RRC Group D Previous Year Paper 20 (Held On: 17 Dec 2018 Shift 1)

The correct answer is 96 m.

Key Points

• The second equation of motion gives the position-time relation, i.e. s = ut + (1/2) at2.
• Where S is the displacement=?
• U is the initial velocity = 0 m/s
• The acceleration is given as 3.0 ms-2
• The time t is given as 8 s.
• Substituting, we get s = (0 x 8) + (0.5 x 3 x 64)  = 96 m.

Correct Option - 4 - Priyanka Chopra

Priyanka Chopra played lead actress in the Mary Kom movie. 

Some facts about Movie - 

• The movie was a biography of Mary Kom.
• It was released in 2014.
• The movie was directed by Omung Kumar under the production of Sanjay Leela Bhansali.

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About Mary Kom-

• She was born in Kangathei village of Manipur.
• She excelled in boxing and won many awards.
• She was awarded Rajiv Gandhi Khel Ratna Award, Padma Shri and Padma Bhushan.
• For the upcoming Olympics 2020, she has been selected as the female representative of boxing athlete ambassador by the International Olympic Committee.

66 × 32 ÷ 2³ + 8

⇒ 66 × 32 ÷ 8 + 8

⇒ 66 × 4 + 8

⇒ 264 + 8

⇒ 272

CONCEPT:

Electric potential (V):

• The potential difference between two points in an electric field may be defined as the amount of work done in moving a unit positive charge from one point to the other against the electrostatic force i.e.,

${\rm{Electric;potential;}}\left( {\rm{V}} \right) = \frac{{{\rm{Work;done;}}\left( {\rm{W}} \right)}}{{{\rm{Charge;}}\left( {\rm{q}} \right)}}$

• The electric potential is a scalar quantity and it has no direction.

EXPLANATION:

• The electric potential can be written as

${\rm{Electric;potential;}}\left( {\rm{V}} \right) = \frac{{{\rm{Work;done;}}\left( {\rm{W}} \right)}}{{{\rm{Charge;}}\left( {\rm{q}} \right)}}$

• As we know that, SI unit of work done is joule and the SI unit of charge is the coulomb, then

$1 V = \frac{J}{C}$

• Joule/coulomb is the same as 1 V. Therefore option 4 is correct.

Correct Option - 2 - Maharashtra

About Tarapur Atomic Power Station - 

• Tarapur Atomic Power station is located in Tarapur, Maharashtra.
• It was the first commercial atomic power station of India commissioned on 28th October 1969.
• It was commissioned under 123 agreements signed between India, the United States and International Atomic Energy Agency.
• The station is operated by the National power corporation of India.
  

Other important Atomic Power stations in India - 

The mirror image of the given figure is,

Hence, option 2 is the correct answer.

Shortcut Trick

Identify the Highest Common Factor (HCF) first: 145 and 87 are both multiples of 29.

Numbers can be written as: 145 = 29 × 5 and 87 = 29 × 3.

LCM = Common factor × remaining factors = 29 × 5 × 3.

LCM = 145 × 3 = 435.

∴ The correct answer is 435.

Alternate Method

Given: Numbers are 145 and 87.

Formula Used: Prime Factorization Method.

⇒ Prime factors of 145 = 5 × 29

⇒ Prime factors of 87 = 3 × 29

⇒ LCM = Product of highest powers of all prime factors involved.

⇒ LCM = 3¹ × 5¹ × 29¹

⇒ LCM = 15 × 29

⇒ LCM = 435

∴ The correct answer is 435.

Additional Information

LCM and HCF Relationship

For any two numbers a and b, the product of the numbers is equal to the product of their HCF and LCM: a × b = HCF(a, b) × LCM(a, b).

Co-prime Numbers

If two numbers are co-prime (HCF = 1), then their LCM is simply the product of the two numbers.

LCM of Fractions

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

The pattern followed is,

There is a gap of 2 between the given terms.

4 W X Z 8 Q P O J 6 G T M V E U H 5 3 B

There is a gap of two letters between W8, P6, and HB.

Similarly,

There is a gap of two letters between TE.

Hence, “TE” is the correct answer.

Or,

Hence, “TE” is the correct answer.

Assumption 1: This is implicit , since it is mentioned in the statement that Rajesh’s condition will be improved after operation

Assumption 2: This is not implicit , since it not given that Rajesh cannot be operated.

Hence, “only assumption 1” is implicit.

Drawing the diagram according to the given instructions,

At point C, the man is facing East.

Hence, “East” is the correct answer.

NOTE : In the question we have to find the direction at Point C,  not at the final point F.

Drawing the diagram according to the given instructions,

If a car enters the parking area through the entrance gate following a straight path and makes a 90° turn to the right and gets place to park, the car’s bonnet faces North.

Hence, “north” is the correct answer.

Shortcut Trick

Rationalize the numerator of the expression (1 + cos θ) / sin θ by multiplying both the numerator and denominator by (1 − cos θ).

Logic: (1 + cos θ) (1 − cos θ) = 1 − cos² θ = sin² θ.

Expression → [sin² θ] / [sin θ (1 − cos θ)] → sin θ / (1 − cos θ).

∴ The correct answer is sin θ / (1 − cos θ).

Alternate Method

Given: (1 + cos θ) / sin θ

Formula Used: sin² θ + cos² θ = 1 ⇒ sin² θ = 1 − cos² θ = (1 − cos θ)(1 + cos θ)

⇒ [(1 + cos θ) / sin θ] × [(1 − cos θ) / (1 − cos θ)]

⇒ (1 − cos² θ) / [sin θ (1 − cos θ)]

⇒ sin² θ / [sin θ (1 − cos θ)]

⇒ sin θ / (1 − cos θ)

∴ The correct answer is sin θ / (1 − cos θ).

Additional Information

Trigonometric Identities

Fundamental identity: sin² θ + cos² θ = 1. Also 1 + tan² θ = sec² θ and 1 + cot² θ = cosec² θ.

Half Angle Formulas

1 + cos θ = 2cos²(θ/2) and sin θ = 2sin(θ/2)cos(θ/2). Dividing these gives cot(θ/2).

Rationalization Rule

To simplify fractions involving 1 ± cos θ or 1 ± sin θ, multiply by the conjugate to create a single squared term.

Correct Option -1- Increases, decreases

• Electronegativity is defined as the ability to attract bonding electrons towards themselves by atoms.
• If the atoms bonded together have the same electronegativity then the shared electrons will be equally shared.
• Electronegativity increases from left to right in a row in the periodic table and electro positivity decreases from left to right in a row in the periodic table.

Shortcut Trick

Total percentage = 100% + 18% = 118%

118% of amount = ₹531

Original amount = 531 ÷ 1.18 = 450

∴ The correct answer is ₹450.

Alternate Method

Given:

Final fare including surcharge = ₹531

Surcharge rate = 18%

Formula Used:

Original Amount = (Final Amount × 100) ÷ (100 + Percentage Surcharge)

Calculations:

⇒ Let the amount without surcharge be x.

⇒ x + 18% of x = 531

⇒ 1.18x = 531

⇒ x = 531 ÷ 1.18

⇒ x = 53100 ÷ 118

⇒ x = 450

∴ The correct answer is ₹450.

Additional Information

Percentage Increase

When a value is increased by r%, the new value is Original Value × (1 + r/100). To find the original value, divide the new value by the multiplier (1 + r/100).

Base Change Rule

If value A is 18% more than value B, then value B is not 18% less than value A. The base changes from B to A, requiring the formula: Decrease % = [r ÷ (100 + r)] × 100.

The pattern followed is,

Hence, “K11O15” is the correct answer.

Shortcut Trick

Apply Alligation on speed to find the ratio of Time taken.

Speed 1 (60 km/h) and Speed 2 (80 km/h) with Average Speed (72 km/h).

Ratio of Time = (80 − 72) : (72 − 60) = 8 : 12 = 2 : 3.

Given 2 units = 8 hours ⇒ 1 unit = 4 hours ⇒ 3 units = 12 hours.

∴ The correct answer is 12 hours.

Alternate Method

Given: Initial speed = 60 km/h, Initial time = 8 hours, Final speed = 80 km/h, Target average speed = 72 km/h.

Formula Used: Average Speed = Total Distance ÷ Total Time

⇒ Let the time for which he drives at 80 km/h be t hours.

⇒ Total Distance = (60 × 8) + (80 × t)

⇒ Total Distance = 480 + 80t

⇒ Total Time = 8 + t

⇒ Average Speed = (480 + 80t) ÷ (8 + t) = 72

⇒ 480 + 80t = 72 × (8 + t)

⇒ 480 + 80t = 576 + 72t

⇒ 80t − 72t = 576 − 480

⇒ 8t = 96

⇒ t = 12 hours

∴ The correct answer is 12 hours.

Additional Information

Average Speed Concept

When equal distances are covered at speeds x and y, Average Speed = (2 × x × y) ÷ (x + y).

Alligation for Speed

Applying alligation on speeds gives the ratio of the time taken during each interval.

Relative Speed

If two objects move in the same direction, relative speed = |s₁ − s₂|; in opposite directions, relative speed = s₁ + s₂.

Shortcut Trick

Total Simple Interest percentage = Rate × Time = 7.5% × 4 = 30%.

Total Maturity Amount in percentage = 100% (Principal) + 30% (Interest) = 130%.

Given that 130% corresponds to ₹689.

Original Sum (100%) = (689 ÷ 130) × 100 = 5.3 × 100 = ₹530.

∴ The correct answer is ₹530.

Alternate Method

Given:

Maturity Amount (A) = ₹689

Rate of Interest (R) = 7.5% per annum

Time Period (T) = 4 years

Formula Used:

Amount (A) = Principal (P) + Simple Interest (SI)

A = P + (P × R × T) ÷ 100

Calculations:

⇒ 689 = P + (P × 7.5 × 4) ÷ 100

⇒ 689 = P + (P × 30) ÷ 100

⇒ 689 = P + 0.3P

⇒ 689 = 1.3P

⇒ P = 689 ÷ 1.3

⇒ P = 530

∴ The correct answer is ₹530.

Additional Information

Simple Interest Formula

Simple Interest (SI) is calculated only on the initial principal amount: SI = (P × R × T) ÷ 100.

Rate and Time relationship

If the Rate is doubled while Time remains constant, the Simple Interest also doubles.

Interest for Fractional Time

When time is given in months, divide by 12 to convert to years. When given in days, divide by 365.

Giving names to all the points in the diagram.

Counting number of straight lines:

Vertical Lines: AD, EG, FH, BC = 4

Horizontal lines: EF, AB, DC, GH = 4

Big cross lines: EC, KI, AH, DF, GB = 5

Small cross lines: JM, LN, EK, HI, FL, JG = 6

Total = 4 + 4 + 5 + 6 = 19

Hence, 19 is the correct answer.

Shortcut Trick

Statement 1 provides the slope-intercept form equation with an unknown slope (m) and a known y-intercept (c = 2).

Statement 2 provides a specific coordinate point (2, 1) that lies on the line.

By substituting the values of x = 2 and y = 1 into the equation from Statement 1, we can uniquely solve for m.

Since neither statement alone provides enough information to determine m, but together they form a solvable linear equation, both are required.

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

Alternate Method

Given:

Statement 1: Equation of the line is y = mx + 2

Statement 2: The line passes through the point (2, 1)

Formula Used:

Slope-intercept form: y = mx + c

Calculations:

From Statement 1, the equation is y = mx + 2.

From Statement 2, we know the line passes through (x, y) = (2, 1).

⇒ 1 = m × 2 + 2

⇒ 1 − 2 = 2m

⇒ −1 = 2m

⇒ m = −1/2

Both statements together provide a unique value for the slope (m).

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

Additional Information

Slope-Intercept Form

The equation of a line is y = mx + c, where m is the slope and c is the y-intercept (the point where the line crosses the y-axis).

Slope from Two Points

If a line passes through two points (x₁, y₁) and (x₂, y₂), the slope m is calculated as m = (y₂ − y₁) ÷ (x₂ − x₁).

Point-Slope Form

A line equation can also be written as (y − y₁) = m(x − x₁) when the slope and one point are known.

Correct Option - 3 - Bone

Bone cells are embedded in a hard matrix that is composed of calcium and phosphorus.

Functions of Bone are:

• It provides structural support for the mechanical actions of soft tissues.
• It protects soft organs and tissues.
  

Ligaments: It is the bundle of tissues made of collagenous fibers. They work as a connector between bones and form joints. 

Blood: a liquid substance that carries oxygen and other nutrients in the body through veins.

Cartilage: These are the protective shelf of elastic tissues at the end of bones.

The correct answer is Quality.

Key Points

• The characteristic of sound by which we can distinguish between two sounds of the same loudness and pitch is known as Quality.  It is also known as timbre.
• Amplitude: It is used to check the loudness of sound.
• Pitch: It is the frequency of sound that is caught by the brain.
• Loudness: It is used to check the energy capacity that reaches to ear per second.

Correct Option - 4 - The rotation of the blades of a ceiling fan

• The rotation of the blades of a ceiling fan is not an example of a non-uniform motion.
• Motion: It is defined as the change in the position of an object over a period of time.
• Types of Motion -

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1. Uniform motion - When the certain object moves or travels specific distance which is equal to the time intervals.

For example - The rotation of the blades of a ceiling fan, Rotation of Earth etc.

2. Non-uniform motion - When a certain object moves or travels different distances which in the same interval of time.  

For example - A man running an 800 m race, A car moving on a crowded street, A person jogging in a park, etc.

Correct option - 1 - Karnataka

• Gauri Lankesh, who was shot dead in 2017 hails from Bangalore, Karnataka.
• She was a prominent journalist and Social activist worked in Lankesh Patrike.
• She was awarded the Politkovskaya Award.

The correct answer is option 4 i.e Sacrolemma,

• Sacrolemma is not a part of the neuron.
• It is a kind of skeletal muscle cell.
• Its function is to work as fencing between extracellular and intracellular compartments.
• Nissl granules: It is a part found in neurons and is responsible for the synthesis of proteins.
• Neurilemma: It worked as a protective shield of nerve fibers and does not affect when any damage occurs.
• Axon: It is responsible for sending signals to synapse from the cell body.

The correct answer is option 4 i.e Unique Identification Authority of India

• The Unique Identification Authority of India, a statutory body.
• It was established under the Aadhar (Targeted Delivery of Financial and other Subsidies benefits and services) Act, 2016 which is also known as the Aadhar act 2016.
• It works under the Ministry of Electronics and Information technology.
• Before its establishment as a statutory body, it was working as an attached body under Planning Commission (now NITI Aayog).

UIDAI

• Headquarter: Delhi
• CEO: Dr Saurabh Garg (2022)

The number of triangles in the given figure are,

Hence, “8” is the correct answer.

The correct answer is option 1 i.e The weight of the body

• The thrust exerted by a body on a surface is equal to The weight of the body.
• Thrust: It is defined as the force exerted by an object perpendicular to the surface.
• It defines Newton's Third Law of Motion i.e For every action, there is an equal and opposite reaction.
• SI unit of Thrust is Newton

The correct answer is option 4 i.e Reactivity

Reactivity series: 

• It is a series of metals in which metals are arranged according to their reactivity i.e from highest to lowest.
• It is used to determine the products of single displacement reactions in which metal A (high reactivity) will replace another metal B in a solution.
• Only the metal which has high reactivity can displace another metal (low reactivity)
  

Conductivity: It is the process of measuring the easiness of heat of electric charge passes through the material. 

Resistivity: It is the parameter through which the resistance of a material is measured.

Testability: It is a property that is used to measure the logic and practical feasibility of an empirical hypothesis.

Shortcut Trick

Required number = LCM(8, 12, 15, 16) + Remainder

LCM of 8, 12, 15, and 16 is 240.

Required number = 240 + 7 = 247.

∴ The correct answer is 247.

Alternate Method

Given: Divisors = 8, 12, 15, 16 and Remainder = 7.

To find the least natural number, we first calculate the Least Common Multiple (LCM) of the given divisors:

⇒ Prime factorization of 8 = 2³

⇒ Prime factorization of 12 = 2² × 3

⇒ Prime factorization of 15 = 3 × 5

⇒ Prime factorization of 16 = 2⁴

⇒ LCM = 2⁴ × 3 × 5 = 16 × 15 = 240

As per the condition, the number leaves a remainder of 7 in each case.

⇒ Required Number = LCM + Remainder

⇒ Required Number = 240 + 7 = 247

∴ The correct answer is 247.

Additional Information

LCM Concept

The smallest number exactly divisible by a set of numbers is their LCM.

Remainder Property

If a number N leaves remainder 'r' when divided by x, y, and z, then N = LCM(x, y, z) × k + r (where k is a natural number).

Common Difference Remainder

If divisors are (a, b, c) and remainders are (r1, r2, r3) such that (a−r1) = (b−r2) = (c−r3) = K, then the number is LCM(a, b, c) − K.

Drawing the Venn diagram,

Conclusion 1: Some panthers are cheetahs → False (Possible but not definite)

Conclusion 2: No panther is a cheetah → False (Possible but not definite)

But,

 The two conclusions form a complementary pair.

Hence, “either conclusion 1 or conclusion 2” follow.

Shortcut Trick

Let the total number of bananas be the LCM of 10 and 8 = 40.

Cost Price (CP) of 40 bananas = (8 ÷ 10) × 40 = Rs. 32.

Selling Price (SP) of 40 bananas = (10 ÷ 8) × 40 = Rs. 50.

Profit on 40 bananas = 50 − 32 = Rs. 18.

To earn Rs. 18 profit, bananas sold = 40. To earn Rs. 90 profit, bananas sold = (40 ÷ 18) × 90 = 200.

∴ The correct answer is 200 bananas.

Alternate Method

Given: CP of 10 bananas = Rs. 8 | SP of 8 bananas = Rs. 10 | Target Profit = Rs. 90.

Formulas: CP per unit = Total Cost ÷ Quantity | Profit = SP − CP.

⇒ Cost Price of 1 banana = 8 ÷ 10 = Rs. 0.8.

⇒ Selling Price of 1 banana = 10 ÷ 8 = Rs. 1.25.

⇒ Profit per banana = 1.25 − 0.8 = Rs. 0.45.

⇒ Number of bananas for Rs. 90 profit = 90 ÷ 0.45.

⇒ Number of bananas = 9000 ÷ 45 = 200.

∴ The correct answer is 200 bananas.

Additional Information

Unitary Method in Profit and Loss

To simplify calculations involving different quantities, find the CP and SP for a single unit or an LCM of the quantities to work with whole numbers.

Profit Percentage

Profit% = (Profit ÷ CP) × 100. In this case, Profit% = (0.45 ÷ 0.8) × 100 = 56.25%.

Option 1 → Pathology is the study of the causes and effects of disease or injury.

Option 2 → Nephrology is a specialty of medicine and paediatric medicine that concerns itself with the kidneys.

Option 3 → Shell is a protective outer layer created by an animal that lives in the sea.

Option 4 → Psychology is the scientific study of the human mind and its functions.

All the other options are related to diseases or study of diseases, except shells.

So, “shell” is odd one out.

Shortcut Trick

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

Since AB = BC, we have ∠A = ∠C = 75°.

Using the angle sum property of a triangle:

∠B = 180° − (∠A + ∠C)

⇒ ∠B = 180° − (75° + 75°) = 30°

∴ The correct answer is 30°.

Alternate Method

Given:

⇒ In ΔABC, AB = BC

⇒ ∠C = 75°

Formula Used:

⇒ Isosceles Triangle Property: Angles opposite to equal sides of a triangle are equal.

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

Calculations:

Since the sides AB and BC are equal, the angles opposite to them must also be equal:

⇒ ∠A = ∠C

Given that ∠C = 75°:

⇒ ∠A = 75°

Now, applying the angle sum property in ΔABC:

⇒ ∠A + ∠B + ∠C = 180°

⇒ 75° + ∠B + 75° = 180°

⇒ 150° + ∠B = 180°

⇒ ∠B = 180° − 150°

⇒ ∠B = 30°

Why other options are incorrect:

⇒ Option (2) 60°: If ∠B = 60°, the sum of angles would be 75° + 60° + 75° = 210°, which violates the angle sum property of 180°.

⇒ Option (3) 75°: If ∠B = 75°, the sum of angles would be 75° + 75° + 75° = 225°, which violates the angle sum property of 180°.

⇒ Option (4) 52.5°: If ∠B = 52.5°, the sum of angles would be 75° + 52.5° + 75° = 202.5°, which violates the angle sum property of 180°.

∴ The correct answer is 30°.

Additional Information

Isosceles Triangle Theorem

If two sides of a triangle are equal, then the angles opposite to those sides are also equal. Conversely, if two angles of a triangle are equal, then the sides opposite to them are also equal.

Angle Sum Property of Triangles

The sum of the measures of the three interior angles of any triangle in Euclidean geometry is always exactly 180°.

Classification of Triangles by Sides

Triangles are classified as equilateral (all three sides equal), isosceles (at least two sides equal), or scalene (all three sides unequal).

The correct answer is option 3 i.e Fallopian tube.

• Fertilisation occurs in the Fallopian tube.
• It is a process of meeting eggs with sperm. After this, a cell formed known as Zygote cell which is a fertilised egg. 
  

The minimum number of horizontal and vertical straight lines required to make the given figure are,

Hence, “8” is the correct answer.

Stool and bench are both used for sitting.

Similarly,

Foot – rule and yardstick, both are used to take measurements.

Hence, “foot-rule : yardstick” is the correct answer.

The Great Indian Desert is also known as Thar desert.

It is given that,

⇒ O2 = 0.2 moles, N₂ = 0.4 moles, NH3 = 0.1 moles and He = 0.3 moles

⇒ xN₂ = nN₂/(nO₂ + nN₂ + nNH₃ + nH_e)

= 0.4/(0.2 + 0.4 + 0.1 + 0.3) = 0.4/1 = 0.4

Partial pressure of nitrogen,

⇒ pN₂ = xN₂ × P

Where P is the total pressure

⇒ P_N2= 0.4 × 1 atm = 0.4 atm

Shortcut Trick

Total Capacity (LCM of 8.7 and 5.8) = 17.4 units.

Efficiency: Pipe A (Inlet) = +2, Pipe B (Outlet) = −3.

In a cycle of 2 hours (B then A), net drainage = −3 + 2 = −1 unit.

Emptying process: To avoid over-emptying, stop before the last drainage step: 17.4 − 3 = 14.4 units.

14 cycles (28 hours) empties 14 units. Remaining 3.4 units: B empties 3 units in 1 hour, then A fills 2 units, then B empties again.

∴ The correct answer is 30 hr 48 min.

Alternate Method

⇒ Total work to be emptied = 17.4 units (starting from a full cistern).

⇒ Pattern: 1st hour Pipe B (−3), 2nd hour Pipe A (+2). Net in 2 hours = −1 unit.

⇒ In 14 cycles (28 hours), amount emptied = 14 × 1 = 14 units. Remaining = 17.4 − 14 = 3.4 units.

⇒ 29th hour: Pipe B works, empties 3 units. Remaining = 3.4 − 3 = 0.4 units.

⇒ 30th hour: Pipe A works, fills 2 units. Remaining to empty = 0.4 + 2 = 2.4 units.

⇒ 31st hour: Pipe B works to empty 2.4 units. Time taken = 2.4 ÷ 3 = 0.8 hours.

⇒ 0.8 hours = 0.8 × 60 = 48 minutes.

⇒ Total time = 30 hours + 48 minutes = 30 hr 48 min.

∴ The correct answer is 30 hr 48 min.

Additional Information

Alternate Pipe Concept

When pipes work alternately, the work done in one full cycle is the sum of their individual efficiencies. Total time = (Number of cycles × hours per cycle) + time for remaining work.

Negative Efficiency

In Cistern problems, inlet pipes have positive efficiency and outlet/leakage pipes have negative efficiency.

Emptying Logic

For emptying/filling problems with alternate work, always check if the task is completed within the last step of a cycle to avoid counting extra cycles.

The correct answer is option 4 i.e The weight of the book and the height of the bookshelf

• A student lifts a heavy book from the floor of a room to put it in the bookshelf at a height 2 m. For this process, the student takes 5 s.
• The work done by the student will depend upon the weight of the book and the height of the bookshelf.

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Work: It is defined as the amount of force required to move an object.

• Work Done = Force × Displacement 
  

Force: The push/pull required to change the state of object or direction of the object.

• Work done is not related to the amount of time taken to complete the work.

In the given circle, there are 6 blank parts and 2 shaded parts. I,e. ratio = 3: 1

Vertical diagram shows that ratio 3:1, 3 parts on upward side and 1 part on downward side.

In the second circle ratio of blank to the highlighted is 1:1.

Vertical diagram will have same parts upward and downwards.

Hence, option 4 is the correct answer.

The pattern followed is the addition of lines at the end of each edge.

The figure that will replace the given question mark is,

The complete pattern is,

Hence, option 4 is the correct answer.

The correct answer is option 3 i.e Golf

The child will be a male if the zygote has an XY combination.

Zygote: 

• It is a cell which is formed after the fusion of male sperms and eggs cells. Which is also known as a Fertilised egg. And over the period of time, this zygote develops and forms an embryo.
• The combination of Chromosome determines the sex of the child. Combination of the Y chromosome of male with XX chromosome of female results in the child being a male.

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Chromosome:

• It is a thread-like structure found in the nucleus.
• It is visible during cell division.
• The bead like structure found in the chromosome is called gene.

The correct answer is option 1 i.e 80 J

An object of mass 10 kg is moving with a uniform velocity of 4 ms-1. The kinetic energy possessed by the object is 80 J. 

Kinetic Energy: It is defined as the energy possessed by an object due to its motion.

Given: 

Mass of an object = 10 kg 

Velocity = 4 ms-1

Kinetic Energy = 1/2 × Mass of Object × (Velocity)²

⇒ Kinetic Energy = 1/2 ×10 × 4 × 4 

⇒Kinetic Energy = 80 J

The mirror image along the line MN is,

Hence, option 2 is the correct answer.

Let the present age of daughter be X years and the mother be Y years.

Given,

X + Y = 46

Y = 46 - X

Mothers age after 4 years will be twice the age of her daughter

Y + 4 = 2(X + 4)

Y + 4 = 2X + 8

46 – X = 2X + 4

46 – 4 = 3X

3X = 42

X = 14

The daughter’s present age is 14 years.

Hence, “14 years” is the correct answer.

The correct answer is option 1 i.e I = Q/t 

• Electric current: It is defined as the flow of electric charge through the surface in a specific amount of time.
• Electric current (​I) = Q/t 
  

where, Q = Electric charge, t =Time

• The unit of Electric current is Ampere.

A Memorandum of Understanding (MoU) was signed between the Indian Army and State Bank of India on the former’s Defence Salary Package. 

Important Highlights of the MoU - 

• First MoU was signed in 2011.
• It was renewed in February 2015.
• It was signed to provide facilities to Indian soldiers and their families.
• Under the provisions of MoU, free accidental cover will be provided.
• The validity of this MoU is January 2019.
  

State Bank of India - 

• It was established on 1st July 1955.
• Before 1955 it was known as Imperial bank.
• Headquarter - Mumbai, Maharashtra
• The Present Chairman of SBI is Dinesh Kumar Khara.

Conclusion 1: This does not follow, because it is not given that Mr .X did not like Mr. Y.

Conclusion 2: This does not follow, because it is not given that Mr. X was not popular in the office.

Hence, “neither conclusion 1 nor conclusion 2” follow.

Drawing the family tree,

Nilesh is the son of Prakash’s only sister’s father’s wife.

Hence, “son” is the correct answer.

Verifying the equation by placing the given options and using BODMAS rule,

→ 1) -, ×, ÷

((20 - 100) × 4) ÷ 10 = -10

-320 ÷ 10 is not equal to -10

→ 2) -, ÷, +

((20 - 100) ÷ 4) + 10 = -10

-80 ÷ 4 + 10 = - 10

-20 + 10 = - 10

→ 3) +, ÷, ÷

((20 + 100) ÷ 4) ÷ 10 = -10

(120 ÷ 4) ÷ 10 = - 10

30 ÷ 10 is not equal to -10

→ 4) +, ×, ×

((20 + 100) × 4) × 10 = - 10

(120 × 4) × 10 is not equal to -10

Hence, option 2 is the correct answer.

3.0005 - 1.748 = 1.2525

Alternate:

3.0005 × 10000 = 30005

1.748 × 10000 = 17480

30005 - 17480 = 12525

∴ 12525/10000 = 1.2525

The correct answer is option 4 i.e Shooting

Ankur Mittal was awarded the Arjuna Award (2018) for Shooting. Along with Ankur Mittal, 22 other sportspersons were also awarded the award.

About Ankur Mittal - He has created history by winning many events. He became world champion at 52nd ISSF world championship held in Korea.

About Arjun Award - 

• It was started in 1961 by the government of India.
• Ministry of Youth Affairs and sports awards best sportspersons.
• Those who have shown constantly good performance for 4 years at the international level will be choosen for this award.
• The Awardee will be awarded a cash prize worth Rs. 50,000 and a bronze statue.
• Krishna Das was the first person to be awarded the Arjun Award in 1984

The correct answer is option 1 i.e Dispur 

Shortcut Trick

Ratio of Amit (A) to Pankaj (P): (15/29) × A = (3/5) × P

A/P = (3/5) × (29/15) = 29/25

Total ratio parts = 29 + 25 = 54 units

54 units = ₹1080 → 1 unit = ₹20

Amit's share = 29 × 20 = ₹580

∴ The correct answer is ₹580.

Alternate Method

Given:

Total amount (Amit + Pankaj) = ₹1080

Relation: (15/29) × Amit = (3/5) × Pankaj

Calculations:

⇒ Amit / Pankaj = (3/5) ÷ (15/29)

⇒ Amit / Pankaj = (3/5) × (29/15)

⇒ Amit / Pankaj = 29/25

⇒ Let Amit = 29x and Pankaj = 25x

⇒ 29x + 25x = 1080

⇒ 54x = 1080

⇒ x = 1080 ÷ 54 = 20

⇒ Amit's amount = 29 × 20 = 580

∴ The correct answer is ₹580.

Additional Information

Ratio and Proportion

If a/b = c/d, then it is a simple proportion. To find individual shares, divide the total quantity by the sum of ratio parts and multiply by the respective ratio part.

Invertendo Property

If a/b = c/d, then b/a = d/c. This is useful when isolating variables in fractional equations.

Unitary Method in Ratios

Value of 1 unit = Total Value ÷ Total Ratio Sum. This is the fastest way to solve distribution problems.

Gentle and Harsh are Antonyms.

Similarly,

The antonym of Ignore is Notice.

Hence, “notice” is the correct answer.

Drawing the Venn diagram,

Conclusion 1: All pets are loving → True (This is definitely true)

Conclusion 2: Some beautiful are pets → True (This is definitely true)

Hence, “all conclusion” follow.

The correct answer is option 1 i.e Odisha

About Odisha:

• Animal: Sambar
• Bird: Indian roller
• Tree: Banyan
• Flower: Lotus

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Important mines in India - 

Shortcut Trick

A perfect square never ends with the digits 2, 3, 7, or 8 at the unit place.

Check the unit digit of the given options:

(1) 7569 ends in 9 | (2) 6084 ends in 4 | (3) 3368 ends in 8 | (4) 1444 ends in 4.

Since 3368 ends in 8, it cannot be a perfect square; hence its square root is irrational.

∴ The correct answer is 3368.

Alternate Method

Given: Four numbers (1) 7569, (2) 6084, (3) 3368, (4) 1444.

Property: An irrational square root occurs for any positive integer that is not a perfect square.

⇒ √7569 = 87 (Rational)

⇒ √6084 = 78 (Rational)

⇒ √1444 = 38 (Rational)

⇒ √3368 ≈ 58.034 (Irrational)

∴ The correct answer is 3368.

Additional Information

Unit Digits of Perfect Squares

Perfect squares always end with 0, 1, 4, 5, 6, or 9. If a number ends in 2, 3, 7, or 8, its square root is always irrational.

Digital Sum Rule

The digital sum (sum of digits reduced to a single digit) of a perfect square is always 1, 4, 7, or 9. For 3368, the digital sum is 3+3+6+8 = 20 → 2+0 = 2, confirming it is not a perfect square.

Irrational Numbers

Numbers that cannot be expressed as a simple fraction p/q are irrational. Square roots of non-perfect squares are classic examples.

An element has an atomic number 15.  N(7) show similar chemical properties.

• The valence electrons of the atomic number 15 have 5 electrons in its outermost shell.
• Nitrogen also has 5 electrons in its outermost shell. It also belongs to the 15th group and has the same chemical properties.
• Others (Be, O, Ne) have 2,6 and 8 electrons in their outermost shell respectively.

 

The correct answer is option 4 i.e Mukesh Khanna

As of February 2018, the Chairperson for Children’s Film Society of India is Mukesh Khanna. 

Children's Film Society of India - 

• It was established on 11 May 1955.
• It is one of the nodal organisation which works under the Ministry of Information and Broadcasting.
• Headquarter - Mumbai

Shortcut Trick

For a right-angled triangle, the circumradius (R) is always half of the hypotenuse.

Hypotenuse = 14√2 cm → R = 7√2 cm.

Area of circumcircle = πR² = (22/7) × (7√2)² = (22/7) × 98 = 22 × 14 = 308 cm².

∴ The correct answer is 308 cm².

Alternate Method

Given:

Hypotenuse (h) of the right-angled triangle = 14√2 cm

Value of π = 22/7

Formula Used:

1. Circumradius of right triangle (R) = Hypotenuse ÷ 2
2. Area of circle = π × R²

Calculations:

⇒ Circumradius (R) = (14√2) ÷ 2

⇒ R = 7√2 cm

⇒ Area = π × (7√2)²

⇒ Area = (22/7) × (49 × 2)

⇒ Area = (22/7) × 98

⇒ Area = 22 × 14

⇒ Area = 308 cm²

∴ The correct answer is 308 cm².

Additional Information

Circumcenter Location

In a right-angled triangle, the circumcenter always lies at the midpoint of the hypotenuse.

Inradius of Right Triangle

The inradius (r) is calculated as (Perpendicular + Base − Hypotenuse) ÷ 2.

Area via Inradius and Circumradius

Area of any triangle can also be expressed as r × s, where s is the semi-perimeter.

Shortcut Trick

Let filling time be A = 12 hr and combined time (filling − emptying) be (A − B) = 16 hr.

Emptying time B = (xy) ÷ (y − x), where x = 12 and y = 16.

B = (12 × 16) ÷ (16 − 12) = 192 ÷ 4 = 48 hr.

∴ The correct answer is 48 hr.

Alternate Method

Given: Filling pipe (P₁) = 12 hr, Combined (P₁ + P₂) = 16 hr.

Formula Used: Total Work = LCM of time taken; Efficiency = Work ÷ Time.

⇒ Efficiency of Pipe 1 (Fill) = 4 units/hr

⇒ Combined efficiency of Pipe 1 − Pipe 2 = 3 units/hr

⇒ Efficiency of Pipe 2 (Empty) = 4 − 3 = 1 unit/hr

⇒ Time taken by Pipe 2 to empty the full tank = 48 ÷ 1 = 48 hr

∴ The correct answer is 48 hr.

Additional Information

Pipes & Cisterns Rule

Filling efficiency is taken as positive (+), while emptying (leakage) efficiency is taken as negative (−).

Net Work Formula

If two pipes fill and empty respectively, net efficiency = 1/x − 1/y, where x is filling time and y is emptying time.

The 48th and present chief justice is NV Ramana.

Sharad Arvind Bobde was 47th Chief Justice of India. 

As of December 2018, Dipak Misra was the Chief Justice of India. 

Important Points

Chief Justice of India - 

• Justice Uday Umesh Lalit is the current and 49th Chief Justice of India (CJI).
• He succeeded Justice N V Ramana, who retired on 26 August 2022.
• Article 124 to 147 deals with the Supreme court of India.
• Chief justice of India is appointed by President after consultation with judges of Supreme court and High Court.
• He served until he attains the age of 65 years.
• He can be removed by President on the parliamentary recommendation.

The correct answer is option 1 i.e Biplab Kumar Deb

Chief ministers of Northeastern states - 

The correct answer is option 4 i.e pH = 0

pH -

• It is used to measure the acidic or basic of the water solution.
• It shows the concentration of hydrogen ions in solution. Higher the concentration of hydrogen ions lowers the pH of that solution.
• The pH of the solution is inversely proportional to the number of Hydrogen ions. On the scale of 0 to 14, if pH is lower than 7 than it is considered as acidic and if it is more than 7 than it is considered as basic. 
  

The pH of some solutions - 

The correct answer is option 1 i.e Vishal Bhardwaj

• ‘’The Blue Umbrella’’, which is a famous Children’s movie, is directed by Vishal Bharadwaj.
• It was released in 2005.
• The movie was based on the novel The Blue Umbrella, written by Ruskin bond

 

Total boards = 5

Statement 1: There are 3 square boards.

Statement 1 alone is not enough to tell the number of the circular board.

The number of the circular board can be 2 or 0.

Statement 2: The number of rectangular boards is one-third of the number of square boards.

Here, the number of square boards is not given, so any possibility can be true.

Statement 2 alone is not enough to tell the number of the circular board.

Combining both the statement

Square board = 3, rectangle board = 1 (one-third of square boards) and circular board = 1

Hence, statement 1 and statement 2 together are sufficient.

Drawing the Venn diagram,

Conclusion 1: Some bowls are caps→ False (There is no direct relation between caps and bowls so it can be possible but not definite, hence, false)

Conclusion 2: No bowl is a cap → False  (There is no direct relation between caps and bowls so it can be possible but not definite, hence, false)

Both the conclusions form a complementary pair.

When we combining the statement I and II we can say that either I or II follows

Hence, “either 1 or 2” follows.

Additional Information

Conditions of Either-or case:

1. Individually both the conclusions should be false.
2. One conclusion should be positive and one conclusion should be negative (Complementary pair)

The two complementary pairs are:

1. All + Some not

2. No + Some

Note: Some + Some not is not considered under Either -or case.

The correct answer is option 4 i.e C4H6

• Butyne is a member of the alkyne series which has a general formula C_nH_2n-2.
• They are unsaturated hydrocarbons having a triple bond between two carbon atoms in them.
• Out of the three bonds, two are pi and one is sigma.

Characteristics of Butyne - 

• It is a highly inflammable gas.
• Its chemical formula is C₄H₆, which has 4 carbon and one alkyne.
• The two isomers of Butyne are - 1-Butyne and 2-Butyne.

The correct answer is option 2 i.e Meghalaya and Mizoram

• The Cabinet Committee on Economic Affairs (CCEA) approved North East Road Network Connectivity Project (NERNCP) Phase I for development of 403 km of national highways in Meghalaya and Mizoram.
  

Some highlights of the projects are:

• 52 km of the highway work will be in Meghalaya and remaining 351 km will be in Mizoram.
• Total outlay of the project is expected to be Rs. 6271 crore.
• Japan International cooperative agency will provide loan assistance.
• Deadline of the project is 2025.

The correct answer is option 4 i.e At the focal point

• If an object is at infinity,  the position of an image formed due to the convex lens is at the focal point.
• Convex lens converge parallel rays coming from object at infinity and a highly diminished - point sized, real and inverted image is formed at principal focus.

​Properties of the image formed

• The image formed is highly diminished, real and inverted.

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There are two types of lenses - ​

• Convex Lens: This type of lens is also known as Converging lens as when light passes through it converges at one point.
• Concave Lens: This type of lens is also known as Diverging lens as all the rays diverged when light passes through it.

Shortcut Trick

Number of factors for n = a^p × b^q is (p+1)(q+1).

To have 10 factors, the product of powers+1 must be 10 (10 or 2×5).

Case 1: a⁹ ⇒ 2⁹ = 512.

Case 2: a⁴ × b¹ ⇒ 2⁴ × 3¹ = 16 × 3 = 48.

Comparing 512 and 48, the smallest is 48.

∴ The correct answer is 48.

Alternate Method

Given: Exact number of factors = 10.

Formula: If N = p₁^a × p₂^b, then Total Factors = (a + 1)(b + 1).

⇒ Case A: (a + 1) = 10 ⇒ a = 9. Smallest number = 2⁹ = 512.

⇒ Case B: (a + 1)(b + 1) = 5 × 2 ⇒ a = 4, b = 1. Smallest number = 2⁴ × 3¹ = 16 × 3 = 48.

⇒ Checking options: 36 (factors: 1,2,3,4,6,9,12,18,36 = 9 factors); 24 (8 factors); 16 (5 factors); 48 (1,2,3,4,6,8,12,16,24,48 = 10 factors).

∴ The correct answer is 48.

Additional Information

Total Number of Factors

For any composite number N = p^aq^br^c, total factors = (a+1)(b+1)(c+1) where p, q, r are prime numbers.

Perfect Square Factors

A natural number has an odd number of factors if and only if it is a perfect square.

Prime Factorization

To find the smallest number for a fixed number of factors, assign the highest exponents to the smallest prime bases (2, 3, 5, etc.).

The correct answer is option 4 i.e DNA of the male gamete

• The sex of an offspring is determined by DNA of the male gamete.
• In male, sex chromosome is XY and in female sex chromosome is XX.
• In male gamete formation, half of the sperm contains X chromosome and other half contain Y chromosome.
• In female gamete contains the only X chromosomes.
• When a male gamete chromosome fertilizes an ova, the zygote develops into a female. When a sperm carrying Y chromosomes fertilizes an egg, the zygote develops into a male.

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DNA: Deoxyribonucleic acid

• It is found in cells of organisms.
• It is a molecule that contains the biological instructions that make each species unique.
• There are four chemical bases which store information about DNA they are - Adenine, Thymine, Guanine and Cytosine.

Shortcut Trick

To identify the rational number, find the radicand that is a perfect fourth power.

Check the powers: 2⁴ = 16, 3⁴ = 81, 4⁴ = 256.

Since 81 = 3⁴, then ⁴√81 = 3, which is an integer and thus rational.

Other values like 49, 64, and 36 are perfect squares but not perfect fourth powers of integers.

∴ The correct answer is ∜81.

Alternate Method

Given: Four radical expressions: ⁴√81, ⁴√49, ⁴√64, and ⁴√36.

Evaluate each option by simplifying the fourth root:

⇒ ⁴√81 = (3⁴)^1/4 = 3 (This is a Rational Number as it is an integer)

⇒ ⁴√49 = (7²)^1/4 = 7^2/4 = 7^1/2 = √7 (Irrational)

⇒ ⁴√64 = (8²)^1/4 = 8^2/4 = 8^1/2 = √8 = 2√2 (Irrational)

⇒ ⁴√36 = (6²)^1/4 = 6^2/4 = 6^1/2 = √6 (Irrational)

∴ The correct answer is ∜81.

Additional Information

Rational Numbers

A number that can be expressed as a fraction p/q where p and q are integers and q ≠ 0. Terminating or repeating decimals are also rational.

Irrational Numbers

Numbers that cannot be written as a simple fraction. Their decimal expansions are non-terminating and non-repeating (e.g., √2, π).

Radical Property

For any positive integer n and non-negative real number a, the n^th root ⁿ√a is rational only if 'a' is a perfect n^th power of a rational number.

The correct answer is option 2 i.e Forces

The Forces between two bodies are always equal and opposite.

Inertia: It is a property of a body by which a body opposes other agents to be in motion or causes to change magnitude or direction of its velocity. 

Pressure: When an object is in contact with another object and a continuous force is applied against or on it is called pressure. 

Momentum: It is the quantity which is measured by the product of mass and velocity of the moving body.

Correct Option - 4 - 1 – B, 2 – D, 3 – A, 4 - C

• Som Veda is not a Veda.
• Vedas are written in Sanskrit and oldest text about Hindu culture.
• They are also known as Sruti.
• Vedvyasa is known to be compiled Vedas.

The pattern followed is,

Hence, “5VE22” is the correct answer.

Correct Option -  Punjab

• Shiromani Akali Dal is the regional political party of Punjab.
• It was created on 14 December 1920 by Shiromani Gurudwara Prabandhak Committee.
• The first president of the party was Sardar Sarmukh Singh Chubbal and presently led by  Sukhbir Singh Badal. 
  

Regional parties of Different states

Shortcut Trick

Efficiency Ratio (Type 1 : Type 2) = 2.5 : 1 = 5 : 2

Total Work = 12 Type-1 workers × 10 days = 12 × 5 × 10 = 600 units

Combined Efficiency of 4 Type-1 and 15 Type-2 = (4 × 5) + (15 × 2) = 20 + 30 = 50 units/day

Time Required = 600 ÷ 50 = 12 days

∴ The correct answer is 12 days.

Alternate Method

Given:

Efficiency of Type 1 (E₁) = 2.5 × Efficiency of Type 2 (E₂)

Formula Used:

Total Work = Number of workers × Efficiency × Time

Calculations:

⇒ Total Work = 12 × E₁ × 10

⇒ Let E₂ = 1, then E₁ = 2.5

⇒ Total Work = 12 × 2.5 × 10 = 300 units

⇒ Combined Efficiency of (4 Type-1 + 15 Type-2) = (4 × 2.5) + (15 × 1)

⇒ Total Efficiency = 10 + 15 = 25 units/day

⇒ Time Taken = 300 ÷ 25 = 12 days

∴ The correct answer is 12 days.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken to complete a task. If efficiency is in ratio a:b, time taken is in ratio b:a.

Work Equivalence Formula

Use M₁D₁E₁ = M₂D₂E₂ where M is number of men, D is days, and E is efficiency.

Man-Days Concept

Total work is often calculated in man-days, which is the product of the number of workers and the number of days they work.

Argument 1: This follows , because it is given about traditional cold pressed methods in the statement

Argument 2: This does not follow, because information about the cost about cold pressed oil is not given.

Hence, “only argument 1” is strong.

Conclusion 1: This does not follow, because information about citizens support is not given in the statement.

Conclusion 2: This does not follow, because information about powerful countries is not given.

Hence, “neither conclusion 1 nor conclusion 2” follow.

Correct Option - 1 - President

Under Article 72 of the constitution of India President has the power to Pardon, Commute, Remit, Respite, and Reprieve the sentence. 

• Pardon - President can pardon the sentence of any convicted person and bring him to the position where all his deeds of crime will not carry any punishment.
• The scope of the pardoning power of the President under Article 72 is wider than the pardoning power of the Governor under Article 161 which differs in the following two ways:
• Court Martial: The power of the President to grant pardon extends in cases where the punishment or sentence is by a Court Martial but Article 161 does not provide any such power to the Governor.
• Death sentence: The President can grant pardon in all cases where the sentence given is the sentence of death but the pardoning power of the Governor does not extend to death sentence cases.
• Commute - President can reward lesser punishment to the person in place of rigorous punishment.
• Remit- by remitting the power President lessens the term of imprisonment.
• Respite - In this, the President considers some cases and decreases the punishment of the offender.
• Reprieve - In case of a death sentence, the President can hold the punishment.

The position of the Indian men’s hockey team in the Commonwealth Games 2018 was 4^th.

Commonwealth Games 2018 - 

• It was the XXI edition of commonwealth games held in Gold Coast, Australia.
• The motto of the games - 'Share the dream'.
• Australia topped the medal tally with 198 medals.
• India ranked 3^rd in the overall medal tally.

India and Commonwealth games 2018 - 

• Medal tally - 26 Gold, 20 Silver, 20 Bronze.
• Indian men's hockey team ranked 4^th.

Shortcut Trick Net efficiency = Efficiency of Inlet Pipe A − Efficiency of Outlet Pipe B. Time taken = (A × B) ÷ (B − A) = (4 × 6) ÷ (6 − 4). Time taken = 24 ÷ 2 = 12 hours. ∴ The correct answer is 12 hours. Alternate Method Given: Time taken by Pipe A (Inlet) = 4 hours Time taken by Pipe B (Outlet) = 6 hours Formula Used: Total Work = LCM of individual times; Efficiency = Total Work ÷ Time

Pipe Time (hrs) Total Capacity (Units) Efficiency (Units/hr) Pipe A (+) 4 12 +3 Pipe B (−) 6 −2 Calculations: ⇒ Total Capacity of tank = LCM(4, 6) = 12 units. ⇒ Efficiency of Pipe A = 12 ÷ 4 = +3 units/hr. ⇒ Efficiency of Pipe B = 12 ÷ 6 = −2 units/hr (negative because it empties). ⇒ Combined efficiency of (A + B) = 3 − 2 = 1 unit/hr. ⇒ Time required to fill the tank = Total Capacity ÷ Combined Efficiency ⇒ Time = 12 ÷ 1 = 12 hours. ∴ The correct answer is 12 hours. Additional Information Inlet and Outlet Pipes An Inlet pipe fills the tank (positive work), while an Outlet pipe (or leak) empties the tank (negative work). Net Work Formula If pipe A fills in 'x' hours and pipe B empties in 'y' hours (where y > x), the net part filled in 1 hour is (1/x − 1/y). Pipes and Cisterns Logic This concept is identical to Time and Work, where efficiency is added for contributors and subtracted for destructors.

Shortcut Trick

Let the initial daily allowance be x.

Total amount remains constant ⇒ 10 × x = 16 × (x − 45)

10x = 16x − 720 ⇒ 6x = 720 ⇒ x = ₹120

Total Sanctioned Amount = 10 × 120 = ₹1,200

∴ The correct answer is ₹1,200.

Alternate Method

Given: Initial days = 10, Extended days = 6, Total days = 16, Reduction in daily allowance = ₹45.

Formula Used: Total Amount = Average Daily Allowance × Number of Days

Let the original average daily allowance be A.

⇒ Total Sanctioned Amount = 10 × A

⇒ New average daily allowance = (A − 45)

⇒ Total days = 10 + 6 = 16

⇒ 10 × A = 16 × (A − 45)

⇒ 10A = 16A − 720

⇒ 16A − 10A = 720

⇒ 6A = 720

⇒ A = 120

⇒ Total Sanctioned Amount = 10 × 120 = 1200

∴ The correct answer is ₹1,200.

Additional Information

Weighted Average Concept

When a group is divided into parts, the total sum is the addition of the sum of each part: Total Sum = n₁a₁ + n₂a₂.

Constant Product Rule

If the total amount is constant, the daily allowance is inversely proportional to the number of days (Allowance ∝ 1/Days).

Average Change

Net Change in Average = (New Sum − Old Sum) ÷ Total Quantity.