RRB Group D Previous Year Paper (Held on: 18 Sept 2022 Shift 3)

The correct answer is Brihaspati

Key Points

• Brihaspati, Agni, Soma, and Prithvi are all Vedic gods that fall under the category of “Prithivisthana” or Terrestrial Gods:
• Brihaspati: Also known as Jupiter, Brihaspati is a benevolent god and part of the Hindu zodiac system.
• He is the heavenly prototype of the Brahmans and the earthly purohita, or family priest.
• Agni: The chief god during the later Vedic period.
• Soma: A god, plant, and ritual drink that was considered to bring health and wealth.
• Prithvi: A terrestrial god.
• In the Vedic Age, there were around 33 gods that were classified into three categories: Terrestrial, Aerial, and Celestial.

Additional Information

• Vishnu, Indra, and Varuna are all deities in Hinduism and Vedic religion:
• Vishnu
• The protector and preserver of the universe, Vishnu returns to Earth to restore balance between good and evil.
• Hindus believe he will be reincarnated one last time near the end of the world.
• Indra
• Indra controls the universe and created rivers and streams by shaping mountains and valleys.
• He is often depicted with a thunderbolt and riding an elephant. Indra and Brahma are often shown giving the infant Buddha his first bath.
• Varuna
• The first lord of the Cosmos, Varuna was usurped by Indra. In East Asian Buddhism, Varuna is a dharmapāla and is often called "Suiten" (water deva) in Japan.
• Other deities in Vedic religion include:
• Agni, Dyaus, Rudra, Soma, Ashvinas, Mitra, Vayu, and Surya.

Given a sequence of numbers is 

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

The series after dropping all odd numbers is 

2 4 4 2 4 6 4 6 4 8

The eighth place from the right in the modified series is 4.

Hence, the correct answer is "4".

Additional Information

• The numbers that are divisible by 2 are even numbers.

According to the given information,

In the given group of numbers/symbols, the first element is an odd number and the last element is an even number. Thus it satisfies the (ii) condition. Therefore the first and last elements are to be coded as ©. All others are coded as per given code.

So, 7 % # @ 4  is coded as ©LFO©

Hence, “©LFO©” is the correct answer.

Shortcut Trick

The standard form of a quadratic equation is strictly defined as ax² + bx + c = 0.

Identify the equation where the highest power (degree) of the variable x is exactly 2.

The equation must be a polynomial, meaning exponents must be non-negative integers.

Only the first option 5x² + 3x − 1 = 0 fits the ax² + bx + c = 0 structure perfectly.

∴ The correct answer is 5x² + 3x − 1 = 0.

Alternate Method

Given: A set of mathematical equations to identify the quadratic equation in standard form.

Formula: A quadratic equation is a second-degree polynomial equation. Its standard form is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

⇒ Option 1: 5x² + 3x − 1 = 0. Here, a = 5, b = 3, and c = −1. It matches the standard form exactly.

⇒ Option 2: x³ + 5x² + 3 = x⁴. This contains x⁴ and x³, making it a quartic equation (degree 4).

⇒ Option 3: x⁻² + 7x = 8. This is not a polynomial because the exponent −2 is negative.

⇒ Option 4: 5x² + 3 = 1/x. Multiplying by x gives 5x³ + 3x = 1, which is a cubic equation (degree 3).

⇒ Thus, only the first equation satisfies all the conditions of a quadratic equation in standard form.

∴ The correct answer is 5x² + 3x − 1 = 0.

Additional Information

Discriminant and Nature of Roots

The value D = b² − 4ac determines the nature of the roots. If D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are imaginary.

Quadratic Formula

The roots of the equation ax² + bx + c = 0 are calculated using the formula x = (−b ± √(b² − 4ac)) / 2a.

Sum and Product of Roots

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

Given:

The expression to evaluate is:

$\frac{(0.1 \times 0.1 \times 1 + 0.02 \times 0.02 \times 0.02)}{(0.2 \times 0.2 \times 0.2 + 0.04 \times 0.04 \times 0.04)}$

Solution:

Numerator:

0.1 × 0.1 × 0.1 = 0.001

0.02 × 0.02 × 0.02 = 0.000008

Now, add the two values:

0.01 + 0.000008 = 0.001008

Denominator:

0.2 × 0.2 × 0.2 = 0.008

0.04 × 0.04 × 0.04 = 0.000064

Now, add the two values:

0.008 + 0.000064 = 0.008064

Final Step:

Now, divide the numerator by the denominator:

$\frac{0.001008}{0.008064} = 0.125$

∴ The value of the expression is approximately 0.125.

The correct answer is INS Vikrant

Key Points

• The name of India's first indigenous aircraft carrier is INS Vikrant.
• The ship was launched on August 12, 2013, acquired on July 28, 2022, and commissioned on September 2, 2022.
• The name Vikrant comes from the Sanskrit word vikrānta which means "courageous" or "bold".
• The name was also used for India's first aircraft carrier, which was commissioned in 1961.
• The ship is 262 meters long and has a carrying capacity of 40,000 metric tons.
• The ship can accommodate up to 30 aircraft, including the MiG-29K fighter jets, Kamov-31 helicopters, and MH-60R multi-role helicopters.
• The ship was built at Cochin Shipyard Limited and has an indigenous content of 76%.
• The ship has a ski-jump for launching aircraft and a set of "arrester wires" for recovering them.
• It also uses a novel aircraft-operation mode called STOBAR (Short Take-Off but Arrested Landing)

Additional Information

• INS Viraat
• Type: Aircraft Carrier
• Commissioned: May 12, 1987 (into the Indian Navy)
• Decommissioned: March 6, 2017
• Notable Features:
• Originally commissioned in the Royal Navy as HMS Hermes in 1959.
• Played a significant role in various operations, including Operation Jupiter in Sri Lanka (1989) and Operation Parakram (2001–2002).
• It was the flagship of the Indian Navy for nearly 30 years.
• INS Visakhapatnam
• Type: Guided Missile Destroyer (Project 15B Class)
• Commissioned: November 21, 2021
• Notable Features:
• Equipped with state-of-the-art weapons and sensors, including BrahMos missiles and Barak-8 air defense systems.
• Incorporates stealth technologies to reduce radar and infrared signatures.
• Designed for multi-role operations including anti-air, anti-surface, and anti-submarine warfare.
• INS Vijaya
• Type: Patrol Vessel
• Commissioned: September 2018
• Notable Features:
• Second ship of the Saryu-class offshore patrol vessels (OPVs).
• Designed for coastal and offshore surveillance, anti-piracy operations, and maritime patrolling.
• Equipped with modern navigation and communication systems.

The correct answer is the motion of the conductor

Key Points

• According to Fleming's Right Hand Rule, the thumb indicates the motion of the conductor
• Fleming's Right Hand Rule is used to determine the direction of the induced current (or EMF) when a conductor moves in a magnetic field.
• Thumb:
• Indicates the motion of the conductor (or the direction of force applied).
• Forefinger:
• Points in the direction of the magnetic field.
• Middle finger:
• Indicates the direction of the induced current or EMF.
• This rule is applicable in electromagnetic induction, such as in generators.

The logic followed here is:

Hence, the correct answer is "732".

The correct answer is adipose tissue

Key Points

• The tissue that stores fat is called adipose tissue. Adipose tissue is a type of loose connective tissue that stores excess nutrients as fat.
• It's made up of fat cells called adipocytes, which contain lipid droplets of stored triglycerides.
• Adipose tissue is found in several locations, including: Beneath the skin, Around internal organs, Between muscles, and Bone marrow.
• Adipose tissue has several important functions, including:
• Storing and releasing energy: Adipose tissue stores energy and releases it to fuel the body.
• Releasing hormones: Adipose tissue releases hormones that are important to the body's needs.
• Protecting the body: Adipose tissue protects the visceral parts of the body.
• Insulating and maintaining body temperature: Adipose tissue insulates and maintains the body temperature.
• In mammals, there are two types of adipose tissue: white adipose tissue (WAT) and brown adipose tissue (BAT)

Additional Information

• Epithelial Tissue​
• A type of tissue that forms the covering or lining of all body surfaces, cavities, and hollow organs. It also makes up glands.
• Functions:
• Protection (e.g., skin).
• Absorption (e.g., intestinal lining).
• Secretion (e.g., glands).
• Filtration (e.g., kidney tubules)
• Connective Tissue
• A tissue that connects, supports, binds, or separates other tissues or organs.
• It is characterized by an abundance of extracellular matrix.
• Functions:
• Structural support (e.g., bones).
• Transport of nutrients (e.g., blood).
• Energy storage (e.g., adipose tissue).
• Immunological defense (e.g., lymph).
• Areolar Tissue
• A type of loose connective tissue that is widely distributed under the skin and around organs.
• Functions:
• Binds skin to underlying structures.
• Provides cushioning and support.
• Plays a role in immune defense by containing cells like macrophages and mast cells.

The correct answer is Marginal propensity to save

Key Points

• The change in savings divided by the change in income is the marginal propensity to save (MPS)
• MPS = δ S / δ Y
• δ S is the change in savings, δ Y is the change in income
• MPS is a key component of Keynesian macroeconomics theory.
• It can be used to determine the Keynesian multiplier, which measures the effect of increased government spending or investment as an economic stimulus.

Additional Information

• Average propensity to save (APS): The amount of savings in every 1 rupee of income for all levels of income. APS can never be greater than 1.
• Average propensity to consume: Consumption divided by income.
• Marginal propensity to consume (MPC): The change in consumption divided by the change in income.

According to the given information:

1. Supriya is the immediate neighbour of Tanmay and Wasim.

2. Umesh is to the immediate right of Tanmay.

3. Viplav is the immediate neighbour of Umesh and Wasim.

So, Wasim is sitting to the immediate left of Supriya.

Hence, the correct answer is "Wasim".

The correct answer is Should have 10 years of experience in the parliament

Key Points

• The Constitution of India outlines the eligibility criteria for a candidate to become the President of India in Article 58.
• These are:
• The candidate must be a citizen of India.
• The candidate must have completed the age of 35 years.
• The candidate must not hold any office of profit under the Government of India or any state government or under any local or other authority under their control.
• Experience in Parliament is not a requirement to become the President of India.

The correct answer is 5%

Key Points

• The SAFE (SIDBI Assistance to Facilitate Emergency response against Coronavirus) scheme was introduced by the Small Industries Development Bank of India (SIDBI) in March 2020.
• This scheme was specifically designed to support micro, small, and medium enterprises (MSMEs) in their efforts to manufacture essential goods needed to combat the COVID-19 pandemic.
• SIDBI provides loans to MSEs at a low rate of interest of 5% within 48 hours and thereby making it easier for them to facilitate tasks that can help tackle the pandemic.
• The maximum loan amount offered under the scheme was ₹50 lakh.
• The repayment period was up to 36 months (3 years).
• Included a moratorium period of 6 months during which businesses didn’t have to pay installments.
• MSMEs already producing COVID-related goods.
• MSMEs intending to start manufacturing these goods.

Given:

Simplify the given expression:

6.5 × [22.6 ÷ {14.5 + 2.8 - 4.2 ÷ 0.7}]

Solution:

First, simplify the innermost expression:

4.2 ÷ 0.7 = 6

Now substitute this value back into the expression:

6.5 × [22.6 ÷ {14.5 + 2.8 - 6}]

Next, simplify inside the brackets:

14.5 + 2.8 = 17.3

17.3 - 6 = 11.3

Now, the expression becomes:

6.5 × [22.6 ÷ 11.3]

Next, divide 22.6 by 11.3:

22.6 ÷ 11.3 = 2

Now, multiply by 6.5:

6.5 × 2 = 13

∴ The simplified value of the expression is 13.

Given: 15 May 2001 was Tuesday.

Now,

2001 to 2013= 12 Years (9 Ordinary Year and 3 Leap Years).

And, In 12 Years = 3 Leap years and 9 Ordinary Years.

So, 3 Leap Years have 6 odd days,

And, 9 Ordinary Years have 9 odd days.

Total odd days = 6 + 9 = 15.

13 odd days → 15/7 = 2 week and 1 odd days.

then, 15 May 2013 will be Tuesday + 1 = Wednesday.

Now, the number of days between 15 May 2013 to 11 June 2013

= 16(May 2012) + 11(June 2012)= 27 days.

= 27 days →27/7 = 3 week 6 odd days 

So, 11 June 2013 will be Wednesday + 6 = Tuesday.

Hence, the correct answer is "Option 3".

Shortcut Trick

The ratio between the smaller number and the larger number is 1 : 3.

Difference in ratio units = 3 − 1 = 2 units.

According to the question, 2 units = 26.

Value of 1 unit (smaller number) = 26 ÷ 2 = 13.

∴ The correct answer is 13.

Alternate Method

Given:

Difference between two numbers = 26

One number = 3 × other number

Formula used:

Linear equation formulation: Larger number − Smaller number = Difference

Let the smaller number be x.

The larger number is 3x.

⇒ 3x − x = 26

⇒ 2x = 26

⇒ x = 26 ÷ 2

⇒ x = 13

∴ The correct answer is 13.

Additional Information

Linear Equations

Equations of the form ax + b = 0 where x is the unknown variable and a, b are constants.

Unitary Method

A technique where you find the value of a single unit first and then multiply it by the required number of units.

Ratio Property

If numbers are in ratio a : b, their difference corresponds to the difference in their ratio parts (b − a).

Shortcut Trick

Inside Area of an Open Drum = CSA + Base Area

Area = (π × d × h) + (π × r²)

Area = (22/7 × 21 × 7) + (22/7 × 10.5 × 10.5) = 462 + 346.5

Area = 808.5 m²

∴ The correct answer is 808.5 m².

Alternate Method

Given:

Height (h) = 7 m

Diameter (d) = 21 m ⇒ Radius (r) = 21/2 = 10.5 m

Formula Used:

Surface Area of Open Cylinder = 2πrh + πr²

Calculations:

⇒ Curved Surface Area (CSA) = 2 × (22/7) × 10.5 × 7

⇒ CSA = 2 × 22 × 10.5 = 44 × 10.5 = 462 m²

⇒ Base Area = (22/7) × 10.5 × 10.5

⇒ Base Area = 22 × 1.5 × 10.5 = 33 × 10.5 = 346.5 m²

⇒ Total Painted Area = 462 + 346.5 = 808.5 m²

∴ The correct answer is 808.5 m².

Additional Information

Total Surface Area of Cylinder

For a closed cylinder, TSA = 2πr(h + r), which includes the curved surface and two circular bases.

Volume of Cylinder

The capacity or volume of a cylindrical drum is given by V = πr²h.

Hollow Cylinder

For a pipe with thickness, the material volume is π(R² − r²)h, where R is outer and r is inner radius.

Shortcut Trick

Volume of a cuboid = Length × Breadth × Height.

Factorize the expression 5a² − 80b² by taking 5 as common.

⇒ 5(a² − 16b²) = 5[a² − (4b)²].

Apply algebraic identity x² − y² = (x − y)(x + y).

⇒ 5(a − 4b)(a + 4b).

∴ The correct answer is 5, a - 4b, a + 4b.

Alternate Method

Given: Volume = 5a² − 80b²

Formula Used: Volume of Cuboid = Length × Breadth × Height

Step-by-step factorization:

⇒ Volume = 5(a² − 16b²)

⇒ Volume = 5[(a)² − (4b)²]

⇒ Using (x² − y²) = (x − y)(x + y)

⇒ Volume = 5 × (a − 4b) × (a + 4b)

⇒ The possible dimensions are 5, (a − 4b), and (a + 4b).

∴ The correct answer is 5, a - 4b, a + 4b.

Additional Information

Algebraic Identity

The expression is a difference of two squares: a² − b² = (a − b)(a + b).

Cuboid Properties

Total Surface Area of a cuboid = 2(lb + bh + hl) and Diagonal = √(l² + b² + h²).

Factorization Rule

Always look for a Highest Common Factor (HCF) first before applying algebraic identities.

The correct answer is decomposition of silver chloride into silver and chlorine by light.

Key Points 

• Silver chloride is a photosensitive compound, which means it reacts to light by decomposing.
• When silver chloride is exposed to sunlight, the energy from the light causes the compound to break down into silver and chlorine ions.
• The silver ions combine with other substances in the environment to form a white precipitate, which gives the appearance of the silver chloride turning white.
• This process is reversible, and the white precipitate can turn back into silver chloride when removed from sunlight.

Additional Information

• Application of this phenomenon:
• As this process is reversible, as the grey color can fade when the silver chloride is shielded from light or heated.
• This property has historical significance in photography, as it was used in the early photographic process known as the daguerreotype.
• Redox reaction:
• Redox reactions are chemical processes involving oxidation and reduction in which the oxidation states of the reactants change.
• In a chemical reaction, the material that is being reduced is referred to as the oxidizing agent, and the substance that is being oxidized is referred to as the reducing agent.
• Displacement reaction:
• When an atom in a molecule is displaced by another atom, this is known as a displacement reaction.

Given number:-

Left 5384972 Right

New number after arranging each digit of the given number in ascending order:-

Left 2345789 Right

Digits whose position will remain unchanged as compared to that in original number → 3

Hence, the correct answer is "One".

The correct answer is 1 ∶ 2.

Key Points

• The induced EMF in a coil is directly proportional to the number of loops in the coil, according to Faraday’s Law of Induction.
• The formula for induced EMF is $\varepsilon =-N\frac{d\phi}{dt}$, where N is the number of loops and $\frac{d\phi}{dt}$ is the rate of change of magnetic flux.
• In coil A, let the number of loops be N, and in coil B, the number of loops is 2N. Therefore, the EMF in coil B will be twice that in coil A.
• Since the rate of change of magnetic flux is constant, the ratio of the induced EMF in coil A to coil B is 1 : 2.

Additional Information

• Faraday's Law of Induction: Faraday's Law states that the induced EMF in a coil is proportional to the rate of change of magnetic flux through the coil and the number of turns in the coil.
• Magnetic Flux: Magnetic flux (Φ) is the measure of the magnetic field passing through a given area. It is given by the formula Φ = B * A * cos(θ), where B is the magnetic field, A is the area, and θ is the angle between the field and the normal to the surface.
• Rate of Change of Magnetic Flux: The rate of change of magnetic flux, (dΦ/dt), is a key factor in determining the induced EMF. A higher rate of change leads to a higher EMF.
• Electromagnetic Induction: The principle of electromagnetic induction is fundamental to devices like transformers, electric motors, and generators, where changing magnetic fields generate electric currents in conductors.

According to the given information:

The shaded part represents professors are there who are women and also poets.

Thus, 2 professors are there who are women and also poets.

Hence, the correct answer is "2".

Given:

The expression to evaluate is:

6⁰ × 4² × 2^-4

Solution:

Step 1: Evaluate 6⁰:

Any non-zero number raised to the power of 0 is 1. So:

6⁰ = 1

Step 2: Evaluate 4²:

4 raised to the power of 2 is:

4² = 16

Step 3: Evaluate 2^-4:

A negative exponent means the reciprocal of the base raised to the positive exponent. So:

2^-4 = 1 / 2⁴ = 1 / 16

Step 4: Multiply the results:

Now, multiply all the results together:

1 × 16 × 1 / 16 = 1

∴ The value of the expression is 1.

According to the given information:

1) Vinod is sitting at the extreme right end. 

2. Piyush is an immediate neighbour of both Vinod and Taman, while Rudir is an immediate neighbour of both Taman and Biswas.

3. There are only two advocates to the left of Biswas.

If no other advocate is sitting in the row,

So, Seven is the total number of advocates seated in that row.

Hence, the correct answer is "Seven".

Shortcut Trick

Identify the identity: a³ − b³ = (a − b)(a² + ab + b²).

Here, a = 16 and b = 12.

Calculation: (16 − 12)(16² + 16 × 12 + 12²) = 4 × (256 + 192 + 144) = 4 × 592 = 2368.

Alternatively, use cubes directly: 4096 − 1728 = 2368.

∴ The correct answer is 2368.

Alternate Method

Given:

Expression = 16³ − 12³

Formula Used:

x³ = x × x × x

Calculations:

⇒ First, calculate 16³:

⇒ 16 × 16 × 16 = 256 × 16 = 4096

⇒ Next, calculate 12³:

⇒ 12 × 12 × 12 = 144 × 12 = 1728

⇒ Subtract the two values:

⇒ 4096 − 1728 = 2368

∴ The correct answer is 2368.

Additional Information

Algebraic Identities

Difference of cubes: a³ − b³ = (a − b)(a² + ab + b²). Sum of cubes: a³ + b³ = (a + b)(a² − ab + b²).

Cube Shortcuts

Memorizing cubes from 1 to 20 helps in fast simplification and number series questions.

Unit Digit Check

Unit digit of 6³ is 6 and 2³ is 8. Therefore, 6 − 8 → 16 − 8 = 8. The result must end in 8.

The logic followed here is:

Hence, the correct answer is "465".

The correct answer is Kerala

Key Points

• The Kerala Police introduced the Pink Beat patrol to enhance the safety of women and children in public places.
• The Pink Beat is a part of the Kerala Police's Pink Protection Project, which aims to create a safe environment for women in public, private, and digital spaces.
• The project includes:
• Pink Patrol: Specially trained women police personnel patrol on KSRTC and private stage carriers and are present at bus stops and schools
• Pink Janamaithri beat: A part of the project
• Pink control room: A part of the project
• Pink Shadow: A part of the project
• Pink Romeo: A part of the project
• Counseling facilities: A part of the project
• Mobile application for women protection: A part of the project
• The project was launched in response to the increasing number of crimes against women in Kerala and across the country.
• The project aims to prevent crimes such as dowry-related issues, cyberbullying, and public humiliation.

The correct answer is Hibiscus and mustard

Key Points

• Hibiscus and mustard are bisexual flowers, while watermelon and papaya are unisexual flowers:
• Bisexual flowers
• Contain both male and female reproductive parts in the same flower.
• The male reproductive parts are the stamens, which produce pollen, and the female reproductive parts are the pistil, which contains the ovary and stigma.
• Examples of bisexual flowers include hibiscus and mustard.
• Unisexual flowers
• Contain either the male or female reproductive organs. Examples of unisexual flowers include watermelon and papaya.

Shortcut Trick

If x + 1/x = k, then x² + 1/x² = k² − 2.

Given: x + 1/x = 3 ⇒ x² + 1/x² = 3² − 2 = 7.

Let n = x² + 1/x² = 7. Then x⁶ + 1/x⁶ = (x²)³ + 1/(x²)³ = n³ − 3n.

⇒ 7³ − 3(7) = 343 − 21 = 322.

∴ The correct answer is 322.

Alternate Method

Given: x + 1/x = 3

Formula Used: (a + b)² = a² + b² + 2ab and (a + b)³ = a³ + b³ + 3ab(a + b)

Squaring both sides of the given equation:

⇒ (x + 1/x)² = 3²

⇒ x² + 1/x² + 2(x)(1/x) = 9

⇒ x² + 1/x² + 2 = 9

⇒ x² + 1/x² = 7

Cubing both sides of this new equation:

⇒ (x² + 1/x²)³ = 7³

⇒ (x²)³ + (1/x²)³ + 3(x²)(1/x²)(x² + 1/x²) = 343

⇒ x⁶ + 1/x⁶ + 3(1)(7) = 343

⇒ x⁶ + 1/x⁶ + 21 = 343

⇒ x⁶ + 1/x⁶ = 343 − 21

⇒ x⁶ + 1/x⁶ = 322

∴ The correct answer is 322.

Additional Information

Standard Algebraic Identities

If x + 1/x = k, then x² + 1/x² = k² − 2 and x³ + 1/x³ = k³ − 3k.

Negative Sign Identity

If x − 1/x = k, then x² + 1/x² = k² + 2 and x³ − 1/x³ = k³ + 3k.

Higher Power (n=4 and n=5)

x⁴ + 1/x⁴ = (x² + 1/x²)² − 2 and x⁵ + 1/x⁵ = (x² + 1/x²)(x³ + 1/x³) − (x + 1/x).

Shortcut Trick

Solve Numerator: 13 − (−2) × {6 − 4} ⇒ 13 − (−4) = 17

Solve Denominator: 4 × {5 + 12} ⇒ 4 × 17 = 68

Result = 17 ÷ 68 = 1/4

∴ The correct answer is 1/4.

Alternate Method

Given:

[13 − (−2) × {6 − (7 − 3)}] ÷ [4 × {5 + (−2) × (−6)}]

Formula Used:

BODMAS Rule: Brackets → Orders → Division/Multiplication → Addition/Subtraction.

Calculations:

Step 1: Simplify the numerator [13 − (−2) × {6 − (7 − 3)}]

⇒ Solve the innermost bracket (7 − 3) = 4

⇒ The numerator becomes: [13 − (−2) × {6 − 4}]

⇒ Solve curly braces {6 − 4} = 2

⇒ Multiply: (−2) × 2 = −4

⇒ Numerator = 13 − (−4) = 13 + 4 = 17

Step 2: Simplify the denominator [4 × {5 + (−2) × (−6)}]

⇒ Multiply inside the curly brace: (−2) × (−6) = 12

⇒ Add: 5 + 12 = 17

⇒ Now, multiply by 4: 4 × 17 = 68

Step 3: Divide Numerator by Denominator

⇒ Expression value = 17 ÷ 68

⇒ 17/68 = 1/4

∴ The correct answer is 1/4.

Additional Information

BODMAS Rule

It determines the strict sequence of operations in mathematical simplifications: Brackets → Orders (Powers/Roots) → Division → Multiplication → Addition → Subtraction.

Sign Rules for Multiplication

Multiplying two numbers with the same signs results in a positive product: (−) × (−) = (+) and (+) × (+) = (+). Multiplying two numbers with opposite signs gives a negative product: (+) × (−) = (−).

Hierarchy of Brackets

Always resolve brackets from innermost to outermost in this specific order: Vinculum (Line bracket) → Parentheses () → Curly Braces {} → Square Brackets [].

Given Statement: W ≤ P < S > Y = R ≥ T > M

Now,

Conclusions:

Option 1: Y < P → False (P < S > Y It gives P < S > Y)

Option 2: S > W → True (W ≤ P < S It gives S > W)

Option 3: Y ≥ P → False (P < S > Y It gives Y > P)

Option 4: M > R → False (R ≥ T > M It gives R > M)

Hence, the correct answer is "Option 2".

The correct answer is 12 times that of B

Key Points

• The resistance ( R) of a wire is given by the formula:
• ​$R=ρ A/ L$
• where:
• R is the resistance,
• ρ is the resistivity (same for both wires as they are made of the same material),
• L is the length of the wire,
• A is the cross-sectional area.
• Given Data:
• Length of wire A (LA ) =  3×L_B
• Cross-sectional area of wire A ( AA ) = $1/4$×A_B
• _{8 814×AB} For wire A, since its length is 3 times (Lb) and its cross-sectional area is (1/4) times (Ab), its resistance (Ra) is: Ra = ρ 3Lb ×1/4Ab  = ρ (3 ×  4Lb)/Ab = 12ρ Lb/Ab, Ra = 12Rb

Given:

The graph shows the number of units produced and the number of units exported by a company over the years. We are asked to determine during which year the units produced declined.

Solution:

By analyzing the graph, we observe the following trends:

 The blue line represents the number of units produced.

 The red line represents the number of units exported.

Step 1: Identify the trend in the number of units produced (blue line):

The blue line steadily increases until the year 2004. After 2004, it begins to decline, indicating a decrease in the number of units produced.

Step 2: Identify the year when the decline starts:

The decline in the number of units produced starts between the years 2004 and 2005.

∴ The units produced declined between the years 2004 - 2005.

Answer: 4) 2004 - 2005

Shortcut Trick

Ratio of A : B : C = 3 : 2 : 1(1/3) = 3 : 2 : 4/3 = 9 : 6 : 4.

Difference between A and B in units = 9 − 6 = 3 units.

Given, 3 units = Rs. 1,500 ⇒ 1 unit = Rs. 500.

Share of C = 4 units = 4 × 500 = Rs. 2,000.

∴ The correct answer is Rs. 2,000.

Alternate Method

Given: Ratio A : B : C = 3 : 2 : 4/3

⇒ Multiply by 3 to remove fraction: 9 : 6 : 4

⇒ Let shares be 9x, 6x, and 4x

⇒ Difference (A − B) = 9x − 6x = 3x

⇒ 3x = 1500

⇒ x = 500

⇒ C's share = 4x = 4 × 500 = 2000

∴ The correct answer is Rs. 2,000.

Additional Information

Ratio Simplification

To simplify a ratio with fractions, multiply all terms by the LCM of the denominators to convert them into integers.

Partnership Profit Distribution

In a partnership, unless specified otherwise, the profit/sum is distributed in the ratio of the capitals invested: Profit Ratio = C₁ × T₁ : C₂ × T₂.

The correct answer is Magnus Carlsen

Key Points

• In 2022, 16-year-old Indian chess player Rameshbabu Praggnanandhaa defeated world chess champion Magnus Carlsen in an online tournament:
• When: February 22, 2022
• Where: In an online tournament with 16 elite players
• How it happened: Praggnanandhaa improved on his play from the first day of the tournament and avoided a draw against Carlsen
• Praggnanandhaa was the youngest person to defeat Carlsen since he became world champion in 2013.
• Praggnanandhaa has beaten Carlsen several times, including:
• In the Champions Chess Tour in 2022
• At the Superbet Grand Chess Tour in Warsaw, where he beat Carlsen for the first time in over-the-board chess
• At the Norway Chess Tournament, where he defeated Carlsen in classical chess for the first time

Additional Information 

• Garry Kasparov
• A Russian chess grandmaster and former World Chess Champion. He was born in Baku, Soviet Union (now Azerbaijan) in 1963. In 1999, he achieved a peak FIDE chess rating of 2851, which was the highest recorded until 2013.
• Magnus Carlsen
• A Norwegian chess grandmaster and the current world number one. He has won the World Chess Championship five times, the World Rapid Chess Championship five times, the World Blitz Chess Championship seven times, and the Chess World Cup Championship.
• Bobby Fischer
• The first and only American world chess champion. He won 20 consecutive games against world-class opponents from 1970 to 1971. He is considered by many to be the most famous chess player ever.
• Anatoly Karpov
• A Russian and former Soviet chess grandmaster and former World Chess Champion. He is also a politician.

Given Statements:

Some blues are greens.

All greens are emeralds.

All emeralds are gems.

The least possible Venn diagram:

Conclusions:

I. Some blues are gems. - True (Because Some blues are greens, All greens are emeralds and All emeralds are gems. So, Some blues are also gems)

II. Some gems are greens. - True (Because All greens are emeralds and All emeralds are gems. So, Some gems are also greens)

So, Both conclusions I and II follow.

Hence, the correct answer is "Both conclusions I and II follow".

The correct answer is Article 15

Key Points

• The prohibition of discrimination on grounds of religion, race, caste, sex, or place of birth is laid under Article 15 of the Constitution of India:
• Article 15
• Prohibits discrimination against citizens based on the five protected grounds of religion, race, caste, sex, or place of birth.
• It also states that citizens cannot be subject to any disability, liability, restriction, or condition based on these grounds.

Additional Information

• Other articles
• Other articles in the Constitution of India that ensure the Right to equality for all Indians include:
• Article 14: Equality before the law
• Article 16: Equality of opportunity in matters of public employment
• Article 17: Abolition of untouchability
• Article 18: Abolition of titles
• Fundamental rights are the rights that grant individuals equality in every aspect irrespective of race, color, caste, religion, birthplace, or gender.

The correct answer is 5- year

Key Points

• As of August 2022, the objective of the Maulana Azad National Fellowship Scheme (MANF) is to provide integrated five-year fellowships in the form of financial assistance to students from six notified minority communities (Buddhist, Christian, Jain, Muslim, Parsi, and Sikh) to pursue M.Phil. and Ph.D. degrees.
• This scheme aims to support the educational advancement of students from these minority communities by covering academic expenses, enabling them to focus on their research without financial constraints.
• The University Grants Commission (UGC) is responsible for implementing the MANF scheme, ensuring transparency and efficient disbursal of funds to eligible candidates.
• Fellows receive monthly allowances, such as:
• Junior Research Fellowship (JRF): Higher stipend during the initial two years.
• Senior Research Fellowship (SRF): Enhanced stipend for the remaining tenure, subject to performance evaluation.

The correct answer is Odisha

Key Points

• Nuakhai is an agricultural festival mainly observed by people of Odisha, India:
• Nuakhai is celebrated in Western Odisha and Southern Chhattisgarh.
• Nuakhai is a festival to welcome the new rice of the season.
• The word "nua" means "new" and "khai" means "food".
• Nuakhai is a culturally rich and important festival in Odisha.
• It is especially significant for farmers and the agricultural community.
• Nuakhai is celebrated a day after Ganesh Chaturthi.
• It is celebrated at a specific time of the day called lagan.
• Nuakhai is also known as Nabanna.

Given:

The total number of boys and girls together is 11,500.

The ratio of boys to girls is 2 : 3.

Boys who like peaches = 19% and Girls who like peaches = 19%.

Solution:

Step 1: Find the number of boys and girls using the ratio.

The total ratio parts for boys and girls is:

2 + 3 = 5 parts

Since the total number of boys and girls together is 11,500, we can find the number of boys and girls using the ratio:

 Number of boys = (2/5) × 11,500 = 4,600

 Number of girls = (3/5) × 11,500 = 6,900

Step 2: Find the number of boys and girls who like peaches.

Boys who like peaches:

19% of 4,600 = (19/100) × 4600 = 874

Girls who like peaches:

19% of 6,900 = (19/100) × 6900 = 1,311

Step 3: Conclusion

The number of boys who like peaches is 874 and the number of girls who like peaches is 1,311.

Shortcut Trick

Let the number of apples of each variety be 3 (LCM of 3 and 1).

Total apples = 3 + 3 = 6.

Total Cost Price (CP) = 2 + 3 = Rs. 5.

Total Selling Price (SP) = 6 × 1 = Rs. 6.

Profit% = (6 − 5) ÷ 5 × 100 = 1 ÷ 5 × 100 = 20%.

∴ The correct answer is 20%.

Alternate Method

Given: CP₁ = Rs. 2 for 3 apples, CP₂ = Rs. 1 per apple, SP = Rs. 1 per apple. Equal quantity purchased.

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

⇒ Let quantity of each variety = x. Total quantity = 2x.

⇒ Cost Price of variety 1 = (2 ÷ 3) × x = 2x/3.

⇒ Cost Price of variety 2 = 1 × x = x.

⇒ Total CP = 2x/3 + x = 5x/3.

⇒ Total SP = 1 × 2x = 2x.

⇒ Profit = 2x − 5x/3 = x/3.

⇒ Profit% = (x/3 ÷ 5x/3) × 100 = 1/5 × 100 = 20%.

∴ The correct answer is 20%.

Additional Information

Unitary Method for CP

Always calculate the price of a single unit (Price ÷ Quantity) to standardize the Cost Price when dealing with different rates.

Profit and Loss Percentage

Profit or Loss percentage is always calculated on the Cost Price (CP) unless stated otherwise in the question.

The correct answer is Resemblance of hydrogen to alkali metals as well as halogens and no specific position was assigned to hydrogen.

Key Points

• Mendeleev's periodic table did not assign a specific position to hydrogen due to its resemblance to both alkali metals and halogens.
• This resemblance created confusion because hydrogen shares properties with Group 1 (alkali metals) and Group 17 (halogens).
• Hydrogen can form H₂ like halogens (Cl₂, Br₂, etc.) and also forms compounds like HCl, similar to halogen acids (HBr, HI).
• Hydrogen also forms ionic compounds like NaH, similar to alkali metals.

Additional Information

• Mendeleev's Periodic Table
• Developed by Dmitri Mendeleev in 1869, it organized elements based on atomic mass and chemical properties.
• Mendeleev left gaps in his table for undiscovered elements, predicting their properties accurately.
• He arranged elements in increasing order of atomic masses, but some elements did not fit this order perfectly (e.g., Te and I).
• The modern periodic table, developed later, arranges elements by atomic number, resolving many of Mendeleev's inconsistencies.
• Alkali Metals
• Group 1 elements in the periodic table, including lithium, sodium, potassium, rubidium, cesium, and francium.
• They have a single electron in their outer shell and are highly reactive, especially with water.
• Alkali metals form strong bases (alkalies) when they react with water.
• Halogens
• Group 17 elements, including fluorine, chlorine, bromine, iodine, and astatine.
• They have seven electrons in their outer shell and are highly reactive, particularly with alkali metals and alkaline earth metals.
• Halogens form salts when they react with metals (e.g., sodium chloride).

The logic followed here is:

Given Sequence: _ T U _ R T _ S_ _ W S R T X _

Now, putting the letters in the blank spaces given in the option one by one:

Option 1) RSVRTR → R T U S / R T V S / R T W S / R T X R

Option 2) RSVTRR → R T U S / R T V S / T R W S / R T X R

Option 3) RSVRTS → R T U S / R T V S / R T W S / R T X S

Here, R, T and S are fixed letter and third letter is increased by 1.

U + 1 = V; V + 1 = W; W + 1 = X

Option 4) RTUSRX → R T U T / R T U S / S R W S / R T X X

Hence, the correct answer is "Option 3".

The correct answer is Brahmaputra

Key Points

• ​The Brahmaputra River passes through Tibet, Arunachal Pradesh, Assam, and Bangladesh:
• The Brahmaputra forms the world's largest number of freshwater riverine islands, including Majuli, the world's largest freshwater riverine island.
• The Brahmaputra is known as the Yarlung Tsangpo in Tibet.
• It originates in the Chemayungdung glacier in the Himalayas near Mount Kailash.
• The Brahmaputra flows through the Indian states of Arunachal Pradesh and Assam.
• In Assamese, it is known as Brahmaputra or Luit.
• The Brahmaputra is known as the Jamuna in Bangladesh.
• It joins the Ganga in Bangladesh and eventually drains into the Bay of Bengal.
• Other names
• The Brahmaputra is also known as the Siang/Dihang River in Arunachali.
• The word "Brahmaputra" means "son of Brahma" in Sanskrit
• The Brahmaputra is India's largest river by volume.
• It has one of the largest river basins in South Asia.

Additional Information

• Ramganga River
• Origin: The Ramganga River originates from the Doodhatoli ranges in the Garhwal region of Uttarakhand, India.
• Flow:
• It flows southeast through the Jim Corbett National Park in Uttarakhand.
• Then, it enters Uttar Pradesh and passes through cities like Moradabad, Bareilly, and Badaun.
• Finally, it merges into the Ganga River near Kannauj in Uttar Pradesh.
• Brahmani River
• Origin: The Brahmani River is formed by the confluence of the Koel and Sankh Rivers near Rourkela in Odisha, India.
• Flow:
• It flows eastward through Odisha.
• Major cities and regions along its course include Angul, Talcher, and Dhenkanal.
• It eventually drains into the Bay of Bengal near Dhamra in Odisha.
• Mahanadi River
• Origin: The Mahanadi River originates from the Sihawa Hills in the Dhamtari district of Chhattisgarh, India.
• Flow:
• It flows eastward through Chhattisgarh and Odisha, covering major cities like Raipur, Cuttack, and Sambalpur.
• The river forms an extensive delta before emptying into the Bay of Bengal near Paradeep in Odisha.
• It is also known for the Hirakud Dam, one of the largest dams in India.

The correct answer is Priyanka Mangesh Mohite

Key Points

• Priyanka Mohite was one of the seven recipients of the 2020 Tenzing Norgay National Adventure Award for land adventure:
• Mountaineer from Maharashtra who scaled some of the world's highest peaks, including Mt Everest, Mt Lhotse, and Mt.Makalu
• Other achievements
• First Indian woman to climb Mt Annapurna, the 10th highest mountain peak in the world
• 2020 Tenzing Norgay National Adventure Award, 2017-2018 Maharashtra Government's Shiv Chhatrapati State award for adventure sports
• The Tenzing Norgay National Adventure Award is India's highest adventure sports honor, and is awarded annually by the Ministry of Youth Affairs and Sports.

Additional Information

• Lt. Col. Servesh Dhadwal:
• A member of the Indian Army, he was honored with the 2020 Tenzing Norgay National Adventure Award in the air adventure category.
• He is a skilled skydiver and an instructor for the Indian Army Skydiving Team.
• Over his career, he has completed over 7,000 skydives and trained numerous personnel, including those in Special Forces.
• His contributions also extend to providing skydiving training for National Security Guards (NSG)​
• Jai Kishan: A
• Group Captain in the Indian Air Force, Jai Kishan has received the Tenzing Norgay National Adventure Award twice.
• His lifetime achievement award in 2021 recognizes his extensive contributions to adventure sports, including skydiving at the base of Mt. Everest and leading expeditions in the Sikkim Himalayas.
• He has six world records in adventure sports and has trained thousands in mountaineering and parachuting​
• Srikaanth Viswanathan:
• He is Honored with the award in the water adventure category in 2020, he is notable for completing the "Triple Crown" of open-water swimming, a prestigious feat involving swims across the English Channel, Catalina Channel, and around Manhattan Island. T
• his accomplishment highlights his remarkable endurance and dedication to water-based adventures​

The logic followed here is:

Logic: (1st number + 22) = 2nd number.

Now,

For, 33 : 55

⇒ 33 + 22 = 55 

For, 46 : 68

⇒ 46 + 22 =68

Similarly, for 68 ∶ ?

⇒ 68 + 22 = 90

Hence, the correct answer is "Option 3".

The correct answer is Pir Panjal Range

Key Points

• The Pir Panjal Range is the longest range in the Lesser Himalayas:
• Location: The Pir Panjal Range runs through the states of Jammu and Kashmir and Himachal Pradesh.
• Elevation: The average elevation of the range is 5,000 meters above sea level.
• Notable features: The range includes the Jawahar tunnel, Atal tunnel, and Banihal tunnel.
• The Banihal Railway Tunnel is India's longest railway tunnel.
• The range also includes the peaks of Deo Tibba and Indrasan.
• Rivers: The Jhelum, Kishanganga, and Chenab rivers flow through the range.

Additional Information

• The Zanskar Range, Ladakh Range, and Karakoram Range are all mountain ranges in the Ladakh region of India.
• The Zanskar Range is located south of the Ladakh Range, which is in turn located south of the Karakoram Range.
• Karakoram Range
• Part of a complex of mountain ranges that also includes the Hindu Kush, Himalaya, and Pamir ranges.
• The Karakoram Range has eight mountains with peaks over 7,500 meters (24,600 ft) high, and four of those are higher than 8,000 meters (26,000 ft).
• Ladakh
• A cold desert in the northernmost part of India, Ladakh is home to some of the world's highest mountain peaks.
• Many of these peaks are unclimbed and unnamed due to security reasons.
• Zanskar Range
• One of the main ranges in Ladakh, along with the Ladakh Range, Kailas, and Karakoram

The correct answer is Fermentation

Key Points

• Pyruvate is converted into ethanol and carbon dioxide during fermentation:
• Pyruvate is broken down to form ethanol and carbon dioxide
• Type of respiration
• Anaerobic respiration, which means it takes place in the absence of air (oxygen)
• Fermentation is a process that regenerates the electron carrier from the produced in glycolysis.
• The extra reactions in fermentation allow glycolysis to keep running by ensuring a steady supply of the electron carrier.

Additional Information

• Diffusion
• The movement of molecules from a region of higher concentration to a region of lower concentration.
• Diffusion is a passive process that occurs across membranes and over short distances.
• It's important for photosynthesis, as carbon dioxide diffuses into the leaves from the stomata.
• Diffusion also occurs during transpiration, when water and oxygen diffuse from the leaves into the environment.
• Translocation
• The bulk movement of substances, such as organic compounds, through the vascular tissues of a plant over long distances.
• Translocation is an active and passive process that occurs in the xylem and phloem.
• Transpiration
• The evaporation of water from the leaves of a plant in the form of water vapour.
• Transpiration can occur through the stomata or through the cuticle, a waxy covering on the surface of the leaves.

According to the given information:

1. Q, who is second to the left of O has K and E as immediate neighbours.

2. O is neither an immediate neighbour of M nor E.

3. C is the immediate neighbour of Z and M.

So, Z is sitting to the immediate right of O.

Hence, the correct answer is "Z".

The correct answer is 1975

Key Points

• Coal India Limited (CIL) was founded in November 1975 by the Government of India.
• It operates in the coal mining industry and has its headquarters in Kolkata, India.
• CIL is the world's largest coal mining company.
• It operates in 83 mining areas across eight Indian states, managing 322 mines.
• CIL also runs workshops, hospitals, training institutes, and vocational training centers.

The correct answer is Calcium hydroxide

Key Points

• The correct product formed by the combination reaction of calcium oxide (CaO) with water is Calcium hydroxide (Ca(OH)₂)
• When calcium oxide reacts with water, it forms calcium hydroxide, which is commonly known as slaked lime.
• The chemical reaction is:CaO+H₂O→Ca(OH)₂
• This is a typical combination reaction where two reactants combine to form a single product.
• Calcium hydroxide is used in various industrial processes, such as water treatment and in the production of lime for construction​

Additional Information

• Calcium Carbonate (CaCO₃)
• Calcium carbonate is not formed by the combination of calcium oxide with water. Instead, it is typically produced when calcium hydroxide reacts with carbon dioxide (CO₂). The reaction would be:
• Ca(OH)₂+CO₂→CaCO₃+H₂O
• Calcium carbonate is commonly found in nature as limestone and is used in various industries like construction and agriculture.
• Calcium Bicarbonate (Ca(HCO₃)₂)
• Calcium bicarbonate is not directly formed by the combination of calcium oxide with water either. It forms when calcium carbonate dissolves in carbonic acid or in water containing dissolved CO₂. The reaction is:
• CaCO₃+CO₂+H₂O→Ca(HCO₃)₂
• This compound is important in natural processes, such as the dissolution of limestone in water to form hard water.

The correct answer is v2 > v1 > v3

Key Points

• The refractive index (n) of a medium is related to the speed of light (v) in that medium by the following equation:
• n = c / v
• where c is the speed of light in a vacuum.
• Therefore, the speed of light in a medium is inversely proportional to its refractive index.
• Given:
• Refractive index of medium 1 (n1) = 1.50
• Refractive index of medium 2 (n2) = 1.36
• Refractive index of medium 3 (n3) = 1.54
• From the equation, we can see that:
• A higher refractive index corresponds to a lower speed of light.
• Therefore, the correct order of speeds is:
• v2 > v1 > v3

Shortcut Trick

Identify the extra weight added: 70 − 50 = 20 kg.

Distribute this excess weight among the total number of people (11 students + 1 teacher = 12 people).

Average increase = 20 ÷ 12 = 5 ÷ 3 = 1.666... kg.

New Average = Old Average + Increase = 50 + 1.66 = 51.66 kg.

∴ The correct answer is 51.66 kg.

Alternate Method

Given:

Number of students = 11 | Average weight = 50 kg | Teacher’s weight = 70 kg

Formula Used:

Average = Sum of all observations ÷ Total number of observations

⇒ Total weight of 11 students = 11 × 50 = 550 kg

⇒ Total weight including teacher = 550 + 70 = 620 kg

⇒ Total number of people = 11 + 1 = 12

⇒ New average = 620 ÷ 12

⇒ New average = 51.666...

∴ The correct answer is 51.66 kg.

Additional Information

Net Deviation Method

If an observation ‘x’ is added to a group with average ‘A’, the new average becomes A + (x − A) ÷ (n + 1), where n is the initial number of people.

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the new average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Concept of Replacement

If one person is replaced, the change in total weight is simply (New weight − Old weight), and the change in average is (Net Change) ÷ (Total Strength).

According to the given information:

1. Only three players were born before Aman.

2. None of them were born after Druv, who was born on the date which is immediately after Elia.

3. Only two players were born between Chahal and Elia.

4. Bidya was not born after Chahal.

Thus, Flintoff was born on 3rd.

Hence, the correct answer is "Flintoff".

The correct answer is option 2

Key Points

• In a displacement reaction, a more reactive metal displaces a less reactive metal from its compound.
• Iron (Fe) is more reactive than copper (Cu), so when iron metal is added to a copper sulphate (CuSO₄) solution, iron displaces copper from the solution and forms iron(II) sulphate (FeSO₄), while copper metal is deposited.
• The chemical equation for the reaction is:
• Fe(s)+CuSO₄(aq)→FeSO₄(aq)+Cu(s)
• This occurs because iron has a greater tendency to lose electrons (oxidize) compared to copper, which allows it to replace copper in the compound.

The correct answer is 1856.

Key Points 

• The Hindu widow remarriage act was passed in the year 1856.
• The act made the remarriage of Hindu widows in all jurisdictions of India under East India Company rule legal.
• The Hindu widow remarriage act was drafted during the tenure of Lord Dalhousie.
• The act was passed by Lord Canning in 1856.
• The remarriage of Hindu widows was first legalized by Lord Canning.
• Hindu widow remarriage act was considered as the first major social reform legislation after the abolition of Sati in 1829.
• Indian social reformer Ishwar Chandra Vidyasagar was the most prominent campaigner of the Hindu widow remarriage act

The correct answer is Y H Malegam committee

Key Points

• The Committee constituted by the Reserve Bank of India (RBI) to study issues and concerns in the Micro Finance Institutions (MFI) sector is the Malegam Committee.
• The Malegam Committee was set up in 2010 under the chairmanship of Dr. Y.H. Malegam, a renowned chartered accountant and former RBI Board member.
• The committee's primary objective was to examine the functioning of MFIs and to propose recommendations to address concerns such as interest rates, transparency, over-indebtedness, and consumer protection in the microfinance sector.
• It suggested capping the interest rates charged by MFIs and recommended the establishment of a microfinance development fund.
• It also proposed the creation of a uniform regulatory framework for all MFIs across the country, including the registration and supervision by the RBI.

Additional Information

• Malhotra Committee (1999): This committee focused on reforming the insurance sector in India. It played a key role in the liberalization of the insurance industry, recommending the opening up of the sector to private players and the establishment of the Insurance Regulatory and Development Authority (IRDA).
• Abid Hussain Committee (1997): This committee was set up to look into the small-scale industries (SSI) sector. It provided suggestions on how to improve the functioning and support to small-scale industries, including recommendations for modernizing and enhancing their competitiveness.
• Kelkar Committee (2002): The Kelkar Committee was formed to examine tax reforms in India. It suggested a comprehensive framework for tax reforms, including recommendations to simplify the tax structure and reduce tax rates for better compliance.

The correct answer is Odisha

Key Points

• According to the Indian Minerals Yearbook 2017, Odisha has the largest reserves of bauxite in India
• Odisha has 51% of the country's bauxite resources
• Andhra Pradesh has 16% of the country's bauxite resources
• Gujarat has 9% of the country's bauxite resources
• Jharkhand has 6% of the country's bauxite resources
• Maharashtra has 5% of the country's bauxite resources
• Madhya Pradesh and Chhattisgarh
• Each has 4% of the country's bauxite resources
• Odisha also has the highest percentage of chromite, manganese, iron ore, and coal in the country

Shortcut Trick

For continued proportion a : b :: b : c, the relation is b² = ac.

Given b = 6 and c = 4a → a = c/4.

Substitute in formula: 6² = (c/4) × c ⇒ 36 = c² / 4.

c² = 144 ⇒ c = 12.

∴ The correct answer is 12.

Alternate Method

Given: a/b = b/c, c = 4a, b = 6

Formula Used: Product of extremes = Product of means (ac = b²)

⇒ a/6 = 6/c

⇒ ac = 36

⇒ Since c = 4a, we have a = c/4

⇒ (c/4) × c = 36

⇒ c² = 36 × 4

⇒ c² = 144

⇒ c = √144 = 12

∴ The correct answer is 12.

Additional Information

Continued Proportion

Three quantities a, b, c are in continued proportion if a : b = b : c, where b is the mean proportional.

Mean Proportional

The mean proportional between two numbers a and c is given by b = √(ac).

Third Proportional

In the ratio a : b :: b : c, c is called the third proportional to a and b, calculated as c = b²/a.

The logic followed here is:

(1st number × 6) = 2nd number

For, 7 : 42

⇒ (7 × 6) = 42

For, 9 : 54

⇒ (9 × 6) = 54

Similarly, for 11 : ?

⇒ (11 × 6) = 66

Hence, the correct answer is "Option 4".

The correct answer is CaSO4.2H2O and CaSO4.1/2H2O

Key Points

• The chemical formulas for gypsum and plaster of Paris are:
• The chemical formula for gypsum is $CaSO 4 ⋅2H 2 O$ and its chemical name is calcium sulfate dihydrate.
• Gypsum is a soft mineral that is commonly used in the production of plaster, drywall, and fertilizers.
• It consists of calcium sulfate combined with two molecules of water (hence "dihydrate").
• The mineral is widely found in nature and forms through the evaporation of water in marine environments or from the evaporation of saline lakes.
• Gypsum plays a crucial role in the construction industry, especially in the form of plaster and board products, and has various applications in agriculture, particularly as a soil amendment to improve soil structure.
• Plaster of Paris
• The chemical formula for plaster of Paris is CaSO₄·½H₂O and its chemical name is calcium sulfate hemihydrate.
• Plaster of Paris is widely used for creating molds, sculptures, and in the medical field for making casts to immobilize broken bones. The reaction can be reversed by adding water, which rehydrates the compound and forms the solid structure again.

[Math Processing Error] CaSO4⋅12H2OCaSO4⋅12H2OCaSO4⋅12H2OCaSO4⋅12H2O[Math Processing Error]CaSO4⋅12H2OCaSO4⋅12H2O

      CaSO4​⋅21​H2​CaSO4⋅12H2OCaSO4⋅12H2OCaSO4⋅12H2OCaSO4⋅12H2O[Math Processing Error]CaSO4⋅12H2OCaSO4⋅12H2O

      CaSO4​⋅21​H2​CaSO4⋅12H2O

Given equation: 490 × 7 + 2 - 8 ÷ 6

If ‘+' means ‘×' , ‘×' means ‘÷’, ‘÷’ means ‘-’, and ‘-’ means ‘+’, 

⇒ 490 ÷ 7 × 2 + 8 - 6

⇒ 70 × 2 + 8 - 6

⇒ 140 + 8 - 6

⇒ 148 - 6

⇒ 142

Hence, the correct answer is "142".

The logic followed here is:

Given word: JUPITER

J is followed by U which is vowel. Then J will be coded by 7 from condition (i):

J → 7; U → @; P → 7; I → 6; T → 7; E → 4; R → 9

The code for JUPITER → 7@76749

Hence, the correct answer is "7@76749".

According to the given information:

Punit was driving a car towards the north direction, then he turned to his left and drove 10 km.

Again, he turned left and drove a distance of 20 km, and further took a left turn and drove a distance of 10 km.

His present location is 10 km south of his starting point. 

Thus, he drives 10km towards the north direction initially.

Hence, the correct answer is "10km".

Shortcut Trick

Cost of 3 kg bananas = 3 × x = 3x

Cost of 5 kg apples = 5 × (x + 5) = 5x + 25

Total cost = 3x + 5x + 25 = 8x + 25

∴ The correct answer is 8x + 25.

Alternate Method

Given:

Price of bananas = ₹x per kg

Price of apples = Bananas + ₹5 = ₹(x + 5) per kg

Formula Used:

Total Price = (Quantity₁ × Rate₁) + (Quantity₂ × Rate₂)

Calculations:

⇒ Total price of 3 kg bananas = 3 × x = 3x

⇒ Total price of 5 kg apples = 5 × (x + 5)

⇒ Total price of 5 kg apples = 5x + 25

⇒ Grand Total Price = 3x + 5x + 25

⇒ Grand Total Price = 8x + 25

∴ The correct answer is 8x + 25.

Additional Information

Algebraic Expressions

An expression containing variables (like x) and constants (like 25) connected by operations like addition and multiplication.

Like Terms

Terms that have the same variable part, such as 3x and 5x, can be added or subtracted directly.

Unitary Pricing

Total cost is always determined by multiplying the quantity by the price per unit (Cost = Quantity × Rate).

The correct answer is deviation in direction of light increases

Key Points

• When the refractive index increases, the deviation in the direction of light also increases.
• This is because a higher refractive index means greater refraction, and therefore a greater angle of deviation.
• Refractive index
• The refractive index of a material determines how much light bends when it passes through that material.
• Angle of deviation
• The angle of deviation is the angle between the incident light and the refracted light.
• Light's path
• When light enters a material with a higher refractive index, it bends towards the normal of the surface.
• The higher the refractive index, the closer to the normal direction the light will travel.

Shortcut Trick

Area of square = 11025 cm²

Side (a) = √Area = √11025 = 105 cm

Diagonal (d) = a√2 = 105√2 cm

∴ The correct answer is 105√2 cm.

Alternate Method

Given: Area of the square = 11025 cm²

Formula Used: Area = Side²; Diagonal = Side × √2

⇒ Let the side of the square be 'a'.

⇒ a² = 11025

⇒ a = √11025

⇒ a = 105 cm

⇒ Diagonal (d) = a × √2

⇒ d = 105 × √2 = 105√2 cm

∴ The correct answer is 105√2 cm.

Additional Information

Properties of a Square

All four sides are equal, and each internal angle is 90°. The diagonals are equal and bisect each other at 90°.

Perimeter of Square

The perimeter is the total length of the boundary, calculated as P = 4 × Side.

Diagonal-Area Relationship

Area can also be calculated using the diagonal (d) as Area = d² ÷ 2.

Shortcut Trick

Assume the overall average of 40 as the baseline for all matches.

Deviation for the first 6 matches = (44 − 40) × 6 = +24.

To maintain the overall average, the last 4 matches must compensate with a deviation of −24.

Adjustment per match for last 4 matches = −24 ÷ 4 = −6.

Average of last 4 matches = 40 − 6 = 34.

∴ The correct answer is 34 runs.

Alternate Method

Given:

Total matches = 10 | Overall average = 40 runs

First 6 matches average = 44 runs

Formula:

Total Runs = Average × Number of Matches

Calculations:

⇒ Total runs for 10 matches = 10 × 40 = 400 runs

⇒ Total runs for first 6 matches = 6 × 44 = 264 runs

⇒ Total runs for last 4 matches = Total runs − Runs of first 6 matches

⇒ Total runs for last 4 matches = 400 − 264 = 136 runs

⇒ Average of last 4 matches = 136 ÷ 4

⇒ Average of last 4 matches = 34 runs

∴ The correct answer is 34 runs.

Additional Information

Weighted Average Formula

When a group is divided into two parts, the combined average is given by: A = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).

Deviation Method

Sum of deviations from the Arithmetic Mean is always zero. This is used to find missing values in datasets quickly.

Inclusion/Exclusion Rule

New value = New Average + (Number of original items × Change in Average). This is helpful when a single person joins or leaves a group.

Given:

The equation to solve is:

7.98 × 2 + 3.96 × 6 - 18 ÷ 2 + 1 = ?

Solution:

Step 1: Perform the multiplication and division first.

7.98 × 2 = 15.96

3.96 × 6 = 23.76

18 ÷ 2 = 9

Step 2: Substitute the values back into the equation.

15.96 + 23.76 - 9 + 1

Step 3: Perform the addition and subtraction.

15.96 + 23.76 = 39.72

39.72 - 9 = 30.72

30.72 + 1 = 31.72

Conclusion:

The value of the expression is approximately 32.

The correct answer is The current at P is greater than the current at Q

Key Points

• The current at P is greater than the current at Q.
• This is because P is located before the branches in the circuit, where the total current flows.
• After splitting at the junction, the current divides between the paths leading to Q, resulting in a lower current at Q compared to P.
• Using Ohm's Law (V=IR), since the voltage is constant, the point before the split (P) carries the total current, making I_P > I_Q.

The correct answer is 2011

Key Points

• Between Gangothri and Diamond Harbour, the Ganges River passes through numerous densely populated and industrial areas, which contribute to its pollution levels.
• Faecal coliform levels are a key indicator of water pollution, particularly from human and animal waste.
• High faecal coliform levels in a water body indicate the presence of pathogens that can pose risks to human health.
• In 2011, environmental studies and reports highlighted particularly high levels of faecal coliform in the Ganges River. Several factors contributed to this:
• Population Growth: Increased urbanization and population growth along the river’s banks led to more sewage and waste being discharged into the river without adequate treatment.
• Industrial Discharge: Industrial effluents, often untreated or partially treated, were directly released into the river, adding to the pollution load.
• Inadequate Infrastructure: Many cities along the Ganges lacked sufficient infrastructure for effective sewage treatment and waste management, resulting in direct discharge of untreated sewage into the river.
• Agricultural Runoff: Runoff from agricultural activities, carrying fertilizers, pesticides, and animal waste, also contributed to the pollution levels.
• Reports and data collected during this time indicated that faecal coliform levels were significantly higher than the acceptable limits for safe bathing water.
• The situation in 2011 became a point of concern for environmentalists, public health officials and the government, prompting discussions and initiatives to address the pollution in the Ganges.
• Thus, 2011 stands out as a year when the faecal coliform levels in the Ganges River from Gangothri to Diamond Harbour were notably high.

Shortcut Trick

For any two similar triangles, the ratio of their corresponding sides is always equal.

Given ΔABC ≈ ΔADE, the corresponding vertices are A → A, B → D, and C → E.

Therefore, the ratio of corresponding sides is: AB/AD = BC/DE = AC/AE.

By comparing with the options, we directly get AB/AD = BC/DE.

∴ The correct answer is (AB)/(AD) = (BC)/(DE).

Alternate Method

Given:

ΔABC is similar to ΔADE (ΔABC ~ ΔADE).

Formula Used:

If two triangles are similar, then their corresponding angles are equal and their corresponding sides are in the same ratio (proportionality of sides).

Calculations:

Since ΔABC ~ ΔADE, we can write the ratio of corresponding sides as:

⇒ AB / AD = BC / DE = AC / AE

Let us analyze each option to find which one is necessarily true:

1. (BC)/(BD) = (CE)/(DE): This ratio involves parts of sides (BD and CE) which do not represent the direct ratio of similarity of the two triangles.

2. (BC)/(BD) = (AB)/(AC): This is not a standard property of similar triangles.

3. (EC)/(AC) = (AD)/(DE): This is also incorrect as EC is only a segment of AC.

4. (AB)/(AD) = (BC)/(DE): This is directly obtained from the first two terms of our similarity ratio: AB / AD = BC / DE.

⇒ Therefore, option (4) is necessarily true.

∴ The correct answer is (AB)/(AD) = (BC)/(DE).

Additional Information

Basic Proportionality Theorem (Thales Theorem)

If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio. Thus, AD/DB = AE/EC.

Properties of Similar Triangles

For any two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides: Area(ΔABC)/Area(ΔADE) = (AB/AD)² = (BC/DE)² = (AC/AE)².

Criteria for Similarity

Two triangles are similar if they satisfy the Angle-Angle (AA), Side-Angle-Side (SAS), or Side-Side-Side (SSS) similarity criteria.

Given:

We are asked to convert the repeating decimal 0.2̅6 (where 6 repeats indefinitely) into a proper fraction.

Solution:

Step 1: Let the repeating decimal be x.

x = $0.2\overline{6}$

Step 2: Eliminate the repeating decimal by multiplying by 10.

10x = $2.\overline{6}$

Step 3: Subtract the original equation from the multiplied equation.

10x - x = $2.\overline{6}$- $0.2\overline{6}$

9x = 2.4

Step 4: Solve for x.

x = 2.4 / 9

Step 5: Simplify the fraction.

x = 24 / 90

x = 4 / 15

Conclusion:

The repeating decimal 0.2̅6 is equivalent to the proper fraction 4 / 15.

Given: 

1. Taruni drives 65 km towards the east to reach city park.
2. Then she turns right and drives another 85 km.
3. Then turns left and drives another 53 km to reach the metro station.

So, She is facing in the 'East' direction.

Hence, the correct answer is "Option 2".

The logic followed here is:

DXB : GSI

KVR : NQY

Similarly, JNP : ?

Hence, the correct answer is "MIW".

According to the given information:

1. G is kept fourth from the bottom and immediately below E and immediately above B.

2. There are only three boxes between C and F where C is place somewhere above F.

3. D is placed at the bottom most position.

Thus, only A is remaining and 7th position is empty.

Thus, Four shoe boxes are placed between A and F.

Hence, the correct answer is "Four".

The correct answer is Training for Emirates Jobs and Skills

Key Points

• The full form of TEJAS is Training for Emirates Jobs and Skills
• Union Minister Shri Anurag Thakur launched TEJAS (Training for Emirates Jobs And Skills), a Skill India International Project to train overseas Indias.
• It is a Skill India International Project to train overseas Indians.
• The project is aimed at skilling, certification and overseas employment of Indians.
• Tejas is aimed at creating pathways to enable the Indian workforce to get equipped for skill and market requirements in UAE.

Additional Information

• Tejas aims at creating a 10,000 strong Indian workforce in UAE during the initial phase.
• The Minister also met prominent Indian film personalities like Shri Kabir Khan and Shri Priyadarshan in a discussion also attended by Film Commissioner of the Abu Dhabi Film Commission Mr Hans Fraikin.
• Subsequently, Shri Thakur embarked on a visit to the India Pavillion at Dubai Expo where he also held a discussion with the Minister of State for International Cooperation in the Government of UAE, Ms Reem Al Hashimi.

Given:

Statement :

People are becoming more conscious about moving towards a healthy lifestyle.

Now,

Arguments :

I. Many people are switching to organic farming as the food is healthier - True (As the statement says people are becoming more conscious about a healthy lifestyle, switching to organic farming is a direct result of this consciousness).

II. People are planning meals and cooking at home more than before - True (Planning meals and cooking at home indicate a shift towards a healthier lifestyle, thus supporting the statement).

So, Both I and II strengthen the statement.

Hence, the correct answer is "Option 4".

Given:

The equation to solve is:

2405 ÷ 13 × 6 + 35

Solution:

Step 1: Perform the division first.

2405 ÷ 13 = 185

Step 2: Now, multiply the result by 6.

185 × 6 = 1110

Step 3: Finally, add 35 to the result.

1110 + 35 = 1145

Conclusion:

The value of 2405 ÷ 13 × 6 + 35 is 1145.

The correct answer is Creatinine.

Glucose, amino acids, salts and high amount of water are reabsorbed in the nephron during the second step of urine formation.

The correct answer is Co and Ni

Key Points

• Newlands placed cobalt and nickel in the same slot and positioned them in the same column with fluorine, chlorine and bromine that possess different properties compared to these two elements (Cobalt and Nickel).
• This is one of the demerits of Newland's law of octaves.
• In Newlands' Octaves, elements were arranged in such a way that similar elements were placed in the same column (group), based on increasing atomic masses. Newlands observed that every eighth element had similar chemical properties, resembling the pattern of musical octaves.

Additional Information

• C and K (Carbon and Potassium)
• Carbon (C) and Potassium (K) do not share similar chemical properties, and they were not placed in the same column in Newlands’ octaves.
• Carbon is a non-metal, and potassium is an alkali metal, so this pair does not fit.
• Cr and Zr (Chromium and Zirconium)
• Chromium (Cr) and Zirconium (Zr) are transition metals but are not placed in the same column in Newlands’ octaves.
• Chromium and Zirconium have distinct properties, and Newlands didn’t group them together.
• P and S (Phosphorus and Sulfur)
• Phosphorus (P) and Sulfur (S) are non-metals and share similar chemical properties as they belong to the same group in the modern periodic table (Group 16).
• However, in Newlands' arrangement, they were not placed in the same column as H, F, Cl, and Br because of the nature of Newlands' grouping based on atomic mass and chemical behavior, which doesn’t perfectly align with the modern periodic table.

The correct answer is option 1

Key Points

• Ionic compounds are solids because of the strong electrostatic forces of attraction between positive (cations) and negative (anions) ions, not weak forces.
• These strong forces result in a rigid lattice structure, making ionic compounds solid at room temperature.
• So this statement is incorrect.

Additional Information

• Ionic compounds have high melting and boiling points due to the strong electrostatic forces that require a significant amount of energy to overcome.
• Ionic compounds are brittle because applying pressure shifts the alignment of ions, causing like charges to repel each other, leading to the breaking of the crystal structure.
• Ionic (electrovalent) compounds are generally soluble in polar solvents like water because water's polarity helps separate the ions. However, they are insoluble in non-polar solvents like petrol.

Given: 465 638 359 987 563

If the positions of the first two digits in each number are reversed, then the numbers become:

645 368 539 897 653

The first digit of the greatest number (897) is: 8

The first digit of the lowest number (368) is: 3

So, the difference between the first digit of the greatest number and the first digit of the lowest number is:

→ 8 - 3 = 5.

The correct answer is "Option 1".