RRB Group D Previous Year Paper (Held on: 6 Sept 2022 Shift 3)

Given: (left) 724 893 720 525 492 (right)

The third digit of the largest number is: 3 (893)

And, 

The first digit of the smallest number is: 4 (492)

So, the addition of the third digit of the largest number and the first digit of the smallest number is:

→ 3 + 4 = 7.

The correct answer is "Option 1".

Shortcut Trick

From the quadratic equation x² − 5x + 3 = 0, the sum of roots α + β = 5 and product αβ = 3.

New sum of roots (S) = α² + β² = (α + β)² − 2αβ = 5² − 2(3) = 19.

New product of roots (P) = α²β² = (αβ)² = 3² = 9.

The required equation is x² − Sx + P = 0 ⇒ x² − 19x + 9 = 0.

∴ The correct answer is x² − 19x + 9 = 0.

Alternate Method

Given: α and β are the roots of the equation x² − 5x + 3 = 0.

Formula Used: For any quadratic equation ax² + bx + c = 0, the sum of roots = −b/a and the product of roots = c/a. A quadratic equation with roots r₁ and r₂ is given by x² − (r₁ + r₂)x + (r₁ × r₂) = 0.

Calculations:

⇒ For x² − 5x + 3 = 0: a = 1, b = −5, c = 3.

⇒ Sum of roots, (α + β) = −(−5)/1 = 5

⇒ Product of roots, (αβ) = 3/1 = 3

⇒ We need an equation with roots α² and β².

⇒ Sum of new roots = α² + β²

⇒ α² + β² = (α + β)² − 2αβ

⇒ Sum of new roots = (5)² − 2(3) = 25 − 6 = 19

⇒ Product of new roots = α² × β² = (αβ)²

⇒ Product of new roots = (3)² = 9

⇒ Forming the new quadratic equation: x² − (19)x + 9 = 0

⇒ x² − 19x + 9 = 0

∴ The correct answer is x² − 19x + 9 = 0.

Additional Information

Relation between Roots and Coefficients

For ax² + bx + c = 0, Sum = −b/a and Product = c/a. These values are essential for transforming roots into new equations.

Nature of Roots

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

Formation of Quadratic Equation

A general quadratic equation is written as x² − (Sum of roots)x + (Product of roots) = 0.

Algebraic Identities for Roots

Commonly used identities: α² + β² = (α + β)² − 2αβ and α³ + β³ = (α + β)((α + β)² − 3αβ).

Shortcut Trick

To find the count of prime numbers from 1 to 50, use the standard distribution code 44223.

1 to 10 → 4 | 11 to 20 → 4 | 21 to 30 → 2 | 31 to 40 → 2 | 41 to 50 → 3

Total count = 4 + 4 + 2 + 2 + 3 = 15.

∴ The correct answer is 15.

Alternate Method

Given: Range of numbers is less than 50.

Method: Listing all prime numbers (numbers with exactly two factors: 1 and itself) up to 50.

⇒ Prime numbers between 1 and 10: 2, 3, 5, 7 (4 numbers)

⇒ Prime numbers between 11 and 20: 11, 13, 17, 19 (4 numbers)

⇒ Prime numbers between 21 and 30: 23, 29 (2 numbers)

⇒ Prime numbers between 31 and 40: 31, 37 (2 numbers)

⇒ Prime numbers between 41 and 50: 41, 43, 47 (3 numbers)

⇒ Total count = 4 + 4 + 2 + 2 + 3 = 15

∴ The correct answer is 15.

Additional Information

Prime Numbers up to 100

There are exactly 25 prime numbers between 1 and 100.

Smallest Prime Number

2 is the only even prime number and the smallest prime number. 1 is neither prime nor composite.

Twin Primes

Pairs of prime numbers with a difference of 2, such as (3, 5), (5, 7), and (11, 13).

Shortcut Trick

Price after 25% and 8% discounts = 500 × 0.75 × 0.92 = 345

Remaining discount factor (100 − x)% = 303.60 ÷ 345 = 0.88 ⇒ x = 12

New single discount = (33 + 12)% = 45%

New Selling Price = 500 × (100 − 45)% = 500 × 55% = 275

∴ The correct answer is ₹275.

Alternate Method

Given:

Marked Price (MP) = ₹500

Successive Discounts = 25%, 8%, and x%

Final Selling Price (SP₁) = ₹303.60

New Discount = (33 + x)%

Calculations:

⇒ Price after 1^st discount = 500 × (100 − 25)/100 = 500 × 75/100 = ₹375

⇒ Price after 2^nd discount = 375 × (100 − 8)/100 = 375 × 92/100 = ₹345

⇒ Price after 3^rd discount = 345 × (100 − x)/100 = 303.60

⇒ (100 − x)/100 = 303.60 ÷ 345 = 0.88

⇒ 100 − x = 88 ⇒ x = 12

⇒ New discount rate = (33 + 12)% = 45%

⇒ New Selling Price = MP × (100 − 45)/100

⇒ New Selling Price = 500 × 55/100 = ₹275

∴ The correct answer is ₹275.

Additional Information

Successive Discount Formula

For two successive discounts a% and b%, the single equivalent discount is (a + b − ab/100)%.

Selling Price Formula

SP = MP × (100 − D₁)/100 × (100 − D₂)/100 × ... where D_n are successive discount percentages.

Marked Price and Selling Price Relation

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

Given:

Now, the group of numbers and symbols is: ! 9 2 7 $ 3

Here, First conditions followed in the given group,

So, Codes of the First and last elements are to be interchanged.

Then, the code for '! 9 2 7 $ 3' is → 'P Y T C D J'.

Hence, the correct answer is "Option 3".

The correct answer is Solar, electrical.

Key Points

• Solar energy is the energy from the sun that is captured by solar panels and converted into electrical energy.
• The process of energy conversion in a solar panel involves photovoltaic cells that absorb sunlight and release electrons, which are then captured as electrical energy.
• Electrical energy is the form of energy that can be used to power homes, buildings, and other electrical devices.

Additional Information

• Solar energy is a renewable source of energy that is becoming increasingly popular as a way to reduce reliance on fossil fuels.
• Electrical energy is a versatile form of energy that can be used for a wide range of applications, from powering homes and businesses to charging electric vehicles.
• Heat energy can be used for heating buildings and water.
• Light energy is a form of electromagnetic radiation that includes visible light, ultraviolet light, and infrared radiation.
• It is used in a wide range of applications, from lighting to communication technologies.

The correct answer is transfusion of contaminated blood.

Key Points

• HIV can be transmitted through transfusion of contaminated blood or blood products.
• This can happen if the blood is not properly screened for HIV before being used in transfusion.
• HIV is not transmitted through soil, water, food or other environmental factors.
• It is only transmitted through specific bodily fluids, including blood, semen, vaginal fluids, and breast milk.

Additional Information

• Human immunodeficiency virus is known as HIV.
• It is a virus that targets the immune system of the body.
• HIV can result in AIDS (acquired immunodeficiency syndrome) if it is not treated.
• As of right now, there's no real cure.
• It is important to note that HIV can also be transmitted through unprotected sex, sharing needles or other injection drug equipment, and from mother to child during pregnancy, childbirth, or breastfeeding.
• It is important to practice safe sex, not share needles, and get tested regularly for HIV if you are at risk.

The correct answer is Neem.

Key Points

• Neem is considered a medicinal plant due to its numerous health benefits and medicinal properties.
• Neem has been used in Ayurvedic medicine for centuries to treat a wide range of ailments, including skin disorders, fever, and digestive issues.
• The leaves, bark, and seeds of the neem tree are all used in traditional medicine to make remedies for various health conditions.
• Neem contains active compounds like azadirachtin, nimbin, and nimbidin, which have anti-inflammatory, antifungal, antibacterial, and antiviral properties.

Additional Information

• Sal is a hardwood tree that is commonly found in India and other parts of Asia.
• It is used to make furniture, railway sleepers, and other products.
• Teak is a tropical hardwood tree that is native to Southeast Asia.
• It is highly valued for its durability and water resistance, and is commonly used in boat-building, furniture-making, and other applications.
• Deodar is a species of cedar tree that is native to the Himalayas.
• It is commonly used in construction and for making furniture.

The correct answer is Nai Udaan.

Key Points

• Nai Udaan is a scheme launched by the Ministry of Minority Affairs, Government of India, to support minority students in clearing competitive exams like UPSC/SSC, State PSC, etc.
• The scheme provides financial assistance for coaching, study material, and other expenses related to the exam preparation.
• The scheme also offers soft skills training, remedial coaching, and mentoring support to help students improve their performance in the exams.

Additional Information

• Maulana Azad National Fellowship is a scholarship scheme for minority students pursuing higher education such as MPhil/PhD.
• Candidates from underprivileged backgrounds who have completed their post-graduation coursework with at least 50% of the required subjects and who choose to work on their research full-time without applying for a UGC-NET or UGC-CSIR NET JRF are eligible.
• Nai Manzil is a skill development and livelihood generation program for school dropouts and unemployed youth from minority communities.
• It was introduced on August 8, 2015.
• Naya Savera is a scheme for providing interest-free loans to minority students for pursuing higher education.
• It was initiated on July 17th, 2007.

Concept:

Sign convention:

Mirror Formula: The following formula is known as the mirror formula, which provided a relation between focal length, image distance, and objects distant as shown below

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

Calculation:

Here, u = - 12cm , v = -18 cm

By using the above formula, 

1/f = 1/(-18) + 1/(-12)

1/f = (-2 - 3)/36

1/f = -5/36

∴ f = - 7.2 cm

The correct answer is 3rd Period and 16th​ Group.

Key Points

• The given element has a total of 16 protons and 16 neutrons, which makes its atomic number 16.
• Based on the atomic number, we can determine that the element belongs to the 3rd period, which is also known as the Li to Ne period, as it contains elements with atomic numbers 3 to 10.
• To determine the group of the element, we need to look at its electronic configuration.
• Since the element has 16 protons, it will have 16 electrons as well.
• The electronic configuration of the element is 1s2 2s2 2p6 3s2 3p6, which means that it has a valence shell configuration of ns2np6.
• This indicates that the element belongs to Group 16, also known as the Oxygen Family.

Additional Information

• The Oxygen Family, to which the given element belongs, is a group of non-metallic elements that have six valence electrons in their outermost shell.
• Some of the common elements in this group include oxygen, sulfur, selenium, and tellurium.
• The 4th period and 13th Group correspond to the Boron Family, which contains elements such as boron, aluminum, gallium, indium, and thallium.
• The 2nd period and 3rd Group correspond to the Carbon Family, which contains elements such as carbon, silicon, germanium, tin, and lead.
• The 3rd period and 2nd Group correspond to the Alkali Earth Metals, which contain elements such as beryllium, magnesium, calcium, strontium, and barium.

The correct answer is The President of India.

Key Points

• The President of India gives a speech on Republic Day at Rajpath.
• The President of India is the head of state of India and is elected by the Electoral College consisting of elected members of both houses of Parliament and of the Legislative Assemblies of the States.
• Since 2022, Droupadi Murmu, a politician and former educator from India, has held the office of 15th President of India.

Additional Information

• The Prime Minister of India is the head of the government and is appointed by the President of India.
• He/she is responsible for running the government and implementing policies.
• The Vice-President of India is the second-highest constitutional office in India after the President.
• He/she is elected by an Electoral College consisting of members of both houses of Parliament.
• The Lieutenant Governor of Delhi is the administrator of the National Capital Territory of Delhi and is appointed by the President of India on the advice of the Prime Minister.

Given: Seven boxes, A, B, C, D, E, F and G, are kept one above the other but not necessarily in the same order.

1. B is placed third from the bottom.

2. Only one box is kept between B and C. How many boxes are kept between G and B?

Case I:

Case II:

3. Only three boxes are kept between A and E.

4. A is placed at any place above E.

Case I:

Case II:

5. F is kept immediately below D. (This cancels Case II, so going with Case I)

And, G will sit on the

Case I:

So, there are '3' boxes kept between G and B.

Hence, the correct answer is "Option 1".

Shortcut Trick

Simplify the brackets using cubic identities: (y − x)(y² + xy + x²) = y³ − x³ and (y + x)(y² − xy + x²) = y³ + x³.

P = (1/xy) [ (y − x)(x² + xy + y²) + (y + x)(x² − xy + y²) ]

P = (1/xy) [ (y³ − x³) + (y³ + x³) ] = 2y³/xy = 2y²/x.

P ÷ Q = (2y²/x) ÷ (y/x) = (2y²/x) × (x/y) = 2y.

∴ The correct answer is 2y.

Alternate Method

Given:

P = ((1/x) − (1/y))[(x + y)² − xy] + ((1/x) + (1/y))[(x − y)² + xy]

Q = y/x

Formula Used:

1. (a + b)² = a² + 2ab + b²
2. (a − b)² = a² − 2ab + b²
3. a³ ± b³ expansion identities.

Calculations:

⇒ P = ((y − x)/xy) [x² + 2xy + y² − xy] + ((y + x)/xy) [x² − 2xy + y² + xy]

⇒ P = ((y − x)/xy) [x² + xy + y²] + ((y + x)/xy) [x² − xy + y²]

⇒ P = (1/xy) [(y − x)(y² + yx + x²) + (y + x)(y² − yx + x²)]

⇒ P = (1/xy) [ (y³ − x³) + (y³ + x³) ]

⇒ P = (1/xy) [2y³] = 2y²/x

⇒ P ÷ Q = (2y²/x) ÷ (y/x)

⇒ P ÷ Q = (2y²/x) × (x/y)

⇒ P ÷ Q = 2y

∴ The correct answer is 2y.

Additional Information

Sum of Cubes Identity

a³ + b³ = (a + b)(a² − ab + b²). This is a core algebraic factorization used to simplify expressions containing quadratic factors.

Difference of Cubes Identity

a³ − b³ = (a − b)(a² + ab + b²). Note the sign change in the middle term of the quadratic factor compared to the sum of cubes.

Division of Fractions

To divide by a fraction, multiply by its reciprocal: (A/B) ÷ (C/D) = (A/B) × (D/C).

BODMAS Rule

Always solve terms within brackets first, followed by division and then addition/subtraction to maintain mathematical accuracy.

Shortcut Trick

Total discount amount = Marked Price (MP) − Selling Price (SP) = 540 − 405 = Rs. 135.

Let the first discount be d% and the second discount be x (where x is the nominal value in Rs. equal to d).

First discount in Rs. = 540 × (d ÷ 100) = 5.4d. Second discount = d. Thus, 5.4d + d = 135.

6.4d = 135 ⇒ d = 135 ÷ 6.4 = 21.09 (Not matching options). Re-evaluating: The problem states second discount has same nominal value as d (the rate).

Let first discount = d% of 540 = 5.4d. Let second discount = d Rs.

5.4d + d = 135 ⇒ 6.4d = 135 ⇒ d = 21.09. Checking alternate interpretation: Both discounts are d%? No. If d = 12.5: 1st disc = 12.5% of 540 = 67.5. 2nd disc = 67.5. Total = 135. SP = 540 − 135 = 405. This fits perfectly.

∴ The correct answer is 12.5.

Alternate Method

Given: MP = Rs. 540, SP = Rs. 405, First discount = d%, Second discount = Rs. d. Formulas: Total Discount = MP − SP | Discount Amount = (Rate ÷ 100) × Base Value

⇒ Total Discount = 540 − 405 = 135. ⇒ According to the question, first discount is d% of 540 and second is Rs. d. ⇒ (d ÷ 100) × 540 + d = 135 ⇒ 5.4d + d = 135 ⇒ 6.4d = 135 ⇒ d = 135 ÷ 6.4 = 21.09 (Note: If the phrasing implies second discount value equals the first discount's rupee value) ⇒ Let first discount amount = x. Then 2x = 135 ⇒ x = 67.5. ⇒ d% of 540 = 67.5 ⇒ d = (67.5 ÷ 540) × 100 = 12.5.

∴ The correct answer is 12.5.

Additional Information

Nominal Value Interpretation

In profit and loss, nominal value usually refers to the absolute numerical value. If two discounts have the same nominal value, their Rupee amounts are identical.

Successive Discount Calculation

When multiple discounts are applied, the first is on the Marked Price, and subsequent ones are on the diminished price unless specified otherwise by 'nominal value'.

The correct answer is digestive.

Key Points

• Buccal cavity is a part of the human digestive system.
• It is also known as the oral cavity or mouth.
• It is the first part of the digestive system where food enters the body and is broken down by the teeth and saliva before being swallowed.
• The buccal cavity also plays a role in speech and taste perception.

Additional Information

• Circulatory system is responsible for the circulation of blood and nutrients throughout the body.
• It includes the heart, blood vessels, and blood.
• Respiratory system is responsible for the exchange of gases (oxygen and carbon dioxide) between the body and the environment.
• It includes the lungs, trachea, and bronchi.
• Excretory system is responsible for the elimination of waste products from the body.
• It includes the kidneys, bladder, and urethra.

Shortcut Trick

Ganga (y%): Ratio 12000 : 14400 → 100 : 120 → y = 20%

Saraswathi (x%): Ratio 10000 : 12500 → 100 : 125 → x = 25%

Target value: ((x − y) ÷ y) × 100 = ((25 − 20) ÷ 20) × 100 = (5 ÷ 20) × 100 = 25%

∴ The correct answer is 25%.

Alternate Method

Given:

Ganga Salary: Last Year = ₹12,000 | This Year = ₹14,400

Saraswathi Salary: Last Year = ₹10,000 | This Year = ₹12,500

Formula Used:

Percentage Increase = ((New Value − Old Value) ÷ Old Value) × 100

Calculations:

⇒ Ganga's percentage increase (y%) = ((14,400 − 12,000) ÷ 12,000) × 100

⇒ y = (2,400 ÷ 12,000) × 100 = 20%

⇒ Saraswathi's percentage increase (x%) = ((12,500 − 10,000) ÷ 10,000) × 100

⇒ x = (2,500 ÷ 10,000) × 100 = 25%

⇒ Required Value = $\rm \left(\frac{x-y}{y}\times100\right)\%$

⇒ Required Value = ((25 − 20) ÷ 20) × 100 = (5 ÷ 20) × 100

⇒ Required Value = 0.25 × 100 = 25%

∴ The correct answer is 25%.

Additional Information

Percentage Change

Percentage change represents the degree of change over time, calculated as (Difference ÷ Original Value) × 100.

Relative Increase Comparison

When comparing two percentage growth rates, the percentage difference is (x − y) ÷ y × 100, which shows how much faster one grew compared to the other.

Shortcut Trick

For three numbers a, b, and c, the Fourth Proportional is calculated as (b × c) ÷ a.

Given values are 15, 10, and 12.

Fourth Proportional = (10 × 12) ÷ 15 = 120 ÷ 15 = 8.

∴ The correct answer is 8.

Alternate Method

Given: First term (a) = 15, Second term (b) = 10, Third term (c) = 12.

Formula Used: If a, b, c, d are in proportion, then a : b = c : d or a × d = b × c.

Let the fourth proportional be x.

⇒ 15 : 10 = 12 : x

⇒ 15 / 10 = 12 / x

⇒ 15 × x = 10 × 12

⇒ 15x = 120

⇒ x = 120 ÷ 15

⇒ x = 8

∴ The correct answer is 8.

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 defined as c such that a : b = b : c, given by c = b² ÷ a.

Compounded Ratio

The compounded ratio of (a : b) and (c : d) is (a × c) : (b × d).

The correct answer is Article 21A.

Key Points

• Article 21A was added to the Indian Constitution through the 86th Constitutional Amendment Act, 2002.
• The amendment made free and compulsory education a fundamental right for children between the ages of six and fourteen.
• The amendment also mandated that the State shall provide infrastructure and resources to ensure that every child has access to quality education.

Additional Information

• Article 19A pertains to the right to freedom of speech and expression.
• It offers freedom of speech, which is the ability to freely and fearlessly express one's opinions in writing, orally, electronically, through the media, or through the press.
• Press freedom is an aspect of freedom of expression.
• It also includes websites and blogs.

Calculation

The total number of employees in all the departments in 2001 = 110 + 245 + 43 + 423 + 44 = 865

The total number of employees in all the departments in 2001 who left = 19 + 37 + 8 + 65 + 4 = 133

133 is less than 20% of 865

The total number of employees in all the departments in 2002 = 121 + 224 + 45 + 423 + 45 = 858

The total number of employees in all the departments in 2002 who left = 20 + 45 + 11 + 92 + 9 = 177

177 is more than 20% of 858

The answer is 2002.

The logic followed here is:

So, '150' will replace the question mark in the given series.

Hence, the correct answer is "Option 2".

The correct answer is Heat produced by electric current.

Key Points

• A fuse works on the principle of heat produced by electric current.
• A fuse is an electrical safety device that protects an electrical circuit from damage caused by overloading or short-circuiting.
• It consists of a metal wire or filament that melts when the current flowing through it exceeds a certain limit, thus breaking the circuit and preventing further damage.

Additional Information

• Light produced by electric current: This principle is used in incandescent bulbs, where a filament is heated by the electric current to produce light.
• Magnetic effect produced current: This principle is used in electromagnets, where a current passing through a coil of wire produces a magnetic field.
• Heat absorbed by electric current: This is not a principle that is used in any electrical device, as it goes against the laws of thermodynamics.
• Heat is always produced when current flows through a wire, not absorbed.

Calculation

$7.8\overline{964}$

= 7(8964 - 8)/(9990)

= 7(8956)/(9990)

= 7(4478)/(4995)

The answer is 7(4478)/(4995).

Given

$\frac{183\times183\times183-73\times73\times73}{183\times183+183\times73+73\times73}$

Calculation

let a = 183 and b = 13

⇒ (a³ - b³) = (a - b)(a² + b² +ab)

= (183 - 73)

= 110

The answer is 110

The correct answer is Surajit Sengupta.

Key Points

• Surajit Sengupta was a former Indian footballer who played as a defender for the Indian national team and various clubs in India.
• He was known for his strong tackles and aerial abilities.
• He started his career with Mohun Bagan and later played for East Bengal, Mohammedan Sporting, and Bengal Nagpur Railway.
• He also represented India in the 1978 Asian Games and the 1984 AFC Asian Cup.
• After retiring from playing, Sengupta went on to become a coach and managed various clubs in India, including Mohammedan Sporting, East Bengal, and Mohun Bagan.
• He passed away on 8th February 2022 at the age of 71 due to age-related ailments.
• His demise was mourned by the Indian football fraternity, with many players and coaches paying tribute to him on social media.

Additional Information

• Arun Ghosh is a former Indian footballer who played as a goalkeeper for East Bengal and Mohun Bagan.
• ​He was known for his acrobatic saves and quick reflexes.
• Subhas Bhowmick is a former Indian footballer and coach who played as a striker for East Bengal and Mohun Bagan.
• He later went on to coach both the teams and led them to numerous titles.
• Sukhwinder Singh is a former Indian footballer who played as a midfielder for the Indian national team and various clubs in India.
• He is also a former coach of the Indian national team.

The correct answer is larger, about the same.

Key Points

• Milk appears white in the surrounding of white light because the particles in milk are larger than the wavelength of different colours in white light that falls on it.
• This means that the light waves scatter in all directions when they come in contact with the particles in milk, making the milk appear white.
• Larger is the correct answer as the size of the particles in milk is larger than the wavelength of different colours in white light.

Additional Information

• Milk is an example of a colloid, which is a mixture where one substance is dispersed in another substance.
• In the case of milk, the fat and protein particles are dispersed in water.
• The size of the particles in milk can vary depending on the type of milk and the processing it undergoes.
• For example, whole milk has larger particles than skim milk.
• The scattering of light by particles in a colloid is called the Tyndall effect, which is used to determine if a mixture is a solution or a colloid.
• If the mixture scatters light, it is a colloid.
• The Tyndall effect is also used in various industries, such as pharmaceuticals, to determine the size and concentration of particles in a colloid.

Given:

When Rajesh reached the toy shop he noted that he lost his brother Anoop in the market.

He walked for 60 m to the east and then turned right and went 10 m.

He then turned right again and walked for 10 m to look for his brother at the ice cream shop but his brother was not there.

He then turned towards the north and walked for 10 m before he saw his brother in the street.

So, The toy shop is at the 'West' from Rajesh’s present position.

Hence, the correct answer is "Option 2".

The correct answer is 1959.

Key Points 

• The Panchayati Raj system is a decentralized form of governance that aims to involve local communities in decision-making processes.
• It was first introduced in India through the 73rd Amendment Act of 1992, which made it mandatory for all states to establish Panchayati Raj institutions.
• However, the first Panchayati Raj system in India was actually implemented in the state of Rajasthan in 1959, almost three decades before the constitutional amendment.
• The system was introduced by the then Chief Minister of Rajasthan, Mohan Lal Sukhadia, as a way to empower rural communities and promote local self-governance.
• The Rajasthan Panchayati Raj Act of 1959 established a three-tier system of Panchayati Raj institutions at the village, block, and district levels.
• The institutions were given powers and functions related to local development planning, resource mobilization, and service delivery.
• The success of the Rajasthan Panchayati Raj system inspired other states to adopt similar models of decentralization.
• Today, Panchayati Raj institutions exist in all states of India and play a crucial role in grassroots democracy and development.

Additional Information

• In rural India, the Panchayati Raj system governs villages locally.
• Their duties include "economic development, strengthening social justice and implementation of Central and State Government Schemes including those 29 subjects listed in the Eleventh Schedule."
• The provision of the Indian Constitution that deals with panchayats is called Part IX.
• It adds that there are three PRI levels in states or Union Territories with populations greater than two million.
• the village-level gram panchayats.
• the block-level panchayat samiti, also known as the block samiti or mandal parishad.
• the district panchayat, or district council, at the local level.

The correct option is 1.

The logic followed here is:

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

Now,

For, 3 : 12

⇒ 32 + 3

⇒ 9 + 3 = 12.

For, 5 : 30

⇒ 52 + 5

⇒ 25 + 5 = 30.

Similarly, for 9 : ?

⇒ 92 + 9

⇒ 81 + 9 = 90.

Hence, the correct answer is "Option 3".

The correct answer is V ∝ I at constant temperature.

Key Points

• According to Ohm's law, the relationship between voltage (V), current (I), and resistance (R) is given by V = IR.
• "V ∝ I at constant temperature" is a correct statement as per Ohm's law.
• It means that if the temperature remains constant, the voltage across a conductor is directly proportional to the current flowing through it.

Additional Information

• Only when the given temperature and the other physical parameters stay constant does Ohm's law apply.
• In some components, the temperature rises when the current is increased.
• A light bulb's filament serves as an illustration of this, wherein increasing current causes the filament's temperature to rise.
• Ohm's law cannot be applied in this situation.
• The filament of the lightbulb defies Ohm's Law.

The correct answer is Mg(OH)₂.

Key Points

• Hyper acidity is a condition where the stomach produces excessive acid, leading to symptoms such as heartburn, indigestion, and stomach pain.
• Mg(OH)₂ works by neutralizing the excess acid in the stomach, providing relief from hyper acidity symptoms.
• It is essentially insoluble in water and has little action until it comes into contact with the stomach's hydrochloric acid.
• It is known as milk of magnesia.

Additional Information

• NaCl, sodium chloride, is table salt.
• It is essential for maintaining the body's fluid balance.
• C₆H₁₂O₆ is the formula for glucose.
• It is a sugar that provides energy to the body.
• NaOH (sodium hydroxide) is a strong base that is used in industries for various purposes and should not be consumed as a medicine.
• It can cause further damage to the stomach lining in the case of hyper acidity.

Shortcut Trick

Number of sides (n) = (Sum of interior angles ÷ 180) + 2

n = (2700 ÷ 180) + 2

n = 15 + 2

n = 17

∴ The correct answer is 17.

Alternate Method

Given:

Sum of all interior angles of a regular polygon = 2700°

Formula Used:

Sum of interior angles of a polygon with n sides = (n − 2) × 180°

Calculations:

⇒ (n − 2) × 180 = 2700

⇒ n − 2 = 2700 ÷ 180

⇒ n − 2 = 15

⇒ n = 15 + 2

⇒ n = 17

∴ The correct answer is 17.

Additional Information

Sum of Exterior Angles

The sum of all exterior angles of any convex polygon is always 360°.

Each Interior Angle

For a regular polygon, each interior angle = [(n − 2) × 180°] ÷ n.

Each Exterior Angle

Given: Reena and Meena are walking together.

From the park they started walking towards the south.

After walking for 50 metres they turned to their left and walked for 30 metres.

After this they turned to the right and walked for 50 metres.

So, Reena is facing 'South' now.

Hence, the correct answer is "Option 1".

The correct answer is 4.

Key Points

• Carbon has an atomic number of 6, which means it has 6 electrons.
• In its valence shell, which is the outermost shell, it has 4 electrons.
• The valence shell of an atom is the outermost shell that contains electrons, and it determines the chemical properties of the atom.
• The number of electrons in the valence shell of an atom is determined by the group number of the element in the periodic table.
• Carbon belongs to group 4, which means it has 4 valence electrons.

Additional Information

• Valence electrons are involved in chemical bonding, and they are the electrons that are gained, lost, or shared in chemical reactions.
• A shared pair arises in a single covalent bond when each of the bond's two atoms contributes one valence electron.
• A valence electron can only be found in the outermost electron shell of a main-group element; however, in a transition metal, it can also be found in an inner shell.
• Chemical inertness is typically associated with an atom that has a closed shell of valence electrons, which corresponds to a noble gas configuration.

Shortcut Trick

Total Work = LCM(18, 15, 12) = 180 units.

Combined Efficiency (2 × (A + B + C)) = 10 + 12 + 15 = 37.

Efficiency of (A + B + C) = 37 ÷ 2 = 18.5 units/day.

Time taken = 180 ÷ 18.5 = 360 ÷ 37 = 9(27/37) days.

∴ The correct answer is 9(27/37) days.

Alternate Method

Given:

Time taken by (A + B) = 18 days

Time taken by (B + C) = 15 days

Time taken by (C + A) = 12 days

Formula Used:

Total Work = LCM of individual days; Efficiency = Total Work ÷ Days

Calculations:

⇒ Adding all efficiencies: (A + B) + (B + C) + (C + A) = 10 + 12 + 15

⇒ 2(A + B + C) = 37

⇒ Efficiency of (A + B + C) = 37/2

⇒ Time taken by (A + B + C) = Total Work ÷ Efficiency

⇒ Time = 180 ÷ (37/2) = (180 × 2) ÷ 37

⇒ Time = 360 ÷ 37 = 9(27/37) days

∴ The correct answer is 9(27/37) days.

Additional Information

Combined Work Formula

If A and B work together, their combined efficiency is the sum of their individual efficiencies. Efficiency is inversely proportional to time.

Paired Work Rule

When people work in pairs (AB, BC, CA), the sum of their efficiencies equals twice the total efficiency of all three individuals (2(A+B+C)).

Work and Days Relationship

Total Work = Efficiency × Time. To find individual efficiency of A, use (A+B+C) efficiency − (B+C) efficiency.

Shortcut Trick

Identify the mode by finding the observation with the maximum frequency.

Frequency of 69 is 4 times.

Frequency of 83 is 5 times.

All other numbers (66, 71, 74, 84, 90) appear fewer than 5 times.

Since 83 appears most frequently, it is the mode.

∴ The correct answer is 83.

Alternate Method

Given Data: 66, 69, 83, 69, 84, 74, 71, 83, 69, 84, 73, 83, 69, 71, 84, 74, 83, 66, 74, 71, 83, 66, 90, 90

Formula Used: Mode = Value with the highest frequency in the data set.

Frequency Distribution Table:

⇒ Number 66 appears 3 times.

⇒ Number 69 appears 4 times.

⇒ Number 71 appears 3 times.

⇒ Number 73 appears 1 time.

⇒ Number 74 appears 3 times.

⇒ Number 83 appears 5 times.

⇒ Number 84 appears 3 times.

⇒ Number 90 appears 2 times.

⇒ Since the value 83 has the highest frequency (5), the mode is 83.

∴ The correct answer is 83.

Additional Information

Empirical Relationship

For a moderately skewed distribution, the relationship between mean, median, and mode is: Mode = 3 Median − 2 Mean.

Bimodal and Multimodal Data

A dataset with two modes is called bimodal, and a dataset with more than two modes is called multimodal.

Property of Mode

The mode is the only measure of central tendency that can be used for nominal (categorical) data as well as numerical data.

Given terms: (Left) R 5 $3 9 G C P$ E 2 # 8 @ M # 1 D Z 4 Q & (Right)

If all the symbols are dropped from the series then the arrangements are:

(Left) R 5 3 9 G C P E 2 8 M 1 D Z 4 Q (Right)

Here,

Fifth from the right end is: '1'.

Hence, the correct answer is "Option 4".

The correct answer is The Ghatprabha is one of its many tributaries.

Key Points

• The Godavari river is the second-longest river in India, after the river Ganges.
• It originates from the Trimbakeshwar plateau in Maharashtra and flows for a distance of 1,465 km before draining into the Bay of Bengal.
• The river has many tributaries, including the Pranhita, Indravati, Sabari, Manjira, and Wainganga rivers.
• The Godavari river basin covers an area of 312,812 km, spread over several states, including Maharashtra, Telangana, Andhra Pradesh, Chhattisgarh, and Odisha.

Additional Information

• The Ghatprabha river is a tributary of the river Krishna, which originates in the Western Ghats and flows through the states of Karnataka and Maharashtra before joining the Krishna river.
• The European White Stork, Demoiselle Crane, and other migratory bird species are among the many that make Ghataprabha notable.
• The Ghataprabha river has the Markandeya and Hiranyakeshi rivers as tributaries.

Shortcut Trick

Divide the quadrilateral ABCD into two triangles: ΔABC and ΔADC.

Check for Pythagorean triplets: For ΔABC, 8² + 15² = 64 + 225 = 289 = 17². It is a right-angled triangle.

For ΔADC, 9² + 12² = 81 + 144 = 225 = 15². It is also a right-angled triangle.

Total Area = (1/2 × 8 × 15) + (1/2 × 9 × 12) = 60 + 54 = 114 cm².

∴ The correct answer is 114 cm².

Alternate Method

Given: AB = 17 cm, BC = 8 cm, CD = 9 cm, AD = 12 cm, and diagonal AC = 15 cm.

Formula: Area of right triangle = 1/2 × base × height

⇒ In ΔABC: sides are 17, 8, 15. Since 17² = 8² + 15², ∠BCA = 90°.

⇒ Area(ΔABC) = 1/2 × 8 × 15 = 60 cm².

⇒ In ΔADC: sides are 9, 12, 15. Since 15² = 9² + 12², ∠ADC = 90°.

⇒ Area(ΔADC) = 1/2 × 9 × 12 = 54 cm².

⇒ Total Area = Area(ΔABC) + Area(ΔADC) = 60 + 54 = 114 cm².

∴ The correct answer is 114 cm².

Additional Information

Heron's Formula

For a triangle with sides a, b, c, Area = √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2.

Pythagorean Triplets

Common sets like (3,4,5), (8,15,17), and (9,12,15) satisfy a² + b² = c² and form right-angled triangles.

Quadrilateral Area

If a diagonal divides a quadrilateral into two triangles, the total area is the sum of the areas of those two triangles.

The correct answer is God Vishnu.

Key Points

• According to Hinduism, the deity symbolising as the preserver and protector of the world is God Vishnu.
• God Vishnu is considered one of the three main deities in Hinduism, along with Brahma and Shiva.
• Vishnu is often depicted with blue skin and four arms, and he holds various objects that represent his powers and attributes.
• Vishnu is believed to have taken several incarnations (avatars) to protect the world and restore balance, including the popular ones like Rama and Krishna.
• Vishnu is also associated with the concept of dharma, which refers to righteousness, duty, and moral law.

Additional Information

• God Shiva is another important deity in Hinduism, but he is usually associated with the role of destroyer or transformer rather than preserver.
• Shiva is often depicted with a third eye, a crescent moon on his forehead, and a snake around his neck.
• Goddess Sarasvati is the Hindu goddess of knowledge, music, and arts.
• She is often depicted with a veena (musical instrument) and a book or scroll.
• Goddess Lakshmi is the Hindu goddess of wealth, prosperity, and fortune.
• She is often depicted with gold coins, lotus flowers, and an owl.

The correct answer is Anasuya Sarabhai.

Key Points

• The founder of Ahmedabad Textile Labour Association (Majoor Mahajan Sangh) was Anasuya Sarabhai, who founded the union in 1920.
• Anasuya Sarabhai was a social worker, and a pioneer in the labour movement in India.
• She was also the first woman to run for the post of the President of the Indian National Congress in 1921.
• The Ahmedabad Textile Labour Association (Majoor Mahajan Sangh) is India's oldest union of textile workers and has played a significant role in improving the working conditions and wages of textile workers in the country.

Additional Information

• Poornima Arvind Pakvasa was an Indian social worker and politician, who played a crucial role in the upliftment of women and children in Gujarat.
• She received the Padma Bhushan award in 2004 in recognition of her contributions to society.
• Hansa Jivraj Mehta was a prominent social worker, feminist, and writer from Gujarat, who worked towards the betterment of women's rights and education.
• In 1959, Hansa Mehta received the Padma Bhushan.
• Indumati Chamamlal was an Indian social worker and politician, who was associated with the Indian National Congress and played an active role in the Indian independence movement.
• She held the positions of Gujarat's education minister and Bombay State's deputy minister of education.

According to the given Venn diagram:

The shaded area shows the "total number of students are studying Physics but NOT studying Mathematics".

So, the total number of students are studying 'Physics but NOT studying Mathematics' = 230 + 17 + 5 = 252.

Hence, the correct answer is "Option 3".

Given: 7 4 & @ 3 4 % @ $4 @ 3 4 \% 4$ 5 * @ 4 3 4 5 * 3

Now,

Symbols immediately followed by a number,

So, needed pattern is: Symbol - Number

Here,

Here, 'Seven' such symbols are there in the above series which are immediately followed by a number.

Hence, the correct answer is "Option 2".

The correct answer is 30 cm.

Key Points

• The given mirror is a concave mirror and the object is placed beyond its focus.
• When the object is placed beyond the focus of a concave mirror, its image is always formed between the focus and the mirror.
• The distance of the image from the mirror can be calculated using the mirror formula: 1/f = 1/v + 1/u, where f is the focal length of the mirror, u is the distance of the object from the mirror, and v is the distance of the image from the mirror.
• Plugging the given values in the formula, we get: 1/15 = 1/v + 1/30, which gives v = 30 cm.
• Therefore, the image is formed at a distance of 30 cm from the mirror.

Additional Information

• The image cannot be formed between the object and the mirror as it violates the basic laws of reflection.
• The image cannot be formed at a distance less than the focal length of the mirror as it will be virtual and erect, which is not possible for a concave mirror.
• The image cannot be formed beyond infinity as it is not a physical location and violates the laws of reflection.
• A concave mirror is a curved mirror in which the inner side of the curved shape is the reflecting surface.
• Its surface has an inward curvature that makes it resemble the interior surface of a hollow sphere.
• Because concave mirrors enable light beams to converge or come together after reflection, they are also known as converging mirrors.

The correct answer is Gajendra Singh Shekhawat.

Key Points

• Gajendra Singh Shekhawat launched the Digital Dashboard for District Ganga Committees Performance Monitoring System in April 2022.
• The Digital Dashboard is a web-based platform that provides real-time updates on the performance of the District Ganga Committees in cleaning and rejuvenating the river Ganga.
• The platform will help in monitoring the progress of the committees and ensuring timely implementation of various projects related to the cleaning of the river.
• Gajendra Singh Shekhawat is the Union Minister of Jal Shakti, which is responsible for the management and conservation of water resources in India.

Additional Information

• Nitin Jairam Gadkari is the Union Minister of Road Transport and Highways.
• He has launched various initiatives related to infrastructure development and road safety in India.
• Raj Nath Singh is the Union Minister of Defence.
• He is responsible for the defence policies and strategies of India.
• Piyush Goyal is the Union Minister of Commerce and Industry.
• He is responsible for promoting trade and commerce in India and formulating policies related to industrial development.

The correct answer is inversely proportional.

Key Points

• Atmospheric pressure and the rate of transpiration are inversely proportional.
• This means that as the atmospheric pressure increases, the rate of transpiration decreases, and vice versa.
• This is because transpiration is the process of water movement through plants from roots to leaves, and it occurs due to the difference in water potential between the soil and the atmosphere.
• As the atmospheric pressure increases, it becomes harder for water to evaporate from the leaves, and the rate of transpiration decreases.

Additional Information

• Atmospheric pressure refers to the force exerted by the weight of the atmosphere on the Earth's surface.
• It is measured in units of pressure such as pascals or millibars.
• Transpiration is the loss of water from plants through evaporation from the leaves and stems.
• It is an important process for plant growth and survival, as it helps to transport nutrients and minerals from the roots to the rest of the plant.
• Other factors that can affect the rate of transpiration include humidity, temperature, wind speed, and soil moisture.

Given equation: (12 - 17 ÷ 21) × 15 + 9 = ?

Decoding the given information :

Now, replacing the sign from left to right and using BODMAS rule, we get :

New equation : (12 - 17 ÷ 21) × 15 + 9 = ?

Calculation :

⇒ (12 × 17 + 21) ÷ 15 - 9 = ?

⇒ (204 + 21) ÷ 15 - 9 = ?

⇒ 225 ÷ 15 - 9 = ?

⇒ 15 - 9 = 6.

Hence, the correct answer is "Option 2".

Shortcut Trick Net filling rate = (A × B) ÷ (B − A) Where A = 15 hours (filling) and B = 24 hours (emptying). Time taken = (15 × 24) ÷ (24 − 15) Time taken = 360 ÷ 9 = 40 hours. ∴ The correct answer is 40 hr. Alternate Method Given: Filling pipe time = 15 hr, Emptying pipe time = 24 hr. Formula Used: Total Work = LCM of individual times; Efficiency = Total Work ÷ Time.

Person Days Total Work Efficiency

Pipe A (Fill) 15 120 +8

Pipe B (Empty) 24 −5

⇒ Total Work (Capacity of Tank) = LCM(15, 24) = 120 units. ⇒ Net efficiency when both open = 8 − 5 = 3 units/hr. ⇒ Time taken to fill the tank = Total Work ÷ Net Efficiency ⇒ Time = 120 ÷ 3 = 40 hr. ∴ The correct answer is 40 hr. Additional Information Inlet and Outlet Pipes An inlet pipe fills the tank (positive work), while an outlet pipe empties it (negative work). Pipes & Cisterns Efficiency If a pipe fills a tank in 'x' hours and another empties it in 'y' hours (y > x), net work done in 1 hour = (1/x − 1/y). Time and Work Relation Time taken to complete a task is inversely proportional to the efficiency of the worker or pipe.

The correct answer is CO₂.

Key Points

• Natural gas is primarily composed of methane (CH₄), which is a hydrocarbon.
• When natural gas is burned in the presence of oxygen, it undergoes combustion, which results in the release of energy and the formation of new compounds.
• One of the main products of the combustion of natural gas is carbon dioxide (CO₂), which is a greenhouse gas that contributes to global warming.
• Other products of the combustion of natural gas can include water vapor (H₂O) and nitrogen oxides (NO_x), which can contribute to air pollution and have negative health effects.

Additional Information

• NH₃ is ammonia, which can be produced by other processes, such as the Haber-Bosch process for synthesizing fertilizer.
• N₂ is nitrogen gas, which is an inert gas that does not typically react during combustion.
• However, some **nitrogen oxides (**NOx) can be produced as byproducts of combustion.
• H₂ is hydrogen gas, which can be produced by the decomposition of methane under certain conditions.
• Hydrogen gas is also a potential fuel source that is being explored as an alternative to fossil fuels.

Shortcut Trick

Using Ratio Method: 20% decrease = 4/5 and 125% increase = 9/4.

Volume depends on r² × h.

Ratio of Volumes = (5 → 4)² × (4 → 9) = (25 × 4) → (16 × 9) = 100 → 144.

Percentage increase = 144 − 100 = 44%.

∴ The correct answer is 44%.

Alternate Method

Given: Decrease in radius (r) = 20%, Increase in height (h) = 125%.

Formula Used: Volume of Cylinder (V) = πr²h

⇒ Let initial radius (r₁) = 5 units and initial height (h₁) = 4 units.

⇒ New radius (r₂) = 5 − (20% of 5) = 4 units.

⇒ New height (h₂) = 4 + (125% of 4) = 4 + 5 = 9 units.

⇒ Initial Volume (V₁) = π × 5² × 4 = 100π.

⇒ New Volume (V₂) = π × 4² × 9 = 144π.

⇒ Increase in Volume = 144π − 100π = 44π.

⇒ Percentage increase = (44π / 100π) × 100 = 44%.

∴ The correct answer is 44%.

Additional Information

Successive Percentage Change

When a value changes by x%, y%, and z% successively, the net change is calculated using the multiplying factors or the formula [a + b + (ab/100)].

Volume of 3D Figures

For figures like cylinders and cones, Volume ∝ r²h. For a sphere, Volume ∝ r³.

Base Change Rule

If radius decreases by 1/n, the area/volume calculation must account for the square of the remaining fraction (n−1)/n.

The correct answer is concentric circles.

Key Points

• The direction of the magnetic field is perpendicular to the direction of the current flow.
• The strength of the magnetic field is directly proportional to the magnitude of the current flowing through the conductor.
• The magnetic field lines around a straight current-carrying conductor are concentric circles centered on the conductor.
• The magnetic field lines around a loop of current-carrying wire are similar to those around a straight conductor, but the lines are more tightly packed and the direction of the magnetic field inside the loop is opposite to that outside the loop.

 Additional Information

• Magnetic field lines are not parallel to each other and do not have a semi-circular shape as they always form closed loops.
• Magnetic field lines do not intersect with each other as it would mean that the direction of the magnetic field at that point would be undefined.
• Magnetic field lines are those in a magnetic field whose density indicates the field's size and whose tangent at any given place indicates the field's direction.
• The quantity of magnetic field lines determines the strength of the magnetic field.

Shortcut Trick Empirical Relation: Mode = 3 × Median − 2 × Mean Given Mode = Mean + 6, then Mean = Mode − 6. Substituting values: Mode = 3(13) − 2(Mode − 6) ⇒ Mode = 39 − 2 × Mode + 12 ⇒ 3 × Mode = 51 ⇒ Mode = 51 ÷ 3 = 17 ∴ The correct answer is 17.

Alternate Method Given: Median = 13 Mode − Mean = 6 Formula Used: Mode = 3 × Median − 2 × Mean

Calculations: ⇒ Let Mean = x ⇒ Mode = x + 6 ⇒ x + 6 = 3 × 13 − 2 × x ⇒ x + 6 = 39 − 2x ⇒ x + 2x = 39 − 6 ⇒ 3x = 33 ⇒ x = 11 ⇒ Mean = 11 ⇒ Mode = 11 + 6 = 17 ∴ The correct answer is 17.

Additional Information Empirical Formula For a moderately skewed distribution, the relationship is: Mode = 3 × Median − 2 × Mean. Symmetric Distribution In a perfectly symmetric distribution (like a Normal Distribution), Mean = Median = Mode. Positively vs Negatively Skewed If Mean > Median > Mode, the data is positively skewed. If Mode > Median > Mean, it is negatively skewed.

Shortcut Trick

The difference between a two-digit number and its reverse is always 9 × (difference of its digits).

Difference of digits (x − y) = 18 ÷ 9 = 2.

The number is 7 × (sum of digits). Check multiples of 7 with a digit difference of 2: 42 (Sum = 6, 7 × 6 = 42).

Product of digits = 4 × 2 = 8.

∴ The correct answer is 8.

Alternate Method

Given:

Let the tens digit be x and the units digit be y.

Original Number = 10x + y

Reversed Number = 10y + x

Equation 1: Number = 7 × (Sum of digits)

⇒ 10x + y = 7(x + y)

⇒ 10x + y = 7x + 7y

⇒ 3x = 6y

⇒ x = 2y

Equation 2: Reversed number = Original number − 18

⇒ 10y + x = (10x + y) − 18

⇒ 10x + y − 10y − x = 18

⇒ 9x − 9y = 18

⇒ x − y = 2

Solving for digits:

Substitute x = 2y in x − y = 2

⇒ 2y − y = 2

⇒ y = 2

⇒ x = 2 × 2 = 4

Product of digits:

⇒ x × y = 4 × 2 = 8

∴ The correct answer is 8.

Additional Information

Digit Reversal Properties

The difference between a 2-digit number and its reversal is always 9|x − y|. The sum of a 2-digit number and its reversal is always 11(x + y).

Digit Limitations

For any 2-digit number 10x + y, the digits x and y must be integers where 1 ≤ x ≤ 9 and 0 ≤ y ≤ 9.

Divisibility Rule of 9

Since the difference between a number and its digit-reversed counterpart is 9(x − y), the difference is always divisible by 9.

The correct answer is (iv).

Key Points

• A combination reaction is a type of chemical reaction where two or more substances combine to form a single new substance.
• In other words, it is a reaction where the reactants combine to form a product.
• is a combination reaction as hydrogen and chlorine combine to form hydrochloric acid.

Additional Information

• ZnCO3 (s) → ZnO (s) + CO2 (g) is a decomposition reaction as zinc carbonate breaks down into zinc oxide and carbon dioxide.
• 2KBr (aq) + BaI2 (aq) → 2KI (aq) + BaBr2 (s) is a double displacement reaction as the positive and negative ions of two compounds switch places to form two new compounds.
• Mg (s) + 2HCl (aq) → MgCl2 (aq) + H2 (g) is a single displacement reaction as magnesium replaces hydrogen in hydrochloric acid to form magnesium chloride and hydrogen gas.
• It is important to identify the type of reaction as it helps in predicting the products of the reaction and understanding the underlying chemistry.

Shortcut Trick

Assume all 50 items were the cheaper item, i.e., pencils at ₹5 each.

Total hypothetical cost = 50 × 5 = ₹250.

The difference from the actual total spend = 273 − 250 = ₹23.

Price difference between a pen and a pencil = 6 − 5 = ₹1.

Number of pens = Total difference ÷ Unit price difference = 23 ÷ 1 = 23.

∴ The correct answer is 23.

Alternate Method

Given:

Total items = 50 | Total expenditure = ₹273

Cost of one pen = ₹6 | Cost of one pencil = ₹5

Let the number of pens be x.

Then, the number of pencils = 50 − x.

According to the question:

⇒ (Number of pens × 6) + (Number of pencils × 5) = 273

⇒ 6x + 5(50 − x) = 273

⇒ 6x + 250 − 5x = 273

⇒ x + 250 = 273

⇒ x = 273 − 250

⇒ x = 23

∴ The correct answer is 23.

Additional Information

Linear Equations in Two Variables

Problems involving two types of items with different costs can be solved using the system of equations x + y = Total Quantity and ax + by = Total Cost.

Alligation Method

Ratio of quantity = (Higher Price − Average Price) : (Average Price − Lower Price), where Average Price = Total Cost ÷ Total Quantity.

Unitary Method for Costs

Useful for calculating individual prices or quantities when the total sum and individual rates are known.

Shortcut Trick

Factor out sin 70° from the numerator and cos 70° from the denominator.

Numerator = sin 70° (1 − 2 sin² 70°). Denominator = cos 70° (2 cos² 70° − 1).

Both (1 − 2 sin² θ) and (2 cos² θ − 1) are equal to cos 2θ.

They cancel out, leaving sin 70° / cos 70° = tan 70°.

∴ The correct answer is tan 70°.

Alternate Method

Given: Expression = (sin 70° − 2 sin³ 70°) / (2 cos³ 70° − cos 70°)

Formula Used: cos 2θ = 1 − 2 sin² θ = 2 cos² θ − 1

⇒ Expression = [sin 70° (1 − 2 sin² 70°)] / [cos 70° (2 cos² 70° − 1)]

⇒ Expression = [sin 70° × cos (2 × 70°)] / [cos 70° × cos (2 × 70°)]

⇒ Expression = [sin 70° × cos 140°] / [cos 70° × cos 140°]

⇒ Expression = sin 70° / cos 70°

⇒ Expression = tan 70°

∴ The correct answer is tan 70°.

Additional Information

Double Angle Formulas

sin 2θ = 2 sin θ cos θ and cos 2θ = cos² θ − sin² θ.

Tangent Relations

tan θ = sin θ / cos θ and cot θ = cos θ / sin θ.

Trigonometric Identities

sin² θ + cos² θ = 1, which leads to the alternative forms of cos 2θ used here.

The correct answer is Only (a).

Key Points

• The statement (a) is correct.
• The degree of closeness of magnetic field lines indicates the strength of the magnetic field.
• The closer the lines, the stronger the magnetic field.
• The statement (b) is incorrect.
• Magnetic field lines not only have magnitudes but also have directions.
• The direction of the magnetic field is indicated by the direction of the lines, which always point from the north pole to the south pole.
• Magnetic fields are areas around magnets or moving electric charges where a magnetic force can be observed.
• The strength of a magnetic field is measured in units of tesla (T) or gauss (G).
• The direction of the magnetic field can be determined by using a compass.
• The north end of the compass needle points towards the south pole of the magnet, and vice versa.

Additional Information

• Magnetic field lines are those in a magnetic field whose density indicates the field's size and whose tangent at any given place indicates the field's direction.
• They form closed loops.
• Magnetic field lines do not intersect with each other as it would mean that the direction of the magnetic field at that point would be undefined.

The correct answer is Amylase.

Key Points

• Starch is a complex carbohydrate that needs to be broken down into simple sugars for the body to use it as energy.
• Amylase is the enzyme responsible for breaking down starch into simple sugars like glucose and maltose.
• The majority of amylase in your body is produced by the salivary glands and pancreas.

Additional Information

• Pepsin is an enzyme produced in the stomach.
• It breaks down proteins into amino acids.
• Trypsin is an enzyme produced in the pancreas.
• It breaks down proteins into smaller peptides.
• Lipase is an enzyme that breaks down fats into fatty acids and glycerol.

The logic followed here is:

For, '15 PK is related to 225 SQ'

For, '16 TQ is related to 256 WW'

Similarly, for '14 OK'

So, '14 OK' will be related to '196 RQ'

Hence, the correct answer is "Option 4".

Shortcut Trick

Equate Total Work: (3M + 2W) × 8 = (2M + 3W) × 10

⇒ 24M + 16W = 20M + 30W ⇒ 4M = 14W ⇒ 1M = 3.5W

Total Work in terms of Women = (3 × 3.5W + 2W) × 8 = 12.5W × 8 = 100 units

Required Efficiency (2M + 1W) = (2 × 3.5W + 1W) = 8W

Required Days = 100 ÷ 8 = 12.5 days

∴ The correct answer is 12.5 days.

Alternate Method

Calculations:

⇒ 3M + 2W = 5 --- (i)

⇒ 2M + 3W = 4 --- (ii)

⇒ Multiplying (i) by 3 and (ii) by 2: 9M + 6W = 15 and 4M + 6W = 8

⇒ Subtracting gives 5M = 7 ⇒ M = 1.4

⇒ Substitute M in (ii): 2(1.4) + 3W = 4 ⇒ 2.8 + 3W = 4 ⇒ 3W = 1.2 ⇒ W = 0.4

⇒ Total Work = efficiency × days = 5 × 8 = 40 units

⇒ Required Efficiency (2M + 1W) = 2(1.4) + 0.4 = 2.8 + 0.4 = 3.2

⇒ Required Time = 40 ÷ 3.2 = 12.5 days

∴ The correct answer is 12.5 days.

Additional Information

Work Equivalence Formula

Total Work = (m₁ × d₁ × h₁) / w₁ = (m₂ × d₂ × h₂) / w₂, where m is efficiency, d is days, and h is hours.

Efficiency Ratio

In combined work problems, always find the efficiency ratio between different entities (Men, Women, Children) to standardize the work units.

Pipes & Cisterns Analogy

Similar logic applies where filling pipes are like workers and leakages are negative efficiency, using LCM to find Total Capacity.

Shortcut Trick

Sum of roots (α + β) = 2 + (−3) = −1

Product of roots (αβ) = 2 × (−3) = −6

The quadratic equation formula is x² − (Sum of roots)x + (Product of roots) = 0.

Substituting the values: x² − (−1)x + (−6) = 0 ⇒ x² + x − 6 = 0.

∴ The correct answer is x² + x − 6 = 0.

Alternate Method

Given:

First root (α) = 2

Second root (β) = −3

Formula Used:

If α and β are the roots, the equation is (x − α)(x − β) = 0

Calculations:

⇒ (x − 2)(x − (−3)) = 0

⇒ (x − 2)(x + 3) = 0

⇒ x(x + 3) − 2(x + 3) = 0

⇒ x² + 3x − 2x − 6 = 0

⇒ x² + x − 6 = 0

∴ The correct answer is x² + x − 6 = 0.

Additional Information

Nature of Roots

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

Relationship between Coefficients and Roots

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

Standard Form

A quadratic equation is a second-degree polynomial equation in a single variable x, expressed in the general form ax² + bx + c = 0.

The logic followed here is:

Given number: 83752964.

Odd digits is decreased by - 2

and, Even digits is increased by + 1

After arrange the numbers:

83752964 ⇒ 91533775

Now, third digit from the left: 5

And, second digit from the right: 7

So, the sum of third from the left and second from the right digit is: 5 + 7 = 12.

Hence, the correct answer is "Option 4".

The correct answer is 73rd.

Key Points

• The 73rd Amendment to the Constitution of India was passed in 1992 and it added a new Part IX to the Constitution, which deals with Panchayats.
• This amendment envisaged the Gram Sabha as the foundation of the Panchayat Raj System.
• Gram Sabha is a body consisting of all persons registered as voters in a village or in a group of villages within a Panchayat area.
• The Panchayat Raj System is a three-tier system of local self-government in India, consisting of the village level (Gram Panchayat), intermediate level (Panchayat Samiti), and district level (Zilla Parishad).
• This amendment also made it mandatory to hold regular elections to Panchayats every five years and reserved seats for Scheduled Castes, Scheduled Tribes, and women in Panchayats.

Additional Information

• 76th Amendment deals with the incorporation of the Konkani, Meitei, and Nepali languages in the Eighth Schedule to the Constitution.
• 79th Amendment extended the reservation of seats for Scheduled Castes and Scheduled Tribes in the Lok Sabha and State Legislative Assemblies for another ten years, i.e., till 2020.
• 71st Amendment provided for the creation of a new State of Uttarakhand from the existing State of Uttar Pradesh.

The logic followed here is:

So, '171' will replace the question mark in the given series.

Hence, the correct answer is "Option 4".

The correct answer is HIV infection cannot be transmitted by sharing toilets with an HIV-positive person.

Key Points

• HIV (Human Immunodeficiency Virus) is a virus that attacks the immune system of the human body, making it difficult for the body to fight infections and diseases.
• HIV can be transmitted through the exchange of certain bodily fluids, including blood, semen, vaginal fluids, and breast milk.
• However, HIV cannot be transmitted through casual contact such as sharing toilets, utensils, or hugging.

Additional Information

• Repeated blood transfusions can actually increase the risk of HIV transmission if the donated blood is not screened properly for the virus.
• Sharing needles or syringes while taking medications can also increase the risk of HIV transmission as the virus can be present in the blood of an infected person.
• HIV-positive mothers can transmit the virus to their babies during pregnancy, childbirth, or breastfeeding.
• However, with proper medical care and treatment, the risk of mother-to-child transmission can be significantly reduced.
• It is important to note that HIV infection is preventable through safe sex practices, avoiding sharing needles or syringes, and getting tested regularly for the virus.
• Treatment options are also available to manage the virus and prevent it from progressing to AIDS (Acquired Immunodeficiency Syndrome).

Given Statements:

1. Some toys are pianos.
2. Some pianos are white.
3. All white are guitars.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some white are toys - False (Because, No definite relation given between White and Toys, So, it can be possible only).

II. Some guitars are toys - False (Because, No definite relation given between guitars and Toys, So, it can be possible only).

III Some guitars are pianos - True (Because, those part of guitars which is white will also pianos).

So, Only conclusion III is true.

Hence, the correct answer is "Option 1".

Shortcut Trick

When interest is compounded half-yearly, the rate is halved and the time periods are doubled.

Effective Rate = 20% ÷ 2 = 10% per half-year for 2 periods.

Successive percentage increase = 10 + 10 + (10 × 10)/100 = 21%.

Total Amount = 121% of 16,000 ⇒ 1.21 × 16000 = ₹19,360.

∴ The correct answer is ₹19,360.

Alternate Method

Given: Principal (P) = ₹16,000, Rate (R) = 20% p.a., Time (T) = 1 year (compounded half-yearly).

Formula Used: Amount (A) = P[1 + (R/200)]²ⁿ where R is annual rate and n is years.

⇒ Half-yearly rate = 20% ÷ 2 = 10%

⇒ Number of half-yearly periods (n) = 1 × 2 = 2

⇒ A = 16000 × [1 + 10/100]²

⇒ A = 16000 × (11/10) × (11/10)

⇒ A = 160 × 121

⇒ A = ₹19,360

∴ The correct answer is ₹19,360.

Additional Information

Compounding Frequency

If interest is compounded quarterly, the rate is divided by 4 and time periods are multiplied by 4.

Successive Percentage Method

For two interest periods, net interest rate = x + y + (xy/100)%, where x and y are the rates for each period.

CI vs SI for One Year

When compounded annually, CI = SI for 1st year. When compounded half-yearly, CI > SI even for the 1st year.

The logic followed here is:

So, 'D31SL' will replace the question mark in the given series.

Hence, the correct answer is "Option 4".

The correct answer is 15.

Key Points

• The given chemical equation represents the reaction between iron (Fe) and water (H₂O) to form iron(III) oxide (Fe₃O₄) and hydrogen gas (H₂).
• According to the equation, there are 3 atoms of iron, 4 atoms of hydrogen, and 4 atoms of oxygen in the products.
• Hence, the total number of atoms in products is 3+4+4 = 11.
• Reactants and products are stated in terms of their corresponding chemical formulae in chemical equations, which are symbolic representations of chemical reactions.

Additional Information

• Iron(III) oxide is a commonly occurring mineral that is also known as hematite.
• It is used in the production of iron and steel as a source of iron.
• The reaction between iron and water is an example of a redox reaction, where the iron gets oxidized and the water gets reduced to form hydrogen gas.
• The reaction is exothermic, which means that it releases heat energy.

Given digits: 6287451

Now, arranged in ascending order from left to right: 6287451.

So, there are 'One' digits remain in the same position.

Hence, the correct answer is "Option 3".

Given: Seven people, A, B, C, D, E, F and G, are sitting in a straight row, facing north.

1. Only three people sit between A and F.

2. Only two people sit to the left of A.

3. G is not an immediate neighbour of F.

4. G sits second to the right of C.

5. B sits to the immediate right of D.

And, E will sit at the remaining place.

So, 'E' sits at the extreme left end of the row.

Hence, the correct answer is "Option 4".

The correct answer is Selenium.

Key Points

• Selenium is NOT a metalloid.
• Metalloids are elements that exhibit properties of both metals and non-metals.
• Selenium is a non-metal element that is found in soil, water, and some foods.
• It is an essential nutrient for humans and animals in small amounts, but can be toxic in larger amounts.

Additional Information

• Silicon is a metalloid that is commonly used in electronic devices such as computer chips and solar cells.
• It is also used in glass, ceramics, and other materials.
• Antimony is a metalloid that has been used in alloys with lead and other metals to increase their hardness and strength.
• It is also used in batteries, flame retardants, and as a semiconductor.
• Arsenic is a metalloid that has been used in pesticides, wood preservatives, and as a doping agent in semiconductors.
• It is highly toxic and exposure to it can cause serious health problems.

Shortcut Trick

For any two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.

⇒ Area(ΔPQR) ÷ Area(ΔABC) = (QR ÷ BC)²

Given, BC ÷ QR = 1 ÷ 5 ⇒ QR ÷ BC = 5 ÷ 1

⇒ Area(ΔPQR) ÷ Area(ΔABC) = (5 ÷ 1)² = 25

∴ The correct answer is 25.

Alternate Method

Given:

ΔABC is similar to ΔPQR (ΔABC ~ ΔPQR)

BC ÷ QR = 1 ÷ 5

Formula Used:

If two triangles are similar, then the ratio of their areas is equal to the square of the ratio of their corresponding sides:

Area(ΔPQR) ÷ Area(ΔABC) = (QR ÷ BC)²

Calculations:

We are given the ratio of the corresponding sides:

⇒ BC ÷ QR = 1 ÷ 5

Taking the reciprocal to find the ratio of QR to BC:

⇒ QR ÷ BC = 5 ÷ 1 = 5

Now, applying the area of similar triangles theorem:

⇒ Area(ΔPQR) ÷ Area(ΔABC) = (QR ÷ BC)²

Substitute the value of QR ÷ BC into the equation:

⇒ Area(ΔPQR) ÷ Area(ΔABC) = (5)²

⇒ Area(ΔPQR) ÷ Area(ΔABC) = 25

Explanation of Options:

⇒ Option (1) 1/25: This represents the ratio of Area(ΔABC) ÷ Area(ΔPQR), which is the inverse of the required ratio.

⇒ Option (2) 25: This is the correct ratio of Area(ΔPQR) ÷ Area(ΔABC) obtained by squaring the side ratio 5/1.

⇒ Option (3) 5: This is simply the ratio of the corresponding sides QR ÷ BC, not their areas.

⇒ Option (4) 1/5: This is the ratio of the corresponding sides BC ÷ QR, not their areas.

∴ The correct answer is 25.

Additional Information

Area of Similar Triangles Theorem

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides, corresponding altitudes, corresponding medians, or corresponding angle angle bisectors.

Perimeter of Similar Triangles

The ratio of the perimeters of two similar triangles is equal to the ratio of their corresponding sides: Perimeter(ΔABC) ÷ Perimeter(ΔPQR) = AB ÷ PQ = BC ÷ QR = AC ÷ PR.

The correct answer is Avinash Sable.

Key Points

• Avinash Sable is an Indian athlete who broke a 30-year-old national record in the men's 5000 m when he clocked 13:25:65 at the Sound Running Track Meet in San Juan Capistrano, USA in 2022.
• At the 2022 Asian Games, Avinash Sable won the first gold medal for India in the steeplechase and the silver medal in the 5000 meters.
• He hails from Maharashtra.

Additional Information

• Siddhanth Thingalaya is an Indian athlete who is a sprint hurdler.
• ​With a timing of 13.48 seconds, set in June 2017 at the Altis Invitational Meet in the USA, he now owns the national record in the 110-meter hurdles.
• Rahamatulla Molla is an Indian athlete who is a long-distance runner.
• ​As a member of the Indian 4 x 100-meter relay team, he took home a bronze medal from the 2010 Commonwealth Games.
• Ayyasamy Dharun is an Indian athlete who is a sprinter.
• ​He competed in the 2016 Summer Olympics in the 4 × 400-meter relay.

Calculation

The amount of profit earned on investment by Company A in 2021 = Rs. 24.60 lakh

The amount of profit earned on investment by Company A in 2021 = 70.8%

70.8% → 24.60 lac

100% → 24.60/70.8 × 100 = 34,74,576.27

The answer is 34,74,576.27.

The correct answer is vascular tissue.

Key Points

• Complex plants have well-developed vascular tissue, which is composed of xylem and phloem.
• The xylem tissue transports water and minerals from the roots to the leaves, while the phloem tissue transports organic nutrients from the leaves to the rest of the plant.
• The presence of vascular tissue allows complex plants to grow taller and larger, as they can transport water and nutrients over longer distances.
• This feature has made their survival in terrestrial environments possible.

Additional Information

• Meristematic tissue is the primary growth tissue in plants, responsible for the production of new cells.
• It is present in all plants, including simple ones like algae.
• Parenchyma tissue is the most common type of plant tissue, found in all plant organs.
• It is responsible for various functions, such as storage, photosynthesis, and secretion.
• Sclerenchyma tissue is a type of plant tissue that provides mechanical support to the plant.
• It is composed of cells with thick, lignified walls, and is present in various plant organs, such as stems, leaves, and fruits.