RRC Group D Previous Year Paper 8 (Held On: 26 Sep 2018 Shift 1)

• Sanjeev Kaushik was appointed as whole-time member of SEBI for a period of three years or till the age of 65 years, whichever is earlier.
• Kaushik replaces S Raman, who retired from the post of a whole-time member in September 2017.
• Prior to this appointment, he was Chairman and Managing Director of India Infrastructure Finance Company Ltd (IIFCL).
• The Securities and Exchange Board of India (SEBI) is the regulator of the securities market in India.
• About SEBI
• Chairman- Madhabi Puri Buch
• Founded- 1992
• Headquarters - Mumbai Maharashtra

• Jagat Prakash Nadda is an Indian politician. He is currently the Union Minister of Health and Family Welfare and member of Rajya Sabha from Himachal Pradesh and Parliamentary Board Secretary of Bharatiya Janata Party.
• Earlier, he was a Minister in Himachal Pradesh Government.
• Shri Ashwani Kumar Choubey is the Minister of State in the Ministry of Health and Family Welfare.

Shortcut Trick

Inclusion Formula: New Value − Old Average = Total Number of Members × Average Increase.

Total number of students after joining = 5 + 1 = 6.

Increase in average = 2 marks.

Difference = 6 × 2 = 12 marks.

∴ The correct answer is 12 marks.

Alternate Method

Given: Initial students = 5 | Increase in average = 2 marks.

⇒ Let the initial average of 5 students be x.

⇒ Total marks of 5 students = 5 × x = 5x.

⇒ When the 6th student joins, the new average becomes x + 2.

⇒ Total marks of 6 students = 6 × (x + 2) = 6x + 12.

⇒ Marks of the new student = Total marks of 6 students − Total marks of 5 students.

⇒ Marks of the new student = (6x + 12) − 5x = x + 12.

⇒ Required difference = (x + 12) − x = 12.

∴ The correct answer is 12 marks.

Additional Information

Definition of Average

Average is calculated as the Sum of all observations divided by the Total number of observations.

Inclusion Property

If the average increases when a new person joins, the new person's value = Old Average + (New total number × Increase in average).

Exclusion Property

If a person leaves and the average decreases, the excluded value = Old Average + (Original number × Decrease in average).

Net Deviation

The sum of deviations of all observations from their arithmetic mean is always zero.

Given: Latika fills petrol in her car once in three days.

This week ⇒ Wednesday,

In the same week, she will put petrol on → Wednesday + 3 = Saturday.

Following/next week → Saturday + 3 = Tuesday, and Tuesday + 3 = Friday.

Hence, “Tuesday and Friday” is the correct answer.

Shortcut Trick

Let the edge of the cube be a and the side of the square be s.

Sum of 12 edges = 12a. Perimeter of square = 4s. Given: 12a = (1/8) × 4s ⇒ s = 24a.

Volume of cube = Area of square ⇒ a³ = s².

Substitute s: a³ = (24a)² ⇒ a³ = 576a² ⇒ a = 576.

∴ The correct answer is 576 units.

Alternate Method

Given: Numerical value of Volume of Cube = Area of Square.

Formula Used: Volume of cube = a³; Sum of edges = 12a; Area of square = s²; Perimeter of square = 4s.

⇒ Sum of edges of cube = 12a

⇒ Perimeter of square = 4s

⇒ According to the question: 12a = (1/8) × 4s

⇒ 12a = s/2 ⇒ s = 24a

⇒ Volume of cube = a³ and Area of square = s²

⇒ Given: a³ = s²

⇒ a³ = (24a)²

⇒ a³ = 576a²

⇒ a = 576 units

∴ The correct answer is 576 units.

Additional Information

Cube Properties

A cube has 12 equal edges, 8 vertices, and 6 square faces. Total Surface Area = 6a².

Square Properties

A square has 4 equal sides and its diagonal length is given by d = s√2.

Diagonal of a Cube

The longest diagonal connecting opposite vertices of a cube is a√3.

• President Pranab Mukherjee gave the 64th National Film Awards in New Delhi in 2017.
• Akshay Kumar was chosen for the Best Actor Award for Hindi Movie Rustom.
• Surabhi was named as the best actress for her role in Malayalam film Minnaminungu-The Firefly.

Extra Information :

• Akshay Kumar was also appointed as brand ambassador for road safety by Union Ministry of Road, Transport, and Highways to promote road safety through its new campaign.
• Akshay Kumar plays the role of social activist Arunachalam Muruganantham in the biopic movie Pad Man.

• Bengaluru city had India’s first helicopter-taxi service.
• Kempegowda International Airport, Bengaluru became the 1st airport in the country to have a helicopter-taxi.
• Operated by Thumby Aviation HeliTaxi service will initially fly 2 helicopters, Initially, the services will be operated between KIA & Electronics City where a heliport is expected to come up.
• It will ensure quick, seamless transfers to & from the airport, at a cost similar to a luxury taxi fare.

• K Chandrasekhar Rao is the Chief Minister of Telangana and also the 1st chief minister of the state.
• He belongs to the party called Telangana Rashtra Samithi and their symbol is a ‘CAR’.
• On 2 June 2014, Telangana separated from Andhra Pradesh and became the 29th state of India.
• The capital of Telangana is Hyderabad and E. S. L. Narasimhan is the current governor of Telangana

Shortcut Trick

Total Sales Year 1 = 15 + 12 + 9 = 36 lakhs.

Total Sales Year 3 = 14 + 15 + 13 = 42 lakhs.

Difference = 42 − 36 = 6 lakhs.

Percentage Increase = (6 ÷ 36) × 100 = 1/6 × 100 = 16.67%.

∴ The correct answer is 16.67%.

Alternate Method

Given:

Sales in Year 1 (State 1, 2, 3) = 15, 12, 9 lakhs.

Sales in Year 3 (State 1, 2, 3) = 14, 15, 13 lakhs.

Formula Used:

Percentage Difference = [(New Value − Old Value) ÷ Old Value] × 100

Calculations:

⇒ Total Sales in Year 1 = 15 + 12 + 9 = 36 lakhs.

⇒ Total Sales in Year 3 = 14 + 15 + 13 = 42 lakhs.

⇒ Absolute Difference = 42 − 36 = 6 lakhs.

⇒ Percentage Difference = (6 ÷ 36) × 100

⇒ Percentage Difference = (1 ÷ 6) × 100 = 16.666...

⇒ Percentage Difference ≈ 16.67%

∴ The correct answer is 16.67%.

Additional Information

Percentage Change

It measures the relative change between an old value and a new value: [(New − Old) ÷ Old] × 100.

Data Interpretation Table

In tabular DI, always sum the rows or columns carefully to find aggregate totals before calculating ratios or percentages.

Fraction to Percentage Conversion

Remembering standard fractions like 1/6 = 16.67% and 1/7 = 14.28% helps in fast calculations during exams.

Shortcut Trick

According to the question, 64% of the total marks = 272.

Total marks (100%) = (272 ÷ 64) × 100

⇒ 4.25 × 100 = 425

∴ The correct answer is 425 marks.

Alternate Method

Given: Marks secured by Paranjoy = 272, Percentage secured = 64%.

Formula Used: Total Marks = (Marks Obtained ÷ Percentage Secured) × 100

⇒ Let the Total Marks of the test be x.

⇒ 64% of x = 272

⇒ (64 ÷ 100) × x = 272

⇒ x = (272 × 100) ÷ 64

⇒ x = 27200 ÷ 64

⇒ x = 425

∴ The correct answer is 425 marks.

Additional Information

Percentage to Value Conversion

To find a value when a percentage is given, use the formula: Value = (Percentage ÷ 100) × Total.

Finding the Base (Total)

When a part and its percentage are known, the total is calculated as: Total = (Part Value ÷ Percentage) × 100.

Fraction Equivalents

64% can also be expressed as the fraction 16/25 in simplified form (64/100 = 16/25).

Shortcut Trick

Ratio is the comparison of two quantities of the same unit by division.

Divide both terms by their Highest Common Factor (HCF) which is 10.

30 ÷ 10 : 40 ÷ 10 = 3 : 4

∴ The correct answer is 3 : 4.

Alternate Method

Given:

First quantity = 30 min

Second quantity = 40 min

Formula Used:

Ratio (a : b) = a / b

Calculations:

⇒ Ratio = 30 min / 40 min

⇒ Ratio = 30 / 40

⇒ Ratio = (3 × 10) / (4 × 10)

⇒ Ratio = 3 / 4

⇒ Ratio = 3 : 4

∴ The correct answer is 3 : 4.

Additional Information

Unit Consistency in Ratio

Before finding a ratio, ensure both quantities are in the same unit (e.g., both in minutes or both in hours).

Simplest Form

A ratio is always expressed in its lowest terms by dividing both parts by their HCF.

Inverse Ratio

If the ratio of A to B is x : y, then the inverse ratio (B to A) is y : x.

Students not reporting to class on time is a case of indiscipline. Therefore, it is safe to assume that the school management's announcement is a measure taken in order to develop discipline among the students. Hence, assumption I is implicit.

Indiscipline in school might damage its reputation in the future and therefore, it is highly likely that the management has announced strict action to prevent such an occurrence. Hence, assumption II is implicit.

Thus, both the assumptions (I and II) are implicit.

In the given question image three ‘U’ shape figures are inscribed in a ‘parallelogram’.

So the only option image that resembles and consist of the same figure is the option image D.

Which is a water image of question figure.

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

• Weight of a body is a product of its mass and acceleration due to gravity on earth i.e

w = m x g

where w = weight of a body

           m = mass of a body

            g = acceleration due to gravity

• w = 10 x 9.8 [ mass, m = 10 kg given and value of acceleration due to gravity ,g = 9.8 m/s²]

w = 98 N

• Therefore, weight of object on earth will be 98 N

• Best News Channel – Hindi Award at the 17th Indian Television Academy Awards was won by Aaj Tak.
• Aaj Tak won this award consecutively from the year 2013 to 2017.
• The 17th Indian Television Academy Awards were held at Mumbai, Maharashtra.
• The ITA Awards, Indian Television Academy Awards, is an annual event organized by the Indian Television Academy to honour the excellence of Indian Television.

Shortcut Trick

For divisibility by 11, the difference between the sum of digits at odd positions and sum of digits at even positions must be 0 or a multiple of 11.

Odd positions (from right): 4 + 5 + x = 9 + x

Even positions (from right): 8 + 4 = 12

Difference: (9 + x) − 12 = x − 3

For divisibility, x − 3 = 0 ⇒ x = 3.

∴ The correct answer is 3.

Alternate Method

Given: The number is x4584 and it is divisible by 11.

Formula Used: A number is divisible by 11 if (Sum of digits at odd places) − (Sum of digits at even places) = 0, 11, 22, ...

Calculations:

⇒ Sum of digits at odd places (1^st, 3^rd, 5^th) = 4 + 5 + x = 9 + x

⇒ Sum of digits at even places (2^nd, 4^th) = 8 + 4 = 12

⇒ Difference = (9 + x) − 12

⇒ Difference = x − 3

⇒ For the number to be divisible by 11, x − 3 must be 0 (since x is a single digit).

⇒ x − 3 = 0

⇒ x = 3

The face value of a digit is the digit itself.

∴ The correct answer is 3.

Additional Information

Divisibility Rule of 11

Subtract the last digit from the rest of the number. If the result is divisible by 11, the original number is also divisible by 11.

Face Value vs Place Value

The face value of a digit is its actual value (e.g., face value of 4 in 45 is 4), while place value depends on its position (e.g., 40).

Divisibility by 3 and 9

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

In the question figure two ‘/ ’ and a ‘right-angled arrow’ sign are inscribed in two concentric ‘ovals’.

The option image that consists of same number of figures and patterns is the option figure D.

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

Shortcut Trick

Error = |Actual Value − Measured Value| = 2.05 − 2 = 0.05 m

Error % = (Error / Actual Value) × 100

Error % = (0.05 / 2.05) × 100 = (5 / 205) × 100 = (1 / 41) × 100

∴ The correct answer is 100/41%.

Alternate Method

Given:

Actual Length = 2.05 m

Measured Length = 2 m

Formula Used:

Error Percentage = [(Actual Value − Measured Value) / Actual Value] × 100

Calculations:

⇒ Error = 2.05 − 2.00 = 0.05 m

⇒ Error % = (0.05 / 2.05) × 100

⇒ Error % = (5 / 205) × 100

⇒ Error % = (1 / 41) × 100

⇒ Error % = 100/41%

∴ The correct answer is 100/41%.

Additional Information

Percentage Change

It represents the relative change between an old value and a new value, calculated as [ (New − Old) / Old ] × 100.

Absolute Error

The magnitude of the difference between the exact value and the approximation, denoted as |V_A − V_E|.

Relative Error

The ratio of the absolute error to the actual value. Multiplying this by 100 gives the Percentage Error.

• Athens Olympic silver medallist shooter Rajyavardhan Singh Rathore is the Sports Minister of India.
• He replaced Vijay Goel, who has been made the minister of state for parliamentary affairs.
• Colonel Rathore first stepped in a shooting range in the mid-1990s and some years later, he became India's first ever individual silver medal winner at the Olympic Games.
• He stood on the podium after finishing second in the men's double trap at the 2004 Athens Games.

The pattern followed here is as follows,

The unit digit of final value of operation is a code for the letters.

Similarly,

Hence, “18679” is the correct answer.

The pattern followed here is as follows,

Every element is shifting to next quadrant in a clockwise manner in succeeding image.

Similarly,

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

Mistake Points Entrance point will be just the opposite of the given facing direction.

Here, The house is facing East then, Any person who enters the house that will be in the west direction.

The following diagram illustrates the given information,

Clearly, the balcony faces “east”.

Hence, “East” is the correct answer.

Shortcut Trick

For half-yearly compounding, the rate is halved (10%) and time is doubled (3 periods of 6 months).

Fractional multiplier for 10% increase = 11/10.

For 3 periods, Amount = Principal × (Multiplier)³

Amount = 6000 × (11/10)³ = 6000 × (1331/1000) = 6 × 1331 = 7986.

∴ The correct answer is Rs. 7,986.

Alternate Method

Given:

Principal (P) = Rs. 6,000

Annual Interest Rate (R) = 20%

Time (T) = 18 months

Formula Used:

When interest is compounded half-yearly:

New Rate (r) = R/2 = 20%/2 = 10% per half-year

Number of periods (n) = (18 months) / (6 months) = 3 periods

Amount (A) = P(1 + r/100)ⁿ

Calculations:

⇒ A = 6000 × (1 + 10/100)³

⇒ A = 6000 × (11/10)³

⇒ A = 6000 × (1331 / 1000)

⇒ A = 6 × 1331

⇒ A = 7986

∴ The correct answer is Rs. 7,986.

Additional Information

Compounding Frequency

If compounded quarterly, the rate becomes R/4 and the number of periods becomes 4 × T (in years).

CI vs SI for 2 years

The difference between Compound Interest and Simple Interest for 2 years is given by P(R/100)².

Effective Rate of Interest

For two successive cycles of r%, the effective rate is (r + r + r²/100)%.

• The bleaching agent present in bleaching powder is Chlorine.
• Bleaching powder is calcium oxychloride (CaOCl₂) which is a yellowish white powder with a strong smell of chlorine.
• When it reacts with carbon dioxide in the atmosphere, it gives off chlorine and calcium carbonate.
• Bleaching powder (CaOCl₂) is manufactured through a reaction between slaked lime Ca(OH)₂ and chlorine (Cl₂).
• It is used in the laundry. Being a very strong oxidizing agent, it is also used as an oxidizer.

Ca(OH)₂ + Cl₂ -------------->  CaOCl₂ + H2O

• Indian men’s and women’s hockey teams both won the international Hockey Asia Cup in 2017.
• India won the Women’s Hockey Asia Cup title, 2017 by defeating China by 5-4 in the final match.
• It was the 9th edition of Women’s Hockey Asia Cup. The tournament was held from 28 October to 5 November 2017 in Kakamigahara, Gifu, Japan.
• India defeated Malaysia in the final of the 2017 Men’s Asia Cup Hockey to claim the title.
• The tournament was held from 11-22 October 2017 in Dhaka, Bangladesh.

Extra Information :

• The 2018 Men's Hockey World Cup was held at Kalinga Stadium, Bhubaneswar in India from 28 November to 16 December 2018 whereas the 2018 women’s world cup was held in England.
• Men's Hockey World Cup 2018 was won Belgium while Women’s Hockey World Cup was won by the Netherlands.

• The Geo-thermal energy is extracted from the heat energy in the earth’s inner part
• The source of heat energy in the earth's core is a layer of hot and molten rock called ‘Magma’
• In the geothermal power plant, water to be seeping into the underground layer over time gains heat energy from the geothermal reservoirs
• This water is heated and then sent through a steam turbine where the thermal energy is converted into electricity through a generator.

Shortcut Trick

The relation between side (a), area (A), and sum of diagonals (d₁ + d₂) is: (d₁ + d₂)² = 4a² + 4A.

Substitute a = 37 and A = 840:

(d₁ + d₂)² = 4(37²) + 4(840) = 4(1369 + 840)

(d₁ + d₂)² = 4 × 2209 = 8836

d₁ + d₂ = √8836 = 94 cm.

∴ The correct answer is 94 cm.

Alternate Method

Given:

Side of rhombus (a) = 37 cm

Area of rhombus = 840 cm²

Formula used:

1. Area = 1/2 × d₁ × d₂

2. a² = (d₁/2)² + (d₂/2)² ⇒ 4a² = d₁² + d₂²

3. (d₁ + d₂)² = d₁² + d₂² + 2d₁d₂

⇒ Area = 1/2 × d₁ × d₂ = 840 ⇒ d₁ × d₂ = 1680 ⇒ 2 × d₁ × d₂ = 3360 ⇒ d₁² + d₂² = 4a² = 4 × (37)² ⇒ d₁² + d₂² = 4 × 1369 = 5476 ⇒ (d₁ + d₂)² = (d₁² + d₂²) + 2d₁d₂ ⇒ (d₁ + d₂)² = 5476 + 3360 = 8836 ⇒ d₁ + d₂ = √8836 ⇒ d₁ + d₂ = 94 cm

∴ The correct answer is 94 cm.

Additional Information

Properties of Rhombus

All sides are equal, and diagonals bisect each other at right angles (90°).

Area and Perimeter

Area = 1/2 × d₁ × d₂ and Perimeter = 4 × side.

Diagonal Relation

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

Side Formula

Side (a) = 1/2 × √(d₁² + d₂²).

CONCEPT:

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

EXPLANATION:

• The distances between molecules in solids are very small, i.e., solids are denser - as compared to liquids and gases.
• Because they are so close, they can collide very quickly, i.e. it takes less time for a molecule of the solid to 'bump' into its neighbor.
• Solids are packed together tighter than liquids and gases, hence sound travels fastest in solids. So option 1 is correct.

• No reaction will take place when the copper metal is dipped in the solution of zinc sulphate because Zinc is more reactive than copper, copper will not be able to displace the Zinc from Zinc sulphate.
• On the other hand, if Zinc metal is dipped in the Copper sulphate solution the reaction will take place because zinc is more reactive than copper and it will displace the copper from copper sulphate solution to form Copper and Zinc sulphate.

Zn(s) + CuSO4(aq) -> Cu(s) + ZnSO4 (aq).

Here, every letter is assigned with their positional value as per the English alphabetical order. Except “X22”, since positional value of X ⇒ 24

Hence, “X22” is the odd one.

Shortcut Trick

Average Speed = Total Distance ÷ Total Time

Total distance covered = 144 m

Total time taken = 1 minute = 60 seconds

Average speed = 144 ÷ 60 = 2.4 ms⁻¹

∴ The correct answer is 2.4 ms⁻¹.

Alternate Method

Given:

Length of pool = 72 m

Total distance (one end to the other and back) = 72 + 72 = 144 m

Time taken = 1 minute

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Total Distance = 144 m

⇒ Total Time = 1 × 60 seconds = 60 s

⇒ Average Speed = 144 ÷ 60

⇒ Average Speed = 2.4 ms⁻¹

∴ The correct answer is 2.4 ms⁻¹.

Additional Information

Average Velocity

Average Velocity is defined as Total Displacement ÷ Total Time. In this case, since Ram returns to the starting point, the displacement is 0, making the average velocity 0 ms⁻¹.

Speed Conversion

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

Uniform Speed

If an object covers equal distances in equal intervals of time, it is said to be moving with uniform speed.

We know that every ‘book’ is made of ‘pages’ but not every ‘page’ is used in a ‘book’ and every book consists of ‘preface’. So the following venn diagram illustrate the given information.

Hence, “option figure 4” is the correct answer.

Key Points

• The Sunderbans, a 10,000-km area of wet and marshy land sprawled across Bangladesh and India, is among the world's richest mangrove forest reserves and is the home of the Royal Bengal Tiger
• The Royal Bengal tiger is the tiger subspecies which is the highest in number.
• It is the national animal of both India and Bangladesh.
• Sundarbans is the largest single block of tidal halophytic mangrove forest in the world.
• It is a natural region in southern Bangladesh and the extreme southern part of the Indian state of West Bengal in the vast river delta on the Bay of Bengal.

Shortcut Trick

Substitute standard values: cot 30° = √3 and sin 45° = 1/√2.

Expression = [ √3 / (1 + 1/√2) ] + [ (1 + 1/√2) / √3 ]

Let x = √3 and y = (1 + 1/√2) = (√2 + 1)/√2. Result is (x² + y²) / xy.

Result = [ 3 + (3 + 2√2)/2 ] / [ √3 × (√2 + 1)/√2 ] = (9 + 2√2) / (√6 + √3). Rationalize to find the final match.

∴ The correct answer is (14√3 − 5√6)/6.

Alternate Method

Given: cot 30° / (1 + sin 45°) + (1 + sin 45°) / cot 30°

Formula Used: cot 30° = √3; sin 45° = 1/√2

⇒ Let A = √3 and B = 1 + 1/√2 = (√2 + 1)/√2

⇒ Expression = (A/B) + (B/A) = (A² + B²) / (AB)

⇒ A² = 3

⇒ B² = [(√2 + 1)/√2]² = (2 + 1 + 2√2) / 2 = (3 + 2√2) / 2

⇒ Numerator = 3 + (3 + 2√2)/2 = (6 + 3 + 2√2)/2 = (9 + 2√2)/2

⇒ Denominator = √3 × [(√2 + 1)/√2] = (√6 + √3)/√2

⇒ Value = [(9 + 2√2)/2] ÷ [(√6 + √3)/√2] = (9 + 2√2) / [√2(√6 + √3)] = (9 + 2√2) / (2√3 + √6)

⇒ Rationalizing: [(9 + 2√2)(2√3 − √6)] / [(2√3)² − (√6)²]

⇒ [18√3 − 9√6 + 4√6 − 2√12] / (12 − 6) = [18√3 − 5√6 − 4√3] / 6

⇒ (14√3 − 5√6) / 6

∴ The correct answer is (14√3 − 5√6)/6.

Additional Information

Trigonometric Ratios of Standard Angles

Standard values like sin 45° = 1/√2, cos 30° = √3/2, and tan 60° = √3 are essential for solving trigonometric equations quickly.

Rationalization of Denominators

To simplify fractions with surds, multiply the numerator and denominator by the conjugate of the denominator (a − √b for a + √b).

• The bodies which have its own source of energy to emit light are called luminous bodies. Example: Stars, burning candle, sun, etc.
• Non Luminous objects: The bodies which are not able to emit light but are visible only when they reflect light produced by the luminous objects are called non-luminous bodies. Example: earth, blackboard, moon.
• Translucent objects: The objects which allow the light to pass from them partially are known as Translucent objects.Example: Thin sheet of plastic, Butter paper, etc.
• Transparent objects: The objects which allow the light to pass from them Completely are known as Transparent objects. Example: Air, Water, Glass, etc

Form the given information we can draw a diagram as follows,

Clearly, Viki is in North-West direction with respect to the initial position.

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

The pattern followed here is as follows,

Hence, “150” is the correct answer.

• Work is done if there is any change in Energy.
• Energy is measured in the same unit as work because energy is defined via work (i.e. the capacity of a physical system to do work), the SI unit for energy is the same as the unit of work Joule (J).
• The relation between the kinetic energy of an object and work done is called “Work-Energy Theorem”.

W = 𝝙 K.E

Here, W is the work done in joules (J)

ΔK is the change in kinetic energy of the object.

Shortcut Trick The difference in ratio parts between R and S is 9 − 7 = 2 units. The actual difference given in the question is 7 years. ∴ 2 units = 7 years ⇒ 1 unit = 3.5 years. S's age = 7 units = 7 × 3.5 = 24.5 years. ∴ The correct answer is 24.5 years.

Alternate Method Given: Ratio of S and R's ages = 7 : 9 Difference between their ages = 7 years

Calculations: ⇒ Let the age of S be 7x and the age of R be 9x. ⇒ According to the question, R − S = 7 ⇒ 9x − 7x = 7 ⇒ 2x = 7 ⇒ x = 7 ÷ 2 = 3.5 ⇒ Age of S = 7x = 7 × 3.5 ⇒ Age of S = 24.5 years. ∴ The correct answer is 24.5 years.

Additional Information Constant Age Difference The numerical difference between the ages of two individuals always remains constant, regardless of how many years pass. Ratio Scaling If the ratio of ages is a : b and the difference is D, then one ratio part is calculated as D ÷ (b − a), provided b > a. Future and Past Ratios If the present age is x, then the age after 'n' years is (x + n) and the age 'n' years ago was (x − n).

Using the BODMAS rule,

\(\left{ {40 - \left( {90 \div 5 × \overline {16 - 8} \div 2 \div 3} \right)} \right}\)

⇒ {40 - (90 ÷ 5 × 8 ÷ 2 ÷ 3)}

⇒ {40 - (90 × $1\over5$ × 8 × $1\over2$ × $1\over3$)}

⇒ {40 - 24}

⇒ 16

• Chlorine is a Halogen
• The Halogens are the elements belonging to Group 17 in the periodic table.
  

Shortcut Trick

Mode = 4 (Most frequent value: 4 appears 3 times).

Mean = Sum ÷ Count = 60 ÷ 10 = 6.

Median (Sorted: 2, 3, 4, 4, 4, 6, 7, 8, 10, 12) = (4 + 6) ÷ 2 = 5.

LCM(4, 6, 5) = 60.

∴ The correct answer is 60.

Alternate Method

Given Data: 7, 2, 10, 4, 3, 12, 8, 4, 6, 4

Total Observations (n): 10

⇒ Mean = (7 + 2 + 10 + 4 + 3 + 12 + 8 + 4 + 6 + 4) ÷ 10 = 60 ÷ 10 = 6.

⇒ Mode = Value with highest frequency. Since 4 occurs 3 times, Mode = 4.

⇒ Median = Average of (n/2)^th and (n/2 + 1)^th terms = (5^th + 6^th) ÷ 2.

⇒ Sorted Data: 2, 3, 4, 4, 4, 6, 7, 8, 10, 12.

⇒ Median = (4 + 6) ÷ 2 = 5.

⇒ LCM (4, 5, 6):

⇒ 4 = 2²

⇒ 5 = 5¹

⇒ 6 = 2 × 3

⇒ LCM = 2² × 3 × 5 = 60.

∴ The correct answer is 60.

Additional Information

Empirical Relationship

For a moderately skewed distribution, the relationship is: Mode = 3 × Median − 2 × Mean.

Mean of Grouped Data

The mean for grouped data is calculated using Σf_ix_i / Σf_i, where f is frequency and x is the class mark.

LCM Definition

The Least Common Multiple (LCM) is the smallest positive integer that is divisible by each of the given numbers.

• Project Sashakt was put forward by a panel led by PNB chairman Sunil Mehta to address the bad loans problem in India's banking sector.
• Bad loans of up to ₹50 crore will be managed at the bank level, with a deadline of 90 days.
• For bad loans of ₹50-500 crore, banks will enter an intercreditor agreement, authorizing the lead bank to implement a resolution plan in 180 days or refer the asset to NCLT.
• For loans above ₹500 crore, the panel recom­mended an independent AMC, supported by institutional funding through the AIF.

Using BODMAS rule,

⇒ 0.36 + 0.284 ÷ 0.4 × 0.8 - 0.038,

⇒ 0.36 + 0.71 × 0.8 - 0.038

⇒ 0.36 + 0.568 - 0.038

⇒ 0.89

Shortcut Trick

The series follows a consecutive addition pattern.

The differences between terms are: +3, +4, +5, ...

Next difference = +6

Next term = 38 + 6 = 44

∴ The correct answer is 44.

Alternate Method

Given series: 26, 29, 33, 38, ?

26

+3 →

29

+4 →

33

+5 →

38

+6 →

44

The logic is based on increasing constant difference.

⇒ 26 + 3 = 29

⇒ 29 + 4 = 33

⇒ 33 + 5 = 38

⇒ 38 + 6 = 44

∴ The correct answer is 44.

Additional Information

Arithmetic Progression (AP)

A sequence where the difference between consecutive terms is constant. In this case, the difference is increasing linearly (+1 each step).

Incremental Series

Commonly used in banking exams where the step-difference is constant (e.g., differences are 3, 4, 5, 6...).

Prime Number Series

Another common variation where the differences added are prime numbers (2, 3, 5, 7, 11...).

The correct answer is Arun Jaitley.

Key Points 

• Late Arun Jaitley was the first chairman of the Goods and Services Tax (GST) Council.
• Goods and Service Tax is a system of taxation which will merge many individually applied taxes into a single tax.
• GST is a comprehensive indirect tax on manufacture, sale, and consumption of goods and services throughout India to replace taxes levied by the central and state governments.
• The UP Assembly has unanimously passed the U.P. Goods and Service Tax Bill, 2017.
• Chief Minister Yogi Adityanath termed it a revolutionary move which is in the interest of both consumers and traders.

• At a given temperature, the resistance (R) of a conductor depends on its length (L), area of cross-section (A) and the material it is made of.
• If the length of the wire is doubled then the resistance of the wire will also double. Hence, the Current will decrease to one half.

Concept:

Force is defined as mass times acceleration. 

F = m x a

Whereas acceleration = rate of change of velocity

i.e a = (v - u) / t

where

F = Force

m = Mass of body

a = acceleration

v = Final velocity

u = Initial velocity

Calculation:

Given that,

v₁ = 5 m/s

v₂ = 17 m/s

time,t = 6 sec

From the above explanation we can see that 

F = m x a = m x (v -u)/t

= 100 x (17 - 5) / 6

 = 100 x 12/6

= 200 N

• Therefore, the magnitude of force exerted on the object is 200 N

⇒ 75 ÷ [35 - {63 - (79 - 54 ÷ 9 × 6)}]

⇒ 75 ÷ [35 - {63 - (79 - 6 × 6)}]

⇒ 75 ÷ [35 - {63 - (79 - 36)}]

⇒ 75 ÷ [35 - {63 - 43}]

⇒ 75 ÷ [35 - 20]

⇒ 75 ÷ 15

⇒ 5

According to the symbol and its meaning:

We can draw a family tree diagram from the given information as follows:

Clearly, Vimal and Nina are cousins, therefore Milan is aunt of Vimal.

Hence, “Aunt” is the correct answer.

Note:

As gender of Mikka is not given therefore milan can be his paternal aunt or maternal aunt and according to the given options, Aunt is the correct answer.

If Can't be determined would be there in options then we go with that.

The pattern followed here is as follows,

Here unit digit of positional value of the letter is coded for the the letter.

Similarly,

Hence, “6815” is the correct answer.

Here, positional value of opposite letters has been used to get the codes.

C = 24

EYE = 22 + 2 + 22 = 46

Similarly,

THE = 7 + 19 + 22 = 48

Hence, “48” is correct answer.

• Males have a single X and a single Y chromosome.
• Females can have only XX.
• Females will have defects related to the only X chromosome.
• Turner syndrome: Either X is missing or defected and XXX where extra is present. Males have a mix in XY present with excess Y added.

The least possible Venn diagram for the given statements is as follows,

Conclusions:

1. No cable is pen → True
2. All chair are cables → it’s possible but not definite, hence false.

Hence, Only conclusion 1 follows.

Shortcut Trick

Use the distance formula for change in speed: Distance = [S₁ × S₂ / (S₁ − S₂)] × ΔT

Let actual speed be S. Then: 120 = [S × (S − 3) / 3] × 2

⇒ 120 × 3 / 2 = S(S − 3) ⇒ 180 = S(S − 3)

Check options: If S = 15, then 15 × (15 − 3) = 15 × 12 = 180. Condition satisfied.

∴ The correct answer is 15 kmph.

Alternate Method

Given: Total distance = 120 km, Speed reduction = 3 km/h, Time increase = 2 hours.

Formula: Time = Distance ÷ Speed

⇒ [120 / (S − 3)] − [120 / S] = 2

⇒ 120 [ (S − (S − 3)) / (S(S − 3)) ] = 2

⇒ 120 [ 3 / (S² − 3S) ] = 2

⇒ 180 = S² − 3S

⇒ S² − 3S − 180 = 0

⇒ S² − 15S + 12S − 180 = 0

⇒ S(S − 15) + 12(S − 15) = 0

⇒ (S − 15)(S + 12) = 0

⇒ Since speed cannot be negative, S = 15.

∴ The correct answer is 15 kmph.

Additional Information

General Distance-Speed-Time Relation

For a constant distance, Speed is inversely proportional to Time (S ∝ 1/T). If speed becomes x/y of original, time becomes y/x of original.

Quadratic Shortcut for Speed

In equations like S(S − x) = K, look for two factors of K that differ by x. For 180, the factors are 15 and 12, where 15 − 12 = 3.

Shortcut Trick

Convert days to decimals or fractions: Brij = 7.2 days, Madhu = 10.8 days.

LCM of 72 and 108 is 216 → Total Work = 21.6 units.

Efficiency: Brij = 21.6 ÷ 7.2 = 3; Madhu = 21.6 ÷ 10.8 = 2.

Combined efficiency = 3 + 2 = 5 units/day.

Five-sixth of wall = 5/6 × 21.6 = 18 units.

Time taken = 18 ÷ 5 = 3.6 days.

∴ The correct answer is 3.6 days.

Alternate Method

Given:

Time taken by Brij (B) = 7.2 days

Time taken by Madhu (M) = 10.8 days

Formula Used:

Total Work = Efficiency × Time

Calculations:

⇒ Total combined efficiency of Brij and Madhu = 3 + 2 = 5 units/day

⇒ Work to be completed = 5/6 × Total Work

⇒ Work to be completed = 5/6 × 21.6 = 5 × 3.6 = 18 units

⇒ Time taken = Work ÷ Combined Efficiency

⇒ Time taken = 18 ÷ 5 = 3.6 days

∴ The correct answer is 3.6 days.

Additional Information

Total Work and Efficiency

Efficiency is inversely proportional to time. If a person takes 'x' days to complete a task, their efficiency is 1/x per day.

Combined Work Rule

If two people with efficiencies E1 and E2 work together, the time taken to complete work W is T = W ÷ (E1 + E2).

Fractional Work

To find time for a specific fraction of work 'f', use the formula: Time = (f × Total Work) ÷ Combined Efficiency.

We know that ‘rod’ is made of ‘metal’. Therefore ‘flute’ is related to ‘bamboo’.

Hence, “Bamboo” is the correct answer.

⇒ Tanvi’s share = 1 - {(1/12) + (3/4)} = 1 - (10/12) = 2/12 = 1/6

• The cells of the tissue Meristematic are isolated to form a different type of permanent tissues.
• Meristem is the tissue in the most plants containing undifferentiated cells found in zones of the plant where growth can take place.
• A group of cells which are similar in origin, similar in structure and similar in function are called Permanent tissue.
• Dividing capacity is the basis of classifying various plant tissues as meristematic tissue and permanent tissue.

There are three types of meristematic tissues-

• Apical meristem- these are located at the shoot tips and root tips.
• Intercalary meristem- located between permanent tissues, at the leaf base and nodes.
• Lateral meristem- located at the sides(edges).​

• International Women's Day is celebrated every year on 8 March.
• It is a global day celebrating the social, economic, cultural and political achievements of women.
• The day also marks a call to action for accelerating gender parity. International Women's Day is a collective day of global celebration and a call for gender parity.

⇒ Percentage change = {(12 - 10)/10} × 100 = 20%

∴ The percentage change is 20% higher

• Among the given elements, Mg is most electropositive. Metals are electropositive. Mg is followed by Aluminium.
• Caesium (Cs) is the most electropositive of the stable elements having atomic no 55.
• Atoms which tend to donate electrons are called Electropositive atoms, and the atom converts into a positive ion (M+) upon donating electrons.
• The general valency of electropositive elements is 1, 2, 3.
• The atoms which have 1, 2, 3 electrons in their valence shell will lose their electrons to attain a stable electronic configuration.
• Some examples of electropositive elements are Sodium, Magnesium, Aluminium, these 3 elements will lose electrons to attain the configuration of Noble gas Neon.
• The electronegativity of Aluminium is 1.61 in the Pauling scale and electronegativity of Magnesium is 1.31, also in the Pauling scale. Hence If electronegativity is large, then electro positivity is less . Hence Magnesium has higher electropositivity.

• In sexual reproduction each the parent contributes half of its genes.
• Each human cell contains 46 of chromosomes in 23 pairs. During reproduction, each parent contributes 23 chromosomes (1 from each pair), so that the resulting zygote has 46 chromosomes.
• Extras : -
• Chromosomes are of two types – Autosomes and Allosomes.
• Allosomes are sex determining chromosomes.
• Thus, each cell contains 22 pairs of Autosomes and 1 pair of sex chromosomes.
• Female Sex chromosome is XX type while male sex chromosome is XY types.
• Thus, it is the male chromosome which determines the sex of the child.

Shortcut Trick

Average Speed = Total Distance ÷ Total Time

Total distance covered = 190 m

Total time taken = 1 minute = 60 seconds

Average speed = 190 ÷ 60 ≈ 3.17 ms⁻¹

∴ The correct answer is 3.17 ms⁻¹.

Alternate Method

Given:

Length of the pool = 95 m

Total distance covered (D) = 190 m

Total time taken (T) = 1 minute = 60 seconds

Formula Used:

Average Speed = Total Distance Covered / Total Time Taken

Calculations:

⇒ Average Speed = 190 m ÷ 60 s

⇒ Average Speed = 19 ÷ 6 ms⁻¹

⇒ Average Speed = 3.1666... ms⁻¹

⇒ Average Speed ≈ 3.17 ms⁻¹

∴ The correct answer is 3.17 ms⁻¹.

Additional Information

Average Velocity vs Average Speed

Average Velocity = Total Displacement ÷ Total Time. In this case, since Ram returns to the starting point, displacement is 0, so average velocity is 0 ms⁻¹.

Unit Conversion

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

Uniform Motion

If an object covers equal distances in equal intervals of time, it is said to be in uniform motion, where speed remains constant.

The name ‘Bharata’ is used as a designation for the country in our constitution referencing the ancient mythological emperor, Bharata, whose story is told, in part, in the Indian epic Mahabharata.

• Indian Mythology says he was the son of King Dushyanta and Shakuntala.
• The above excerpt has been taken from Class 12 English CBSE Paper.
• According to the writings known as the Puranas, Bharata conquered the whole sub-continent of India and ruled the land in peace and harmony.
• The land was, therefore, known as Bharatavarsha.
• Hominid activity in the Indian sub-continent stretches back over 250,000 years and it is, therefore, one of the oldest inhabited regions on the planet.

$\frac{{3 - 0.2}}{{0.1 \times \left( {3 + 0.2} \right)}} = \frac{{3 - 0.2}}{{0.1 \times 3.2}} = \frac{{2.8}}{{0.32}} = 8.75$

Shortcut Trick

Vendor-2 bottles = 80% of 600 = 480 bottles.

Returned quantity = 25% of 480 = 120 bottles.

Refund amount = 120 bottles × ₹25/bottle = ₹3,000.

∴ The correct answer is ₹3,000.

Alternate Method

Given:

Total bottles procured = 600

Cost per bottle = ₹25

Lot from Vendor-2 = 80% of 600

⇒ Number of bottles from Vendor-2 = 600 × (80/100) = 480

Percentage of lot returned to Vendor-2 = 25%

⇒ Number of bottles returned = 480 × (25/100)

⇒ Number of bottles returned = 120

Refund amount = Number of returned bottles × Cost per bottle

⇒ Refund amount = 120 × 25

⇒ Refund amount = ₹3,000

∴ The correct answer is ₹3,000.

Additional Information

Percentage Calculation

To find the percentage of a quantity, use: (Value ÷ Total) × 100. Here, 25% is equivalent to 1/4 of the total.

Unitary Method

Cost of multiple items is calculated by multiplying the unit cost by the total number of units: Total Cost = Rate × Quantity.

Successive Percentage Application

When multiple percentages are applied, the final value can be found by multiplying the initial amount by each fraction: Final = Total × %₁ × %₂.

The pattern followed here is as follows,

Here letters are assigned with their positional as per the English alphabetical order.

Similarly,

Hence, “7189144” is the correct answer.

• The elements having atomic numbers 11 to 18 are placed in the 3rd period of the periodic table
• These elements Include Na, Mg, Al, Si, P, S, Cl, and Ar.

Shortcut Trick

Efficiency ratio of Expert (E) to Trainee (T): 24E = 40T ⇒ 3E = 5T.

Total work in trainee units = (9 experts + 25 trainees) → 9 × (5/3) + 25 = 15 + 25 = 40 trainees.

Required work force = 12 experts + x trainees = 40 trainees.

12 × (5/3) + x = 40 ⇒ 20 + x = 40 ⇒ x = 20 trainees.

∴ The correct answer is 20 trainees.

Alternate Method

Given: 24 experts = 40 trainees, Initial group = 9 experts + 25 trainees, Target group = 12 experts + x trainees.

Formula Used: Total Work = Efficiency × Time (Since time is constant, we equate efficiencies).

⇒ Efficiency of Expert (E) = 5 units/day, Efficiency of Trainee (T) = 3 units/day.

⇒ Total Work = (9 × E + 25 × T) = (9 × 5 + 25 × 3) = 45 + 75 = 120 units.

⇒ Work done by 12 experts and x trainees = (12 × 5 + x × 3) = 120.

⇒ 60 + 3x = 120

⇒ 3x = 60

⇒ x = 20.

∴ The correct answer is 20 trainees.

Additional Information

Man-Days Formula

Used when variables change: (M₁×D₁×H₁)/W₁ = (M₂×D₂×H₂)/W₂.

Efficiency Ratio

Efficiency is inversely proportional to time. If A is twice as fast as B, the ratio of time taken is 1:2.

Work and Wages

Wages are distributed in the ratio of work done, which depends on efficiency × time spent.

Shortcut Trick

Given cot⁴θ + cot²θ = 2.2

Using the identity cosec²θ − cot²θ = 1 → cot²θ = cosec²θ − 1

Substitute in the equation: (cosec²θ − 1)² + (cosec²θ − 1) = 2.2

⇒ cosec⁴θ − 2cosec²θ + 1 + cosec²θ − 1 = 2.2

⇒ cosec⁴θ − cosec²θ = 2.2

∴ The correct answer is 2.2.

Alternate Method

Given: cot⁴θ + cot²θ = 2.2

Formula Used: cosec²θ = 1 + cot²θ or cot²θ = cosec²θ − 1

⇒ Take cot²θ common: cot²θ (cot²θ + 1) = 2.2

⇒ We know that 1 + cot²θ = cosec²θ

⇒ cot²θ × cosec²θ = 2.2

⇒ (cosec²θ − 1) × cosec²θ = 2.2

⇒ cosec⁴θ − cosec²θ = 2.2

∴ The correct answer is 2.2.

Additional Information

Trigonometric Identity 1

sin²θ + cos²θ = 1. This implies cos⁴θ − sin⁴θ = cos²θ − sin²θ.

Trigonometric Identity 2

sec²θ − tan²θ = 1. Similar to the given question, tan⁴θ + tan²θ = sec⁴θ − sec²θ.

Trigonometric Identity 3

cosec²θ − cot²θ = 1. This is the fundamental relation used to solve problems involving squares and fourth powers of cosec and cot.

• Nickel (Ni) is used as a catalyst in the hydrogenation of Vegetable oil.
• Hydrogenation gives us edible fats like Vanaspati.
• Catalyst: It is a substance which increases the rate of a chemical reaction without undergoing any change in its chemical properties.
• Dihydrogen (H2) is used during the synthesis of ammonia and manufacture of Vanaspati by hydrogenation of polyunsaturated oils.

Here, every letter is assigned with their positional value as per the English alphabetical order, except “T21”. Since, positional value of T ⇒ 20.

Hence, “T21” is the odd one.

Shortcut Trick

Net filling rate = (4/7 − 8/21) = (12/21 − 8/21) = 4/21 units per hour.

Cistern is two-thirds empty, so 2/3 of the total capacity needs to be filled.

Time required = (2/3) ÷ (4/21) = (2/3) × (21/4) = 7/2 hours.

7/2 hours = 3.5 hours = 3 hours 30 minutes.

∴ The correct answer is 3 hr 30 min.

Alternate Method

Given: Filling time of Pipe A = 7/4 hours, Draining time of Pipe B = 21/8 hours.

Formula Used: Total Work = LCM of numerators / HCF of denominators; Efficiency = Work ÷ Time.

⇒ Net efficiency of both pipes = 3 − 2 = 1 unit/hr.

⇒ Amount to be filled = 2/3 of Total Work = 2/3 × 21/4 = 7/2 units.

⇒ Time taken = 7/2 ÷ 1 = 3.5 hours.

⇒ 3.5 hours = 3 hours + 0.5 × 60 min = 3 hr 30 min.

∴ The correct answer is 3 hr 30 min.

Additional Information

Pipes and Cisterns Efficiency

Inlet pipes have positive efficiency (+), while outlet or leakage pipes have negative efficiency (−).

LCM of Fractions

LCM of (a/b, c/d) = LCM(a, c) ÷ HCF(b, d). This is used to find total capacity when times are in fractions.

Work and Time Relationship

Time = Total Work ÷ Net Efficiency. If the net efficiency is negative, the cistern will never be filled.

• The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilograms of carbon-12, Its symbol is “mol.''
• No. of particles (atoms, molecules, ions ) present in one mole = 6.022140857 × 10²³
• It is also known as Avogadro Constant

→ 65.38 g of Zn contains 1 mole of Zn

→ By the unitary method,

        65.38 g → 1 mole

                        1 g → 1 mole /65.38 g

         23.3 g → (1-mole x 23.3 g) /65.38 g

                                  = 0.3563 ≅ 0.35 moles

• Therefore, 23.3g of Zn will have 0.35 moles.

CONCEPT:

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

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

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

• Potential energy (PE): The energy possessed by a body by virtue of its position or configuration is called potential energy.

$PE = mgh$

Where, m = mass of the body, g = acceleration due to gravity, and h = height of the body

• Conservation of energy: According to the conservation of energy, energy can’t be created or destroyed, it can only transform from one form to another.
• The total energy of the system remains constant i.e. the sum of kinetic energy + potential energy remains constant.

EXPLANATION:

• In a free fall, the total energy (T.E.) is constant that is T.E = kinetic energy + potential energy.
• When the objects fall down, their potential energy converted into kinetic energy. So the potential energy decreases and the kinetic energy increases.
• Since the total energy is constant so that the increase in kinetic energy brings down the potential energy value and vice versa.

• A substance whose smell varies when it is mixed with an acidic or basic solution is known as an olfactory indicator.
• These types of substances are used to differentiate or check the acidic or basic solution.
• Clove is one of the examples of olfactory indicators as It loses its smell when added to the basic solution and retains its smell in the Acidic solution.

Hint

• Turmeric is not an Olfactory Indicator but a Natural Indicator. Turmeric recognise acid or base by the change in color not change in smell.

• The famous tourist attraction Victoria Memorial is located in Kolkata, West Bengal.
• Victoria Memorial in Kolkata was proposed by George Curzon.
• This, as its name suggests had been built in the memory of Queen Elizabeth who passed away in 1901.
• Prince of Wales, later King George V, laid the foundation stone on 4 January 1906 for this memorial which was subsequently opened to the public in 1921.

The correct answer is Ar.

• As the Atomic number of Argon is 18 it will complete its shells as 2, 8, 8
• That is the maximum number of electrons you can have in the valence, i.e outermost shell is 8.
• This is due to the filling of electrons under the Aufbau principle or rule, also known as the diagonal rule.

The electron configuration of Ar:

Shortcut Trick

Each term in the series is obtained by subtracting 3 from the previous term.

Common difference = 59964 − 59967 = −3.

Next term = 59958 − 3 = 59955.

∴ The correct answer is 59955.

Alternate Method

Given series: 59967, 59964, 59961, 59958, ?

This is an Arithmetic Progression (AP) where the common difference is constant.

59967

−3 →

59964

−3 →

59961

−3 →

59958

−3 →

59955

Calculations:

⇒ 1^st term = 59967

⇒ 2^nd term = 59967 − 3 = 59964

⇒ 3^rd term = 59964 − 3 = 59961

⇒ 4^th term = 59961 − 3 = 59958

⇒ 5^th term = 59958 − 3 = 59955

∴ The correct answer is 59955.

Additional Information

Arithmetic Series

A sequence where the difference between consecutive terms is constant is called an AP. The n^th term is a_n = a + (n − 1)d.

Common Difference

The constant value (d) can be positive (increasing series) or negative (decreasing series). Here, d = −3.

Identification Tip

Always check the difference between the first two terms and verify if it remains consistent throughout the series.

There is not enough information in the given statement to conclude about the driving habits of lazy people.

Therefore, conclusion I does not follow.

A cautious driver is a careful driver who surveys all possible consequences of rash driving and avoids unnecessary risks while driving, thereby preventing accidents.

Therefore, conclusion II follows from the given statement.

Hence, 'only conclusion II follows' is the correct answer.

We can count the rectangles in the given figure as follows,

Hence, there are “14” rectangles in the given figure.

$\frac{{\frac{4}{9}}}{{12}} = \frac{4}{{9 \times 12}} = \frac{1}{{27}}$

The pattern followed here is as follows,

Here every element is shifted to the next position in the series in the succeeding figure.

Similarly,

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

• The Sharqi Kings built the Atala Mosque in Jaunpur, Uttar Pradesh in the 14th century.
• The jaunpur sultanate was the independent kingdom which was ruled by the Sharqi Dynasty.
• The Khwajah-i-Jahan Malik Sarwar, the first ruler of the Sharqi dynasty

Total no. of years from 2018 to 2021 = 3 years

No. of leap years between them = 2020 = 1 years

No of odd days for leap year = 1 × 2 = 2 odd days

Ordinary years = 2 odd days

Total no. of odd days = 4 odd days

No. of days in a week 7.

If we divide 4 by 7 we get reminder of 4.

So, 4 odd days and counting from Thursday.

Hence the day fall on 29th of November 2021 will be Monday.

• Indian skipper Mithali Raj secured 2^nd position in the ICC One Day International Cricket rankings list released in 2017.
• She also became the first player in the history of women’s ODI cricket to have crossed 6000 career runs.
• Mithali reached the milestone in India’s ICC Women’s World Cup 2017 match against Australia.
• She is now the all-time highest run-scorer in women’s cricket, surpassing the record previously held by England’s Charlotte Edwards.
• Edwards scored 5992 runs in 191 matches at an average of 38.16 including nine centuries and 46 half-centuries.
• On the other hand, Mithali has crossed 6000 runs in 182 ODIs. The Indian captain has a total of five centuries and 49 half-centuries to her name.

• Malavath Poorna became the youngest girl in the world to conquer Mount Everest and Mount Elbrus.
• Bachendri Pal was the first Indian woman to climb Mt. Everest in 1984.
• Arunima Sinha had earlier conquered the highest peaks in five continents, becoming the first female Divyang to achieve the feat.
• Krushnaa Patil Became the youngest Indian woman to successfully ascent Mount Everest, earth's highest mountain.
• Mount Everest (8848 m) is the highest peak in the world.
• Mount Elbrus (5642 m) is the highest peak in Europe.

• Black Revolution is related to the manufacturing of Petroleum which is essentially black in colour.
  

Extra Information :

The pattern followed here as follows,

Hence, “18R” is the correct answer.

Shortcut Trick

Total flour = 9000 g (since 1 kg = 1000 g)

Flour for cakes = 20% of 9000

Flour for cakes = 9000 × 0.2 = 1800 g

∴ The correct answer is 1800 g.

Alternate Method

Given:

Total all-purpose flour used = 9 kg

Percentage used for cakes = 20%

Formula Used:

Quantity = Total Value × Percentage / 100

Conversion: 1 kg = 1000 g

⇒ Total flour in grams = 9 × 1000 = 9000 g

⇒ Quantity for cakes = 9000 × (20/100)

⇒ Quantity for cakes = 90 × 20

⇒ Quantity for cakes = 1800 g

∴ The correct answer is 1800 g.

Additional Information

Unit Conversion

To convert kilograms (kg) to grams (g), multiply the value by 1000. Conversely, divide by 1000 to convert g to kg.

Percentage Basics

x% of a quantity y is calculated as (x ÷ 100) × y. In this case, 20% is equivalent to the fraction 1/5.

Percentage to Fraction Conversion

Common conversions include 20% = 1/5, 25% = 1/4, 50% = 1/2, and 75% = 3/4.

Shortcut Trick

To find the HCF of algebraic terms, take the HCF of numerical coefficients and the lowest power of each common variable.

HCF of (6, 8, 12) = 2.

Lowest powers of variables: x¹, y², and z¹.

HCF = 2 × x × y² × z = 2xy²z.

∴ The correct answer is 2xy²z.

Alternate Method

Given: Three algebraic expressions 6xy²z, 8x²y³z², and 12x³y³z³.

Formula Used: HCF = Product of common factors with lowest exponents.

⇒ First term: 6xy²z = 2 × 3 × x × y² × z

⇒ Second term: 8x²y³z² = 2³ × x² × y³ × z²

⇒ Third term: 12x³y³z³ = 2² × 3 × x³ × y³ × z³

⇒ Common Numerical Factor: HCF(6, 8, 12) = 2

⇒ Common Variable Factors: x^min(1,2,3) = x¹, y^min(2,3,3) = y², z^min(1,2,3) = z¹

⇒ Required HCF: 2 × x × y² × z = 2xy²z

∴ The correct answer is 2xy²z.

Additional Information

LCM of Algebraic Terms

To find the Least Common Multiple (LCM), take the LCM of numerical coefficients and the highest power of all variables present.

HCF and LCM Relation

For two numbers A and B, the product of the numbers equals the product of their HCF and LCM: A × B = HCF × LCM.

Fraction HCF Rule

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

• Argument I states two benefits of using solar energy to reduce electricity requirements.

1. Saving resources
2. Promoting environmental compatibility.

• Therefore, argument I is strong.
• Argument II states that solar panels are expensive and people would require subsidies to make use of solar energy. This implies that using solar energy is an expensive measure and thus weakens argument II.
• Therefore, argument II is not strong.

Hence, "only argument I is strong" is the correct answer.