RRC Group D Previous Year Paper 1 (Held On: 17 Sep 2018 Shift 1)

Shortcut Trick

In an Arithmetic Progression with 5 terms, the Average is always the middle term (C).

Average = 720 ÷ 5 = ₹144. So, C = ₹144.

Given E − A = 4d = 40, so common difference d = 10.

B = C − d = 144 − 10 = ₹134.

∴ The correct answer is ₹134.

Alternate Method

Given: Total sum = ₹720, Number of people = 5 (A, B, C, D, E), Difference E − A = ₹40.

Formula Used: Sum of AP = (n/2) × [2a + (n−1)d]

⇒ Let the amounts be a, a+d, a+2d, a+3d, a+4d.

⇒ E − A = 40 → (a + 4d) − a = 40 ⇒ 4d = 40 ⇒ d = 10.

⇒ Sum = 5a + 10d = 720.

⇒ 5a + 10(10) = 720 ⇒ 5a + 100 = 720.

⇒ 5a = 620 ⇒ a = 124.

⇒ B = a + d = 124 + 10 = 134.

∴ The correct answer is ₹134.

Additional Information

Arithmetic Progression Properties

For an odd number of terms in AP, the middle term is equal to the Average of the series (Sum ÷ n).

General Term of AP

The n^th term is given by T_n = a + (n − 1)d, where 'a' is the first term and 'd' is the common difference.

Sum of n terms

S_n = (n/2) × [first term + last term]. In this case, 720 = (5/2) × [A + E].

• Ranveer Singh portrayed the character of Allauddin Khilji in the controversial movie ‘Padmavat’.
• Ranveer Singh got the Filmfare Critics Award for the Best Actor in the year 2019 for portray of his role as Allauddin Khilji.

• India won 16 medals in US Open Karate Championship held in Las Vegas held April in the year 2017.
• India won three golds, two sliver and 11 bronze medals in the championship.

The correct answer is Arya Samaj.

Key Points

• Dayanand Saraswati founded the Arya Samaj in 1875 in Bombay.
• Arya Samaj was a reform movement within Hinduism.
• It aimed to promote values based on the Vedas and sought to rid Hinduism of practices like idol worship, caste discrimination, and ritualism.
• The motto of Arya Samaj was "Krinvanto Vishwam Aryam," meaning "Make the World Noble."
• Arya Samaj also emphasized education, social reform, and the empowerment of women.

Additional Information

• Brahmo Samaj: Brahmo Samaj was founded by Raja Ram Mohan Roy in 1828. It was a reform movement within Hinduism that focused on the worship of one God and opposed idol worship, caste discrimination, and superstitions. It played a significant role in modernizing Indian society.
• Chinmaya Mission: Chinmaya Mission was founded by Swami Chinmayananda in 1953. It focuses on spreading the teachings of Vedanta as expressed in the Bhagavad Gita and the Upanishads. The mission emphasizes spiritual growth and self-realization through education and service.
• Prarthana Samaj: Prarthana Samaj was founded in 1867 in Bombay by Atmaram Pandurang. It emphasized monotheism and opposed rituals, idol worship, and caste discrimination. It sought to reform Hinduism and promote social equality and justice.

• Let the mass of the earth be M.
• Mass of the other object on earth is m.
• We know the value of Gravitational Constant (G) = 6.67259 × 10^-11 Nm²/kg².
• We know the formula for the force between two objects (F) = G m¹ m²/r².
• Now the radius of the earth (r) = 6.3781 × 10⁶ m.
• We know that F = mg
• Now by substituting the values, we get mg = G M m/r².

M = g r²/G

M = (9.81) (6.3781 × 10⁶)²/6.67259 × 10^-11

M = 6 × 10²⁴ kg.

The mass of the earth (M) is 6 × 10²⁴ kg.

The pattern followed here is as follows:

Hence, “25S” is the correct answer.

• In the statement student 1 is asking for notes prepared by student 2 for studying, thus we can assume that student 2 “has prepared the notes”.
• The statement clearly mentions that student 1 wants the notes “to study”, hence we cannot assume that he “wants to verify his understanding”.
• Therefore, only assumption I is implicit.

Shortcut Trick

Relative speed (opposite direction) = Sum of individual speeds = Total distance ÷ Time taken.

Total Distance = 152.5 + 157.5 = 310 m

Combined Speed = 310 ÷ 9.3 = 100 ÷ 3 m/s

Convert to km/hr = (100 ÷ 3) × (18 ÷ 5) = 120 km/hr

∴ The correct answer is 120 km/hr.

Alternate Method

Train 1: 152.5 m

V₁

Train 2: 157.5 m

V₂

Total Distance = 152.5 + 157.5 = 310 m

Time taken to cross = 9.3 s

Given:

Length of the first train (L₁) = 152.5 m

Length of the second train (L₂) = 157.5 m

Time taken to cross each other (T) = 9.3 seconds

Formula Used:

When two objects move in opposite directions, their relative speed is the sum of their individual speeds.

Relative Speed = Total Distance ÷ Time

Total Distance = L₁ + L₂

Speed in km/hr = Speed in m/s × (18 ÷ 5)

Calculation:

⇒ Total Distance = 152.5 + 157.5

⇒ Total Distance = 310 m

⇒ Combined Speed (m/s) = 310 ÷ 9.3

⇒ Combined Speed (m/s) = 3100 ÷ 93 = 100 ÷ 3 m/s

⇒ Combined Speed in km/hr = (100 ÷ 3) × (18 ÷ 5)

⇒ Combined Speed in km/hr = 20 × 6 = 120 km/hr

∴ The correct answer is 120 km/hr.

Additional Information

Relative Speed in Opposite Directions

When two bodies travel in opposite directions, their relative speed is the sum of their individual speeds: S_relative = S₁ + S₂.

Relative Speed in Same Direction

When two bodies travel in the same direction, their relative speed is the difference of their individual speeds: S_relative = |S₁ − S₂|.

Speed Unit Conversion

To convert speed from km/hr to m/s, multiply by (5 ÷ 18). To convert speed from m/s to km/hr, multiply by (18 ÷ 5).

Trains Crossing a Stationary Object

When a train crosses a point-sized object (like a pole or man), the distance covered equals the length of the train. If it crosses a platform or bridge, the distance is the length of the train plus the length of the object.

Key Points

• The elements in 18 group of the periodic table have a complete Outer Shell.
• In the 18^th group of the modern periodic table, the noble gases placed.

There are 7 noble gases in the periodic table.

They are Helium (He) with atomic number 2,

• Neon (Ne) with atomic number 10,
• Argon (Ar) with atomic number 18,
• Krypton (Kr) with atomic number 36,
• Xenon (Xe) with atomic number 54,
• Radon (Rn) with atomic number 86,
• Ununoctium (Sun)/Oganesson (Og) with atomic number 118.

The pattern followed here is as follows,

Hence, “H19S” is the correct answer.

As per the given pattern figure B is the most possible correct answer.

From 1st figure to 2nd figure:

Similarly,

From 3rd figure to 4th figure:

Hence, “B” is the correct answer.

Key Points

• Atomic Mass of the Hydrogen = 1
• Atomic Mass of the oxygen = 16

Explanation:

1 mole of hydrogen = 1gm

1 mole of oxygen = 16gm

Water (H2O) = 2 Hydrogen atoms + 1 Oxygen atom

2 mole of hydrogen = 2gm

1 mole of oxygen = 16 gm

The ratio of the mass of Hydrogen: Ratio of mass of Oxygen =  2/16 = 1/8 

The ratio of the mass of Hydrogen to the mass of Oxygen in water is always 1:8.

Animals from class Aves are warm-blooded.

• Aves class represents birds and their characteristic features are feathers, a beak, and the forelimbs are modified into wings.
• They are warm-blooded animals i.e. they will be able to maintain constant body temperature.

• The United States of America (USA) host the Academy (Oscars) Awards for excellence in the cinema every year.
• The 91^st Academy Awards were presented at the Dolby Theatre in Los Angeles, California.
• Best Picture – Green Book.
• Best Actor in a Leading Role – Rami Malek for Bohemian Rhapsody.
• Best Actress in a Leading Role – Olivia Colman for The Favourite.
• Best Directing – Alfonso Cuarón for Roma.
• Best Supporting Actor – Mahershala Ali for Green Book.

Shortcut Trick

Twin Primes are pairs of prime numbers that differ by exactly 2.

Check the difference between given pairs:

(37, 41) → diff = 4 | (3, 7) → diff = 4 | (43, 47) → diff = 4 | (71, 73) → diff = 2.

Since 71 and 73 are both prime numbers and their difference is 2, they are twin primes.

∴ The correct answer is (71, 73).

Alternate Method

Given: Four pairs of numbers to identify Twin Primes.

Condition for Twin Primes:

1. Both numbers in the pair must be Prime (divisible only by 1 and itself).
2. The absolute difference between the numbers must be 2.

Evaluating the options:

⇒ Option 1: (37, 41) → Both are prime, but 41 − 37 = 4 (≠ 2).

⇒ Option 2: (3, 7) → Both are prime, but 7 − 3 = 4 (≠ 2).

⇒ Option 3: (43, 47) → Both are prime, but 47 − 43 = 4 (≠ 2).

⇒ Option 4: (71, 73) → 71 is prime, 73 is prime, and 73 − 71 = 2.

∴ The correct answer is (71, 73).

Additional Information

Prime Numbers

A Prime Number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Co-prime Numbers

Two numbers are Co-prime if their Highest Common Factor (HCF) is 1. Example: (8, 9).

Prime Triplet

A Prime Triplet is a set of three prime numbers of the form (p, p+2, p+6) or (p, p+4, p+6). The only triplet with difference 2 is (3, 5, 7).

• The number of water molecules present is washing soda is 10.
• We know the molecular formula for Washing Soda is Na₂CO₃.10H₂O.
• Recrystallisation of Sodium Carbonate (Na₂CO₃) gives washing soda.
• In a Washing soda, water is present in the form of crystals.

• Satyawart Kadiyan is related to Wrestling sport.
• He was given Arjuna Award in 2017.
• He was married to Olympic bronze medallist Sakshi Malik in 2017.

• Aluminium (Al) metal reacts with steam to form a metal oxide and hydrogen.
• This reaction can be given as

2Al + 3H₂O (g) → Al₂O₃ + 3H₂ (g)

• Other metals of this type are Iron (Fe) and Zinc (Zn).
• But these metals do not react with either hot or cold water.

Silver, Lead and Copper do not react with water whether the water is in the form of liquid or gas.

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Shortcut Trick

Shift one vertex to the origin (0, 0) by subtracting its coordinates from all vertices.

Subtract (1, 2) from all: (1−1, 2−2) → (0, 0) | (−4−1, −3−2) → (−5, −5) | (4−1, 1−2) → (3, −1).

Area = 1/2 |x₁y₂ − x₂y₁| = 1/2 |(−5 × −1) − (−5 × 3)|.

Area = 1/2 |5 − (−15)| = 1/2 |20| = 10 sq. units.

∴ The correct answer is 10 sq. units.

Alternate Method

Given: Vertices of the triangle are A(1, 2), B(−4, −3), and C(4, 1).

Formula Used: Area of triangle = 1/2 |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|

⇒ Area = 1/2 |1(−3 − 1) + (−4)(1 − 2) + 4(2 − (−3))|

⇒ Area = 1/2 |1(−4) + (−4)(−1) + 4(2 + 3)|

⇒ Area = 1/2 |−4 + 4 + 4(5)|

⇒ Area = 1/2 |0 + 20|

⇒ Area = 1/2 × 20 = 10 sq. units.

∴ The correct answer is 10 sq. units.

Additional Information

Shoelace Formula

Here, the objective is to make homes energy efficient for sustainable development.

• Replacing incandescent light bulbs with energy-efficient compact fluorescent lamps (CFLs) is suggested considering the statement says that making homes energy-efficient is important for sustainable development.

Therefore, assumption I is implicit in the statement.

• One cannot relate the auspiciousness of good landscaping around one's house on the west side with efficient energy consumption at home using the information from the statement.

Therefore, assumption II is not implicit

Hence, only assumption I is implicit.

• The honourable President of India, Ram Nath Kovind felicitated 112 exceptional woman achievers and titled them as "First Ladies" of the country.
• Those included Miss World 1994 Aishwarya Rai Bachchan and Miss Earth 2010 Nicole Faria.
• The award ceremony was hosted by Minister of Women and Child Development, Shri Maneka Sanjay Gandhi, who felicitated and congratulated the women achievers.

Shortcut Trick

Co-prime numbers are defined as numbers having no common factor other than 1.

By definition, the Highest Common Factor (HCF) of any two co-prime numbers is always 1.

Example: 8 and 15 are co-prime; Factors of 8 (1, 2, 4, 8) and 15 (1, 3, 5, 15) share only 1.

∴ The correct answer is 1.

Alternate Method

Given: Two numbers are co-prime.

Concept: Two numbers are said to be co-prime if their greatest common divisor is 1.

⇒ Let the numbers be x and y.

⇒ If x and y are co-prime, factors of x ∩ factors of y = {1}.

⇒ Highest Common Factor (HCF) = 1.

∴ The correct answer is 1.

Additional Information

LCM of Co-prime Numbers

The Least Common Multiple (LCM) of two co-prime numbers is always equal to their product (x × y).

Consecutive Numbers

Any two consecutive natural numbers (e.g., 14 and 15) are always co-prime to each other.

Prime Numbers Property

Any two distinct prime numbers are always co-prime, as they only have 1 as a common factor.

• The resistance of a conductor does not depend upon pressure.
• The type of material defines an element as either Conductor or Insulator or semiconductor.
• We know the formula Resistance (R) =  pL/A.
• Where p is resistivity, L is the length and A is Area of Cross section.

Shortcut Trick

Using Trigonometric Identity: sin²Ø + cos²Ø = 1.

Given expression: (cos²Ø + sin²Ø) + 17 = x.

⇒ 1 + 17 = x ⇒ x = 18.

⇒ x² = 18² = 324.

∴ The correct answer is 324.

Alternate Method

Given: (cos²Ø + 1/cosec²Ø) + 17 = x

Formula Used: sinØ = 1/cosecØ and sin²Ø + cos²Ø = 1

⇒ x = (cos²Ø + sin²Ø) + 17

⇒ x = 1 + 17

⇒ x = 18

⇒ x² = (18)²

⇒ x² = 324

∴ The correct answer is 324.

Additional Information

Reciprocal Identities

Basic reciprocal relations: sinØ = 1/cosecØ, cosØ = 1/secØ, and tanØ = 1/cotØ.

Pythagorean Identities

Standard identities: sin²Ø + cos²Ø = 1, 1 + tan²Ø = sec²Ø, and 1 + cot²Ø = cosec²Ø.

Squares of Numbers

It is helpful to memorize squares up to 30: 17² = 289, 18² = 324, 19² = 361.

• Weight is a measure of the force of gravity acting on an object.

Concept:

Explanation:

From the above explanation, we can see that

The gravitational pull by the earth is equal to the weight of the object.

The weight of any object on the planet is given by:

Weight (W) = m g = Force due to gravity

Where

m is mass

g is acceleration due acceleration of the planet.

• The Figure A, C, and D have the 2 Trapezium but Problem Figure has 3 Trapezums.

In Problem Figure:

In Figure B:

Here, figure B has the closest resemblance to the question figure.

Hence, “B” is the correct answer.

• The theme of the 2016 Indian Film Festival of Melbourne (IFFM) was ‘Female Empowerment’.
• Along with Sonam Kapoor, Nawazuddin Siddiqui won the Best Actor (Male) award.
• IFFM is presented by the State Government of Victoria to foster close ties between India and Australia film industries.

We can count triangles in the given figure as follows,

Clearly, we can say that there are “27” triangles in the given figure.

• Sai Praneeth was the badminton player that won his maiden Super Series title in Singapore in April 2017.
• Sai Praneeth beat fellow Indian Kidami Srikanth to win his first maiden Super Series title.

Let the weight of each box be x.

Statement 1:

⇒ (1/3) × x = 10

⇒ x = 30 kg

As, each box weighs the same, total weight of 20 boxes can be calculated

∴ Statement 1 alone is sufficient

Statement 2:

⇒ Weight of 6 boxes = weight of 4 boxes + 40

⇒ 6x = 4x + 40

⇒ 2x = 40

⇒ x = 20

As, each box weighs the same, total weight of 20 boxes can be calculated

∴ Statement 2 alone is also sufficient

• Oxygen is liberated during Photosynthesis.
• Photosynthesis is the process through which green plants manufacture food by converting solar energy into chemical energy.
• In this process, water and carbon dioxide react in the presence of sunlight to give off oxygen and form glucose molecules.
• Photolysis of water is the source of oxygen liberated in photosynthesis.

CONCEPT:

• Sound: A local disturbance whose propagation is facilitated by the collisions between particles this disturbance propagates in a longitudinal wave, imagine one molecule hitting the next molecule, and then that molecule hitting the next, and so forth.
• It is a mechanical wave that needs a medium to travel.
• The speed of sound is maximum in solid then it is in liquid and slowest in gases.
• Speed of sound: The distance traveled per unit time by sound waves as it propagates through an elastic medium.

The velocity of sound  in a gaseous medium is given by:

$\Rightarrow v=\sqrt {\frac {γ P}{ρ}}$

Where P = pressure, ρ = density, and γ = ratio of two principal specific heats of the gas

• The speed of sound remains almost the same for all frequencies in a given medium under the same physical conditions.
• A state of matter is one of the distinct forms in which matter can exist.
• The four fundamental states of matters are - solids, liquids, gases, and plasma.

EXPLANATION:

• Solid-state is one of the four fundamental states of matter, in which the constituent particles (ions, atoms, etc) are closely packed together.
• The speed of sound is maximum in solids and least in gases. So option 4 is correct.

EXTRA POINTS

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

Concept Used:

a/b and c/d are two numbers,

then (a × d) and (b × c) are need to be compared.

Calculation:

We have, 9/16 and 13/24 

⇒ 9 × 24 = 216

⇒ 13 × 16 = 208

⇒ 216 > 208

⇒ 9/16 > 13/24.

∴ Option 3 is correct.

Concept:

Work done: 

Work is said to be done when a force applied on the body displaces the body through a certain distance in the direction of a force.

• $Work;done;\left( W \right) = \vec F \cdot \vec s\cos \theta = Fs;cos\theta$
• Where F = force, s = distance, and cos θ = angle between F and s.
• The SI unit of work done is N-m or Joule (J).

Key Points Work is done whenever the given condition is satisfied:

(i) A force should act on an object

(ii) There is a displacement of the body caused by the applied force along the direction of the applied force.

Explanation:

Here,

1. A force has acted on an object without causing any displacement of it. - Doesn't satisfy the condition.
2. Only when an object is displaced. - Doesn't satisfy the condition.
3. Only when force has acted on the object. - Doesn't satisfy the condition.
4. Any of the above - Doesn't satisfy the condition.

So the correct option is None of the above.

It will only be true when force is applied and displacement is in the direction of the force.

(The original question has been asked in Railways Group D but due to discrepancy, the question has been rejected. we have updated the question to make it correct)

• The launching of a rocket illustrates Newton’s third law of motion.
• Newton's Third Law of Motion states that 'To every action, there is an equal and opposite reaction'.
• When the rocket is ignited, it releases gases from its thrusters thereby creating a force that will push rocket upwards.
• A fielder pulling his hand back while catching a ball is an application of Newton's second law of motion.
• Newton's Second Law of motion states that the rate of change of momentum of an object is proportional to the applied force in the direction of the force. i.e. F=ma. Where F is the force applied, m is the mass of the body, and a is the acceleration produced.
• When a bus starts suddenly, the passengers receive a backward jerk an application of Newton's first law of motion.
• Newton First law states that Every object remains in uniform motion in a straight line unless compelled to change its state by the action of an external force.
• When we stop pedalling, the bicycle slows down due to the frictional force acting on the bicycle.

• A committee under the chairmanship of Uday Kotak was constituted in 2017 to improve efficiency in Corporate Governance.
• SEBI has set up a committee under the chairmanship of Uday Kotak, executive vice chairman and managing director of Kotak Mahindra Bank Ltd, to advise it on issues relating to corporate governance in Indian firms.
• The 21-member panel includes representatives from other companies, stock exchanges, professional bodies, investor groups, law firms, academicians, research professionals and SEBI officials.

Important Points

• About SEBI: As of May 2022
• Chairman- Madhabi Puri Buch
• Founded- 1992
• Headquarters - Mumbai Maharashtra

The correct answer is the uterus.

Key Points

• The fertilised egg, the zygote, gets implanted in the uterus.
• The egg is fertilized up in the fallopian tube then travels to the uterus and it implants in the tissue lining the uterus.
• When the fertilized egg pushes itself into the tissue on the wall of the uterus, it is called implantation

Additional Information

• When a body moves on a circular path, the force that acts on the revolving body towards the centre is called centripetal force.
• The Centripetal force is required to maintain a body in Uniform Circular Motion.
• Centripetal Force acts when a body moves around in a circular path, the force that causes this acceleration and keeps the body moving along a circular path is acting towards the centre

Concept used:

Calculation:

\(56 \div \left[\frac{1}{3}\left{ {15 + 12 - \left( {9 + 6 - \overline {5 + 7} } \right)} \right} \right] \)

⇒ 56 ÷ [(1/3){15 + 12 - (9 + 6 - 12)}]

⇒ 56 ÷ [(1/3){15 + 12 - (15 - 12)}]

⇒ 56 ÷ [(1/3){15 + 12 - 3}]

⇒ 56 ÷ [(1/3){27 - 3}]

⇒ 56 ÷ [(1/3)(24)]

⇒ 56 ÷ 8

⇒ 7 

∴ ? = 7

Important Points

If in any simplification problem there is (  ̅  ) bar sign above any operation then we should perform the operation at the beginning, whatever the operation is. Then we will follow the chart given above.

• Indore was the first city in India to use a robot for traffic control.
• It is a 14-foot-tall robot that has an inbuilt public address system and has cameras.
• It can also issue challans to traffic offenders.

Venn diagram:

Conclusions:

I. All flowers are yellow → False (it is possible but not definite)

II. All yellows are petals → False (it is possible but not definite)

Hence, none of the conclusion follows.

• Amazon became the second to hit $900 billion market capitalisation after Apple.
• Amazon is an e-Commerce company based in Seattle in the United State of America.
• Its founder Jeff Bezos is the richest person on the earth.

• The Union Textiles Minister Smriti Irani has launched PowerTax India Scheme to boost power loom sector.
• It was launched by her in Bhiwandi, Thane district, Maharastra.
• It also launched simultaneously across 43 location across in India.
• The comprehensive scheme has the following components
• In-situ Upgradation of Plain Powerlooms.
• Group Workshed Scheme (GWS).
• Yarn Bank Scheme.
• Common Facility Centre (CFC).
• Pradhan Mantri Credit Scheme for Powerloom Weavers.
• Solar Energy Scheme for Powerlooms.
• Facilitation, IT, Awareness, Market Development and Publicity for Powerloom Schemes.
• Tex Venture Capital Fund.
• Grant-in-Aid and Modernisation & Upgradation of Powerloom Service Centres (PSCs).

• The State Government of Maharashtra launched the ‘Quit India movement 2 from Swaraaj to Suraaj initiative at the historic August Kranti Maidan in August 2016.
• It was launched to against various social evils to commemorate the Platinum Jubilee Anniversary of the Quit India movement launched in August Kranti Maidan in 1942.

• British journalist and former BBC India correspondent Sir William Mark Tully had been awarded for 2018 RedInk award for lifetime achievement in journalism.
• Tully worked with the BBC for 30 years before resigning in July 1994. He held the position of Chief of Bureau, BBC, Delhi, for 20 years.
• The RedInk awards for excellence in journalism are given by the Mumbai Press Club.

Here, horse, monkey and tiger all are animals but there is no connection between them.

Therefore, “option 1” is the best suitable venn diagram.

Shortcut Trick

Use the direct formula for two people where one person's time is to be found: (A × B) ÷ (B − A).

Here, Rohan + Rohit = 10 days and Rohan = 15 days.

⇒ Rohit = (15 × 10) ÷ (15 − 10)

⇒ Rohit = 150 ÷ 5 = 30 days.

∴ The correct answer is 30 days.

Alternate Method

Given:

Time taken by Rohan and Rohit together = 10 days

Time taken by Rohan alone = 15 days

Formula Used:

Total Work = LCM of individual days

Efficiency = Total Work ÷ Time

Calculations:

⇒ Efficiency of Rohit = Efficiency of (Rohan + Rohit) − Efficiency of Rohan

⇒ Efficiency of Rohit = 3 − 2 = 1 unit/day

⇒ Time taken by Rohit alone = Total Work ÷ Efficiency of Rohit

⇒ Time taken by Rohit = 30 ÷ 1 = 30 days

∴ The correct answer is 30 days.

Additional Information

Work and Efficiency Relationship

Efficiency is inversely proportional to the time taken to complete a work. If a person finishes work in n days, their 1-day work is 1/n.

Combined Work Formula

If A takes x days and B takes y days, together they take (xy) ÷ (x + y) days to complete the same work.

LCM Method for Total Work

Taking the LCM of the given number of days as Total Work simplifies calculations by using whole number efficiencies instead of fractions.

Shortcut Trick

For semi-annual compounding, rate r = 10% ÷ 2 = 5% and periods n = 2 × 2 = 4.

Use the Ratio Method for 4 periods → 4 : 6 : 4 : 1

1st part: 5% of 1,60,000 = 8,000 | 2nd: 5% of 8,000 = 400 | 3rd: 5% of 400 = 20 | 4th: 5% of 20 = 1

CI = (8,000 × 4) + (400 × 6) + (20 × 4) + (1 × 1) = 32,000 + 2,400 + 80 + 1 = ₹34,481.

∴ The correct answer is ₹34,481.

Alternate Method

Given: Principal (P) = ₹1,60,000, Rate (R) = 10% p.a., Time (T) = 2 years.

For semi-annual compounding, the rate is halved and time is doubled:

⇒ Effective Rate (r) = 10% ÷ 2 = 5% per half-year.

⇒ Number of periods (n) = 2 × 2 = 4 half-years.

Formula: Amount (A) = P × (1 + r/100)ⁿ

⇒ A = 1,60,000 × (1 + 5/100)⁴

⇒ A = 1,60,000 × (21/20)⁴

⇒ A = 1,60,000 × (194481 ÷ 160000)

⇒ A = ₹1,94,481

⇒ Compound Interest (CI) = A − P

⇒ CI = 1,94,481 − 1,60,000 = ₹34,481

∴ The correct answer is ₹34,481.

Additional Information

Compounding Periods

If interest is compounded quarterly, the rate becomes R/4 and time becomes 4T. For monthly, it is R/12 and 12T.

Effective Rate of Interest

When compounded semi-annually, the effective annual rate is (1 + r/200)² − 1. Here, 5% twice gives 10.25% annually.

CI vs SI for 2 Years

The difference between CI and SI for 2 years is given by the formula: Difference = P × (R/100)².

The given statement is a proverb which means that everything which looks attractive need not be valuable or the appearance of a person need not be a good indicator of his/her nature.

Clearly, both the given conclusions have comprehended the meaning properly.

Hence, both conclusions I and II follow.

CONCEPT:

• Work-energy theorem: It states that the sum of work done by all the forces acting on a body is equal to the change in the kinetic energy of the body i.e.,

Work done by all the forces = Kf - Ki

$W = \frac{1}{2}m{v^2} - \frac{1}{2}m{u^2} = {\bf{Δ }}K$

Where v = final velocity, u = initial velocity and m = mass of the body

EXPLANATION:

Given that:

• Mass of the Object (m) = 1 kg
• Initial velocity of the object (u) = 4m/s
• Final velocity of the object (v) = 8m/s
• Total net work is done W _(net) = Kinetic energy (During final velocity) – Kinetic Energy (During Initial Velocity).
• Now by substituting the values in the above equation, we get

W_(net) = ½ mv² – ½ mu²

= ½ (1)×(8)² – ½ (1)×(4)²

= 32 - 8 Joule

= 24 Joules.

• Therefore, the total work done by the force is 24 J.

Explanation:

• As long as an unbalanced force is applied to a body, there is a continuous change in its speed.
• Newton's Second Law of motion states that the rate of change of momentum of an object is proportional to the applied force in the direction of the force. i.e. F=ma. Where F is the force applied, m is the mass of the body, and a is the acceleration produced.
• As the rate of change of speed is acceleration and hence, when an unbalanced force acts on an object it speeds changes accordingly.

• Ammonium Chloride is an example of a salt gives an aqueous solution of pH less than 7.
• We know the reaction between Ammonium Chloride (NH₄Cl)
• NH₄Cl + H₂O → NH₄OH + HCl

All the other salts when mixed with water give basic solution.

• The amount of charge (q) = 4 C
• Potential difference between two points (v) = 18 v
• Now work done (w) = q v
• Now by substituting the value, we get

w = (4) (18)

= 72 Joules

• The total amount of work done is 72 J.

The correct answer is Kodaikanal

Key Points

• Kodaikanal is known as the Princess of the Hill Stations with an elevation of 2100 mt.
• It is in the state of Tamil Nadu and located in Palani Hills (Part of Western Ghats).

Additional Information

• Shram Award is given to recognises workers for their distinguished performance, innovative ability, and outstanding contribution in the field of productivity and exhibition of exceptional courage and presence of mind.
• Prime Minister Shram Awards were instituted in 1985 to recognize the contributions made by workers as defined in the Industrial Disputes Act, 1947.

Shortcut Trick

Let Delhi price (X) be 100 units. Chandigarh CP = 80 units.

Total CP = 80 units + Rs. 600. SP = 100 units.

Profit% = 100/7% = 1/7 in fraction. ∴ SP = CP × 8/7.

100 units = (80 units + 600) × 8/7 ⇒ 700 units = 640 units + 4800.

60 units = 4800 ⇒ 1 unit = 80. ∴ X (100 units) = 80 × 100 = 8000.

∴ The correct answer is Rs. 8000.

Alternate Method

Given: Delhi Price = Rs. X, Discount = 20%, Transport = Rs. 600, Profit = 100/7 %.

Formulas: CP = MP × (100 − D%)/100 | Profit% = (SP − CP)/CP × 100 | SP = CP × (1 + P/100).

⇒ Cost Price in Chandigarh = X − 20% of X = 0.8X.

⇒ Total Cost Price including transport = 0.8X + 600.

⇒ Selling Price in Delhi = X.

⇒ Profit% = 100/7% ⇒ SP = CP × (1 + 1/7) = CP × 8/7.

⇒ X = (0.8X + 600) × 8/7.

⇒ 7X = 6.4X + 4800.

⇒ 0.6X = 4800 ⇒ X = 4800 ÷ 0.6 = 8000.

∴ The correct answer is Rs. 8000.

Additional Information

Total Cost Price

When overhead expenses like transportation, repairs, or labor are involved, they are always added to the Purchase Price to calculate the effective Cost Price.

Profit Percentage to Fraction

To simplify calculations, convert percentages to fractions: 100/7 % = (100/7) ÷ 100 = 1/7. A profit of 1/7 means SP is 1 + 1/7 = 8/7 of CP.

Shortcut Trick

Given sec⁴θ − sec²θ = 3.

Factorize: sec²θ(sec²θ − 1) = 3.

Using 1 + tan²θ = sec²θ, we know sec²θ − 1 = tan²θ.

Substitute: (1 + tan²θ)(tan²θ) = 3 → tan²θ + tan⁴θ = 3.

∴ The correct answer is 3.

Alternate Method

Given: sec⁴θ − sec²θ = 3

Formula Used: sec²θ = 1 + tan²θ

⇒ sec⁴θ − sec²θ = 3

⇒ sec²θ(sec²θ − 1) = 3

⇒ (1 + tan²θ)(tan²θ) = 3

⇒ tan²θ + tan⁴θ = 3

∴ The correct answer is 3.

Additional Information

Fundamental Trigonometric Identities

1. sin²θ + cos²θ = 1 | 2. 1 + tan²θ = sec²θ | 3. 1 + cot²θ = cosec²θ.

Reciprocal Relations

secθ = 1/cosθ and tanθ = sinθ/cosθ.

Important Substitution

Whenever powers of sec and tan are given together, look for the factor (sec²θ − tan²θ = 1).

The minimum possible Venn diagram of the given statements,

Conclusions:

I. Some cows are cats → False

II. Some cows have mustache → False (it is possible but not definite)

Hence, no conclusion follows.

Figure 1 to Figure 2:

Figure 3 to Figure 4:

Hence, “A” is the correct answer.

• Rajya Sabha is known as the Upper house of the Indian Parliament.
• Article 80 of the Indian Constitution lays down the maximum strength of Rajya Sabha as 250, out of which 12 members are nominated by the President and 238 are representatives of the States and of the two Union Territories.
• Vice President of India will act as Ex-Officio chairman of Rajya Sabha.

• We know that ships travel on the oceans
• Similarly, whales live in the ocean. But we can not relate ships and whales.

Hence, the most suitable venn diagram is “option 2”.

The minimum possible Venn diagram of the given statements,

Conclusions:

1. All iron are metals → False (it is possible but not definite)
2. All heavy are metals → False (it is possible but not definite)

Hence, no conclusion follows.

• ‘Hausala 2017’ is the celebration of Children’s rights.
• It was held from 16^th November to 20^th November 2017 by the Ministry of Women and Child Development and celebrated as child Rights Week.

⇒ Part of cake left with 5^th friend = 1 – {(1/8) + (1/6) + (5/12) + (1/12)} = 1 – {(3 + 4 + 10 + 2)/24} = 1 – (19/24) = 5/24

• Non-Metals can exist in solid, liquid and gaseous forms.
• Physical Properties of non-metals:
• Density: Non-metals have low densities.
• Lustre: Non-metals do not have lustre, except diamond and iodine crystals.
• Brittleness: Solid non-metals are brittle, and some non-metals are soft. Diamond (an allotrope of carbon) is an exception, which is the hardest natural substance.
• Ductility & Malleability: Non-metals are neither ductile nor malleable.
• Conduction of Heat & Electricity: Non-metals are bad conductors of heat and electricity except graphite.
• Physical State: At ordinary temperature non-metals occur as solids, liquids, and gases.

For example, Solids: Carbon, Sulphur, Phosphorus, Liquids: Bromine 

Gases: Hydrogen, Nitrogen.

The logic followed here is:-

• All the symbols are moving clockwise one behind the other.
• Triangle (

) rotates 900 anticlockwise directions in each step.

• Both symbols 

 rotate one place in the clockwise direction in each step.

• Symbols (

) rotate in the clockwise direction in each step and symbol 

 changes to symbol ± in alternate steps.

• The symbol 

 rotates in the clockwise direction in each step.

So, the next image of the given series is figure D.

Hence, “Option 3” is the correct answer.

The minimum possible Venn diagram of the given statements,

Conclusions:

1. All four-wheelers are cars → False (Because all jeeps are four-wheelers so some four-wheelers can be jeeps but all four-wheelers is definitely false)
2. Some four-wheelers are Jeeps → True (Because all jeeps are four-wheelers so some four-wheelers can be jeeps, it is definitely true)

Hence, Only conclusion 2 follows.

Given, at 3 pm

Now at 3.40 pm

In every 5 minutes movement minute hand will make an angle of 30°, thus between 3.30 pm and 3.40 pm it will make an angle of 60° (5 min. + 5 min. = 30° + 30° )

Therefore minute hand is pointing 60° west (9) of the south (6).

Hence, “60° west of south” is the correct answer.

Shortcut Trick

Combined efficiency 2(A + B + C) = (Total Work ÷ (A+B)) + (Total Work ÷ (B+C)) + (Total Work ÷ (A+C))

LCM of (6, 10, 7.5) = 30 units (Total Work)

Efficiency: (A+B) = 5, (B+C) = 3, (A+C) = 4

Efficiency of A = [ (A+B) + (A+C) − (B+C) ] ÷ 2 = (5 + 4 − 3) ÷ 2 = 3

Time for A = 30 ÷ 3 = 10 hrs

∴ The correct answer is 10 hr.

Alternate Method

Given: Time (A+B) = 6 hr, (B+C) = 10 hr, (A+C) = 7.5 hr.

⇒ Adding efficiencies: 2(A + B + C) = 5 + 3 + 4 = 12

⇒ A + B + C = 12 ÷ 2 = 6

⇒ Efficiency of A = (A + B + C) − (B + C) = 6 − 3 = 3

⇒ Time taken by A alone = Total Work ÷ Efficiency of A

⇒ Time = 30 ÷ 3 = 10 hr

∴ The correct answer is 10 hr.

Additional Information

Total Work and Efficiency

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

Combined Work Formula

If A and B work together, their combined efficiency is the sum of their individual efficiencies (E_total = E_A + E_B).

Pipes and Cisterns

Inlet pipes have positive efficiency, while outlet (leak) pipes have negative efficiency in work calculations.

The Mayor is promoting to keep his city clean, pollution-free, beautiful, and green. As we know that ecological park has trees and diverse ecological systems, we can say “ecological parks improve green cover”.

And since we know that trees absorb Carbon dioxide, it can be safely assumed that having an ecological park in the city will “reduce air pollution”.

Thus, both the assumption can be implicit from the given statement.

The pattern followed here is:

• T and its water image

• V and its water image

• not the water image of N.
• Water image of N will be as follows: 

• A and its water image

Hence, “C” is the correct answer.

Shortcut Trick

Apply Cross-Multiplication to the given expression.

Numerator = (sin A + sin B)(sin A − sin B) + (cos A + cos B)(cos A − cos B)

⇒ (sin² A − sin² B) + (cos² A − cos² B)

⇒ (sin² A + cos² A) − (sin² B + cos² B) = 1 − 1 = 0

∴ The correct answer is 0.

Alternate Method

Given: [(sin A + sin B) / (cos A − cos B)] + [(cos A + cos B) / (sin A − sin B)]

Formula Used: (a + b)(a − b) = a² − b² and sin² θ + cos² θ = 1

Calculations:

⇒ Take LCM: (cos A − cos B)(sin A − sin B)

⇒ Numerator: (sin A + sin B)(sin A − sin B) + (cos A + cos B)(cos A − cos B)

⇒ Using (a+b)(a-b): (sin² A − sin² B) + (cos² A − cos² B)

⇒ Rearranging: (sin² A + cos² A) − (sin² B + cos² B)

⇒ Substituting 1: 1 − 1 = 0

⇒ Expression: 0 / [(cos A − cos B)(sin A − sin B)] = 0

∴ The correct answer is 0.

Additional Information

Trigonometric Identities

Fundamental identities include sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ.

CD Formulas

Alternative solution involves sin C + sin D and cos C − cos D transformations to simplify ratios into tan or cot functions.

• The element Iron (26) has the chemical symbol that is derived from Latin.
• It's chemical symbol is Fe which is derived from Iron’s Latin name Ferrous.

Shortcut Trick

Identify the algebraic identity: If the sum of three terms is zero (x + y + z = 0), then the sum of their cubes is equal to three times their product (x³ + y³ + z³ = 3xyz).

Let x = a − b, y = b − c, and z = c − a. Summing them: (a − b) + (b − c) + (c − a) = 0.

Thus, the numerator becomes 3(a − b)(b − c)(c − a).

The expression simplifies to: 3(a − b)(b − c)(c − a) ÷ 3(a − b)(b − c)(c − a) = 1.

∴ The correct answer is 1.

Alternate Method

Given:

Expression: [(a − b)³ + (b − c)³ + (c − a)³] ÷ [3(a − b)(b − c)(c − a)]

Formula Used:

If x + y + z = 0, then x³ + y³ + z³ = 3xyz

Calculations:

Let us assume:

x = a − b

y = b − c

z = c − a

⇒ x + y + z = (a − b) + (b − c) + (c − a)

⇒ x + y + z = a − a + b − b + c − c = 0

⇒ According to the identity, x³ + y³ + z³ = 3xyz

⇒ (a − b)³ + (b − c)³ + (c − a)³ = 3(a − b)(b − c)(c − a)

Now, substitute the value of the numerator back into the original expression:

⇒ Value = [3(a − b)(b − c)(c − a)] ÷ [3(a − b)(b − c)(c − a)]

⇒ Value = 1

∴ The correct answer is 1.

Additional Information

Standard Algebraic Identity

The general identity is a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca). If a + b + c = 0, the entire right side becomes zero.

Special Case: a = b = c

If a = b = c, then a² + b² + c² − ab − bc − ca = 0, which also results in a³ + b³ + c³ = 3abc.

Application in Fractions

This identity is frequently used to simplify complex cyclic fractions where variables cancel out to leave a constant value, often 1 or 3.

Shortcut Trick

Convert speed to kmph: 15 × (18/5) = 54 kmph.

Convert time to hours: 3 hours 20 mins = 3 + (1/3) = 10/3 hours.

Distance = 54 × (10/3) = 18 × 10 = 180 km.

∴ The correct answer is 180 km.

Alternate Method

Given: Speed = 15 m/s, Time = 3 hours 20 minutes.

Formula Used: Distance = Speed × Time

⇒ Speed in kmph = 15 × (18/5) = 54 kmph

⇒ Time in hours = 3 + (20/60) = 3 + 1/3 = 10/3 hours

⇒ Distance = 54 × (10/3)

⇒ Distance = 18 × 10 = 180 km

∴ The correct answer is 180 km.

Additional Information

Unit Conversion

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

Average Speed

When a distance is covered at speed x and the same distance at speed y, Average Speed = (2 × x × y) ÷ (x + y).

Relative Speed

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

⇒ Mobile phone manufactured by LMN = 30% of total mobile = 30% of 1240000 = 372000

Given,

By combining in best possible way.

Hence, image “B” is formed from the two shapes gives the problem figure.

Total no. of years difference between 2010 – 2018 = 8

Number of leap years till 2018 = 2 (2012 and 2016)

Number of ordinary years till 2018 = 6

Number of odd days till 2018 = 6 + (2 × 2) = 6 + 4 = 10 odd days

Total number of odd days till 1^st January 2018 = 10 odd days = 3 odd days

So, we have move 3 days backward from Monday i.e., Friday.

Hence, “Friday” is the correct answer.

Shortcut Trick

Total Investment = 100%

Total Expenditure = 30% (Furnishing) + 20% (Necessary things) = 50%

Remaining percentage for inventory = 100% − 50% = 50%

Leftover money = 50% of ₹25,000 = ₹12,500

∴ The correct answer is Rs. 12,500.

Alternate Method

Given:

Initial Investment = ₹25,000

Furnishing Expense = 30%

Other Necessary Things = 20%

Calculations:

⇒ Total spending percentage = 30% + 20% = 50%

⇒ Remaining percentage = 100% − 50% = 50%

⇒ Leftover amount = (50 ÷ 100) × 25,000

⇒ Leftover amount = 0.5 × 25,000 = 12,500

∴ The correct answer is Rs. 12,500.

Additional Information

Percentage Expenditure

When expenditures are given as a percentage of the initial total, they are simply added together: Total % = P₁ + P₂ + ... + P_n.

Remaining Balance Method

If the question says percentage of remaining amount, use the successive method: Final = Initial × (100−P₁)/100 × (100−P₂)/100.

Fractional Conversion

Converting percentages to fractions (e.g., 50% = 1/2) often simplifies multiplication during exams.

Clearly, figure “A” is the correct answer.

The pattern followed here is:

A) 

- The orientation of trapezium and oval is resembles closet to the question figure.

B) 

• The orientation of trapezium is not correct as per the given question figure.

C) 

• The orientation of trapezium is not correct as per the given question figure.

D) 

- The orientation of trapezium is not correct as per the given question figure.

Hence, the correct answer is "Option 4".

Shortcut Trick

For a number to be divisible by 11, the difference between the sum of digits at odd places and the sum of digits at even places must be 0 or a multiple of 11.

Sum at odd places (x, 4, 1) = x + 4 + 1 = x + 5

Sum at even places (4, 6) = 4 + 6 = 10

Difference: (x + 5) − 10 = 0 ⇒ x − 5 = 0 ⇒ x = 5

∴ The correct answer is 5.

Alternate Method

Given: The number is x4461 and it is divisible by 11.

Formula Used: Divisibility rule of 11: |Sum_odd − Sum_even| = 0, 11, 22, ...

⇒ Sum of digits at odd places = x + 4 + 1 = x + 5

⇒ Sum of digits at even places = 4 + 6 = 10

⇒ According to rule: (x + 5) − 10 = 0 (since x is a single digit)

⇒ x − 5 = 0

⇒ x = 5

∴ The correct answer is 5.

Additional Information

Face Value and Place Value

The face value of a digit is the digit itself, regardless of its position in the number.

Divisibility by 3 and 9

A number is divisible by 3 or 9 if the sum of its digits is divisible by 3 or 9 respectively.

Divisibility by 11 Rule

Difference = |∑Digits_odd − ∑Digits_even|. If Difference ÷ 11 has remainder 0, the number is divisible by 11.

Shortcut Trick

Property: Angles subtended by the same arc (or chord) at the circumference of a circle are always equal.

From Information 1: Chord AB subtends ∠ACB and ∠ADB at the circumference. ∴ ∠ACB = ∠ADB.

From Information 2: ∠D (or ∠ADB) = 60°.

Combining both: ∠ACB = 60°.

∴ The correct answer is Both 1 and 2 are sufficient.

Alternate Method

Given:

Information 1: A circle with points A, B, C, D on its circumference and chord AB.

Information 2: The measure of angle ∠D = 60°.

Formula Used:

Angles in the same segment of a circle are equal.

Calculations:

⇒ In Information 1, points A, B, C, D are concyclic (lie on the same circle).

⇒ Chord AB subtends ∠ACB and ∠ADB in the major segment.

⇒ According to the geometric theorem: ∠ACB = ∠ADB.

⇒ From Information 2: ∠ADB = 60°.

⇒ ∴ ∠ACB = 60°.

⇒ Since we used both the geometric setup from Info 1 and the numerical value from Info 2, both are required.

∴ The correct answer is Both 1 and 2 are sufficient.

Additional Information

Angle at the Centre

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle (Angle at centre = 2 × Angle at circumference).

Angle in a Semi-circle

The angle subtended by a diameter at the circumference is always a right angle (90°).

Cyclic Quadrilateral

In a cyclic quadrilateral, the sum of opposite angles is always 180° (∠A + ∠C = 180° and ∠B + ∠D = 180°).

• Porpoises can produce ultrasound.
• Sound waves with a frequency greater than 20 kHz are called ultrasound
• Bats, mice, dolphins, etc, can also produce ultrasound.

The various applications of ultrasonic sound waves are:

• For cleaning aeroplanes and machinery parts of clocks.
• For measurement of the depth of the sea.
• It is used in ultrasonography.

Shortcut Trick

Loss = 1/7 of CP ⇒ Ratio of Loss : CP = 1 : 7.

SP₁ = CP − Loss = 7 − 1 = 6 units.

6 units = Rs. 144 ⇒ 1 unit = Rs. 24 ⇒ CP = 7 × 24 = Rs. 168.

New SP₂ = Rs. 189 ⇒ Profit = 189 − 168 = Rs. 21.

Profit% = (21 ÷ 168) × 100 = 1/8 × 100 = 12.5%.

∴ The correct answer is 12.5%.

Alternate Method

Given: SP₁ = Rs. 144, Loss = 1/7 of CP, SP₂ = Rs. 189.

Formulas: SP = CP − Loss | Profit = SP − CP | Profit% = (Profit ÷ CP) × 100.

⇒ Let Cost Price (CP) be x.

⇒ Loss = x/7.

⇒ Selling Price (SP₁) = CP − Loss = x − x/7 = 6x/7.

⇒ 144 = 6x/7 ⇒ x = (144 × 7) ÷ 6 = 24 × 7 = 168.

⇒ For SP₂ = 189, Gain = 189 − 168 = 21.

⇒ Gain% = (21 ÷ 168) × 100 = 12.5%.

∴ The correct answer is 12.5%.

Additional Information

Cost Price & Selling Price Relation

Profit or Loss is always calculated on the Cost Price unless specified otherwise. Formula: CP = [100 ÷ (100 ± Gain/Loss%)] × SP.

Fraction to Percentage Conversion

Standard fractions like 1/8 equal 12.5% and 1/7 approximately 14.28%. Using fractions simplifies multi-step calculations.

Shortcut Trick

HCF of fractions = HCF of Numerators ÷ LCM of Denominators.

Numerators: 2, 8, 10, 32 → HCF = 2 (highest common divisor).

Denominators: 3, 9, 27, 81 → LCM = 81 (all are powers of 3, take the highest power).

Resulting HCF = 2/81.

∴ The correct answer is 2/81.

Alternate Method

Given Fractions: 2/3, 8/9, 10/27, 32/81

Formula Used: HCF of (a/b, c/d, e/f) = HCF(a, c, e) / LCM(b, d, f)

Step 1: Calculate HCF of Numerators (2, 8, 10, 32).

⇒ 2 = 2¹

⇒ 8 = 2³

⇒ 10 = 2 × 5

⇒ 32 = 2⁵

⇒ HCF (Numerators) = 2

Step 2: Calculate LCM of Denominators (3, 9, 27, 81).

⇒ 3 = 3¹

⇒ 9 = 3²

⇒ 27 = 3³

⇒ 81 = 3⁴

⇒ LCM (Denominators) = 3⁴ = 81

Step 3: Apply Fraction HCF formula.

⇒ HCF of Fractions = 2 / 81

∴ The correct answer is 2/81.

Additional Information

LCM of Fractions

To find the LCM of fractions, use the formula: LCM = (LCM of Numerators) ÷ (HCF of Denominators).

HCF and LCM Relation

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

Co-prime Numbers

The HCF of two co-prime numbers is always 1, and their LCM is the product of the numbers.

Here, Virat kohli is a cricketer ( a sports person) and all the others are inventers.

Hence, “Virat kohli” is the correct answer.

The correct answer is Canada.

Key Points

• Canada has the longest coastline (202, 080 km) in the world.
• The currency of Canada is Canadian dollar and it's Prime Minister is Justin Trudeau.
• Canada is the second largest country in the world after Russia.
• Indonesia is the largest archipelago in the world.
• Australia is the Sixth largest country in the world.
• Norway ranked as number 6th in ‘World Happiness Report’ in the Year 2023.

We can draw diagram from the given information as follows,

Hence, “North-East” is the correct answer.

The logic followed here is:

Code for weekdays:

Note: Multiple of 400 years i.e. 800, 1200, 1600, 2000 have 0 odd days.

Calculating leap year: For Finding the number of leap year (1 - 99) years, divide the number of years by 4 and the quotient will be the number of leap years.

We will find the day on 1st March 2005 = (2000 years + Period from 1.1.2005 to 1.3.2005)

As mentioned above:

• Odd days in 1600 years = 0
• Odd days in 400 years = 0
• Number of leap years till 2004 = 1 (in 2004) = 2 odd days
• Number of ordinary years till 2004 = 3 (2001, 2002, 2003) = 3 odd days
• Now number of odd days in:
• Jan, Feb, and March = 31 + 28 + 1 = 60 days = 4 odd days
• Total number of odd days = (0 + 0 + 2 + 3 + 4) = 9 days = 2 odd days

Since 2 is the code for Tuesday

• So on 1st March, 2005 it was Tuesday.

Therefore, Friday = 1st March + 3 days = 4th March.

• Friday will repeat after 7 days.
• ⇒ 4th March + 7 = 11th March.
• Thus, in March, 2005 Friday falls on 4th, 11th, 18th and 25th.

Hence, the correct answer is "Option 3".

Other method:

We solve these sum by odd day method , like if we want to find day of 60th day we will just divide it by 7 we get( 60/7=78 + 4 ) here we get 4 as remainder. so 1st day Monday , 2nd day Tuesday , 3rd day Wednesday , 4th day Thursday which our ans. .. so on 60th  day there will be Thursday.                                                                             FIND Friday fall on which dasy of March 2005 = ?                            For 2000 years there will be 0 odd days                                               For 2001- 2004 there is 5 odd days .             ..(1)                                because 2001= 1 odd day   , for 2002= 1 odd day                              for 2003 = 1 odd day , for 2oo4 = 2 odd days (leap year)                  so january,2005 = 31 days , feb 2005 = 28 days.....(2)                      so from (1) & (2) we get                                                                        odd days 2001-2004, + jan2005 + feb2005= 5 +31+28=64                 Now 64/7=79 + 1    remainder = 1                                                      so there will be Monday on 28th feb 2005                                         1st March = Tuesday                                                                          2nd March = wednesday                                                                      3rd March = Thursday                                                                        4th March = Friday                                                                                 with gap of 7 days other friday fall on 11,18 & 25

• The struggle between France and England called the Hundred Years' War was the longest war in recorded history.
• It lasted, with some interruptions, through the reigns of five English kings (Edward III to Henry V) and five French kings (Philip VI to Charles VII).

• Collenchyma consists of living cells and is characterised by the presence of cellulose.
• Collenchyma is a mechanical tissue in young dicotyledonous stems and provides mechanical support and elasticity.
• It provides great tensile strength with flexibility to those organs in which it is found. It allows easy bending in various parts of a plant mainly young growing stem without breaking them.