RRB Group D Previous Year Paper (Held on: 26 Sept 2022 Shift 3)

Shortcut Trick

For Compound Interest over 2 years, the ratio of Amount (A) to Principal (P) is the square of the multiplier (1 + R/100).

Ratio A/P = 11025 ÷ 10000 = 441 ÷ 400

For 1 year, multiplier = √(441 ÷ 400) = 21 ÷ 20

Interest on 1 unit = 21 − 20 = 1 unit

Rate % = (1 ÷ 20) × 100% = 5%

∴ The correct answer is 5%.

Alternate Method

Given:

Principal (P) = ₹10,000

Amount (A) = ₹11,025

Time (n) = 2 years

Formula Used:

A = P(1 + R/100)ⁿ

Calculations:

⇒ 11025 = 10000(1 + R/100)²

⇒ 11025 ÷ 10000 = (1 + R/100)²

⇒ 1.1025 = (1 + R/100)²

⇒ √1.1025 = 1 + R/100

⇒ 1.05 = 1 + R/100

⇒ R/100 = 1.05 − 1

⇒ R/100 = 0.05

⇒ R = 0.05 × 100 = 5%

∴ The correct answer is 5%.

Additional Information

Effective Rate of Interest

For a rate R% compounded annually for 2 years, the effective rate is given by R + R + (R × R) ÷ 100.

CI and SI Difference

The difference between Compound Interest and Simple Interest for 2 years is D = P × (R ÷ 100)².

Rule of 72

To find the approximate time required to double an investment, divide 72 by the annual rate of interest (n ≈ 72 ÷ R).

According to english alphabet series 

The pattern followed here is :

'SOLVE' is coded as 'QRJYC'

Similarly,

 FENCE' is coded as 'DHLFC'

'TASTE' is coded as 'RDQWC'

Hence, the correct answer is "Option 2"

The pattern followed here is :

NALAYAK ∶ KAYALAN 

And,

 BEAUTY ∶ YTUAEB 

Similarly,

 POWERTY ∶ YTREWOP

Hence, the correct answer is "Option 3"

Five girls, A, B, C, D, and E are sitting around a circular table facing the centre. 

• D is second to the right of E.
• C is an immediate neighbour of D and B.
• E is the immediate neighbour of A and B.

A is seated Second to the right of B.

Hence, the correct answer is "Option 4"

The correct answer is ₹3,00,000.

Key Points

• A microfinance loan is defined as a collateral-free loan granted to a household with an annual household income of up to ₹3,00,000 in accordance with Reserve Bank of India (Regulatory Framework for Microfinance Loans) Directions, 2022.
• The term "household" in this context refers to a single family unit, consisting of a husband, wife, and any unmarried children.

Additional Information

• All collateral-free loans supplied to low-income households, defined as households with annual incomes up to ₹3,00,000, will be regarded as microfinance loans, regardless of end use and manner of application, processing, or disbursal (either through physical or digital channels).
• The loan cannot be secured by a lien on the borrower's deposit account in order to maintain the microfinance loan's collateral-free status.
• The REs must have a board-approved policy that allows them to customize the repayment schedule for micro-loans to meet the needs of the borrowers.

Shortcut Trick

To identify a quadratic equation, simplify both sides and check if the highest power (degree) of the variable is exactly 2.

In options (1), (3), and (4), the x² terms on both sides have the same coefficient and will cancel out, leaving linear equations.

In option (2), the cubic terms (x³) cancel out, but the quadratic terms (x²) do not, resulting in a degree of 2.

∴ The correct answer is (x + 2) (x + 2) (x - 1) = x³ + 5x² + 6x + 4.

Alternate Method

Given: Equation (x + 2)(x + 2)(x − 1) = x³ + 5x² + 6x + 4

Formula: A quadratic equation is of the form ax² + bx + c = 0, where a ≠ 0.

⇒ (x + 2)²(x − 1) = x³ + 5x² + 6x + 4

⇒ (x² + 4x + 4)(x − 1) = x³ + 5x² + 6x + 4

⇒ x(x² + 4x + 4) − 1(x² + 4x + 4) = x³ + 5x² + 6x + 4

⇒ x³ + 4x² + 4x − x² − 4x − 4 = x³ + 5x² + 6x + 4

⇒ x³ + 3x² − 4 = x³ + 5x² + 6x + 4

⇒ 3x² − 4 = 5x² + 6x + 4 (Subtracting x³ from both sides)

⇒ 2x² + 6x + 8 = 0

Since the degree of the simplified equation is 2, it is a quadratic equation.

∴ The correct answer is (x + 2) (x + 2) (x - 1) = x³ + 5x² + 6x + 4.

Additional Information

Standard Form

A quadratic equation in the variable x is an equation of the form ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0.

Degree of Polynomials

The degree is the highest power of the variable. Degree 1 is linear, degree 2 is quadratic, and degree 3 is cubic.

Roots of Quadratic Equation

A quadratic equation can have at most two real roots, determined by the discriminant D = b² − 4ac.

Shortcut Trick

Initial amounts of Ram and Shyam are ₹4 and ₹7 respectively.

Initial difference = 7 − 4 = 3 units.

Final ratio = 7 : 9. Final difference = 9 − 7 = 2 units.

Since an equal amount is added, the difference remains constant. Multiply initial values by 2 and final ratio by 3.

New Initial: 8 and 14 | New Final: 21 and 27. Amount added = 21 − 8 = 13 units.

Since we doubled the initial values, 1 unit here corresponds to ₹0.50. Added amount = 13 × 0.5 = ₹6.50.

∴ The correct answer is ₹6.50.

Alternate Method

Given: Initial amount of Ram = ₹4, Initial amount of Shyam = ₹7. Final ratio = 7 : 9.

Formula Used: Ratio = (Initial Value + Addition) ÷ (Initial Value + Addition)

Let the equal amount given by Jatin be x.

⇒ (4 + x) / (7 + x) = 7 / 9

⇒ 9 × (4 + x) = 7 × (7 + x)

⇒ 36 + 9x = 49 + 7x

⇒ 9x − 7x = 49 − 36

⇒ 2x = 13

⇒ x = 13 / 2

⇒ x = 6.5

∴ The correct answer is ₹6.50.

Additional Information

Ratio and Proportion Property

When an equal amount is added to or subtracted from both terms of a ratio, the absolute difference between the terms remains unchanged.

Cross-Multiplication Method

For a/b = c/d, the property ad = bc is used to find an unknown variable in linear equations involving fractions.

The correct answer is Jawaharlal Nehru.

Key Points

• Under Jawaharlal Nehru's leadership, Subhash Chandra Bose founded the National Planning Committee in 1938.
• National Planning Committee
• The intention of the National Planning Committee was to create an economic strategy with the primary objective of guaranteeing an adequate standard of living for the population.
• A fifteen-member National Planning Committee was then established, with the Committee emphasizing in a memo that national independence is a crucial precondition for adopting any actions that may be discovered to be required for implementing the plan in all of its varied components.
• Near the end of 1938, nine years before independence, the Indian National Congress established a National Planning Committee to emphasize the significance of social and economic goals as well as the necessity of learning from other nations' experiences with planned development through national plans.​

Additional Information

• Maulana Abul Kalam Azad
• ​​Abul Kalam Ghulam Muhiyuddin Ahmed bin Khairuddin Al-Hussaini Azad was a senior member of the Indian National Congress, an Islamic theologian, and a supporter of Indian independence. He lived from 11 November 1888 until 22 February 1958.
• Lal Bahadur Shastri​
• Indian politician and leader Lal Bahadur Shastri was born on October 2, 1904, and passed away on January 11, 1966. Between 1961 and 1963, he served as India's sixth home minister and as the country's second prime minister between 1964 and 1966.
• Sardar Vallabhbhai Patel
• Vallabhbhai Jhaverbhai Patel, better known by his stage name Sardar Patel, was an Indian lawyer, prominent political figure, and politician who lived from October 31, 1875, to December 15, 1950. From 1947 until 1950, he was India's first deputy prime minister and home minister.

The correct answer is $\frac{1}{2}$.

Key Points

• The set quantity of water molecules found in one salt formula unit constitutes the water of crystallisation.
• CaSO4. $\frac{1}{2}$H2O  is the plaster of Paris's chemical formula.
• As a result, one plaster of Paris molecule contains $\frac{1}{2}$ water for crystallisation.
• It is also known as calcium sulphate hemihydrate for this reason.

Additional Information

• No water of crystallisation remains at $393 K$, and anhydrous calcium sulphate, CaSO₄, is created instead.
• This is referred to as "dead burned plaster."
• Uses
• Plaster of Paris is mostly used in the building sector, along with plasters.
• When a bone is broken or sprained, it is used to immobilise the damaged area of the organ.
• Additionally, it is used in dentistry, decorative arts, and the casting of statues and busts.

The correct answer is 2013.

Key Points

• In 2013, the state of Uttarakhand saw unusually heavy rain from June 13 to June 17.
• As a result, the Mandakini river erupted and the Chorabari glacier began to melt.
• Large portions of Western Nepal, Himachal Pradesh, and Uttarakhand were also hit by the floods.

Additional Information

• One such glacier is India's Chorabari Glacier, which feeds important rivers like the Ganges.
• This glacier, which is located between the village of Kedarnath and the Kedarnath mountain to the north and south, creates a ferocious stream that finally joins the Ganges River.
• At Rudraprayag, the river Mandakini, which is the most significant river flowing from the Kedarnath peak's slopes, joins the Alaknanda.
• Actually, the Chorabari Glacier's snowmelt feeds the river's springs, which are located around one mile above Kedarnath Temple.

The correct answer is 15-18 times.

Key Points

• An adult human breathes 15 to 18 times per minute on average while at rest. However, the rate of breathing might vary depending on the circumstances.
• When we are working, we breathe more quickly. As a result, the cells can receive enough oxygen as the breathing rate increases with the intensity of the task.
• Approximately 12 to 16 breaths per minute are taken by a healthy adult, according to the University of Rochester Medical Center.
• Children breathe more quickly than adults. An infant, for instance, breathes between 30 and 60 times per minute, while a school-age youngster breathes between 18 and 30 times per minute.

Additional Information

• Respiratory rates:
• The respiratory rate of a person in a resting posture is the same as their resting respiratory rate, which is 15–18 breaths per minute.
• Here, sleeping is the position that leaves you feeling the most rested, whereas watching TV only necessitates a few more breaths.
• While engaging in vigorous physical activity, the respiratory rate rises.
• A brisk walk necessitates moving quickly, which results in a strenuous physical workout and increased respiratory rate.
• Cycling, on the other hand, calls for the use of more muscles than brisk walking does, which raises the respiratory rate needed to give the extra oxygen needed while cycling.

The correct answer is IIT Bombay.

Key Points

• The Union Minister of Education travelled from his home to his workplace on the Energy Swaraj Yatra Bus.
• The bus is outfitted with solar power and is fully functional as both a work and living space.
• The IIT Bombay professor who designed and built the bus, Dr Chetan Singh Solanki, is with the Minister.

Additional Information

• Chetan Singh Solanki is a researcher, educator, innovator, and instructor for the Art of Living's happiness programme.
• The concept of the "Energy Swaraj Yatra" is based on "Gandhian beliefs" in order to combat climate change and maintain the sustainability of the energy supply.
• Due to the emergency status of climate change, public measures are now needed to reduce it.
• The goal of the Energy Swaraj Movement is to raise public knowledge of the issue of climate change and encourage participation in its solution.

According to the given statement

Conclusion I follow this because it provides a suitable explanation for the given statement. (Because it is mentioned that, A has many friends with similar business interest.)

Conclusion II does not follow because nothing about the interest of B is given.

Only conclusion I follow

Hence, the correct answer is "Option 3"

Calculation:

Here, we have (32/243)^k = 8/27 

As, we can write 32 as 2⁵ , 243 = 3⁵ 

Also 8 = 2³ and 27 = 3³

⇒ (2/3)^5k = (2/3)³ 

⇒ 5k = 3 

⇒ k = 3/5 

Hence, the required value of k is 3/5 .

The logic followed in the given sets is:

(First term + Third term) × 4 = Second term

Now we apply the pattern on the given sets:

(13, 84, 8) 

(13 + 8) × 4 = 84

21 × 4 = 84 

84 = 84

(21, 136, 13)

(21 + 13) × 4 =136

34 × 4 = 136

136 = 136

Now we apply the pattern on the given options:

Option 1) (14, 56, 8)

(14 + 8) × 4 = 56

22 × 4 = 56

88 ≠ 56

Option 2) (16, 23, 156)

(16 + 156) × 4 = 23

172 × 4 = 23

688 ≠ 23

Option 3) (8, 71, 19)

(8 + 19) × 4 = 71

27 × 4 = 71

108 ≠ 71

Option 4) (27, 140, 8)

(27 + 8) × 4 = 140

35 × 4 = 140

140 = 140

Hence, the correct answer is Option 4.

Shortcut Trick

To find the ratio of the first term (A) to the last term (C), multiply the intermediate ratios directly.

Ratio A : C = (A ÷ B) × (B ÷ C)

⇒ A ÷ C = (4 ÷ 5) × (3 ÷ 4) = 3 ÷ 5

∴ The correct answer is 3 : 5.

Alternate Method

Given:

Ratio of A's salary to B's salary = 4 : 5

Ratio of B's salary to C's salary = 3 : 4

A : B = 4 : 5

B : C = 3 : 4

Common B Combine via LCM of B (5 × 3 = 15)

To find the combined ratio, equalize the value of B in both ratios:

⇒ A : B = 4 : 5 = (4 × 3) : (5 × 3) = 12 : 15

⇒ B : C = 3 : 4 = (3 × 5) : (4 × 5) = 15 : 20

⇒ Combined Ratio A : B : C = 12 : 15 : 20

⇒ Ratio of A : C = 12 : 20

⇒ Simplifying by dividing by 4: 3 : 5

∴ The correct answer is 3 : 5.

Additional Information

Compounded Ratio

When two or more ratios are multiplied together, the result is called a compounded ratio. For a : b and c : d, it is (ac) : (bd).

Equating Ratios

To link two ratios with a common term, find the LCM of the common term's values in both ratios and adjust accordingly.

Duplicate Ratio

The duplicate ratio of a : b is a² : b², and the triplicate ratio is a³ : b³.

The correct answer is Helium.

Key Points

• Hydrogen is regarded as diatomic because it has two hydrogen atoms in its molecule, but helium is considered monoatomic since it has one atom in its molecule.
• Due to its totally filled valency shell structure, helium has no chemical affinity. Helium cannot form a diatomic molecule.
• Since helium belongs to noble gases, it has an electron-filled outer shell.
• Helium ($He$) is an inert gas and a chemical element belonging to Periodic Table Group 18 (noble gases).

Additional Information

• Monatomic gas
• ​Monatomic is a compound word made up of the letters "mono" and "atomic," which stand for a single atom. This phrase refers to the gases as monatomic gases and is used in both physics and chemistry.
• Due to their lack of reactivity, noble gases are considered monatomic gases.
• Examples of monatomic gases: Helium ($He$), Radon ($Rn$), Neon ($Ne$), Xenon ($Xe$), Argon ($Ar$) and Krypton ($Kr$).
• Diatomic molecules
• ​Diatomic molecules are ones that have just two atoms in them. A diatomic molecule is referred to as homonuclear if it is made of only one element, and as heteronuclear if it is made of two separate elements.
• Examples of Diatomic molecules: Hydrogen ($H$₂), Nitrogen ($N$₂), Fluorine ($F$₂), Oxygen ($O$₂), Iodine ($I$₂), Chlorine ($Cl$₂) and Bromine ($Br$₂).

Shortcut Trick

Since the ages of Rimmy, Rosy, and Rani are in an arithmetic progression (difference of 1 year each), the average age is exactly the middle person's age.

Total persons = 3 (Rimmy, Rosy, Rani)

Middle person (Rosy) age = Sum of ages ÷ Number of persons

Rosy age = 48 ÷ 3 = 16 years

∴ The correct answer is 16 years.

Alternate Method

Given: Sum of ages = 48 years. Rani > Rosy by 1 year. Rosy > Rimmy by 1 year.

Formula Used: Sum of ages = Age₁ + Age₂ + Age₃

Let Rosy's age be x years.

⇒ Rimmy's age = (x − 1) years

⇒ Rani's age = (x + 1) years

⇒ (x − 1) + x + (x + 1) = 48

⇒ 3x = 48

⇒ x = 48 ÷ 3

⇒ x = 16 years

∴ The correct answer is 16 years.

Additional Information

Ages in Arithmetic Progression

If the ages of 'n' people differ by a constant value, the middle value is always the average of their ages (Sum ÷ n).

Linear Equation Method

Always assume the variable 'x' for the person whose age is asked to minimize calculation steps at the end.

Shortcut Trick

Use the algebraic identity: (a + b)² + (a − b)² + (a + b)(a − b) = 3a² + b².

Here, a = 3x and b = 4.

Result = 3(3x)² + 4² ⇒ 3(9x²) + 16 ⇒ 27x² + 16.

∴ The correct answer is 27x² + 16.

Alternate Method

Given: (3x + 4)² + (3x − 4)² + (3x + 4)(3x − 4)

Formula Used:

1. (a + b)² = a² + 2ab + b²
2. (a − b)² = a² − 2ab + b²
3. (a + b)(a − b) = a² − b²

Calculations:

⇒ Expansion of (3x + 4)² = (3x)² + 2(3x)(4) + 4² = 9x² + 24x + 16

⇒ Expansion of (3x − 4)² = (3x)² − 2(3x)(4) + 4² = 9x² − 24x + 16

⇒ Expansion of (3x + 4)(3x − 4) = (3x)² − 4² = 9x² − 16

⇒ Sum = (9x² + 24x + 16) + (9x² − 24x + 16) + (9x² − 16)

⇒ Combining like terms: (9x² + 9x² + 9x²) + (24x − 24x) + (16 + 16 − 16)

⇒ 27x² + 0 + 16

⇒ 27x² + 16

Therefore, the correct option is (2).

∴ The correct answer is 27x² + 16.

Additional Information

Sum of Squares Identity

The sum of (a+b)² and (a-b)² is always equal to 2(a² + b²), which simplifies calculations involving symmetric binomials.

Difference of Squares

The product of the sum and difference of two terms is given by (a + b)(a − b) = a² − b².

Difference of Squares Subtraction

Subtracting the square of the difference from the square of the sum results in (a + b)² − (a − b)² = 4ab.

The correct answer is coal tar.

Key Points

• Naphthalene balls are made from coal tar.
• Moths and other insects are repelled by naphthalene balls.
• The deadly white solid naphthalene, which has a pungent odour, is frequently employed as a moth repellant.
• Coal gas contains flammable gases.
• Petroleum or coal tar can be used to make naphthalene.
• Coal tar distillation and fractionation are the most typical production processes.
• The naphthalene is subsequently purified by fractionation, decolourization, and crystallisation.

Additional Information

• Coke ​
• Coke is produced by heating coal or oil without the presence of air, which is a damaging distillation process.
• Coke is a grey, hard, and porous fuel with a high carbon content and minimal impurities.
• Coal gas
• ​A fuel comprised of hydrogen, methane, and carbon monoxide known as coal gas is created through destructive distillation, which is the continuous heating of bituminous coal without the presence of air.
• With various amounts of other elements including hydrogen, sulphur, oxygen, and nitrogen, coal is mostly composed of carbon.
• Coal
• One of the most practical fossil fuels is coal.
• A combination of gases that were once utilised for lighting and heating and obtained by the destructive distillation of coal.
• The majority of its components are hydrocarbons and carbon, both of which contain energy that can be released when burned (burning).

According to the given conditions:

 she is facing west direction.

Hence, the correct answer is "Option 2"

Shortcut Trick

In similar triangles, the ratio of corresponding sides is always equal.

Ratio of sides AB : DE = 6.5 : 3.9 = 5 : 3.

Therefore, the ratio of sides BC : EF must also be 5 : 3.

EF = (3 ÷ 5) × BC ⇒ 0.6 × 5.15 = 3.09 cm.

∴ The correct answer is 3.09 cm.

Alternate Method

Given:

AB = 6.5 cm, DE = 3.9 cm, BC = 5.15 cm, and ΔABC ∼ ΔDEF.

Formula Used:

For two similar triangles, the ratio of their corresponding sides is equal:

AB ÷ DE = BC ÷ EF = AC ÷ DF

Calculations:

⇒ AB ÷ DE = BC ÷ EF

⇒ 6.5 ÷ 3.9 = 5.15 ÷ EF

⇒ (6.5 × EF) = 3.9 × 5.15

⇒ 6.5 × EF = 20.085

⇒ EF = 20.085 ÷ 6.5

⇒ EF = 3.09 cm

∴ The correct answer is 3.09 cm.

Additional Information

Similarity Criteria

Two triangles are similar if their corresponding angles are equal (AA) or their corresponding sides are in the same ratio (SSS or SAS).

Ratio of Areas

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides: Area(ΔABC) ÷ Area(ΔDEF) = (AB ÷ DE)².

Ratio of Perimeters

The ratio of the perimeters of two similar triangles is equal to the ratio of their corresponding sides: Perimeter(ΔABC) ÷ Perimeter(ΔDEF) = AB ÷ DE.

According to english alphabet positional value

The pattern followed here is :

Hence, the correct answer is "Option 2"

Given expression: 5 – 5 ÷ 6 × 6 + 3

By interchanging symbols and using BODMAS rule we get,

5 × 5 – 6 + 6 ÷ 3

5 × 5 – 6 + 2

25 – 6 + 2

27 - 6

21 

Hence, the correct answer is "Option 1"

Given table : 

According to the given conditions:

Given code: 5 6 * @ %

Condition (iii) is applied.

So, the code will be :  NS*YV.

Hence, the correct answer is "Option 3"

The correct answer is Both (a) and (b) are incorrect.

Key Points

• Whether light reflects off a flat surface or a curved surface, it always does so in accordance with the law of reflection. It is possible to pinpoint the location of an object's image by using reflection rules.
• The point from which all reflected light appears to diverge is known as the image location.
• Any incident ray that approaches the mirror while travelling perpendicular to the main axis will, upon reflection, pass through the focal point.
• Any incident ray that makes it to the mirror through the focal point will reflect parallel to the main axis.

Additional Information

• Concave mirror
• By splitting a hollow sphere into parts, painting the external surface, and using the internal surface as the reflecting surface, a mirror can be created. These mirrors are concave mirrors.
• Concave mirror characteristics:
• Light converges at a single point when it strikes and reflects back from the concave mirror's reflecting surface. The term "converging mirror" is occasionally used to describe it because of this.
• The concave mirror can be placed very close to the object to produce a magnified, upright, and virtual image.
• However, as the distance between the object and the mirror grows, the size of the picture diminishes, producing a true and inverted image instead.
• ​​Convex mirror
• If the cut piece is painted from the inside, the hollow spherical object's exterior surface serves as the reflective surface. Convex mirrors are the name for this form of a mirror.
• Convex mirror characteristics:
• ​Because a convex mirror diverges light beams when they hit its reflecting surface, it is also known as a diverging mirror.
• Convex mirrors always produce imaginary, erect, and truncated pictures regardless of how far an object is from the mirror.

From the given information:

Now we substitute the values in the given equation and solve it using the BODMAS rule:

Given:

45 + 9 – 4 × 15 ÷ 2 = ?

After interchanging symbols:

45 ÷ 9 × 4 + 15 - 2 = ?

5 × 4 + 15 - 2 = ?

20 + 15 - 2 = ?

35 - 2 = ?

33 = Answer

Hence the correct answer is option 2)

Shortcut Trick

Total frequency N = 8 + 7 + 9 + 12 + 11 = 47. Half of N = 23.5.

Identify Median Class: Cumulative frequencies are 8, 15, 24 (contains 23.5). Median class = 20−30.

Apply Median = l + [((N/2) − cf) ÷ f] × h = 20 + [(23.5 − 15) ÷ 9] × 10.

Calculation: 20 + (8.5 × 10) ÷ 9 = 20 + 85/9 = (180 + 85) ÷ 9 = 265/9.

∴ The correct answer is 265/9.

Alternate Method

Given: Frequency distribution with classes 0−10, 10−20, 20−30, 30−40, 40−50 and frequencies 8, 7, 9, 12, 11 respectively.

Formula Used: Median = l + [((N ÷ 2) − cf) ÷ f] × h

Step 1: Calculate Cumulative Frequency (cf):

⇒ For 0−10: cf = 8

⇒ For 10−20: cf = 8 + 7 = 15

⇒ For 20−30: cf = 15 + 9 = 24

⇒ For 30−40: cf = 24 + 12 = 36

⇒ For 40−50: cf = 36 + 11 = 47

Step 2: Find the Median Class:

⇒ Total N = 47

⇒ N/2 = 47 ÷ 2 = 23.5

⇒ Cumulative frequency just greater than 23.5 is 24, which belongs to class 20−30.

Step 3: Calculate Median:

⇒ l = 20 (lower limit), f = 9 (frequency), cf = 15 (previous cf), h = 10 (width)

⇒ Median = 20 + [((47 ÷ 2) − 15) ÷ 9] × 10

⇒ Median = 20 + [(23.5 − 15) ÷ 9] × 10

⇒ Median = 20 + [8.5 ÷ 9] × 10

⇒ Median = 20 + 85/9

⇒ Median = (180 + 85) ÷ 9 = 265/9

∴ The correct answer is 265/9.

Additional Information

Mean for Grouped Data

Calculated as ∑f_ix_i ÷ ∑f_i, where x_i is the class mark (midpoint) of each interval.

Mode for Grouped Data

Mode = l + [(f₁ − f₀) ÷ (2f₁ − f₀ − f₂)] × h, where f₁ is the frequency of the modal class.

Empirical Relationship

For a moderately skewed distribution: 3 × Median = Mode + 2 × Mean.

The correct answer is Zakat.

Key Points

• Zakat is known as an Islamic finance term referring to the obligation that an individual has to donate a certain proportion of wealth each year to charitable causes.
• One of the primary methods of Islamic social financing is Zakat, the Muslim obligation to donate 2.5% of one's annual wealth to charity.
• It is frequently utilised in Muslim nations to finance domestic development and poverty-reduction initiatives and the express goal is to alleviate inequality.
• The calculation of zakat depends on both income and asset value.

Additional Information

• Mudarabah
• ​Profit and Loss: The term "sharing" (also known as "PLS" or "participatory banking") describes equity financing methods that adhere to Sharia law, such as musharakah and mudarabah. The majority of Muslims adhere to a religious restriction against borrowing interest, which is respected by these systems.
• While Musharakah refers to an equity participation arrangement, Mudarabah is a "trustee finance" or passive partnership deal.
• Ijarah
• Ijarah, a phrase used in Islamic banking and finance, denotes "providing services and goods temporarily for a wage" or "giving something on rent." (a noun, not a verb).
• According to classical fiqh, it refers to a contract that normally has a set duration and price and is used to hire people, rent or lease services, or provide "usufruct" over the property.
• Musharakah
• A joint venture or partnership known as a "musharakah" in Islamic finance enables partners to divide an enterprise's profits and losses.
• Since benefiting from interest on loans is prohibited by Islamic law (Sharia), musharakah permits the financier of a project or business to receive a return in the form of a percentage of the real profits in accordance with a predetermined ratio.

The correct answer is Sodium hydroxide.

Key Points

• A base is sodium hydroxide.
• Red litmus is changed to blue by the base. Sodium hydroxide converts red litmus into blue in this way.
• Blue paper won't alter when exposed to a sodium hydroxide solution that is dilute.
• Since sodium hydroxide (pH-12) is an alkali, it will cause the pH paper to turn blue.

Additional Information

Acid and Base

Five boxes numbered 36, 74, 27, 51 and 92 are kept one above the other.

1. Box 51 is on the topmost position

2. Only one box is above box 27

3. Only box 92 is between box 74 and box 36

4. Box 36 is not at the bottom most position

Box 36 is kept in the exact middle position.

Hence, the correct answer is "Option 3"

Shortcut Trick For any quadratic equation ax2 + bx + c = 0, the sum of roots is given by −b/a. Comparing x2 + 19x + 60 = 0, we have a = 1 and b = 19. Sum of roots = −19 / 1 = −19. ∴ The correct answer is -19. Alternate Method Given: Quadratic equation: x2 + 19x + 60 = 0 Formula Used: Standard form of a quadratic equation: ax2 + bx + c = 0 Relationship between roots and coefficients: Sum of roots (α + β) = −b / a = − (coefficient of x) / (coefficient of x2) Calculations: ⇒ Comparing x2 + 19x + 60 = 0 with ax2 + bx + c = 0: ⇒ a = 1 (coefficient of x2) ⇒ b = 19 (coefficient of x) ⇒ c = 60 (constant term) ⇒ Sum of roots = −b / a ⇒ Sum = −19 / 1 ⇒ Sum = −19 ∴ The correct answer is -19. Additional Information Product of Roots The product of roots (αβ) of a quadratic equation ax2 + bx + c = 0 is equal to c/a. For the given equation, the product is 60/1 = 60. Nature of Roots The nature is determined by the Discriminant (D) = b2 − 4ac. Here, D = 192 − 4(1)(60) = 361 − 240 = 121. Since D > 0 and is a perfect square, the roots are real, distinct, and rational. Quadratic Formula The roots can be found using x = [−b ± √(b2 − 4ac)] / 2a. For this equation, the roots are x = (−19 ± 11) / 2, which gives x = −4 and x = −15.

Given series : 2 7 3 5 7 1 5 7 3 5 7 1 9 7 3 5 7 1 7 3 6 5 7 1 8 1 4 7 3 5

The pattern followed here is,

5 → 7 → 1

2 7 3 5 7 1 5 7 3 5 7 1 9 7 3 5 7 1 7 3 6 5 7 1 8 1 4 7 3 5

There are Total Four 7s  in the following sequence which is immediately followed by 1 and immediately preceded by 5.

Hence, the correct answer is "Option 2"

Formula used:

a³ - b³ = ( a - b) ( a² + b² + a b ) 

Where, a and b are 1st and 2nd term respectively 

Calculation:

Here, we have  $[( 0.68)^2 + ( 0.32)^2 + 16 \times 0.0136]\over[( 0.68)^3- (0.32)^3]\div (0.3)^2$ 

Now, multiply by ( 0.68 - 0.32) in both numerator and denominator respectively

⇒ $(0.68 - 0.32) [(0.68)^2 + (0.32)^2 + 0.2176] \over(0.68-0.32)[(0.68)^3 - (0.32)^3]\div (0.3)^2$  

Now, the numerator of this equation is in the form of 

(a - b) (a² + b² + ab) = (a³ - b³) 

Where a = 0.68 and b = 0.32 

⇒ $[(0.68)^3 - (0.32)^3] \over (0.68 - 0.32) [(0.68)^3 - 0.32)^3]\div (0.3)^2$ = $1\over0.36 \div0.09$ = 1/4 

Hence, the required value of the equation is 1/4 .

The correct answer is Scrutinises and approves budgets of the Block Samities.

Key Points

• The administrative functions of Gram Panchayats are:
• Maintenance, repair, and building of wells drains, bridges, and other public works and welfare projects.
• Install and maintain good street lamps.
• Give forth primary education to the children.
• The economic and social functions (not obligatory) of Gram Panchayats are:
• Build libraries, wedding venues, etc.
• Create and manage cooperative credit societies and fair-priced businesses.
• Create orchards, ponds, and gardens.
• Judicial activities (Nyaya Panchayat; the state judicial service decides jurisdiction) of Gram Panchayats are:
• Ensure prompt and affordable justice.
• Can levy fines of up to 100 rupees.
• Not using legal counsel.

Important Points

• The Gram Panchayat may request modifications to the budget, which the Zilla Parishad may approve or reject within the time frame specified.

Additional Information

• In Indian villages, the basic local governing body is called the Gram Panchayat.
• In India, the grassroots level has a democratic structure. It is a political organisation that serves as the cabinet of the village.
• The Gram Sabha serves as the Gram Panchayat's main body. The Gram Sabha elects the individuals that make up the Gram Panchayat.
• India has well over 250,000 Gram Panchayats.

The correct answer is doubled.

Key Points

• Resistance is inversely correlated with wire cross-sectional area and directly correlated with wire length.
• The resistance doubles if the length of a wire is increased by adding more wire, while the cross-sectional area remains unchanged.
• $Resistance (R)=$ $ρL/A$
• We know that 
• $R=$(ρL/A\) $----(i)$
• If the wire's length doubles, a new resistance will result.
• $R'=$ $ρ2L/A$ $------(ii)$
• By adjusting equation (ii), we obtain
• $R'=$ $2R$
• Therefore, it follows that the new resistance will similarly double as the wire's length increases.

Additional Information

• Resistance
• The ability of an electric conductor to resist the flow of current through it is known as the conductor's resistance.
• $R$ serves as a symbol for it.
• Ohm (Ω) is the SI unit for resistance.
• $Resistance (R)=$ $ρL/A$
• Where $l$ is the conductor's length, $A$ is its cross-sectional area, and $ρ$ is the conductor's resistivity?

Shortcut Trick

Co-prime numbers have a Highest Common Factor (HCF) of 1.

Check divisibility: (156, 234) are even → HCF ≥ 2.

(196, 343) are multiples of 7 → HCF ≥ 7.

(228, 247) are multiples of 19 → HCF = 19.

(161, 192): 161 = 7 × 23, while 192 is not divisible by 7 or 23.

∴ The correct answer is (161, 192).

Alternate Method

Given Pairs: (156, 234), (161, 192), (196, 343), (228, 247)

Step-by-step Verification:

⇒ For (156, 234): Both are even numbers. HCF(156, 234) = 78 ≠ 1.

⇒ For (196, 343): 196 = 7 × 28 and 343 = 7 × 49. HCF(196, 343) = 49 ≠ 1.

⇒ For (228, 247): 228 = 12 × 19 and 247 = 13 × 19. HCF(228, 247) = 19 ≠ 1.

⇒ For (161, 192): Factors of 161 are 1, 7, 23, 161. Factors of 192 are 1, 2, 3, 4, 6, 8... 192. Only common factor is 1.

∴ The correct answer is (161, 192).

Additional Information

Definition of Co-prime

Two numbers are co-prime (or relatively prime) if they share no common positive factors other than 1.

Consecutive Integers

Any two consecutive integers (e.g., 15, 16) are always co-prime to each other.

Prime Numbers Rule

Two different prime numbers are always co-prime. However, a pair of co-prime numbers does not necessarily need to be prime (e.g., 8 and 9).

The correct answer is combination of nervous and muscular tissues.

Key Points

• Animals can move quickly in reaction to stimuli thanks to both their muscular and neurological systems.
• Neurons take in a stimulus and send it on to the brain and spinal cord for processing.
• Motor neurons then transmit the response impulse back to the effector organ, which is typically a muscle in most situations.
• Muscles respond to an impulse by moving in the desired direction.

Additional Information

• Connective tissue
• Supporting tissue protects and supports the body's other tissues and organs.
• In addition to helping to transport nutrients and other substances between tissues and organs, connective tissue also helps to store fat and mend damaged tissue.
• A gel-like substance, fibres, and cells make up connective tissue.
• Epithelial tissue
• The epithelium is a type of body tissue that covers all of the internal and exterior body surfaces, lines hollow organs and body cavities, and makes up the majority of glandular tissue.
• Muscular tissue
• Specialized cells called muscle fibres make up the muscular system. Its primary characteristic is its capacity to contract.
• Muscles that are attached to bones, internal organs, or blood arteries are what move things.
• Skeletal, smooth, and cardiac muscle tissue are the three different types of muscle tissue.

The correct answer is Kerala.

Key Points

• The Western Ghats of Kerala, a coastal state in India, are where the Arabian Sea Branch of the Southwest Monsoon enters the country, making this area the first to see rainfall from the monsoon.
• Kerala, an Indian coastal state, is the first state in India to experience rainfall from the Southwest Monsoon because the Arabian Sea Branch of the monsoon strikes the Western Ghats first.

Additional Information

• In general, it is anticipated that the southwest monsoon would start around the beginning of June and terminate by the end of September.
• The Arabian Sea Branch and the Bay of Bengal Branch are formed when the moisture-laden winds split upon reaching the southernmost tip of the Indian Peninsula, which is a result of its topography.

The correct answer is Article 343.

Key Points

• Article 343 of the Indian Constitution stipulates that Hindi written in Devanagari script should be the Union's official language.
• The Devanagari script of Hindi is designated as the official language of the Union under Article 343 (1) of the Constitution.
• The use of English in official Union business may continue for a further 15 years (i.e., until January 25, 1965) following the Constitution's start date, according to Article 343 (2).
• English will still be used for official purposes even after January 25, 1965, according to Article 343(3) of the Constitution.
• For a number of predetermined purposes, such as Resolutions, General Orders, Rules, Notifications, Administrative and Other Reports, Press Communiqués, Administrative and Other Reports and Official Papers to be Presented Before a House or the Houses of Parliament, Contracts, Agreements, Licensing and Permits, Tender Notices and Forms of Tender, etc., both Hindi and English must be used in accordance with Section 3(3) of the Act.

Additional Information

• Article 345
• ​The legislature of a state may select "any one or more of the languages in use in the State or Hindi as the language or languages to be used for all or any of the official purposes" of the concerned State, as per Article 345 of the Constitution.
• Article 342
• ​The provisions relating to Scheduled Tribes are covered by Article 342. It states that the President may specify the tribes or tribal communities, or portions of or groups within tribes or tribal communities, which shall, for the purposes of this constitution, deemed to be scheduled tribes in relation to that State or Union Territory, as the case may be, after consulting with the Governor thereof by public notification.
• Article 343
• ​The official language of the Union will be Hindi in Devanagari script. Indian numerals in their international format must be utilised for all official purposes by the Union.

The correct answer is investment.

Key Points

• A multiplier is a numerical coefficient that illustrates how changes in total national investment affect total national income  in economics,
• It is equivalent to the proportion of changes in investments to the changes in overall revenue.

Additional Information

• The multiplier's magnitude is determined by the proportion of deposits that banks must retain in their reserves.
• The money supply reserve multiplier rises when the reserve requirement is decreased and falls the opposite way.
• The fiscal multiplier measures the relationship between an increase in a nation's national income and the original increase in expenditure or decrease in taxes that generated that income.

The correct answer is Only iii and i.

Key Points

• A type of reaction called a double displacement reaction involves the exchange of ions between two reactants to create two new molecules.
• As an unintended consequence of double displacement processes, precipitates frequently occur.
• A colour shift could or might not be the outcome of a twofold replacement reaction.
• The interaction between potassium iodide with lead nitrate solution. This reaction causes the colour to shift from colourless to yellow.

Additional Information

• Double displacement reaction 
• ​When two chemicals interact by transferring ions, a double displacement reaction occurs, creating two new molecules.
• In the twofold displacement process, positive ions trade places with negative ions.
• In water-soluble ionic compounds, numerous double displacement reactions take arise.
• A double displacement process involves the movement of atoms from two different substances.
• Example: $Na$₂$S+2HCl→2NaCl+H$₂$S$

The least possible venn diagram of the given statement is:

Conclusions:

(I) Some Books are Designs. → False (as there is no definite relation between Books and designs as shown in Venn diagram)

(II) All Pages are Catalogues. → True (according to the statement All Pages are Books and All Books are Catalogues so, all pages are catalogues)

Only conclusion (II) follows.

Hence, the correct answer is "Option 4"

The correct answer is Cell B or D.

Key Points

• Recyclable
• ​The process of recycling waste into new materials and objects is called recycling.
• This idea frequently includes the process of extracting energy from waste.
• The capacity of a material to reacquire its original properties determines its recyclability.
• It is an alternative to "conventional" waste disposal that can help reduce emissions of greenhouse gases while also saving material.
• The third step in the "Reduce, Reuse, and Recycle" waste hierarchy is recycling, which is one of the most important aspects of modern waste reduction.
• Non- Recyclable
• ​Materials that cannot be recycled in your dry-mixed recycling are referred to as non-recyclable waste. Polystyrene, pet waste, bubble wrap, windows, mirrors, and plastic film are examples of these.
• In EfW (energy from waste), waste that cannot be recycled or is not biodegradable can be used as fuel.
• These facilities burn waste, generating steam that powers a steam turbine to generate electricity.
• In turn, that turbine generates heat for homes and businesses in the area.

Additional Information

• Combustibility and flammability
• ​Anything that can burn, or combust, in the air is a combustible substance.
• If a material easily ignites at ambient temperatures, it is flammable.
• To put it another way, a combustible substance can be ignited with some effort, whereas a flammable substance ignites immediately upon being exposed to flame.
• Air's degree of flammability or combustibility is largely determined by the material's volatility, which is related to the temperature-dependent composition-specific vapour pressure.

Formula used:

100% = Total numbers of cars sold 

Calculation:

Here, total numbers of cars sold = 80 

As 100% = 80 

⇒ 1% =  0.8 

Now, cars sold in Delhi =  25% 

⇒ 25 × 0.8 = 20 

Now, according to the given question 

Numbers of cars sold to female : male = 2 : 3 

Numbers of cars sold to female customers = 2/5 × 20 = 8 

Hence, the numbers of cars sold to female customers in Delhi is 8 .

Given statement : 

L > M ≥ 2 > N > O = P ≤ Q < R

I.O < R → True (as O = P ≤ Q < R gives; as R > Q ≥  P = O so, O < R is true)

II. M > Q → False( as  M ≥ 2 > N > O = P ≤ Q < R as no clear relation between M and Q)

Only conclusion I is true

Hence, the correct answer is "Option 3"

The correct answer is October.

Key Points

• On October 2, 1869, in Porbandar, Gujarat, Mahatma Gandhiji was born.
• In India, a national holiday called Gandhi Jayanti is observed to commemorate Mahatma Gandhi's birth.
• One of India's three national holidays, it is observed on the second of October each year.
• Since he was a nonviolent freedom fighter, the UN General Assembly announced on June 15, 2007, that it had passed a resolution designating October 2 as the International Day of Non-Violence.

Additional Information 

• On October 2, people around the world honour Gandhi.
• It is a federal holiday that is celebrated across the nation's states and territories.
• All around India, especially at Gandhi's tomb, Raj Ghat, in New Delhi, where he was cremated, prayer services and tributes are held to commemorate Gandhi Jayanti.
• Prayer gatherings and commemoration celebrations held by colleges, local government agencies, and socio-political organizations in many cities are popular activities.

Formula used:

Average = Sum of values / No. of values 

Calculation:

Number of boys in school P = 200

Number of boys in school Q = 90

Number of boys in school R = 190 

Number of boys in all the three schools  = 200+ 90 + 190 = 480

Number of schools = 3 

Average = Sum of values/No. of values 

⇒ 480/3 = 160 

Hence, average number of boys in three schools is 160.

According to given condition :

He drives 12 Km (13 - 5 = 8 + 4 Km ) in order to reach Point A from Point B

And he is towards the west direction in order to reach Point A from Point B

Hence, the correct answer is "Option 4"

Shortcut Trick First number = (55 × 18) + 11 = 990 + 11 = 1001 Using the Product Rule: Number1 × Number2 = HCF × LCM Number2 = (77 × 5005) ÷ 1001 Since 5005 ÷ 1001 = 5, then Number2 = 77 × 5 = 385 ∴ The correct answer is 385.

Alternate Method Given: LCM = 5005 | HCF = 77 For the first number (N1): Divisor = 55, Quotient = 18, Remainder = 11 Formula Used:

1. Dividend = (Divisor × Quotient) + Remainder
2. N1 × N2 = HCF × LCM

Calculations: ⇒ N1 = (55 × 18) + 11 ⇒ N1 = 990 + 11 = 1001 ⇒ N1 × N2 = 77 × 5005 ⇒ 1001 × N2 = 77 × 5005 ⇒ N2 = (77 × 5005) ÷ 1001 ⇒ N2 = 77 × 5 ⇒ N2 = 385 ∴ The correct answer is 385.

Additional Information Fundamental Property of HCF and LCM The product of any two positive integers is equal to the product of their HCF and LCM. Formula: a × b = HCF(a, b) × LCM(a, b). Division Algorithm For any two integers, the Dividend is found using: Dividend = (Divisor × Quotient) + Remainder, where 0 ≤ Remainder < Divisor. HCF as a Factor of LCM For any set of numbers, the HCF is always a factor of the LCM. If the HCF does not divide the LCM perfectly, such numbers cannot exist.

Shortcut Trick

Distance covered in 1 revolution = Circumference = π × d

Distance in 1 revolution = (22/7) × 63 = 22 × 9 = 198 cm

Distance covered in 100 revolutions = 100 × 198 = 19800 cm

Convert to meters (1 m = 100 cm): 19800 ÷ 100 = 198 m

∴ The correct answer is 198 m.

Alternate Method

Given:

Diameter of the wheel (d) = 63 cm

Number of revolutions (n) = 100

Formula Used:

Circumference of a wheel = π × d

Total distance covered = n × Circumference

d = 63

1 Rev = π × d = 198 cm Distance (100 Rev) = 100 × 198 cm = 19800 cm = 198 m

Calculation:

⇒ Circumference = (22/7) × 63 cm

⇒ Circumference = 22 × 9 = 198 cm

⇒ Total distance covered in 100 revolutions = 100 × 198 cm

⇒ Total distance = 19800 cm

⇒ Since 1 meter = 100 cm, Total distance in meters = 19800 ÷ 100 m

⇒ Total distance = 198 m

∴ The correct answer is 198 m.

Additional Information

Wheel Revolutions Concept

When a circular wheel makes exactly one full rotation along the ground, the linear distance it travels perfectly equals its perimeter, which is the circumference (C = 2πr or C = πd).

Number of Revolutions Formula

Number of revolutions (n) = Total distance covered ÷ Circumference of the wheel. Always ensure the total distance and circumference are measured using the same units.

Basic Unit Conversions

1 meter (m) = 100 centimeters (cm)
1 kilometer (km) = 1000 meters (m)
1 kilometer (km) = 100,000 centimeters (cm)

The correct answer is Maximum.

Key Points

• The generated current in the wire is known as induced current since it is caused by a shifting magnetic field. The magnetic flux's rate of change would be directly proportional to the induced current.
• When the coil is moving at a straight angle to the magnetic field, the induced current is at its maximum.
• As the flux cutting is greatest in this situation, the induced current is highest when the coil is moving in a direction that is 90° or perpendicular to the magnetic field.
• The coil will cut the least amount of flux when it is moving in a direction that is parallel to or at an angle of 180 degrees to the magnetic field.

Additional Information

• Induced current
• An emf is induced in a wire coil whenever the magnetic field surrounding the coil changes. If the conductor circuit is closed, current will also flow through the circuit together with this induced emf. The induced current is the name of this current.
• The following techniques can be used to alter the magnetic field:
• By angling a magnet in relation to the coil.
• By shifting the coil's position in relation to the magnetic field.
• By adjusting the coil's surface area in the magnetic field
• Through the coil's rotation in relation to the magnet.

The pattern followed here is ;

Hence, the correct answer is "Option 4"

The correct answer is 2.26 × 108$\rm \frac{m}{s}$ 

Key Points

• Calculation
• Given,
  

Refractive index = 1.33

We know, 

n= c/v

1.33= 299792458/ v

v= 299792458/1.33

v= 2.25 × 10⁸ m/s​

Additional Information

• Refractive index
• ​In optics, an optical medium's refractive index (or refraction index) is a dimensionless number that indicates its ability to bend light.
• The degree to which light travels through a material is determined by its refractive index.
• Snell's law of refraction, n1 sinθ1 = n2 sinθ2, where n1 and n2 are the angles of incidence and refraction of a ray crossing the interface of two media with refractive indices n1 and n2, respectively, describes this.
• In addition, the critical angle for total internal reflection, their intensity (Fresnel's equations), and Brewster's angle are all determined by the refractive indices when light reaches the interface.
• The ratio of the speed of light in a vacuum, c = 299792458 m/s, to the phase velocity v of light in the optical medium is known as the absolute refractive index n. 
  

n= c/v

Shortcut Trick

A whole work = 10 × 3 = 30 days; B whole work = 30 × 4 = 120 days; A+B+C = 12 days.

Total Work (LCM of 30, 120, 12) = 120 units.

Efficiencies: A = 4, B = 1, A+B+C = 10 ⇒ C = 10 − (4+1) = 5.

Day 1 (A+B) = 4+1 = 5; Day 2 (A+C) = 4+5 = 9. 2-day cycle = 14 units.

8 cycles (16 days) = 14 × 8 = 112 units. Remaining = 8 units. Day 17 (A+B) = 5 units. Left = 3 units.

Time on Day 18 = 3 ÷ 9 = 1/3 day. Total = 17 1/3 days.

∴ The correct answer is 17 1/3 days.

Alternate Method

Given: A completes 1/3 work in 10 days; B completes 1/4 work in 30 days; A+B+C together in 12 days.

Formula: Total Work = Time × Efficiency.

⇒ Efficiency of C = (A+B+C) − A − B = 10 − 4 − 1 = 5

⇒ Work on Day 1 (A + B) = 4 + 1 = 5 units

⇒ Work on Day 2 (A + C) = 4 + 5 = 9 units

⇒ Work in 2 days = 5 + 9 = 14 units

⇒ Work in 16 days (8 cycles) = 14 × 8 = 112 units

⇒ Remaining work = 120 − 112 = 8 units

⇒ Day 17 work (A + B) = 5 units; Remaining = 8 − 5 = 3 units

⇒ Time for remaining work by (A + C) = 3/9 = 1/3 day

⇒ Total time = 16 + 1 + 1/3 = 17 1/3 days

∴ The correct answer is 17 1/3 days.

Additional Information

Alternate Day Work

In alternate day problems, calculate the work done in one complete cycle (usually 2 or 3 days) and then divide the total work by the cycle total to find the number of full cycles.

Efficiency and Time

Efficiency is inversely proportional to time. If A takes T days to do work W, efficiency η = W ÷ T.

Combined Work Formula

If individuals A, B, and C can do work in a, b, and c days respectively, then (1/a + 1/b + 1/c) × Time = 1.

Given statement : K ≥ U = N > Q < R = T ≤ P

I. T < R → False ( as R = T but not T < R)

II. Q > U → False ( as  N > Q and U = N then U = N > Q not possible)

III. K = N → False (as K ≥ U = N not K = N)

IV. K > Q → True (as K ≥ U = N > Q so, K > Q)

Hence, the correct answer is "Option 4"

The correct answer is Promotion of feudalism.

Key Points The following is a list of some of the key elements of the Indian Constitution:

• Federalism: Separation of federal and state powers
• Government by the People under a Parliamentary System
• Fundamental Rights: The division of powers between the legislative, executive, and judicial branches
• Secularism: Separation of State and Religion

Additional Information

• Feudalism in India was defined by a class of landowners and a class of subject peasants who both lived in an economy that was mostly agrarian, characterised by a drop in trade and urbanisation as well as a sharp decline in the use of metal money.
• Promotion of feudalism is not a key feature or the basic feature of the Indian Constitution.

The correct answer is Girls should consume chips and packed or tinned snacks to meet nutritional needs.

Key Points

• Good menstrual hygiene and health habits will help you avoid infections, lessen odours, and keep you at ease while you're on your period.
• Prior to using a menstruation product, wash your hands both before and after using the restroom.
• Used menstruation products should be properly disposed of.
• Regardless of how little the flow is, change sanitary pads every few hours. If your period is heavy, change them more regularly.
• A single tampon should not be worn for longer than 8 hours at a time.
• Every day after use, clean the cups. After your period has ended, sanitise menstruation cups by giving them a good rinse and then putting them in a pot of boiling water for one to two minutes.
• The majority of washable period underwear is made to be reused.

Additional Information

• While on your period, you may maintain your health and comfort by following these hygiene precautions:
• Put on breathable, lightweight clothing (such as cotton underwear). Tight clothing can keep heat and moisture in, which helps bacteria grow.
  

Regularly replace your menstruation products.

• Maintain a clean genital area. Every day, wash the outside of your vagina and bottom.
• Use pads, tampons, or toilet paper without scents. The skin can become inflamed, and your natural pH balance can be affected by scented hygiene products.
• Obtain plenty of liquids. By washing out your urinary system, you can avoid diseases like vaginal candidiasis.
• Keep tabs on your period. Your menstrual cycle serves as an important barometer of your general health. Period irregularities may indicate health issues like diabetes, thyroid issues, or celiac disease.

The correct answer is Phloem.

Key Points

• The vascular tissue in plants that carries food is called phloem.
• The many storage organs receive the food molecules that the leaves have created. such as fruits, stems, and roots.
• The phloem carries nutrients from the leaves to the roots.
• A plant component called phloem consists of companion cells, sieve tubes, phloem fibres, and phloem parenchyma cells.

Additional Information

• Sclerenchyma
• ​It is a kind of supporting tissue that often consists of dead cells with walls that have been heavily thickened with lignin.
• The mature sections of the plant are where it is primarily found.
• Xylem
• ​The Greek word "xylon," which means wood, is where the term "xylem" comes from.
• The term xylem was created by Carl Nägeli. The vascular tissue known as the xylem is found in plants and is largely responsible for moving water and nutrients from the roots to the stem and leaves.
• They also give the plants mechanical strength.
• Collenchyma
• ​Two cellular structures called parenchyma and collenchyma make up the majority of plant tissues.
• Collenchyma cells are live cells, just like parenchyma cells. They are made of cellulose and water, which aids in the maintenance of the plant's morphology.

Shortcut Trick

Age difference remains constant. Ratio 5 years ago (Ramesh:Rajiv) = 3:1 (diff 2 units).

Ratio 10 years later (Ramesh:Rajiv) = 2:1 (diff 1 unit). To equate difference, multiply by 2 → 4:2.

Change in units = 4 − 3 = 1 unit. Real time gap = 10 − (−5) = 15 years.

1 unit = 15 years. Ramesh's age 5 years ago = 3 units = 3 × 15 = 45 years.

Present age of Ramesh = 45 + 5 = 50 years.

∴ The correct answer is 50 years.

Alternate Method

Let present ages of Ramesh and Rajiv be R and r respectively.

Condition 1 (10 years later): R + 10 = 2(r + 10) ⇒ R − 2r = 10 --- (i)

Condition 2 (5 years ago): R − 5 = 3(r − 5) ⇒ R − 3r = −10 --- (ii)

Subtract (ii) from (i): (R − 2r) − (R − 3r) = 10 − (−10)

⇒ r = 20 years (Rajiv's present age)

Substitute r in (i): R − 2(20) = 10 ⇒ R − 40 = 10

⇒ R = 50 years

∴ The correct answer is 50 years.

Additional Information

Constant Age Difference

The difference between the ages of two people remains the same regardless of how many years pass.

Ratio Balancing Method

If ratios at two different times are given, multiply the terms of each ratio by the difference of the other ratio to make the age gap units consistent.

Linear Equations in Ages

Age problems are easily solved by setting 'x' for the present age and forming equations for 'n' years ago (x − n) or 'n' years hence (x + n).

The correct answer is Fleming's right-hand rule.

Key Points

• Using Fleming's right-hand rule, we may determine the direction of current produced in a wire travelling in a magnetic field.
• The rule states that if we extend our right hand's forefinger, middle finger, and thumb perpendicular to one another as shown in the figure, with the thumb pointing toward the conductor's motion and the forefinger pointing toward the direction of the magnetic field, the middle finger will give us the direction of the flow of induced current in the circuit

Additional Information

• Maxwell's right-hand screw rule
• ​According to Maxwell's screw rule, the magnetic field's direction can be determined by rotating a right-handed screw so that it advances in the same direction as the regular current. The Maxwell corkscrew rule is another name for the right-hand thumb rule.
• Maxwell's left-hand screw rule
• ​It is used to establish the direction of the magnetic field encircling a conductor that is capable of carrying straight current. If the direction of the magnetic field lines connected to the current-carrying conductor is known, it can be utilised to calculate the direction of the electric current in that conductor.
• Fleming's left-hand rule
• ​To identify the direction of force acting on a current-carrying wire positioned in a magnetic field, utilise Fleming's left-hand rule. The thumb indicates the direction of force acting on the wire if the thumb, index finger (along the magnetic field), and middle finger (along the current) are kept mutually perpendicular.

The correct answer is Assam.

Key Points

• In February 2022, Assam became the 1st state in the country to launch night navigation mobile app in rivers.
• For crossings on the Brahmaputra river in Assam, the first night navigation smartphone application in rivers in the country was launched.
• The transport department and K Raju, the head scientist at IIT Madras, collaborated to build the night navigation mobile application, which will measure the rivers' draught.
• By using these services, district transport offices' (DTOs') annual foot traffic is predicted to drop by roughly four lakhs.

Additional Information

• The State Transport Department's ten contactless Aadhar-based services were also introduced by the Chief Minister to speed up and reduce the cost of delivering public services.
• The CM also introduced an electronic ticketing system for ferry services between Dhubri and Silchar.
• A memorandum of understanding (MoU) was also signed between the State Transport Department and the Common Service Centres (CSCs) under the Ministry of Electronics and Information Technology (MeitY) to provide online services at the panchayat level.

Shortcut Trick

Number of coins = (Volume of original cylinder) ÷ (Volume of each coin)

Ratio of Radius (R/r) = 5 / 0.5 = 10

Ratio of Height (H/h) = 2 / 0.2 = 10

Number = (R/r)² × (H/h) = 10² × 10 = 1000

∴ The correct answer is 1000.

Alternate Method

Given:

Original Cylinder: Diameter = 10 cm, Height = 2 cm

Cylindrical Coin: Diameter = 1 cm, Thickness (Height) = 0.2 cm

Formula Used:

Volume of Cylinder = πr²h

Calculations:

⇒ Radius of large cylinder (R) = 10 / 2 = 5 cm

⇒ Radius of coin (r) = 1 / 2 = 0.5 cm

⇒ Volume of large cylinder = π × (5)² × 2 = 50π cm³

⇒ Volume of one coin = π × (0.5)² × 0.2 = π × 0.25 × 0.2 = 0.05π cm³

⇒ Number of coins = (50π) / (0.05π)

⇒ Number of coins = 50 / 0.05 = 5000 / 5 = 1000

∴ The correct answer is 1000.

Additional Information

Conservation of Volume

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

Cylinder Properties

Curved Surface Area (CSA) = 2πrh and Total Surface Area (TSA) = 2πr(h + r).

Recasting Shortcut

If dimensions are scaled by factor k, volume scales by k³ for similar shapes.

The correct answer is Nai Roshni.

Key Points

• A Central Sector Program called Nai Roshni-a Leadership Development Program for Minority Women is available to women from minority communities who are between the ages of 18 and 65 and it began in 2012–2013.
• By giving knowledge, resources, and tactics to sync with government processes, banks, and other organisations at all levels, the programme aims to empower and instil confidence in minority women.

Additional Information Significance of Nai Roshni scheme are as follows:

• In addition to being important for achieving equity, women's empowerment is also a key component of our efforts to eliminate poverty, spur economic growth, and promote civil society.
• In a family living in poverty, women and children always suffer the most and require support and is even more crucial to empower women, especially mothers, because it is in the house they raise their children and shape their character.
• In addition to claiming their fair share of government development benefits for bettering their lives and living conditions, it empowers minority women to leave the safety and secure environment of their homes and communities and taking their leadership roles and assert their rights to access services, facilities, skills, and opportunities.

Formula used:

Angle between the hands = 11 × m/2 - 30H 

Where m denotes the minute hand 

H denotes the hour hand 

Calculation:

The hands of clock can't be together between 2:30 and 3:00 

So, we have to look for time between 3:00 and 3:30

The formula for finding the angle between the hour hand and the minute hand is 

Angle between the hands = 11 × m/2 -30H 

Here, angle = 0 , H = 3

⇒ 0 = 11 × m/2 - 30 × 3

⇒ m = 180/11 = (16 + 4/11)

Hence, at (16 + 4/11) minutes past 3 the hands of a clock are together.

The correct answer is C and Ge.

Key Points

• Each of the following elements has four valence electrons: germanium, silicon, and carbon.
• The production of semiconductor devices uses the rare element germanium. Germanium shares a lot of similarities with silicon in terms of its physical and chemical characteristics.
• Coal, ore, and germanite all contain semi-metal germanium. Germanium is a gray-white metal that crystallizes.
• Group 14 is where both carbon and silicon belong. As a result, both elements have a valence electron with a value of four.
• The nearest substitute for carbon is silicon. Tetravalent elements like carbon and silicon both create mostly covalent non-ionic molecules.
• Therefore, elements that show similar valency as that of silicon are C and Ge.

Additional Information

• Chemically speaking, silicon is an element with the symbol Si and atomic number 14.
• It is a tetravalent metalloid and semiconductor that has a blue-gray metallic sheen and is a tough, brittle crystalline solid.
• With carbon above it and germanium, tin, lead, and flerovium below it on the periodic table, it belongs to group 14.
• The element is a crucial component of bricks and ceramics. Since it is a semiconductor, the element is used to create transistors.

The correct answer is 1/1.3.

Given:

Refractive Index (n) is 1.3

To find:

The value of ${sin y\over sinx}$

Calculation:

Laws of refraction states that "The ratio of sine of the incident angle and the refracted angle is a constant". This constant value is called as refractive index.

Here:

Angle of incidence is x and angle of refraction is y.

So we have:

$n={sin x\over siny}$

$1.3={sin x\over siny}$

${1\over1.3}={sin y\over sinx}$

Therefore the value is ${1\over 1.3}$.

The answer is 200 Watt.

Given:

Resistors of 0.2 Ω, 0.4 Ω, 0.6 Ω, 0.8 Ω are connected in series across a voltage of 20 V.

To find:

Net power (P)

Formula:

$Rs=R1+R2+R3+R4$

$P={V^2\over R}$

Calculations:

Here since the resistors are in series we have:

$Rs=R1+R2+R3+R4$

$Rs=0.2+0.4+0.6+0.8=2Ω$2 Ω

Now the power is given by,

$P={V^2\over R}$

$P={20^2\over 2}={400\over 2}=200Watt$

Thus, the power in the circuit is 200 Watt.

The correct answer is Rohit Sharma.

Key Points

• Rohit Sharma, the captain of India, became the first captain in the history of cricket to win 13 straight T20Is.
• This accomplishment was made by Rohit Sharma in Southampton's first T20I of a three-match series against England.
• Indian cricketer Rohit Gurunath Sharma, who was born on April 30, 1987, currently serves as the team's captain.
• One of the greatest opening batters in history. For his timing, eloquence, six-hitting prowess, and leadership, Rohit Sharma is renowned.
• In both domestic cricket and the IPL, he bats right-handedly for Mumbai Indians and Mumbai.
• In a single World Cup, Rohit Sharma holds the record for most 100-point performances.
• The Mumbai Indians, who are the most successful team in the history of the event, are also captained by Rohit Sharma in the IPL.

Additional Information

• Virat Kohli
• Right-handed batter Virat Kohli competes for Royal Challengers Bangalore in the IPL and for Delhi in domestic cricket in India. He is a former captain of the Indian national cricket team and an international player from India.
• He is recognised as one of cricket's all-time great batsmen. He is second among cricket batsmen in terms of the most hundreds scored in international play.
• Babar Azam
• Pakistan's national cricket squad in all formats is captained by Mohammad Babar Azam, an international cricketer from Pakistan. He is regarded as one of the best batters in modern cricket and the only player in the world to rank in the top five in every format.
• He is ranked as the best batter in ODIs, fifth in Tests, and fourth in T20 Internationals.
• Mahendra Singh Dhoni
• ​Mahendra Singh Dhoni, sometimes referred to as MS Dhoni is a former Indian cricketer who played as a wicket-keeper.
• He served as captain of the Indian national team in limited-overs forms from 2007 to 2017 and in Test cricket from 2008 to 2014. Additionally, he serves as Chennai Super Kings' current captain in the Indian Premier League.

The pattern followed here is :

Hence, the correct answer is "Option 1"

Shortcut Trick

Using the empirical relationship: Mode = 3 × Median − 2 × Mean

⇒ 2 × Mean = 3 × Median − Mode

⇒ 2 × Mean = 3(12) − 15 = 36 − 15 = 21

⇒ Mean = 21/2

⇒ 3 × Mean = 3 × (21/2) = 63/2

∴ The correct answer is 63/2.