RRC Group D Previous Year Paper 6 (Held On: 24 Sep 2018 Shift 1)

• According to the statement, a story-telling session has been made compulsory by the headmistress.
• A story-telling session is an activity of telling or writing stories.
• Thus, this can be safely assumed that the headmistress wants the children to read stories because the session is for "storytelling"
• Hence, the assumption I is implicit.
• Now, assumption II specifies that the children are asked to write "their own stories". Now the type of stories (whether their own stories or stories about someone else) to be written is not suggested in the statement.
• Hence, assumption II is not implicit.

Hence, “Only I is implicit”.

• The total number of resistors are 5
• The resistance of each individual resistor is $\left( {\frac{1}{5}} \right){\rm{\Omega }}$.
• The maximum resistance is obtained when resistors are connected in series connection
• We know that in series R_(Total) = R₁ + R₂ +R₃………Rn.
• R _(Total =  $\left( {\frac{1}{5}} \right){\rm{\Omega }} + {\rm{;}}\left( {\frac{1}{5}} \right){\rm{\Omega }} + {\rm{;}}\left( {\frac{1}{5}} \right){\rm{\Omega }} + \left( {\frac{1}{5}} \right){\rm{\Omega }} + \left( {\frac{1}{5}} \right){\rm{\Omega }}.{\rm{;;}}$
• = 1 Ω.
• The maximum value of resistance is obtained when connected in series is 1 Ω (Ohms).

• Group 18 in the periodic table includes all the Noble gases/ Inert Gases.
• They are Helium (He), Neon (Ne), Argon (Ar), Krypton (Kr), Xenon (Xe), Radon (Rn) & Oganesson (Og) or Ununoctium (Uno).
• These gases are also called inert gases because they do not form any compounds when reacted with other elements and have either octet or duplet configuration.

The pattern followed here is as follows,

Hence, “W” is the correct answer.

• Malavath Poorna became the youngest girl in the world to conquer Mount Everest and Mount Elbrus.
• In the year 2019, she became the first tribal woman to climb four highest mountains located in four continents with the other two being Mount Kilimanjaro in Africa and Mount Aconcagua in South America.
• Mount Everest (8848 m) is the highest peak in the world.
• Mount Elbrus (5642 m) is the highest peak in Europe.

CONCEPT:

• Momentum (p): The product of mass and velocity is called momentum. It is a vector quantity.
• The SI unit of momentum is kg m/s.

Momentum (p) = Mass (m') × Velocity (v')

EXPLANATION:

Given that:

The mass of an object (m') is ½ m

The velocity (v') of an object  is 2v

We know that momentum (p) = mass × velocity = ((m/2) × 2 v) = m v​

• The momentum of the object is mv kg m/s. Hence option 4 is correct.

• Viswanathan Anand, the India chess master had clinched the 2018 Tal Memorial Rapid Chess tournament in Moscow.
• He was the first awardee to receive Rajiv Khel Ratna in the year 1992.
• He secured 5th place in the Shamkir Chess 2019 tournament held in Shamkir, Azerbaijan.

As per the given information,

Hence, Nikita is 1 km far from her starting point.

Here, as we know there is no relation between pen, paper and computer. Thus, the following venn diagram will be best suitable for given information.

Hence, “option figure 2” is the correct answer.

Shortcut Trick

Present ratio of Naresh and Suparna = 7 : 3 (Difference = 4 units)

Ratio after 3 years = 2 : 1. To equate difference, multiply by 4 → 8 : 4

Change in units = 8 − 7 = 1 unit → 3 years

Naresh present age = 7 units = 7 × 3 = 21 years

∴ The correct answer is 21 years.

Alternate Method

Given: Present age ratio = 7 : 3 | Age after 3 years ratio = 2 : 1

Let the present ages be 7x and 3x.

⇒ (7x + 3) / (3x + 3) = 2 / 1

⇒ 1 × (7x + 3) = 2 × (3x + 3)

⇒ 7x + 3 = 6x + 6

⇒ 7x − 6x = 6 − 3

⇒ x = 3

⇒ Naresh present age = 7x = 7 × 3 = 21

∴ The correct answer is 21 years.

Additional Information

Ratio Difference Method

When the same value is added to both parts of a ratio, the numerical difference between the ratio parts should be equalized by multiplying the ratios with appropriate factors.

Cross-Multiplication Method

For age problems, (Initial Ratio 1 × Final Ratio 2) − (Initial Ratio 2 × Final Ratio 1) = Value added × (Final Ratio 1 − Final Ratio 2).

• India won the 2016 Kabaddi World Cup in Men’s Category.
• India hosted the 2016 Kabaddi World Cup and 12 countries participated in the competition.
• India also won the 2016 Kabaddi World Cup in Women’s Category.

The pattern followed here is as follows,

Here, the number in the right is the positional value associated with the letter in the middle.

Hence, “81R18” is the correct answer.

Shortcut Trick

For a cuboid, if the areas of three adjacent faces are A₁, A₂, and A₃, then:

Volume (V) = √(A₁ × A₂ × A₃)

V = √(25 × 32 × 32) = 5 × 32 = 160

∴ The correct answer is 160 m³.

Alternate Method

Given:

Area of first face (l × b) = 25 m²

Area of second face (b × h) = 32 m²

Area of third face (l × h) = 32 m²

Calculations:

⇒ (l × b) × (b × h) × (l × h) = 25 × 32 × 32

⇒ l² × b² × h² = 25 × 1024

⇒ (l × b × h)² = 25600

⇒ Volume (V) = l × b × h = √25600

⇒ V = 160 m³

∴ The correct answer is 160 m³.

Additional Information

Total Surface Area of Cuboid

The total surface area (TSA) is given by the formula: 2(lb + bh + hl).

Diagonal of a Cuboid

The length of the longest rod that can be placed in a cuboid is √(l² + b² + h²).

Volume of a Cube

If all sides are equal (l = b = h = a), then the volume of the cube is a³.

Shortcut Trick Let the required number be x. According to the given condition: x2 + 2x = 3 By testing the options: For x = 1 ⇒ 12 + 2(1) = 3 (Satisfied) For x = −3 ⇒ (−3)2 + 2(−3) = 9 − 6 = 3 (Satisfied) ∴ The correct answer is 1 or −3.

Alternate Method Given: Let the unknown number be x. Square of the number added to two times the number equals 3. Equation: x2 + 2x = 3 Calculations: ⇒ x2 + 2x − 3 = 0 ⇒ x2 + 3x − x − 3 = 0 ⇒ x(x + 3) − 1(x + 3) = 0 ⇒ (x − 1)(x + 3) = 0 ⇒ x − 1 = 0 or x + 3 = 0 ⇒ x = 1 or x = −3 ∴ The correct answer is 1 or −3.

Additional Information Standard Form of Quadratic Equation A quadratic equation is of the standard form ax2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. Nature of Roots The value of the discriminant D = b2 − 4ac determines whether the roots are real and distinct (D > 0), real and equal (D = 0), or imaginary (D < 0). Sum and Product of Roots For the equation ax2 + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a.

Shortcut Trick

Sum of ratio parts = 1 + 2 + 3 = 6 units.

Total sum of angles in a triangle = 180°.

6 units → 180°

1 unit → 180° ÷ 6 = 30°.

The smallest angle corresponds to 1 unit = 30°.

∴ The correct answer is 30°.

Alternate Method

Given:

Ratio of angles of the triangle = 1 : 2 : 3

Formula Used:

Angle Sum Property: The sum of all interior angles of a triangle is always 180°.

⇒ Let the angles of the triangle be 1x, 2x, and 3x.

⇒ According to the Angle Sum Property:

⇒ 1x + 2x + 3x = 180°

⇒ 6x = 180°

⇒ x = 180° ÷ 6

⇒ x = 30°

⇒ The angles are 30°, 60°, and 90°.

⇒ Smallest angle = 1x = 30°.

∴ The correct answer is 30°.

Additional Information

Angle Sum Property

• The Rihand River Valley Project is in Uttar Pradesh.
• It is on the Rihand River which is the tributary of the Son River.
• The catchment area of this dam is spread out in Uttar Pradesh, Madhya Pradesh & Chhattisgarh.

Shortcut Trick

Distance = [Product of Speeds ÷ Difference of Speeds] × [Difference in Time]

Product of speeds = 54 × 48; Difference of speeds = 54 − 48 = 6 km/h

Total time difference = 3 minutes (early) + 1 minute (late) = 4 minutes = 4/60 hours

Distance = (54 × 48 ÷ 6) × (4 ÷ 60) = 432 × (1 ÷ 15) = 28.8 km

∴ The correct answer is 28.8 km.

Alternate Method

Given: Speed₁ (S₁) = 54 km/h, Speed₂ (S₂) = 48 km/h

Time Difference: Early 3 min and Late 1 min ⇒ ΔT = 3 + 1 = 4 minutes

Formula Used: Distance = S₁ × S₂ × (ΔT / 60) ÷ (S₁ − S₂)

⇒ Distance = (54 × 48) ÷ (54 − 48) × (4 ÷ 60)

⇒ Distance = (2592 ÷ 6) × (1 ÷ 15)

⇒ Distance = 432 ÷ 15

⇒ Distance = 28.8 km

∴ The correct answer is 28.8 km.

Additional Information

Speed-Time Relation

When distance is constant, speed is inversely proportional to time (S ∝ 1/T). Ratio of speeds S₁:S₂ = T₂:T₁.

Time Difference Rule

If one case is early and the other is late, add the times to find the total difference. If both are early or both are late, subtract them.

Average Speed

For two equal distances covered at speeds S₁ and S₂, Average Speed = 2 × S₁ × S₂ ÷ (S₁ + S₂).

• Going from fluorine to chlorine, to bromine and then to iodine, the electronegatively decreases.
• It is defined as the ability of an atom in a chemical Compound to attract a shared electron to itself.
• The electronegativity increases across the period from left to right
• Example: Lithium to Fluorine.
• The electronegativity decreases down the group.
• Example: Fluorine to Astatine.
• Pauling Scale is widely used to measure electronegativity.

As shown in the following figure we can number the question figure can find the answer figure as follows,

Hence, “option figure A” is the correct answer.

The pattern followed herer is as follows,

Hence, “option figure D” is the correct answer.

• Methane is a pure substance.
• A pure substance consists of a single type of particles such as atoms or molecules and not mixed up with other substances.
• A two or more pure substance are combined to form a Mixture.
• Milk is a mixture of fats, water, proteins etc. and Air is a mixture of different gases and Sugar Solution consists of sugar and water.
• Hence above three are not pure substances but are mixtures.

The correct answer is a member of Rajya Sabha.

• The Prime Minister of India cannot participate in voting on a no-confidence motion against her/his government if she/he is a member of the Rajya Sabha.
• The no-confidence motion is a motion that is introduced against the ruling government in the elected house i.e Lok Sabha and not in the upper house i.e Rajya Sabha.
• As it is a motion brought up only in Lok Sabha, if the Prime Minister is a member of Rajya Sabha, then she/he cannot vote in a No-Confidence motion.
• Process for the No-Confidence Motion:
• A requirement for the introduction of a No-Confidence motion is given to the speaker of the house which is to be supported by a minimum of 50 members.
• The Speaker will give time within the next 10 days for discussion on the motion in the house.
• After the discussion, the voting takes place.
• If the No-Confidence Motion is passed in the House the Council of Ministers must resign as they have lost majority in the House.

• As of August 2018, the lieutenant governor of Puducherry was Kiran Bedi.
• As of May 2019, Kiran Bedi is still the lieutenant governor of Puducherry
• She was the first women to join the Indian Police Service (IPS).

The pattern followed here is as follows,

Every element is shifted to the next quadrant in the succeeding image.

Similarly,

Hence, “option figure D” is the correct answer.

• Acetic Acid is the common name of ethanoic acid.
• The chemical Formulae for Acetic Acid is CH₃COOH.
• It belongs to a group called carboxylic acid and hence they are weak acids.
• When acetic acid is diluted in water with a percentage of 5-8 then vinegar is formed.
• The melting point of acetic acid is 290k and it often freezes at room temperature, hence it has another name called Glacial Acetic Acid.

The correct answer is Persian.

Mistake Points

• Baburnama was written in the Turkish language.
• Babur wrote his autobiography 'Tuzk-e-Babri' in the Turkish Language.
• Abdul Rahim Khan-i-Khana translated 'Tuzk-e-Babri' into Persian Language.
• Babur established the Mughal empire in India by defeating Ibrahim Lodi at the Battle of Panipat in the year 1526.​
• Babur had to move east and conquer northern India in 1526; he died in Agra in 1530. Throughout his years in the flat, dusty plains of India he missed his home country and thus wished to be buried in Kabul. His body was transferred to Bagh-e Babur by his widow around 1544.

Additional Information

• Babur was the first emperor of the Mughal Empire.
• Babur conquered the first battle of Panipat by defeating Ibrahim Lodi in 1526 AD.
• Ibrahim Lodi was the last ruler of the Lodi dynasty of the Delhi Sultanate.
• Babur defeated Rana Sanga of Mewar in the Battle of Khanwa in the year 1527 AD.
• Humayun was his son and Akbar was his grandson.
• On December 26, 1530, AD, Mughal emperor Babur died in Agra,
• Initially, he was buried in Agra against his wishes.

⇒ Divya’s saving into decimal = 45.5/100 = 0.4550

• Medha Patkar actively participated in the campaign against the Narmada Valley Project.
• She actively participated in Narmada Bachao Andolan which is the name of the movement against the Narmada Valley project.

• The Deodar plant bears naked seeds.
• The Deodar belongs to the gymnosperms category of the plant.
• Gymnosperm plants are those in which ovules are not covered by any ovary wall.
• The ovules in gymnosperms remain exposed both before and after fertilization.
• The seeds that develop post-fertilization are not covered. Hence they are called naked seeds.

⇒ \(162 \div \left[ {51 - \left{ {29 - \left( {9 - \overline {6 + 7} } \right)} \right}} \right]\)

⇒ \(162 \div \left[ {51 - \left{ {29 - \left( {9 - 13} \right)} \right}} \right]\)

⇒ $162 \div {\rm{[}}51 - {\rm{{ }}29 - ( - 4{\rm{)} }}$

⇒ \(162 \div \left[ {51 - \left{ {29 + 4} \right}} \right]\)

⇒ \(162 \div \left[ {51 - \left{ {33} \right}} \right]\)

⇒ 162 ÷ 18

⇒ 9

Revenue generated from learning block = 15% of total revenue = (15/100) × 3872000 = Rs. 580800

We can count the triangles as follow,

Hence, there are “7” triangles in the given figure.

Shortcut Trick

Total capacity in mL = (4 × 1000) + 500 = 4500 mL.

Number of containers = 4500 ÷ 25.

Quick division: (45 × 100) ÷ 25 = 45 × 4 = 180.

∴ The correct answer is 180.

Alternate Method

Given:

Total acid in the barrel = 4 L 500 mL

Capacity of one container = 25 mL

Formula Used:

Number of containers = Total volume of acid ÷ Capacity of one container

1 Liter (L) = 1000 Milliliters (mL)

Calculations:

⇒ Total acid volume = (4 × 1000) mL + 500 mL

⇒ Total acid volume = 4000 mL + 500 mL = 4500 mL

⇒ Number of containers = 4500 ÷ 25

⇒ Number of containers = 180

∴ The correct answer is 180.

Additional Information

Metric Conversion for Capacity

Standard conversion units: 1 Liter (L) = 1000 Milliliters (mL) and 1 Kiloliter (kL) = 1000 L.

Unit Consistency Rule

Before performing division or multiplication, ensure all quantities are in the same unit (convert everything to either L or mL).

Volume and Container Count

If V is total volume and c is unit capacity, then n = V/c, where n is the total number of containers filled.

• Deoxyribonucleic Acid (DNA) carries hereditary material.
• DNA is a molecule that carries most of the genetic instructions used in the development, functioning and reproduction of all known living organisms and many viruses.
• DNA molecules are very long but are packed into compact structures called chromosomes.
• Each DNA molecule consists of two twisted strands of bases that form a shape called a double helix.
• The two strands are held together by hydrogen bonds between pairs of bases.
  

The pattern followed here is as follows,

Hence, “112” is the correct answer.

Shortcut Trick

In a rectangle, the diagonals are equal and bisect each other, forming isosceles triangles with the sides.

The acute angle between the diagonals is equal to twice the angle of inclination to the side (if the inclination is less than 45°).

Acute angle = 2 × 25° = 50°.

∴ The correct answer is 50°.

Alternate Method

Given: The inclination of the diagonal to one side of the rectangle is 25°.

Formula Used: Properties of a rectangle (diagonals are equal and bisect each other) and the Exterior Angle Theorem.

Let the rectangle be ABCD where diagonals AC and BD intersect at O.

⇒ OA = OB (Diagonals of a rectangle are equal and bisect each other).

⇒ In ΔOAB, ∠OAB = ∠OBA = 25° (Angles opposite to equal sides are equal).

⇒ ∠AOB = 180° − (∠OAB + ∠OBA)

⇒ ∠AOB = 180° − (25° + 25°) = 130°.

⇒ The angle between diagonals ∠BOC = 180° − 130° = 50° (Linear pair).

Alternatively, by the Exterior Angle Theorem for ΔOAB:

⇒ ∠BOC = ∠OAB + ∠OBA = 25° + 25° = 50°.

∴ The correct answer is 50°.

Additional Information

Rectangle Diagonals

The diagonals of a rectangle are equal in length and bisect each other. They are not necessarily perpendicular unless the rectangle is a square.

Isosceles Triangle Property

In an isosceles triangle, the angles opposite to the equal sides are always equal.

Exterior Angle Theorem

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

The pattern followed here is as follows,

Every element is shifted to the next quadrant in the succeeding image.

Similarly,

Hence, “option figure C” is the correct answer.

• The SI Unit of acceleration is m/s².
• Acceleration is defined as the rate of change in velocity with respect to time.
• Hence it can be written as ∆v/ ΔT.
• Unit of velocity is meter (m) per second (s) and for time is second (s).
• Hence it can be written as m/s².

Shortcut Trick

If tan α = √5 − 2, then cot α = 1/(√5 − 2) = √5 + 2.

Difference: tan α − cot α = (√5 − 2) − (√5 + 2).

⇒ tan α − cot α = √5 − 2 − √5 − 2 = −4.

∴ The correct answer is -4.

Alternate Method

Given: tan α = √5 − 2

Formula Used: cot α = 1 / tan α

Calculations:

⇒ cot α = 1 / (√5 − 2)

⇒ Rationalizing the denominator: [1 × (√5 + 2)] / [(√5 − 2) × (√5 + 2)]

⇒ cot α = (√5 + 2) / (5 − 4) = √5 + 2

⇒ tan α − cot α = (√5 − 2) − (√5 + 2)

⇒ tan α − cot α = √5 − 2 − √5 − 2

⇒ tan α − cot α = −4

∴ The correct answer is -4.

Additional Information

Reciprocal Relations

In trigonometry, tan θ × cot θ = 1. Therefore, if tan θ = x, then cot θ = 1/x.

Rationalization of Surds

To rationalize a denominator of the form √a − b, multiply the numerator and denominator by its conjugate √a + b.

Difference Property

If x = √a − √b and a − b = 1, then 1/x = √a + √b and x − 1/x = −2√b.

According to Table; April, May, June, July and Oct have the same price of vegetable over the 2 years time-frame.

The correct answer is Mass.

Key Points

• The value of acceleration due to gravity does not get affected by Mass.
• We know that Force due to gravity F = GM_E m/r².
• Here G is gravitational Constant, M_E is the Mass of earth and r is the distance from the centre of the earth
• We also know that F = Mg (Here a is replaced by g is the acceleration is due to gravity).
• Now equating the both we get gravity (g) = GM_E/r².
• Hence, the value of acceleration due to gravity does not get affected by Mass.
• As G is gravitational Constant, M_E is Mass of the earth are constant then g = 1/r².
• Here r is the distance from the centre of earth hence thereby depending upon the Shape of the earth as the radius changes so do the value of g.
• Similarly, we have equation acceleration due to gravity g**(h) = g (1- 2h/R_E)** and acceleration due to gravity due to depth g(d) = g (1-d/R_E) shows that acceleration due to gravity affected by depth and height.

• The 48^th International Film Festival of India held in Goa in the year 2017.
• The 49^th International Film Festival of India was also held in Goa in the year 2018.
• The opening film at 49^th International Film Festival of India was Malayalam film named Olu.

• On August 29^th, Major Dhyanchand’s birthday is celebrated as National Sports Day in India.
• Major Dhyanchand was an Indian Hockey player who is also known as “The Wizard of Hockey” for his extraordinary goal-scoring feats.
• He was a three-time gold medalist for hockey in Olympic 1928, 1932 and 1936.
• The Dhyanchand Award also known as the Dhyanchand Award for Lifetime Achievement in Sports and Games is awarded in his honour.
• Satyadev Prasad (Archery), Bharat Kumar Chetri (Hockey) and Bobby Aloysius (Athletics). Chougale Dodu Dattatray (Wrestling) received the Dhyanchand Award in the year 2018.

Additional Information

• List of Major Dhyan Chand Khel Ratna 2021 Awardees 
• Neeraj Chopra (Javelin), Ravi Dahiya (Wrestling), Sunil Chhetri (Football), Mithali Raj (Cricket), P Sreejesh (Hockey), Lovlina Borgohain (Boxing), Pramod Bhagat (Para-badminton player), Avani Lekhara (Para rifle shooter), Sumit Antil (Para javelin thrower), Krishna Nagar (Para-badminton), Manish Narwal (Para pistol shooter), Manpreet Singh (Hockey).

Shortcut Trick

For a set of n numbers arranged in order, the Range can be calculated using the averages of the subsets.

Range = (Average of largest (n−1) numbers − Average of smallest (n−1) numbers) × (n−1)

Here, n = 4, so (n−1) = 3.

Range = (29.5 − 25.5) × 3 = 4 × 3 = 12

∴ The correct answer is 12.

Alternate Method

Given: Four numbers w, x, y, z are in ascending order (w ≤ x ≤ y ≤ z).

Formula: Sum = Average × Number of observations

⇒ Average of the smallest three (w, x, y) = 25.5

⇒ w + x + y = 25.5 × 3 = 76.5 — (Equation 1)

⇒ Average of the largest three (x, y, z) = 29.5

⇒ x + y + z = 29.5 × 3 = 88.5 — (Equation 2)

⇒ To find the Range (z − w), subtract Equation 1 from Equation 2:

⇒ (x + y + z) − (w + x + y) = 88.5 − 76.5

⇒ z − w = 12

∴ The correct answer is 12.

Additional Information

Range of a Data Set

The Range is the simplest measure of dispersion, calculated as the difference between the maximum and minimum values: Range = X_max − X_min.

Arithmetic Mean

The Mean or Average is the sum of all observations divided by the total number of observations (n). Sum = Mean × n.

Median for Even Observations

When the number of observations (n) is even, the Median is the average of the (n/2)^th and (n/2 + 1)^th terms after arranging them in order.

The pattern followed here is as follows,

Hence, “28U” is the correct answer.

Shortcut Trick

Statement 1 is a perfect square: (n − 10)² = 0, which gives a unique value n = 10.

Statement 2 involves three variables (n, x, y) in only one equation, making it impossible to determine a unique value for n.

Therefore, only the first statement provides sufficient data to solve the problem.

∴ The correct answer is Only statement 1 is sufficient.

Alternate Method

Given:

Statement 1: n² − 20n + 100 = 0

Statement 2: n² + x² + y² + 2 = 2n + 5

Evaluating Statement 1:

⇒ n² − 2 × n × 10 + 10² = 0

⇒ (n − 10)² = 0

⇒ n − 10 = 0

⇒ n = 10

Since we get a definite and unique value for n, Statement 1 is sufficient.

Evaluating Statement 2:

⇒ n² − 2n + x² + y² + 2 − 5 = 0

⇒ (n² − 2n + 1) + x² + y² − 4 = 0

⇒ (n − 1)² + x² + y² = 4

This is an equation representing a sphere in a 3D coordinate system. Without knowing the values of x and y, the variable n can take infinitely many values within the range [−1, 3].

⇒ Statement 2 is not sufficient.

∴ The correct answer is Only statement 1 is sufficient.

Additional Information

Data Sufficiency Rule

To find unique values for k variables, at least k independent linear equations are generally required.

Quadratic Discriminant

For a quadratic equation ax² + bx + c = 0, if the Discriminant (D = b² − 4ac) is zero, the equation has real and equal roots, providing a unique solution for the variable.

Algebraic Identities

Recall the identity (a − b)² = a² − 2ab + b², which was used here to simplify Statement 1 directly.

From the statement it is clear that “he consumes only healthy food”. Thus, we can assume that “he does not eat junk food” as it is known that junk food is bad for health.

There is no mention about his life during the “weekends”, so, we cannot assume anything regarding his walking habits on weekends.

Hence, “Only assumption I is implicit”.

Shortcut Trick

Total decrease in age = Total girls × Decrease in average age

⇒ 20 × 2 months = 40 months = 3 years 4 months

Age of new girl = Age of replaced girl − Total decrease

⇒ 18 years − 3 years 4 months = 14 years 8 months

∴ The correct answer is 14 years 8 months.

Alternate Method

Given: Total girls = 20, age of replaced girl = 18 years, average decrease = 2 months.

Formula Used: Age of new member = Age of replaced member + (Total strength × Change in average)

⇒ Change in average = −2 months (since it decreased)

⇒ Age of new girl = 18 years + (20 × (−2 months))

⇒ Age of new girl = 18 years − 40 months

⇒ 40 months = 36 months + 4 months = 3 years 4 months

⇒ Age of new girl = 18 years − 3 years 4 months

⇒ Age of new girl = 14 years 8 months

∴ The correct answer is 14 years 8 months.

Additional Information

Average Concept

Average = Sum of observations ÷ Total number of observations. It represents the central value of a data set.

Replacement Rule

When one member is replaced, the total count remains the same. Total change = Count × (New Average − Old Average).

Unit Conversion

Always ensure units (years and months) are standardized before subtraction: 1 Year = 12 Months.

• Allahabad Bank is the oldest public-Sector bank of India.
• It was established in the year 1865.
• Its current chairman of the bank is SS Mallikarjuna Rao.

Allahabad Bank has been merged with Indian Bank.

Shortcut Trick

Isolate the square root term by dividing the numerator 1120 by 80.

√x = 1120 ÷ 80 = 14

Square the result to find the value of x: x = 14² = 196.

∴ The correct answer is 196.

Alternate Method

Given: 1120 ÷ √x = 80

Formula Used: If a ÷ √x = b, then √x = a ÷ b and x = (a ÷ b)²

⇒ 1120 / √x = 80

⇒ 1120 = 80 × √x

⇒ √x = 1120 ÷ 80

⇒ √x = 112 ÷ 8

⇒ √x = 14

⇒ x = 14²

⇒ x = 196

∴ The correct answer is 196.

Additional Information

Inverse Operations

The square root (√) is the inverse of squaring a number. To eliminate a square root, square both sides of the equation.

BODMAS and Transposition

When moving dividing factors across the equality sign, they become multiplying factors, which is a fundamental rule in algebraic simplification.

Important Squares

For quick banking exams calculation, memorize squares up to 30: 13² = 169, 14² = 196, 15² = 225, etc.

• The valency of a Magnesium (Mg) atom is +2.
• The number of electrons present in the outer most orbit of an atom is called Valency.
• We know the outer electronic configuration of Magnesium is 1s², 2s², 2p⁶, 3s².
• As every atom tries to reach the octet configuration and thereby having a full outer shell.
• Hence to reach an octet configuration a magnesium atom will lose 2 electrons in from its outermost orbit to reach the stable configuration of Neon (Ne).

Here close is the reverse/antonym of open, thus, in the similar way cut will relates with attach.

Hence, “attach” is the correct answer.

• The distance between two consecutive crests is L.
• The number of waves is n = 2
• We know that wavelength (λ) = 2 L/n
• Now by substituting we get = 2(L)/ 2

= L

The wavelength between those two consecutive crests is ‘L’.

• Assam state has the traditional dress of men known as “Sola or Fotua” and “Eri Chaddar”.
• The Gamocha also is known as bihuwaans is a hand-woven cloth, is the symbol of Assam weaving craft.

• Metallurgy is the process of extracting metals from its ores.
• Most Metals do not exist in their free state but in always in mixture with other compounds.
• These mixtures are called minerals and minerals from where metals can be extracted profitably are called ores.
• These metals are extracted from these ores depending on their reactivity.
• Metals of high reactivity such as Potassium, Sodium are refined through Electrolysis of their molten ore and Metals of medium reactivity like Zinc, Iron, Lead etc. are refined through reduction and metals of low reactivity such as gold, Silver are refined through Roasting.

⇒ 5476 = 2² × 37²

⇒ √5476 = 2 × 37 = 74

Here, in the statement, as the parents are ready to pay any cost for the “good education”. So we can conclude that “parents want to provide good education to their children”.

There is no information available in the statement from which it can be concluded that “good education can only be provided at a high fee”.

Hence, “Only conclusion I is implicit”.

Shortcut Trick

Total age 11 years ago = 54 − (11 × 2) = 54 − 22 = 32 years.

Ratio of ages 11 years ago = 3 : 1 (Total units = 4).

Value of 4 units = 32 → 1 unit = 8.

Older cousin's age 11 years ago = 3 × 8 = 24 years.

Present age of older cousin = 24 + 11 = 35 years.

∴ The correct answer is 35 years.

Alternate Method

Given: Sum of present ages = 54 years. 11 years ago, Ratio = 3 : 1.

Let the present age of the older cousin be x and the younger cousin be y.

⇒ x + y = 54 --- (i)

⇒ (x − 11) = 3(y − 11)

⇒ x − 11 = 3y − 33

⇒ x − 3y = −22 --- (ii)

Subtracting (ii) from (i):

⇒ (x + y) − (x − 3y) = 54 − (−22)

⇒ 4y = 76

⇒ y = 19

⇒ x = 54 − 19 = 35

∴ The correct answer is 35 years.

Additional Information

Age Difference Property

The difference between the ages of two persons remains constant at any point in time.

Sum of Ages over Time

If the sum of ages of 'n' people is S today, then 't' years ago, the sum was S − (n × t).

Ratio Method for Ages

When a ratio is given for a past or future time, it is always easier to calculate the total sum of ages for that specific time period first.

• The first equation of motion gives the relation between "velocity and time".
• The first equation of motion is v = u +at.
• Here, v is the final velocity, u is the initial velocity, a is the acceleration and t is the time.
• The velocity-time relation gives the first equation of motion and can be used to find acceleration.
• The position-time relation gives the second equation of motion, i.e. s = ut + (1/2) at².
• The position-velocity relation gives the third equation of motion, i.e**. 2as = v² – u².**

The water image will be formed as shown in the following figure.

Hence, “option figure A” is the correct answer.

The pattern followed here is as follows,

Here, the number assigned to the letter is the positional value of that letter as per the English alphabetical order.

Similarly,

Hence, “208120” is the correct answer.

Shortcut Trick

In ΔABC, since D, E, and F are the midpoints of the sides, the quadrilaterals BDEF and CDEF are parallelograms.

The diagonals of a parallelogram bisect each other, which means:

X is the midpoint of BE and Y is the midpoint of DE.

In ΔBDE, X and Y are the midpoints of sides BE and DE respectively.

By the Midpoint Theorem, XY = BD ÷ 2 = (BC ÷ 2) ÷ 2 = BC/4.

∴ The correct answer is BC/4.

Alternate Method

Given:

In ΔABC, D, E, and F are the midpoints of sides BC, CA, and AB respectively.

BE and DF intersect at X, and DE and CF intersect at Y.

Theorem Used:

Midpoint Theorem: The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half of its length.

Step-by-Step Calculations:

By the Midpoint Theorem in ΔABC:

⇒ FE || BC and FE = BC ÷ 2

⇒ Since D is the midpoint of BC, we have BD = DC = BC ÷ 2.

⇒ Therefore, FE || BD and FE = BD.

⇒ This makes quadrilateral BDEF a parallelogram.

⇒ Since the diagonals of a parallelogram bisect each other, the intersection point X of diagonals BE and DF is the midpoint of BE.

Similarly, for quadrilateral CDEF:

⇒ FE || CD and FE = CD.

⇒ This makes quadrilateral CDEF a parallelogram.

⇒ The intersection point Y of diagonals CF and DE is the midpoint of DE.

Now, consider ΔBDE:

⇒ X is the midpoint of BE.

⇒ Y is the midpoint of DE.

⇒ By applying the Midpoint Theorem to ΔBDE, we get:

⇒ XY = BD ÷ 2

⇒ Since BD = BC ÷ 2, we substitute this value:

⇒ XY = (BC ÷ 2) ÷ 2 = BC ÷ 4

Why other options are incorrect:

• Option (1) BC/2: This is the length of the midsegment FE, which is twice the length of XY.
• Option (3) BC/3: This ratio does not correspond to the midpoint division of the diagonals in the parallelograms.
• Option (4) 2BC/3: This value is greater than the midsegment FE (BC/2), which is geometrically impossible since XY is a sub-segment within the midsegment triangle.

∴ The correct answer is BC/4.

Additional Information

Properties of Midsegment Triangles

The four smaller triangles formed by joining the midpoints of a triangle are congruent to each other, and each has an area equal to 1/4 of the original triangle's area.

Parallelogram Diagonal Bisection

A quadrilateral is a parallelogram if and only if its diagonals bisect each other. This property is crucial for locating midpoints of internal segments.

The pattern followed here is as follows,

Here, the number assigned to the letter is the positional value of that letter as per the English alphabetical order.

Similarly,

Hence, “6-15-15-4” is the correct answer.

• The Union Government has lowered interest rates on nine small savings schemes by 0.1% for the April-June quarter as compared to the January-March quarter.

⇒ 0.0324 = 324/10000 = 18²/100²

⇒ √0.0324 = √(18²/100²) = 18/100 = 0.18

• Fertilisation results in the formation of zygote.
• The fusion of male gamete and female gamete is called fertilisation.
• Fertilisation is the process of reproduction in plants.
• It takes place in the flowers where ripe pollen from an anther of the same kind of flower catches on the stigma, each pollen grain sends out a tiny threadlike tube.
• The tube grows down through the style and pierces one of the ovules in the ovary located inside the flower.
• This will form a Zygote.
  

The pattern followed here is as follows,

Similarly,

Hence, “GDM” is the correct answer.

Shortcut Trick

Total ratio parts = 12 + 29 = 41 units.

41 units → 24.6 m

1 unit → 24.6 ÷ 41 = 0.6 m

Longer piece (29 units) = 29 × 0.6 = 17.4 m.

∴ The correct answer is 17.4 m.

Alternate Method

Given:

Total length of wire = 24.6 m

Ratio of division = 12 : 29

Formula Used:

Value of a part = (Ratio of part ÷ Total Ratio) × Total Value

Calculations:

⇒ Sum of ratio terms = 12 + 29 = 41

⇒ Length of the longer piece = (29 ÷ 41) × 24.6

⇒ Length = 29 × (24.6 ÷ 41)

⇒ Length = 29 × 0.6

⇒ Length = 17.4 m

∴ The correct answer is 17.4 m.

Additional Information

Ratio and Proportion

A ratio compares two quantities. To divide a total value S in the ratio a : b, the parts are (a/(a+b))×S and (b/(a+b))×S.

Unitary Method

Find the value of a single unit by dividing the total quantity by the total number of units, then multiply by the required number of units.

Compounded Ratio

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

• India’s first Videsh Bhavan will be established in Maharashtra.
• The Union Minister of External Affairs Sushma Swaraj launched this program in the year 2017.
• Videsh Bhavan in Mumbai integrates the Regional Passport office, Protector of Emigrants Office, Branch Secretariat and the Regional Office of Indian Council of Cultural Relations are brought under one roof.

Shortcut Trick

Curved Surface Area (CSA) of cone ÷ Width of cloth = Length of cloth.

Radius (r) = 16 ÷ 2 = 8 m, Slant height (l) = 5.6 m, Width = 4 m.

Length = (π × r × l) ÷ Width = (22/7 × 8 × 5.6) ÷ 4.

Length = (22 × 8 × 0.8) ÷ 4 = 22 × 2 × 0.8 = 35.2 m.

∴ The correct answer is 35.2 m.

Alternate Method

Given:

Diameter (d) = 16 m ⇒ Radius (r) = 8 m

Slant Height (l) = 5.6 m

Width of cloth (w) = 4 m

Formula Used:

Curved Surface Area of cone = πrl

Area of rectangular cloth = Length × Width

Calculations:

⇒ Area of tent (CSA) = (22/7) × 8 × 5.6

⇒ Area of tent = 22 × 8 × 0.8 = 140.8 m²

⇒ Area of cloth = Area of tent

⇒ Length × 4 = 140.8

⇒ Length = 140.8 ÷ 4

⇒ Length = 35.2 m

∴ The correct answer is 35.2 m.

Additional Information

Total Surface Area (TSA) of Cone

The total surface area includes the curved area plus the circular base area: TSA = πr(l + r).

Relation between h, r, and l

In a right circular cone, the slant height is the hypotenuse: l² = h² + r², where h is vertical height.

Volume of Cone

The volume is one-third that of a cylinder with same base and height: V = (1/3)πr²h.

The minimum possible Venn diagram of the given statements,

Conclusions:

1. All locusts are worms → True.
2. All insects are locusts → False (it is possible but not definite)

Hence, “Only conclusion 1 follows”.

• Irrfan Khan was honoured with the Icon Award at the London Film Festival in 2018.
• Actor Manoj Bajpayee was also won the Icon Award at the same ceremony.
• Irrfan Khan was famous for his role in movies like Life of Pi, Slumdog Millionaire etc.

Shortcut Trick

Average Quarterly Sales = ₹12,00,000

Average Monthly Sales = 12,00,000 ÷ 3 = ₹4,00,000

Potato Chips Sales (70%) = 0.70 × 4,00,000 = ₹2,80,000

∴ The correct answer is ₹2,80,000.

Alternate Method

Given:

⇒ Average Quarterly Sales = ₹12,00,000

⇒ Potato Chips Sales Percentage = 70%

⇒ Number of months in a quarter = 3 months

Calculations:

⇒ Total sales of Potato Chips per quarter = 70% of 12,00,000

⇒ Quarterly Potato Sales = (70 ÷ 100) × 12,00,000 = ₹8,40,000

⇒ Average Monthly Sales of Potato Chips = Quarterly Sales ÷ 3

⇒ Monthly Potato Sales = 8,40,000 ÷ 3 = ₹2,80,000

∴ The correct answer is ₹2,80,000.

Additional Information

Quarterly to Monthly Conversion

A quarter consists of 3 months. To find the average monthly value from a quarterly total, divide the total by 3.

Percentage of a Value

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

Averages

Average = (Sum of all observations) ÷ (Total number of observations).

Shortcut Trick

Identify the easiest polynomial to factorize: 3x² − 2x = x(3x − 2).

The HCF must be a factor of every expression, so it must be either x or (3x − 2).

Check (3x − 2) in 3x² + x − 2: substituting x = 2/3 gives 3(4/9) + 2/3 − 2 = 4/3 + 2/3 − 2 = 0.

Since (3x − 2) is a factor of the simplest terms, it is the HCF.

∴ The correct answer is 3x − 2.

Alternate Method

Given: Polynomials 15x² + 8x − 12, 3x² + x − 2, 3x² − 2x, and 9x² − 12x + 4.

Factorizing each expression:

⇒ 15x² + 8x − 12 = 15x² + 18x − 10x − 12 = 3x(5x + 6) − 2(5x + 6) = (3x − 2)(5x + 6)

⇒ 3x² + x − 2 = 3x² + 3x − 2x − 2 = 3x(x + 1) − 2(x + 1) = (3x − 2)(x + 1)

⇒ 3x² − 2x = x(3x − 2)

⇒ 9x² − 12x + 4 = (3x)² − 2(3x)(2) + 2² = (3x − 2)²

⇒ The common factor in all four expressions is (3x − 2).

∴ The correct answer is 3x − 2.

Additional Information

Highest Common Factor (HCF) of Polynomials

The HCF is the product of the common factors with the lowest powers present in all given polynomials.

Factor Theorem

If (ax − b) is a factor of P(x), then P(b/a) = 0. This is useful for checking potential HCF candidates from options.

Relationship between HCF and LCM

For two polynomials A(x) and B(x), A(x) × B(x) = HCF(A,B) × LCM(A,B).

Key Points

• The Liver secretes bile in the human digestive system.
• Bile helps in emulsification of fats i.e. breaking of fats into very small molecules.
• Bile also helps to activate lipase which is secreted by the pancreas.

The pattern followed here is, in the 1^st figure there are three circles upper circle is slightly bigger than the below two circles and on shifting to the 2^nd figure below two circles are inscribed in the bigger circle. Similarly, 3^rd figure consists of one rectangle that is in the upper side and two circles below the square thus on shifting two circles in the rectangle and only “figure B” shows the exact pattern.

Hence, “option figure B” is the correct answer.

• Britishers through The Indian Councils Act of 1892, in the year 1892 for the first time introduced the system of indirect election in India.
• This act was the first major achievement of the Indian National Congress.
• It increased the additional members of the central legislative council.
• They were not less than 10 but not more than 16 members and members were allowed to discuss budget and are allowed to criticise the financial policy of the government.

• Roger Federer of Switzerland has retained his Men’s Singles title by winning 2018 Australian Open.
• In the year 2019, the Australian Open was won by Novak Djokovic of Serbia.
• The 2019 Australian Open women’s title was won by Naomi Osaka.
• The 2019 Australian Open doubles mixed was won by American tennis player Rajeev Ram along with Barbora Krejcikova.

As we know ray are emitted by sun thus, they are the part of the sun. but we cannot relate ocean with either ray or sun. So, the venn diagram that most resembles the information is as follows,

Hence, “option figure 1” is the correct answer.

• Samaveda mentions about music.
• It is also called the book of melodies.
• It is a part of four Vedas namely Rig Veda, Sama Veda, Yajur Veda, Atharvana Veda.
• It’s Upaveda Gandharva Veda.
  

The pattern followed here is as follows,

Every element is shifting to the next position in the series in the succeeding figure.

Hence, “option figure D” is the correct answer.

The pattern followed here is that every arrow is pointed towards the anticlockwise direction, except arrow of figure C which is pointed in the clockwise direction.

Hence, “figure C” is the odd one.

CONCEPT:

• Power (P): The rate of work done is called power.
• Work done is measured as the force on the body times the distance through which that force is applied.

⇒ Work done (W) =  Force (F) x Distance (s).

⇒ Power (P) = work done (W)/ Time taken.

⇒ Energy (E) = power (P) x time (t).

EXPLANATION:

• Work done by an agent (W) is W
• Time taken (t) is t
• We know the formulae for power P = work /time
• Now by substituting the above formula, we get

⇒ P = W/t

• Power is given by W/t (W)watt.

⇒ Mass of the luggage (m)= 20 kg

⇒ Height above the ground (h) = 2m

⇒ Now the work done by porter on luggage is

⇒ P.E = mgh = (20)×(10)×(2) = 400 J

⇒ The work done by the porter is 400 Joules.

The correct answer is  **A copper rod.**​

• The force of attraction between the particles of matter is maximum in a copper rod.
• The intermolecular forces of attraction (attractive forces between molecules or atoms) is more in solids hence they are densely packed together.
• The forces of attraction between particles are lower in liquids and lowest in gases.

Shortcut Trick

Total Work = LCM(10, 15, 12) = 60 units.

Efficiency of (A+B) = 6, (B+C) = 4, (C+A) = 5.

2 × (A+B+C) efficiency = 6 + 4 + 5 = 15 ⇒ (A+B+C) efficiency = 7.5.

Time Taken = 60 ÷ 7.5 = 8 days.

∴ The correct answer is 8 days.

Alternate Method

Given:

Time taken by A and B = 10 days

Time taken by B and C = 15 days

Time taken by C and A = 12 days

Calculations:

⇒ Adding efficiencies: (A + B) + (B + C) + (C + A) = 6 + 4 + 5

⇒ 2(A + B + C) = 15

⇒ Combined Efficiency of A, B, and C = 15 ÷ 2 = 7.5 units/day

⇒ Time taken by all three together = Total Work ÷ Combined Efficiency

⇒ Time = 60 ÷ 7.5

⇒ Time = 8 days

∴ The correct answer is 8 days.

Additional Information

Work and Efficiency Relation

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

Combined Work Formula

If (A+B) take x days, (B+C) take y days, and (C+A) take z days, then (A+B+C) take 2xyz ÷ (xy + yz + zx) days.

Individual Efficiency

Efficiency of A = Efficiency of (A+B+C) − Efficiency of (B+C).

• The colour of a neutral litmus solution is purple.
• Litmus solution is made up of purple dye which is extracted from Lichens.
• It is a natural Indicator and it is used to indicate the presence of an acid or a base.
• A litmus paper will turn red in the presence of an acid and it turns blue in the presence of a base.

• A Galvanometer is used to detect the direction of the current.
• This device is used for detecting and measuring a small amount of electric current.
• Johann Schweigger invented the device in 1820.
  

\(\Rightarrow 119 \div \left[ {22 - \left{ {90 \div \left( {23 - 105 \div \overline {7 \times 3} } \right)} \right}} \right]\)

⇒ 119 ÷ [22 – {90 ÷ (23 – 105 ÷ 21)}]

⇒ 119 ÷ [22 – {90 ÷ (23 – 5)}]

⇒ 119 ÷ [22 – {90 ÷ 18}]

⇒ 119 ÷ [22 – {5}]

⇒ 119 ÷ [17]

⇒ 7

• Tungsten is the metal used for making the filament of the light bulb.
• The melting point of tungsten is 3,422 °C.
• Due to its high melting point, tungsten is used as filament in an incandescent bulb
• It is represented with W (Wolfram) and has an atomic number of 74.
• It belongs to transition elements in a periodic table.

The correct answer is Pupil.

Key Points

• The amount of light entering the eye is controlled by the pupil.
• The pupil is a small empty space surrounded by the iris.
• The iris contracts and relaxes to regulate the size of the pupil.
• When it is dark, the pupil expands to allows more light to enter the eye.
• Iris controls the pupil which inturn controls the amount of light entering the eye.The pupil is just an adjustable opening, the iris is a membrane.
• When it is bright, the pupil contracts to prevent more light from entering the eye.

Key Points

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

Shortcut Trick

Since the expression is an identity and independent of the value of x, we can substitute a convenient value for x.

Let x = 0°.

Then sin 0° = 0 and cos 0° = 1.

Expression = 3[0 − 1]⁴ + 6[0 + 1]² + 4[0⁶ + 1⁶]

⇒ 3(1) + 6(1) + 4(1) = 3 + 6 + 4 = 13.

∴ The correct answer is 13.

Alternate Method

Given: 3[sin x − cos x]⁴ + 6[sin x + cos x]² + 4[sin⁶x + cos⁶x]

Formula Used: (a ± b)² = a² + b² ± 2ab; sin²x + cos²x = 1; a³ + b³ = (a + b)(a² − ab + b²)

⇒ [sin x − cos x]⁴ = ([sin x − cos x]²)² = (sin²x + cos²x − 2sin x cos x)² = (1 − 2sin x cos x)²

⇒ (1 − 2sin x cos x)² = 1 + 4sin²x cos²x − 4sin x cos x

⇒ [sin x + cos x]² = 1 + 2sin x cos x

⇒ sin⁶x + cos⁶x = (sin²x)³ + (cos²x)³ = (sin²x + cos²x)(sin⁴x − sin²x cos²x + cos⁴x)

⇒ 1[(sin²x + cos²x)² − 2sin²x cos²x − sin²x cos²x] = 1 − 3sin²x cos²x

⇒ Total = 3[1 + 4sin²x cos²x − 4sin x cos x] + 6[1 + 2sin x cos x] + 4[1 − 3sin²x cos²x]

⇒ 3 + 12sin²x cos²x − 12sin x cos x + 6 + 12sin x cos x + 4 − 12sin²x cos²x

⇒ 3 + 6 + 4 = 13.

∴ The correct answer is 13.

Additional Information

Trigonometric Identities

Standard identities like sin²x + cos²x = 1, sec²x − tan²x = 1, and cosec²x − cot²x = 1 are true for all values of x.

Value Substitution Method

In objective exams, if an expression is independent of the variable, substituting values like 0°, 45°, or 90° saves significant time.

Algebraic Expansion

Higher powers of sine and cosine can be simplified using (sin²x + cos²x)ⁿ expansion formulas.

• Khangchendzonga Biosphere Reserve has been included in the UNESCO’s World Network of Biosphere Reserve (WNBR) in 2018.
• The Khangchendzonga Biosphere Reserve has become the 11th Biosphere Reserve from India that has been included in the UNESCO designated World Network of Biosphere Reserves.
• Khangchendzonga Biosphere Reserve in Sikkim is one of the highest ecosystems in the world.
• The core zone – Khangchendzonga National Park was designated a World Heritage Site in 2016 under the ‘mixed’ category.
• There are eleven bio-reserves of India based on the UNESCO Man and the Biosphere (MAB) Programme list. They are as follows:
  

• Fe₂O₃ xH₂O is the formula for rust.
• When iron is exposed to moist air, a reddish-brown coating of hydrated Iron (III) Oxide (Fe₂O₃) is deposited on its surface. This reddish-brown coating is called rust.
• Rust is an iron oxide, which occurs when iron or an alloy that contains iron, like steel, is exposed to oxygen and moisture for a long period of time.
• The chemical equation for the formation of rust is:
• Iron + Water + Oxygen = Rust. i.e. Ferric oxide with water as hydrated crystals in it.
• i.e. 4Fe(s) + 6H₂O(l) + 3O₂(g) → 4Fe(OH)₃(s).
• Therefore, the chemical formula for rust is Fe₂O₃.xH₂O.
• Here x indicates the number of moles of water absorbed by ferric oxide.