RRB Group D Previous Year Paper (Held on: 29 Sept 2022 Shift 1)

Shortcut Trick For any roots α and β, the quadratic equation is x2 − (Sum)x + (Product) = 0. Sum of roots = 2 + (−3) = −1 Product of roots = 2 × (−3) = −6 Equation ⇒ x2 − (−1)x + (−6) = x2 + x − 6 = 0. ∴ The correct answer is x2 + x − 6 = 0. Alternate Method Given: The roots of the required quadratic equation are 2 and −3. Formula Used: If α and β are the roots, then the equation is x2 − (α + β)x + αβ = 0 Calculations: ⇒ Let α = 2 and β = −3 ⇒ Sum of roots (α + β) = 2 + (−3) = −1 ⇒ Product of roots (αβ) = 2 × (−3) = −6 ⇒ Substituting these values into the formula: ⇒ x2 − (−1)x + (−6) = 0 ⇒ x2 + x − 6 = 0 ∴ The correct answer is x2 + x − 6 = 0. Additional Information General Form of Quadratic Equation A quadratic equation is typically expressed as ax2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. Nature of Roots The discriminant D = b2 − 4ac determines the nature: D > 0 (real and distinct), D = 0 (real and equal), and D < 0 (imaginary). Vieta's Formulas For the equation ax2 + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a.

Given:

'Peaches were sweet' is written as 'go la ba'

'Sour grapes and sweet apples' is written as 'bimb ko da go sa'

The code for 'Sweet' is 'go'.

Hence, the correct answer is "Option 1".

Shortcut Trick

Since Area is constant, Length and Breadth are inversely proportional.

Length Ratio → 20 : 25 = 4 : 5

Breadth Ratio → 5 : 4

Original breadth (5 units) = 8 cm ⇒ 1 unit = 1.6 cm

New breadth (4 units) = 4 × 1.6 = 6.4 cm

∴ The correct answer is 6.4 cm.

Alternate Method

Given: Original Length (L₁) = 20 cm, Original Breadth (B₁) = 8 cm, New Length (L₂) = 25 cm.

Formula Used: Area of Rectangle = Length × Breadth

⇒ Original Area = L₁ × B₁ = 20 × 8 = 160 cm²

⇒ Since Area remains same, New Area = 160 cm²

⇒ L₂ × B₂ = 160

⇒ 25 × B₂ = 160

⇒ B₂ = 160 ÷ 25

⇒ B₂ = 6.4 cm

∴ The correct answer is 6.4 cm.

Additional Information

Perimeter of Rectangle

The total boundary length is given by P = 2 × (Length + Breadth).

Diagonal of Rectangle

The distance between opposite corners is found using Pythagoras theorem: d = √(L² + B²).

Area and Percentage Change

If Length increases by x% and Breadth decreases by y%, net change in area = [x − y − (xy/100)]%.

The correct answer is 1784.

Key Points

• ​Sir William Jones (an Anglo philologist) created the Asiatic Society to promote oriental research and studies in India.
• The Asiatic Society publishes books in different series, viz.,
• Bibliotheca Indica,
• Monograph,
• Seminar & Public Lecture,
• Catalogues
• Bibliographical Works besides some books under Miscellaneous publications.
• Moreover, it publishes periodicals, i.e. a quarterly Journal of the Asiatic Society and Monthly Bulletin of the Asiatic Society.
• James Prinsep bought the first issue of the journal, The Journal of the Asiatic Society of Bengal.

Shortcut Trick

Rate 5% = 1/20 → Ratio is 20 : 21.

For 2 years, Principal : Installment ratio:

Year 1: 20 × 21 : 21 × 21 = 420 : 441

Year 2: 20² : 21² = 400 : 441

Total Principal = 420 + 400 = 820 units.

820 units = ₹28,700 ⇒ 1 unit = ₹35.

Installment = 441 units × 35 = ₹15,435.

∴ The correct answer is ₹15,435.

Alternate Method

Given:

Debt (P) = ₹28,700

Time (n) = 2 years

Rate (r) = 5% p.a.

Formula Used:

P = x / (1 + r/100) + x / (1 + r/100)²

Where x = Equal Annual Installment.

Calculations:

⇒ 28,700 = x / (1 + 5/100) + x / (1 + 5/100)²

⇒ 28,700 = x / (21/20) + x / (21/20)²

⇒ 28,700 = 20x/21 + 400x/441

⇒ 28,700 = (420x + 400x) / 441

⇒ 28,700 = 820x / 441

⇒ x = (28,700 × 441) / 820

⇒ x = 35 × 441

⇒ x = 15,435

∴ The correct answer is ₹15,435.

Additional Information

CI Installment General Formula

For n installments, P = [x / k¹] + [x / k²] + ... + [x / kⁿ], where k = (1 + r/100).

SI Installment Formula

Installment (x) = [100 × Due Debt] / [100t + rt(t−1)/2], used for simple interest debts.

Present Value Concept

Each installment represents the present value of the debt component discounted at the given interest rate.

The correct answer is Jawaharlal Nehru.

Key Points

• The third five-year plan had set a target of a 5.6 percent growth rate but it could only achieve a 2.5 percent growth.
• The third five-year plan was incorporated in the period from 1961 to 1966 which saw two wars and a draught.
• The wars were fought between India and China in 1962 and between India and Pakistan in 1965.
• India was hit by drought in 1965 and 1966 across different parts of the country.
• The lower growth rate during that period can be attributed to these natural and man-made calamities.
• The main target of this plan was to make the economy independent. The stress was laid on agriculture and the improvement in the production of wheat.
• However, after the wars, India recognized the need to focus on the development of its defense sector.
• After this combination of events, India had to face Inflation, which is a common term used for the rise in prices of items of common use.
• The prime minister of India during that period was Jawaharlal Nehru.
• This plan is also called Gadgil Yojna, after the Deputy Chairman of Planning Commission D.R. Gadgil.
• Basic information about planning commission and 5- year plans:
• Planning commission founded: 1950.
• Planning Commission head: Prime Minister
• First five-year plan launched: 1951
• A total number of 5- year plans: 12.
• Last five-year plan: 2012 to 2017 (Under PM Manmohan Singh).
• Planning Commission dissolved: 2014 (By PM Narendra Modi).

Given:

Statement:

Eating foods which have been heated in plastic containers causes cancer, therefore it should be avoided.

Assumptions:

(I) Only storing food in plastic containers is not harmful for health - False (Nothing mention about the storing food in the statement, so it does not followed).

(II) Non-plastic containers which can be used to heat food are available - True (There is clearly mention plastic containers should be avoided, it gives the other containers will be available in the market to store food).

So, Only assumption II is implicit.

Hence, the correct answer is "Option 1".

Shortcut Trick

Let the total work be 60 units (LCM of 12, 10, 15).

Efficiencies: Eduardo (E) = 5, Abraham (A) = 6, Xavier (X) = 4.

E worked for 2 days (5 × 2 = 10 units). Remaining = 50 units.

Trick: Total days (D) = (Remaining Work + Work of person leaving before end) ÷ (Combined Efficiency of remaining persons).

D = (50 + 6 × 3) ÷ (6 + 4) = 68 ÷ 10 = 6.8 days.

∴ The correct answer is 6.8 days.

Alternate Method

Given: Time taken by Eduardo = 12 days, Abraham = 10 days, Xavier = 15 days.

Let the total work be completed in x days.

⇒ Work done by Eduardo = 5 × 2 = 10 units (left after 2 days).

⇒ Work done by Abraham = 6 × (x − 3) units (left 3 days before end).

⇒ Work done by Xavier = 4 × x units (worked till the end).

⇒ 10 + 6(x − 3) + 4x = 60

⇒ 10 + 6x − 18 + 4x = 60

⇒ 10x − 8 = 60

⇒ 10x = 68

⇒ x = 6.8 days

∴ The correct answer is 6.8 days.

Additional Information

Leaving from Beginning vs End

When a person leaves after n days from the start, subtract their work. When a person leaves n days before completion, add their potential work to the total.

Efficiency Formula

Efficiency = Total Work ÷ Time taken. Efficiency is inversely proportional to time taken to complete a task.

The correct answer is Classical Music.

Key Points

• Purandaradasa was a renowned 16th-century Carnatic music composer and saint.
• He is revered as the "Pitamaha" (grandfather) of Carnatic music for his significant contributions to its development and systematization.
• The Purandaradasa Aradhana is an annual festival held in his honor, primarily in Hampi, Karnataka, where he lived and attained Samadhi.
• The festival is observed on Pushya Bahula Amavasya day, the new moon day in the Pushya month of the Indian lunar calendar, which usually falls in February or March.
• During the Aradhana, numerous Carnatic music concerts are held, featuring performances by renowned musicians.
• These concerts showcase the rich heritage of Carnatic music and pay homage to Purandaradasa's invaluable contributions to this art form.
• The festival attracts a large number of music enthusiasts and devotees from across India and beyond, making it a significant cultural event in Karnataka.
• The Purandaradasa Aradhana serves as a platform for the appreciation and propagation of Carnatic music, keeping alive the legacy of this legendary composer and saint.

The correct answer is light will disperse.

Key Points

• Dispersion of light:

• The white light is formed by seven visible colours called VIBGYOR. (Violet, Indigo, Blue, Green, Yellow, Orange, Red).

• Dispersion of light is the phenomenon of splitting of a beam of white light into its constituent colours when passing through a prism.

• The band of seven colours so obtained is called the (visible) spectrum.

• Dispersion of white light occurs because the colours of white light travel at different speeds through the glass prism.

• All colours have different wavelengths.

• Light bends when its travels from one medium to another. So, it bends when it travels from air to the prism.

• The light with the least wavelength bends the most. Red bends the least as it has a maximum wavelength and violet bends the most.

• The white light is formed by seven visible colours called VIBGYOR. Among these, the light bent the most after Violet is Indigo following the sequence VIBGYOR.

• So, the light which will bend most is Violet. and least is Red.

The correct answer is 14 - digit.

Key Points

• Ayushman Bharat Health Account (ABHA): A health savings account that allows individuals to store and access their health records digitally, issued by the National Health Authority (NHA) under the Ayushman Bharat Pradhan Mantri Jan Arogya Yojana (AB-PMJAY).
• ABHA ID: A 14-digit unique identification number provided under the Ayushman Bharat Health Account, allowing individuals to access healthcare services and store medical records.
• Ayushman Bharat Pradhan Mantri Jan Arogya Yojana (AB-PMJAY): A government health insurance scheme aimed at providing affordable healthcare to economically weaker sections of society.
• National Health Authority (NHA): The apex body responsible for implementing India's public health insurance scheme, including Ayushman Bharat.

Given: Eight persons are sitting around a circular table facing the centre.

1. Z is second to the left of X.

2) U sits third to the left of X.

3. S is an immediate neighbour of both U and T.

4. Z is an immediate neighbour of both U and V.

5. W is an immediate neighbour of T.

6. Y sits second to the right of V.

So, 'X' sits third to the left of T.

Hence, the correct answer is "Option 4".

Shortcut Trick

The average of a set of numbers in an Arithmetic Progression (AP) with an odd number of terms is always the middle term.

The first 7 multiples of 3 are: 3, 6, 9, 12, 15, 18, 21.

In a set of 7 terms, the middle term is the 4^th term.

4^th multiple of 3 = 3 × 4 = 12.

∴ The correct answer is 12.

Alternate Method

Given: We need to find the average of the first 7 multiples of 3.

Formula Used: Average of an Arithmetic Progression = (First term + Last term) ÷ 2

⇒ First term (a) = 3 × 1 = 3

⇒ Last term (l) = 3 × 7 = 21

⇒ Total terms (n) = 7

⇒ Average = (3 + 21) ÷ 2

⇒ Average = 24 ÷ 2

⇒ Average = 12

∴ The correct answer is 12.

Additional Information

Average of First n Multiples of x

The formula to directly calculate the average of the first n multiples of a number x is [x × (n + 1)] ÷ 2.

Sum of First n Multiples

The sum of the first n multiples of x is x × [n(n + 1) ÷ 2]. For n = 7 and x = 3, Sum = 3 × [7 × 8 ÷ 2] = 3 × 28 = 84.

Middle Term in AP

If the number of terms n is odd, the average is the [(n + 1) ÷ 2]^th term. If n is even, the average is the mean of the (n ÷ 2)^th and [(n ÷ 2) + 1]^th terms.

The logic followed here is:

'SLEEK' is written as 'QICBI',

For, 'FROGS' is written as 'DOMDQ’,

Similarly, for 'HOPES':

So, 'HOPES' will be written as 'FLNBQ'.

Hence, the correct answer is "Option 3".

The correct answer is Some sort of movement, either growth-related or respiration.

Key Points

• Metabolism: Living organisms undergo continuous chemical reactions to maintain life, such as breaking down food for energy (respiration) and building new cells (growth).
• Growth and Development: Living things increase in size and complexity over time. This can involve physical changes, like getting taller, and internal changes, like developing specialized organs.
• Reproduction: Living organisms produce offspring, passing on their genetic information to the next generation. This ensures the continuation of the species.
• Response to Stimuli: Living things react to changes in their environment. For example, plants turn towards the sun, and animals move away from danger.
• Homeostasis: Living organisms maintain a stable internal environment despite external changes. This includes regulating temperature, fluid balance, and pH levels.
• Cellular Organization: All living things are composed of one or more cells, the basic units of life. Cells carry out the essential functions that keep an organism alive.
• Adaptation and Evolution: Living organisms can adapt to changes in their environment over time, allowing them to survive and reproduce. This process of adaptation drives the evolution of species.

The correct answer is (S - I) only.

Key Points

• The point in the center of the sphere from which the glass was sliced is known as the center of the curve and is denoted by the letter C in the illustration.
• This point is equidistant from all points on the reflecting face of the glass.
• The shaft illustration for the image conformation by a hollow glass when the size of an object and its image are the same is given above.
• Then, in the illustration, if we put the object in the center of the curve also the image will have the same size as that of the object.

Additional Information

• Mirror Formula:
• Mirror Formula is given by:-
  

$1/f=1/v+1/u$1/u

​where,

f = Focal length of the mirror.

v = Distance of image from the mirror.

u = Distance of the object from the mirror.

Shortcut Trick

Ratio of edges = 1 : 2 : 3. Let edges be 1x, 2x, 3x.

Volume = 1x × 2x × 3x = 6x³ = 1296 ⇒ x³ = 216 ⇒ x = 6.

Ratio of Surface Area = 2(1×2 + 2×3 + 3×1) = 2(2 + 6 + 3) = 22 units.

Surface Area = 22 × x² = 22 × 36 = 792 cm².

∴ The correct answer is 792 cm².

Alternate Method

Given: Ratio of length (l), breadth (b), and height (h) = 1 : 2 : 3. Volume = 1296 cm³.

Formula Used: Volume of cuboid = l × b × h; Total Surface Area = 2(lb + bh + hl).

⇒ Let the dimensions be x, 2x, and 3x.

⇒ Volume = x × 2x × 3x = 6x³

⇒ 1296 = 6x³

⇒ x³ = 216 ⇒ x = 6 cm

⇒ Dimensions: l = 18 cm, b = 12 cm, h = 6 cm

⇒ Surface Area = 2[(18 × 12) + (12 × 6) + (6 × 18)]

⇒ Surface Area = 2[216 + 72 + 108]

⇒ Surface Area = 2[396] = 792 cm²

∴ The correct answer is 792 cm².

Additional Information

Diagonal of a Cuboid

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

Lateral Surface Area

The area of the four walls of a room (cuboid) is 2h(l + b).

Cube Properties

When l = b = h = a, Volume = a³ and Total Surface Area = 6a².

Shortcut Trick

Dishonest dealer gain% = (Error ÷ (True Weight − Error)) × 100.

Let the actual weight be x gm. True weight = 1000 gm.

14 = ((1000 − x) ÷ x) × 100 ⇒ 14x = 100000 − 100x.

114x = 100000 ⇒ x = 100000 ÷ 114 ≈ 877.19 gm.

Rounding to the nearest whole number, we get 877 gm.

∴ The correct answer is 877 gm.

Alternate Method

Given: Rice sold at Cost Price, Profit% = 14%, Standard Weight = 1000 gm. Formula: Actual Weight = (100 × True Weight) ÷ (100 + Gain%).

⇒ Let the Cost Price of 1 gm be Re. 1. True CP of 1000 gm = Rs. 1000.

⇒ Since he sells at CP, Selling Price = Rs. 1000.

⇒ CP of actual weight = (SP × 100) ÷ (100 + Profit%).

⇒ CP of actual weight = (1000 × 100) ÷ 114.

⇒ Actual Weight = 100000 ÷ 114 = 877.1929... gm.

∴ The correct answer is 877 gm.

Additional Information

Dishonest Dealer Concept

When a shopkeeper claims to sell at Cost Price but uses less weight, the Profit% is calculated on the Actual weight given, not the True weight.

Weight-Ratio Relation

The ratio of True Weight to Actual Weight is equivalent to the ratio of Selling Price to Cost Price: (100 + P%) : 100.

The correct answer is Viharas.

Key Points

• Viharas:
• These were Buddhist monasteries, serving as dwelling places for monks and nuns.
• They provided living quarters, spaces for meditation and study, and often included shrines for worship.

Additional Information

• Chaityas:
• These were prayer halls or temples within a Buddhist monastery.
• They typically housed a stupa, a dome-shaped structure containing relics of the Buddha or other sacred objects, which served as a focal point for worship.
• Stupas:
• As mentioned above, stupas are dome-shaped structures that hold relics of the Buddha or other sacred figures.
• They are considered sacred sites for Buddhist pilgrimage and meditation.
• Grihas:
• While "Griha" generally refers to a house or dwelling in Sanskrit, it is not typically used specifically in the context of Buddhist monasteries.
• The terms "Vihara" and "Chaitya" are more commonly used to describe the different structures within a monastic complex.

Given: Six friends A, B, C, D, E and F.

1. C is taller than only two other friends.

__ > __ > __ > C > __ > __

2. E is shorter than only one friend.

__ > E > __ > C > __ > __

3. B is shorter than C but taller than A.

__ > E > __ > C > B > A

4. D is shorter than F.

F > E > D > C > B > A

So, 'A' is the shortest among all the friends.

Hence, the correct answer is "Option 4".

Statement:

Some teeth are brushes.

All brushes are pastes.

Some pastes are gels.

The least possible diagram for the given statements is as follows:

Conclusions:

(i) Some brushes are gels - False (Because No definite relation given between brushes and gels, so it can be possible only).

(ii) Some teeth are pastes - True (Those Teeth who are Brushes is definitely Pastes).

So, Only conclusion (II) follows.

Hence, the correct answer is "Option 3".

Shortcut Trick

For the equation x² + 8x + 15 = 0, find two factors of the constant 15 that add up to the middle coefficient 8.

The factors are 5 and 3 (since 5 + 3 = 8 and 5 × 3 = 15).

The roots are obtained by reversing the signs of these factors: −5 and −3.

Comparing the two roots, −5 is smaller than −3.

∴ The correct answer is x = −5.

Alternate Method

Given: The quadratic equation is x² + 8x + 15 = 0.

Method: Factorization by splitting the middle term.

⇒ x² + 5x + 3x + 15 = 0

⇒ x(x + 5) + 3(x + 5) = 0

⇒ (x + 3)(x + 5) = 0

⇒ Set each factor to zero: x + 3 = 0 or x + 5 = 0

⇒ x = −3 or x = −5

⇒ The two roots are −3 and −5. The smaller value is −5.

∴ The correct answer is x = −5.

Additional Information

Nature of Roots

For a quadratic equation ax² + bx + c = 0, the nature of roots is determined by the discriminant D = b² − 4ac. If D > 0, the roots are real and distinct.

Sum and Product of Roots

The sum of the roots is given by −b/a and the product of the roots is given by c/a.

Quadratic Formula

Roots can also be found using the formula x = [−b ± √(b² − 4ac)] / 2a.

The correct answer is seven.

Key Points

• The government further extended the validity of industrial licences to as much as seven years from three to encourage domestic manufacturing.
• “As a measure of ‘ease of doing business’, henceforth, two extensions of two years each in the initial validity of three years of (an) industrial licence shall be allowed up to seven years,” the department of industrial policy and promotion (DIPP) said in a notification.
• In July, DIPP had extended the validity of an industrial licence to three years from two, as part of measures to cut red tape.
• The BJP government is working to promote India as a manufacturing hub, with Prime Minister Narendra Modi launching the ‘Make In India’ drive last month. Manufacturing contracted by 0.7% in 2013-14, but recovered to 3.5% in the first quarter of the fiscal.

The correct answer is PV Sindhu.

Key Points

• Indian shuttler PV Sindhu clinched her maiden Women's Single title of the Singapore Open Badminton tournament on 17 July 2022.
• She defe in the final of the Singapore Open.
• Sindhu has won three titles in 2022 - the Swiss Open, Syed Modi India International, and now the Singapore Open.​

Additional Information

• The Singapore Open tournament:
• The Singapore Open is an annual badminton tournament held in Singapore.
• It is part of the BWF World Tour and is a Super 500 level event, which makes it one of the most prestigious badminton tournaments in the world.
• The tournament features events for men's and women's singles, doubles, and mixed doubles, and attracts top players from around the world.
• The Singapore Open has been held since 1987 and is organized by the Badminton Association of Singapore.
• The tournament offers significant prize money and world ranking points, making it an important event for professional badminton players.
• The Singapore Open is typically held in April each year and has been won by many of the greatest badminton players in history.

The correct answer is Kamet.

Key Points

• Kamet Peak is the highest point in the Zanskar range located at an altitude of 7756 meters.
• Zaskar Range also called Zanskar, group of mountains in the Himalayas, of northern India and the western Tibet Autonomous Region of China.
• They extend southeastward for some 640 km from the Karcha  River to the upper Karnali River.
• The most important passes are Shipki, Lipu Lekh, and Mana.
• Zaskar is drained by the Zaskar River which flows northward, joining the Indus River below Leh.

Additional Information 

• Dhaulagiri 
• Mount Dhaulagiri is located in the west-central Nepal.
• Mount Dhaulagiri, at 8,167 metres (26,795 feet) above sea level, is the seventh-highest mountain in the world and the tallest mountain that is entirely contained inside one nation's borders (Nepal).
• Around 40 miles (65 km) northwest of Annapurna, it is located on the western side of the vast Kali (Kali Gandak) River valley.
• The majority of the Himalayas, the highest mountain range in the world, are found in Nepal. The nation is home to eight of the fourteen eight-thousanders, either entirely or in part by way of a shared border with China or India.
• Mount Everest, the tallest mountain in the world, and 1,310 other peaks that rise beyond 6,000 metres are both found in Nepal.

The correct answer is he kept numerical count of the progeny.

Key Points

Mendel chose to study pea plants (Pisum sativum) for his experiments, and this choice proved to be highly advantageous. Pea plants exhibit several characteristics that made them ideal for genetic studies:

• Clearly defined traits: Pea plants display a variety of easily distinguishable traits, such as flower color (purple or white), seed shape (round or wrinkled), and plant height (tall or short). This clear-cut distinction allowed Mendel to accurately observe and categorize the inheritance patterns of these traits.
• Self-pollination and controlled cross-pollination: Pea plants can self-pollinate, meaning that pollen from the same plant can fertilize its own ovules. However, they can also be easily cross-pollinated by manually transferring pollen from one plant to another. This control over pollination allowed Mendel to precisely manipulate the breeding process and study the inheritance of specific traits.
• Short life cycle and high fecundity: Pea plants have a relatively short life cycle, allowing Mendel to conduct multiple generations of experiments within a reasonable timeframe. Additionally, they produce a large number of offspring, providing ample data for statistical analysis.

The correct answer is Fuse.

Key Points

• Fuse 
• A fuse is a short piece of metal, inserted in the series with the circuit, which melts when excessive current flows through it and thus breaks the circuit.
• The function of a fuse is to carry the normal current without overheating but when the current exceeds its normal value.
• It rapidly heats up to the melting point and disconnects the circuit protected by it.

Additional Information

• ​Electric heater
• The Element of an electric heater is made up of Nichrome.
• This is because Nichrome has very high melting point when compared to other elements.
• Hence Nichrome converts the Electrical energy into Heat energy.

Shortcut Trick

Total Work = LCM of 8, 18, and 12 = 72 units.

Combined Efficiency = (72 ÷ 8) + (72 ÷ 18) + (72 ÷ 12) = 9 + 4 + 6 = 19 units/day.

Time Required = Total Work ÷ Combined Efficiency = 72 ÷ 19 days.

∴ The correct answer is 72/19 days.

Alternate Method

Given:

Time taken by A = 8 days

Time taken by B = 18 days

Time taken by C = 12 days

Formula Used:

Efficiency = Total Work ÷ Time Taken

Calculations:

⇒ Total efficiency of A + B + C = 9 + 4 + 6 = 19

⇒ Total work to be completed = 72 units

⇒ Days required = Total Work ÷ Total Efficiency

⇒ Days required = 72 ÷ 19

∴ The correct answer is 72/19 days.

Additional Information

Combined Work Formula

For three people working together, if they take x, y, and z days respectively, the total time T is given by 1/T = 1/x + 1/y + 1/z.

Pipes & Cisterns

The same logic applies where inlet pipes have positive efficiency and outlet (leakage) pipes have negative efficiency.

Work & Wages

Wages are distributed in the ratio of the work done, which is equivalent to the ratio of efficiencies if everyone works for the same duration.

The correct answer is 60/11Ω, 11A.

Key Points 

• For resistors in parallel, 

the reciprocal of the total resistance (1/R_total) is equal to the sum of the reciprocals of the individual resistances.

• 1/R_total ¹ = 1/R1 + 1/R2 + 1/R3 1/R_total = 1/10 + 1/20 + 1/30 1/R_total = (6 + 3 + 2) / 60 1/R_total = 11/60 R_total = 60/11Ω

• In a parallel circuit, the voltage across each resistor is the same (220V in this case).

• Using Ohm's Law (V = I * R), we can find the current through the 20 Ω resistor:

I = V / R I = 220V / 20 Ω I = 11 A

The correct answer is CH4, C2H6, C3H8, C4H10.

Key Points

• Hydrocarbons
• Compounds made of carbon and hydrogen atoms only are called hydrocarbons.
• Saturated hydrocarbons:
• The hydrocarbons in which carbon atoms are singly bonded are called saturated hydrocarbons.
• Saturated hydrocarbons are also called alkanes or paraffin.
• The general formula of alkane– CnH2n+2.
• Unsaturated hydrocarbons:
• The hydrocarbons in which carbon atoms are either doubly or triply bonded are called unsaturated hydrocarbons.
• Doubly bonded (carbon atoms) hydrocarbons are called alkenes.
• The general formula of alkene is CnH2n.
• Triply-bonded carbon:
• Hydrocarbons containing at least one carbon-carbon triple bond between two carbon atoms are called alkynes.
• The general formula of alkynes is CnH2n-2.

Given: 

Left 106, 91, 131, 95, 144, 123, 88, 93, 127, 73 Right

Now, The numbers given below are arranged in descending order,

Here, the second number from the right end is 88.

And, the fifth number from the left end is 106.

then sum of the numbers is: 88 + 106 = 194.

Hence, the correct answer is "194".

The logic followed here is:

So, '35' will complete the series.

Hence, the correct answer is "35".

Given word: 'RIPOSTE'

Now, checking the pairs in both forward and backward directions:

The pairs in forward direction are: ST

The pairs in backward direction are: OP, OR, PR

So, Total four pairs are formed from the given word.

Hence, the correct answer is "Option 3".

Shortcut Trick

Directly expand the brackets: 2(2x − 3) = 4x − 6.

Simplify the second expression: 4 × (x²/2 − 3x + 4) = 2x² − 12x + 16.

Combine the resulting like terms: 2x² + (4x − 12x) + (−6 + 16) = 2x² − 8x + 10.

∴ The correct answer is 2x² − 8x + 10.

Alternate Method

Given Expression: 2(2x − 3) + 4((x²/2) − 3x + 4)

To simplify, we apply the Distributive Property (a(b + c) = ab + ac) to both parts of the expression:

⇒ [2 × 2x + 2 × (−3)] + [4 × (x²/2) + 4 × (−3x) + 4 × 4]

⇒ [4x − 6] + [2x² − 12x + 16]

Now, group the like terms (terms with the same power of x):

⇒ 2x² + (4x − 12x) + (−6 + 16)

⇒ 2x² − 8x + 10

∴ The correct answer is 2x² − 8x + 10.

Additional Information

BODMAS Rule

Always prioritize operations in the order of Brackets, Orders, Division/Multiplication, and Addition/Subtraction.

Distributive Property

The rule states that a × (b + c) = (a × b) + (a × c). This is essential for removing parentheses in algebraic expressions.

Combining Like Terms

Only terms with the exact same variable and exponent can be combined through addition or subtraction.

The correct answer is Opposite.

Key Points

• Fleming's Left-hand rule states that if we arrange our thumb, forefinger, and middle finger of the left - hand perpendicular (900) to each other, then the thumb points towards the direction of the force experienced by the conductor, the forefinger points towards the direction of magnetic field and the middle finger points towards the direction of electric current.

Additional Information

• When a current-carrying conductor is placed in an external magnetic field, the conductor experiences a force perpendicular to both the field and the current flow's direction.
• Application of Fleming's left-hand rule-
• Fleming's left-hand rule is used to find the direction of the force acting on the current-carrying conductor placed in a magnetic field.
• This rule is used for Electric motors.
• Fleming's right-hand rule states that if we arrange our thumb, forefinger, and middle finger of the right-hand perpendicular to each other, then the thumb points towards the direction of motion of the conductor relative to the magnetic field, the forefinger points towards the direction of magnetic field and the middle finger points towards the direction of the induced current.
• This rule is used for Electric Generators.

According to the given Venn diagram:

The shaded area shows the interior decorators are there who are NEITHER architects NOR dancers.

So, there are '150' interior decorators are there who are NEITHER architects NOR dancers.

Hence, the correct answer is "150".

The correct answer is Decrease in ozone levels in the upper layers of the atmosphere.

Key Points

Fossil fuels:

• Fossil fuels are obtained from dead remains of living organisms buried under the earth crust millions of years ago.
• Fossil fuels are combustible hydrocarbons formed millions of years ago from the dead decaying plants and animals buried under sediment.
• Over millions of years, these decaying remains of living organisms were covered by layers and layers of silt and buried deep underground.
• The pressure and heat at those depths transformed them into fossil fuels oil, natural gas and coal.

Thus we can conclude that Fossil fuels are obtained from dead remains of living organisms.

Shortcut Trick

Convert all terms to base 2 using the substitution y = 2^3x.

Term 1: 4^3x = (2²)^3x = (2^3x)² = y².

Term 2: 8^x+1 = 2^3(x+1) = 2^3x × 2³ = 8y.

Substitute these into 4^3x − 8^x+1 + 16 = 0 to get y² − 8y + 16 = 0.

∴ The correct answer is y² − 8y + 16 = 0.

Alternate Method

Given: Equation 4^3x − 8^x+1 + 16 = 0 and y = 2^3x.

Formula Used: Indices rules: (a^m)ⁿ = a^mn and a^m+n = a^m × aⁿ.

⇒ 4^3x − 8^x+1 + 16 = 0

⇒ (2²)^3x − 8^x × 8¹ + 16 = 0

⇒ 2^{2 × 3x} − (2³)^x × 8 + 16 = 0

⇒ (2^3x)² − 2^3x × 8 + 16 = 0

⇒ Now, substitute y = 2^3x into the equation:

⇒ y² − y × 8 + 16 = 0

⇒ y² − 8y + 16 = 0

∴ The correct answer is y² − 8y + 16 = 0.

Additional Information

Laws of Indices

Key rules include (a^m)ⁿ = a^m×n and a^m × aⁿ = a^m+n, which are essential for changing bases in exponential equations.

Standard Quadratic Form

A quadratic equation is generally expressed as ax² + bx + c = 0, where a, b, and c are constants.

Perfect Square Trinomial

The expression y² − 8y + 16 can be factored as (y − 4)², which represents a perfect square where the discriminant D = 0.

Shortcut Trick

When two articles are sold at the exact same selling price, one at a profit of x% and the other at a loss of x%, the entire transaction always results in an overall loss.

Overall Loss % = (x² ÷ 100)%

⇒ Overall Loss % = (8² ÷ 100)% = (64 ÷ 100)% = 0.64%

∴ The correct answer is 0.64% loss.

Alternate Method

Given:

Selling Price (SP) of the table = ₹9936

Selling Price (SP) of the swing = ₹9936

Profit on the table = 8%

Loss on the swing = 8%

CP1 = 9200

Profit = +8% (+736)

SP1 = 9936

CP2 = 10800

Loss = −8% (−864)

SP2 = 9936

Total CP = 20000 | Total SP = 19872 | Loss = 128 Overall Loss % = (128 ÷ 20000) × 100 = 0.64%

Calculations:

⇒ Total Selling Price = 9936 + 9936 = ₹19872

⇒ Cost Price of the table (CP₁) = SP × [100 ÷ (100 + Profit%)]

⇒ CP₁ = 9936 × (100 ÷ 108) = 9936 × (25 ÷ 27) = ₹9200

⇒ Cost Price of the swing (CP₂) = SP × [100 ÷ (100 − Loss%)]

⇒ CP₂ = 9936 × (100 ÷ 92) = 9936 × (25 ÷ 23) = ₹10800

⇒ Total Cost Price = 9200 + 10800 = ₹20000

⇒ Total Loss = Total CP − Total SP = 20000 − 19872 = ₹128

⇒ Overall Loss % = (Total Loss ÷ Total CP) × 100

⇒ Overall Loss % = (128 ÷ 20000) × 100 = 0.64%

∴ The correct answer is 0.64% loss.

Additional Information

Same SP, Same Profit & Loss %

When two items are sold at the same selling price, one at a profit of x% and the other at a loss of x%, there is always a net loss. The loss percentage is consistently determined using the formula (x² ÷ 100)%.

Same CP, Same Profit & Loss %

When two items are bought at the identical cost price, and one is sold at a profit of x% while the other at a loss of x%, the net result is zero, meaning there is no net profit and no net loss overall.

Marked Price and CP Relation

The direct ratio comparing Marked Price (MP) and Cost Price (CP) when dealing with profit and discount is written directly as: MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

The correct answer is a proportional increase in all inputs results in an increase in output by the same proportion.

Key Points

• There are three types of returns to scale: increasing returns to scale, constant returns to scale, and decreasing returns to scale.
• When all inputs in a production process are tripled, the scale of production is increased by a factor of three.
• If the output is also tripled, then there are constant returns to scale, because the increase in output is proportional to the increase in inputs.
• However, if the output is more than tripled, then increasing returns to scale apply.
• This means that the increase in output is greater than the increase in inputs, indicating that the production process is becoming more efficient as the scale of production increases.
• On the other hand, if the output is less than tripled, then decreasing returns to scale apply. This means that the increase in output is less than the increase in inputs, indicating that the production process is becoming less efficient as the scale of production increases.

The correct answer is 100.

Key Points

• The Rajasthan government announced in the 2022-2023 budget that it would provide free electricity of up to 50 units for domestic users consuming up to 100 units per month.
• This was part of a larger initiative to provide relief to domestic consumers, with subsidies also offered for those using between 100 and 300 units.
• The government estimated that this scheme would cost approximately Rs 4,500 crore.

Given: 

625 × 31 ÷ 233 – 59 = ?

Concept used:

Calculation:

⇒ 625 × 31 ÷ 233 – 59 = ?

⇒ 83.15 – 59 = ?

⇒ 24.15 = ?

⇒ ? ≈ 24 

∴ Option 1 is the correct answer.

Given word: 'FORMULIZED'

Now, the first and second, third and fourth, fifth and sixth, seventh and eighth, ninth and tenth is interchanged.

then,

Now, the ninth letter from the left after interchange is 'D'.

Hence, the correct answer is "D".

Shortcut Trick

Sum of numbers = Difference of squares ÷ Difference of numbers

Sum = 360 ÷ 18 = 20

Larger number = (Sum + Difference) ÷ 2

Larger number = (20 + 18) ÷ 2 = 19

∴ The correct answer is 19.

Alternate Method

Given:

Difference (x − y) = 18

Difference of squares (x² − y²) = 360

Formula Used:

x² − y² = (x − y)(x + y)

⇒ x² − y² = (x − y)(x + y)

⇒ 360 = 18 × (x + y)

⇒ x + y = 360 ÷ 18 = 20

⇒ Now, adding (x + y) and (x − y):

⇒ (x + y) + (x − y) = 20 + 18

⇒ 2x = 38

⇒ x = 38 ÷ 2 = 19

∴ The correct answer is 19.

Additional Information

Algebraic Identity

The formula for the difference of two squares is a² − b² = (a − b)(a + b), which is useful for simplifying quadratic expressions.

Finding Numbers from Sum and Difference

If the sum (S) and difference (D) of two numbers are known, the larger number is (S + D) ÷ 2 and the smaller number is (S − D) ÷ 2.

Consecutive Integers Property

For any two consecutive integers n and n+1, the difference of their squares (n+1)² − n² is always equal to their sum (2n + 1).

Shortcut Trick

Solve the expression by simplifying from the innermost square root moving outwards.

First part: √(6 + 3) = √9 = 3

Second part: √(19 − 3) = √16 = 4

Final part: √(21 + 4) = √25 = 5

∴ The correct answer is 5.

Alternate Method

Given: √(21 + √(19 − √(6 + 3)))

Following the BODMAS rule, we evaluate the operations inside the radical signs sequentially:

⇒ √(21 + √(19 − √9))

⇒ √(21 + √(19 − 3))

⇒ √(21 + √16)

⇒ √(21 + 4)

⇒ √25

⇒ 5

∴ The correct answer is 5.

Additional Information

Perfect Squares

A perfect square is an integer that is the square of another integer. Common examples include 3² = 9, 4² = 16, and 5² = 25.

VBODMAS Rule

In nested mathematical operations, Vinculum (Bar), Brackets, and operations inside Orders (Roots/Powers) are prioritized from the innermost level to the outermost level.

Surds Property

While √(a × b) = √a × √b, it is important to remember that √(a + b) ≠ √a + √b.

Given:

Priyanka walks 9 m towards the south.

She turns left and walks 7 m.

Then she turns right and walks 5 m.

She again turns right and walks 9 m.

So, Priyanka is facing at the 'West' direction now.

Hence, the correct answer is "West".

The correct answer is A single product is formed from two or more reactants.

Key Points

• Combination reaction
• ​A combination reaction is when two or more reactants combine to form a single product.
• The three types of combination reactions are between two elements, two compounds, or between an element and a compound.

Additional Information

• Displacement reaction:
• The reaction in which an ion (or an atom) in a compound is replaced by an ion (or an atom) of another element is known as a displacement reaction.
• It is denoted by X + YZ  → XZ+Y
• Fe (s) + CuSO4 (aq) → FeSO4 (aq) + Cu (s)
• In the above reaction, iron is more reactive than copper, it displaces copper, resulting in the formation of ferrous sulphate.
• Fe2O3 (s) + 2Al (s) → Al2O3 (s) + 2F3 (s)
• In the above reaction, aluminium is more reactive than iron, it displaces iron, resulting in the formation of aluminium oxide.
• Decomposition reaction:
• In a Decomposition reaction, a compound breaks down into two or more components, in which one component must be in the elemental state.
• Decomposition reaction is the opposite reaction of the combination reaction.
• CaCO3 (s) → CaO (s) + CO2 (g)

Given: A certain number of people are sitting in a straight line facing north.

1. Only one person is sitting to the left of C.

2. Only one person is sitting between C and R.

3) R is sitting to the immediate left of F.

4. Only two people are sitting to the right of F. 

Here, Total '7' people are sitting in the row.

Hence, the correct answer is "Option 3".

Shortcut Trick

Identify the corresponding vertices by matching the equal sides given in the problem:

1. AB = DE and BC = DF ⇒ Vertex B (common to AB, BC) corresponds to D (common to DE, DF).
2. AB = DE and AC = EF ⇒ Vertex A (common to AB, AC) corresponds to E (common to DE, EF).
3. BC = DF and AC = EF ⇒ Vertex C (common to BC, AC) corresponds to F (common to DF, EF).

Mapping the vertices: A → E, B → D, and C → F.

∴ The correct answer is Δ ABC ≅ Δ EDF.

Alternate Method

Given: AB = DE, AC = EF, and BC = DF.

Formula Used: SSS (Side-Side-Side) Congruence Theorem states that if three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.

A B C E D F c a b c

The correct answer is A, B, C, and D.

Key Points

• In a first of its kind policy consultation, Science and Technology Minister Harsh Vardhan interacted with the highly-skilled Indian diaspora to facilitate channels for them to contribute to India’s Science Technology and Innovation Policy (STIP) 2020.
• The Minister stressed that India aims to connect the diaspora with the Indian scientific and economic ecosystem to accelerate the growth.

Given: A certain number of people are sitting in a row facing north.

1) M sits third to the right of A.

2. M is second to the left of P.

3) Only one person sits between P and S.

4. Q sits to the immediate right of S. 

Here, Total '9' people are sitting in the row.

Hence, the correct answer is "Option 4".

The correct answer is Part IVA.

Key Points

• Article 51 A in Part IV of the Indian constitution deals with the fundamental duties of the citizens.
• They serve as a reminder to the citizens that while enjoying their rights, they should also be conscious of duties they owe to their country, their society and to their fellow citizens.
• The features of Fundamental duties are as follows:
• Fundamental duties are non-enforceable in nature.
• Citizens are morally obligated by the Constitution to perform these duties.
• The fundamental duties are not enforceable in nature. No legal sanction can be enforced by the government in case of their violation.
• From the above, it is clear that Fundamental Duties do not enjoy any legal sanction.

Additional Information

There is a total of eleven fundamental duties enshrined in the constitution. They are as follows:

• to abide by the Constitution and respect its ideals and institutions, the National Flag and the National Anthem;
• to cherish and follow the noble ideals which inspired our national struggle for freedom;
• to uphold and protect the sovereignty, unity and integrity of India;
• to defend the country and render national service when called upon to do so;
• to promote harmony and the spirit of common brotherhood amongst all the people of India transcending religious, linguistic and regional or sectional diversities; to renounce practices derogatory to the dignity of women;
• to value and preserve the rich heritage of our composite culture;
• to protect and improve the natural environment including forests, lakes, rivers and wildlife, and to have compassion for living creatures;
• to develop the scientific temper, humanism and the spirit of inquiry and reform;
• to safeguard public property and to abjure violence;
• to strive towards excellence in all spheres of individual and collective activity so that the nation constantly rises to higher levels of endeavour and achievement;
• who is a parent or guardian to provide opportunities for education to his child or, as the case may be, ward between the age of six and fourteen years.

Calculation:

5/12 = 0.4166666.... = $0.41\bar{6}$

∴ Option 3 is the correct answer.

Shortcut Trick

Find the minimum difference between any two given numbers: 16 − 12 = 4.

Check if 4 divides all the given numbers: 12, 16, and 24 are all perfectly divisible by 4.

Thus, the greatest common divisor is 4.

∴ The correct answer is 4.

Alternate Method

Given numbers: 12, 16, and 24.

Write the prime factorization of each number:

⇒ 12 = 2 × 2 × 3 = 2² × 3

⇒ 16 = 2 × 2 × 2 × 2 = 2⁴

⇒ 24 = 2 × 2 × 2 × 3 = 2³ × 3

To find the HCF (Highest Common Factor), take the lowest power of the common prime factors:

⇒ Common prime factor is 2, and its lowest power is 2².

⇒ HCF = 2² = 4

∴ The correct answer is 4.

Additional Information

Highest Common Factor (HCF)

The greatest number that divides two or more numbers without leaving any remainder is called their HCF or GCD (Greatest Common Divisor).

Least Common Multiple (LCM)

The smallest positive integer that is perfectly divisible by each of the given numbers. For any two numbers a and b, HCF(a, b) × LCM(a, b) = a × b.

HCF of Fractions

The HCF of given fractions is calculated as: HCF = (HCF of Numerators) ÷ (LCM of Denominators).

Shortcut Trick

Ratio 2 years ago = 4 : 5 (Diff = 1 unit)

Ratio 3 years hence = 5 : 6 (Diff = 1 unit)

Change in ratio units = 5 − 4 = 1 unit (for both Subash and Pranav)

Total time gap = 2 + 3 = 5 years

⇒ 1 unit = 5 years

⇒ Pranav's age 2 years ago = 5 × 5 = 25 years

∴ The correct answer is 27 years.

Alternate Method

Given: Ratio 2 years ago = 4 : 5 | Ratio 3 years hence = 5 : 6

Let the ages of Subash and Pranav 2 years ago be 4x and 5x.

⇒ Present age of Subash = 4x + 2

⇒ Present age of Pranav = 5x + 2

According to the condition 3 years hence:

⇒ (4x + 2 + 3) / (5x + 2 + 3) = 5 / 6

⇒ (4x + 5) / (5x + 5) = 5 / 6

⇒ 6 × (4x + 5) = 5 × (5x + 5)

⇒ 24x + 30 = 25x + 25

⇒ x = 5

⇒ Present age of Pranav = 5(5) + 2 = 25 + 2 = 27 years

∴ The correct answer is 27 years.

Additional Information

Ratio Difference Method

If the difference between ratio terms is the same (5 − 4 = 1 and 6 − 5 = 1), the increase in units directly corresponds to the total time elapsed.

Age Problems Logic

The difference between the ages of two people remains constant regardless of the number of years that pass.

Cross Multiplication Shortcut

For equations of type (ax + b)/(cx + d) = m/n, use n(ax + b) = m(cx + d) to find x rapidly.

The correct answer is Three .

Key Points

Article 243Q: Constitution of Municipalities

• Core Function: This article deals with the establishment of different types of municipalities in every state. It recognizes the need for varying levels of urban governance based on the size and needs of the urban area.
• Types of Municipalities:
• Nagar Panchayat: For transitional areas, meaning those transitioning from rural to urban.
• Municipal Council: For smaller urban areas.
• Municipal Corporation: For larger urban areas.
• Key Points:
• The specific type of municipality to be constituted in a particular area is determined by factors like the size of the area, the level of urbanization, and the municipal services required.
• The establishment and functioning of these municipalities are governed by state laws enacted under the provisions of Part IXA of the Constitution.

Part IXA of the Constitution (Articles 243P to 243(ZT))

Part IXA, introduced by the 74th Amendment Act, 1992, deals with the constitution of municipalities and their powers, authorities, and responsibilities. Here's a brief overview of some key articles:

• Article 243P: Defines "municipality" and outlines the objectives of municipal governance.
• Article 243R: Deals with the composition of municipalities, including provisions for reservation of seats for Scheduled Castes, Scheduled Tribes, and other backward classes.
• Article 243S: Outlines the powers, authorities, and responsibilities of municipalities, covering a wide range of areas such as urban planning, public health, sanitation, and social welfare.
• Article 243T: Provides for the constitution of finance commissions in states to review the financial position of municipalities and recommend measures for their financial upgradation.
• Article 243U: Establishes state finance commissions to review the financial position of panchayats and recommend measures for their financial upgradation.

Shortcut Trick

To find the longest possible length of the tiles, calculate the HCF of the dimensions.

Length = 735 cm, Width = 525 cm.

HCF(735, 525) = 105 cm.

∴ The correct answer is 105 cm.

Alternate Method

Given:

Length of the courtyard = 7.35 m = 735 cm

Width of the courtyard = 5.25 m = 525 cm

Formula Used:

Side of the largest square tile = HCF (Length, Width)

Calculations:

⇒ Prime factors of 735 = 3 × 5 × 7 × 7

⇒ Prime factors of 525 = 3 × 5 × 5 × 7

⇒ Common factors = 3 × 5 × 7

⇒ HCF = 105

⇒ Longest possible length of the tile = 105 cm

∴ The correct answer is 105 cm.

Additional Information

HCF (Highest Common Factor)

The greatest number that divides two or more numbers without leaving a remainder. Used to find the maximum size or greatest length.

Number of Tiles

Total number of tiles required = (Area of Floor) ÷ (Area of one Tile) = (L × W) ÷ (Side²).

LCM (Least Common Multiple)

The smallest number that is a multiple of two or more numbers. Used for problems involving minimum time or next meeting point.

Shortcut Trick According to Karl Pearson's empirical formula for a moderately skewed distribution: Mode = 3 × Median − 2 × Mean Adding Mean to both sides gives: Mean + Mode = 3 × Median − Mean Rearranging the equation yields: Mean − Mode = 3(Mean − Median) ∴ The correct answer is Mean − Mode = 3 (Mean − Median).

Alternate Method Given: Options showing relationships between mean, median, and mode. Formula Used: Empirical relationship: Mode = 3 × Median − 2 × Mean

Mode Median Mean

x

3x

Mean − Mode = 3 × (Mean − Median)

Calculations: ⇒ Mode = 3 × Median − 2 × Mean ⇒ Mode = 3 × Median − 3 × Mean + Mean ⇒ Mean − Mode = 3 × Mean − 3 × Median ⇒ Mean − Mode = 3(Mean − Median) ∴ The correct answer is Mean − Mode = 3 (Mean − Median).

Additional Information Symmetric Distribution In a perfectly symmetric or normal distribution, the values of all three measures are equal: Mean = Median = Mode.

Positively Skewed Distribution The tail of the distribution extends to the right. In this case, the order of averages is generally: Mean > Median > Mode.

Negatively Skewed Distribution The tail of the distribution extends to the left. The order of averages follows: Mean < Median < Mode.

Karl Pearson's Coefficient of Skewness Skewness = (Mean − Mode) ÷ Standard Deviation, which can also be approximated as 3(Mean − Median) ÷ Standard Deviation.

The logic followed here is:

Logic: (2nd number × 4) + (2nd number ÷ 2) = 1st number.

Now,

For, 27 : 6

→ (6 × 4) + (6 ÷ 2)

⇒ 24 + 3 = 27.

For, 36 : 8

→ (8 × 4) + (8 ÷ 2)

⇒ 32 + 4 = 36.

Similarly, for 18 : ?

→ (4 × 4) + (4 ÷ 2)

⇒ 16 + 2 = 18.

So, ? = 4.

Hence, the correct answer is "Option 1".

Given equation: 25 × 9 – 74 + 459 ÷ 3 = 52.

BODMAS Table: 

Let's check each option one by one.

Option 1) 9 and 3 

Given: 25 × 9 – 74 + 459 ÷ 3 = 52.

After interchanging the numbers we get;

⇒ 25 × 3 – 74 + 459 ÷ 9 = 52

⇒ 25 × 3 – 74 + 51 = 52

⇒ 75 – 74 + 51 = 52

⇒ 126 - 74 = 52

⇒ 52 = 52

⇒ LHS = RHS

Option 2) 74 and 3 

Given: 25 × 9 – 74 + 459 ÷ 3 = 52

After interchanging the numbers we get;

⇒ 25 × 9 – 3 + 459 ÷ 74 = 52

⇒ 25 × 9 – 3 + 6.2 = 52

⇒ 225 – 3 + 6.2 = 52

⇒ 231.2 - 3 = 52

⇒ 228.2 ≠ 52

⇒ LHS ≠ RHS

Option 3) 25 and 74

Given: 25 × 9 – 74 + 459 ÷ 3 = 52

After interchanging the numbers we get;

⇒ 74 × 9 – 25 + 459 ÷ 3 = 52

⇒ 74 × 9 – 25 + 153 = 52

⇒ 666 – 25 + 153 = 52

⇒ 819 - 25 = 52

⇒ 794 ≠ 52

⇒ LHS ≠ RHS

Option 4) 25 and 3

Given: 25 × 9 – 74 + 459 ÷ 3 = 52

After interchanging the numbers we get;

⇒ 3 × 9 – 74 + 459 ÷ 25 = 52

⇒ 3 × 9 – 74 + 18.36 = 52

⇒ 27 – 74 + 18.36 = 52

⇒ 45.36 - 74 = 52

⇒ -28.64 ≠ 52

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 1".

Shortcut Trick

Put θ = 0° to simplify the trigonometric expression quickly.

Expression ⇒ cosec 47° − sec 43° + tan 61° − cot 29° + cos 45° − sin 45°

Using complementary angles: cosec 47° = sec 43°, tan 61° = cot 29°, and cos 45° = sin 45°.

The terms cancel out: (sec 43° − sec 43°) + (cot 29° − cot 29°) + (1/√2 − 1/√2) = 0.

∴ The correct answer is 0.

Alternate Method

Given: cosec (47° + θ) − sec (43° − θ) + tan (61° + θ) − cot (29° − θ) + cos (45° + θ) − sin (45° − θ)

Formula Used:

1. cosec A = sec (90° − A)
2. tan A = cot (90° − A)
3. cos A = sin (90° − A)

Calculations:

⇒ [sec (90° − (47° + θ))] − sec (43° − θ) + [cot (90° − (61° + θ))] − cot (29° − θ) + [sin (90° − (45° + θ))] − sin (45° − θ)

⇒ sec (43° − θ) − sec (43° − θ) + cot (29° − θ) − cot (29° − θ) + sin (45° − θ) − sin (45° − θ)

⇒ 0 + 0 + 0

⇒ 0

∴ The correct answer is 0.

Additional Information

Complementary Angle Trigonometric Ratios

When two angles A and B sum to 90°, sin A = cos B, tan A = cot B, and sec A = cosec B.

Trigonometric Substitution

In identity-based questions, substituting common angles like 0°, 30°, or 45° for θ can quickly yield the numerical result if the answer is independent of θ.

Given: Tomorrow is Sunday.

It means,

Today is Sunday - 1 = Saturday.

Now, after 121 days from today.

As, we know 7 days = 1 week.

So, 121 days = 121/7 = 17 week and 2 odd days.

Then,

After 121 days from today will be Saturday + 2 = Monday.

Hence, the correct answer is "Monday".

The logic followed here is:

So, '10.5' will complete the series.

Hence, the correct answer is "Option 1".

The correct answer is +0.33.

Key Points 

To find the magnification, we'll use the lens formula:

1/f = 1/v - 1/u  

where:

• f = focal length of the lens (-30 cm for a concave lens)
• v = image distance
• u = object distance (-60 cm, as it's placed in front of the lens)

Plug in the values:

1/(-30) = 1/v - 1/(-60)

Simplify:

-1/30 = 1/v + 1/60

Find a common denominator:

-2/60 = 1/v + 1/60

Isolate 1/v:

1/v = -2/60 - 1/60

1/v = -3/60

1/v = -1/20

Therefore, v = -20 cm

Now, calculate the magnification (m):

m = v/u

m = (-20) / (-60)

m = +1/3

The magnification of the image is +1/3 = +0.33.

Explanation:

• Negative Magnification: The negative sign indicates that the image is virtual and erect.
• Value less than 1: The absolute value of the magnification is less than 1, which means the image is smaller than the object.

In summary, when an object is placed 60 cm from a concave lens with a focal length of 30 cm, a virtual, erect, and diminished image is formed with a magnification of +1/3 = +0.33.

The correct answer is CnH2n.

Key Points

Hydrocarbons:

• These are organic compounds composed of carbon (C) and hydrogen (H).
• The carbon atoms join together to form the framework of the compound, and the hydrogen atoms attach to them in many different configurations.
• They are classified into aliphatic and aromatic hydrocarbons on the basis of their structure.

​Explanation: 

Aliphatic hydrocarbons are divided into three main groups according to the types of bonds they contain: alkanes, alkenes, and alkynes.

Alkanes:

• The hydrocarbons in which all the bonds are single.
• They are characterized by the molecular formula: CnH2n + 2 (where n is an integer).
• The simplest alkane is methane (CH4).

Alkenes

• These hydrocarbons contain a carbon-carbon double bond.
• They are characterized by the molecular formula: CnH2n.
• The simplest alkene is ethene (C2H4).

Alkyne:

• These hydrocarbons have a carbon-carbon triple bond.
• They are characterized by the molecular formula: CnH2n − 2.
• The simplest alkyne is ethyne (C2H2).

The Correct answer is 33.3 cm, 3D

Given: 

Focal length of convex lens (f₁) = 20 cm

Focal length of the concave lens (f₂) = -50 cm 

Formulas Used:

To find the effective focal length (F) and power (P) of a doublet made with a convex lens and a concave lens, we use the following formulas:

1/F = 1/f₁+ 1/f₂

P = 1/F

Calculations:

Effective focal length (F) of the doublet:

1/F = $\frac{1}{20} + \frac{1}{-50}$

1/F = 1/20 - 1/50

1/F = 3/100

1/F = 33.33 cm

Power (P) of the doublet:

P = 1/F 

Here F = 33.33 cm = 0.333 m

P = 1/ 0.33

P = 3D

The effective focal length and power of the doublet are:33.3 cm, 3D

∴ The Correct answer is Option 1: 33.3 cm, 3D

Given:

Veer starts from Point A and drives 7 km towards the north.

He then takes a right turn, drives 8 km, 

turns right and drives 19 km.

He then takes a right turn and drives 3 km,

takes a right turn and drives 12 km and stops at Point B.

So, the distance between A to B is: 8 - 3 = 5 km.

And, Veer should drive '5 km towards the West' direction to reach Point A from Point B.

Hence, the correct answer is "Option 2".

The correct answer is Gujarat Institute of Disaster Management.

Key Points

• 23 January 2022, marked the 125th birth anniversary of freedom fighter Netaji Subhas Chandra Bose.
• The day will also be celebrated as ‘Parakram Diwas’ from 2022 onwards.
• PM Modi conferred the Subhas Chandra Bose Aapda Prabandhan Puraskars, for the years 2019, 2020, 2021, and 2022.
• The award carries a cash prize of Rs 51 lakh for an institution and Rs 5 lakh for an individual.

Additional Information

• For the award this year, nominations were solicited from 1st July, 2021 onwards.
• In response to the award scheme, 243 valid nominations were received from institutions and individuals.
• For the year 2022, the following have been selected for the Subhash Chandra Bose Aapda Prabandhan Puraskar for their excellent work in Disaster Management:
• Gujarat Institute of Disaster Management (in the Institutional category)
• Professor Vinod Sharma (in the Individual category).

The correct answer is 1992 - 93.

Key Points

• National Bank for Agriculture and Rural Development (NABARD):
• India's top development bank, NABARD, aims to support fair and sustainable rural and agricultural development.
• The Sivaraman Committee, which was constituted on March 30, 1979, recommended the establishment of NABARD.
• As per the National Bank for Agriculture and Rural Development Act, 1981, it is a statutory body that was founded in 1982 by Parliament.
• Its headquarter is located in Mumbai, India.
• It supervises Regional Rural Banks (RRBs) and Cooperative Banks, assisting them in establishing safe banking procedures and integrating them with the CBS (Core Banking Solution) system.
• Chairman: Shri. Shaji K V
• It was established with the aim of providing credit flow for the development of agriculture, cottage and village industries, handicrafts, and small-scale industries in rural areas.
• Self Help Group - Bank Linkage Programme (SHG-BLP):
• It is the world's largest microfinance initiative initiated by NABARD in 1992 and has since been growing.
• It was started to provide financial assistance to self-help groups (SHGs) through banks with the objective to promote financial inclusion and empower women through microfinance.
• Banks were permitted to open savings accounts for SHGs under this policy.
• Components of SHG-BPL:
• Bank Branch Managers: Education and Sensitization
• Bank Sakhis' orientation and training at rural bank branches
• Community Based Repayment Mechanism (CBRM) should be implemented in rural bank branches.
• SHG Credit Linkage

The correct answer is Hyderabad.

Key Points

• Maulana Azad National Urdu University (MANUU) was established by an Act of Parliament in 1998.
• It is a central university located in Hyderabad, Telangana. It was named after Maulana Abul Kalam Azad, who was a freedom fighter, an educationist, and the first Education Minister of independent India.
• The university is known for promoting Urdu language and literature. It has a dedicated Department of Urdu, which offers courses in Urdu language, literature, and culture.
• It has campuses in Hyderabad, Lucknow, and Srinagar. It also has centers in various cities across India.

 Additional Information

Maulana Abul Kalam Azad:

• He was the nation's first minister of education from 1948 to 1958.
• He led the Khilafat movement from the front.
• He chose the pen name "Azad," which means "freedom," in order to distance himself from dogmatic religious beliefs.
• He fought for children's right to free education until the age of fourteen.
• He was also a pioneer in the establishment of India's higher education board, the University Grants Commissi

The logic followed here is:

Logic: 1st number + (2nd number × 2) = 3rd number.

Now,

For (6, 17, 40)

→ 6 + (17 × 2)

⇒ 6 + 34 = 40.

(13, 9, 31)

→ 13 + (9 × 2)

⇒ 13 + 18 = 31.

Now, checking the options:

Option 1: (6, 13, 25)

→ 6 + (13 × 2)

⇒ 6 + 26 = 32 ≠ 25.

Option 2: (27, 14, 49)

→ 27 + (14 × 2)

⇒ 27 + 28 = 55 ≠ 49.

Option 3: (21, 15, 51)

→ 21 + (15 × 2)

⇒ 21 + 30 = 51.

Option 4: (31, 16, 45)

→ 31 + (16 × 2)

⇒ 31 + 32 = 63 ≠ 45.

Hence, the correct answer is "Option 3".

The correct answer is different physical as well different chemical properties.

Key Points

• Mendeleev's Periodic Law: The physical and chemical properties of elements are periodic functions of their atomic masses.
• Mendeleev arranged all the elements known at that time in increasing order of atomic mass and this arrangement became a periodic table.
• In Mendeleev's Periodic Table: The total number of periods in the periodic table was seven and the total number of groups was nine.
• That is, 63 elements were known when Mendeleev started his work.​

Additional Information

s-block element

• The elements in which the valence electron is present in the outermost s-orbital of an atom are called s-block elements.
• The elements of groups 1 and 2 are called s-block elements.

p-block elements

• The elements in which the valence electron is present in the outermost p-orbital of an atom are called p-block elements.
• The elements of groups 13, 14, 15, and 16 are the p-block elements except for the helium atom.

d-block elements

• The transition metal elements are d-block elements.
• The d-block elements are formed due to the addition of the last electrons in the d-sublevel of an atom.
• The series of the d-block element is classified as 3d, 4d, 5d, and 6d series.
• They are good conductors of heat and electricity

f-block elements

• The elements in which the valence electron is present in the outermost f-orbital of an atom are called f-block elements.
• The elements of lanthanide and actinide series are the f-block elements.

Given: Six presidents O, P, S, B, N and K.

1. B sits at the immediate right of K.

2) P sits exactly between B and S.

3) O sits at the immediate right of S.

4. N sits exactly between K and O.

So, 'P' sits second to the left of O.

Hence, the correct answer is "Option 4".

Given: A, B, C, D, E and F live on six different floors of the same building.

1. Only one person lives above E.

2. B lives immediately below A and immediately above C.

3. Neither B nor C lives on the lowermost floor.

4. A does not live on the topmost floor.

5. Only two people live between A and D (This implies D will lives in 1st floor).

And, 'F' will lives on the remaining floor.

So, 'D' lives immediately below C.

Hence, the correct answer is "Option 2".

The correct answer is Baking soda.

Key Points

Baking Soda

• Chemical Name: Sodium Bicarbonate (NaHCO3)
• Properties: White crystalline powder, slightly alkaline, reacts with acids to produce carbon dioxide gas.
• Uses:
• Cooking: Leavening agent in baked goods, neutralizes acidic ingredients in recipes.
• Cleaning: Deodorizes refrigerators, cleans surfaces, removes stains.
• Health: Can be used as an antacid to relieve heartburn.

Additional Information

Washing Soda

• Chemical Name: Sodium Carbonate (Na2CO3)
• Properties: White, water-soluble powder, strong alkaline nature.
• Uses:
• Cleaning: Water softener, boosts the effectiveness of detergents, cleans greasy surfaces.
• Industrial Applications: Used in glass and paper manufacturing.

Baking Powder

• Composition: A mixture of baking soda (sodium bicarbonate) and a dry acid (like cream of tartar).
• Properties: Fine white powder, reacts with moisture to release carbon dioxide gas.
• Uses:
• Cooking: Primary leavening agent in many baked goods, provides a more consistent rise than baking soda alone.

Bleaching Powder

• Chemical Name: Calcium Oxychloride (CaOCl2)
• Properties: Strong oxidizing agent, produces chlorine gas when exposed to moisture or acids.
• Uses:
• Water Treatment: Disinfecting water supplies.
• Bleaching: Used to bleach textiles and paper.
• Sanitation: Disinfecting surfaces and equipment.

The correct answer is HIV attacks your immune system by entering your red blood cells.

Key Points

• The full form of HIV is Human Immunodeficiency Virus.
• The human immunodeficiency viruses are two species of Lentivirus that infect humans.
• Over time, they cause acquired immunodeficiency syndrome, a condition in which progressive failure of the immune system allows life-threatening opportunistic infections and cancers to thrive.

 Additional Information

• HIV (human immunodeficiency virus) is a virus that attacks the immune system, the body's natural defence system.
• Without a strong immune system, the body has trouble fighting off disease.
• Both the virus and the infection it causes are called HIV. White blood cells are an important part of the immune system.

The correct answer is 1970 s.

Key Points

• Tawa Reservoir is a reservoir on the Tawa River in central India. It is located in Itarsi of Hoshangabad District of Madhya Pradesh state, above Betul district.
• The reservoir was formed by the construction of the Tawa Dam, which began in 1958 and was completed in 1978.
• The dam provides water for irrigation in Hoshangabad and Harda districts.
• The Tawa reservoir forms the western boundary of Satpura National Park and Bori Wildlife Sanctuary.

 Additional Information

• The Tawa Matsya Sangh – a federation of Fisherworker’s cooperatives – an organization fighting for the rights of the displaced forest dwellers of the Satpura forest in Madhya Pradesh.
• The newly formed Tawa Matsya Sangh (TMS) organized rallies and a chakka jam (road blockade), demanding their right to continue fishing for their livelihood.
• In response to their protests, the government created a committee to assess the issue.
• The committee recommended that fishing rights be granted to the villagers for their livelihood.
• In 1996, the Madhya Pradesh government decided to give to the people displaced by the Tawa dam the fishing rights for the reservoir.

The correct answer is CaCl2.

Key Points

 CaCl2 (Calcium Chloride)

• Chemical Nature: An inorganic salt composed of calcium and chlorine ions.
• Properties: White, crystalline solid, highly soluble in water, hygroscopic (absorbs moisture from the air).
• Uses: De-icing roads, dust control, food additive, desiccant (drying agent).

Additional Information

NaCl (Sodium Chloride)

• Chemical Nature: Common table salt, an ionic compound of sodium and chlorine.
• Properties: White, crystalline solid, readily dissolves in water, essential for human and animal life.
• Uses: Seasoning food, preserving food, industrial applications (e.g., chemical production).

MgCl2 (Magnesium Chloride)

• Chemical Nature: An inorganic salt of magnesium and chlorine.
• Properties: White, crystalline solid, highly soluble in water, deliquescent (absorbs moisture from the air and dissolves in it).
• Uses: De-icing roads, fireproofing agents, magnesium production, nutritional supplement.

LiCl (Lithium Chloride)

• Chemical Nature: An inorganic salt of lithium and chlorine.
• Properties: White, crystalline solid, highly soluble in water and polar organic solvents.
• Uses: Batteries (lithium-ion batteries), air conditioning systems, psychiatric medications.

Given word: 'FATIGUE'

After arranged in alphabetical order:

After arranged in alphabetical order,

Fourth alphabet from the left end is: G,

Second alphabet from the right is: T,

Now,

there are 12 letters between G and T.

Hence, the correct answer is "Option 2".

The correct answer is appointed as Judge of the Supreme Court.

Key Points

• Attorney General of India is part of the Union Executive of India. AG is the highest law officer of India.
• Article 76 talks about the office of the Attorney General of India.
• AG is the chief legal advisor to the government of India.
• AG is not considered a government servant.
• The remuneration of the Attorney General is determined by the President.

Hence, Article 76 of the Indian Constitution deals with the provision of the Attorney-General of India.

Additional Information

Eligibility: 

• She/ He must be qualified to be appointed as Supreme Court judge.
• Must be a citizen of India.
• Served as a Judge of the High Court for 5 years as an advocate.
• Should be an eminent jurist in the President's opinion.
• Appointment: Appointed by the President on the advice of the government.
• The tenure of AG is not fixed by the Constitution.
• AG holds office during the pleasure of the government. She/He can be removed by the President any time.
• Functions of Attorney General:
• Performs legal duties on behalf of the Government of India.
• Right to participate in the proceedings of the Parliament and though he/she does not have the right to vote.
• Appears on behalf of the Government of India in all cases in the apex court.
• AG is assisted by two Solicitor Generals and four Additional Solicitor Generals.

The correct answer is Point 2.

Key Points

Human Excretory system: Kidney

• The organ system which is used to remove the waste product from the body is called the human excretory system and Kidneys play an important role.
• Therefore Option 2 is Correct.
• The major waste product generated in the human body is urea, along with which some other toxins are also generated.
• Urea is eliminated by kidneys by the process of urination and solid wastes are removed from the body by the intestines.

Kidney

• The kidney is a bean-shaped organ.
• Its function is to clean blood and eliminate the waste from the blood in form of urine
• It is present in the abdomen, just below the diaphragm, and is protected by ribs.
• Each kidney weighs 120 g to 170 g and 10-12 cm long and 5-7 cm wide and is the size of a fist.
• Kidneys are made up of subunits called Nephron.

Explanation-

• Each kidney has nearly one million complex tubular structures called Nephrons.
• A nephron can be divided into the following regions-
• Bowman's capsule- Within the Bowman's capsule a network or tuft of capillaries is present, it is called Glomerulus.
• Malpighian body
• Loop of Henle
• PCT and DCT

Shortcut Trick

Initial Value = 5650

Increase = 15%

Multiplying Factor = 1 + 0.15 = 1.15

New Value = 5650 × 1.15 = 6497.50

∴ The correct answer is 6497.50.

Alternate Method

Given:

Original Number = 5650

Percentage Increase = 15%

Formula Used:

Final Value = Original Value + (Original Value × Increase% ÷ 100)

Calculations:

⇒ Amount of increase = 5650 × 15 ÷ 100

⇒ Amount of increase = 5650 × 0.15 = 847.50

⇒ Final Value = 5650 + 847.50

⇒ Final Value = 6497.50

∴ The correct answer is 6497.50.

Additional Information

Percentage Change

Percentage change = (New Value − Old Value) ÷ Old Value × 100.

Successive Percentage

If a value is increased by a% and then by b%, effective increase = (a + b + ab/100)%.

Base Change Rule

If A is x% more than B, then B is [x ÷ (100 + x)] × 100% less than A.

The correct answer is 50 Hz.

Key Points

• As per Indian standard for our domestic power supply we us A.C current, which is also known as alternating current, since they change its polarity at a certain interval of time.
• Now the two principal properties of the A.C electric power supply are Voltage and frequency.
• And we use 220 V and 50 Hz power supply for our common domestic use
• Where 220 V is potential difference and 50 Hz is its frequency

The correct answer is Transpiration.

Key Points

Transpiration

• Definition: The process by which plants lose water vapor through their leaves, primarily through tiny pores called stomata.
• Mechanism: Water is absorbed by roots, transported through the plant's vascular system (xylem), and exits as vapor from the leaves.
• Significance:
• Cooling: Cools the plant by evaporative cooling.
• Water Transport: Creates a pulling force (transpiration pull) that helps move water and minerals from roots to leaves.
• Mineral Transport: Facilitates the transport of essential minerals from the soil to the plant.

Additional Information

Root Pressure

• Definition: The upward pressure exerted by the roots of a plant that forces water and dissolved minerals into the plant's vascular system.
• Mechanism: Roots actively absorb water and minerals, creating a higher concentration of solutes within the root cells. This osmotic pressure drives water movement upwards.
• Significance: Contributes to the initial upward movement of water in plants, especially in young plants and at night when transpiration is low.

Absorption

• Definition: The process by which plant roots take in water and dissolved minerals from the soil.
• Mechanism: Roots have specialized structures like root hairs that increase their surface area for absorption. Water and minerals are absorbed through the root hairs and transported to the root cortex.
• Significance: Provides essential nutrients and water for plant growth, development, and survival.

Photosynthesis

• Definition: The process by which green plants and some other organisms convert light energy into chemical energy.
• Mechanism: In the presence of sunlight, chlorophyll in plant cells captures light energy and uses it to convert carbon dioxide (CO2) and water (H2O) into glucose (sugar) and oxygen (O2).
• Significance:
• Energy Production: Provides the primary source of energy for most living organisms.
• Oxygen Production: Releases oxygen into the atmosphere, essential for the survival of many organisms.
• Food Production: Produces glucose, the building block for plant growth and development.

The correct answer is 10.

Key Points

We have to find the highest and lowest total resistance that can be secured by the combinations of 2 ohm, 3 ohm and 5 ohm.

Take R1 = 5 ohm, R2 = 3 ohm, R3 = 2 ohm.

There are two ways to find the resistance. First by using series combination and second by using parallel combination.

To find lowest resistance we have to add the resistors in the parallel combination and to find the highest resistance we have to add the resistors in the series combination.

For highest resistance:

Rs = R1 + R2 + R3

Rs = 5 + 3 + 2

Rs = 10 ohm