RRB Group D Previous Year Paper (Held on: 2 Sept 2022 Shift 3)

The logic follows here is as,

Second number = First number x ( First number +2)

Hence, '63' is the correct answer.

The correct answer is 'Petroleum'.

Key Points

• Petroleum is a natural resource.
• Petrol and diesel are obtained from a natural resource called petroleum.
• The word petroleum is derived from petra (rock) and oleum (oil) as it is mined from between the rocks under Earth.

Additional Information 

• Coke: It is a grey, hard, and porous coal-based fuel with a high carbon content and few impurities, made by heating coal or oil in the absence of air, a destructive distillation process.
• Bitumen: It is a substance produced through the distillation of crude oil. Bitumen is known for its waterproofing and adhesive properties and is commonly used in the construction industry, notably for roads and highways.
• Coal Tar:  It is a thick dark liquid that is a by-production of coke and coal gas from coal.

Given: 

Concept used:

Count total crop production for both the years for each state. Calculate ratio for answer.

Calculation:

Total production of crops in Uttar Pradesh in the years 2021 and 2022 = 559 + 637 = 1196

Total production of crops in Madhya Pradesh in the years 2021 and 2022 = 534 + 645 = 1179

Total production of crops in Andhra Pradesh in the years 2021 and 2022 = 398 + 594 = 992

Total production of crops in Bihar in the years 2021 and 2022 = 589 + 546 = 1135

Total production of crops in West Bengal in the years 2021 and 2022 = 436 + 354 = 790

Total production of crops in Delhi in the years 2021 and 2022 = 245 + 251 = 496

Now calculate Ratios,

Option 1: Ratio of total crop production for both the years of Delhi and Uttar Pradesh = \({496\over 1196}= {31\over74 }\)

Option 2: Ratio of total crop production for both the years of West Bengal and Andhra Pradesh =\({790\over 992}={395\over 496}\) 

Option 3: Ratio of total crop production for both the years of Delhi and Andhra Pradesh = \({496\over 992}={1\over 2}\)

Option 4: Ratio of total crop production for both the years of West Bengal and Madhya Pradesh = \({790\over 1179}\)

Here, Delhi and Andhra Pradesh pair of states/UTs is the ratio of total crop production for both the years 1 : 2.

Hence, 'option 3' is the correct answer.

Given:

Object distance \(u=-40 \ cm\)

Focal length \(f=20 \ cm\)

Formula Used:

The Lens formula is given by  

\(\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}}\) [Here v is the image distance]

Calculation:

Now putting the values 

\(\frac{1}{\mathrm{v}}=\frac{1}{\mathrm{f}}+\frac{1}{\mathrm{u}}\Rightarrow \frac{1}{\mathrm{v}}=\frac{1}{20}+\frac{1}{(-40)}=\frac{1}{20}-\frac{1}{40}\Rightarrow \frac{1}{\mathrm{v}}=\frac{2-1}{40}=\frac{1}{40}\Rightarrow v=40 \ cm\)

Magnification 

\(\mathrm{m}=\frac{\mathrm{v}}{\mathrm{u}}=\frac{(40)}{(-40)}=-1\)

Hence the image will be real,inverted and of same size.

Shortcut Trick

Since AB || CD, the angle ∠BEF and ∠PEB are supplementary (linear pair).

∠BEF = 180° − ∠PEB = 180° − 78° = 102°.

The angle ∠GEF is the difference between ∠BEF and ∠BEG: ∠GEF = 102° − 18° = 84°.

In ΔEGF, the sum of angles is 180°: ∠EGF = 180° − (∠GEF + ∠GFE).

∠EGF = 180° − (84° + 30°) = 180° − 114° = 66°.

∴ The correct answer is 66°.

Alternate Method

Given:

Line AB || CD, transversal PQ intersects them at E and F.

∠PEB = 78°, ∠BEG = 18°, and ∠GFE = 30°.

Formula Used:

1. Linear Pair Axiom: Sum of angles on a straight line is 180°.
2. Angle Sum Property: Sum of interior angles of a triangle is 180°.

Calculations:

⇒ Since PQ is a straight line, ∠PEB + ∠BEF = 180°

⇒ 78° + ∠BEF = 180°

⇒ ∠BEF = 180° − 78° = 102°

⇒ Given ∠BEG = 18°, we find ∠GEF = ∠BEF − ∠BEG

⇒ ∠GEF = 102° − 18° = 84°

⇒ In ΔEGF, the sum of angles is 180°:

⇒ ∠GEF + ∠GFE + ∠EGF = 180°

⇒ 84° + 30° + ∠EGF = 180°

⇒ 114° + ∠EGF = 180°

⇒ ∠EGF = 180° − 114° = 66°

∴ The correct answer is 66°.

Additional Information

Parallel Lines and Transversals

When a transversal intersects two parallel lines, alternate interior angles are equal, and consecutive interior angles are supplementary (sum to 180°).

Angle Sum Property of a Triangle

The sum of all three interior angles of any triangle is always exactly 180°.

Linear Pair of Angles

Angles that lie on a straight line and share a common vertex and side always add up to 180°.

Shortcut Trick

A root of a quadratic equation must satisfy the equation when substituted for x.

Substitute x = 0.5 in 2x² + bx + 3 = 0:

2(0.5)² + b(0.5) + 3 = 0

0.5 + 0.5b + 3 = 0 ⇒ 0.5b = −3.5 ⇒ b = −7

∴ The correct answer is -7.

Alternate Method

Given:

Equation: 2x² + bx + 3 = 0

Smaller root (x₁) = 0.5

Formula Used:

For a quadratic equation ax² + bx + c = 0:

Product of roots (x₁ × x₂) = c ÷ a

Sum of roots (x₁ + x₂) = −b ÷ a

Calculations:

⇒ 0.5 × x₂ = 3 ÷ 2

⇒ 0.5 × x₂ = 1.5

⇒ x₂ = 1.5 ÷ 0.5 = 3

⇒ x₁ + x₂ = −b ÷ 2

⇒ 0.5 + 3 = −b ÷ 2

⇒ 3.5 = −b ÷ 2

⇒ 3.5 × 2 = −b

⇒ 7 = −b

⇒ b = −7

∴ The correct answer is -7.

Additional Information

Nature of Roots

The nature of roots is determined by the Discriminant (D) = b² − 4ac. If D > 0, roots are real and distinct; if D = 0, roots are real and equal.

Quadratic Formula

The roots of ax² + bx + c = 0 can be found using x = (−b ± √(b² − 4ac)) ÷ 2a.

Vieta's Formulas

For any polynomial, the sum of roots is always −(coefficient of second highest power) ÷ (leading coefficient).

The code for each word is shown below:

The code for 'are' is 458.

Hence, ‘458’ is the correct answer.

The logic follows here is:

• Vowel \(\rightarrow\) Consonant \(\rightarrow\) Vowel

 

A F R C D S Y H N T E D C I D Q A C V Y U I N G R F S C W R

Here, no consonants are there each of which is immediately preceded by a vowel and also immediately followed by a vowel.

Hence, 'option 1' is the correct answer.

Given: 

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

Solution:

(1) B sits fourth to the right of E.

(2) C sits third to the right of B.

(3) A sits sixth to the left of E.

(4) There are only two persons between C and D. 

Here is 17 persons seated.

Hence, 'option 3' is the correct answer.

Given:

Power of toaster \(P=2200\ W\).

Voltage of toaster \(V=220 \ V\)

Formula Used:

The resistance of the electric \(R=\frac{V^2}{P}\)

Calculation:

The resistance of the toaster \(=\frac{(220)^2}{2200}\=22 \ ohm\)

The resistance of the toaster 22 ohm.

Shortcut Trick

Upstream speed = 12.6 km ÷ (21/60) hr = 36 kmph.

Ratio of Boat speed (u) to Stream speed (v) = 7 : 2.

Upstream speed (u − v) = 7 − 2 = 5 units = 36 kmph ⇒ 1 unit = 7.2 kmph.

Downstream speed (u + v) = 7 + 2 = 9 units = 9 × 7.2 = 64.8 kmph.

Total time = (43.2 ÷ 36) + (38.88 ÷ 64.8) = 1.2 + 0.6 = 1.8 hours.

∴ The correct answer is 1.8 hours.

Alternate Method

Given: Upstream distance = 12.6 km, Time = 21 min, Speed ratio Boat : Stream = 7 : 2.

Formula Used: Speed = Distance ÷ Time; Downstream speed = u + v; Upstream speed = u − v.

⇒ Upstream speed = 12.6 / (21/60) = (12.6 × 60) / 21

⇒ Upstream speed = 0.6 × 60 = 36 kmph.

⇒ Let Boat speed (u) = 7x and Stream speed (v) = 2x.

⇒ u − v = 7x − 2x = 5x = 36 ⇒ x = 7.2.

⇒ Downstream speed = 7x + 2x = 9x = 9 × 7.2 = 64.8 kmph.

⇒ Time for 43.2 km Upstream = 43.2 / 36 = 1.2 hours.

⇒ Time for 38.88 km Downstream = 38.88 / 64.8 = 0.6 hours.

⇒ Total Time = 1.2 + 0.6 = 1.8 hours.

∴ The correct answer is 1.8 hours.

Additional Information

Upstream and Downstream Logic

Downstream speed (D) = Speed in still water (u) + Speed of stream (v). Upstream speed (U) = u − v.

Speed in Still Water

The speed of the boat in still water can be calculated as u = (D + U) / 2.

Speed of Stream

The speed of the water current or stream can be calculated as v = (D − U) / 2.

The correct answer is 'Gregor Mendel'.

Key Points

• Gregor Mendel, through his work on pea plants, discovered the fundamental laws of inheritance.
• He deduced that genes come in pairs and are inherited as distinct units, one from each parent.
• Mendel tracked the segregation of parental genes and their appearance in the offspring as dominant or recessive traits.
• Mendel's law of inheritance are as follows:
• Law of segregation: During gamete formation, the alleles for each gene segregate from each other so that each gamete carries only one allele for each gene.
• Law of independent assortment: Genes for different traits can segregate independently during the formation of gametes.

Additional Information

• ​ Watson and Crick discovered the double helix ,the twisted ladder structure of DNA(Deoxyribonucleic acid)
• Carl Linnaeus is famous for the invention of the naming system of plants and animal.
• Charles Darwin is famous for the theory of natural selection.

Shortcut Trick

Ratio of Amount (A) to Principal (P) = 15680 : 12500 = 784 : 625

Since the time period is 2 years, take the square root of the ratio parts.

Square root ratio = √784 : √625 = 28 : 25

Rate x = [(28 − 25) ÷ 25] × 100 = (3 ÷ 25) × 100 = 12%

∴ The correct answer is 12.

Alternate Method

Given:

Principal (P) = ₹12,500

Amount (A) = ₹15,680

Time (n) = 2 years

Formula Used: A = P(1 + r/100)ⁿ

Calculations:

⇒ 15680 = 12500 × (1 + x/100)²

⇒ 15680 ÷ 12500 = (1 + x/100)²

⇒ 1568 ÷ 1250 = (1 + x/100)²

⇒ 784 ÷ 625 = (1 + x/100)²

⇒ (28 ÷ 25)² = (1 + x/100)²

⇒ 28 ÷ 25 = 1 + x/100

⇒ x/100 = (28 ÷ 25) − 1

⇒ x/100 = 3 ÷ 25

⇒ x = (3 × 100) ÷ 25

⇒ x = 12

∴ The correct answer is 12.

Additional Information

Compound Interest Formula

The amount A is calculated as A = P(1 + r/100)ⁿ, where P is principal, r is rate per annum, and n is time in years.

Effective Rate for 2 Years

The effective compound interest rate for two years can be found using the successive change formula: x + x + (x × x)/100.

CI and SI Difference

For a period of 2 years, the difference between Compound Interest and Simple Interest is given by D = P(r/100)².

The correct answer is 'Gujrat'.

Key Points

• The first of its kind World Health Organization Global center for Traditional Medicine in Jamnagar, Gujrat.
• This centre will be set up at the Institute of Training and Research in Ayurveda in Gujrat.
• The primary objective of GCTM is to harness the potential of traditional medicine from across the world.
• It will be established under the Ministry of AYUSH.

Shortcut Trick

Current Selling Price (SP₁) = 130% of Cost Price (CP) = ₹19.50.

New Selling Price (SP₂) required = 140% of CP.

Using ratio-unitary method: 130 units = 19.50 ⇒ 1 unit = 19.50 ÷ 130 = 0.15.

Required increase in price = (140% − 130%) = 10% of CP.

Required increase = 10 × 0.15 = ₹1.50.

∴ The correct answer is ₹1.50.

Alternate Method

Given: SP₁ = ₹19.50, Profit₁% = 30%, Profit₂% = 40%. Formulas: CP = SP × 100 ÷ (100 + P%), SP = CP × (100 + P%) ÷ 100.

⇒ Cost Price (CP) = 19.50 × 100 ÷ 130 = ₹15.

⇒ New Selling Price (SP₂) = 15 × 140 ÷ 100 = ₹21.

⇒ Increase in Sales Price = SP₂ − SP₁ = 21 − 19.50 = ₹1.50.

∴ The correct answer is ₹1.50.

Additional Information

Direct SP Ratio

When CP is constant, the ratio of Selling Prices is equal to the ratio of (100 + Profit%). SP₁ : SP₂ = (100 + P₁) : (100 + P₂).

Cost Price

The base price on which profit or loss is always calculated unless specified otherwise. CP = 100% of itself.

Shortcut Trick

The HCF (Highest Common Factor) cannot be greater than the smallest difference between any two numbers.

Difference between 86 and 64 = 86 − 64 = 22.

Difference between 108 and 86 = 108 − 86 = 22.

The HCF must be a factor of 22 (1, 2, 11, 22). Checking options, only 2 divides all given numbers.

∴ The correct answer is 2.

Alternate Method

Given Numbers: 64, 86, 108, 260

Method: Prime Factorisation

⇒ 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶

⇒ 86 = 2 × 43 = 2¹ × 43¹

⇒ 108 = 2 × 2 × 3 × 3 × 3 = 2² × 3³

⇒ 260 = 2 × 2 × 5 × 13 = 2² × 5¹ × 13¹

⇒ HCF = Product of the lowest power of common prime factors

⇒ HCF = 2¹ = 2

∴ The correct answer is 2.

Additional Information

HCF (Highest Common Factor)

The greatest number that divides two or more numbers without leaving a remainder. Also known as GCD (Greatest Common Divisor).

Relation between HCF and LCM

For two numbers A and B: HCF(A, B) × LCM(A, B) = A × B.

HCF of Fractions

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

The correct answer is 'Plastic'.

Key Points

• Non-biodegradable waste: Those materials which cannot be broken down or decomposed into the soil by micro-organisms and natural agents are labeled as non-biodegradable.
• These substances consist of plastic materials, metal scraps, aluminum cans and bottles, etc.
• Plastic can not be decomposed by bacteria .

Additional Information​ Biodegradable Waste can be defined as the waste which can be broke by the microorganism. The example of this waste are food waste, paper waste and green waste.

The logic follows here is as,

Similarly, 

Hence, 'option 1' is the correct answer.

Given:

Value of resistors is = 12 Ω.

Formula Used:

Equivalent resistance in parallel combination

\(\frac{1}{R_e}=\frac{n}{R}\) [Where  n is the number of resistors]

Calculation:

Now it can be written as 

\(\frac{1}{4}=\frac{n}{12}\Rightarrow n=12 \times \frac{1}{4}\Rightarrow n=3 \Omega\)

Hence the numbers of resistors connected is '3'.

The logic follows here is:

Similarly,

Hence, 'option 4' is the correct answer.

Shortcut Trick

Use the standard count of prime numbers in ranges: 1 to 50 has 15, and 51 to 100 has 10.

Between 20 and 80, the primes are: 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79.

Total count = 14.

∴ The correct answer is 14.

Alternate Method

Given: Range between 20 and 80.

List all prime numbers (numbers with exactly two factors: 1 and itself) in the specified range:

⇒ Primes in 20s: 23, 29 (2 numbers)

⇒ Primes in 30s: 31, 37 (2 numbers)

⇒ Primes in 40s: 41, 43, 47 (3 numbers)

⇒ Primes in 50s: 53, 59 (2 numbers)

⇒ Primes in 60s: 61, 67 (2 numbers)

⇒ Primes in 70s: 71, 73, 79 (3 numbers)

⇒ Total Count = 2 + 2 + 3 + 2 + 2 + 3 = 14

∴ The correct answer is 14.

Additional Information

Prime Number Definition

A natural number greater than 1 that has no positive divisors other than 1 and itself. 2 is the only even prime number.

Prime Counts (1-100)

There are exactly 25 prime numbers between 1 and 100.

Co-prime Numbers

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

The correct answer is '2AgBr(s) \(\rm \xrightarrow{Sunlight}\) 2Ag(s) + Br2(g)'.

Key Points

• A displacement reaction is the one wherein the atom or a set of atoms is displaced by another atom in a molecule.
• For instance, when iron is added to a copper sulphate solution, it displaces the copper metal.
• A + B-C → A-C + B.
• The above equation exists when A is more reactive than B.

Additional Information

• The displacement reaction is the one whether the atom or group of atom are displaced by the atom or group of atoms.
• The starting materials are always pure elements, such as a pure zinc metal or hydrogen gas, plus an aqueous compound.

​

The correct answer is 'It conducts consolidated supervision of the financial sector in India.'.

Key Points

• The Reserve Bank of India was established on April 1, 1935 in accordance with the provisions of the Reserve Bank of India Act, 1934.
• It is India's central bank and regulatory body responsible for the regulation of the Indian Banking system.
• It conducts consolidated supervision of the financial sector in India.

Additional Information

• The Banking Regulation Act, 1949 empowers the Reserve Bank of India to inspect and supervise commercial banks.
• The Reserve Bank of India Act, 1934 requires the Central Government to entrust the reserve bank with all its money, remittance, exchange and banking transactions in India and the management of its public debt.

Shortcut Trick

Volume of a cube = (side)³

Given side = 12 cm

Volume = 12³ = 12 × 12 × 12 = 1728 cm³

∴ The correct answer is 1728 cm³.

Alternate Method

Given:

Side of the cube (a) = 12 cm

Formula used:

Volume (V) = a³

Calculations:

⇒ Volume = 12 × 12 × 12

⇒ Volume = 144 × 12

⇒ Volume = 1728 cm³

∴ The correct answer is 1728 cm³.

Additional Information

Total Surface Area of Cube

The total surface area (TSA) of a cube is calculated as 6a², where 'a' is the side length.

Diagonal of a Cube

The longest diagonal of a cube is given by the formula d = a√3.

Lateral Surface Area

The lateral surface area (LSA) which excludes the top and bottom faces is 4a².

The correct answer is 'Hadith'.

Key Points

• Hadith refers to the belief of the words, actions, and silent approval of the Islamic prophet Muhammad.
• It is transmitted reports attributed to what Muhammad said and did.
• It is called as the Backbone of Islamic civilization.
• Many authority takes Hadith as a source for religious law and moral guidance ranks second only to that of the Quran.

The logic follows here is as,

Hence, '35' is the correct answer.

Shortcut Trick

Let the Cost Price (CP) of 1000 gm be 1000 units.

Selling at 10% loss ⇒ Selling Price (SP) = 1000 − 10% of 1000 = 900 units.

Overall Gain is 15%, so SP = CP × (115 ÷ 100).

900 = (Actual Weight Used) × 1.15.

Actual Weight = 900 ÷ 1.15 = 782.608... gm.

∴ The correct answer is 782.6 gm.

Alternate Method

Given → Loss% = 10%, Profit% = 15%, True Weight = 1000 gm. Formulas: Gain% = [(True Weight − Actual Weight) ÷ Actual Weight] × 100 | Net Effect = Successive multiplication of ratios.

⇒ Let the actual weight used be 'x' gm. ⇒ Effective CP for the shopkeeper = x units. ⇒ Effective SP for the shopkeeper = 1000 × (100 − 10) ÷ 100 = 900 units. ⇒ According to the question: 15 = [(900 − x) ÷ x] × 100. ⇒ 15x = 90000 − 100x. ⇒ 115x = 90000 ⇒ x = 90000 ÷ 115. ⇒ x = 782.608... ≈ 782.6 gm.

∴ The correct answer is 782.6 gm.

Additional Information

Dishonest Dealer Concept

When a dealer sells goods at CP but uses less weight, Gain% = [Error ÷ (True Value − Error)] × 100.

Net Profit with Weight and Price Manipulation

Final Multiplier = (Weight Ratio) × (Price Ratio). Here, (1000 ÷ x) × (90 ÷ 100) = 115 ÷ 100.

Shortcut Trick

Directly divide the given total by the multiplier.

Value = 65 ÷ 5

Value = 13

∴ The correct answer is 13.

Alternate Method

Given:

Five times a number is 65.

Calculations:

Let the required number be x.

⇒ 5 × x = 65

⇒ x = 65 ÷ 5

⇒ x = 13

∴ The correct answer is 13.

Additional Information

Linear Equations

An equation involving only one variable with a power of 1 is called a linear equation in one variable.

Inverse Operations

Division is the inverse operation of multiplication. To isolate the variable in 5x = 65, we divide by the coefficient 5.

Transposition Method

Moving a term from one side of the equation to another involves changing its sign or operation (multiplication becomes division).

The correct answer is 'MnO2 is reduced to MnCl₂'.

Key Points

• A REDOX reaction is where oxidation and reduction occur simultaneously in a reaction.
• The reaction in which oxygen is either gained or hydrogen is lost by a substance is called oxidation reaction.The reaction in which hydrogen is gained or oxygen is lost by a substance is called reduction reaction.
• A substance is oxidised when: It gains Oxygen.
• It loses Hydrogen.

The correct answer is 'The ratio of V and I'.

Key Points

• Conductor resistance is a property of a conductor at a specific temperature.
• it is defined as the amount of opposition there is to the flow of electric current through a conducting medium.
• Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Therefore, V = RI where R is a constant called resistance.
• R depends on the dimensions of the conductor and also on the material of the conductor.

Shortcut Trick

Directly substitute a = 5 into the given expression.

⇒ √(4 × 5² − 4 × 5 + 1) + 6 × 5

⇒ √(100 − 20 + 1) + 30

⇒ √81 + 30 = 9 + 30 = 39

∴ The correct answer is 39.

Alternate Method

Given:

Expression: √(4a² − 4a + 1) + 6a

Value of a = 5

Formula Used:

(x − y)² = x² − 2xy + y²

Calculations:

We can simplify the algebraic expression inside the square root first by expressing it as a perfect square.

⇒ 4a² − 4a + 1 = (2a)² − 2(2a)(1) + (1)²

⇒ 4a² − 4a + 1 = (2a − 1)²

Now substitute this squared term back into the original expression:

⇒ √((2a − 1)²) + 6a

⇒ (2a − 1) + 6a

⇒ 8a − 1

Now, substitute the given value a = 5 into the simplified expression:

⇒ 8 × 5 − 1

⇒ 40 − 1 = 39

∴ The correct answer is 39.

Additional Information

Algebraic Identities

Important perfect square identities frequently used in simplification are (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

Square Root of Perfect Squares

The square root of a squared number is mathematically its absolute value: √x² = |x|. Since 2a − 1 is positive for a = 5, we can directly evaluate it as 2a − 1 without negative signs.

BODMAS Rule

When directly substituting numeric values into an equation, operations must follow the standard sequence: Brackets, Orders (Powers/Roots), Division, Multiplication, Addition, and Subtraction.

The shaded part represents boys are there who are racers and gymnasts:

 

The number representing boys are there who are racers and gymnasts = 4

Hence, ‘4’ is the correct answer.

The shaded part represents male students are neither singers nor dancers.

 

The number representing male students are neither singers nor dancers = 5

Hence, ‘5’ is the correct answer.

The correct answer is 'Bhangar'.

Key Points

• Bhangar is older alluvial soil which represents the upland alluvial tract.
• The soil is rich in humus and it gives a high yield due to rich amount of minerals and humus in the soil.
• It comprises calcium carbonate nodules called 'Kankars' which are impure in nature.
• These soils are coarser in texture.

Additional Information

• Khadar - This is the new soil formed due to alluvial deposits along the course of the river, The land slit comprises silt, mud, clay, and sand and are finer in nature.
• Bhabar -  The rivers, after descending from the mountains deposits pebbles in a narrow belt of about 8 to 16 km in width lying parallel to the slopes of Shiwaliks forming Bhabar.
• Terai -  South of bhabar belt, the streams and rivers re-emerge and create a wet, swampy, and marshy region known as Terai. Dudhwa National Park lies in this region.

Given : 

A certain number of people are sitting in a row and all are facing north.

Solution:

(1) Exactly one person is sitting between G and K.

(2) H is sitting to the immediate right of G.

(3) M is sitting at the second position to the left of K.

• It is possible only in case 1.

(4) Exactly four persons are sitting between I and K.

(5)  I is sitting third to the right of J. 

• It is possible in case 2.

Here is 12 peoples in the row.

Hence, 'option 1' is the correct answer.

Shortcut Trick

Number of dices = Volume of large cuboid ÷ Volume of one small dice

Number = (4 × 10 × 15) ÷ (2 × 2 × 2)

Number = 600 ÷ 8 = 75

∴ The correct answer is 75 dices.

Alternate Method

Given:

Dimensions of metallic cuboid: Length (L) = 15 cm, Breadth (B) = 10 cm, Height (H) = 4 cm.

Dimensions of small dice (cube): Side (a) = 2 cm.

Formula Used:

Volume of cuboid = L × B × H

Volume of cube = a³

Calculations:

⇒ Total Volume of cuboid = 4 × 10 × 15 = 600 cm³

⇒ Volume of one dice = 2 × 2 × 2 = 8 cm³

⇒ Number of dices = Total Volume ÷ Volume of one dice

⇒ Number = 600 ÷ 8

⇒ Number = 75

∴ The correct answer is 75 dices.

Additional Information

Conservation of Volume

When a solid is melted and recast into other shapes, the total volume remains constant.

Surface Area of Cuboid

The Total Surface Area (TSA) of a cuboid is given by 2(LB + BH + HL).

Cube Properties

For a cube of side 'a', the Volume is a³ and the Diagonal is a√3.

The correct answer is 'Only (b)'.

Key Points

• When two circular coils A and B are placed close to each other, and the current in the coil A is changed then some current will be induced in the coil B and the magnetic field associated with it also changes.
• Thus the magnetic field around coil B also changes. This change in the magnetic field lines around coil B induces an electric current in it. This process is known as electromagnetic induction.

Shortcut Trick

Successive Remaining method: Savings = Income × (100−r₁)% × (100−r₂)% × (100−r₃)%

Savings = 5,62,400 × 80% × 85% × 70%

Savings = 5,62,400 × 0.8 × 0.85 × 0.7 = 5,62,400 × 0.476

Savings = 2,67,702.4

∴ The correct answer is ₹2,67,703.

Alternate Method

Given: Annual Income = ₹5,62,400, Rent = 20%, Food = 15% (remaining), Education = 30% (remaining).

⇒ Step 1: Income after House Rent = 5,62,400 × (100 − 20)% = 5,62,400 × 0.80 = ₹4,49,920

⇒ Step 2: Income after Food = 4,49,920 × (100 − 15)% = 4,49,920 × 0.85 = ₹3,82,432

⇒ Step 3: Final Savings = 3,82,432 × (100 − 30)% = 3,82,432 × 0.70 = ₹2,67,702.4

⇒ Final value: Approximating to the nearest whole number ≈ ₹2,67,703

∴ The correct answer is ₹2,67,703.

Additional Information

Successive Percentage Change

When values are reduced from the remaining balance, use the multiplying factor method: Final = Initial × (1−r₁/100) × (1−r₂/100)...

Effective Percentage Decrease

Two successive decreases of a% and b% result in a total decrease of (a + b − ab/100)%.

Base Value Rule

Always ensure whether the percentage is calculated on the original income or the remaining income to avoid calculation errors.

The correct answer is 'Churu'.

Key Points

• Churu, a district in Rajasthan, is known for its abrupt temperatures over the years.
• It is located close to the Thar desert, one of the hottest regions of India.
• It recorded 1.1 degrees Celcius on Saturday, December 18, 2021.
• The Lowest temperature recorded in Churu is -2.5 degrees Celcius.

Shortcut Trick

The first 7 odd prime numbers are 3, 5, 7, 11, 13, 17, and 19.

Sum = 3 + 5 + 7 + 11 + 13 + 17 + 19 = 75

Mean = Sum ÷ Count

⇒ Mean = 75 ÷ 7 = 10.714...

∴ The correct answer is 10.71.

Alternate Method

Given:

We need to find the mean of the first 7 odd prime numbers.

Formula Used:

Mean = (Sum of observations) ÷ (Number of observations)

First 7 Odd Prime Numbers

3 5 7 11 13 17 19

Sum = 75 Mean = 75 ÷ 7 ≈ 10.71

Calculations:

⇒ A prime number has exactly two factors: 1 and itself.

⇒ 2 is the only even prime number, so odd primes start from the number 3.

⇒ The first 7 odd prime numbers are: 3, 5, 7, 11, 13, 17, and 19.

⇒ Total number of observations = 7

⇒ Sum of observations = 3 + 5 + 7 + 11 + 13 + 17 + 19

⇒ Sum of observations = 75

⇒ Mean = 75 ÷ 7

⇒ Mean ≈ 10.714...

∴ The correct answer is 10.71.

Additional Information

Prime Numbers

A natural number greater than 1 with exactly two distinct factors: 1 and itself. Example: 2, 3, 5, 7, 11.

Even vs Odd Primes

The number 2 is the only even prime number. Every other prime number is odd.

Averages (Mean)

The arithmetic mean is defined as the sum of all values divided by the total count of values.

Given: 

 If 2 is added to each odd digit and 2 is subtracted from each even digit in the number 485136785:

 

Second from the left is 6 and third from the right is 9 = 9 - 6 = 3

 The difference between the digits which are second from the left and third from the right is '3'.

The correct answer is 'sodium carbonate'.

Key Points

• When baking powder is heated or mixed in water, CO₂ gas is produced.
• When baking powder is heated or mixed with water it evolves carbon dioxide gas which gets converted into sodium carbonate.
• The chemical reaction is as followed \(\mathrm{NaHCO}_3 \rightarrow \mathrm{Na}_2 \mathrm{CO}_3+\mathrm{CO}_2+\mathrm{H}_2 \mathrm{O}\).
• When sodium hydrogen carbonate is dissolved in water, it slightly gets hydrolyzed.

Given:

 letter and symbol series:

(Left) E # R & H & @ J & M N # B & V & & D # P @ W % & Q & A % & # E & (Right)

If all the symbols are dropped from the series:

 Then, third from the left is H.

 

The correct answer is 'H'.

Shortcut Trick

Find mid-points: 5, 15, 25, 35, 45.

Total frequency ∑f = 41 + x.

Sum of (Frequency × Mid-point) = 60 + 240 + 150 + 245 + 45x = 695 + 45x.

Apply Mean formula: 22 × (41 + x) = 695 + 45x ⇒ 902 + 22x = 695 + 45x ⇒ 207 = 23x.

∴ The correct answer is 9.

Alternate Method

Given:

Mean (&bar;x) = 22

Class Intervals and Frequencies (f): 0-10 (12), 10-20 (16), 20-30 (6), 30-40 (7), 40-50 (x)

Formula Used:

Arithmetic Mean (&bar;x) = ∑f_ix_i / ∑f_i, where x_i is the class mark (mid-value).

Calculations:

⇒ Sum of frequencies (∑f_i) = 12 + 16 + 6 + 7 + x = 41 + x

⇒ Sum of product (∑f_ix_i) = (12 × 5) + (16 × 15) + (6 × 25) + (7 × 35) + (x × 45)

⇒ ∑f_ix_i = 60 + 240 + 150 + 245 + 45x = 695 + 45x

⇒ Mean = ∑f_ix_i / ∑f_i

⇒ 22 = (695 + 45x) / (41 + x)

⇒ 22 × (41 + x) = 695 + 45x

⇒ 902 + 22x = 695 + 45x

⇒ 902 − 695 = 45x − 22x

⇒ 207 = 23x

⇒ x = 207 ÷ 23

⇒ x = 9

∴ The correct answer is 9.

Additional Information

Assumed Mean Method

It simplifies calculation for large data: &bar;x = A + (∑f_id_i / ∑f_i), where A is the assumed mean and d_i = x_i − A.

Empirical Relationship

The relationship between the three measures of central tendency is: 3 Median = Mode + 2 Mean.

Class Mark

The class mark of a class interval is the average of its upper and lower limits: (Upper Limit + Lower Limit) ÷ 2.

Given:

letter, number, symbol series:

(Left) N 3 F P # 1 C B 5 $ L Q 6 & N 8 D @ K 9 R (Right)

symbols are there which are immediately preceded by a letter and also immediately followed by a number:

Letter → Symbols → Number

 

The correct answer is '1'.$

The correct answer is 'Nagar Panchayat'.

Key Points

• The 74^th Amendment Act of 1992 provides for the constitution of the following three types of municipalities in every state:

1. Nagar Panchayat - For Transitional area, i.e., an area in transition from a rural area to an urban area.
2. Municipal Council- For smaller urban areas, as specified by state legislation.
3. Municipal Corporation- For larger urban area that is an area of population of more than 1 million.

Additional Information

74^th Amendment Act of 1992:

• This act added a new Part IX-A- 'The Municipalities' to the constitution of India.
• The new part consists of provisions from Articles 243-P to 243-ZG.
• The Act also added a new Twelfth Schedule to the constitution.
• This Schedule contains 18 functional items of municipalities and deal with Article 243-W.

The correct answer is 'Search engines and internet'.

Key Points

• The right to be forgotten allows a person to seek deletion of private information from the internet.
• It has been acknowledged by the Supreme Court in its 2017 landmark judgement as a facet of the right to privacy.

The correct answer is 'Odisha and Chhattisgarh'.

Key Points

• Red and Yellow soils can be easily found in the parts of Odisha, Chhattisgarh, Maharashtra, Southern Karnataka, Tamil Nadu, Madhya Pradesh, and Rajasthan.
• Due to higher degree of hydration of ferric oxide the soil acquired yellow color.
• Red color is due to the diffusion of iron in crystalline and metamorphic rocks.
• The pH of this type of soil ranges between 5.5 to 8.5.

The correct answer is 9 cm.

Key Points

• The New Cartesian Sign Convention has several rules:
• The object is always placed to the left of the mirror.
• This means all distances measured to the right of the mirror (along + x-axis) are taken as positive, while those measured to the left are taken as negative.
• The heights measured upwards and perpendicular to the principal axis are taken as positive.
• Those measured downwards are taken as negative.
• For a spherical mirror (convex or concave), the radius of curvature (R) is twice the focal length (f).
• This is expressed in the mirror formula as R = 2f.
• Given that the centre of curvature (which equals the radius of curvature) of a convex mirror is located at +18 cm, the focal length would be half of this.
• However, because the mirror is convex, the focus is virtual and is found on the same side as the light being reflected.
• According to the New Cartesian Sign Convention, this side of the mirror is the negative side.
• So, the focus of the mirror would be at 9 cm.

Given:

There are 88 mobile phones, each of separate brands, arranged in a straight row at a mobile centre.

 \

The K brand mobile is 47^th from the left side of the row and the M brand mobile is 34^th from the right side of the row. 

 

→ 47^th  = 47 

→34^th = 54 

Then, 54 -47 = 7 

 

​

Mobile phones are between K and M brands are '7'.

The correct answer is '1^st to 8^th March'.

Key Points

• International Women's Day is celebrated on 8^th March every year.
• It was officially announced by the United Nations in 1977.
• It is one of the important days of the year:

1. Celebrate women's achievements.
2. Raise awareness about women's equality.
3. Celebrate tech women and innovation.
4. Applaud equality for women in sports.
5. Educate women on health choice decisions.
6. Forge women's empowerment worldwide.

Additional Information

• There are three colors that symbolize International Women's Day.

1. Purple signifies justice and dignity.
2. Green symbolizes hope.
3. White represents purity.

• The colors originated from the Women's Social and Political Union (WSPU) in the UK in 1908.

Shortcut Trick Identify the last digit: 9. The square root must end in 3 or 7. Group the digits: 745 | 29. Find the nearest square smaller than 745. 272 = 729 and 282 = 784. Since 729 < 745, the first two digits are 27. Possible answers are 273 or 277. Since 745 is closer to 729 than 784, the answer is the smaller one. ∴ The correct answer is 273.

Alternate Method Given: Number = 74529 Formula Used: Long Division Method for Square Root ⇒ Step 1: Pair digits from right to left: 7, 45, 29. ⇒ Step 2: 22 = 4. 7 − 4 = 3. Bring down 45. New dividend = 345. ⇒ Step 3: Double 2 to get 4. Find x such that 4x × x ≤ 345. Let x = 7. ⇒ Step 4: 47 × 7 = 329. 345 − 329 = 16. Bring down 29. New dividend = 1629. ⇒ Step 5: Double 27 to get 54. Find y such that 54y × y = 1629. Let y = 3. ⇒ Step 6: 543 × 3 = 1629. Remainder is 0. ∴ The correct answer is 273.

Additional Information Unit Digit Property If a perfect square ends in 9, its square root must end in either 3 or 7 because 32 = 9 and 72 = 49. Range Estimation To estimate, check 2002 = 40,000 and 3002 = 90,000. The result must lie between 200 and 300. Digital Sum Test Digital sum of 74529 is 7+4+5+2+9 = 27 → 9. Digital sum of 273 is 12 → 3. Since 32 = 9, the answer is consistent.

Shortcut Trick

Put θ = 45° to find the value of the expression directly.

First term: √[ (sec²45° + cosec²45°) ÷ (tan²45° − sin²45°) ] = √[ (2 + 2) ÷ (1 − 1/2) ] = √[ 4 ÷ (1/2) ] = √8 = 2√2

Second term: [ (1 + tan²45°) sin²45° ] ÷ [ (cosec 45° − cot 45°)(1 + cos 45°) ] = [ 2 × (1/2) ] ÷ [ (√2 − 1)(1 + 1/√2) ] = 1 ÷ [ (√2 − 1)(√2 + 1)/√2 ] = 1 ÷ [ (2 − 1)/√2 ] = √2

Multiplying both terms: 2√2 × √2 = 4

Checking options for θ = 45°: cosec²45° sec²45° = 2 × 2 = 4

∴ The correct answer is cosec²θ sec²θ.

Alternate Method

Given:

The trigonometric expression is: \(\sqrt {\frac{{{\rm{se}}{{\rm{c}}^{\rm{2}}}{\rm{\theta }},,{\rm{ + }},,{\rm{cose}}{{\rm{c}}^2}{\rm{\theta }}}}{{{{\tan }^2}{\rm{\theta }} - ,{{\sin }^2}{\rm{\theta }}}}} , \times ,,\frac{{\left( {1 + {{\tan }^2}{\rm{\theta }}} \right),{{\sin }^2}{\rm{\theta }}}}{{\left( {{\rm{cosec}},{\rm{\theta }},{\rm{ - }},{\rm{cot}},{\rm{\theta }}} \right)\left( {1 + \cos ,{\rm{\theta }}} \right)}}\)

Formula Used:

1. sec²θ + cosec²θ = sec²θ cosec²θ
2. tan²θ − sin²θ = tan²θ sin²θ
3. 1 + tan²θ = sec²θ
4. cosec θ − cot θ = (1 − cos θ) ÷ sin θ

Calculations:

⇒ Simplify the term inside the square root:

⇒ Num = sec²θ + cosec²θ = 1/cos²θ + 1/sin²θ = (sin²θ + cos²θ)/(sin²θ cos²θ) = 1/(sin²θ cos²θ) = sec²θ cosec²θ

⇒ Den = tan²θ − sin²θ = sin²θ/cos²θ − sin²θ = sin²θ (1/cos²θ − 1) = sin²θ tan²θ

⇒ Square root term = √[ (sec²θ cosec²θ) ÷ (sin²θ tan²θ) ] = (sec θ cosec θ) ÷ (sin θ tan θ) = [ (1/cos θ)(1/sin θ) ] ÷ [ sin θ (sin θ/cos θ) ] = 1/(sin³θ)

⇒ Simplify the second term:

⇒ Num = (1 + tan²θ) sin²θ = sec²θ sin²θ = sin²θ/cos²θ = tan²θ

⇒ Den = (cosec θ − cot θ)(1 + cos θ) = [ (1 − cos θ)/sin θ ] × (1 + cos θ) = (1 − cos²θ)/sin θ = sin²θ/sin θ = sin θ

⇒ Second term = tan²θ ÷ sin θ = sin²θ/(cos²θ sin θ) = sin θ/cos²θ

⇒ Multiplying both simplified terms:

⇒ Result = [ 1/(sin³θ) ] × [ sin θ/cos²θ ] = 1/(sin²θ cos²θ) = cosec²θ sec²θ

∴ The correct answer is cosec²θ sec²θ.

Additional Information

Trigonometric Identity for Sum and Product

The sum of squares of secant and cosecant is equal to their product: sec²θ + cosec²θ = sec²θ cosec²θ.

Trigonometric Identity for Difference and Product

The difference of squares of tangent and sine is equal to their product: tan²θ − sin²θ = tan²θ sin²θ.

Reciprocal Conjugate Property

cosec θ − cot θ is the reciprocal of cosec θ + cot θ, which helps simplify rational expressions containing trigonometric ratios.

The correct answer is 'Five'.

Key Points

• To carry out talent identification, the country has been divided into five zones.
• The five zones are namely, North, East, West, South, and North-East Zones.

Additional Information

• The 'Khelo India' programme has been introduced to revive the sports culture in India at the grass-root level by building a strong framework for all sports played in our country and establishing India as a great sporting nation.
• It was launched by PM Narendra Modi on 27 February 2019, at the Youth Indian Parliament in Vigyan Bhawan, New Delhi
• The 'Khelo India' programme consists of 12 components.
• Among them is the 'Talent search and Development'.

Statement: Country B has been importing 80% of its crude oil and petroleum from country Y for a few decades now to fulfil their fuel needs. However, owing to the current financial crisis in country Y, it exports the crude oil and petroleum to other countries at 30% higher prices now.

Conclusion I: The car resale industry in country B will be on verge of a total shut down in the coming months - False

(This is not the permanent solution, As, Country B has been importing 80% of its crude oil and petroleum from country Y for a few decades now to fulfil their fuel needs. So, it will not shut down in the coming months and also not mentioned in the statement) 

So, Conclusion I does not follow.

Conclusion II: Country B will increase fuel tax by 30% - False

(This is not the permanent solution, As, it exports the crude oil and petroleum to other countries at 30% higher prices now as mentioned in the statement).

So, Conclusion II does not follow.

Thus, 'Neither I nor II can be concluded from the given information'.

Shortcut Trick Sum of roots (S) = −2/3 + (−3/2) = −13/6 Product of roots (P) = (−2/3) × (−3/2) = 1 For roots of the form −a/b and −b/a, the quadratic equation is (ab)x2 + (a2 + b2)x + (ab) = 0. Substituting a = 2, b = 3: (2×3)x2 + (22 + 32)x + (2×3) = 0 ⇒ 6x2 + 13x + 6 = 0. ∴ The correct answer is 6x2 + 13x + 6 = 0.

Alternate Method Given: First root (α) = −2/3 Second root (β) = −3/2 Formula Used: A quadratic equation with roots α and β is given by: x2 − (α + β)x + αβ = 0 Calculations: ⇒ Sum of roots (α + β) = (−2/3) + (−3/2) ⇒ Sum = (−4 − 9) ÷ 6 = −13/6 ⇒ Product of roots (αβ) = (−2/3) × (−3/2) = 6/6 = 1 ⇒ The required equation is: x2 − (−13/6)x + 1 = 0 ⇒ x2 + (13/6)x + 1 = 0 ⇒ 6x2 + 13x + 6 = 0 ∴ The correct answer is 6x2 + 13x + 6 = 0.

Additional Information Relationship between Roots and Coefficients For an equation ax2 + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a. Nature of Roots The nature is determined by the Discriminant (D) = b2 − 4ac. If D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are imaginary. Quadratic Formula The roots of ax2 + bx + c = 0 can be found using x = [−b ± √(b2 − 4ac)] ÷ 2a.

Given:

13 + 6 ÷ 12 - 4 × 5 = 4

Calculation:

13 + 6 ÷ 12 - 4 × 5 

Case 1: 

13 ÷ 6 + 12 - 4 × 5 

2.16 + 12 - 4×5

2.16 + 12 - 20

14.16 - 20 

-5.84

Case 1 is not applicable. 

Case 2: 

13 + 6 - 12 ÷ 4 × 5

13+ 6 - 3 × 5

13+ 6 - 15 

19- 15

Case 2 is applicable.

Thus, two signs should be interchanged is ' ÷ and -'.

the correct answer is 'Sanskrit'.

Key Points

• The 8^th schedule of the Indian constitution consists of languages to be used by states for official purposes.
• This schedule consists of 22 languages.
• There are 6 languages so far considered as classical languages:

1. Tamil in 2004,
2. Sanskrit in 2005,
3. Telugu in 2008,
4. Kannada in 2008,
5. Malayam in 2013,
6. Odia in 2014.

Additional Information

• The following criteria were laid down to find the eligibility of languages to be classified as classical language.

1. ​High antiquity of its early texts in history over a period of 1500-2000 years.
2. A body of ancient literature that is considered a valuable heritage by generations of speakers.
3. The literary tradition is original and not borrowed from another speech community.
4. The classical language and literature being distinct from modern, there may also be a discontinuity between the classical language and its later forms or its offshoots.

The correct answer is 'Si'.

Key Points

• Silicon is a Non-Metal, it is a Metalloid.
• The elements that show properties that are intermediate between metals and non-metals are called metalloids.
• Metalloid lies at the borderline between metals and non-metals.
• Metalloids have nonmetallic chemical properties in general.
• Metalloids are usually **too brittle to have any structural uses.**​

Additional Information

• Silicon is a chemical element atomic number 14.
• Silicon is mainly used in computer chips as it is a semiconductor.
• Silicon in silicones can be used as a waterproof sealant on roofs, around water pipes.
• It was iscovery by Jons Jacob Berzelius in 1823. Silicon was named by Thomas Thomson in 1817.

The Correct answer is Only (i) and (ii).

Key Points

• Element X combines with chlorine to form the compound XCl.
• Since X is placed on the left side of the periodic table, it is likely to be an alkali metal (Group 1).
• Alkali metals have one valence electron, which they readily lose to form a positive ion (X⁺).
• Alkali metals are known to be metals and solids at room temperature.
• Therefore, the statements (i) and (ii) are correct for element X.

Additional Information

• Option (iii):
• Non-metals that are gases at room temperature are typically found on the right side of the periodic table (e.g., oxygen, nitrogen).
• Since element X is on the left side, it is unlikely to be a non-metal or a gas.
• Option (iv):
• Elements with five valence electrons belong to Group 15 of the periodic table (e.g., nitrogen, phosphorus).
• These elements are not found on the left side of the periodic table, hence this option is incorrect for element X.

Given:

Six classmates L, M, N, O, P and Q compare the IGCSE results of their final exam. Each of them scored different marks.

According to given information, we have the possible arrangements as follows:

1. O scored more than N but less than L:

 L > O > N

2. P scored less than N but more than Q. L scored less than M. M scored more than N

M > L > O > N > P > Q

After combining all the arrangements, we get:

M > L > O > N > P > Q

 Among the six 'M' scored the most.

Given:

188, 187, 183, 174, 158,?

The logic in this pattern is:

 

The correct answer is '133'.

The correct answer is 'Independence Day'.

Key Points

• The Prime Minister hoists the National Flag of India at the Red fort in old Delhi on Independence Day.
• India becomes Independent on 15^th August 1947.
• On that day the British flag flying on the Red fort was removed and India's national flag was hoisted.
• Pandit Jawaharlal Nehru, The first Prime Minister of India hoisted the flag on this day.
• since then, every year the Prime Minister hoists the flag on Red fort and addresses the nation.

Shortcut Trick

Time for P = 18 × (4/3) = 24 hours; Time for Q = 12 × (5/3) = 20 hours.

LCM(24, 20) = 120 (Total Capacity). Efficiencies: P = 5, Q = 6.

In 4 hours, water filled = (5 + 6) × 4 = 44 units.

Efficiency of R = 44 ÷ 5.5 = 8 (Emptying).

Combined efficiency (P + Q − R) = 5 + 6 − 8 = 3. Time = 120 ÷ 3 = 40 hours.

∴ The correct answer is 40 hr.

Alternate Method

Given: P fills 3/4 in 18 hrs; Q fills 3/5 in 12 hrs. R empties filled part in 5.5 hrs.

⇒ Full time for P = 18 × (4/3) = 24 hours

⇒ Full time for Q = 12 × (5/3) = 20 hours

⇒ Work done by P and Q in 4 hours = (5 + 6) × 4 = 44 units

⇒ Efficiency of R (Emptying) = 44 ÷ (11/2) = 44 × (2/11) = 8 units/hr

⇒ Net efficiency (P + Q + R) = 5 + 6 − 8 = 3 units/hr

⇒ Total time required = 120 ÷ 3 = 40 hours

∴ The correct answer is 40 hr.

Additional Information

Pipes and Cisterns Efficiency

Efficiency is inversely proportional to time. Filling pipes have positive efficiency while emptying pipes (leaks) have negative efficiency.

Net Work Done

Total Work = Net Efficiency × Total Time. If the net efficiency is positive, the tank fills; if negative, the tank empties.

Drawing the diagram according to the given information,

1. Sharad walks 4 km towards the west and then turns right and walks 5 km. 2.  Again, he turns left and walks 7 km. 3. Finally, he turns to his left and walks 5 km. 

 

Hence, he is '11 km' far from the starting point.

The correct answer is '10'.

Key Points

• 10 teams are scheduled to play in the 15^th edition of the Indian Premier League, in 2022.
• In this edition**, Gujrat Titans defeated Rajasthan Royals by 7 wickets.**
• CVC Captain partners own the franchise.
• The team played under the captaincy of Hardik Pandey and was coached by Ashish Nehra.
• It was the maiden IPL for Gujrat Titans.
• The final match took place at Narendra Modi Stadium, in Ahmedabad.

Additional Information

• Tata Group was declared the official sponsor of the Indian Premier League, 2022.
• Tata Group will also be the title sponsor of IPL, 2023.

The correct answer is 'Paternal and maternal DNA'.

Key Points

• Genes carry the information that determines your traits (say: trates), which are features or characteristics that are passed on to you — or inherited — from your parents.
• Each cell in the human body contains about 25,000 to 35,000 genes.
• DNA, or deoxyribonucleic acid, is the hereditary material in humans and almost all other organisms. Nearly every cell in a person's body has the same DNA.

Shortcut Trick

For any quadrilateral ABCD, the angle formed by the bisectors of two adjacent angles (say, ∠C and ∠D) is equal to half the sum of the other two angles (∠A and ∠B):

∠DOC = (∠A + ∠B) ÷ 2

⇒ ∠DOC = (86° + 72°) ÷ 2

⇒ ∠DOC = 158° ÷ 2 = 79°

∴ The correct answer is 79°.

Alternate Method

Given:

In quadrilateral ABCD, ∠A = 86° and ∠B = 72°.

The bisectors of ∠C and ∠D meet at O.

Formula Used:

1. Sum of interior angles of a quadrilateral = 360°
2. Sum of angles of a triangle = 180°

Calculations:

In quadrilateral ABCD, the sum of all interior angles is 360°:

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ 86° + 72° + ∠C + ∠D = 360°

⇒ 158° + ∠C + ∠D = 360°

⇒ ∠C + ∠D = 360° − 158°

⇒ ∠C + ∠D = 202°

Since OC and OD are the angle bisectors of ∠C and ∠D respectively:

⇒ ∠OCD = ∠C ÷ 2

⇒ ∠ODC = ∠D ÷ 2

In ΔDOC, the sum of angles is 180°:

⇒ ∠DOC + ∠OCD + ∠ODC = 180°

⇒ ∠DOC + (∠C ÷ 2) + (∠D ÷ 2) = 180°

⇒ ∠DOC + (∠C + ∠D) ÷ 2 = 180°

⇒ ∠DOC + 202° ÷ 2 = 180°

⇒ ∠DOC + 101° = 180°

⇒ ∠DOC = 180° − 101°

⇒ ∠DOC = 79°

Option Analysis:

• Option (1) 91°: Incorrect, as this would imply the sum of ∠C and ∠D is 178°, which does not satisfy the quadrilateral angle sum property with the given ∠A and ∠B.

• Option (2) 69°: Incorrect, as this would require the sum of ∠C and ∠D to be 222°, which is mathematically inconsistent with the given values.

• Option (3) 101°: Incorrect, as 101° is the value of half the sum of ∠C and ∠D, not the angle ∠DOC itself.

• Option (4) 79°: Correct, as calculated using the angle sum properties of quadrilaterals and triangles.

∴ The correct answer is 79°.

Additional Information

Angle Bisector Theorem in Quadrilaterals

The angle formed by the bisectors of two adjacent angles of a quadrilateral is equal to half the sum of the remaining two angles. For example, ∠DOC = (∠A + ∠B) ÷ 2.

Sum of Interior Angles of a Polygon

The sum of the interior angles of any n-sided polygon is given by the formula (n − 2) × 180°. For a quadrilateral (n = 4), the sum is (4 − 2) × 180° = 360°.

Angle Bisectors of Opposite Angles

If the bisectors of opposite angles of a quadrilateral (say, ∠A and ∠C) intersect, the angle between them is equal to half the difference of the other two angles: |∠B − ∠D| ÷ 2.

Given:

 Digits in the number 417593286 is arranged in ascending order from left to right.

Digits that will remain unchanged as compared to that in the original number is 1.

Hence, the correct answer is Option (2).

Shortcut Trick

For a mean proportion 3.2 : x :: x : 16.2, we use the property x² = a × b.

x = √(3.2 × 16.2)

x = √(32 × 162 ÷ 100) = √(16 × 2 × 81 × 2 ÷ 100)

x = (4 × 2 × 9) ÷ 10 = 72 ÷ 10 = 7.2

∴ The correct answer is 7.2.

Alternate Method

Given: 3.2 : x :: x : 16.2

Formula Used: Product of Means = Product of Extremes

⇒ x × x = 3.2 × 16.2

⇒ x² = 51.84

⇒ x = √51.84

⇒ x = 7.2

∴ The correct answer is 7.2.

Additional Information

Mean Proportion

If a, b, and c are in continued proportion such that a : b :: b : c, then b is the mean proportional to a and c, where b = √(ac).

Third Proportional

If a : b :: b : c, then c is called the third proportional to a and b, calculated as c = b² ÷ a.

Fourth Proportional

If a : b :: c : d, then d is the fourth proportional to a, b, and c, calculated as d = (b × c) ÷ a.

The pattern followed here is:

Therefore, the correct answer is '48U36'.

Statements:

Some woods are charcoals

Some petrol is diesel

All diesel are fossils

Conclusions :

(I) Some petrol are charcoals → False (No direct relationship is given between petrol and charcoals, so it may be possible but not defined)

(II) Some fossils are petrol → True (Some petrol is diesal and all diesal are fossils, so some fossils are petrol)

(III) Some woods are diesel → False (No direct relationship is given between woods and diesel, so it may be possible but not defined)

Hence, 'Only conclusion II follows'.

According to the given information, we have the following possible arrangements:

1) Q is taller than T but shorter than U

U > Q > T

2) U is shorter than P

U < P

3) R is taller than only three other friends and T is taller than only one friend

-- > -- > R > Q > T > S

After combining all the arrangements, we get

P > U > R > Q > T > S

Therefore, 'U' is the second tallest among all the friends.

The correct answer is 'Directive principles of state policy'.

Key Points

• The main feature borrowed from the constitution of  Ireland is the Directive principles of state policy in 1937, but the idea was generated in Spain.
• DPSP are an integral part of Indian Constitution and is listed in Part IV, article 36- 51.
• DPSP are non-justiciable in nature.
• The Sapru community in 1945 suggested two categories of individual rights i.e. Justiciable and non-justiciable rights.
• The instrument and instructions from GOI Act 1935 were taken as DPSP in the constitution.

Alphabetic series 

LOVABLE

Such pair is AB.

Thus, the correct answer is '1'.

The correct answer is 'i - b, ii - d, iii - c, iv - e, v - a'

Key Points

• The formula of Benzene is C₆H_6.
• The formula of Ethylene is H₂C=CH₂.
• The formula of Acetaldehyde is CH₃-CHO.
• The formula of Acetone is CH₃COCH₃.
• The formula of Ethane is CH₃CH₃.

Total exports of Company B

22.6 + 32.1 + 30.6 + 34.5 + 32.4 + 38.6 + 45.3 = 236.1

⇒ Average exports of Company B = 33.73

Total exports of Company C

21.9 + 29.4 + 37.8 + 33.2 + 34.2 + 47.3 + 42.4 = 246.2

⇒ Average exports of Company C = 35.17

Required percentage = [(33.73) / (35.17)] × 100 = 95.90%

The correct answer is 'Stethoscope'.

Key Points

• Heartbeat is the periodic signal resulting from double circulation.
• It is caused by relaxation and contraction of heart muscles.
• The instrument used to measure heartbeat:
• A stethoscope is used as an instrument to measure heartbeat.
• The normal heart rate of a human being is 72 beats per minute.

Shortcut Trick

Each term in the expression follows the pattern (A × var − B) ÷ var = A − (B ÷ var).

The equation simplifies to: (15 − 9/x) + (15 − 9/y) + (15 − 9/z) = 0.

Combine constants: (15 + 15 + 15) − 9(1/x + 1/y + 1/z) = 0 ⇒ 45 = 9 × Sum.

Direct Calculation: Sum of reciprocals = 45 ÷ 9 = 5.

∴ The correct answer is 5.

Alternate Method

Given:

((15x − 9)/x) + ((15y − 9)/y) + ((15z − 9)/z) = 0

Formula Used:

Algebraic expansion: (a − b)/c = (a/c) − (b/c)

Calculations:

⇒ (15x/x − 9/x) + (15y/y − 9/y) + (15z/z − 9/z) = 0

⇒ (15 − 9/x) + (15 − 9/y) + (15 − 9/z) = 0

⇒ 15 + 15 + 15 − 9/x − 9/y − 9/z = 0

⇒ 45 − 9(1/x + 1/y + 1/z) = 0

⇒ 9(1/x + 1/y + 1/z) = 45

⇒ (1/x + 1/y + 1/z) = 45 ÷ 9

⇒ 1/x + 1/y + 1/z = 5

∴ The correct answer is 5.

Additional Information

Fraction Splitting Rule

For any expression (ax + b)/x, it can be decomposed into a + b/x. This is a fundamental technique for simplifying algebraic fractions.

Sum of Reciprocals

In symmetric equations involving variables x, y, and z, the sum of reciprocals (1/x + 1/y + 1/z) often appears as a consolidated term after simplification.

Linear Symmetry

When variables appear in identical structures within an equation, the system is symmetric, and the variables often share a common relationship to the final constant.

The correct answer is 'KAVACH'.

Key Points

• 'Kavach' system is an anti-collision test conducted by the Indian Railways to check the indigenous development system to avoid rail accidents.
• This will be the world's cheapest automatic train collision protection system.
• It will cost 50 lakh rupees per kilometer to operate compared to about 2 crore rupees worldwide.

Additional Information

• The test involved two trains -  one with the railway minister on board and the other with the chairman of the Railway Board - hurtling towards each other at full speed.
• 'Kavach' automatically stopped the train before 380 meters of other Locomotive at the front.

The correct answer is 'Bharat Financial Inclusion Limited'.

Key Points

• The Board of Directors of IndusInd Bank Ltd. (“IndusInd”) and the Board of Directors of Bharat Financial Inclusion Limited at their respective meetings held today, have approved a merger of the two entities to create a stronger and more sustainable platform for Financial Inclusion.
• The merger will be effected through an all-stock transaction of Bharat Financial Inclusion Limited into IndusInd through a Composite Scheme of Arrangement (“Scheme”).
• The Scheme contemplates merger of Bharat Financial with IndusInd and simultaneous transfer of Bharat Financial Inclusion Limited’s Business Correspondent operations into a Wholly Owned Subsidiary of IndusInd, which shall be incorporated after receipt of requisite regulatory approvals (“BC-WOS”).

The correct answer is '(c) - A coil and a bar magnet moving in the same direction with the same speed'.

Key Points

• Faraday's law of electromagnetic induction states that when the magnetic flux linked with a coil changes, an emf is induced in it.
• It is clear that in all given methods, magnetic flux linked with coil is changing, therefore voltage will induce in coil by all the given methods.

.The correct answer is 'carbon'.

Key Points

• Carbon shows catenation to a maximum extent because of its electronic configuration and tendency to form strong covalent bonds.
• Strength of Carbon-Carbon Bonds: The carbon-carbon (C-C) bond is very strong, making carbon chains and rings stable under a wide range of conditions. This stability is critical for the existence of long-chain molecules, which are ubiquitous in organic compounds..
• Versatility of Carbon Compounds: The capacity for catenation, combined with the ability of carbon to form stable bonds with other elements such as hydrogen, oxygen, nitrogen, and sulfur, leads to an extraordinary variety of compounds. This diversity is the basis of organic chemistry and is crucial for the biochemical processes of living organisms.
• The bond energy of C-C bond is greater than N-N bond and thus catenation in nitrogen is restricted to 2 or 3 nitrogen atoms.

The correct answer is 'Phosphorus'.

Key Points

• ADP is continually converted to ATP by the addition of a phosphate during the process of cellular respiration.
• ATP carries much more energy than ADP.
• As the cell requires more energy, it uses energy from the breakdown of food molecules to attach a free phosphate group to an ADP molecule in order to make ATP.

The correct answer is 'option3'.

Key Points

• After reflection, a ray of light incident parallel to the principal axis passes through the focus in case of a Convex lens.

Given: 

A, B, C, D, W, X, Y and Z are sitting around a square table facing the centre of the table. Some of them are sitting at the corners, while some are sitting at the middle of the sides.

Solution:

(1) C sits at one of the corners.

(2)  C sits third to the left of W.

(3)  A does not sit at any of the corners.

(4) A is not an immediate neighbour of C.

(5)  Y sits second to the right of A.

(6) Only three people sit between B and D.

(7)  B is an immediate neighbour of Z.

• It is possible only in Case 1.

(8) X will be sit on unoccupied seat.

Here, A sits second to the left of Y.

Hence, 'option 4' is the correct answer.

Shortcut Trick

Venkat's present age = 21 − 12 = 9 years.

Suman's age is twice Venkat's age.

Suman's present age = 9 × 2 = 18 years.

∴ The correct answer is 18 years.

Alternate Method

Given:

Suman's present age (S) = 2 × Venkat's present age (V)

Venkat's age after 12 years = 21 years

Calculations:

⇒ V + 12 = 21

⇒ V = 21 − 12

⇒ V = 9 years

⇒ S = 2 × V

⇒ S = 2 × 9

⇒ S = 18 years

∴ The correct answer is 18 years.

Additional Information

Ages in Ratio

If the ratio of ages of A and B is x:y, their ages can be assumed as xk and yk respectively.

Age After 'n' Years

If the present age is 'x', then the age after 'n' years will be (x + n).

Age 'n' Years Ago

If the present age is 'x', then the age 'n' years ago was (x − n).

The correct answer is 'Barchan'.

Key Points

• Barkhans are produced by the action of wind in one direction.
• They are created in the desert when huge amounts of sands are complemented by the supply of steady wind from one direction.
• The change in the direction of the wind and the amounts of sands determine the shapes of the sand dune.
• Barkhans constitute a crescent-shaped sand dune.
• The term was coined in 1881 by Russian naturalist Alexander von Middendorf.
• Barkhans are spelled synonymously with barchans, these crescent-shaped sand dunes are created by the direction of continuous wind coming from one side. Barchan’s convex side is towards the direction of the wind.
• In India, they are commonly found in That desert, Rajasthan.

Shortcut Trick

Total Capacity (LCM of 60, 30) = 60 units.

Efficiency of A = 1 unit/min; Efficiency of B = 2 units/min.

Average efficiency per minute = (Efficiency of B + Combined efficiency of A & B) ÷ 2

Average efficiency = (2 + 3) ÷ 2 = 2.5 units/min.

Time required = Total capacity ÷ Average efficiency = 60 ÷ 2.5 = 24 minutes.

∴ The correct answer is 24 min.

Alternate Method

Given: Filling time for A = 60 min, B = 30 min. For half time (t/2) only B works, for remaining (t/2) both A and B work.

Formula Used: Total Work = Efficiency × Time

⇒ Total capacity = LCM(60, 30) = 60 units.

⇒ Efficiency of Pipe A = 60 ÷ 60 = 1 unit/min.

⇒ Efficiency of Pipe B = 60 ÷ 30 = 2 units/min.

⇒ Efficiency of (A + B) = 1 + 2 = 3 units/min.

⇒ Let the total time be t minutes.

⇒ (t/2) × (Efficiency of B) + (t/2) × (Efficiency of A + B) = 60

⇒ (t/2) × 2 + (t/2) × 3 = 60

⇒ t + 1.5t = 60

⇒ 2.5t = 60

⇒ t = 60 ÷ 2.5 = 24 minutes.

∴ The correct answer is 24 min.

Additional Information

Pipes & Cisterns Efficiency

Efficiency is inversely proportional to time. If a pipe fills a tank in x hours, its efficiency is 1/x per hour.

Combined Efficiency Rule

When multiple pipes work together, their individual efficiencies are added. For inlet pipes it is positive, and for outlet/leakage pipes it is negative.

Alternate Work Pattern

In problems where pipes work for specific durations, calculate the work done in one complete cycle or specific time slots before summing to equal the total capacity.

The correct answer is 'Connective tissue'. 

Key Points 

• Bone is a type of specialized connective tissue.
• Connective tissues are specialized to connect and anchor Bones.
• They give support to various parts of creating packaging around the organs.
• The tissue is composed of a gel-like intercellular substance called medium or matrix, which forms the main bulk.
• Bones is a porous, highly vascular, mineralized, hard, and rigid.

Additional Information

• Muscular tissue: The muscular system is composed of specialized cells called muscle fibers. Their predominant function is contractibility.
• Epithelial tissue: The epithelium is a type of body tissue that forms the covering on all internal and external surfaces of your body, lines cavities, and hollow organs and is the major issue in glands.
• Nervous tissue: Nervous or nerve tissue is the main tissue of our nervous system. It monitors and regulates the functions of the body.