.
• This process is utilized for metals whose ore is soaked in oil and whose gangue is soaked in water.
• The oil preferably wets the sulfide ores, whereas the water wets the gangue.
• The froth flotation procedure is primarily used to concentrate sulfide ores.
• This approach separates particles based on differences in the capacity of air bubbles in mineral water slurry to selectively bind to various mineral surfaces.

• The family tree is given below:-

• Among the given options, the most suitable one is maternal grandfather.

• Therefore, W's brother is Y's maternal grandfather.

Hence, "option 3" is the correct answer.

Shortcut Trick According to the Remainder Theorem, when f(x) is divided by (ax + b), the remainder is f(−b/a). Substitute 3x + 2 = 0 ⇒ x = −2/3 into the polynomial expression. Remainder = 27(−2/3)3 − 9(−2/3)2 + 3(−2/3) − 8 Remainder = 27(−8/27) − 9(4/9) − 2 − 8 = −8 − 4 − 2 − 8 = −22. ∴ The correct answer is −22. Alternate Method Given: Dividend f(x) = 27x3 − 9x2 + 3x − 8 and Divisor = 3x + 2. Formula: If a polynomial f(x) is divided by (ax + b), the remainder is f(−b/a).

⇒ Divisor: 3x + 2 = 0 ⇒ 3x = −2 ⇒ x = −2/3 ⇒ f(−2/3) = 27 × (−2/3)3 − 9 × (−2/3)2 + 3 × (−2/3) − 8 ⇒ f(−2/3) = 27 × (−8/27) − 9 × (4/9) + (−2) − 8 ⇒ f(−2/3) = −8 − 4 − 2 − 8 ⇒ Remainder = −22 ∴ The correct answer is −22. Additional Information Remainder Theorem It states that the remainder of the division of a polynomial f(x) by a linear polynomial (x − a) is equal to f(a). Factor Theorem A special case of the remainder theorem where if f(a) = 0, then (x − a) is a factor of the polynomial f(x). Division Algorithm For any polynomial, Dividend = (Divisor × Quotient) + Remainder, where degree(Remainder) < degree(Divisor).

Shortcut Trick

Total work = Charlie + Lola × 20

Work done in 15 days = 15/20 = 3/4 of total work.

Remaining work = 1 − 3/4 = 1/4.

Charlie finishes 1/4 work in 12 days.

Full work by Charlie alone = 12 × 4 = 48 days.

∴ The correct answer is 48 days.

Alternate Method

Given: Combined time = 20 days. Work done for 15 days.

Formula: Work = Efficiency × Time

⇒ Total Work = 20 units (assuming efficiency of both is 1 unit/day).

⇒ Work completed in 15 days = 1 × 15 = 15 units.

⇒ Remaining work = 20 − 15 = 5 units.

⇒ Charlie completes these 5 units in 12 days.

⇒ Charlie's efficiency = 5 ÷ 12 = 5/12 units/day.

⇒ Time taken by Charlie alone = Total Work ÷ Charlie's efficiency

⇒ Time = 20 ÷ (5/12) = 20 × (12/5) = 4 × 12 = 48 days.

∴ The correct answer is 48 days.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken. If a person completes work in 'n' days, their one-day work (efficiency) is 1/n.

Remaining Work Concept

If a fraction 'x/y' of work is finished, the remaining work is always (1 − x/y).

Combined Work Formula

If A takes 'a' days and B takes 'b' days, together they take (a × b) ÷ (a + b) days to complete the work.

Given that:-

• Total number of students = 850
• Muslim students = 44%
• Hindu students = 28%
• Sikh students = 10%
• Remaining students = (100 - 44 - 28 - 10)% = (100 - 82) = 18%
• Remaining students = ${850 × 18{} \over 100}$ = ${15300{} \over 100}$ = 153

Hence, "option 3" is the correct answer.

The correct answer is 2.

Key Points

• The number of moles present in 54 grams of aluminium is 2 moles.
• Number of Moles = Mass of Substance/ Mass of One mole.
• Mass of substance= 54 grams
• Mass of one mole(molar mass) aluminum= 27g.
• The number of moles= 54/27=2 moles
• Hence, Option 1 is correct.

Additional Information

• Aluminium:
• Aluminium is a chemical element with the symbol Al and atomic number 13.
• Aluminium is soft, non-magnetic, and ductile.
• Aluminium is the most plentiful metal in the earth's crust.
• It is found in the form of aluminium oxide in an ore called bauxite.
• Aluminium oxide is a chemical compound of aluminium and oxygen with the chemical formula Al2O3.
• Alumina and bauxite are the two main raw materials in the aluminium-making process.
• Aluminium is obtained by the electrolysis of alumina which extracts pure aluminium metal from alumina.

Given:

$\sqrt{1369}$ = 37

Calculation:

$\sqrt{13.69} + \sqrt{0.1369} + \sqrt{0.001369} +\sqrt{0.00001369} + 2$

⇒ 3.7 + 0.37 + 0.037 + 0.0037 + 2

⇒ 6.1107

∴ The required value of $\sqrt{13.69} + \sqrt{0.1369} + \sqrt{0.001369} +\sqrt{0.00001369} + 2$ is 6.1107.

Given:

The logic followed here is:-

• Adjacent faces should be:

From option 1:-

and 

 are opposite, so it is not correct.

From option 2:-

• This is the correct cube pattern.

From option 3:-

• Figure in option 3 when folded, gives the following cube and hence is incorrect:

From option 4:-

• Figure in option 4 when folded, gives the following cube and hence is incorrect:

Hence, "option 2" is the correct answer.

The correct answer is little Magician.

Key Points

• The film Little Magician was awarded the Best Film Award on Family Welfare at the National Film Awards 2017.
• Little Magician is a short film directed by Neha Sharma and based on ten-year-old Kanika.
• The 64th National Film Awards was an event at which the Directorate of Film Festivals presented its annual National Film Awards to recognize the best films in Indian cinema in 2016.
• The winners were revealed on April 7th, and the ceremony took place on May 3rd.

Key Points​

• The National Film Awards are India's most prestigious film honours.
• Since 1973, the Directorate of Film Festivals of the Indian government has been in charge of it, along with the International Film Festival of India and the Indian Panorama.
• Every year, the winning entry is chosen by a national panel appointed by the government, and the prizes are presented in New Delhi by the President of India.

Calculation:

$\frac{625}{8}$

⇒ 78.125

∴ The required value of $\frac{625}{8}$ is 78.125.

The correct answer is Vyas Samman 2016.

Key Points

• Surendra Verma, a well-known Hindi scholar, litterateur, and playwright, has been chosen for the prestigious Vyas Samman 2016.
• His novel Kaatna Shami Ka Vriksha: Padma Pankhuri Ki Dhar Se, which was released in 2010, was chosen for this honour.
• In 1991, the K.K. Birla Foundation established the Vyas Samman Award.
• It is an away every year to an Indian person who has written and published exceptional Hindi literary work in the previous ten years.
• A monetary reward of 2.5 lakh rupees, a citation, and a plaque are all included in the prize.

Important Points

• The Saraswati Samman is an annual literary prize for outstanding prose or poetry in any of India's 22 official languages, as mentioned in Schedule VIII of the Indian Constitution.
• The Bharatiya Jnanpith Honor is India's oldest and highest literary award, given annually to an author for "great contribution to literature" by the Bharatiya Jnanpith.
• The Sahitya Akademi, or National Academy of Letters of India, is a non-profit organization dedicated to promoting literature in Indian languages.
• It was founded on March 12, 1954, and is supported by the Indian government while remaining independent.
• Its headquarters are in Delhi's Rabindra Bhavan, near Mandi House.

Calculation:

Total production of R = (10 + 15 + 10 + 5) = 40 units

Production of R in the state B = 15 units

% = 15/40 × 100% = 37.5%

∴ 37.5% of state B is in the total production of grain R.

The logic followed here is:-

Hence, "option 4" is the correct answer.

The correct answer is Bangalore.

Key Points

• M. Chinnaswamy stadium (previously Karnataka State Cricket Association Stadium) is a cricket stadium in Bangalore, Karnataka.
• This five-decade-old stadium is located in the heart of Bangalore, surrounded by the gorgeous Cubbon Park, Queen's Road, Cubbon, and uptown MG Road.
• It holds 40,000 people and hosts Test cricket, One Day Internationals (ODI), Twenty20 Internationals (T20i), and other First-class cricket matches, as well as musical and other events.

Additional Information

List of some international cricket grounds in India

The correct answer is Only A is correct

Key Points

• The speed of sound depends on the properties of the medium through which it travels.
• The speed of sound in water (sea), the speed of sound is 1531 m/s.
• So A is correct.
• The velocity of a sound wave is affected by two properties of Material Type.
• Speed of Sound (m/s) in ethanol in 1207 m/s.
• So B is incorrect.

Sound: 

• It is a form of energy produced by vibration or disturbance that propagates in a medium.
• It travels in the form of longitudinal waves (Compression or rarefaction)

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.

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

Shortcut Trick

Ratio of coins (5 : 10 : 2 : 1) = 40% : 20% : 30% : 10% = 4 : 2 : 3 : 1

Ratio of values = (4 × 5) : (2 × 10) : (3 × 2) : (1 × 1) = 20 : 20 : 6 : 1

Total value units = 20 + 20 + 6 + 1 = 47 units → ₹940

1 unit = ₹20. Number of ₹5 coins = 4 × 20 = 80.

∴ The correct answer is 80 coins.

Alternate Method

Given: Total amount = ₹940. Percentage distribution of ₹5, ₹10, ₹2, and ₹1 coins is 40%, 20%, 30%, and remaining 10% respectively.

Let total number of coins be 'x'.

⇒ Total Value = (0.40x × 5) + (0.20x × 10) + (0.30x × 2) + (0.10x × 1)

⇒ 940 = 2.0x + 2.0x + 0.6x + 0.1x

⇒ 940 = 4.7x

⇒ x = 940 ÷ 4.7 = 200

⇒ Number of ₹5 coins = 40% of 200 = 0.40 × 200 = 80

∴ The correct answer is 80 coins.

Additional Information

Coin Problems Rule

Total Value = ∑(Number of coins × Denomination). If ratio of coins is a:b, then value ratio is (a × Val₁):(b × Val₂).

Percentage to Ratio

Always convert percentages to the simplest ratio to avoid heavy decimal calculations in competitive exams.

Ratio and Proportion

When values are given for parts of a whole, ensure the sum of parts (100% or ratio sum) matches the total quantity/value.

The logic followed here is:-

• Figures A, B, and C have two lines.

-  2 lines

 - 2 lines

 - 2 lines

• Figure D has 1 line.

 - 1 line

So, figure D is different from others.

Hence, "option 1" is the correct answer.

The correct answer is Sugarcane.

Key Points

• Uttar Pradesh is India's largest sugarcane growing state. In India, sugarcane is a vital crop.
• Sugarcane is used to make a variety of different goods, including sugar and jaggery.
• As of 2013-14, it accounted for around 38.61 percent of total sugarcane production. In terms of sugarcane production, India ranks second in the world.
• Sugar, Gur (Jaggery), Khansari, and molasses are all made using sugarcane as a raw material.
• Uttar Pradesh, Maharashtra, Karnataka, Tamil Nadu, Andhra Pradesh, Telangana, Bihar, Punjab, and Haryana are the major sugarcane-producing states in India.

The correct answer is The fuse will melt if the current exceeds 8A.

Key Points

• A fuse rated at 8A can withstand the heat generated by an 8A current flowing through its resistor for one second; But, if the current exceeds 8A, the heat generated will exceed the value it can withstand. As a result, the fuse wire will melt.
• If a wire is rated 8A, this indicates that the resistance has been set to the point where it will overheat and eventually burn out if 8A of current is sent through it.
• It is worth noting that the melting point of a wire is not entirely determined by the amount of current passing through it or the resistance of the wire. Rather, it is determined by the sum of these values.
• However, if a value is kept constant, such as resistance, a factor can be used for comparison.

The correct answer is 2.

Key Points

• The K shell of an atom can hold 2 electrons.
• The "K" shell is closest to the nucleus, whereas the "Q" shell is the furthest away.
• Those "n" values are also known as energy levels for simple atoms since they usually correspond to the row number on the periodic table.
• The second description examines how electrons behave within the shells.
• An electron shell is an orbit that electrons follow around an atom's nucleus.

Additional Information

• Each orbit can hold a maximum of 2n2 electrons, where n is number of orbit.
• The electronic configuration of an element gives the distribution of electrons in each of the orbits.

The electronic configuration of an element(Bohr-bury Rules):

• The electrons in an atom arranged by certain rules known as Bohr-bury rules.
• The electrons revolved in fixed orbit around the nucleus of an atom.
• The orbits are numbered from the center outward. The first orbit closest to the nucleus numbered as 1 and named it as K - shell, next is numbered as 2 and denoted as L - shell, the next with 3 as M - shell, 4 as N - shell and so on.
• The maximum number of electrons in the outermost shell cannot be exceed 8 and in the second last shell 18, irrespective of the shell number.

Shortcut Trick

Apply the direct algebraic identity: x² + y² = (x + y)² − 2xy

Substitute the given sum (15) and product (45):

Value = 15² − 2 × 45 = 225 − 90

Value = 135

∴ The correct answer is 135.

Alternate Method

Given:

Sum of variables (x + y) = 15

Product of variables (xy) = 45

Formula Used:

Standard expansion of a binomial square: (x + y)² = x² + y² + 2xy

Calculations:

⇒ (15)² = x² + y² + 2 × 45

⇒ 225 = x² + y² + 90

⇒ x² + y² = 225 − 90

⇒ x² + y² = 135

∴ The correct answer is 135.

Additional Information

Square of Difference Identity

The identity for the square of a difference is (x − y)² = x² + y² − 2xy. It can also be expressed as (x − y)² = (x + y)² − 4xy.

Sum and Difference of Cubes

Related higher-power identities include x³ + y³ = (x + y)(x² − xy + y²) and x³ − y³ = (x − y)(x² + xy + y²).

Product and Sum Relation

The value of x² + y² is always non-negative for real numbers x and y, which implies (x + y)² ≥ 2xy.

The logic followed here is:-

• People are entertained in theatres.

Similarly,

• People pray in temples.

Hence, "option 4" is the correct answer.

Shortcut Trick

Net profit percentage can be calculated using the successive percentage formula: a + b + (ab ÷ 100).

Here, Markup percentage (a) = +25% and Discount percentage (b) = −5%.

Profit% = 25 − 5 + (25 × (−5) ÷ 100)

Profit% = 20 − 1.25 = 18.75%.

∴ The correct answer is 18.75%.

Alternate Method

Given: Markup% = 25% and Discount% = 5%.

Formulas: MP = CP × (100 + Markup%) ÷ 100 | SP = MP × (100 − Discount%) ÷ 100 | Profit% = (SP − CP) ÷ CP × 100.

⇒ Let Cost Price (CP) be 100.

⇒ Marked Price (MP) = 100 + 25% of 100 = 125.

⇒ Selling Price (SP) = 125 − 5% of 125 = 125 − 6.25 = 118.75.

⇒ Profit = SP − CP = 118.75 − 100 = 18.75.

⇒ Profit% = (18.75 ÷ 100) × 100 = 18.75%.

∴ The correct answer is 18.75.

Additional Information

Relation between CP and MP

The ratio of Marked Price to Cost Price can be expressed as: MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

Marked Price & Discount

Discount is always calculated on the Marked Price (MP), whereas Profit or Loss is generally calculated on the Cost Price (CP).

The correct answer is 8th.

Key Points

• Articles 344 (1) and 351 of the Indian Constitution deal with languages.
• The eighth schedule, which recognizes 22 languages, includes them.

Important Points

• Any language designated by a state legislature as the official language of that state receives constitutional status as "Official languages" of the union under Article 345 of the Indian Constitution.
• The Union's official language will be Hindi written in Devanagari script. The international form of Indian numbers shall be utilized for official Union purposes.
• The Legislature of a State may, subject to the provisions of articles 346 and 347, adopt any one or more of the languages in use in the State, or Hindi as the language to be used for all or any of the State's official purposes: Provided, however, that the English language shall continue to be used for those official purposes within the State for which it was being used immediately before the commutation.

• The water image of the given word picture is:-

Hence, "option 2" is the correct answer.

• The number of routes by sea or road is not sufficient to determine the faster mode of transport between Muscat and Mumbai.

 Therefore, statement 1 alone is not sufficient.

• Reaching quickly from Mumbai to Muscat does not necessarily make the travel less expensive.

Therefore, statement 2 alone is not sufficient.

• When statements 1 and 2 are combined together, we cannot compare the expense of travelling via sea or road as neither statement offers any information to conclude this.

Hence, "option 1" is the correct answer.

The correct answer is Development of Affordable Urban Plans Using Remote Sensing and Geographic Information Systems.

Key Points

• In January 2018, Development of Affordable Urban Plans Using Remote Sensing and Geographic Information Systems is the first venture launched under the Global Initiative for Educational Networks (GIAN) program of the Ministry of Human Resource Development.
• The Ministry of Human Resources and Development's Global Initiative of Academic Networks (GIAN) program.
• In this national endeavor, IIT Kharagpur has taken the lead in coordinating the program across the country, and it has been a huge success.

Important Points

• The Government of India's Global Initiative of Academic Networks (GIAN) in Higher Education is a promising project run by the Ministry of Human Resource Development.
• GIAN intends to engage a talent pool of scientists, specialists, and entrepreneurs with India's higher education institutions in order to supplement the country's existing academic resources, speed up quality improvements and strengthen India's scientific and technical capabilities.

The correct answer is Sound wave.

Key Points

• Sound is a longitudinal wave in which the motion of the constituent particles of the medium is parallel to the energy transfer direction.
• Transverse waves are those in which the particles travel perpendicular to the direction of energy transport, such as light waves, string vibrations, and water surface ripples.
• Light and radio waves are two separate frequencies/wavelengths of electromagnetic radiation, which are made up of two components: electric and magnetic waves that are perpendicular to each other.

Important Points

• A transverse wave is a wave whose oscillations are perpendicular to the wave's advanced direction in physics.
• A longitudinal wave, on the other hand, travels in the direction of its oscillations.

The correct answer is India.

Key Points

• On January 19, 2018, India became the 43rd member of the Australia Group's export control regime.
• The inclusion is intended to boost India's nonproliferation profile and aid in the acquisition of crucial technology.
• Despite not being a party to the Non-Proliferation Treaty, India has been admitted to the Missile Technology Control Regime (MTCR), the Wassenaar Arrangement, and the Australia Group (NPT).

Additional Information

• The Australia Group is a multilateral export control regime (MECR) and an informal grouping of countries (now joined by the European Commission) established in 1985 (after Iraq's use of chemical weapons in 1984) to identify those exports to member states.
• To help what needs to be controlled so as not to contribute to the spread of chemical and biological weapons.

The correct answer is There is a single bond between the carbon atoms.

Key Points

• A saturated hydrocarbon is one in which all of the carbon-carbon bonds are single.
• A hydrocarbon is an organic substance with solely carbon and hydrogen as components.
• Saturated hydrocarbons are hydrocarbons in which all of the carbon atoms are bound to four other atoms and are 'saturated,' implying that there are no carbon-carbon multiple bonds in these organic compounds.
• A propane molecule may be shown to be 'saturated' with hydrogen atoms and cannot fit any more into the parent chain.

Important Points

• A few more saturated hydrocarbon examples are provided below.
• Butane (C₄H₁₀)
• Octane (C₈H₁₈)
• Cyclohexane (C₆H₁₂)
• Cyclopropane (C₃H₆)

The correct answer is Allahabad Bank.

Key Points

• Allahabad Bank was a nationalised Indian bank with headquarters in Kolkata.
• The bank, which was founded in Allahabad in 1865 and nationalised by the Indian government in 1969, offered banking and financial services for 155 years before merging with Indian Bank in 2020.
• It was also India's oldest joint-stock bank.
• CEO: S. S. Mallikarjuna Rao (19 Sept 2018–)

Important Points

The correct answer is Gene variant.

Key Points

• A variant form of a gene is known as an allele. Some genes exist in several distinct versions, all of which are found at the same genetic locus on a chromosome.

Important Points

• Humans are referred to as diploid organisms because they have two alleles at each genetic locus, one from each parent.
• For each gene, an individual inherits two alleles, one from each parent.
• The individual is homozygous for that gene if the two alleles are identical. The individual is heterozygous if the alleles are different.
• Though the term allele was originally intended to describe gene variation, it is now also used to denote variation in non-coding DNA sequences.

• Figure D which is the water image closely resembles the question figure.

Hence, "option 2" is the correct answer.

Shortcut Trick

Check for Pythagorean triplets where the difference between two sides is 7 cm.

The standard triplet 5, 12, 13 satisfies: 12 − 5 = 7 cm.

Area = 1/2 × 5 × 12 = 30 cm² (Matches given data).

Perimeter = 5 + 12 + 13 = 30 cm.

∴ The correct answer is 30 cm.

Alternate Method

Given:

Area = 30 cm², Difference (h − b) = 7 cm ⇒ h = b + 7

Formula Used:

Area of triangle = 1/2 × base × height

Pythagoras Theorem: k² = b² + h²

Calculations:

⇒ 30 = 1/2 × b × (b + 7)

⇒ 60 = b² + 7b

⇒ b² + 7b − 60 = 0

⇒ b² + 12b − 5b − 60 = 0

⇒ (b + 12)(b − 5) = 0 ⇒ Base (b) = 5 cm (since side cannot be negative)

⇒ Height (h) = 5 + 7 = 12 cm

⇒ Hypotenuse (k) = √(5² + 12²) = √(25 + 144) = √169 = 13 cm

⇒ Perimeter = 5 + 12 + 13 = 30 cm

∴ The correct answer is 30 cm.

Additional Information

Pythagorean Triplets

Sets of three integers (a, b, c) that satisfy a² + b² = c². Common examples: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25).

Perimeter of a Triangle

The sum of all three sides of a triangle. For a right-angled triangle, P = base + height + hypotenuse.

Quadratic Roots Shortcut

For ax² + bx + c = 0, identify factors of (a×c) that sum up to b to find the sides of the triangle quickly.

Shortcut Trick

Find the LCM of 15, 25, and 40 first.

LCM (15, 25, 40) = 600.

Check options for the smallest perfect cube divisible by 600.

27000 ÷ 600 = 45 (Divisible and a perfect cube 30³).

∴ The correct answer is 27000.

Alternate Method

Given: Numbers are 15, 25, and 40.

Formula Used: Prime factorization to find LCM and making powers multiples of 3 for a perfect cube.

⇒ Prime factors of 15 = 3¹ × 5¹

⇒ Prime factors of 25 = 5²

⇒ Prime factors of 40 = 2³ × 5¹

⇒ LCM = 2³ × 3¹ × 5² = 8 × 3 × 25 = 600

⇒ To make it a perfect cube, every prime factor power must be a multiple of 3.

⇒ Current powers: 2³ (already cube), 3¹ (needs 3²), 5² (needs 5¹).

⇒ Smallest Cube = (2³ × 3¹ × 5²) × (3² × 5¹)

⇒ Smallest Cube = 2³ × 3³ × 5³ = 8 × 27 × 125 = 27000.

∴ The correct answer is 27000.

Additional Information

Perfect Cube Property

A number is a perfect cube if the exponents of all its prime factors are multiples of 3.

LCM and HCF Relationship

The Least Common Multiple (LCM) is the smallest positive integer that is divisible by all numbers in a given set.

Smallest Square Number

To find the smallest square number divisible by a set, multiply the LCM by missing factors to make all prime exponents even.

The correct answer is 225 C.

Key Points

• Given:
• Current (I) = 0.75 A
• Time (t) = 5 min = 5 x 60 sec
• A current (I) is flowing through the filament of an electric bulb for time,
• I = $\frac{q}{t}$
• q = I x t
• q = 0.75 × 5 × 60sec
• q = 225 C
• The amount of electric charge flowing through the electric current = 225 C

Shortcut Trick

For a number to be divisible by 6, it must be divisible by its prime factors.

The factors of 6 are 1, 2, 3, and 6.

Since 6 = 2 × 3, any number divisible by 6 must be divisible by both 2 and 3.

∴ The correct answer is 2 and 3.

Alternate Method

Given: A number is divisible by 6.

Rule Used: Divisibility rule for composite numbers.

⇒ If a number is divisible by 6, it satisfies the condition of being even (divisible by 2) and having the sum of its digits divisible by 3.

⇒ Example: Take 12, 18, 24, 30.

⇒ 12 is divisible by 2 and 3.

⇒ 18 is divisible by 2 and 3.

⇒ Thus, the number is always divisible by 2 and 3.

∴ The correct answer is 2 and 3.

Additional Information

Divisibility Rule of 6

A number is divisible by 6 if it is divisible by both 2 (last digit is 0, 2, 4, 6, or 8) and 3 (sum of digits is a multiple of 3).

Composite Divisibility

If a number is divisible by two co-prime numbers a and b, then it is also divisible by their product (a × b).

Divisibility by 4

A number is divisible by 4 if its last two digits are divisible by 4. Note that not all numbers divisible by 6 are divisible by 4 (e.g., 18).

Shortcut Trick

Time for one pipe to fill half cistern = 2 hours.

For the remaining half, total pipes = 1 + 3 = 4 pipes.

Time taken by 4 pipes = 2 hours ÷ 4 = 1/2 hour = 30 min.

Total time = 2 hours + 30 min = 2 hr 30 min.

∴ The correct answer is 2 hr 30 min.

Alternate Method

Given: Filling time of one pipe = 4 hours.

Formula Used: Total Work = Efficiency × Time

⇒ Half cistern capacity = 4 ÷ 2 = 2 units.

⇒ Time taken by first pipe to fill 2 units = 2 ÷ 1 = 2 hours.

⇒ Remaining capacity = 2 units.

⇒ Total pipes opened now = 1 + 3 = 4 pipes.

⇒ Combined efficiency of 4 pipes = 4 × 1 = 4 units/hr.

⇒ Time for remaining half = 2 ÷ 4 = 1/2 hour = 30 minutes.

⇒ Total time = 2 hours + 30 minutes = 2 hr 30 min.

∴ The correct answer is 2 hr 30 min.

Additional Information

Combined Efficiency

When multiple pipes of the same capacity work together, their efficiencies are additive. Total Efficiency = n × Efficiency of one pipe.

Pipes and Cisterns

Filling pipes are taken as positive efficiency while outlet/leakage pipes are taken as negative efficiency.

Work Equality

M₁D₁H₁/W₁ = M₂D₂H₂/W₂ can be applied here considering the number of pipes as 'men'.

The correct answer is Uttar Pradesh.

Key Points

• Honorable President of India Ram Nath Kovind belongs to Uttar Pradesh.
• Ram Nath Kovind is an Indian politician who has been the country's 14th and current president since 2017.
• He is also the first President of India from the state of Uttar Pradesh.
• Prior to becoming president, he served as the 26th governor of Bihar from 2015 to 2017 and as a Rajya Sabha member from 1994 to 2006.
• He was a lawyer for 16 years before entering politics, practicing in the Delhi High Court and the Supreme Court of India until 1993.

Important Points

• The ceremonial head of state of India and commander-in-chief of the Indian Armed Forces is the president of India, officially the president of the Republic of India. 
• The president's office was established when India became a republic on January 26, 1950, when its constitution went into effect.

Given that:-

29 > 30 $ 5 < 4

• Putting the value on above equation:-

29 + 30 ÷ 5 - 4

• Apply BODMAS rule:-

= 29 + 6 - 4

= 35 - 4

= 31

Hence, "option 3" is the correct answer.

1. A appears at the second position.

• _ A ...
• Here, there is no information given about the letters of T, M, and E. Therefore, statement 1 alone is not sufficient.

2. E appears last.

• _ _ _ E(last)
• No information is given about the letters A, T, and M. Therefore, statement 2 alone is not sufficient.
• From statements 1, and 2:-
• T/M  A  M/T  E
• The first letter is either T or M. It is also possible that there are more than 4 letters in the word.

1. Here, statements 1, and 2 together are insufficient.

Hence, "option 1" is the correct answer.

The Venn diagram is given below:-

The F represents Football,

The H represents Hockey,

The B represents Basketball.

The total number of students who play F and B but not H is 13.

Hence, "option 4" is the correct answer.

The correct answer is Thallophytes.

Key Points

• Thallophytes are a non-motile polyphyletic group of organisms known as "thalloid plants," "very basic plants," or "lower plants.
• Lichens and algae, as well as bryophytes, bacteria, and slime molds make up an abandoned division of the Plantae kingdom.
• Thallophytes have a secreted reproductive system, so they are classified as part of the family Cryptogamae (together with ferns) rather than as Phanerogamae.

Important Points

• A pteridophyte is a vascular plant with xylem and phloem that disperses spores.
• Bryophytes, or small non-vascular plants, include mosses, liverworts, and hornworts.
• Angiosperms, or blooming plants, reproduce by the use of developed ovaries, or fruits, whereas gymnosperms, or vascular plants, reproduce by means of an exposed seed, or ovule.

The statement only talks about excessive use of sunscreen.

• Since excessive use of sunscreen is not good for the body, it is advisable that people avoid using it at least when they are exercising in the open air. This is a justifiable course of action and hence strong.
• Argument II states that sun rays are harmful so we should use sunscreen always, i.e. all the time, which is incorrect. Not all sunrays are harmful, and if sunscreen is used all the time, it will lead to deficiency of Vitamin D, the argument does not answer this fact. Hence, argument II is not strong.

Hence the correct answer is option 3.

• The family tree is given below:-

• S is the great-grandmother of Y.

Hence, "option 2" is the correct answer.

The least possible Venn diagram is given below:-

Conclusion:

I. Some soldiers are peons. → True ( Some peons are soldiers. So, we can say that some soldiers are peons.)

II. Some cooks are soldiers. → False (it is possible but not definite)

Hence, "option 1" is the correct answer.

The correct answer is Chemical energy is converted into muscular energy and then into kinetic energy.

Key Points

The sequence of the conversion of various forms of energy while cycling:

• At the start of the ride, the cyclist initially has chemical energy stored in his/her body as a result of the cyclist’s food intake.
• This chemical energy is converted by him/her into muscular energy due to which, he/she is able to apply force on the paddle during the cycling.
• This muscular energy in the cyclist is then converted to kinetic energy after the bike attains a certain velocity

The correct answer is Odometer.

Key Points

• An odometer is a device that measures a vehicle's distance travelled.
• The length is measured on a metre scale.
• However, it is unable to continuously gather information on how far a vehicle has travelled, making it unsuitable for tracking vehicle distance.

Important Points

• A vehicle's speed is measured using a speedometer.
• Temperature is measured with a thermometer.
• A tachometer is a mechanism that measures the rotation speed of a shaft or disc, such as in a motor.

The correct answer is The potential energy will remain constant.

Key Points

• The energy that exists in each object due to its position or shape is called potential energy.
• According to the question, increasing the velocity of an object moving at a certain height four times will change its kinetic energy and not the potential energy.
• Therefore, the potential energy of that object will remain constant. Hence, Option 1 is correct.
• Potential energy
• It is stored energy that depends upon the relative position of various parts of a system.
• Spring has more potential energy when it is compressed or stretched.
• A steel ball has more potential energy raised above the ground than it has after falling to Earth.

Shortcut Trick

Subtract the remainders from the numbers: 63 − 3 = 60, 77 − 5 = 72, 98 − 2 = 96.

Find the HCF of 60, 72, and 96.

Differences: 72 − 60 = 12, 96 − 72 = 24.

The HCF is 12 as it divides all three numbers perfectly.

∴ The correct answer is 12.

Alternate Method

Given: Numbers 63, 77, 98 and remainders 3, 5, 2.

Formula Used: Required Number = HCF((N₁ − R₁), (N₂ − R₂), (N₃ − R₃))

⇒ First number = 63 − 3 = 60

⇒ Second number = 77 − 5 = 72

⇒ Third number = 98 − 2 = 96

⇒ 60 = 2² × 3 × 5

⇒ 72 = 2³ × 3²

⇒ 96 = 2⁵ × 3

⇒ HCF = 2² × 3 = 4 × 3 = 12

∴ The correct answer is 12.

Additional Information

Highest Common Factor (HCF)

The largest number that divides two or more numbers without leaving any remainder is called their HCF or GCD.

HCF with Same Remainder

To find the greatest number which divides x, y, z leaving the same remainder 'r' in each case, the answer is HCF of (x−r), (y−r), and (z−r).

Least Common Multiple (LCM)

The smallest number which is exactly divisible by each of the given numbers. Relationship: LCM × HCF = Product of two numbers.

The correct answer is 2 February 2006.

Key Points

• Mahatma Gandhi Rural Employment Guarantee Act was launched on 2 February 2006.
• The National Rural Employment Guarantee Act of 2005 (or NREGA No 42, later renamed "Mahatma Gandhi National Rural Employment Guarantee Act" or MGNREGA) is an Indian labour law and social security measure aimed at ensuring the "right to work."
• This act was passed on August 23, 2005, by Prime Minister Dr. Manmohan Singh's UPA government.
• Gram panchayats would be the primary implementers of the MGNREGA (GPs). Contractor participation is prohibited.

The logic followed here is:-

• Left side of the diagonal is shaded from figure 1 to figure 2.

• Top side of the circle is shaded from figure 3 to figure 4.

Hence, "option 4" is the correct answer.

Given:

$1 - \frac{2}{3}\left( {1 - \frac{5}{6} \times 18} \right) + \frac{3}{2}$

Concept used:

Calculation:

$1 - \frac{2}{3}\left( {1 - \frac{5}{6} \times 18} \right) + \frac{3}{2}$

⇒ 1 - 2/3 (1 - 15) + 3/2

⇒ 1 + 28/3 + 3/2 

⇒ 71/6

∴ The required value of $1 - \frac{2}{3}\left( {1 - \frac{5}{6} \times 18} \right) + \frac{3}{2}$ is 71/6.

The pattern followed here is:

 - 4 aeroplanes: 1 red, 1 blue, 1 yellow and 1 green. 2.  - 4 aeroplanes: 1 red, 1 blue, 1 yellow and 1 green. 3.  - 4 aeroplanes: red, blue, yellow and green. 4. - 4 aeroplanes: 1 red, 2 blue, and 1 green

Hence, figure D is the correct answer.

Given:

The difference between the two different numbers is 5/9.

The smallest fraction is 5/6.

Calculation:

Let the larger number be x

Now, A/Q

x - 5/6 = 5/9

⇒ x = 5/9 + 5/6

Hence, the larger fraction = (5/9 + 5/6) = 25/18

∴ 25/18 is the larger fraction.

The correct answer is Germany.

Key Points

• Germany won the Confederations Football Cup in the men's category in 2017.

Additional Information

• The FIFA Confederations Cup was an international association football tournament for men's national teams, held every four years by FIFA. It was contested by the holders of each of the six continental championships (AFC, CAF, CONCACAF, CONMEBOL, OFC, and UEFA), along with the current FIFA World Cup holder and the host nation, to bring the number of teams up to eight.
• Between 2001 and 2017 (with an exception in 2003), the tournament was held in the country that would host the World Cup the following year, acting as a test event for the larger tournament.
• The last champions were Germany, who won the 2017 FIFA Confederations Cup by defeating Chile 1–0 in the final to win their first title.
• In March 2019, FIFA confirmed that the tournament would no longer be staged, with its slot replaced by an expansion of the FIFA Club World Cup, as well as the 2021 FIFA Arab Cup as a prelude to the 2022 FIFA World Cup.

The correct answer is Murshidabad.

Key Points

• Murshid Quli Khan declared himself the Nawab of Bengal and shifted his capital from Dhaka to Murshidabad.

Additional Information

• Murshid Quli Khan, also known as Mohammad Hadi and born as Surya Narayan Mishra, was the first Nawab of Bengal, serving from 1717 to 1727.
• Born a Hindu in the Deccan Plateau c. 1670, Murshid Quli Khan was bought by Mughal noble Haji Shafi.
• After Shafi's death, he worked under the Divan of Vidarbha, during which time he piqued the attention of the then-emperor Aurangzeb, who sent him to Bengal as the divan c. 1700.
• However, he entered into a bloody conflict with the province's subahdar, Azim-us-Shan.
• After Aurangzeb's death in 1707, he was transferred to the Deccan Plateau by Azim-us-Shan's father the Mughal Emperor Bahadur Shah I.
• The capital was shifted from Dhaka to Murshidabad.

The correct answer is Elephant.

Key Points

• The Bahujan Samaj Party is recognized by the symbol of the Elephant.

Additional Information

• The Bahujan Samaj Party (BSP) is a national-level political party in India that was formed to represent Bahujans referring to Scheduled Castes, Scheduled Tribes, and Other Backward Classes (OBC), along with religious minorities.
• According to Kanshi Ram, when he founded the party in 1984, the Bahujans comprised 85 percent of India's population but were divided into 6,000 different castes.
• The party claims to be inspired by the philosophy of Gautama Buddha, B. R. Ambedkar, Mahatma Jyotiba Phule, Narayana Guru, Periyar E. V. Ramasamy, and Chhatrapati Shahuji Maharaj.
• Its election symbol is an elephant.
• The same symbol was used by Dr. Ambedkar.

• The figure is given below:-

The total number of triangles of the above figure is 21.

Hence, "option 1" is the correct answer.

The correct answer is 500 N.

Key Points

• Given
• t 0.02 second
• Momentum = 10 kg ms^-1
• force (F) = change in momentum/ time=10/0.02=1000/2=500N. Hence, Option 3 is correct.

Additional Information

• Momentum
• It refers to the quantity of motion that an object has.
• If an object is in motion (on the move) then it has momentum.
• Momentum can be defined as "mass in motion."
• All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion.
• The amount of momentum that an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. Momentum depends upon the variables mass and velocity.
• In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object.
• Momentum = mass • velocity
• In physics, the symbol for the quantity momentum is the lower case p.
• Thus, the above equation can be rewritten as p = m • v
• where m is the mass and v is the velocity. The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity.

The correct answer is Gurinder Chadha.

Key Points

• Gurinder Chadha was awarded the Sikh Jewel Award in 2017.
• Gurinder Chadha who has treated us with bhaji on the Beach, Bend It Like Beckham, Bride, and Prejudice has been honored with the Sikh Jewel Award for 2017 for her immense contribution to British cinema.
• The world’s first annual Sikh Awards ceremony was held on October 10, 2010, as a tribute to the skills, achievements, and successes of the Sikh community.
• The event was organized by The Sikh Directory.

Additional Information

• Kuldip Kaur was an Indian film actress who worked in Hindi and Punjabi films.
• Known for her roles as negative characters, she was cited as Indian cinema's "most polished vamps" and actor Pran's "opposite number".
• Geeta Bali was an Indian film actress who appeared in Hindi language films.

Shortcut Trick

Multiply the first two terms: (3 − √5) × (2 + √5) = 6 + 3√5 − 2√5 − 5 = 1 + √5.

Now multiply the result with the third term: (1 + √5) × (1 − √5).

Use the Algebraic Identity (a + b)(a − b) = a² − b².

⇒ 1² − (√5)² = 1 − 5 = −4.

∴ The correct answer is -4.

Alternate Method

Given:

Expression = (3 − √5)(2 + √5)(1 − √5)

Formula Used:

1. FOIL Method: (a + b)(c + d) = ac + ad + bc + bd

2. Difference of Squares: (a + b)(a − b) = a² − b²

Calculations:

⇒ (3 − √5) × (2 + √5) × (1 − √5)

⇒ [3(2) + 3(√5) − √5(2) − (√5)(√5)] × (1 − √5)

⇒ [6 + 3√5 − 2√5 − 5] × (1 − √5)

⇒ (1 + √5) × (1 − √5)

Applying the Difference of Squares identity (a + b)(a − b) where a = 1 and b = √5:

⇒ (1)² − (√5)²

⇒ 1 − 5

⇒ −4

∴ The correct answer is -4.

Additional Information

Algebraic Identity

The product of the sum and difference of two terms is given by (a + b)(a − b) = a² − b².

Properties of Surds

The square of a square root of a number is the number itself: (√x)² = x.

Rationalizing Factor

For a Surd expression like (a + √b), its conjugate (a − √b) is its rationalizing factor because their product is a rational number.

The logic followed here is:-

Hence, "option 3" is the correct answer.

The argument suggests that students should remain unbiased i.e. they should not be partial or judgemental while reporting the feedback on their teacher. At the same time, it also means that they should not be afraid of reporting the feedback. Being neutral means stating the facts without bias.

• Assumption I suggests that students may be reluctant or unwilling to give a proper feedback if they are not asked for it, or not made aware of it. Since the argument is advising students to be neutral, assumption I logically agrees with it. So, argument I follows.
• Feedback reports from students will make the teacher understand how well she can reach the students, thus it will help them improve if there seems to be a need. So, assumption II also follows with the argument.

Hence the correct answer is option 1.

The correct answer is Only A is true.

Key Points 

Irreversible chemical reactions can occur in only one direction.

• The reactants can change to the products, but the products cannot change back to the reactants.

Reversible chemical reactions can occur in both directions.

• The reactants can change to the products, and the products can also change back to the reactants.​​
• Example
• N2(g) + 3H2(g) $\rightleftharpoons$  2NH3(g)
• Hence statement A is true.

2Mg(s) + O2(g) ⟶ 2MgO(s)

• Double Displacement Reaction - The two reactants exchange ions to form two new compounds in this reaction.
• In most cases, precipitation takes place.
• The reaction takes place in this manner-----> AB + CD → AD + CB
• Hence statement B is not true.

Additional Information

A  combination reaction is a reaction where two or more elements or compounds combine to form a single compound. Such reactions are represented by equations of the following form: X + Y → XY.

The combination of two or more elements to form one compound is called a combination reaction.

Other types of Chemical Reactions:

• Decomposition reaction: The opposite of a combination reaction, a complex molecule breaks down to make simpler ones.
• AB → A + B.
• Precipitation reaction: Two solutions of soluble salts are mixed resulting in an insoluble solid (precipitate) forming.
• A + Soluble salt B  → Precipitate + soluble salt C.
• Neutralization reaction: An acid and a base react with each other. Generally, the product of this reaction is salt and water.
• Acid + Base → Salt + Water.
• Combustion reaction: Oxygen combines with a compound to form carbon dioxide and water. These reactions are exothermic, meaning they give off heat. 
• A + O2 → H2O + CO2.
• Displacement reaction: One element takes place with another element in the compound. 
• A + BC → AC + B.

The correct answer is Mahendra and Sanghamitra.

Key Points

• Emperor Ashoka propagated the ideals of Buddhism. He sent missionaries to distant places so that people could inspire their lives by the teachings of Lord Buddha. His son Mahendra and daughter Sanghmitra were also included in these missionaries.
• He sent embassies to regions ruled by Greek kings like Antiochus II Theos of Syria, Ptolemy II Philadelphus of Egypt, Magas of Cyrene, Antigonus Gonrates of Macedonia, and Alexander of Epirus.
• His son Mahendra and daughter Sanghamitra were sent to Sri Lanka to spread the teachings of the Buddha.
• Ashoka wanted to spread the concept of Dhamma.
• So, he sends missionaries to spread the concept of Dhamma to unite the various sects and sections of the society and to promote the ideas of peaceful coexistence and universal brotherhood.

Additional Information

• Buddhism is an Indian religion or philosophical tradition based on a series of original teachings attributed to the 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 Basic Teachings of Buddha which are core to Buddhism are The Three Universal Truths; The Four Noble Truths; and • The Noble Eightfold Path.

Shortcut Trick

Ratio of Father and Son = 2 : 1

Product of ratio units = 2 × 1 = 2 units²

2 units² = 200 ⇒ 1 unit² = 100 ⇒ 1 unit = 10

Present ages: Father = 20, Son = 10

Ages after 5 years: (20 + 5) : (10 + 5) = 25 : 15 = 5 : 3

∴ The correct answer is 5 : 3.

Alternate Method

Given: Ratio = 2 : 1, Product = 200

Formula Used: Product of ages = (First Age) × (Second Age)

⇒ Let the present ages be 2x and x.

⇒ (2x) × (x) = 200

⇒ 2x² = 200

⇒ x² = 100

⇒ x = 10

⇒ Present age of Father = 2 × 10 = 20 years

⇒ Present age of Son = 1 × 10 = 10 years

⇒ Age after 5 years: Father = 25, Son = 15

⇒ Required Ratio = 25 : 15 = 5 : 3

∴ The correct answer is 5 : 3.

Additional Information

Ratio and Proportions

If the ratio of two quantities is a : b, they can be represented as ax and bx where x is the common multiplier.

Age Problems

To find the age after 'n' years, add 'n' to the present age. To find the age 'n' years ago, subtract 'n' from the present age.

Product of Ages

When multiplying terms in a ratio, ensure the variable power increases (e.g., x × x = x²).

The correct answer is Midnight Children.

Key Points

• Midnight Children's book is written by Salman Rushdie.
• Midnight's Children is a 1981 novel by author Salman Rushdie.
• It portrays India's transition from British colonial rule to independence and the partition of India.
• It is considered an example of postcolonial, postmodern, and magical realist literature.
• The story is told by its chief protagonist, Saleem Sinai, and is set in the context of actual historical events.
• The style of preserving history with fictional accounts is self-reflexive.
• Midnight's Children won both the Booker Prize and the James Tait Black Memorial Prize in 1981.

Additional Information

• Mohandas Karamchand Gandhi's My Early Life (1932)-an adaptation of his authoritative autobiography-is one of the earliest books developed by the Press in India.
• My tooth book was written by Mo Willems.
• A Million Mutinies Now is a nonfiction book by V. S. Naipaul published in 1990.
• It is a travelogue written during the author's sojourn in his ancestral land of India.

The correct answer is Urethra.

Key Points

• The urethra of the male reproductive system forms a single passage for both sperm and urine.
• The urethra is the final passage in the urinary tract.
• It extends from the apex of the trigone (internal meatus) of the bladder and opens into the vestibule of the valve as the external urethral meatus, in females, passes between the levator and muscle and is enclosed in the membranous sphincter of the urethra in the outer layer of the anterior vaginal wall.
• The urethra is tubular in shape and about 4cm long in females but becomes elongated during labor.

Additional Information

• The uterus is a hollow muscular organ located in the female pelvis between the bladder and rectum.
• Once the egg has left the ovary it can be fertilized and implanted in the lining of the uterus.
• The main function of the uterus is to nourish the developing fetus prior to birth.
• The vas deferens, or ductus deferens, is part of the male reproductive system of many vertebrates.
• The ducts transport sperm from the epididymis to the ejaculatory ducts in anticipation of ejaculation.
• Scrotum: The bag of skin that holds and helps to protect the testicles.
• The testicles make sperm and, to do this, the temperature of the testicles needs to be cooler than the inside of the body.

Shortcut Trick

By the standard algebraic identity: a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca).

If the condition a + b + c = 0 is given, the right-hand side (RHS) of the equation becomes 0.

⇒ a³ + b³ + c³ − 3abc = 0 × (a² + b² + c² − ab − bc − ca) = 0.

⇒ a³ + b³ + c³ = 3abc.

Comparing this with a³ + b³ + c³ = ? × abc, we get ? = 3.

∴ The correct answer is 3.

Alternate Method

Given: a + b + c = 0

Method: Value Substitution

⇒ Let us assume values for a, b, and c that satisfy the condition a + b + c = 0.

⇒ Let a = 1, b = 1, and c = −2.

⇒ Check: 1 + 1 + (−2) = 0 (Condition satisfied).

⇒ Now, calculate a³ + b³ + c³:

⇒ (1)³ + (1)³ + (−2)³ = 1 + 1 − 8 = −6.

⇒ Next, calculate the product abc:

⇒ 1 × 1 × (−2) = −2.

⇒ Substitute these values into the given expression: a³ + b³ + c³ = ? × abc

⇒ −6 = ? × (−2)

⇒ ? = −6 ÷ −2

⇒ ? = 3

∴ The correct answer is 3.

Additional Information

Conditional Identity

The expression a³ + b³ + c³ = 3abc also holds true if a = b = c, even if their sum is not zero.

Square of a Trinomial

A related identity is (a + b + c)² = a² + b² + c² + 2(ab + bc + ca). If a + b + c = 0, then a² + b² + c² = −2(ab + bc + ca).

Factorization Rule

The term (a² + b² + c² − ab − bc − ca) can also be written as ½[(a−b)² + (b−c)² + (c−a)²].

The correct answer is Vitamins.

Key Points

• Vitamin is not a macro nutrient.
• Macronutrients are the nutrients required by our bodies in large amounts.
• Examples include carbohydrates, proteins, fats, antioxidants, fiber, and water.
• Plant-based nutrients are essential in large quantities as our body cannot produce them by itself.
• Macro-nutrients provide energy and support the different metabolic systems, growth, and development of the body.
• Calcium, iron, vitamins, iron, minerals, and vitamin C are all micronutrients.
• Macronutrients are nutrients that are required in large amounts.
• Humans require three macronutrients: carbohydrates (sugar), lipids (fats), and proteins.

Shortcut Trick

Net efficiency = Efficiency of Tap A + Efficiency of Tap B − Efficiency of Tap C.

L.C.M of 8, 6, and 4 is 24 units (Total Capacity).

Net efficiency = 3 + 4 − 6 = 1 unit/hr.

Time required = 24 ÷ 1 = 24 hours.

∴ The correct answer is 24 hr.

Alternate Method

Given:

Time taken by Tap A = 8 hours

Time taken by Tap B = 6 hours

Time taken by Tap C (emptying) = 4 hours

Formula Used:

Efficiency = Total Work ÷ Time

Calculations:

⇒ Total Capacity of the tank = LCM(8, 6, 4) = 24 units

⇒ Combined efficiency of (A + B + C) = 3 + 4 − 6

⇒ Combined efficiency = 1 unit/hr

⇒ Time taken to fill the tank = Total Capacity ÷ Combined efficiency

⇒ Time taken = 24 ÷ 1 = 24 hours

∴ The correct answer is 24 hr.

Additional Information

Inlet and Outlet Pipes

An inlet pipe fills the tank (positive work), while an outlet pipe (leak) empties it (negative work).

Net Work Formula

If pipe A fills in 'x' hours and pipe B empties in 'y' hours, net work done in 1 hour = (1/x) − (1/y).

Pipes and Cisterns vs Time and Work

Concept is identical to Time and Work, where filling is positive efficiency and emptying is negative efficiency.

The statement makes a suggestion that if the quality of cinema is improved, then the number of viewers will increase.

• So, it can be assumed that cinema is a fair medium of entertainment because it can drive an audience and increase viewership when its quality is improved. Thus, assumption I is implicit.
• The statement has used the word "will", so it cannot be assumed that the quality of cinema has already improved. It is more of a suggestion or opinion. So, assumption II is not implicit.

Hence the correct answer is option 1.

Shortcut Trick

Time = 2 years 9 months = 2 + 9/12 = 11/4 years.

Net Rate of Interest = 8% × 11/4 = 22%.

Amount (in %) = 100% + 22% = 122%.

Given 122% = Rs. 915 ⇒ 1% = 915 ÷ 122 = 7.5.

Principal (100%) = 7.5 × 100 = Rs. 750.

∴ The correct answer is Rs. 750.

Alternate Method

Given:

Amount (A) = Rs. 915

Rate (R) = 8% per annum

Time (T) = 2 years 9 months = 2 + 9/12 = 2.75 years

Formula Used:

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

Amount (A) = P + SI = P × [1 + (R × T) ÷ 100]

Calculations:

⇒ 915 = P × [1 + (8 × 2.75) ÷ 100]

⇒ 915 = P × [1 + 22 ÷ 100]

⇒ 915 = P × [1 + 0.22]

⇒ 915 = P × 1.22

⇒ P = 915 ÷ 1.22

⇒ P = 750

∴ The correct answer is Rs. 750.

Additional Information

Simple Interest Definition

Simple interest is calculated only on the initial principal amount throughout the period: SI = (P × R × T) / 100.

Time Conversion

Always convert time into years if the rate is given per annum. Months ÷ 12 = years | Days ÷ 365 = years.

Amount Property

The amount is the sum of the principal and the interest earned: A = P + SI.

The correct answer is Options (A) (C) and (D).

Key Points

• Mole
• The amount of any substance that has the same basic unit (molecule/atom/ion) as the atom in 12 grams of carbon-12" is called a mole.
• It is equal to the gram atomic mass of the substance, equal to the gram molecular weight and 6.022x10²³ molecules of the substance. Hence, statements 1, 2, and 4 are correct and Statement 2 is not correct.
• It is also known as Avogadro Constant and is denoted by N_A.
• SI unit of Mole is mol.
• The word mole was coined by Wilhelm Ostwald, was a German chemist.
• In 1909 Ostwald was awarded the Nobel Prize for Chemistry for his work on catalysis, chemical equilibria, and reaction velocities.