RRC Group D Previous Year Paper 54 (Held On: 11 Oct 2018 Shift 2)

Concept used:

0.0a = a/100

Calculation:

(759/100000) × (10/33)

⇒ 23/10000

⇒ 0.0023

∴ Required answer is 0.0023

The logic followed here is:

i) UBI → Union Bank of India

ii) SBI → State Bank of India

iii) PNB → Punjab National Bank

iv) ONGC → Oil and Natural Gas Corporation.

Here, UBI, SBI, PNB are banking institutions where as ONGC is an institution which deals in oil and natural gas and other petroleum products.

Hence, 'ONGC' is does not belong to the group.

The correct answer is Ar and n2.

Key Points

• Ar and n2 gas is used to fill the electric bulb.
• Filling a bulb with an inert gas slows down the evaporation of the tungsten filament compared to operating it in a vacuum.
• This allows for greater temperatures and therefore greater efficacy with less reduction in filament life.​

Additional Information

• Argon is a commonly used gas, used to fill incandescent light bulbs. It increases the bulb life by preventing the tungsten filament from deteriorating too quickly.
• Other gases such as helium, neon nitrogen, and krypton are also used in lightning.
• Inert gases are reactive towards the burning filament of the bulb. Therefore we have to use either inert gases like Argon or inactive nitrogen.

Important Points

• In 1878, Thomas Edison began serious research into developing a practical incandescent lamp and on October 14, 1878, Edison filed his first patent application for Improvement In Electric Lights.

The correct answer is Aamir Khan.

Key Points

• Aamir Khan played the lead role in the movie 'Dangal' released in 2016.
• Aamir Khan was honoured with the Best Actor Award in 2017 at Filmfare Awards.
• He was awarded for his film Dangal for his role as Mahavir Singh Phogat.

Additional Information

• Alia Bhatt was awarded Best Actress for her film Udta Punjab.
• Best Film was won by film Dangal.
• Nitesh Tiwari won Best Director for the film Dangal.

The correct answer is Resistance.

Key Points

• The current flowing through a resistor is inversely proportional to its resistance.
• ​Resistance is a measure of the opposition to current flow in an electrical circuit.
• Resistance is measured in ohms, symbolized by the Greek letter omega (Ω).
• Ohms are named after Georg Simon Ohm (1784-1854), a German physicist who studied the relationship between voltage, current, and resistance.

Additional Information

• The resistance formula is as follows:
• ​Resistance = voltage drop across a resistor/ current flowing through a resistor.
• R = \frac{V}{I} R = resistance (Ohms, Ω) V = voltage difference which is between the two ends of a resistor (Volts, V).

Important Points

The logic followed here is:

• Neon, Helium, and Xenon are noble gases or inert gases whereas Zinc is a metal.

Hence, Zinc does not belong to the group.

Additional Information

• Neon (Ne), Helium(He), and Xenon (Xe) belong to group 18.
• Zinc (Zn)  is brittle and silvery greyish in colour. It belongs to group 12 of the periodic table.

The logic followed here is:

Here the code for SPANNER is as follows:

Similarly,

NEAR is coded as

Hence, NEAR will be written as 'JBDS' in the given code language.

The correct answer is 8 ms-1

Key Points

• Solution:
• Here, u = 0 , t = 0.8 s , g = 10 m / s 2.
• v = u + g t = 0 + 10 × 0.8
• 8
• 8 ms-1 is the speed when it hits the ground.

The logic followed here is:

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Hence, option 1 is the correct answer.

The logic followed here is:

The place value of A is 1, D is 4, O is 15 and U is 21. 

In each of the given figure the alphabet and its place value are given except  U and 23 in figure D.

Hence, figure D is the odd one from the given figures.

The least possible Venn diagram is as follows:

Conclusion :

1. Some weak are tissues.→ True (as some tissues are weak)
2. Some bones are tissues. → False( as it is possible but not definite).

Hence, only conclusion 1 follows.

The correct answer is 100N.

Key Points

• The mass of an object is 10 kg. Its weight on earth is 100N.
• The weight of a body is a product of its mass and acceleration due to gravity on earth.
• ​Weight varies with location depending upon the acceleration due to gravity.

Additional Information

• Solution details:
• w=mg
• (Here m=10kg,)
• g=10m/s2)
• w=10×10kgm/s2
• w=100N
• Therefore, the weight of the object on earth will be 100N.

The correct answer is 1/u + 1/v = 1/f.

Key Points

• In ray optics, The object distance, image distance, and Focal length are related as 1/u + 1/v = 1/f.
• The relation between the focal length of the mirror, the distance of the object, and the distance of the image are known as the mirror formula.

Additional Information

• A highly polished surface, such as a mirror, reflects most of the light falling on it. Reflection is governed by the following laws:
• The angle of incidence is equal to the angle of reflection, and
• The incident ray, the normal to the mirror at the point of incidence, and the reflected ray, all lie in the same plane.
• Types of the mirror:
• Plane Mirror
• Concave Mirror
• Convex Mirror

The correct answer is propyne.

Key Points

• Propyne (methylacetylene) is an alkyne with the chemical formula CH 3C≡CH.
• It is a component of MAPD gas - along with its isomer propadiene (allene), which was commonly used in gas welding.
• Propyne contains three carbon atoms and four hydrogen atoms in the above structure.
• Carbon-1 is attached to one hydrogen atom through a single bond (sigma bond) and carbon-1 is attached to carbon-2 through a triple bond (one sigma bond and two pi bonds).

Additional Information

• When three pairs of electrons are shared between two carbon atoms, a triple bond is formed between the two carbon atoms.
• A triple bond is made of two pi bonds and one sigma bond.
• Examples of compounds with triple bonds include nitrogen gas, cyanide ion, acetylene, and carbon monoxide.

The correct answer is Roshni Nadar.

Key Points

• Roshni Nadar is the Executive Director and CEO of HCL.
• Roshni Nadar Malhotra is the only child of HCL’s founder, billionaire industrialist, and philanthropist Shiv Nadar.
• She has featured in The World’s 100 Most Powerful Women list compiled and released by Forbes in 2017, 2018, and 2019.
• She is also the richest woman in India, according to IIFL Wealth Hurun India Rich List (2019).
• She established The Habitats Trust in 2018, which aims to work toward protecting India’s natural habitats and its indigenous species.

Additional Information

• As of now, C Vijayakumar is CEO of HCL and he has appointed in October 2016.
• C Vijayakumar joined HCL Technologies in 1994 in the founding startup team of Comnet as a senior technical engineer.

Important Points 

The logic followed here is:

The main figure is 

Figure A:  the above figure is rotated 90 degrees to the right.

Figure B:  the above figure is rotated 90 degrees to the left.

Figure C: the above figure is rotated 180 degrees to the right.

Figure D: this is a mirror image of the above image. Only figure D cannot be obtained by rotation of the main figure.

Hence, figure D does not belong to the group.

The correct answer is Inertia.

Key Points

• The measurement of the mass of an object is called Inertia.
• ​Inertia is the resistance of any physical object to any change in its velocity. This includes changes to the object's speed or direction of motion.
• Inertia is a passive property and does not enable a body to do anything except oppose such active agents as forces and torques.

Additional Information 

Important Points 

The correct answer is Alia Bhatt.

Key Points

• Alia Bhatt was given the 'Best Actress award at the Filmfare Awards 2017.
• She won this award for the role of Bauria in the movie Udta Punjab.

Additional Information

The correct answer is Only A is true.

Key Points

• State of Matter:
• Three states of matter exist – solid, liquid, and gas. Solids have a definite shape and volume. Liquids have a definite volume, but take the shape of the container. Gases have no definite shape or volume.
• The firmness of a solid is due to the forces holding atoms or molecules together.
• The particles in a solid are close together.
• Hence, statement A is True.
• Compressibility:
• It is the property of a substance in which its volume decreases under high pressure and it is called Compressibility, not size.
• This property is found in gases.
• Gases are highly compressible.
• Hence, statement B is Incorrect.

Shortcut Trick

Let Total Work = LCM(5, 7, 14) = 70 units.

Efficiency of Pipe 1 = 70 ÷ 5 = 14 units/hr.

Efficiency of Pipe 2 = 70 ÷ 7 = 10 units/hr.

Efficiency of Outlet Pipe = −(70 ÷ 14) = −5 units/hr.

Combined Efficiency = 14 + 10 − 5 = 19 units/hr.

Time required = 70 ÷ 19 = 3(13/19) hr.

∴ The correct answer is 3(13/19) hr.

Alternate Method

Calculations:

⇒ Total capacity of the tank = LCM of 5, 7, and 14 = 70 units.

⇒ Net efficiency when all pipes are open = Efficiency of A + Efficiency of B − Efficiency of C

⇒ Net efficiency = 14 + 10 − 5 = 19 units/hr.

⇒ Time taken to fill the tank = Total Capacity ÷ Net Efficiency

⇒ Time = 70 ÷ 19

⇒ Time = 3(13/19) hours.

∴ The correct answer is 3(13/19) hr.

Additional Information

Inlet and Outlet Pipes

An Inlet pipe performs positive work (filling), while an Outlet pipe (leak) performs negative work (emptying).

Pipes and Cisterns Formula

If a pipe fills a tank in x hours and another empties it in y hours, the net work in one hour is (1/x − 1/y).

Total Work Concept

Total work is always assumed to be the LCM of individual time durations to simplify calculations into integers.

The correct answer is Ragam.

Key Points

• In January 2016, All India Radio (AIR) launched a non-traditional audio broadcast channel via the Internet, which is readily available through 'Free Dish' for experts in the arts, especially classical music-both Karnataka and Hindustani. It is known as Ragam.
• The channel was launched by Prasar Bharati Chairman Surya Prakash and it will be uplinked from AIR Bengaluru station.
• 'Raagam' will be active round-the-clock and can be downloaded from under the mobile application-All India Radio Live.

 Additional Information

The diagrammatic representation of the given data is as follows

Hence, Sunayata is facing 'North' direction now.

Shortcut Trick

Radius (r) = 10 cm. Distances from center = 6 cm and 8 cm.

Using Pythagorean triplets (6, 8, 10):

Half of Chord 1 = √(10² − 6²) = 8 cm ⇒ Chord 1 = 16 cm.

Half of Chord 2 = √(10² − 8²) = 6 cm ⇒ Chord 2 = 12 cm.

Difference = 16 − 12 = 4 cm.

∴ The correct answer is 4 cm.

Alternate Method

Given: Radius (r) = 10 cm, Distance of first chord (d₁) = 6 cm, Distance of second chord (d₂) = 8 cm.

Formula Used: Length of a chord = 2 × √(r² − d²), where r is the radius and d is the distance from the center.

⇒ Length of the first chord (AB) = 2 × √(10² − 6²)

⇒ AB = 2 × √(100 − 36) = 2 × √64 = 2 × 8 = 16 cm

⇒ Length of the second chord (CD) = 2 × √(10² − 8²)

⇒ CD = 2 × √(100 − 64) = 2 × √36 = 2 × 6 = 12 cm

⇒ Difference in lengths = 16 cm − 12 cm = 4 cm

∴ The correct answer is 4 cm.

Additional Information

Perpendicular Bisector Property

The perpendicular drawn from the center of a circle to a chord always bisects the chord into two equal segments.

Distance between Parallel Chords

If two parallel chords are on opposite sides of the center, the distance between them is d₁ + d₂. If they are on the same side, the distance is |d₁ − d₂|.

Chord Length and Distance

As the distance of a chord from the center increases, the length of the chord decreases. The longest chord is the diameter (distance = 0).

Shortcut Trick

Assume the total area is 100 units. CP = 3,00,000.

Total profit needed = 15% of 100 = +15 units.

Part 1: 25% area at 25% loss ⇒ 25 × (−0.25) = −6.25 units.

Part 2: 40% area at 25% profit ⇒ 40 × 0.25 = +10 units.

Current net profit = −6.25 + 10 = +3.75 units. Remaining profit needed = 15 − 3.75 = 11.25 units.

Remaining area = 100 − 25 − 40 = 35%. SP of remaining part = CP of remaining + profit needed = (35% of 3,00,000) + (11.25% of 3,00,000).

SP of remaining = (46.25 ÷ 100) × 3,00,000 = 1,38,750.

∴ The correct answer is ₹ 1,38,750.

Alternate Method

Given → Total CP = 3,00,000 | Overall Profit = 15% | Plot divided into 25%, 40%, and 35%. Formulas: SP = CP × (100 + P%) ÷ 100 | Profit = SP − CP.

⇒ Total SP required = 3,00,000 × 1.15 = 3,45,000. ⇒ SP₁ (25% area) = (0.25 × 3,00,000) × 0.75 = 75,000 × 0.75 = 56,250. ⇒ SP₂ (40% area) = (0.40 × 3,00,000) × 1.25 = 1,20,000 × 1.25 = 1,50,000. ⇒ Sum of SP₁ and SP₂ = 56,250 + 1,50,000 = 2,06,250. ⇒ SP of remaining plot = Total SP − (SP₁ + SP₂) = 3,45,000 − 2,06,250 = 1,38,750.

∴ The correct answer is ₹ 1,38,750.

Additional Information

Weighted Average Method

For problems involving parts of a whole, use (w₁p₁ + w₂p₂ + w₃p₃) = W_totalP_total where w is the weight and p is the profit/loss percentage.

Profit and Loss on Cost Price

Unless stated otherwise, profit or loss percentage is always calculated on the Cost Price (CP).

The correct answer is 108, 11.

Key Points

• Out of the 108 Upanishads, 11 Upanishads are considered to be the main.
• The word Upanishad means to sit down near someone and denotes a student sitting near his guru to learn.

Additional Information

• The 11 Upanishads that are predominant are called “Mukhya Upanishads“.
• The 11 Mukhya Upanishads are:
• Aitareya Upanishad
• Bṛhadaraṇyaka Upanishad
• Taittiriya Upanaishad
• Chandogya Upanishad
• Kena Upanisahda
• Īsa Upanishad
• Śvetasvatara Upanishad
• Kathopnishad
• Muktika Upnishad
• Maandūkya
• Praśna

• Since Ramu has made a train reservation in April, one month in advance for his travel plan in May, it indicates that it is possible to do rail reservations one month in advance.
• Thus, assumption I is implicit.
• Assumption II talks about trains from Mumbai to Hyderabad which is not mentioned or suggested anywhere in the statement, thus it is not implicit.

Hence the correct answer is option 1.

The correct answer is A and D.

Key Points

• The Jumping of frogs is the activity of voluntary muscles as it is controlled by skeletal muscles.
• Pumping of the heart is involuntary, i.e., it is controlled by cardiac muscles.
• Writing with the hand is voluntary muscles action.
• The movement of chocolate in your intestine is involuntary muscles.
• Heartbeat is an activity of involuntary muscles.

Additional Information

• Voluntary muscles are long, multinucleated cells, containing sarcomeres arranged into bundles.
• They play an important role in allowing the body to move by contracting and relaxing and their actions are mainly under the control of the somatosensory nervous system.
• Involuntary muscles are striated and branched in the case of cardiac muscle.
• The actions of involuntary muscles are mainly controlled by the autonomic nervous system in the body.

The correct answer is 28.

Key Points

• The relative mass of CO is 28g.
• ​The relative formula mass of a substance, shown in grams, is called one mole of that substance. So one mole of carbon monoxide has a mass of 28 g, and one mole of sodium oxide has a mass of 62 g.
• The element Cobalt belongs to group VIII of the periodic table. It is similar to iron and nickel in their physical properties.
• Cobalt is found in plants and animals, air, water, soil, and rocks.
• It may also enter into another environment through wind-blown dust or by rainwater washing down cobalt-containing soil and rock.

Shortcut Trick

Medini = 16 days, Yuki = 16 × 3 = 48 days.

Together they complete full wall in (16 × 48) ÷ (16 + 48) = (16 × 48) ÷ 64 = 12 days.

Time to paint half the wall = 12 ÷ 2 = 6 days.

∴ The correct answer is 6 days.

Alternate Method

Given:

Time taken by Medini = 16 days

Time taken by Yuki = 3 × 16 = 48 days

Calculations:

⇒ Total Efficiency of Medini and Yuki = 3 + 1 = 4 units/day

⇒ Half the work = 48 ÷ 2 = 24 units

⇒ Time taken to complete half work = 24 ÷ 4 = 6 days

∴ The correct answer is 6 days.

Additional Information

Time and Work Relation

Efficiency is inversely proportional to the time taken. If A is 3 times as efficient as B, A takes 1/3^rd the time taken by B.

Combined Work Formula

If two people can complete a task in X and Y days respectively, they together complete it in (X×Y)÷(X+Y) days.

Work and Efficiency

Work Done = Efficiency × Time. For partial work, simply multiply the total time by the required fraction.

Given:

8281

Concept used:

Prime factorisation of a number

Calculation:

Prime factorisation of 8281 = 7 × 7 × 13 × 13

So, √8281 = 7 × 13

⇒ 91

∴ Square root of 8281 is 91

The correct answer is M Subbaraidu.

Key Points

• Shri M. Subbarayudu was appointed as the next Ambassador of India to the Republic of Peru in 2017.
• He joined the Indian Forest Service in the year 1994.
• He has served at the Ministry of External Affairs, New Delhi as Deputy Secretary in the Central Europe Division and Joint Secretary in charge of Development Partnership Administration.

Additional Information

Shortcut Trick

Use the direct relationship between Circumference (C) and Diameter (D): C − D = 15

Substituting πD − D = 15 ⇒ D(π − 1) = 15

D(22/7 − 1) = 15 ⇒ D(15/7) = 15

D = 7 cm ⇒ Radius (r) = D/2 = 3.5 cm

∴ The correct answer is 3.5 cm.

Alternate Method

Given:

Circumference − Diameter = 15 cm

Formula Used:

Circumference (C) = 2πr

Diameter (D) = 2r

Calculations:

⇒ 2πr − 2r = 15

⇒ 2r(π − 1) = 15

⇒ 2r(22/7 − 1) = 15

⇒ 2r(15/7) = 15

⇒ 2r = (15 × 7) ÷ 15

⇒ 2r = 7

⇒ r = 7 ÷ 2

⇒ r = 3.5 cm

∴ The correct answer is 3.5 cm.

Additional Information

Circumference of Circle

It is the perimeter or boundary length of the circle, calculated as 2πr or πd.

Area of Circle

The total space enclosed within the boundary of a circle, given by the formula Area = πr².

Relation between Radius and Diameter

The diameter is always twice the length of the radius (D = 2r).

The logic followed here is as follows:

Shoes, Grass  and Mobile are all three unrelated words.

In other words,

No shoes is Grass

No Grass is Mobile. 

No Mobile is Shoes.

Therefore, the best possible venn diagram representation is as follows:

Hence, the above diagram is the correct answer.

The correct answer is 1526.

Key Points

• The first battle of Panipat was fought in 1526.
• The First Battle of Panipat, on 21 April 1526, was fought between the invading forces of Babur and the Lodi dynasty.
• It took place in North India and marked the beginning of the Mughal Empire from 1526 to 1857 and the end of the Delhi Sultanate.
• Battles of Panipat, (1526, 1556, 1761), three military engagements, important in the history of northern India, fought at Panipat.

Additional Information

• Ibrahim Lodi lost the fight and it denoted the start of the Mughal Empire and the finish of the Delhi Sultanate in India.
• Babur used modern tactics of warfare and introduced the deadly combination of Tulghuma and Araba.
• Tulghuma meant the division of the army into the left, right, and center units, while Araba referred to the carts used to launch cannon fire.

Important Points

• Panipat:
• Panipat is a historic city in Haryana, India.
• The city is famous in India as the City of Weavers and Textile City. It is also known as the cast-off capital due to being the global center for recycling textiles.
• Panipat district was carved out from the erstwhile Karnal district on 1 November 1989.
• On 24 July 1991, it was again merged with Karnal district. On 1 January 1992, it again became a separate district.

The correct answer is 5 Years.

Key Points

• 5 years is the tenure of Lok Sabha members.
• Lok Sabha is composed of representatives of the people chosen by direct election on the basis of adult suffrage.
• The term of a member of parliament of Lok Sabha (dissolved) is five years from the date appointed for its first meeting.
• During a state of emergency, the term however can be extended by the Parliament of India by law for a period not exceeding one year at a time.

Additional Information

• On 26 January 1950, the Indian constitution came into force and the first general elections (under the new constitution) were held in 1951-1952.
• The 1st Lok Sabha was constituted on 17 April 1952 and had 489 constituencies, thereby the first set of elected members of parliament of Lok Sabha in India.
• The maximum permitted strength of members of parliament in the Lok Sabha is 550.
• The first instance of a member of parliament equivalent in India dates back to 9 December 1946, the day the Constituent Assembly of India was formed with the purpose of drafting a constitution for India.

Important Points

• As per Article 93 of the Indian Constitution, the Lok Sabha has a Speaker and a Deputy Speaker.

The correct answer is Metal.

Key Points

• Metal has 1 to 3 electrons in its outermost shell.
• Metals usually have 1, 2, or 3 electrons in their valence shell.
• A valence shell means the outermost shell of an atom containing the valence electrons.
• The greater the number of shells and the lesser the number of valence electrons, the greater is the reactivity of the metal.

Additional Information

• The atom of every element has different electronic configurations.
• ​​For example, Sodium Atomic no.=11
• ​Therefore electronic configuration of Sodium is 2 8 1.

Important Points

• Electron shell diagram:

The correct answer is Hydra.

Key Points

• Hydra can reproduce by the process of regeneration and budding.
• ​Hydra is a small freshwater organism. They are native to temperate and tropical regions.
• When the food is plentiful the asexual reproduction occurs in hydra.
• The process is done by producing buds in the body wall. It grows as a mini form of adult and breaks apart when gets mature.
• Hydra goes through tissue regeneration when injured. If the hydra is cut in half, each part will regenerate as a whole new hydra. This regeneration occurs without the cell division process.

Additional Information

• Yeast:
• While most yeasts reproduce by budding, some also reproduce by fission.
• Plasmodium:
• Plasmodium reproduces both by sexual and asexual methods.
• Planaria:
• Planaria reproduces by methods like fragmentation and spontaneous dropping tails.
• Amoeba:
• An amoeba often called an amoeboid, is a type of cell or unicellular organism which has the ability to alter its shape, primarily by extending and retracting pseudopods.

Important Points

Structure of Hydra:

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The correct answer is 1.

Key Points

• In the modern periodic table, period 1 consists of only gases.
• There are only two elements in the first period: hydrogen and helium.
• Period 1 elements follow the duet rule, they only need two electrons to complete their valence shell.
• The modern Periodic law can be stated as: “The physical and chemical properties of the elements are periodic functions of their atomic numbers”

Additional Information

Shortcut Trick

For a unique solution (only one solution), the ratio of coefficients of x and y must be unequal.

Condition: a₁/a₂ ≠ b₁/b₂

Here, a₁ = 2, b₁ = 3 and a₂ = 2, b₂ = p.

⇒ 2/2 ≠ 3/p

⇒ 1 ≠ 3/p ⇒ p ≠ 3.

∴ The correct answer is any number other than 3.

Alternate Method

Given:

Equation 1: 2x + 3y = −5

Equation 2: 2x + py = 2

Formula Used:

For a system of equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 to have only one solution, the lines must be intersecting.

Condition: a₁/a₂ ≠ b₁/b₂

Calculations:

Comparing equations with the standard form:

⇒ a₁ = 2, b₁ = 3, c₁ = 5

⇒ a₂ = 2, b₂ = p, c₂ = −2

Applying the Unique Solution condition:

⇒ a₁/a₂ ≠ b₁/b₂

⇒ 2/2 ≠ 3/p

⇒ 1 ≠ 3/p

⇒ p ≠ 3

This means the value of p can be any real number except 3.

∴ The correct answer is any number other than 3.

Additional Information

Infinite Many Solutions

A system has infinite solutions if the lines are coincident: a₁/a₂ = b₁/b₂ = c₁/c₂.

No Solution

A system has no solution if the lines are parallel: a₁/a₂ = b₁/b₂ ≠ c₁/c₂.

Consistency of Equations

A system is consistent if it has at least one solution (unique or infinite) and inconsistent if it has no solution.

Shortcut Trick

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

Subtracting (−2, 0) from (3, 5), (−2, 0), and (6, 4) gives (5, 5), (0, 0), and (8, 4).

Area = 1/2 |(x₁ × y₂) − (x₂ × y₁)| = 1/2 |(5 × 4) − (8 × 5)|

Area = 1/2 |20 − 40| = 1/2 |−20| = 10 square units.

∴ The correct answer is 10 square unit.

Alternate Method

Given: Vertices of the triangle are A(3, 5), B(−2, 0), and C(6, 4).

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

⇒ Area = 1/2 |3(0 − 4) + (−2)(4 − 5) + 6(5 − 0)|

⇒ Area = 1/2 |3 × (−4) + (−2) × (−1) + 6 × 5|

⇒ Area = 1/2 |−12 + 2 + 30|

⇒ Area = 1/2 |20|

⇒ Area = 10 square units.

∴ The correct answer is 10 square unit.

Additional Information

Collinear Points

If the area of a triangle formed by three points is zero, then the points are collinear (lie on the same straight line).

The correct answer is Uttarkashi.

Key Points

• 'Gangotri Swachh Iconic Place Project and Swajal' was launched in the Uttarkashi district of Uttarakhand.
• The Union Ministry of Drinking Water and Sanitation has launched the Gangotri Swachh Iconic Place project and Swajal.
• The project will create cleanliness, provide basic amenities to the people of Ganga bank villages, and will also generate employment.

Additional Information

• The SIP (Swachh Iconic Place) is a drive under the Swachh Bharat Mission and aims to improve the sanitation and cleanliness of the 100 most iconic places in the country.
• The project was launched by Uma Bharti (Union Minister - 2018).
• This project is being coordinated by the:
• Department of Drinking Water and Sanitation (DDWS),
• Ministry of Jal Shakti in association with the Ministry of Housing and Urban Affairs (MoHUA),
• Ministry of Tourism,
• Ministry of Culture
• and the concerned State/UT governments.

The correct answer is India.

Key Points

• India became the third-largest country in terms of domestic air traffic in March 2017.
• India's domestic air passenger traffic stood at 100 million in 2016 and was behind only the US (719 million) and China (436 million).
• India acquired the third spot globally by unseating Japan, which flew 97 million domestic passengers in 2016.

Additional Information

• The aviation sector is one of the 25 sectors which has been there under the Make in India scheme.
• Area wise Indira Gandhi International airport (New Delhi) is the biggest airport in India.
• IGI is also the busiest airport in India. In FY 20-21 this airport handled approx 22,583,736 passengers.

The correct answer is Rohit Sharma.

Key Points

• The Mumbai Indians captain Rohit Sharma has won three consecutive IPL titles.
• Rohit Sharma was born on 30 April 1987, Nagpur, Maharashtra, India.
• Rohit Sharma is an Indian international cricketer who captains the India national cricket team in ODIs and T20Is.
• In November 2013, during Sachin Tendulkar's farewell series, Sharma made his Test debut at Eden Gardens in Kolkata.
• Sharma joined the Indian Premier League (IPL) in 2008 when he was signed by the Deccan Chargers franchise.
• In the 2011 auction, he was sold for US$2 million to the Mumbai Indians.

Additional Information

Important Points

• In 2015, Rohit Sharma was honored with Arjuna Award.
• In 2020, Rohit Sharma was honored with Major Dhyan Chand Khel Ratna.

According to the table,

In quarter 3 price difference = 65 - 40 = 25

∴ In quarter 3 price difference was the highest

The correct answer is Vikas Sathe.

Key Points

• Vikas Sathe was awarded the Scientific and Engineering Academy Award at the Oscar Scientific and Technical Awards 2018 held in February 2018 in Los Angeles, California.
• Sathe and his team received the award for his contribution towards conceptualization, designing, engineering, and the implementation of the 'Shotover K1 Camera System' during his stint at Shotover Camera Systems in Queenstown, New Zealand.
• Vikas Sathe is a Pune-born Indian engineer.

Additional Information

• About Shotover K1 Camera System
• ​The Shotover K1 Camera System is a camera mount that is used for aerial filming.
• The six-axis stabilized aerial camera mount can be attached to the base of a helicopter, which carries the camera and lens.
• The primary function of the camera mount is to ensure steady footage by eliminating any vibration from reaching the camera.

The correct answer is Kuttanad.

Key Points

is the lowest Below to sea level of India.

Kuttanad is a region that covers the Alappuzha, Kottayam, and Pathanamthitta Districts, in the state of Kerala. The region has the lowest altitude in the country and is one of the rarest places in the world where farming is carried on around 1.2 to 3.0 meters (4 to 10 ft) below sea level. Paddy is the major cultivation done in the Kuttanad region.

Additional Information

Important places of India

The highest point of India Kanchenjunga.

The lowest Altitude of India Kuttanad.

The coldest point of India Dras, Union Territory of Ladakh

The hottest point of India Jaisalmer, Rajasthan.

The driest point of India Leh, Union Territory of Ladakh

The wettest point of India Mawsynram, Meghalaya

Important Points

Place Details

Wayanad

Wayanad, the green paradise is nestled among the mountains of the Western Ghats, forming the border world of the greener part of Kerala. Wayanad was a part of the Malabar District until 31 March 1877. During British Raj, Wayanad was a Taluk in the erstwhile Malabar District.

Chettinad

Chettinad is a region located mainly in the Sivaganga district historically ruled by the Ramnad kingdom of Pandya Nadu and has a small portion extending into the Pudukottai District in Tamil Nadu, India. In the 19th and early 20th centuries, many residents of Chettinad were trading in South and Southeast Asia, particularly Burma, Ceylon, Vietnam, and Malaysia.

Indira Point

Indira Points refers to the southernmost tip of Great Nicobar Island which is also the Southernmost point of India. The point was formerly known as Pygmalion Point and Parsons Point. The Indira Point lighthouse was commissioned into service on 30 April 1972.

Shortcut Trick

Initial Ratio A : B = 7 : 5. Let common factor be x.

Remaining A after 9L removal = 7x − 9 × (7/12) and B after 10L addition = 5x − 9 × (5/12) + 10.

New ratio: [7x − 5.25] / [5x + 6.25] = 7 / 9.

Solving: 9(x − 0.75) = 5x + 6.25 ⇒ 4x = 13 ⇒ x = 3.25.

Initial quantity of A = 7 × 3.25 = 22.75 liters.

∴ The correct answer is 22.75 liters.

Alternate Method

Given: Initial Ratio A : B = 7 : 5. Replace 9 liters of mixture with 10 liters of liquid B. Final Ratio = 7 : 9.

Step 1: Amount of A removed = 9 × (7 / 12) = 5.25 liters.

Step 2: Amount of B removed = 9 × (5 / 12) = 3.75 liters.

Step 3: Let initial quantities be 7x and 5x.

⇒ (7x − 5.25) / (5x − 3.75 + 10) = 7 / 9

⇒ (7x − 5.25) / (5x + 6.25) = 7 / 9

⇒ 9(7x − 5.25) = 7(5x + 6.25)

⇒ 63x − 47.25 = 35x + 43.75

⇒ 28x = 91

⇒ x = 91 / 28 = 3.25

Step 4: Initial quantity of A = 7x = 7 × 3.25 = 22.75 liters.

∴ The correct answer is 22.75 liters.

Additional Information

Mixture Replacement Rule

When a quantity of mixture is removed, the ratio of liquids remains the same in the remaining mixture.

Alligation Method

Used for finding the proportions in which two or more ingredients at given prices/concentrations are mixed.

Concentration Formula

Final Concentration = Initial Concentration × [1 − (Removed Volume / Total Volume)]ⁿ (valid for repeated replacements).

Preparing the family tree using the following symbols:

 

Hence, the person in the photograph is the Cousin of Naina.

Given:31 × 5 + 16 - 4 ÷ 92

On decoding the given equation:

31 × 5 + 16 - 4 ÷ 92

→ 31 + 5 - 16 ÷ 4 × 92

→ 31 + 5 - 4 × 92

→ 31 + 5 - 368 

→ 36 - 368 

→ - 332

Hence, '- 332 ' is the correct answer.

The correct answer is JBS Haldane.

Key Points

• JBS Haldane:
• Haldane was a professed socialist, Marxist, atheist, and humanist whose political dissent led him to leave England in 1956 and live in India, becoming a naturalized Indian citizen in 1961.
• JBS Haldane was born on 5 November 1892 was a British scientist.
• Haldane's article on abiogenesis in 1929 introduced the primordial soup theory, which became the foundation for the concept of the chemical origin of life.
• Haldane was one of the three major figures to develop the mathematical theory of population genetics, along with Ronald Fisher and Sewall Wright.

Additional Information

<br>

Important Points 

• Constitutional Provisions for Indian citizenship Articles are:
• The Constitution does not define the term ‘citizen’ but details of various categories of persons who are entitled to citizenship are given in Part 2 (Articles 5 to 11).
• Article 5: It provided for citizenship on commencement of the Constitution.
• Article 6: It provided rights of citizenship of certain persons who have migrated to India from Pakistan.
• Article 7: Provided Rights of citizenship of certain migrants to Pakistan.
• Article 8: Provided Rights of citizenship of certain persons of Indian origin residing outside India.
• Article 9: Provided that if any person voluntarily acquired the citizenship of a foreign State will no longer be a citizen of India.
• Article10: It says that every person who is or is deemed to be a citizen of India under any of the foregoing provisions of this Part shall, subject to the provisions of any law that may be made by Parliament, continue to be such citizen.
• Article 11: It empowers Parliament to make any provision with respect to the acquisition and termination of citizenship and all matters relating to it.

The triangles in the given figure are as shown below.

Hence, there are 4 triangles in the given figure.

Shortcut Trick

Total Simple Interest for 6 years = ₹ 15,500 − ₹ 12,500 = ₹ 3,000

Interest for 1 year = 3,000 ÷ 6 = ₹ 500

Rate of Interest (R) = (Annual Interest ÷ Principal) × 100

R = (500 ÷ 12,500) × 100 = 4%

∴ The correct answer is 4%.

Alternate Method

Given:

Principal (P) = ₹ 12,500

Amount (A) = ₹ 15,500

Time (T) = 6 years

Formula Used:

1. Simple Interest (SI) = Amount − Principal
2. SI = (P × R × T) ÷ 100

Calculations:

⇒ SI = 15,500 − 12,500 = 3,000

⇒ 3,000 = (12,500 × R × 6) ÷ 100

⇒ 3,000 = (125 × R × 6)

⇒ 3,000 = 750 × R

⇒ R = 3,000 ÷ 750

⇒ R = 4%

∴ The correct answer is 4%.

Additional Information

Simple Interest Definition

Interest calculated only on the initial Principal amount throughout the entire period. SI = (P × R × T) ÷ 100.

Relationship between A, P, and SI

Total Amount (A) is the sum of Principal (P) and Interest (I). A = P + SI = P(1 + RT/100).

Rate of Interest

The annual percentage of Principal paid as interest. R = (SI × 100) ÷ (P × T).

The logic followed here is:

Hence, 'J64' is the next term in the given series.

Shortcut Trick

Identify prime numbers between 90 and 100.

Numbers to check: 91 (7×13), 92 (even), 93 (3×31), 94 (even), 95 (5×19), 96 (even), 97 (prime), 98 (even), 99 (3×33).

Only 97 is a prime number in this range.

Sum = 97.

∴ The correct answer is 97.

Alternate Method

Given: Range of numbers from 90 to 100.

Formula Used: Definition of a prime number (a number greater than 1 that has no positive divisors other than 1 and itself).

⇒ List numbers: 91, 92, 93, 94, 95, 96, 97, 98, 99.

⇒ Check divisibility for 91: 91 ÷ 7 = 13 (Composite)

⇒ Check divisibility for 93: 93 ÷ 3 = 31 (Composite)

⇒ Check divisibility for 97: Not divisible by 2, 3, 5, 7 (Prime)

⇒ Only prime number found = 97.

⇒ Sum = 97.

∴ The correct answer is 97.

Additional Information

Prime Numbers 1-100

There are exactly 25 prime numbers between 1 and 100. The only even prime number is 2.

Divisibility Rule of 3

A number is divisible by 3 if the sum of its digits is divisible by 3 (e.g., 9+3=12, so 93 is composite).

Co-prime Numbers

Two numbers are co-prime if their Highest Common Factor (HCF) is 1.

Shortcut Trick

To find the total weight, we need the values of two distinct weights and the number of bars for each.

From Statement 1: 1/2 × (2 bars) = 2 kg ⇒ Weight of 1 bar = 2 kg.

From Statement 2: 1/4 × (Weight of bar) = 0.5 kg ⇒ Weight of 1 bar = 2 kg.

Since both statements provide the same weight value (2 kg), they contradict the requirement of 2 different weights.

Even if combined, we lack the value of the second distinct weight and the count of each.

∴ The correct answer is Statements 1 and 2 together are not sufficient.

Alternate Method

Given: Total bars = 10, Number of distinct weights = 2.

Step-by-step Analysis:

From Statement 1:

⇒ Number of bars = 1/5 × 10 = 2 bars

⇒ 1/2 × (Weight of 2 bars) = 2 kg

⇒ Weight of 2 bars = 2 × 2 = 4 kg

⇒ Weight of one bar (w₁) = 4 ÷ 2 = 2 kg

From Statement 2:

⇒ 1/4 × (Weight of a remaining bar) = 0.5 kg

⇒ Weight of one bar (w₂) = 0.5 × 4 = 2 kg

Evaluation:

⇒ If w₁ = 2 kg and w₂ = 2 kg, there is only 1 unique weight, which contradicts 2 different weights.

⇒ We do not have the weight of the second category of bars or the distribution of how many bars are of which weight.

∴ The correct answer is Statements 1 and 2 together are not sufficient.

Additional Information

Data Sufficiency Principles

A question is solvable only when the number of independent equations matches the number of unknown variables (Weights and Quantities).

Weighted Average Formula

Total Weight = (n₁ × w₁) + (n₂ × w₂), where n is the count and w is the individual weight.

Logical Constraint Check

Always verify if the derived values satisfy the constraints mentioned in the question (e.g., different weights).

The correct answer is Millet.

Key Points

• Millet is not a plantation crop.
• Plantation Agriculture is a term used to describe a form of agriculture where the output is sold for commercial purposes, not for personal consumption.
• It usually involves a large area growing a singular crop over a long duration.
• This type of agriculture is mainly found in tropical and subtropical areas of the world.
• Plantation Agriculture requires a large amount of labour and capital.
• Some of the examples of plantation crops include:
• Arecanut (betel nut),
• cardamom,
• cashew,
• cocoa,
• coconut,
• coffee,
• oil palm,
• rubber, and
• tea

Additional Information

• The term plantation crop refers to those crops which are cultivated on an extensive scale in contiguous area, owned and managed by an individual or a company.
• Coconut, cashew nut, cocoa, areca nut, oil palm, and palm yrah come under the Ministry of Agriculture while tea, coffee, and rubber are dealt by Ministry of Commerce.
• Leading plantation crops producing states:

The correct answer is The cerebrum coordinates muscle activity.

Key Points

• ​The cerebrum is the largest part of the brain, constituting about 80% of it.
• It consists of the cerebral cortex and other subcortical structures.
• A deep cleft divides the cerebrum longitudinally into two halves, which are termed the left and right cerebral hemispheres.
• It forms the anterior, superior and lateral sides of the brain i.e., the fore, apex and side of the brain respectively.
• The cerebrum is responsible for thinking, intelligence,  consciousness, and memory.
• It is also responsible for interpreting touch, hearing, and vision.
• The forebrain consists of the cerebrum, thalamus, and hypothalamus.

 Additional Information

• The Cerebellum controls things like posture, balance, muscular activity, and more.
• If the cerebellum is damaged, it could affect balance, slow movements, or produce tremors or shaking.
• The cerebellum is the second largest part of the brain, located in the posterior portion of the medulla and pons.

​

According to the pie chart,

We can see company B manufactured 30% in the year 2017 which is the highest among others,

∴ Company B manufactured the maximum number of tires.

Given:

3√5 + √125 = 17.85 

Calculation:

3√5 + √125 = 17.85

⇒ 3√5 + 5√5 = 17.85 

⇒ 8√5 = 17.85 

Now solve

⇒ √80 + 7√5 = √(16 × 5) + 7√5

⇒ 4√5 + 7√5 = 11√5

⇒ 11√5 = 17.85 × (11√5/8√5)

⇒ 11√5 = 17.85 × (11/8)

⇒ 11√5 = 24.53

∴ The value of √80 + 7√5 is 24.53.

The logic followed here is:

• Here, there are two images a circle and a triangle intersecting each other in figure 1.
• In the next step both the images move apart and a circle is transformed into two concentric circles.

Similarly, 

• In figure 3, two images, a rectangle and a circle intersecting each other are given.
• In the next step, both the images move apart and the figure which is on the upper side i.e. rectangle is transformed into two concentric rectangles.

Hence, the next picture in the given series will be the figure given in option 4.

The correct answer is R venkatramani

Note;

• This question was asked in PYP. Therefore options were given according to that year.
• The current Attorney General of India is Hon'ble Shri R venkatramani

Key Points

• R venkatramani is the current Attorney General of India
• During the time the question was asked the Attorney Genral K k Venugoapal.

Additional Information

• Attorney General of India:
• Attorney General of India is appointed by the President of India under Article 76.
• Article 76 and 78 deal with the Attorney General of India.
• He holds office during the pleasure of the President
• The constitution has not fixed the remuneration of the AG.
• He should be qualified to be appointed a judge of the Supreme Court
• The Attorney General of India is the highest law officer in the country
• The current Attorney General is K. K. Venugopal.
• K. K. Venugopal is the 15th Attorney General of India.
• The current Attorney General of India (16th) -  R Venkataramani (1^st Oct. 2022).

<br>

 

The logic followed here is:

• In each figure A, B, and C, the image is divided into two equal parts and one of the parts is shaded whereas, in figure D more than half of the figure is shaded.

Hence, figure D is the odd one out of the given figures.

The correct answer is Echinodermata.

Key Points

• Starfish belongs to the phylum Echinodermata group.
• Echinodermata are so named owing to their spiny skin (from the Greek “echinos” meaning “spiny” and “dermos” meaning “skin”).
• Echinodermata are exclusively marine organisms. Sea stars, sea cucumbers, sea urchins, sand dollars, and brittle stars are all examples of echinoderms.

Additional Information 

The correct answer is Real and inverted.

Key Points

• The image formed on the retina of the human eye is real and inverted.
• The retina comprises specialized cells that are sensitive to light, known as rod and cone cells.
• These cells get stimulated and send signals to the brain which turns them into erect images that allow us to see.

Additional Information

• The lens system of an eye forms an image on a light-sensitive screen known as the retina.
• Light enters the eye through a thin membrane known as the cornea.
• Behind the cornea, there is a structure, known as the iris. It has a major function to control the size of the pupil.

According to the bar graph,

In 2012 total of 50 Lakhs computers were sold

1 million = 10 lakhs

so 50 lakhs = 5 millions

∴ 5 million personal computers were sold by Company XYZ in 2012

• The statement says that he got on a bus on Wednesday, to go to Hyderabad.
• Thus it cannot be determined whether he reached Hyderabad on the very same day, or the next day or exactly when. Thus, assumption I is not implicit.
• Since it is given that he caught the bus to go to Hyderabad for an event that was on Saturday, it is safe to assume that he would try to reach there before the event ends. Thus, Assumption II is implicit.

Hence the correct answer is option 3.

The correct answer is 48 kilogram.

Key Points

• In November 2017, India's Ritu Phogat won a silver medal in the Under 23 Senior World Wrestling Championship held in Poland. She has won the silver in the 48 kg category.
• She lost against Turkish Wrestler Demirhan in the final and won the Silver medal.
• Ritu had won the National championship in Indore in 2017. She also won a bronze medal at the Asian Championships in May 2017.

Additional Information

• Ritu Phogat is also a female wrestler who won a gold medal at the 2016 Commonwealth Wrestling Championship.
• In November 2016, she won the gold medal at the 2016 Commonwealth Wrestling Championship in Singapore in the 48 kg category.
• In October 2016, Phogat won her second consecutive title at the annual National Wrestling Championships.

The correct answer is Calcium.

Key Points

• Calcium is not from the class of alkali metals.
• Calcium (Ca) is one of the alkaline-earth metals of Group 2 (IIa) of the periodic table.
• Calcium is a chemical element with the symbol Ca and atomic number 20.
• It is the most abundant mineral in the body, and it is vital for bone health.
• Humans need calcium to build and maintain strong bones, and 99% of the body's calcium is in the bones and teeth.

Additional Information

• Alkali elements are Lithium(Li), Sodium(Na), Potassium (K), Rubidium (Rb), Cesium (Cs) and Francium (Fr) occupying successive periods from first to seven.
• The compounds are called alkali metals because when they react with water they usually form alkalies which are nothing but strong bases that can easily neutralize acids.
• Alkali metals belong to the s-block elements occupying the leftmost side of the periodic table.

The mirror image of the given figure is as follows:

Hence, the mirror image of the given figure will be answer figure C.

(Note: In original paper this question has discrepancy. The lines within the figure D in question had to be changed. The lines will be as per the figure given above.)

Shortcut Trick

Product of diagonals (d₁ × d₂) = 2 × Area = 2 × 4 = 8.

Sum of squares of diagonals (d₁² + d₂²) = 4 × side² = 4 × 5 = 20.

Using identity: (d₁ + d₂)² = (d₁² + d₂²) + 2(d₁ × d₂).

(d₁ + d₂)² = 20 + 2(8) = 36.

Sum of diagonals (d₁ + d₂) = √36 = 6 cm.

∴ The correct answer is 6 cm.

Alternate Method

Given:

Side length of rhombus (a) = √5 cm

Area of rhombus (A) = 4 cm²

Formula Used:

Area of rhombus = 1/2 × d₁ × d₂

Relation between side and diagonals: 4a² = d₁² + d₂²

Calculations:

⇒ 4 = 1/2 × d₁ × d₂

⇒ d₁ × d₂ = 8

⇒ 4 × (√5)² = d₁² + d₂²

⇒ 4 × 5 = d₁² + d₂²

⇒ d₁² + d₂² = 20

⇒ (d₁ + d₂)² = d₁² + d₂² + 2d₁d₂

⇒ (d₁ + d₂)² = 20 + 2 × 8

⇒ (d₁ + d₂)² = 36

⇒ d₁ + d₂ = √36 = 6 cm

∴ The correct answer is 6 cm.

Additional Information

Rhombus Diagonals

The diagonals of a rhombus bisect each other at right angles (90°), forming four congruent right-angled triangles.

Area Formula

The area of a rhombus can be calculated as Base × Height or 1/2 × Product of Diagonals.

Side-Diagonal Relation

The sum of the squares of the diagonals is equal to four times the square of the side: d₁² + d₂² = 4a².

The correct answer is Wrestling.

Key Points

• Satyawart Kadian is associated with wrestling sports.
• He was born on 9th November 1993, in Rohtak, Haryana, India.
• The Achievements of Satyawart Kadian:
• A bronze medal in the 100 kg category at the 2010 Youth Olympic Games, held in Singapore.
• Earned a bronze medal in the 96 kg category at the World Junior Championships in 2013 that took place in Sofia.
• Bagged silver and a bronze medal in the 97 kg category at the Commonwealth Games and Asian Championships of 2014.
• Won the title at the 1st Rustam-e-International tournament which was held at Jammu in 2015.
• Clinched a gold medal in the 97 kg category at the Commonwealth Championships of 2016, held in Singapore.
• Claimed a bronze medal in the 97 kg category at the 2019 Asian Championships.

Additional Information

Shortcut Trick

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

⇒ 800 = 20,000 × (R/100)²

⇒ (R/100)² = 800 ÷ 20,000 = 4 ÷ 100

⇒ R/100 = √(4/100) = 2/10

⇒ R = 20%

∴ The correct answer is 20%.

Alternate Method

Given: Principal (P) = ₹ 20,000, Time (T) = 2 years, Difference (D) = ₹ 800.

Formula Used: Difference for 2 years = P × (R/100)²

⇒ 800 = 20,000 × (R/100)²

⇒ 800 ÷ 20,000 = (R/100)²

⇒ 8 ÷ 200 = (R/100)²

⇒ 4 ÷ 100 = (R/100)²

⇒ (2/10)² = (R/100)²

⇒ R/100 = 2/10

⇒ R = (2 × 100) ÷ 10 = 20

∴ The correct answer is 20%.

Additional Information

CI and SI Difference for 3 Years

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

Effective Rate of Interest

For 2 years at R%, the effective Simple Interest rate is 2R% and the effective Compound Interest rate is (2R + R²/100)%.

Relation for 2 Years

The difference (D) between CI and SI for 2 years is also equal to the interest calculated on the first year's interest: D = (SI × R) ÷ 200.

From the given statement, it is clear that Nayan joined the local football team in 2014, and that he helped the team to win 3 championships.

• Winning the 3 championships between 2016 and 2018 for the first time ever can be said to have led the team to reach new heights because it is mentioned that his Nayan's joining had helped the team win. Thus, conclusion I follows.
• Helping the team win 3 championships is not possible unless you are a good player. Winning a championship because of a player indicates that he has made a significant contribution. Nayan has been accredited for the teams' 3 victories. Winning directly implies success. So we can say that conclusion II follows.

Thus the correct answer is option 2.

Shortcut Trick

Average Speed = 45 ÷ 8 = 5.625 km/hr

Using Alligation on speeds: (10 − 5.625) : (5.625 − 3) = 4.375 : 2.625

Ratio of Time (Walking : Cycling) = 4.375 : 2.625 = 5 : 3

Total time 8 hours divided in 5:3 → Cycling time = 3 hours

Cycling distance = 10 km/hr × 3 hours = 30 km

∴ The correct answer is 30 km.

Alternate Method

Given: Cycling speed (S₁) = 10 km/hr, Walking speed (S₂) = 3 km/hr, Total Time (T) = 8 hours, Total Distance (D) = 45 km.

Formula Used: Distance = Speed × Time

⇒ Let time spent cycling be 't' hours. Then walking time = (8 − t) hours.

⇒ (10 × t) + 3 × (8 − t) = 45

⇒ 10t + 24 − 3t = 45

⇒ 7t = 45 − 24

⇒ 7t = 21

⇒ t = 3 hours

⇒ Distance covered by cycle = Speed × Time = 10 × 3 = 30 km

∴ The correct answer is 30 km.

Additional Information

Alligation Rule for Speed

When alligation is applied to speeds, the resulting ratio is always the ratio of the time taken for each part of the journey.

Average Speed Formula

Average Speed = Total Distance traveled ÷ Total Time taken.

Distance Equation

D = (S₁ × T₁) + (S₂ × T₂), where T₁ + T₂ = Total Time.

Shortcut Trick

Original dimension 100% increases by 50% (half), becoming 150% or 1.5 times.

Volume is proportional to the cube of the dimension (side³).

New Volume = (1.5)³ × Original Volume = 3.375 × Original Volume.

Percentage = 3.375 × 100 = 337.5%.

∴ The correct answer is 337.5%.

Alternate Method

Given: Original side of cubical box = a. Increase in dimension = a/2.

Formula Used: Volume of cube = side³ | Percentage = (New/Original) × 100.

⇒ Original Side = a

⇒ New Side = a + a/2 = 1.5a

⇒ Original Volume (V₁) = a³

⇒ New Volume (V₂) = (1.5a)³ = 3.375a³

⇒ Percentage of original volume = (V₂ / V₁) × 100

⇒ Percentage = (3.375a³ / a³) × 100 = 337.5%

∴ The correct answer is 337.5%.

Additional Information

Volume Scaling

If the linear dimensions of a 3D object are multiplied by a factor k, the volume is multiplied by k³.

Surface Area Scaling

If the linear dimensions are multiplied by k, the surface area is multiplied by k² (e.g., 1.5² = 2.25 or 225%).

Percentage Increase in Volume

Percentage increase = [(New Volume − Original Volume) / Original Volume] × 100 = 237.5%.

The correct answer is 175 J.

Concept:

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

The expression for kinetic energy is given by:

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

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

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

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

The relationship between the kinetic energy (KE or k) and Linear momentum is given by:

As we know,

 $KE = \frac{1}{2}m{v^2}$

Divide numerator and denominator by m, we get

$KE = \frac{1}{2}\frac{{{m^2}{v^2}}}{m} = \frac{1}{2}\frac{{;{{\left( {mv} \right)}^2}}}{m} = \frac{1}{2}\frac{{{p^2}}}{m};$ [p = mv]

$\therefore KE = \frac{1}{2}\frac{{{p^2}}}{m};$

$p = \sqrt {2mKE}$

Calculation:

Given, Mass = 14 kg

velocity = 5 ms-1

We know that, 

Kinetic energy = 1/2 × mv²

Kinetic energy = 1/2 × 14 × 5² = 7 × 25 = 175 J

The correct answer is Strong acid and strong base.

Key Points 

• Strong acid and strong base neutralise each other and make a neutral salt solution which carry pH 7.
• For example NaOH strong base mix with Strong Acid HCl form a neutral salt NaCl.
• This is an ordinary salt used in cooking.
• Salts of a strong acid and a strong base are neutral with pH value of 7.
• On the other hand, salts of a strong acid and weak base are acidic with pH value of less than 7
• and those of a strong base and weak acid are basic in nature, with pH value of more than 7.

Additional Information

• pH is defined as the negative logarithm of H+ ion concentration. Hence the meaning of the name pH is justified as the power of hydrogen.
• Solutions having a value of pH ranging 0 to 7 on the pH scale are termed as acidic and the value of pH ranging 7 to 14 on the pH scale are known as basic solutions.
• Pure water has a pH value of 7.
• The basicity decreases as the value of pH decreases from 14 to 7.

The correct answer is Bhangar.

Key Points

• Old alluvial soil is known as Bhangar and is full of Kankars (lime nodules).
• The Bhangar is the older alluvium along the river beds forming terraces higher than the floodplain.
• Bhangar contains fossils of animals like rhinoceros, hippopotamus, elephants, etc.
• This type of soil is found in mountainous regions. This type of soil is found in huge amount in the North Indian Plains.

Additional Information

Shortcut Trick

Number of leap years in 100 years is either 24 or 25.

In a standard 100-year interval (like 1 to 100), the 100^th year is usually not a leap year unless divisible by 400.

Commonly, X = 24 (e.g., years 1801−1900).

Calculation: X − 1 = 24 − 1 = 23.

∴ The correct answer is 23.

Alternate Method

Given: Interval of 100 years.

⇒ A year is a leap year if divisible by 4, but century years must be divisible by 400.

⇒ In any 100-year block, there are at most 25 multiples of 4.

⇒ Case 1: If the century year is not divisible by 400 (e.g., 1900), X = 24.

⇒ Case 2: If the century year is divisible by 400 (e.g., 2000), X = 25.

⇒ Looking at options, if X = 24, then X − 1 = 23.

⇒ Looking at options, if X = 25, then X − 1 = 24.

⇒ Since 23 is provided and standard 100-year intervals (like a century) usually have 24 leap years:

⇒ X − 1 = 24 − 1 = 23.

∴ The correct answer is 23.

Additional Information

Leap Year Rule

A year is a leap year if it is divisible by 4, except for century years which must be divisible by 400.

Odd Days in a Century

100 years contain 5 odd days (76 ordinary years + 24 leap years).

Leap Century

A century like 400, 800, 1200, 1600, 2000 is a leap century and contains 25 leap years.

Shortcut Trick

Profit/Difference between Compound Interest (CI) and Simple Interest (SI) for 2 years = P × (R/100)²

Given Principal (P) = ₹ 22,500 and Rate (R) = 6%

Difference = 22500 × (6/100) × (6/100) = 22500 × 36/10000

Difference = 2.25 × 36 = 81

Since CI is always greater than SI for the same period and rate, it is a Profit.

∴ The correct answer is 81 Profit.

Alternate Method

Given: Principal (P) = ₹ 22,500, Time (T) = 2 years, Rate (R) = 6% per annum.

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

Step 1: Calculate Simple Interest (Borrowing)

⇒ SI = (22500 × 6 × 2) ÷ 100

⇒ SI = 225 × 12 = ₹ 2,700

Step 2: Calculate Compound Interest (Lending)

⇒ CI = 22500 × [(1 + 6/100)² − 1]

⇒ CI = 22500 × [(1.06)² − 1]

⇒ CI = 22500 × [1.1236 − 1]

⇒ CI = 22500 × 0.1236 = ₹ 2,781

Step 3: Calculate Profit

⇒ Profit = CI − SI

⇒ Profit = 2781 − 2700 = ₹ 81

∴ The correct answer is 81 Profit.

Additional Information

Difference between CI and SI for 2 years

The difference is always calculated as P × (r/100)².

Difference between CI and SI for 3 years

The formula is P × (r/100)² × (3 + r/100).

Effective Rate of Compound Interest

For 2 years at rate r%, the effective CI rate is r + r + (r × r)/100.

The right angled triangles in the given figure are as shown below.

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Hence, there are 8 right-angled triangles in the given figure.

Concept Used:  

Follow the BODMAS rule according to the table given below:

Calculation:

(2 + 5) × 4 + (4/2) = ?

⇒ 7 × 4 + 4/2 = ?

⇒ 28 + 4/2 = ?

⇒ 28 + 2 = ?

⇒ 30 = ?

∴ The value of ? is 30

The correct answer is Balakrishna Doshi.

Key Points

• Balakrishna Doshi became the first Indian to win the prestigious Pritzker Prize for his outstanding lifelong contribution to architecture, in March 2018.
• He was awarded the year's Pritzker Prize for being able to interpret architecture and transform it into buildings that respect Eastern culture.
• Pritzker Prize is regarded as architecture's equivalent to the Nobel Prize.

Additional Information

About Pritzker award:

• Pritzker award is awarded each year to a living architect/s for significant achievement, was established by the Pritzker family of Chicago through their Hyatt Foundation in 1979.
• It is granted annually and is often referred to as “architecture’s Nobel” and “the profession’s highest honor.”
• The award consists of $100,000 (US) and a bronze medallion.
• The award is conferred on the laureate/s at a ceremony held at an architecturally significant site throughout the world.