RRB Group D Previous Year Paper (Held on: 12 Sept 2022 Shift 1)

The correct answer is Nagaland.

Key Points

• The Hornbill Festival and the Moatsu Festival are two of the most significant cultural festivals of Nagaland.
• Hornbill festival is celebrated annually from December 1st to December 10th.
• It was started by Government of Nagaland in 2000 and named on Hornbill bird.
• The Hornbill International Rock Contest is a major attraction.
• The festival features traditional Naga cuisine, including smoked pork, bamboo shoot dishes, rice beer, and more.
• The celebration encourgae : ​Cultural Preservation, economic boost, a sense of unity among the diverse tribes of Nagaland.
• Moatsu festival is celebrated Annually in the first week of May  by the Ao tribe.
• It is an agricultural festival celebrated after the completion of sowing and other agricultural activities.
• Peu (Meritorious Feast) where wealthy members of the community host feasts and distribute food and drink as a sign of their prosperity and generosity.

Additional Information

The correct answer is Washing Soda.

Key Points

• Washing soda (Sodium carbonate (Na₂CO3)), is utilized in the chemical process to produce Borax (sodium tetraborate, Na₂B4O₇).
• Borax is usually found in borate minerals such as colemanite, ulexite, and kernite.
• The chemical reaction between boric acid (produced from borate minerals) and washing soda produces borax, which is then refined for various industrial applications.
• It is used in:
• ​ in many household cleaners and detergents and having whitening property.
• in the production of glass and ceramics, particularly borosilicate glass.
• acts as a micronutrient in fertilizers, supplying required boron to crops.
• used to make buffer solutions, which help to maintain stable pH in chemical preparations.

Additional Information

• Chlorine water is an aqueous solution of chlorine gas (Cl2) dissolved in water.
• It is known for its strong oxidizing properties, as a disinfectant and bleaching agent.
• When chlorine gas dissolves in water, it forms a mixture of hypochlorous acid (HOCl) and hydrochloric acid (HCl).
• Bleaching powder, also known as chlorinated lime, is a chemical compound with the formula Ca(OCl)₂.
• It is a mixture of calcium hypochlorite (Ca(OCl)₂), calcium chloride (CaCl₂), and calcium hydroxide (Ca(OH)₂).
• It is used as:
• Disinfectant: in Water Treatment and Sanitizing Surfaces.
• Bleaching Agent: in Textile Industry and Paper Industry.
• Oxidizing Agent: in chemical processes that require oxidation.
• Brine water is a highly concentrated solution of salt (typically sodium chloride, NaCl) in water.
• Other salts and minerals depending on the source (e.g., magnesium chloride, calcium chloride, potassium chloride).
• it is used in: 
• in cooling systems as a secondary refrigerant due to their low freezing points and high thermal capacity.
• used in quenching processes to harden metals.
• Applied on roads and bridges during winter to prevent ice formation and facilitate melting.

The positions of the letters according to the English alphabet series:

By changing vowels to the succeeding letter and changing consonants to the preceding letter, we get

So, the newly formed word is RVQOQJRJMF.

And the letters that appear twice are Q, J and R.

Hence, the correct answer is "3".

Let's create the order using the information given,

1. A has exam on Thursday.

2. Only one person has the exam between D and E.

3. D has the exam on the day immediately before B.

Thus, the final arrangement is:

Here, we can see that C has the exam on Friday.

Hence, the correct answer is "C".

Shortcut Trick

LCM of 8 and 12 is 24.

We need the least 3-digit multiple of 24.

The smallest 3-digit number is 100.

The first multiple of 24 greater than 100 is 24 × 5 = 120.

∴ The correct answer is 120.

Alternate Method

Given:

Numbers = 8 and 12

Smallest 3-digit number = 100

Concept Used:

A number completely divisible by two or more numbers must be a multiple of their Least Common Multiple (LCM).

Calculation:

⇒ Prime factorization of 8 = 2³

⇒ Prime factorization of 12 = 2² × 3

⇒ LCM of 8 and 12 = 2³ × 3 = 24

⇒ We take the smallest 3-digit number, which is 100.

⇒ When dividing 100 by 24, we get a quotient of 4 and a remainder of 4.

⇒ To make it perfectly divisible, we must add the difference between the divisor and the remainder to 100.

⇒ Required number = 100 + (24 − 4)

⇒ Required number = 100 + 20 = 120

∴ The correct answer is 120.

Additional Information

Lowest Common Multiple (LCM)

The smallest positive integer that is a multiple of two or more given numbers. It is calculated by taking the highest powers of all prime factors present in the numbers.

Highest Common Factor (HCF)

The largest positive integer that divides two or more given numbers without a remainder. It is calculated by taking the lowest powers of common prime factors.

Product Rule

For any two positive integers A and B, the product of their LCM and HCF is exactly equal to the product of the numbers themselves: LCM × HCF = A × B.

Divisibility Rules

A number is divisible by 8 if its last three digits form a number divisible by 8. It is divisible by 12 if it is perfectly divisible by both 3 and 4.

The correct answer is pole and principal focus.

Key Points

• Focal Length is the distance from the mirror's surface (along the principal axis) to the focal point.
• The focal length is negative for Concave mirror and is half the distance to the center of curvature.
• For a convex mirror, the focal length is positive and is half the distance to the center of curvature.
• Mathematically Radius of curvature (r) = 2 x focal length (f).

Additional Information

• Some important terms related to spherical mirrors: 
• Spherical mirrors: A mirror with a surface that forms part of the surface of a sphere. There are two types: concave and convex mirrors.
• Concave mirror: A spherical mirror with a reflective surface that curves inward. It converges light rays to a focal point
• Convex mirror: A spherical mirror with a reflective surface that curves outward. It diverges light rays.
• Principal mirror: An imaginary line passing through the center of curvature and the vertex (center of the mirror). It is the optical axis of the mirror.
• Centre of Curvature: The center of the sphere from which the mirror segment is taken. It is a point on the principal axis and is equidistant from all points on the mirror's surface.
• Radius of Curvature: The distance from the mirror's surface to the center of curvature. For spherical mirrors, this is twice the focal length ((R = 2f)).
• Pole (Vertex): The central point on the mirror’s surface. It is the midpoint of the mirror.
• Focal Point: The point on the principal axis where parallel rays of light either converge or appear to converge after reflecting from the mirror. For concave mirrors, it is in front of the mirror; for convex mirrors, it is behind the mirror.
• Focal length: The distance between the mirror's surface (at the vertex) and the focal point. It is half the radius of curvature ((f = R/2)). For concave mirrors, it is negative, and for convex mirrors, it is positive.
• Aperture: The effective diameter of the mirror. It is the portion of the mirror through which light is reflected.
• Real image: An image formed by the actual convergence of light rays. It can be projected onto a screen and is inverted relative to the object.
• Virtual image: An image formed by the apparent divergence of light rays from a point behind the mirror. It cannot be projected onto a screen and is upright relative to the object.

The logic used here is,

(Second Number) = (First Number + Third Number)²

(5, 144, 7):

As per the logic,

144 = (5 + 7)²

144 = (12)²

144 = 144 → (LHS = RHS)

(9, 225, 6):

225 = (9 + 6)²

225 = (15)²

225 = 225 → (LHS = RHS)

Let's check each option,

1) (9, 256, 7):

As per the logic,

256 = (9 + 7)²

256 = (16)²

256 = 256

LHS = RHS → (Satisfies the logic)

2) (9, 99, 10):

As per the logic,

99 = (9 + 10)²

99 = (19)²

99 ≠ 381

LHS ≠ RHS.

3) (4, 100, 5):

As per the logic,

100 = (4 + 5)²

100 = (9)²

100 ≠ 81

LHS ≠ RHS.

4) (10, 145, 13):

As per the logic,

145 = (10 + 13)²

145 = (23)²

145 ≠ 529

LHS ≠ RHS.

Here, we can see that only option 1 satisfies the logic.

Hence, the correct answer is "(9, 256, 7)".

Shortcut Trick

Convert fractions into decimals for faster addition:

⇒ 2¹/₂ = 2.5 and 4/5 = 0.8

⇒ Expression = {14 + (2.5 + 0.8 + 1)} × 1/100

⇒ Expression = {14 + 4.3} ÷ 100

⇒ 18.3 ÷ 100 = 0.183

∴ The correct answer is 0.183.

Alternate Method

Given:

Expression: {14 + (2¹/₂ + 4/5 + 1)} × 1/100

Calculation:

⇒ Convert the mixed fraction into an improper fraction: 2¹/₂ = 5/2

⇒ Solve the inner bracket first (BODMAS rule): (5/2 + 4/5 + 1)

⇒ Take the LCM of the denominators 2, 5, and 1, which is 10.

⇒ Inner bracket sum = (25/10 + 8/10 + 10/10) = 43/10

⇒ Now substitute this back into the original expression:

⇒ {14 + 43/10} × 1/100

⇒ Take LCM to add 14 and 43/10:

⇒ {140/10 + 43/10} × 1/100

⇒ 183/10 × 1/100

⇒ 183 / 1000 = 0.183

∴ The correct answer is 0.183.

Additional Information

BODMAS Rule

Always simplify expressions in the order of Brackets, Orders, Division, Multiplication, Addition, and Subtraction. Inner brackets must be solved first before moving to outer operations.

Converting Fractions to Decimals

Fractions with denominators that are factors of 10 or 100 can be quickly converted to decimals to speed up calculation (e.g., 1/2 = 0.5, 4/5 = 0.8).

Division by Powers of 10

When dividing any number by 10, 100, or 1000, simply shift the decimal point to the left by the number of zeros in the denominator. For example, 18.3 ÷ 100 = 0.183.

Let's make the arrangement using the information given,

1. Only O is seated between P and M.

2. P is seating at immediate left of O.

3. M is not seated at either of the ends.

4. Only R is seated between N and Q.

5. M is not an immediate neighbour of Q.

Here, we can see that N is seating to the immediate right of M.

Hence, the correct answer is " Immediate right of M ".

The logic followed here is;

Hence, the correct answer is "148".

Given: (Left) CAT OWN EYE AND SAD (Right)

If each alphabet is changed to the following letter in the English alphabetical series

(Left) DBU PXO FZF BOE TBE (Right)

Words which have at least one vowel: DBU, PXO​, BOE​, TBE

So, there are 4 words which have at least one vowel.

Hence, the correct answer is "Four".

The correct answer is Relative motion of the coil and magnet.

Key Points

• The process by which electrical energy can be produced in a coil primarily involves the principle of electromagnetic induction.
• This involves changing magnetic fields inducing electromotive force (EMF) in the coil, as described by Faraday's Law of Electromagnetic Induction.
• Some methods to induce emf in a coil are:
• When a magnet is moved towards or away from a coil, or the coil is moved in relation to the magnet, the flux through the coil changes, inducing an EMF.
• In generators, coils of wire are rotated within a magnetic field. As the coil rotates, the angle between the magnetic field and the plane of the coil changes, altering the magnetic flux and inducing an EMF.
• A changing current in an adjacent coil can alter the magnetic field through the primary coil, thereby inducing an EMF in the secondary coil.

 Additional Information

• Lenz's Law states that the direction of the induced EMF (and hence the induced current) will be such that it opposes the change in magnetic flux that caused it.
• Magnetic flux is defined by the product of the magnetic field ( B ), the area of the coil ( A ), and the cosine of the angle between the magnetic field and the normal to the surface of the coil.

Calculation:

According to question:

⇒ (14 .5 + 25 + 20 + 22)/4

⇒ 20375

∴ Option 3 is the correct answer.

Given statement : P > M > N  = O, X > Y > P

On combining the Equation →  (X > Y > P > M > N  = O)

Option 1 → Y < N ( This relationship is NOT true based on the given statement.) "ANSWER"

Option 2 → X > M ( This relationship is TRUE based on the given statement.)

Option 3 → N < Y  ( This relationship is TRUE based on the given statement.)

Option 4 → O < X ( This relationship is TRUE based on the given statement.)

Hence, "Option 1" is the correct answer.

Shortcut Trick

Equate the quantity of mangoes to find the overall profit easily.

LCM of 12 and 9 is 36.

Cost Price (CP) for 36 mangoes = (900 ÷ 12) × 36 = 2,700.

Selling Price (SP) for 36 mangoes = (1,200 ÷ 9) × 36 = 4,800.

Profit % = (4,800 − 2,700) ÷ 2,700 × 100 = 2,100 ÷ 2,700 × 100 = 7 ÷ 9 × 100 = 77(7)/(9)%.

∴ The correct answer is 77(7)/(9)%.

Alternate Method

Given: CP of 12 mangoes = Rs. 900, SP of 9 mangoes = Rs. 1,200.

Formulas: Profit = SP − CP | Profit % = (Profit ÷ CP) × 100

⇒ Cost Price (CP) of 1 mango = 900 ÷ 12 = Rs. 75.

⇒ Selling Price (SP) of 1 mango = 1,200 ÷ 9 = Rs. 400/3 ≈ Rs. 133.33.

⇒ Profit per mango = 400/3 − 75 = (400 − 225)/3 = 175/3.

⇒ Profit % = [(175/3) ÷ 75] × 100 = (175 ÷ 225) × 100 = 7/9 × 100.

⇒ Profit % = 700/9 = 77(7)/(9)%.

∴ The correct answer is 77(7)/(9)%.

Additional Information

Unitary Method in Profit and Loss

Always calculate the price of a single unit or a common multiple of units to compare CP and SP accurately.

Percentage Conversion

The fraction 1/9 is equal to 11(1)/(9)%. Therefore, 7/9 is 7 × 11(1)/(9)% = 77(7)/(9)%.

The pattern followed here is:-

Hence, the correct answer is "125".

Shortcut Trick

Number 688xy is divisible by 11 and 21 (3 × 7), so it must be divisible by LCM(11, 21) = 231.

Divide the largest 5-digit number 68899 by 231 to find the range: 68899 ÷ 231 ≈ 298.26.

Check 231 × 298 = 68838. Comparing 68838 with 688xy, we get x = 3 and y = 8.

Value = (8 × 3 − 3 × 8 + 3 × 8) = 24 − 24 + 24 = 24.

∴ The correct answer is 24.

Alternate Method

Given: Number 688xy is divisible by 11 and 21.

Divisibility Rule: The number must be divisible by 11, 3, and 7.

⇒ Divisibility by 3: (6 + 8 + 8 + x + y) = (22 + x + y) must be a multiple of 3.

⇒ Divisibility by 11: (6 + 8 + y) − (8 + x) = (6 + y − x) must be 0 or 11.

⇒ Case 1: 6 + y − x = 0 ⇒ x − y = 6. Possible pairs (x,y): (6,0), (7,1), (8,2), (9,3).

⇒ Case 2: 6 + y − x = 11 ⇒ y − x = 5. Possible pairs (x,y): (0,5), (1,6), (2,7), (3,8), (4,9).

⇒ Testing Case 2 for 231: If x=3, y=8, number is 68838. 68838 ÷ 231 = 298 (Exact).

⇒ Therefore, x = 3 and y = 8.

⇒ Required value = 8x − 3y + xy = 8(3) − 3(8) + (3 × 8)

⇒ Value = 24 − 24 + 24 = 24.

∴ The correct answer is 24.

Additional Information

Divisibility Rule of 11

The difference between the sum of digits at odd places and the sum of digits at even places must be 0 or a multiple of 11.

Composite Divisibility

If a number is divisible by two co-prime numbers a and b, it is also divisible by their product a × b.

Divisibility Rule of 3

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

The correct answer is diminishing marginal rate of substitution.

Key Points

• ​This principle states that as a person, the additional satisfaction (or utility) gained from consuming an additional unit of that good decreases.
• This principle underpins the shape and slope of indifference curves.
• An indifference curve represents a locus of points that show different combinations of two goods that give a consumer the same level of satisfaction or utility.
• Essentially, the first unit of a good consumed provides more satisfaction than the second, and the second more than the third, and so on.

Given series:

(Left) G $ 5 & 2 P H 8 # T * S 2 F 8 C 2 7 $ Y 6 F (Right)

Symbols are there which are immediately preceded by a letter and also immediately followed by a number.

Letter → Symbol → Number

(Left) G $ 5 & 2 P H 8 # T * S 2 F 8 C 2 7 $ Y 6 F (Right)

The above underlined symbol are immediately preceded by a letter and also immediately followed by a number.

Hence, the correct answer is "1".

The correct answer is 0.1 Ω.

Key Points

• The resistance RR of a wire is given by the formula: R = ρ $l/a$. where  is the resistivity of the material,  is the length of the wire, and  is the cross-sectional area.
• Given that the resistance of the first wire (length  and area ) is : 0.4= ρ $A/L$.
• Now, for the second wire, which has the same length LLL[Math Processing Error]L  but an area of cross-section 4A4A4A[Math Processing Error]4, the resistance can be calculated as follows: $R' = ρ L/4A$.​
• $R' = 1/4 (ρ L/A) = 1/4 * 0.4 = 0.1Ω.$

The correct answer is Seed.

Key Points

• After fertilization in plants, the ovule gets converted into a seed.
• The involves several changes:
• the fertilized egg within the ovule develops into an embryo,
• the ovule itself forms a seed coat, and
• the surrounding ovary tissue typically develops into a fruit.
• This transformation is crucial for the plant's reproductive cycle.
• Within the ovule, the zygote forms an embryo and integuments become the seed coat.

Additional Information

• The zygote is the initial cell formed when two gamete cells (sperm and egg) are fused during fertilization.
• The zygote is a diploid cell, meaning it has two sets of chromosomes—one from the male gamete (sperm) and one from the female gamete (egg).
• The zygote undergoes its first mitotic division to form a two-celled embryo. The division is asymmetric, resulting in two cells of different sizes: a smaller apical cell and a larger basal cell.
• An embryo is a stage of development in multicellular offspring that follows fertilization and occurs before birth or hatching.
• In humans, the embryonic stage spans from the time of fertilization, up to the end of the 8th week of pregnancy.
• During this period, the foundations for all major organs and body systems are established through a series of complex developmental processes.

The correct answer is Malegam Committee.

Key Points

• The committee was set up by the RBI in October 2010, chaired by Y.H. Malegam.
• The committee sets guidelines to ensure the sector's stability and growth while protecting borrowers' interests.
• Imposed a cap on the interest rate MFIs could charge, suggesting an average cost of funds plus a margin cap of 10-12%.
• Suggested that MFIs should lend only to families with an annual income of up to INR 60,000 in rural areas and INR 1,20,000 in urban areas.

Additional Information

• The R. V. Gupta Committee was established in the late 1990s by the Reserve Bank of India (RBI) to examine.
• The committee provide recommendations on issues related to rural credit and microfinance.
• The committee was chaired by R. V. Gupta, a former Deputy Governor of the RBI.
• Key recommendations of committee are: 
• ​Promotion of Self-Help Groups (SHGs) as a means to improve financial inclusion.
• Simplification of the procedures and documentation required for obtaining rural credit.
• Strengthening the role of the National Bank for Agriculture and Rural Development (NABARD).
• Enhanced monitoring and supervision of rural branches and credit institutions.
• The Parthasarathi Shome Committee, also formally known as the Committee on Tax Administration Reforms Commission (TARC), was constituted by the Government of India.
• It was constituted  to suggest measures to reform the country's tax administration system.
• key recommendations are: 
• ​Recommendations to simplify tax procedures and enforcement to increase taxpayer compliance and reduce evasion.
• Enhancing the services provided to taxpayers to make the process more transparent and taxpayer-friendly.
• Greater use of information technology in tax administration to streamline processes and improve data management.
• Providing a framework for the smooth implementation of the Goods and Services Tax (GST).

Shortcut Trick

From the given conditions, father P age is related to Y in two ways:

1. P = 2X = 3Y − 9
2. P = Q + 20 = (Y + 9) + 20 = Y + 29

Equating both expressions for P: 3Y − 9 = Y + 29

2Y = 38 ⇒ Y = 19

∴ The correct answer is 19 years.

Alternate Method

Given:

Present age of X, Y, P (X's father), and Q (Y's sister).

Equation 1: 2X = 3Y − 9

Equation 2: P = 2X

Equation 3: Y = Q − 9 ⇒ Q = Y + 9

Equation 4: P = Q + 20

Calculations:

From Equation 2 and Equation 4:

⇒ 2X = Q + 20

Substitute Equation 1 (2X = 3Y − 9) into the above:

⇒ 3Y − 9 = Q + 20

Substitute Equation 3 (Q = Y + 9) into the above:

⇒ 3Y − 9 = (Y + 9) + 20

⇒ 3Y − 9 = Y + 29

⇒ 3Y − Y = 29 + 9

⇒ 2Y = 38

⇒ Y = 19

∴ The correct answer is 19 years.

Additional Information

Constant Age Difference

The difference between the ages of two individuals remains constant at any point in time.

Age Linear Equations

Always express all individual ages in terms of a single variable (like Y) to simplify the calculation.

Time Shift in Ages

If a person is n years older than another now, they were n years older 10 years ago and will be n years older 10 years later.

The correct answer is always negative.

Key Points

• Focal Length is the distance from the mirror's surface (along the principal axis) to the focal point.
• The focal length is positive for Concave mirror and is half the distance to the center of curvature.
• For a concave mirror, the focal length is positive and is half the distance to the center of curvature.
• Mathematically Radius of curvature (r) = 2 x focal length (f).

Additional Information

• Some important terms related to spherical mirrors:
• ​Spherical mirrors: A mirror with a surface that forms part of the surface of a sphere. There are two types: concave and convex mirrors.
• Concave mirror: A spherical mirror with a reflective surface that curves inward. It converges light rays to a focal point
• Convex mirror: A spherical mirror with a reflective surface that curves outward. It diverges light rays.
• Principal mirror: An imaginary line passing through the center of curvature and the vertex (center of the mirror). It is the optical axis of the mirror.
• Centre of Curvature: The center of the sphere from which the mirror segment is taken. It is a point on the principal axis and is equidistant from all points on the mirror's surface.
• Radius of Curvature: The distance from the mirror's surface to the center of curvature. For spherical mirrors, this is twice the focal length ((R = 2f)).
• Pole (Vertex): The central point on the mirror’s surface. It is the midpoint of the mirror.
• Focal Point: The point on the principal axis where parallel rays of light either converge or appear to converge after reflecting from the mirror. For concave mirrors, it is in front of the mirror; for convex mirrors, it is behind the mirror.
• Focal length: The distance between the mirror's surface (at the vertex) and the focal point. It is half the radius of curvature ((f = R/2)). For concave mirrors, it is positive, and for convex mirrors, it is negative.
• Aperture: The effective diameter of the mirror. It is the portion of the mirror through which light is reflected.
• Real image: An image formed by the actual convergence of light rays. It can be projected onto a screen and is inverted relative to the object.
• Virtual image: An image formed by the apparent divergence of light rays from a point behind the mirror. It cannot be projected onto a screen and is upright relative to the object.

Shortcut Trick

Apply the direct Algebraic Identity: (Difference)² = (Sum)² − 4 × (Product).

Difference² = 34² − 4 × 64

Difference² = 1156 − 256 = 900

Difference = √900 = 30

∴ The correct answer is 30.

Alternate Method

Given:

Sum of two positive numbers (x + y) = 34

Product of the numbers (xy) = 64

Formula Used:

To find the positive difference (x − y), we use the relation:

(x − y)² = (x + y)² − 4xy

Calculations:

⇒ (x − y)² = (34)² − 4 × (64)

⇒ (x − y)² = 1156 − 256

⇒ (x − y)² = 900

⇒ x − y = √900

⇒ x − y = 30

∴ The correct answer is 30.

Additional Information

Important Algebraic Identities

1. (a + b)² = a² + 2ab + b²
   
2. (a − b)² = a² − 2ab + b²
   
3. (a + b)² − (a − b)² = 4ab

Quadratic Equations Connection

If sum (S) and product (P) are given, the numbers are roots of t² − St + P = 0. Here, t² − 34t + 64 = 0 factors into (t − 32)(t − 2) = 0, so numbers are 32 and 2.

Difference calculation

The positive difference is always the absolute value |x − y| = √[ (x + y)² − 4xy ].

The correct answer is Poona.

Key Points

• Maharshi Dhondo Keshav Karve, (known as Maharshi Karve), was a social reformer in India who dedicated his life to the cause of women's education and empowerment.
• His efforts laid the foundation for many educational initiatives for women in India.
• Karve established the first institution Hingane Stree Shikshan Samstha for the education and upliftment of widows at Hingane at Pune, in 1896.
• Karve founded the first women's university in India in 1916, named Shreemati Nathibai Damodar Thackersey (SNDT) Women's University,
• Karve was an active advocate for social reforms. He worked tirelessly to change societal attitudes towards widow remarriage and women's rights.

The correct answer is 3.

Key Points

• The salient features of the act are : 
• Gram Sabha - It is a body consisting of persons registered in the electoral rolls of a village comprised within the area of Panchayat at the village level.
• Three-Tier System - The act provides for a three-tier system of Panchayati raj in every state, that is, panchayats at the village, intermediate, and district levels.
• State Election Commission to hold Election of Members and Chairpersons at every level. Hence, statement 2 is correct.
• Reservation of Seats
• Duration of Panchayats - The act provides for a five-year term of office to the panchayat at every level.
• State Election Commission - The superintendence, direction and control of the preparation of electoral rolls and the conduct of all elections to the panchayats shall be vested in the state election commission. Hence, statement 3 is correct.
• Finance Commission - The governor of a state shall, after every five years, constitute a finance committee to review the financial position of the panchayats.
• Every state shall constitute at the District level, a District planning committee to consolidate the plans prepared by panchayats and municipalities in the District and to prepare a draft development plan for District as a whole. This provision is mandated by the 74th constitutional amendment act, 1992. This provision deals with the Urban Local bodies, Article 243-ZD.

Given statement is:

P < Q = R < T = M, J < N < P 

Combination of statements;

J < N < P < Q = R < T = M 

Conclusion:

1) M > J → Followed (as J < N < P < Q = R < T = M i.e M > J direct relationship established between M and J)

2) N > R → Does not Followed (as N < P < Q = R i.e N < R direct relationship not established between N and R)

3) J > T → Does not Followed (as J < N < P < Q = R < T i.e J < T direct relationship not established between J and T)

4) R < J → Does not Followed (as J < N < P < Q = R i.e J < R direct relationship not established between R and J)

Hence, the correct answer is "M > J".

The correct answer is In mitochondria, one molecule of pyruvate breaks down to give three molecules of carbon dioxide.

Key Points

• Aerobic respiration is a metabolic process that takes place in the presence of oxygen.
• It is the primary method by which cells convert glucose (a type of sugar) into ATP (adenosine triphosphate), the energy currency of the cell.
• It is more efficient than anaerobic respiration and results in the complete oxidation of glucose.
• aerobic respiration consists of four main stages: ​

The correct answer is H = I2 RT.

Key Point

• ​J

oule's Law states that when an electric current passes through a conductor, it produces heat due to the resistance of the conductor. The formula is: $H = I^2 RT$. where,

• H is the heat produced (in joules),
• II  is the current (in amperes),
• RR  is the resistance (in ohms),
• TT  is the time (in seconds) for which the current flows.
• Joule's Law helps us understand the relationship between electricity and heat generation, allowing for safer and more efficient electrical designs.
• It has various applications such as: 
• Electric Heaters: The Joule's Law can applied in electric heating devices, where resistive heating is used to generate warmth.
• Fuses: The heat generated by the excess current discontinue the circuit.
• Wiring: In electrical installations, the resistance of wires must be considered to prevent excessive heat buildup, which can lead to fires.

According to given information:

We can see that the shaded part denotes the number of students are there who are also lawyers but NOT from America = 20

Hence, the correct answer is "20".

The  correct answer is Li.

Key Points

• Atomic radius is defined as the distance from the center of the nucleus to the outermost electron shell.
• As we move across a period from left to right in the periodic table, the atomic number (number of protons) increases.
• The increase in positive charge in the nucleus attracts the electron cloud more strongly.
• This results in a higher effective nuclear charge (net positive charge experienced by electrons), pulling the electrons closer to the nucleus and thus decreasing the atomic radius.
• Atomic radii values (in picometres):
• Lithium (Li): 152 pm
• Beryllium (Be): 112 pm
• Nitrogen (N): 70 pm
• Oxygen (O): 66 pm

The correct answer is CH3OH.

Key Points

• When carbon monoxide (CO) reacts with hydrogen gas (H₂) at high pressures, such as 340 atm, the reaction typically produces methanol (CH₃OH). The reaction can be represented as follows: $CO(g)+〖2H〗_2 (g) ( 340 atm ) ⃗〖CH〗_3 OH(l)$
• This reaction is part of the industrial process known as the "Synthesis Gas" or "Syngas" conversion.
• The use of methanol as a fuel or fuel additive reduces emissions of particulate matter, CO₂, and other pollutants compared to conventional fossil fuels.
• Methanol is used as an antifreeze agent in windshield washer fluid and natural gas pipelines.

Given:

a2 + b2 = 160 and (a - b) = 8

Concept used:

a2 + b2 = (a - b)2 +  2ab

Calculation:

Here,

a2 + b2 = (a - b)2 +  2ab

⇒ 160 = (8)2 +  2 × ab

⇒ 2ab = 160 - 64

⇒ ab = 80 - 32

⇒ ab = 48

∴ Option 3 is the correct answer.

The correct answer is Prajakta Koli.

Key Points

• In January 2022, Prajakta Koli became India’s first UNDP Youth Climate Champion.
• Prajakta Koli is a popular Indian content creator, actress, and well-known for her YouTube channel, "MostlySane,"
• UNDP was founded in 1965 as part of the United Nations system.
• The headquarters of the United Nations Development Programme (UNDP) is located in New York City, United States.

Additional Information

• List of the Youth Climate Champions announced in 2022

Shortcut Trick

Ratio of radius (r) to height (h) is 2 : 1.

Let r = 2x and h = x.

Volume = πr²h ⇒ (22/7) × (2x)² × x = 4312

⇒ (22/7) × 4x³ = 4312 ⇒ x³ = 343 ⇒ x = 7.

CSA = 2πrh = 2 × (22/7) × 14 × 7 = 616 cm².

∴ The correct answer is 616 cm².

Alternate Method

Given: Ratio r : h = 2 : 1 and Volume (V) = 4312 cm³.

Formula Used: Volume of cylinder = πr²h; Curved Surface Area (CSA) = 2πrh.

⇒ Let radius (r) = 2x and height (h) = x.

⇒ Volume = (22/7) × (2x)² × x = 4312

⇒ (22/7) × 4x³ = 4312

⇒ 4x³ = (4312 × 7) / 22

⇒ 4x³ = 196 × 7 = 1372

⇒ x³ = 1372 / 4 = 343

⇒ x = 7 cm.

⇒ Radius (r) = 2 × 7 = 14 cm; Height (h) = 7 cm.

⇒ Curved Surface Area (CSA) = 2 × (22/7) × 14 × 7

⇒ CSA = 2 × 22 × 14 = 616 cm².

∴ The correct answer is 616 cm².

Additional Information

Total Surface Area of Cylinder

It is the sum of CSA and the area of the two circular bases: TSA = 2πrh + 2πr² = 2πr(h + r).

Hollow Cylinder Volume

The volume of a hollow cylinder with outer radius R and inner radius r is V = π(R² − r²)h.

Unit Conversions

1 liter = 1000 cm³ and 1 m³ = 1,000,000 cm³.

Given equation → 13.99 - 4.02 + 19.89 × 5.99 = ?

Approximate value of → 13.99 ≈ 14; 4.02 ≈ 4; 19.89 ≈ 20; 5.99 ≈ 6

Given equation becomes → 14 - 4 + 20 × 6

By using BODMAS rule, we get :-

= 14 - 4 + 20 × 6

= 14 - 4 + 120

= 14 + 116

= 130

Hence, the correct answer is "130".

Calculation:

Let the total number of students in class XII be x.

According to question

⇒ x × 9% = 18

⇒ x = 200

∴ Option 1 is the correct answer.

The least possible Venn diagram for the given statement is as follows:

Conclusion:

I) Some tigers are lions. Not Follows (There is no relationship between tigers and lions)

II) No lion is a tiger. Not Follows (There is no relationship between tigers and lions)

III) Some lions are birds. Follows (Given statement is all birds are lions. So the conclusion follows)

Hence, the correct answer is "Only conclusion III follows".

The correct answer is Zn, Fe, Cu.

Key Points

• Zinc (Zn): Obtained from zinc oxide (ZnO) using carbon.
• Iron (Fe): Extracted from iron ore (Fe2O3 or Fe3O4) using carbon in a blast furnace.
• Copper (Cu): Obtained from copper oxide (CuO) using carbon.
• Atomic no. of Zn, Fe and Cu is 30,26,29 respectively.

Additional Information

The correct answer is 75.

Key Points

• The RBI regulation mandates that at least 75% of the total assets of an NBFC-MFI must be microfinance loans.
• Microfinance loans are small loans provided to individuals or small businesses, typically those who lack access to traditional banking services.
• For households with annual income of up to ₹3 lakh, loans are classified as microfinance.
• Total loans for households with annual income under ₹3 lakh should not exceed 50% of the household income.

Additional Information

• The RBI was established on April 1, 1935, under the Reserve Bank of India Act, 1934.
• Non-Banking Financial Companies that exclusively deal in microfinance. These are regulated by the RBI.
• The RBI sets a cap on how much an MFI can lend to a borrower. For instance, the total indebtedness of a borrower should not exceed ₹1.25 lakh from all sources.
• MUDRA (Micro Units Development and Refinance Agency) Scheme: Provides financial support to small businesses through MFIs, NBFCs, and banks.
• Self-Help Group-Bank Linkage Program (SHG-BLP): Promoted by NABARD, it links SHGs to banks, enabling them to access formal banking services.

Decision:

The Board of Directors of the Digital Marketing Company AMX have decided to shift their headquarters from the city center to the business towers located on the outskirts of the city.

Statements:

I) Low property rent in the outskirts would help reduce the overall expenditure of the company substantially. → Strengthen (It is beneficial as the company income will be increased due to low property rent.)

II) The business towers are the hub of multiple MNCs with frequent visitors from international companies as well. This will give more visibility to AMX.  → Strengthen (This statement is helpful to take decisions for the company because all the MNCs are located nearby as big towers will help MNCs in long-term performance.)

Hence, the correct answer is "Both statements I and II strengthen the decision".

The correct answer is Telangana.

Key Points

• In 2017, Telangana declared Urdu as the second official language of the state.
• Bihar declared Urdu as its second official language in 1981
• Uttar Pradesh declared Urdu as its second official language in 1989.
• Urdu was given the status of an official language in 1950 when the Indian Constitution came into force.

Additional Information

• Urdu was included as one of the 15 languages initially listed in the Eighth Schedule of the Constitution.
• Article 343 of the Indian Constitution: Declares Hindi in the Devanagari script as the official language of the Union.
• The Eighth Schedule of the Constitution lists the recognized languages that are entitled to develop and be promoted by the government.
• Bodo, Dogri, Maithili, and Santhali were the latest additions, included in 2003 by the 92nd Constitutional Amendment.
• India protects minority languages under Article 29 of the Constitution, which provides for the protection of cultural and linguistic rights.

The table is alphabet place value:

The pattern followed is: 

BG - FK - JO →

NS - RW - VA →

Similarly,

DI - HM - LQ →

Hence, the correct answer is "DI - HM - LQ".

The least possible Venn diagram for the given statement is as follows:

Conclusions:

I) Some petals are birds. Follows (In the given statements mentioned some birds are petals. So some petals are birds as follows)

II) Some flowers are birds. Not Follows (In the given statement mentioned no bird is a flower. So some flowers are birds is not followed)

III) Some petals are flowers. Follows (In the given statement mentioned some flowers are petals. So this conclusion is followed)

Hence, the correct answer is "Only conclusions I and III follow".

Shortcut Trick

Total distance = sum of lengths = 160 + 90 = 250 m.

Relative speed (same direction) = 50 − 40 = 10 km/h.

Convert speed to m/s: 10 × (5/18) = 25/9 m/s.

Time = Distance ÷ Relative Speed = 250 ÷ (25/9) = 10 × 9 = 90 sec.

∴ The correct answer is 90 sec.

Alternate Method

Given:

Length of Train 1 (L₁) = 160 m

Length of Train 2 (L₂) = 90 m

Speed of Train 1 (V₁) = 40 km/h

Speed of Train 2 (V₂) = 50 km/h

Formula Used:

Time = (L₁ + L₂) ÷ Relative Speed

Relative Speed (Same Direction) = |V₁ − V₂|

Calculations:

⇒ Total distance to cover = 160 + 90 = 250 m

⇒ Relative speed = 50 − 40 = 10 km/h

⇒ Converting speed into m/s = 10 × (5/18) = 25/9 m/s

⇒ Time taken = 250 ÷ (25/9)

⇒ Time taken = (250 × 9) ÷ 25

⇒ Time taken = 10 × 9 = 90 seconds

∴ The correct answer is 90 sec.

Additional Information

Relative Speed in Opposite Direction

When two objects move in opposite directions, their relative speed is the sum of their individual speeds: V_rel = V₁ + V₂.

Unit Conversion

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

Crossing a Stationary Object

If a train crosses a pole or a man, the distance covered is equal to the length of the train itself.

57, 87, 35, 97, 56, 74

1. The above numbers are multiplied by 2, and we get 114, 174, 70, 112, 148

2. The digits of each number are written in reverse order

114, 174, 70, 112, 148 → 411, 471, 07, 211, 841

3. The numbers are arranged in descending order, and we get: 841, 471, 411, 211, 07

After arranging numbers in descending order only one number 211 does not change its position.

Hence, the correct answer is "One".

Shortcut Trick

In a quadratic equation ax² + bx + c = 0, if a, b, and c all have the same sign (all positive), then the roots must be negative.

Here, a = 11, b = 19, and c = 8 (all positive), so the roots cannot be positive.

Calculate Discriminant D = b² − 4ac = 19² − 4 × 11 × 8 = 361 − 352 = 9.

Since D > 0 and a perfect square, the roots are real, rational, and distinct.

Combining these, the roots are negative real.

∴ The correct answer is Both roots are negative real.

Alternate Method

Given Equation: 11x² + 19x + 8 = 0

We can find the nature of the roots by factorization or by calculating the Discriminant and Sum/Product of roots.

Step 1: Calculate the Discriminant (D)

⇒ D = b² − 4ac

⇒ D = 19² − 4 × 11 × 8

⇒ D = 361 − 352 = 9

⇒ Since D > 0, the roots are real and distinct.

Step 2: Check the signs of the roots

⇒ Sum of roots (α + β) = −b/a = −19/11 (Negative)

⇒ Product of roots (α × β) = c/a = 8/11 (Positive)

⇒ A positive product means both roots have the same sign; a negative sum means that sign must be negative.

Step 3: Solving for roots (Verification)

⇒ 11x² + 11x + 8x + 8 = 0

⇒ 11x(x + 1) + 8(x + 1) = 0

⇒ (11x + 8)(x + 1) = 0

⇒ x = −8/11 and x = −1

⇒ Both roots are negative and real.

∴ The correct answer is Both roots are negative real.

Additional Information

Nature of Roots (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/non-real.

Signs of Roots Rule

For ax² + bx + c = 0, if all coefficients a, b, c have the same sign, roots are negative. If a and c have the same sign but b has the opposite sign, roots are positive.

Sum and Product of Roots

For a quadratic equation, the Sum of roots is −b/a and the Product of roots is c/a.

Perfect Square Discriminant

If D is a perfect square and a, b, c are rational, the roots are rational numbers.

The correct answer is Magnesium chloride (MgCl2).

Key Points

• The compound that will NOT show covalent bonding is Magnesium chloride (MgCl2).
• Magnesium chloride (MgCl2) forms ionic bonds, not covalent bonds.
• Magnesium (Mg) is a metal, and chlorine (Cl) is a non-metal. Magnesium loses two electrons to form a Mg²⁺ ion.
• Each chlorine atom gains one electron to form two Cl⁻ ions, resulting in an ionic bond between them.

Additional Information

• Ammonia (NH3): Shows covalent bonding, with nitrogen sharing electrons with hydrogen atoms.
• Oxygen (O2): Forms a covalent bond between two oxygen atoms through a double bond.
• Methane (CH4): Shows covalent bonding, with carbon sharing electrons with four hydrogen atoms.
• Ionic Bonds are formed through the transfer of electrons from one atom to another.
• Covalent Bonds are formed through the sharing of electrons between atoms.

The correct answer is 15-18.

Key Points

• An adult human typically breathes 15 to 18 times per minute while at rest.
• Children tend to breathe faster, with rates often exceeding 20 breaths per minute.
• Athletes may have lower resting respiratory rates due to more efficient lung function.
• The average resting respiratory rate for adults is generally around 16 breaths per minute.

Additional Information

• External Respiration: The process of exchanging gases (oxygen and carbon dioxide) between the lungs and the blood.
• Internal Respiration: The exchange of gases between the blood and body tissues at the cellular level.
• Inhalation (Inspiration): The Diaphragm contracts and moves downward, and the intercostal muscles contract, expanding the chest cavity and decreasing pressure, allowing air to flow into the lungs.
• Exhalation (Expiration): Diaphragm and intercostal muscles relax, the chest cavity decreases, and air is pushed out of the lungs. This process can be passive at rest or active during exertion.
• Oxygen is transported from the alveoli into the bloodstream, where it binds to hemoglobin in red blood cells.
• Carbon dioxide, produced by cells as a waste product, is transported from the blood to the alveoli to be exhaled.

Shortcut Trick

A completes 1 work in 12 × (3/2) = 18 days.

B completes 1 work in 3 × 4 = 12 days.

Combined Time = (18 × 12) ÷ (18 + 12) = 216 ÷ 30 = 36 ÷ 5 days.

∴ The correct answer is 7(1/5) days.

Alternate Method

Given:

A can do 2/3 of work in 12 days.

B can do 1/4 of work in 3 days.

Formula Used:

Efficiency = Total Work ÷ Time taken

Total time for full work = (Days × Total fraction) ÷ Work fraction

⇒ Total days for A = 12 × (3/2) = 18 days

⇒ Total days for B = 3 × 4 = 12 days

⇒ LCM of 18 and 12 = 36 units (Total Work)

⇒ Combined Efficiency of A + B = 2 + 3 = 5 units/day

⇒ Time taken = 36 ÷ 5 = 7(1/5) days

∴ The correct answer is 7(1/5) days.

Additional Information

Work and Efficiency

Efficiency is inversely proportional to the time taken to complete the work when total work is constant.

Combined Work Formula

If person X takes x days and person Y takes y days, together they take (xy) ÷ (x + y) days.

Fractional Work Rule

If 1/n of work is done in T days, the whole work is done in n × T days.

The correct answer is Tuberculosis. 

Key Points

• The Data-Driven Research initiative launched by the Department of Biotechnology, Ministry of Science and Technology on March 24, 2022, focuses on eradicating Tuberculosis (TB).
• World TB Day: The initiative was announced on World TB Day, which is observed on March 24 each year.
• Global Health Concern TB is a significant public health issue in India, accounting for a substantial number of TB cases worldwide.
• The primary objective of the initiative is to eradicate TB in India by utilizing a data-driven approach.

Additional Information

• AIDS is caused by HIV (Human Immunodeficiency Virus), which attacks the immune system, specifically CD4 cells (T cells).
• HIV is transmitted through blood, semen, vaginal fluids, rectal fluids, and breast milk.
• COVID-19 is caused by the SARS-CoV-2 virus, a novel coronavirus that emerged in late 2019.
• COVID-19 is diagnosed through RT-PCR tests or rapid antigen tests that detect the presence of the virus.
• Cancer is a group of diseases characterized by the uncontrolled growth and spread of abnormal cells in the body.
• There are many types of cancer, classified based on the tissue or organ affected. Common types include breast cancer, lung cancer, prostate cancer, colorectal cancer, and skin cancer.
• Treatment options vary depending on the type and stage of cancer and may include surgery, radiation therapy, chemotherapy, immunotherapy, and targeted therapy.
• New treatments, such as CAR-T cell therapy and personalized medicine, are emerging in oncology.

The correct answer is Walking to nearby places without using vehicles.

Key Points

• Natural resources are materials and components that occur naturally in the environment and can be used for economic gain or to meet human needs.
• They are typically classified into two main categories: renewable and non-renewable resources.
• Renewable Resources are those resources that can be replenished naturally over time.
• Non-renewable resources are those Resources that do not replenish at a sustainable rate.

Additional Information

• Importance of Natural Resources
• Economic Development: Natural resources are crucial for industries and agriculture, driving economic growth.
• Energy Production: Many resources provide energy necessary for modern life, from electricity to transportation.
• Ecosystem Services: They support ecosystems that provide clean air, water, and biodiversity, which are essential for life.
• Raw Materials: Used in manufacturing and construction, contributing to infrastructure and technological advancement.
• Challenges and Issues
• Overexploitation: Unsustainable use of resources can lead to depletion, habitat destruction, and biodiversity loss.
• Pollution: Extraction and use of natural resources can lead to air, water, and soil pollution.
• Climate Change: Fossil fuel consumption significantly contributes to greenhouse gas emissions, affecting global temperatures and weather patterns.
• Resource Conflicts: Competition for limited resources can lead to social and political tensions, especially in areas with scarce water or arable land.

The correct answer is 2030.

Key Points

• The National Air Sports Policy (NASP) 2022 aims to make India one of the top nations in air sports by the year 2030.
• The policy focuses on promoting various air sports such as drones, paragliding, skydiving, hang gliding, and aerobatics.
• The National Air Sports Policy (NASP) 2022 was launched by the Ministry of Civil Aviation in India.
• The National Air Sports Policy (NASP) 2022 was launched by Jyotiraditya Scindia, who was the Minister of Civil Aviation at the time.

Additional Information 

Calculation:

Let the number be x.

According to question:

40% of 60% of $\frac{5}{8}$ × x = 339

⇒ 2/5 × 3/5 × 5/8 × x = 339

⇒ x = 113 × 20

⇒ x = 2260

∴ Option 1 is the correct answer.

The correct answer is atmospheric refraction.

Key Point

• The random wavering of objects seen through a turbulent stream of hot air rising above a fire is atmospheric refraction.
• The refractive index of air is approximately 1.0003 under standard conditions, which means light travels slightly slower in air than in a vacuum.
• Higher humidity decreases the density of air, which can also influence the refractive index.
• Atmospheric refraction causes stars to appear to twinkle as their light passes through varying layers of the atmosphere.

Additional Information

• Total internal reflection is the complete reflection of light within a medium. It occurs when light travels from a medium with a higher refractive index to a medium with a lower refractive index.
• The critical angle is the minimum angle of incidence at which total internal reflection occurs. It is specific to the pair of media involved.
• Dispersion of light is the process by which light separates into its constituent colors when passing through a medium, such as a prism.
• Visible Spectrum: The visible spectrum consists of seven colors, often remembered by the acronym VIBGYOR: Violet, Indigo, Blue, Green, Yellow, Orange, and Red.
• Scattering of light is the process by which light is redirected in various directions as it encounters particles or irregularities in a medium.

Shortcut Trick

Ratio of students in the two groups = 8 : 12 = 2 : 3

Weighted Average score = [ (2 × 60) + (3 × 40) ] ÷ (2 + 3)

Average score = (120 + 120) ÷ 5 = 240 ÷ 5 = 48

∴ The correct answer is 48.

Alternate Method

Given:

Total students in the class = 20

Number of students in Group 1 = 8 | Average score = 60

Number of students in Group 2 = 20 − 8 = 12 | Average score = 40

Formula: Average = (Total sum of scores) ÷ (Total number of students)

⇒ Total score of 8 students = 8 × 60 = 480

⇒ Total score of remaining 12 students = 12 × 40 = 480

⇒ Total score of the whole class = 480 + 480 = 960

⇒ Average score of 20 students = 960 ÷ 20

⇒ Average score = 48

∴ The correct answer is 48.

Additional Information

Weighted Average Formula

When multiple groups are combined, the weighted average is calculated as A_w = (n₁a₁ + n₂a₂ + ...) ÷ (n₁ + n₂ + ...).

Net Deviation Method

The sum of deviations of all observations from their arithmetic mean is always zero (Σ(x_i − x_avg) = 0).

Effect of Operations on Average

If every value in a set is multiplied or divided by a constant k, the average of the set is also multiplied or divided by k.

Given: 

A Sravan leaves point Y and travels 5 km towards the north.

Then he turned right, walked 5 km, turned right and walked 7 km.

Then he turned right and walked 15 km.

Then he turned right and walked 2 km.

Finally, he turns right, travels 5 km and stops at point M. 

Thus, Sravan must travel (15 km - 5 km - 5 km) 5 km from point M to point Y in the east direction.

Hence, "Option 1" is the correct answer.

The correct answer is Hanumanth Commitee.

 Key Points

• The committee constituted for the promotion of small-scale industries is the Hanumanth Committee.
• Hanumanth Committee: Formed in 1997, it focused on issues related to the growth and promotion of small-scale and medium-sized enterprises in India.
• It was headed by Dr. C. H. Hanumantha Rao, an economist and former Director of the National Institute of Rural Development.
• Emphasized the role of small industries in promoting regional development and balancing industrial growth across different areas.

Additional Information

• The Karve Committee, officially known as the “Committee on the Status of Women in India,” was established in 1971.
• The committee was constituted by the Government of India under the chairmanship of Dr. D. D. Karve in 1971.
• The Raja Chelliah Committee, formally known as the Committee on Tax Reforms, was established in 1991.
• It was chaired by Dr. Raja J. Chelliah, an eminent economist and a prominent figure in India's economic policy formulation.
• The Kelkar Committee, officially known as the Task Force on the Goods and Services Tax (GST), was constituted in 2003.
• It was chaired by Dr. Vijay Kelkar, an eminent economist and former Chairman of the Finance Commission.

Shortcut Trick

Apply the difference of squares formula a² − b² = (a − b)(a + b) twice.

x⁴ − 625 = (x²)² − (25)² = (x² − 25)(x² + 25).

Further factorise (x² − 25) as (x − 5)(x + 5).

Final expression: (x − 5)(x + 5)(x² + 25).

∴ The correct answer is (x − 5)(x + 5)(x² + 25).

Alternate Method

Given: Algebraic expression x⁴ − 625.

Formula Used: a² − b² = (a − b)(a + b)

Calculations:

⇒ x⁴ − 625

⇒ (x²)² − (25)²

⇒ (x² − 25)(x² + 25)

⇒ [(x)² − (5)²](x² + 25)

⇒ (x − 5)(x + 5)(x² + 25)

∴ The correct answer is (x − 5)(x + 5)(x² + 25).

Additional Information

Difference of Squares

A polynomial of the form a² − b² is always factorable into (a − b)(a + b).

Sum of Squares

An expression like a² + b² cannot be factorised further using real numbers.

Higher Power Factorisation

For xⁿ − aⁿ, if n is even, it can always be reduced using the difference of squares method repeatedly.

Shortcut Trick

For fourth proportional of a, b, c, use the ratio a : b = c : d.

0.15 : 0.35 ⇒ 15 : 35 ⇒ 3 : 7

If 3 units = 12, then 1 unit = 4.

7 units = 7 × 4 = 28.

∴ The correct answer is 28.

Alternate Method

Given: First term (a) = 0.15, Second term (b) = 0.35, Third term (c) = 12

Formula Used: Fourth Proportional (d) = (b × c) ÷ a

⇒ Let the fourth proportional be x.

⇒ 0.15 / 0.35 = 12 / x

⇒ x = (0.35 × 12) ÷ 0.15

⇒ x = (35 × 12) ÷ 15

⇒ x = (7 × 12) ÷ 3

⇒ x = 7 × 4 = 28

∴ The correct answer is 28.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(a × b).

Third Proportional

The third proportional to two numbers a and b is calculated as b² ÷ a.

Basic Proportion Rule

In any proportion a : b :: c : d, the product of extremes equals the product of means (a × d = b × c).

The correct answer is Article 23.

Key Points

• Article 23 of the Indian Constitution prohibits human trafficking and forced labor.
• Article 23(1) explicitly prohibits the trafficking of human beings and any form of forced labor.
• Article 23(2) provides for exceptions where compulsory service may be mandated for public purposes.
• The Immoral Traffic (Prevention) Act, 1956: This act aims to combat trafficking for commercial sexual exploitation.
• The Bonded Labor System (Abolition) Act, 1976: This act prohibits the bonded labor system, which often leads to forced labor conditions.

Additional Information

• Article 21 states, “No person shall be deprived of his life or personal liberty except according to procedure established by law.”
• Article 26 grants every religious denomination or any section thereof the right to:
• Establish and maintain institutions for religious and charitable purposes.
• Manage its own affairs in matters of religion.
• Own and acquire movable and immovable property.
• Administer such property in accordance with law.
• Article 28 prohibits the state from imposing religious instruction in educational institutions wholly maintained by the state.
• Article 28(1) allows religious instruction in educational institutions administered by a minority community, provided it does not receive government funding.

The logic here is as follows:

The position values of the letters, according to the English alphabet series:

'ADMIT is written as 'BFPMY'

‘ACTOR’ is written as "BEWSW"

Similarly;

'ABUSE' will be written as 

Hence, the correct answer is "BDXWJ".

The correct answer is Casual contacts like handshakes or hugs with the infected people.

Key Points

• HIV is a virus that attacks the body's immune system, specifically targeting CD4 cells (T cells), which are crucial for fighting infections.
• If not treated, HIV can lead to the disease AIDS (Acquired Immunodeficiency Syndrome).
• Initial symptoms may appear 2 to 4 weeks after infection and can include flu-like symptoms such as fever, headache, fatigue, and swollen lymph nodes.
• After the initial infection, the virus may become less active but still remain in the body. This stage can last several years.

Additional Information

• Ways HIV is Transmitted: HIV can be transmitted through:
• Unprotected sexual contact with an infected person.
• Sharing needles or syringes.
• From mother to child during childbirth or breastfeeding.
• Exposure to infected blood or body fluids.
• Common tests include:
• Antibody Tests: Detect antibodies to HIV.
• Antigen Tests: Detect HIV proteins (antigens).
• Nucleic Acid Tests (NAT): Detect the virus itself.

The following arrangement is as follows:

Amit, Bineet, Chandan, Dipti, Gyan and Farhaan live on six different floors of the same building.

1) Dipti lives on an even numbered floor but not on floor number 4 and only two people live between Dipti and Amit.\

Case 1:

 

 

 

 

 

Case 2: 

 

 

 

 

 

2) Farhaan lives on an even numbered floor and Chandan lives immediately below Farhaan.

Case 1: 

 

 

 

 

 

Case 2:

3) Neither Chandan nor Bineet live on the lowermost floor.

Here this conditions contradicts in Case (1), neither Chandan nor Bineet live on the lowermost floor.

 

 

 

 

 

So this is the final arrangement.

Hence, the correct answer is "Farhaan".

The correct answer is 

Key Points

• Commonly used to describe fine ceramic or porcelain dinnerware. The term "China" is derived from the country of China.
• The production of ceramics in China dates back to around 18,000 BCE. The country is known as the birthplace of porcelain.
• The chemical composition of china (or porcelain) is primarily based on kaolin, feldspar, and quartz, with variations for specific types like bone china.
• High-quality china dishes are durable and resistant to chipping, making them suitable for everyday use.

Additional Information

• Types of China:
• Porcelain: Made from kaolin clay, feldspar, and quartz, porcelain is fired at high temperatures, resulting in a strong, durable, and translucent finish.
• Bone China: A type of porcelain that includes bone ash, making it lighter and more chip-resistant than standard porcelain.
• Stoneware: Made from denser clay, stoneware is fired at high temperatures, resulting in a robust product often used for everyday items.
• Chinaware—primarily includes the following components:
• Kaolin (Alumina Silicate): Al₂Si₂O₅(OH)₄
• Feldspar: KAlSi₃O₈ (for potassium feldspar), NaAlSi₃O₈ (for sodium feldspar), CaAl₂Si₂O₈ (for calcium feldspar).
• Quartz (Silica): SiO₂
• Bone Ash (for Bone China): Primarily composed of calcium phosphate (Ca₃(PO₄)₂).

The correct answer is Only (a).

Key Points

• The phenomenon of change in the direction/path of light rays when it travel from one medium to another is called refraction of light.
• When light moves from air (n ≈ 1) to glass (n ≈ 1.5), it slows down and bends towards the normal.
• The First Law of Refraction of Light states that the incident ray, refracted ray, and normal to the interface at the point of incidence all lie in the same plane.
• The second Law of Refraction of Light states that the ratio of the sine of the angle of incidence (i) and the sine of the angle of refraction (r) is constant.

Additional Information

• The visible spectrum ranges from approximately 400 nm (violet) to 700 nm (red). This is the portion of the spectrum visible to the human eye.
• Light can be polarized by reflection, scattering, or passing through polarizing filters.
• Polarization is used in sunglasses to reduce glare and in various optical devices.
• Light exhibits both wave-like and particle-like properties, leading to concepts like wave functions and photon behavior.
• The frequency of visible light ranges from about 400 THz (terahertz) for red light to about 789 THz for violet light.
• The energy of light photons increases with increasing frequency (or decreasing wavelength).

The logic here is as follows:

Logic: Alphabet + 5 and Number + 4.

Hence, the correct answer is "LG29W".

The correct answer is First.

Key Points

• The Fundamental Duties were recommended by the Swaran Singh Committee in 1976.
• Based on its recommendations, the 42nd Amendment Act of 1976 added ten Fundamental Duties to the Indian Constitution1.
• The Fundamental Duties are listed under Article 51A of the Indian Constitution.
• The 11th Fundamental Duty was added later by the 86th Amendment Act of 2002.
• These duties are non-justiciable, meaning they are not enforceable by law but are considered moral obligations for citizens.

Additional InformationAccording to Article 51A, it shall be the duty of every citizen of India:

1. to abide by the Constitution and respect its ideals and institutions, the National Flag and the National Anthem;
2. to cherish and follow the noble ideals that inspired the national struggle for freedom;
3. to uphold and protect the sovereignty, unity and integrity of India;
4. to defend the country and render national service when called upon to do so;
5. to promote harmony and the spirit of common brotherhood amongst all the people of India transcending religious, linguistic and regional or sectional diversities and to renounce practices derogatory to the dignity of women;
6. to value and preserve the rich heritage of the country’s composite culture;
7. to protect and improve the natural environment including forests, lakes, rivers and wildlife and to have compassion for living creatures;
8. to develop scientific temper, humanism and the spirit of inquiry and reform;
9. to safeguard public property and to abjure violence;
10. to strive towards excellence in all spheres of individual and collective activity so that the nation constantly rises to higher levels of endeavor and achievement; and
11. to provide opportunities for education to his child or ward between the age of six and fourteen years. This duty was added by the 86th Constitutional Amendment Act, 2002.

The correct answer is Assam.

Key Points

• The first oil field in independent India was discovered in Assam.
• While oil extraction had already begun in Assam during British rule, the first discovery made after India's independence in 1947 occurred in Nahorkatia, Assam, in 1953.
• This discovery was followed by another in Moran, Assam, in 1956.
• Both were made by the Assam Oil Company (AOC).

Additional Information

• Oil and gas were indeed discovered in Mumbai High, Maharashtra, in 1970s.
• Gujarat has become a major oil and gas producer for India, but significant discoveries began in the 1960s.
• Petroleum is present on Earth as a naturally occurring dark oil liquid beneath the surface.
• Petroleum is the source of both diesel and petrol.

The correct answer is 529 km.

Key Points

• An Earth observation satellite (EOS) is a type of satellite specifically designed to monitor and collect data about the Earth’s surface and atmosphere.
• These satellites play a crucial role in various applications, including environmental monitoring, meteorology, cartography, and disaster management.
• EOS-04 also known as RISAT-1A; it is an Earth Observation Satellite launched by ISRO.
• The satellite was placed at an altitude of 529 km to achieve this orbit.
• A Sun-synchronous orbit keeps a satellite at the same local solar time over a specific part of the Earth.
• EOS-04 was launched on February 14, 2022, from the Satish Dhawan Space Centre.

Important Points

The correct answer is CuCl2 is formed.

Key Points

• Copper oxide (CuO) reacts with hydrochloric acid (HCl) to form copper chloride (CuCl2) and water (H2O).
• The balanced chemical equation for this reaction is: CuO+2HCl→CuCl₂​+H₂​O
• Copper chloride is a soluble salt that forms a blue-green solution in water.
• This reaction is an example of a neutralization reaction where a base (CuO) reacts with an acid (HCl) to form a salt (CuCl2) and water.

Additional InformationCopper Sulfate (CuSO₄)

Typically found as a bright blue crystalline solid in its pentahydrate form (CuSO₄·5H₂O).

• Used as a fungicide and herbicide.
• Utilized in water treatment to control algae growth.
• Highly soluble in water.

Copper (Cu)

Reddish-brown metal with high electrical and thermal conductivity.

• Electrical Wiring
• Forms important alloys like bronze (with tin) and brass (with zinc).
• Reacts with oxygen to form copper oxide but is relatively resistant to corrosion.

Chlorine Gas (Cl₂)

Greenish-yellow gas with a pungent odor.

• Used to disinfect drinking water and swimming pools.
• Bleaching Agent: Employed in the production of paper and textiles.
• Essential in the production of PVC and other chemicals.
• Highly reactive, especially with metals to form chlorides

The following words after arranging as per English alphabetical order are as follows:

 LIKE, LIVE, LOVE, LIME, LUCK

Rearrange letters in alphabetical order

LIKE → EIKL

LIVE → EILV

LOVE → ELOV

LIME → EILM

LUCK → CKLU

Arrange the clusters in dictionary order

Dictionary order of clusters: CKLU, EIKL, EILM, EILV, ELOV

The middle cluster

Number of clusters = 5 → Middle = 3rd cluster = EILM (The 3rd is EILM, which came from LIME.)

The original word = EILM → LIME

Hence, the correct answer is "LIME".

Calculation:

 (225 ÷ 215) × 2⁴

⇒  (2¹⁰) × 24

⇒  214

∴ Option 3 is the correct answer.

Shortcut Trick

Rewrite the equation in standard form: x² + 10x − 24 = 0.

Identify two numbers that multiply to −24 and add up to +10.

The numbers are +12 and −2.

The roots are these numbers with their signs reversed: −12 and +2.

∴ The correct answer is 2, −12.

Alternate Method

Given Equation: x² = 24 − 10x

Method: Factorization of Quadratic Equation

⇒ x² + 10x − 24 = 0

⇒ x² + 12x − 2x − 24 = 0

⇒ x(x + 12) − 2(x + 12) = 0

⇒ (x − 2)(x + 12) = 0

⇒ x − 2 = 0 OR x + 12 = 0

⇒ x = 2 OR x = −12

∴ The correct answer is 2, −12.

Additional Information

Standard Form

A quadratic equation is generally expressed as ax² + bx + c = 0.

Sum and Product of Roots

For the equation ax² + bx + c = 0, the Sum of roots = −b/a and the Product of roots = c/a.

Discriminant (D)

The value D = b² − 4ac determines the nature of roots (real, equal, or imaginary).

Quadratic Formula

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

The correct answer is Region a.

Key Points

• Bowman capsule is a cup-like sac at the beginning of the tubular component of a nephron in the mammalian kidney.
• It performs the first step in the filtration of blood to form urine.
• The Bowman capsule surrounds the glomerulus and together they form the renal corpuscle.
• Blood enters the glomerulus through the afferent arteriole and is filtered through the capillary walls into the Bowman capsule.

The given arrangment is as follows

Six persons, Prem, Amit, Ram, Shyam, Tarun and Uma travelled in different months of the same year

1) Prem travelled in September.

 

 

 

 

 

2) Only one person travelled between Prem and Uma.

3) No one travelled between Tarun and Amit.

4. Amit travelled in a month after Tarun.

5) More than two persons travelled between Amit and Ram.

So, this is this the final arrangement.

Hence the correct answer is "Shyam".

Shortcut Trick

Identify the observation that appears most frequently in the given data set.

By inspection, the number 20 repeats 5 times, while all other numbers appear only once.

Since the mode is defined as the value with the maximum frequency, the result is immediate.

∴ The correct answer is 20.

Alternate Method

Given: Observations = {20, 23, 25, 30, 20, 31, 32, 35, 20, 41, 42, 43, 20, 20}

Formula Used: Mode = Value with the highest frequency (repetition count) in a data set.

⇒ Count of observation 20 = 5

⇒ Count of observation 23 = 1

⇒ Count of observation 25 = 1

⇒ Count of observation 30 = 1

⇒ Count of other individual observations = 1 each

⇒ Comparing all frequencies, 5 is the maximum value.

⇒ The value corresponding to the maximum frequency 5 is 20.

⇒ Mode = 20.

∴ The correct answer is 20.

Additional Information

Measures of Central Tendency

The three main measures are Mean (average), Median (middle value), and Mode (most frequent value).

Empirical Relationship

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

Types of Mode

A data set can be unimodal (one mode), bimodal (two modes), or multimodal (more than two modes).

Given → Six friends E, F, G, H, l and J are seated around a round table facing the centre.

1. E is seated 2^nd to the right of I.

2. Only G is seated between H and J.

3. F will be seated at the empty place around a round table.

Hence, the correct answer is "3^rd to the left of G".

The logic followed here is:-

(First number × 9) + 2

In 9 : 83 →

(9 × 9) + 2 → 81 + 2 = 83

In 5 : 47 →

(5 × 9) + 2 → 45 + 2 = 47

Similarly,

In 4 : 38 →

(4 × 9) + 2 → 36 + 2 = 38

Hence, the correct answer is "38".

Shortcut Trick

Use the CP : MP relationship ratio: CP / MP = (100 − Discount%) / (100 + Profit%).

Given Discount = 20% and Profit = 20%.

Ratio CP : MP = (100 − 20) : (100 + 20) = 80 : 120 = 2 : 3.

Given CP = 2 units = 21,500 ⇒ 1 unit = 10,750.

MP = 3 units = 3 × 10,750 = 32,250.

∴ The correct answer is ₹ 32,250.

Alternate Method

Given Cost Price (CP) = 21,500, Profit% = 20%, Discount% = 20%.

Formulas: SP = CP × (100 + P%) ÷ 100 | MP = SP × 100 ÷ (100 − D%)

⇒ Selling Price (SP) = 21,500 × (120 ÷ 100) = 21,500 × 1.2 = 25,800.

⇒ Let Marked Price (MP) be M. Then M × (80 ÷ 100) = 25,800.

⇒ M = 25,800 × (100 ÷ 80) = 25,800 × 1.25.

⇒ M = 32,250.

∴ The correct answer is ₹ 32,250.

Additional Information

Marked Price & Discount

Discount is always calculated on the Marked Price (MP). SP = MP − Discount.

Cost Price & Profit

Profit is always calculated on the Cost Price (CP). SP = CP + Profit.