RRB Group D Previous Year Paper (Held on: 28 Sept 2022 Shift 1)

The correct answer is 13 cm.

Key Points

Given: A concave mirror forms a real image 3 times the size of the object, we have $m_1=3$ and $v_1=3u_1$.

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

Given: $m_2=6$, the new image distance $v_2=6u_2$, and the screen shift $v_2-v_2=39cm$

We solve the system of equations to find $f$:

From $v_1=3u_1: \frac{1}{f}=\frac{1}{3u_1}+\frac{1}{u_1}=\frac{4}{3u_1}$, Thus $u_1=\frac{4f}{3}$

From $v_2=6u_2: \frac{1}{f}=\frac{1}{6u_2}+\frac{1}{u_2}=\frac{7}{6u_2}$, Thus $u_2=\frac{7f}{6}$

Using $v_2-v_1=39: 6u_2-3u_1=39$.

Substituting $u_1$ and $u_2$: $6\times \frac{7f}{6}-3\times\frac{4f}{3}=39$, which simplifies to $7f-4f=39$.

Hence, $3f=39$, and $f=13cm$.

Additional Information

• Concave Mirror:
• A concave mirror, or converging mirror, has a reflecting surface that curves inward like the inside of a sphere.
• It converges light to a focal point, making it useful for focusing light and forming real images.
• Magnification (m):
• Magnification is the ratio of the height of the image to the height of the object.
• For mirrors, it is also given by the ratio of the image distance to the object distance ($m=-\frac{v}{u}$).
• Mirror Formula:
• The mirror formula relates the object distance (u), image distance (v), and focal length (f) of a mirror: $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$1f=1v+1u1f=1v+1u1f=1v+1u1f=1v+1u1f=1v+1u1f=1v+1u .
• This formula is applicable to both concave and convex mirrors.

The correct answer is option 2) Weak muscles and low-energy

Beriberi is a condition caused by a deficiency of vitamin B1 (thiamine), and it can lead to symptoms such as weakness, muscle atrophy, and fatigue due to the effect of thiamine deficiency on the nervous system and muscle function.

Key Points

• There are two main types of beriberi: Wet beriberi, and Dry beriberi.
• Wet beriberi is characterized by edema and heart-related symptoms,
• Dry beriberi primarily involves nervous system issues.
• Early diagnosis and thiamine supplementation are crucial for the successful treatment of beriberi.
• Supplementation with thiamine and dietary improvements are common approaches to managing the condition.

Additional Information Common symptoms of beriberi include:

The correct answer is Federal Bank.

Key Points

• Federal Bank is a major Indian commercial bank in the private sector headquartered in Aluva, Kochi, Kerala.
• It was incorporated in 1931 and has a strong presence in India with over 1,200 branches and 1,600 ATMs spread across the country.
• The bank offers a variety of products and services including loans, savings and current accounts, debit and credit cards, and investment products.
• Federal Bank has been known for its significant contributions to the banking sector through technological innovations and customer-focused services.

Additional Information

• Bank of Baroda
• It is a public sector bank in India, owned by the government.
• It was founded on July 20, 1908, by Maharaja Sayajirao Gaekwad III.
• Headquartered in Vadodara, Gujarat, it is one of the largest public sector banks in India.
• It offers a wide range of banking products and financial services.
• Punjab National Bank
• It is another major public sector bank in India.
• Founded in 1894, it is one of the oldest banks in India.
• Headquartered in New Delhi, it has a wide network of branches and ATMs across the country.
• It provides a variety of banking and financial services to its customers.
• UCO Bank
• UCO Bank is a public sector bank established in 1943.
• Headquartered in Kolkata, it was formerly known as United Commercial Bank.
• It provides a wide range of banking products and services, including loans, deposits, and payment services.
• UCO Bank has a significant presence in India with numerous branches and ATMs.

Given: Each of six sports persons, Falak, Bala, Renu, Rekha, Priya and Pallavi, has a different weight. 

1) Pallavi is the heaviest.

Pallavi > _ > _ > _ > _ > _

2) Rekha is heavier than only Falak and Renu but lighter than Bala and Priya.

Pallavi > Bala/Priya > Bala/Priya > Rekha > Falak/Renu > Falak/Renu

3) Priya is heavier than Bala and Falak is heavier than Renu.

Pallavi > Priya > Bala > Rekha > Falak > Renu

Thus, according to the final arrangement, Renu is the lightest among all the sports persons.

Hence, "Option 3" is the correct answer.

The correct answer is 2019.

Key Points

• Extremely severe cyclonic storm 'Fani' hit the Indian state of Odisha in May 2019.
• Fani was the strongest tropical cyclone to strike the Indian state of Odisha since the 1999 Odisha cyclone.
• The storm caused widespread damage to infrastructure, homes, and crops, particularly in the coastal regions of Odisha.
• The Indian government and various NGOs launched extensive relief and rehabilitation efforts to support the affected populations.

Additional Information

• Cyclone Fani:
• Cyclone Fani (pronounced as 'Foni') was the first severe cyclonic storm of the 2019 North Indian Ocean cyclone season.
• It originated from a tropical depression that formed west of Sumatra in the Indian Ocean on 26 April 2019.
• Fani intensified into an extremely severe cyclonic storm and made landfall in Odisha near Puri on 3 May 2019.
• The cyclone had wind speeds of up to 215 km/h (130 mph), causing significant destruction.
• Impact and Response:
• The government of India and the Odisha state government conducted one of the largest evacuations in history, moving around 1.2 million people to safer locations.
• Post-cyclone, the government and various organizations provided relief in the form of food, water, medical aid, and temporary shelters.
• Efforts were also made to restore electricity, telecommunications, and other essential services in the affected areas.
• International aid and support were also extended to help with the recovery and rebuilding process.
• Terminologies:
• Extremely Severe Cyclonic Storm: A category in the tropical cyclone intensity scale used by the India Meteorological Department (IMD), which includes cyclones with wind speeds of 166-220 km/h (103-137 mph).
• Landfall: The event of a storm moving over land after being over water, often leading to significant weather changes and potential damage in the affected area.
• Evacuation: The process of moving people from a dangerous place to safety, often used in response to natural disasters like cyclones, floods, and earthquakes.

Shortcut Trick Use the identity tan2α = sec2α − 1. The equation becomes sec2α − secα − 20 = 0. Factorizing the quadratic: (secα − 5)(secα + 4) = 0. Since α is acute, secα = 5 ⇒ cosα = 1/5. ∴ The correct answer is 1/5. Alternate Method Given: tan2α − secα = 19, where α is an acute angle. Formula Used: sec2α − tan2α = 1 ⇒ tan2α = sec2α − 1 Calculations: ⇒ (sec2α − 1) − secα = 19 ⇒ sec2α − secα − 1 − 19 = 0 ⇒ sec2α − secα − 20 = 0 ⇒ sec2α − 5secα + 4secα − 20 = 0 ⇒ secα(secα − 5) + 4(secα − 5) = 0 ⇒ (secα − 5)(secα + 4) = 0 ⇒ secα = 5 or secα = −4 ⇒ Since α is acute (0° < α < 90°), secα must be positive and ≥ 1. ⇒ secα = 5 ⇒ cosα = 1 / secα = 1/5 ∴ The correct answer is 1/5. Additional Information Trigonometric Identities Fundamental Pythagorean identities include sin2θ + cos2θ = 1, 1 + tan2θ = sec2θ, and 1 + cot2θ = cosec2θ. Acute Angle Ratios For an acute angle α, all trigonometric ratios (sin, cos, tan, cot, sec, cosec) are always positive. Reciprocal Relations secα = 1/cosα, cosecα = 1/sinα, and cotα = 1/tanα.

The logic follows here is:

Thus, 32 will replace the question mark in the given series.

Hence, the correct answer is "Option 2".

The correct answer is Great Nicobar island.

Key Points

• Indira Point is the southernmost point of India, located on the Great Nicobar island in the Andaman and Nicobar Islands.
• It was named in honor of the former Prime Minister of India, Indira Gandhi.
• The point is located at latitude 6°45'10" N and longitude 93°49'36" E.
• Indira Point was formerly known as Pygmalion Point and Parsons Point.

Additional Information

• Great Nicobar Island
• Great Nicobar is the largest of the Nicobar Islands, with an area of about 1,045 square kilometers.
• It is located in the Indian Ocean, south of the Andaman Islands, and is part of the Union Territory of Andaman and Nicobar Islands.
• The island is known for its rich biodiversity, including the Great Nicobar Biosphere Reserve, which is home to several endemic species.
• It is sparsely populated, with the majority of its inhabitants being the indigenous Nicobarese people.
• Middle Andaman Island
• Middle Andaman Island is part of the Andaman Islands, located in the Bay of Bengal.
• It is the second largest island in the Andaman group and is known for its lush green forests and diverse wildlife.
• The island is home to several indigenous tribes, including the Jarwa people.
• Middle Andaman Island is also known for its beautiful beaches and tourist attractions.
• Car Nicobar Island
• Car Nicobar is the northernmost island in the Nicobar group, located in the Bay of Bengal.
• It is the administrative capital of the Nicobar district and is known for its coconut plantations and scenic beauty.
• The island was significantly affected by the 2004 Indian Ocean tsunami, which caused extensive damage and loss of life.
• The indigenous Nicobarese people are the main inhabitants of Car Nicobar.
• Little Andaman Island
• Little Andaman is the fourth largest island in the Andaman group, situated south of Port Blair.
• The island is known for its pristine beaches, waterfalls, and dense tropical forests.
• It is home to the Onge tribe, one of the indigenous tribes of the Andaman Islands.
• Little Andaman is a popular destination for eco-tourism and adventure activities.

Given:

Data = 2, 6, 5, 2, 4, 9, 6, 2, 6, 4, 10, 12, 6, 3, 4, 9

Formula used:

If N is an even number, then

Median = Value of [(N/2)^th term + (N/2 + 1)^th term]/2

Where, N = Number of terms

Calculation:

Arranging numbers in ascending order = 2, 2, 2, 3, 4, 4, 4, 5, 6, 6, 6, 6, 9, 9, 10, 12

According to the question

Here, N = 9

Median =[(N/2)th term + (N + 1)/2th term]/2 = [(16/2)th term + (16/2 + 1)th term]/2

⇒  (5 + 6)/2 = 5.5

∴ The median of the given data is 5.5.

∴ Option 4 is the correct answer.

The correct answer is Agra.

Key Points

• The head office of Kendriya Hindi Sansthan is located in Agra.
• Kendriya Hindi Sansthan is an autonomous organization under the Ministry of Education, Government of India.
• It was established in 1960 with the objective of promoting and propagating Hindi as a common link language in India.
• The institute offers various courses and conducts research in Hindi language and literature.

Additional Information

• Kendriya Hindi Sansthan
• Also known as the Central Institute of Hindi, it plays a crucial role in the development and promotion of Hindi language education across India and abroad.
• The institute runs various programs such as teaching Hindi to non-Hindi speakers, advanced research in Hindi, and training teachers in Hindi education.
• It collaborates with several international organizations and institutions to promote Hindi globally.
• Ministry of Education, Government of India
• The Ministry of Education is responsible for the development of educational policies and administration of various educational institutions and initiatives in India.
• It oversees primary, secondary, and higher education and formulates policies to improve the quality of education in the country.
• One of the key objectives of the ministry is to promote the use of Hindi and other regional languages in education.
• Hindi Language
• Hindi is one of the official languages of India and is widely spoken across the country.
• The language has its roots in Sanskrit and has evolved over centuries, incorporating elements from various other languages.
• Efforts are constantly made by the Indian government and various organizations to promote the use and learning of Hindi both within and outside India.

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

The twelfth digit from the left end is: 8

and the eighth digit to the left of 8 is: 2

So, the eighth digit to the left of the twelfth digit from the left end of the series will be '2'.

Hence, the correct answer is "Option 3".

The correct answer is indifference curve.

Key Points

• An indifference curve represents a series of combinations of two goods that provide equal utility or satisfaction to a consumer.
• It is a graphical representation in microeconomics used to illustrate consumer preferences.
• The curve is typically downward sloping, indicating that as the quantity of one good increases, the quantity of the other good must decrease to maintain the same level of satisfaction.
• Indifference curves do not intersect, as each curve represents a different level of utility.

Additional Information

• Consumer Curve:
• There is no specific economic concept termed as a "consumer curve". This term is incorrect in this context.
• Marginal Curve:
• A marginal curve typically represents the marginal utility or marginal cost. Marginal utility refers to the additional satisfaction gained from consuming one more unit of a good.
• Indifference Curve:
• An indifference curve shows combinations of goods that provide the same level of utility to the consumer, implying that the consumer is indifferent between these combinations.
• It is used in consumer theory to analyze consumer preferences and the trade-offs they are willing to make between different goods.
• Utility Curve:
• A utility curve represents the relationship between the quantity of goods consumed and the total utility derived from consuming those goods.
• It is typically used to illustrate the concept of total utility rather than showing combinations of goods that provide equal satisfaction.

The correct answer is Potassium, Calcium and Magnesium.

Key Points

• Potassium helps strengthen cell walls and promotes overall plant health, making crops more resistant to diseases and pests.
• Calcium is crucial for cell wall structure and stability, which can help protect plants against pathogens.
• Magnesium is an essential component of chlorophyll, aiding in photosynthesis and promoting healthy plant growth, indirectly helping in pest resistance.
• These minerals work synergistically to enhance the plant's immune system, thus helping crops withstand various pest attacks.

Additional Information

• Potassium (K)
• It is a vital nutrient for plant growth and development, involved in enzyme activation, photosynthesis, water regulation, and protein synthesis.
• Potassium helps in the formation of strong stalks and enhances resistance to diseases and pests by improving the plant's overall vigor.
• Calcium (Ca)
• It plays a key role in maintaining the structural integrity of cell walls and membranes, which is essential for the plant's defense mechanisms.
• Calcium deficiency can lead to weaker cell walls, making plants more susceptible to diseases and pests.
• Magnesium (Mg)
• It is the central atom in the chlorophyll molecule, which is crucial for photosynthesis and energy production in plants.
• Magnesium also helps in the activation of many plant enzymes needed for growth and contributes to the plant's overall health and resistance to pests.
• Importance of Pest Resistance
• Pest resistance is vital for maintaining crop yields and reducing the need for chemical pesticides, which can be harmful to the environment.
• Healthy plants with adequate nutrition are better equipped to resist pest attacks and recover from any damage caused.

The correct answer is exothermic reaction.

In this process, glucose and oxygen are metabolized in cells to produce carbon dioxide, water, and energy (in the form of ATP), while releasing heat. This release of energy in the form of heat is a characteristic feature of exothermic reactions.

Key Points 

• Respiration begins with the act of breathing, where air is inhaled through the nose and/or mouth and travels into the lungs.
• In the lungs, oxygen from the air is exchanged with carbon dioxide from the bloodstream.
• Oxygen is taken up by red blood cells, and carbon dioxide is released into the lungs.
• Oxygen-rich blood is then pumped by the heart to various tissues and cells in the body via the circulatory system.
• Within cells, oxygen is used in a process called cellular respiration to produce energy (in the form of ATP) from glucose and other organic molecules.
• During cellular respiration, glucose is broken down in a series of chemical reactions, releasing energy that is essential for various cellular functions and activities.
• ATP (adenosine triphosphate) is the primary energy currency of cells and is generated during cellular respiration.
• Carbon dioxide, a waste product of cellular respiration, is produced and transported back to the lungs through the bloodstream.
• Carbon dioxide is expelled from the body when you exhale, completing the respiratory cycle.

Additional Information The main organ systems in the human body;

Given statement: Prices of tomatoes in Kerala will rise sharply as many trucks carrying them from other states have been stopped at the border

Argument I. Tomatoes are mostly brought to Kerala from outside - This argument strengthens the statement because if tomatoes are primarily sourced from outside Kerala, stopping trucks at the border would severely limit the supply, thereby potentially causing prices to rise.

Argument II. The quantity of tomatoes grown in Kerala is not enough to meet the demand in the state - This argument also strengthens the statement because it indicates that Kerala depends on external sources for its tomato supply to meet demand. Thus, if supply lines are disrupted, it's logical that prices would increase due to the scarcity.

Thus, Both I and II strengthen the statement.

Hence, the correct answer is "Option 2".

The correct answer is option 4) pH below 5.5

The critical pH level for tooth decay to start is generally around pH 5.5.

Key Points

• Dental caries, commonly referred to as tooth decay or cavities, is a condition in which the hard surface of the teeth is damaged, leading to small holes.
• Dental decay begins when the pH level in the mouth drops below a critical threshold.
• This drop in pH occurs when acids produced by bacteria in the mouth (often as a result of the fermentation of sugars) erode the enamel of the teeth.
• When the pH falls below 5.5, it causes the demineralization of tooth enamel, leading to the breakdown and the formation of cavities.
• Saliva in the mouth plays a crucial role in neutralizing acids and helping to prevent tooth decay by maintaining a balanced pH level.

Additional Information Main types of dental fillings;

Given:

1.75 m tall person casts 2 m shadow.

 lamp-post casts a shadow 6.4 m.

Calculation:

Let θ be the unknown angle of elevation.

Let the height of lamp post is x m.

⇒ tan θ = 1.75/2 = x/6.4

⇒ 2x = 11.2

⇒ x = 5.6

The height of lamp post is 5.6 m.

∴ Option 2 is the correct answer.

The main objective of the INSPIRE Awards 'MANAK' is to motivate students at early age and studying in classes 6 to 10.

Hence, "Option 1" is the correct answer.

Additional InformationThe first component i.e. INSPIRE Award MANAK (Million Minds Augmenting National Aspiration and Knowledge) scheme, previously known as INSPIRE Award Scheme, is being implemented through State and UT governments with objectives:

(i) to attract young students to study science and pursue research career

(ii) to promote creative thinking and foster a culture of innovation among them.

Shortcut Trick

Rate 12.5% = 1/8. For 3 years (36 months), total interest = 3 × 1/8 = 3/8.

Amount = Principal + Interest = 1 + 3/8 = 11/8 units.

Given Amount = 11 units = ₹19,800 ⇒ 1 unit = ₹1,800.

Principal = 8 units = 8 × 1,800 = ₹14,400.

∴ The correct answer is ₹14,400.

Alternate Method

Given:

Amount (A) = ₹19,800

Rate (R) = 12.5% per annum

Time (T) = 36 months = 36 ÷ 12 = 3 years

Formula Used:

Amount (A) = P + SI = P + (P × R × T) / 100 = P[1 + (R × T) / 100]

Calculations:

⇒ 19,800 = P [1 + (12.5 × 3) / 100]

⇒ 19,800 = P [1 + 37.5 / 100]

⇒ 19,800 = P [1 + 0.375]

⇒ 19,800 = 1.375 × P

⇒ P = 19,800 / 1.375

⇒ P = (19,800 × 1,000) / 1,375

⇒ P = 14,400

∴ The correct answer is ₹14,400.

Additional Information

Simple Interest (SI) Formula

SI = (P × R × T) ÷ 100, where P is Principal, R is Rate, and T is Time in years.

Time Conversion

If time is given in months, convert it to years by dividing by 12. If given in days, divide by 365.

Difference between SI and CI

In Simple Interest, the interest remains constant every year, whereas in Compound Interest, interest is earned on the interest of previous years.

The correct answer is 0.67.

Key Points

• The refractive index (n) of a medium determines how much the path of light is bent, or refracted, when entering a medium.
• The refractive index of medium A relative to medium B is calculated using Snell's Law: $n_1 \times sin(\theta_1)=n_2\times sin(\theta_2)$ .
• Given the angles, we can rearrange the formula to find the relative refractive index: $n(\frac{A}{B})=\frac{sin(\theta_2)}{sin(\theta_1)}$.
• Substituting the given angles: $n\left(\frac{A}{B}\right)=\frac{sin(40^\circ)}{sin(70^\circ)}$.

Additional Information

• Snell's Law:
• Snell's Law describes how light rays are bent when they pass through the boundary between two different isotropic media.
• The law is formulated as $n_1 \times sin(\theta_1)=n_2\times sin(\theta_2)$, where n1 and n2 are the refractive indices of the two media and θ1 and θ2 are the angles of incidence and refraction, respectively.
• Refractive Index:
• The refractive index of a medium is a measure of how much the speed of light is reduced inside the medium.
• It is calculated as the ratio of the speed of light in a vacuum to the speed of light in the medium.
• For example, the refractive index of water is about 1.33, meaning that light travels 1.33 times slower in water than in a vacuum.
• Angles of Incidence and Refraction:
• The angle of incidence is the angle between the incident ray and the normal to the surface at the point of incidence.
• The angle of refraction is the angle between the refracted ray and the normal to the surface at the point of refraction.
• These angles are crucial for calculating the refractive index using Snell's Law.

Shortcut Trick

Raju's age = Sister's age − Age difference

Raju's age = 38 − 6 = 32 years.

∴ The correct answer is 32 years.

Alternate Method

Given:

Sister's age = 38 years

Difference = 6 years (Sister is older)

Formula Used:

Relative Age Equation: Sister's Age = Raju's Age + Difference

Calculations:

⇒ Let Raju's age be x.

⇒ x + 6 = 38

⇒ x = 38 − 6

⇒ x = 32 years

∴ The correct answer is 32 years.

Additional Information

Constant Age Difference

The age difference between two people always remains constant, regardless of how many years pass.

Linear Age Equations

For 'n' years later, add 'n' to current age; for 'n' years ago, subtract 'n' from current age (Age ± n).

The correct answer is Coastal areas.

Key Points

• Mangroves are salt-tolerant trees that grow in coastal intertidal zones.
• They are usually found in tropical and subtropical regions.
• Mangroves have specialized root systems, such as prop roots and pneumatophores, that allow them to thrive in harsh coastal conditions.
• These ecosystems are critical for coastal protection, reducing erosion, and providing habitat for a wide range of marine species.

Additional Information

• Mangrove Ecosystems
• Mangroves are unique ecosystems found at the interface of land and sea in tropical and subtropical coastal regions.
• They act as buffers, protecting coastal areas from storm surges, tsunamis, and erosion.
• Mangrove forests provide critical breeding, feeding, and nursery grounds for a variety of marine and terrestrial species.
• They are highly productive and contribute significantly to coastal food webs and carbon sequestration.
• Adaptations of Mangroves
• Mangroves exhibit several adaptations to survive in saline and anaerobic (low oxygen) conditions.
• They have specialized root structures like prop roots, stilt roots, and pneumatophores that help in gas exchange and stability in soft, muddy soils.
• Some mangrove species excrete excess salt through specialized glands in their leaves.
• Others store salt in their leaves, which are later shed to get rid of the accumulated salt.
• Importance of Mangroves
• Mangroves are crucial for coastal protection, reducing the impact of storm surges and preventing coastal erosion.
• They play a significant role in carbon sequestration, helping to mitigate climate change by absorbing large amounts of CO2.
• Mangrove ecosystems support biodiversity by providing habitat and nursery grounds for numerous marine and terrestrial species.
• They also support local communities by providing resources such as fish, timber, and non-timber forest products.

The correct answer is Option 2. i.e. Joule's heating effect.

Key Points

• Joule's heating effect, also known as Joule heating, is the process by which the passage of an electric current through a conductor produces heat. This effect is named after James Prescott Joule who first discovered it.
• Joule heating is a result of collisions between moving charges in a conductor, typically electrons, and the atomic ions that make up the rest of the material. These collisions transfer energy from the moving charges to the ions, making them vibrate more, which is perceived as heat.
• The amount of heat produced according to Joule's first law can be calculated using the equation:
• H = I²Rt
• Where,
• H = Heat energy produced (in joules) I = Current flow (in amperes) R = Resistance of the conductor (in ohms) t = Time for which the current is applied (in seconds)
• This effect is the principle behind many common applications, such as the heating elements in electric heaters and stoves, electric ovens, incandescent light bulbs, and electric fuses. It can also be unwanted, as in the case of power lines or electronic devices where excess heat can cause damage or reduce efficiency.​

Important Points

Examples of the heating effect of electricity -​

From the given Venn diagram,

The total number of persons who consume both cornflakes and buttered toast is,

100 + 52 = 152

Hence, the correct answer is "Option 1".

The correct answer is Article 40.

Key Points

• Article 40 of the Indian Constitution specifically directs the State to take steps to organize village panchayats and endow them with powers to function as units of self-government.
• This article falls under Part IV of the Constitution, which deals with the Directive Principles of State Policy.
• The aim is to promote democratic decentralization and rural self-governance to improve the socio-economic conditions of the village population.
• This article forms the constitutional basis for the establishment of the Panchayati Raj system in India.

Additional Information

• Directive Principles of State Policy (DPSP)
• DPSPs are guidelines for the framing of laws by the government. These provisions are not enforceable by any court but aim to create social and economic conditions under which the citizens can lead a good life.
• They are included in Part IV (Articles 36-51) of the Constitution of India.
• They embody the concept of a ‘welfare state’ and aim to establish social and economic democracy in the country.
• Panchayati Raj System
• The Panchayati Raj is a three-tier system of rural local governance in India, comprising village, intermediate, and district levels.
• The 73rd Amendment Act of 1992 gave constitutional status to the Panchayati Raj institutions and added Part IX to the Constitution, which deals with the Panchayats (Articles 243 - 243O).
• The Act provides for the establishment of Gram Sabhas and sets out the composition, powers, and functions of the Panchayats.
• Gram Sabha
• The Gram Sabha is the foundation of the Panchayati Raj system. It is a body consisting of persons registered in the electoral rolls of a village within the area of the Panchayat at the village level.
• It is a forum for the people to directly participate in the decision-making process and discuss local issues.
• Decentralization
• Decentralization refers to the transfer of authority and responsibility from higher levels of government to lower levels, particularly to local governments.
• It is aimed at empowering local bodies to manage local affairs, ensuring greater efficiency, accountability, and responsiveness to the needs of the community.

Shortcut Trick

Product of LCM and HCF = Product of Two Numbers

270 = 18 × Other Number

Other Number = 270 ÷ 18 = 15

∴ The correct answer is 15.

Alternate Method

Given:

Product of HCF and LCM = 270

First Number (a) = 18

Formula Used:

LCM × HCF = a × b

Calculations:

⇒ Let the other number be b.

⇒ 270 = 18 × b

⇒ b = 270 ÷ 18

⇒ b = 15

∴ The correct answer is 15.

Additional Information

LCM (Least Common Multiple)

The smallest positive integer that is divisible by both numbers a and b.

HCF (Highest Common Factor)

The largest positive integer that divides each of the numbers a and b without leaving a remainder.

Co-prime Numbers

Two numbers are co-prime if their HCF is 1. For co-prime numbers, LCM is simply the product of the numbers.

Given: A, B, C, D, E and F are sitting around a circular table facing the centre. 

1) B is sitting third to the right of F.

2) F is an immediate neighbour of both C and A.

3. C sits second to the right of B.

4) D is not the immediate neighbour of C.

After positioning D only position is left which will be occupied by the only person left i.e. E.

Thus, according to the final arrangement, B is sitting to the immediate left of E.

Hence, "Option 2" is the correct answer.

The logic follows here is:

Logic: (First number × 2) - (First number ÷ 4) = Second Number

(24, 42) → (24 × 2) - (24 ÷ 4) 

⇒ 48 - 6 = 42 

And,

(36, 63) → (36 × 2) - (36 ÷ 4)

⇒ 72 - 9 = 63

Similarly,

(52, 91) → (52 × 2) - (52 ÷ 4)

⇒ 104 - 13 = 91

Hence, the correct answer is "Option 3".

The correct answer is West Bengal.

Key Points

• The forest department of West Bengal has recognized its shortcomings in reviving the degraded Sal forests in the south-western districts of the state.
• Sal forests are predominantly found in the eastern regions of India, and West Bengal is one of the states where these forests are located.
• The Sal forests are crucial for the ecological balance and livelihood of the local communities in the south-western districts of West Bengal.
• The degradation of these forests has impacted biodiversity and the overall health of the ecosystem in these regions.

Additional Information

• Sal Forests
• Sal (Shorea robusta) is a species of tree that dominates the forests of the eastern and central regions of India.
• These forests are known for their high-quality timber, which is used in construction, furniture, and other industries.
• Sal forests play a vital role in maintaining the ecological balance, supporting biodiversity, and providing livelihoods to local communities.
• The degradation of Sal forests can lead to soil erosion, loss of habitat for wildlife, and adverse climatic changes.
• Forest Degradation
• Forest degradation refers to the decline in forest quality, including the loss of biodiversity, forest structure, and function.
• It is often caused by human activities such as deforestation, over-exploitation of forest resources, and unsustainable land use practices.
• Degraded forests are less capable of providing ecosystem services, such as carbon sequestration, water regulation, and soil protection.
• Restoration efforts are essential to reverse degradation and ensure the sustainability of forest ecosystems.
• Ecological Importance of Forests
• Forests are vital for maintaining the Earth's biodiversity, providing habitat for numerous plant and animal species.
• They play a critical role in the global carbon cycle by sequestering carbon dioxide and mitigating climate change.
• Forests regulate water cycles, prevent soil erosion, and protect watersheds.
• They also offer recreational, cultural, and economic benefits to human societies.

Given number: 25731640

Let's arrange the number in descending order, we get

Since only '0' remains unchanged after the arrangement. Thus, only one digit is unchanged.

Hence, the correct answer is "Option 4".

Calculation:

Decrease in deaths from 2021 to 2022 is = 5000 - 3000 = 2000

% in decrease is given by:

⇒ (2000/5000) × 100

⇒ 40%

Increase in deaths from 2020 to 2021 is = 5000 - 3500 = 1500

% in decrease is given by:

⇒ (1500/3500) × 100

⇒ 42.83%

∴ Option 3 is the correct answer.

The correct answer is Viral particles are abundant in seminal fluid.

Key Points

• HIV (Human Immunodeficiency Virus) is primarily spread through contact with certain body fluids of an infected person, including blood, semen, vaginal fluids, and breast milk.
• During sexual contact, seminal fluid from an infected individual can carry a high concentration of viral particles, facilitating the transmission of the virus to their partner.
• HIV targets the immune system, specifically the CD4 cells (T cells), which are crucial in helping the body fight infections.
• Unprotected sexual intercourse (vaginal, anal, or oral) increases the risk of transmitting HIV, especially if there are cuts or sores present in the genital area which provide an entry point for the virus.

Additional Information

• HIV (Human Immunodeficiency Virus)
• HIV is a virus that targets the immune system and weakens people's defense systems against infections and some types of cancer.
• As the virus destroys and impairs the function of immune cells, infected individuals gradually become immunodeficient.
• HIV is transmitted through the exchange of a variety of body fluids from infected individuals, such as blood, breast milk, semen, and vaginal secretions.
• It is important to note that HIV cannot be transmitted through casual contact such as hugging, shaking hands, or sharing personal objects, food, or water.
• AIDS (Acquired Immunodeficiency Syndrome)
• AIDS is the most severe phase of HIV infection. It occurs when the immune system is badly damaged, and the body becomes vulnerable to opportunistic infections and certain cancers.
• Without treatment, people with AIDS typically survive about three years. Once someone has a dangerous opportunistic illness, life expectancy without treatment falls to about one year.
• Common symptoms include rapid weight loss, recurring fever or profuse night sweats, extreme and unexplained tiredness, prolonged swelling of the lymph glands in the armpits, groin, or neck.
• Prevention of HIV
• Consistent and correct use of condoms during sexual intercourse significantly reduces the risk of HIV transmission.
• Regular testing and treatment for sexually transmitted infections (STIs) can reduce the risk of HIV infection.
• Pre-exposure prophylaxis (PrEP) is an HIV prevention method in which people who do not have HIV take HIV medicine daily to reduce their risk of getting HIV.
• Avoiding the sharing of needles, syringes, or other drug injection equipment can prevent the transmission of HIV among people who inject drugs.
• Treatment of HIV
• While there is no cure for HIV, it can be controlled with proper medical care. Antiretroviral therapy (ART) is the use of HIV medicines to treat HIV infection.
• People on ART take a combination of HIV medicines every day. ART helps to control the virus and live a longer, healthier life, and reduces the risk of HIV transmission.
• Adherence to ART is crucial. Skipping doses can lead to drug resistance and treatment failure.

Given: Six friends, A, B, C, D, E, and F are sitting around a circular table facing the centre.

1) F is second to the right of C and third to the left of A. 

2) C is the immediate neighbour of A and E.

3. B is second to the left of C.

After positioning B only position is left which will be occupied by the only person left i.e. D.

Thus, according to the final arrangement, D is second to the left of A.

Hence, "Option 2" is the correct answer.

The correct answer is Allahabad.

Key Points

• Jawaharlal Nehru, the first Prime Minister of independent India, was born on 14 November 1889 in Allahabad.
• Allahabad, now known as Prayagraj, is a city in the Indian state of Uttar Pradesh.
• He was born into a wealthy and politically active family, with his father Motilal Nehru being a prominent lawyer and nationalist leader.
• Jawaharlal Nehru played a pivotal role in India's struggle for independence and was a central figure in Indian politics both before and after independence.

Additional Information

• Jawaharlal Nehru
• Jawaharlal Nehru was an Indian independence activist and, subsequently, the first Prime Minister of India.
• He emerged as a prominent leader of the Indian independence movement under the tutelage of Mahatma Gandhi.
• Nehru's vision of India was rooted in secularism, socialism, and democracy.
• He is also remembered for his efforts in establishing institutes of higher learning, such as the Indian Institutes of Technology (IITs) and the All India Institute of Medical Sciences (AIIMS).
• Allahabad (Prayagraj)
• Allahabad, officially known as Prayagraj, is a historic city in the state of Uttar Pradesh in India.
• It is one of the oldest cities in India, with a history dating back to ancient times.
• The city is known for its confluence of three rivers – the Ganges, the Yamuna, and the mythical Saraswati – a site called Triveni Sangam.
• Prayagraj is also famous for the Kumbh Mela, a mass Hindu pilgrimage held every 12 years.
• Motilal Nehru
• Motilal Nehru was an Indian lawyer, activist, and politician who was a leader of the Indian National Congress.
• He was a prominent figure in the Indian independence movement and the father of Jawaharlal Nehru.
• Motilal Nehru was an advocate of constitutional reforms and played a key role in the drafting of the Nehru Report, which outlined a proposed constitutional framework for India.

Shortcut Trick

Total Volume = Sum of individual volumes.

V = 4/3 × π × (r₁³ + r₂³ + r₃³)

V = 4/3 × 22/7 × (3³ + 4³ + 5³) = 4/3 × 22/7 × (27 + 64 + 125)

V = 4/3 × 22/7 × 216 = 88/21 × 216 = 88 × 72/7 = 6336/7 = 905 1/7 cm³.

∴ The correct answer is 905 1/7 cm³.

Alternate Method

Given: Radii of three spheres are r₁ = 3 cm, r₂ = 4 cm, and r₃ = 5 cm. π = 22/7.

Formula Used: Volume of a sphere = 4/3 × π × r³.

⇒ Volume of 1st sphere = 4/3 × π × 3³ = 4/3 × π × 27 = 36π

⇒ Volume of 2nd sphere = 4/3 × π × 4³ = 4/3 × π × 64 = 256π/3

⇒ Volume of 3rd sphere = 4/3 × π × 5³ = 4/3 × π × 125 = 500π/3

⇒ Total Volume = 36π + 256π/3 + 500π/3 = (108π + 256π + 500π) / 3

⇒ Total Volume = 864π / 3 = 288π

⇒ Total Volume = 288 × 22/7 = 6336/7

⇒ Total Volume = 905 1/7 cm³

∴ The correct answer is 905 1/7 cm³.

Additional Information

Surface Area of Sphere

The total surface area of a sphere is given by the formula 4πr².

Radius of Resulting Sphere

When n spheres are melted to form one, the new radius R satisfies R³ = r₁³ + r₂³ + ... + r_n³.

Volume of Hemisphere

The volume of a hemisphere is exactly half of a sphere: 2/3 × πr³.

The correct answer is 2021.

Key Points

• Lakhimi Baruah was awarded the Padma Shri in the year 2021 for her contributions in the field of social work.
• She is the founder of the Konoklota Mahila Urban Cooperative Bank, which is dedicated to empowering women in Assam.
• The Padma Shri is the fourth highest civilian award in India, recognizing distinguished contributions in various fields including arts, education, industry, literature, science, sports, medicine, social service and public affairs.
• Lakhimi Baruah's efforts have significantly contributed to the financial independence and empowerment of women in her community.

Additional Information

• Padma Awards
• The Padma Awards are one of the highest civilian honors in India and are categorized into three awards: Padma Vibhushan, Padma Bhushan, and Padma Shri.
• Padma Vibhushan is awarded for exceptional and distinguished service, Padma Bhushan for distinguished service of a high order, and Padma Shri for distinguished service in any field.
• The awards are announced annually on the occasion of Republic Day.
• The awardees are selected based on their contributions to various disciplines such as arts, social work, public affairs, science and engineering, trade and industry, medicine, literature and education, sports, civil service, and others.
• Konoklota Mahila Urban Cooperative Bank
• Founded by Lakhimi Baruah, this bank aims to provide financial services to women, especially those who are economically disadvantaged.
• The bank offers various schemes and financial products that help women in starting their own businesses, thereby promoting women entrepreneurship and economic independence.
• It is a significant initiative towards the financial inclusion of women in the rural and urban areas of Assam.

The correct answer is Valabhi in Gujarat.

Key Points

• The teachings of Mahavira and his followers were compiled and written down in the form of Jain Agamas at Valabhi in Gujarat.
• The Jain Agamas are canonical scriptures of Jainism and were orally transmitted for many centuries before being written down.
• The compilation of these teachings took place around the 5th to 6th century CE.
• Valabhi was an important center of Jain scholarship and education during that period.

Additional Information

• Mahavira:
• Mahavira, also known as Vardhamana, was the 24th Tirthankara of Jainism.
• He was born in 599 BCE in Kundagrama, near Vaishali (now in Bihar).
• Mahavira preached non-violence, truth, and asceticism and is considered a reformer of the Jain community.
• Jain Agamas:
• The Jain Agamas are a collection of texts based on the teachings of Mahavira and his disciples.
• They form the primary scriptures of Jainism, particularly for the Svetambara sect.
• The Agamas were composed of various types of works such as sutras, commentaries, and philosophical texts.
• Compilation at Valabhi:
• Valabhi, located in present-day Gujarat, was a major center of learning and a hub for Jain monks and scholars.
• The Jain council held at Valabhi under the leadership of Devardhigani Kshamashramana is believed to have finalized the compilation of the Agamas.
• This event ensured the preservation and propagation of Jain teachings for future generations.

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

1) No one is sitting to the right of E.

2) Only two people are sitting to the left of B.

3) D is sitting third to the right of B.

4) Only four people are seated between B and F.

5) Only eight people are seated between D and C.

6) E is seated second to the right of C.

Thus, according to the final arrangement, 17 is the total number of persons seated.

Hence, "Option 4" is the correct answer.

Calculation:

⇒ $\sqrt{2187}×\sqrt{432}\over\sqrt{324}$

⇒ $27\sqrt{3}×12\sqrt{3}\over18$

⇒ $54$

∴ Option 3 is the correct answer.

The correct answer is Andhra Pradesh.

Key Points

• The Andhra Pradesh police developed an app called 'Disha' for women's safety in February 2020.
• The 'Disha' app was named after a woman who was a victim of a heinous crime in the state, sparking outrage and a call for enhanced safety measures.
• The app aims to provide rapid assistance to women in distress with features such as SOS, police station locator, and nearby hospital locator.
• It is part of a larger initiative by the Andhra Pradesh government to improve women's safety, including the Disha Act which aims to expedite the trial and punishment of crimes against women.

Additional Information

• Disha App
• The Disha app was developed to enhance the safety and security of women in the state of Andhra Pradesh.
• It includes features such as an SOS button which, when pressed, sends an immediate alert to the nearest police control room.
• The app also provides information on the nearest police stations and hospitals, making it easier for women to seek help in emergencies.
• It is part of the broader Disha initiative, which includes the Disha Act, aimed at fast-tracking the trial and conviction of offenders in crimes against women.
• Women's Safety Initiatives in India
• Various states in India have launched different initiatives to enhance women's safety, including the She Teams in Telangana and the Suraksha app in Karnataka.
• The Ministry of Women and Child Development, Government of India, has also launched initiatives like the One Stop Centre Scheme and the Women's Helpline 181.
• These initiatives aim to provide immediate assistance to women in distress and ensure their safety and protection.

Shortcut Trick

In any parallelogram, the diagonals bisect each other. Let the diagonals AC and BD of parallelogram ABCD intersect at point O.

Since O is the midpoint of diagonal AC, we have OA = OC.

Given that AE = FC, subtracting these equal lengths from OA and OC gives: OA − AE = OC − FC ⇒ OE = OF.

Thus, O is also the midpoint of segment EF, which means the diagonals BD and EF of quadrilateral BEDF bisect each other.

A quadrilateral whose diagonals bisect each other is always a parallelogram.

∴ The correct answer is parallelogram.

Alternate Method

Given:

⇒ ABCD is a parallelogram.

⇒ E and F are points on the diagonal AC such that AE = FC.

Properties Used:

⇒ In a parallelogram, opposite sides are equal and parallel.

⇒ SAS (Side-Angle-Side) Congruence Criterion: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

⇒ If both pairs of opposite sides of a quadrilateral are equal, then the quadrilateral is a parallelogram.

Calculations:

In triangles ΔADE and ΔCBF:

⇒ AD = BC (Opposite sides of parallelogram ABCD are equal)

⇒ ∠DAE = ∠BCF (Alternate interior angles, since AD || BC and diagonal AC is a transversal)

⇒ AE = FC (Given)

⇒ ΔADE ≅ ΔCBF (By SAS congruence criterion)

⇒ DE = BF (By CPCT) --- (Equation 1)

Similarly, in triangles ΔABE and ΔCDF:

⇒ AB = CD (Opposite sides of parallelogram ABCD are equal)

⇒ ∠BAE = ∠DCF (Alternate interior angles, since AB || CD and diagonal AC is a transversal)

⇒ AE = FC (Given)

⇒ ΔABE ≅ ΔCDF (By SAS congruence criterion)

⇒ BE = DF (By CPCT) --- (Equation 2)

In quadrilateral BEDF, from Equation 1 and Equation 2:

⇒ DE = BF and BE = DF

Since both pairs of opposite sides of quadrilateral BEDF are equal, BEDF is a parallelogram.

Why other options are incorrect:

⇒ Rectangle: A rectangle requires all interior angles to be 90°. Since the angles of the original parallelogram ABCD are not specified as 90°, the angles of BEDF are also not necessarily 90°.

⇒ Square: A square requires all sides to be equal and all angles to be 90°, which is not guaranteed here.

⇒ Trapezium, but not a parallelogram: A trapezium has only one pair of parallel sides, whereas BEDF has both pairs of opposite sides parallel and equal, making it a full parallelogram.

∴ The correct answer is parallelogram.

Additional Information

Properties of a Parallelogram

Opposite sides are equal and parallel, opposite angles are equal, consecutive angles are supplementary, and diagonals bisect each other.

Sufficient Conditions for a Quadrilateral to be a Parallelogram

A quadrilateral is a parallelogram if both pairs of opposite sides are equal, both pairs of opposite angles are equal, or its diagonals bisect each other.

SAS Congruence Criterion

If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Given word: NOTED

Let's arrange the letters in alphabetical order, we get

Since the position of none of the letters remains unchanged.

Hence, the correct answer is "Option 4".

The correct answer is 1973.

Key Points

• Steel Authority of India Ltd (SAIL) was incorporated on 24th January 1973.
• SAIL is one of the largest steel-making companies in India and one of the Maharatnas of the country's Central Public Sector Enterprises.
• It operates and owns 5 integrated steel plants at Bhilai, Rourkela, Durgapur, Bokaro, and Burnpur (Asansol) and 3 special steel plants at Salem, Durgapur, and Bhadravathi.
• SAIL traces its origins to the Hindustan Steel Limited (HSL) which was set up in 1954, with which it was merged later on to form a single entity.

Additional Information

• Maharatna Status:
• The Maharatna status is the highest recognition for public sector enterprises in India.
• It allows greater autonomy for investment and operations compared to other public sector enterprises.
• To qualify as a Maharatna, a company must have an annual turnover of more than Rs 25,000 crore, net profit after tax of more than Rs 5,000 crore, and a significant global presence.
• Integrated Steel Plants:
• An integrated steel plant is a factory where all the processes required for steel production are carried out from raw material handling to finished steel production.
• These processes include melting, casting, rolling, and finishing.
• SAIL's integrated steel plants are located at various strategic locations across India, enhancing its production capacity and market reach.
• Public Sector Enterprises:
• Public Sector Enterprises (PSEs) are companies in which the majority of the equity is owned by the government.
• They play a crucial role in the economic development of a country by contributing to GDP, employment, and industrialization.
• In India, PSEs are classified into Maharatna, Navratna, and Miniratna based on their performance and scale of operations.

Statements: B < D, C = E, F > D, E < G, K = G, C < F

Conclusions:

1. G > C → True (C = E < G, it gives G > C)
2. G < C → False (C = E < G, it gives G > C)

Thus, only Conclusion 1 follows.

Hence, the correct answer is "Option 3".

According to the given information,

Rahul drives 80 km towards the north,

then he turns towards the west and drives 100 km.

After that, he turns south and drives 80 km,

He turns east and drives 120 km. 

Thus, the endpoint is 20 km far from the initial point.

Hence, the correct answer is "Option 1".

Shortcut Trick

Curved Surface Area of a cylinder = Base Circumference × Height.

Given Circumference = 77 cm and Height = 23 cm.

CSA = 77 × 23 = 1771 cm².

∴ The correct answer is 1771 cm².

Alternate Method

Given:

Height (h) = 23 cm

Circumference (2πr) = 77 cm

Formula Used:

Curved Surface Area (CSA) = 2 × π × r × h

⇒ 2πr = 77

⇒ CSA = (2πr) × h

⇒ CSA = 77 × 23

⇒ CSA = 1771 cm²

∴ The correct answer is 1771 cm².

Additional Information

Total Surface Area of Cylinder

TSA includes the top and bottom circles: TSA = 2πr(h + r).

Volume of Cylinder

The space occupied by the cylinder is given by Volume = πr²h.

Base Area

The area of the circular base is πr². It can be found from circumference (C) as Area = C² / (4π).

The logic follows here is:

And, 

Similarly,

Thus, 'PURGE' is written as 'SSUEH'.

Hence, the correct answer is "Option 1".

Given solution in given html code format:

Given:

Now, the group of numbers and symbols is: < 9 4 # 2

Here, Here, Third conditions followed in the given group,

So, third element is to be coded as the code for the second element.

Then, the code for '< 9 4 # 2' is → 'PTTFX'.

Hence, the correct answer is "Option 2".

The correct answer is England.

Key Points

• Jhulan Goswami, an Indian cricketer, is one of the most successful bowlers in women's cricket history.
• On 16 March 2022, she became the highest wicket-taker in Women's ODIs by claiming her 250th wicket.
• She achieved this milestone during a match against England.
• Jhulan Goswami is celebrated for her significant contributions to Indian women's cricket, particularly as a bowler.

Additional Information

• Jhulan Goswami
• She made her debut in international cricket in 2002 and has since been a pivotal player for the Indian women's cricket team.
• She is known for her pace and accuracy, making her one of the most feared bowlers in women's cricket.
• In addition to her ODI success, she has also made notable contributions in Test and T20I formats.
• Jhulan has been awarded several honors, including the ICC Women's Player of the Year in 2007.
• Women's One Day International (ODI) Cricket
• ODI cricket is a format of limited overs cricket, played between two teams with international status.
• Each team faces a fixed number of overs, usually 50.
• Women's ODI cricket has gained significant popularity and recognition over the years, with many countries actively participating in international tournaments.
• The ICC Women's Cricket World Cup is the premier international championship of women's ODI cricket.
• Wicket-taking in Cricket
• In cricket, taking a wicket refers to the dismissal of a batsman by the bowler or the fielding team.
• Dismissals can occur in several ways, including being bowled, caught, leg before wicket (LBW), run out, and stumped.
• Wicket-taking is a crucial aspect of the game, as it helps to restrict the opposing team's score and bring about their batting collapse.
• Successful bowlers like Jhulan Goswami play a key role in their team's success by consistently taking wickets.

Shortcut Trick

Relative Speed (Same direction) = 36 − 26 = 10 km/h.

Convert to m/s = 10 × (5/18) m/s.

Total Distance (2L) = Speed × Time = [10 × (5/18)] × 18 = 50 m.

Length of each train (L) = 50 ÷ 2 = 25 m.

∴ The correct answer is 25 metres.

Alternate Method

Given:

Speed of faster train (S₁) = 36 km/h

Speed of slower train (S₂) = 26 km/h

Time taken to cross (t) = 18 seconds

Let the length of each train be 'L' metres.

Formula Used:

Relative Speed (Same Direction) = S₁ − S₂

Distance = Speed × Time

Conversion: 1 km/h = 5/18 m/s

Calculations:

⇒ Relative Speed = 36 − 26 = 10 km/h

⇒ Relative Speed in m/s = 10 × (5/18) = 25/9 m/s

⇒ Total distance covered = Length of Train 1 + Length of Train 2 = L + L = 2L

⇒ 2L = (25/9) × 18

⇒ 2L = 25 × 2

⇒ 2L = 50

⇒ L = 25 m

∴ The correct answer is 25 metres.

Additional Information

Relative Speed Rules

When moving in the same direction, relative speed is (S₁ − S₂). When moving in the opposite direction, relative speed is (S₁ + S₂).

Unit Conversion

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

Crossing Distance

When one train crosses another train (stationary or moving), the total distance to be covered is always the sum of their lengths (L₁ + L₂).

Given Statements: 

Some pliers are levers

All levers are ramps

Some cutters are pliers.

Conclusions:

(I) Some cutters are levers → False (No direct relationship given between cutters and levers so, it is possible but not definite)

(II) Some ramps are cutters → False (No direct relationship given between ramps and cutters so, it is possible but not definite)

(III) All pliers are ramps → False (No direct relationship given between pliers and ramps so, it is possible but not definite)

Thus, None of the Conclusions follow.

Hence, the correct answer is "Option 3".

Shortcut Trick Solve x2 + 4x − 21 = 0: Factors of −21 that sum to 4 are 7 and −3, so roots are −7 and 3. Since p < q, we have p = −7 and q = 3. New roots are (p − 1) = −8 and (q + 1) = 4. Sum of new roots = −8 + 4 = −4; Product of new roots = −8 × 4 = −32. New equation: x2 − (−4)x + (−32) = 0 ⇒ x2 + 4x − 32 = 0. ∴ The correct answer is x2 + 4x − 32 = 0.

Alternate Method Given quadratic equation: x2 + 4x − 21 = 0 To find the roots p and q, we factorize the expression: ⇒ x2 + 7x − 3x − 21 = 0 ⇒ x(x + 7) − 3(x + 7) = 0 ⇒ (x + 7)(x − 3) = 0 ⇒ x = −7 or x = 3 According to the condition p < q: ⇒ p = −7 and q = 3 The roots of the required quadratic equation are: ⇒ First root (α) = p − 1 = −7 − 1 = −8 ⇒ Second root (β) = q + 1 = 3 + 1 = 4 Forming the new equation using the sum and product of roots: ⇒ Sum of roots (α + β) = −8 + 4 = −4 ⇒ Product of roots (αβ) = −8 × 4 = −32 ⇒ The equation is: x2 − (α + β)x + αβ = 0 ⇒ x2 − (−4)x + (−32) = 0 ⇒ x2 + 4x − 32 = 0 ∴ The correct answer is x2 + 4x − 32 = 0.

Additional Information Sum and Product of Roots For any quadratic equation ax2 + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a. Formation of Quadratic Equation If α and β are the roots, the quadratic equation is constructed as x2 − (α + β)x + αβ = 0. Nature of Roots The discriminant (D = b2 − 4ac) determines if roots are real and distinct (D > 0), real and equal (D = 0), or imaginary (D < 0).

The logic follows here is :

And,

Now, let's check the options one by one,

Option 1: QHK : JSP

Option 2: FHL : CIU

Option 3: DUR : APM

Option 4: SIY : NDT

Thus, 'SIY : NDT' follows the same logic.

Hence. the correct answer is "Option 4".

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. All cheese are milk → Does not follow (As all milk are cheese. So it is possible but not definite.)

II. Some custards are cheese → Follow (As some cheese are custards. As some part of cheese is common with custards, therefore it is true.)

∴ Here, Only conclusion II follows.​

Hence, the correct answer is "Option 1".

Given: A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 6.

1) Only one person lives below E.

2) A does not live on the topmost floor. 

3) Only three people live between A and C.

4) C lives below A.

5) D lives immediately above B.

After positioning D and B, only one floor is left which will be occupied by the only person left i.e. F.

Thus, according to the final arrangement, F lives immediately above A.

Hence, "Option 1" is the correct answer.

The correct answer is Option - 2. i.e. Graphite.

Key Points 

• For electricity conduction, Free electrons /ions are needed.
• Graphite is the only allotrope of carbon, in which free electrons are present because of its unique structure.
• Because of this Graphite is a good conductor of electricity.
• Graphite conducts electricity due to its unique electronic structure.
• To understand why, we need to look at the crystalline structure and bonding of graphite.
• Graphite is a form of carbon in which the carbon atoms are arranged in layers in a hexagonal lattice.
• Each carbon atom is bonded to three other carbon atoms. The fourth outer shell electron of each atom is delocalized, allowing for electrons to move freely across the layers - these are the electrons that carry an electric current.
• This structure and the delocalization of an electron in each carbon atom are why graphite can conduct electricity. Furthermore, this conduction is directional, meaning that graphite is a better conductor of electricity along the layers ('ab' plane) than across them.
• This conductivity gives graphite its use in various applications, such as in electrodes in batteries and fuel cells, and in electric motor brushes.
• However, graphite's electrical conductivity is lower than many metals, such as copper, meaning that it won't conduct electricity as efficiently. Despite this, its ability to withstand high temperatures and resist chemical erosion makes it useful in settings where these factors come into play.

Additional InformationStructure of Graphite - 

 Allotropes of Carbon - 

The correct answer is Fleming's right hand rule.

Key Points

• Fleming's right hand rule is used to determine the direction of induced current when a conductor moves through a magnetic field.
• According to this rule, if you point your thumb in the direction of the conductor's motion and your forefinger in the direction of the magnetic field, your middle finger will point in the direction of the induced current.
• It is especially useful in applications involving electromagnetic induction, such as electric generators.
• This rule helps in understanding the relationship between motion, magnetic field, and induced current in a conductor.

Additional Information

• Fleming's Left Hand Rule
• It is used to find the direction of force experienced by a current-carrying conductor in a magnetic field.
• If the thumb, forefinger, and middle finger of the left hand are held mutually perpendicular to each other, and the forefinger points in the direction of the magnetic field and the middle finger in the direction of the current, then the thumb will point in the direction of the force on the conductor.
• This rule is commonly used in the design of electric motors.
• Right Hand Thumb Rule
• This rule is used to find the direction of the magnetic field around a current-carrying conductor.
• If you hold the conductor in your right hand with the thumb pointing in the direction of the current, the direction in which your fingers curl represents the direction of the magnetic field.
• Corkscrew Rule
• The corkscrew rule is similar to the right-hand thumb rule.
• It states that if a right-handed screw is turned in the direction of the current, the direction of advance of the screw represents the direction of the magnetic field lines.

Given word: ADVERSE

According to the question:

Forward pairs: RS

Backward pairs: SV

∴ The total number of pairs in both forward and backward directions is 'two'.

Hence, "Option 2" is the correct answer.

Shortcut Trick

चेक करें कि कौन सा विकल्प दी गई शर्तों को संतुष्ट करता है।

विकल्प (1) के लिए: 198 ÷ 15 → शेषफल = 3 (सत्य)

विकल्प (1) के लिए: 198 ÷ 17 → 17 × 11 = 187; शेषफल = 198 − 187 = 11 (सत्य)

चूंकि विकल्प (1) दोनों शर्तों को पूरा करता है, इसलिए यही सही उत्तर है।

∴ The correct answer is 198.

Alternate Method

दिया गया है:

भाजक₁ = 15, शेषफल₁ = 3

भाजक₂ = 17, शेषफल₂ = 11

सूत्र:

संख्या = (भाजक × भागफल) + शेषफल

गणना:

⇒ N = 15k + 3 और N = 17m + 11

⇒ 15k + 3 = 17m + 11

⇒ 15k = 17m + 8

⇒ k = (17m + 8) ÷ 15

⇒ m = 1 रखने पर: k = 25/15 (पूर्णांक नहीं)

⇒ m = 11 रखने पर: k = (17 × 11 + 8) ÷ 15 = (187 + 8) ÷ 15 = 195 ÷ 15 = 13

⇒ संख्या N = 15(13) + 3 = 195 + 3 = 198

∴ The correct answer is 198.

Additional Information

यूक्लिड विभाजन प्रमेयिका (Euclid's Division Lemma)

किसी भी धनात्मक पूर्णांक a और b के लिए, ऐसी अद्वितीय पूर्ण संख्याएँ q और r विद्यमान हैं कि a = bq + r, जहाँ 0 ≤ r < b है।

चीनी शेषफल प्रमेय (Chinese Remainder Theorem)

यह प्रमेय एक साथ कई रैखिक सर्वांगसमता (linear congruences) समीकरणों के निकाय के लिए एक अद्वितीय समाधान प्रदान करता है जब भाजक सह-अभाज्य (coprime) होते हैं।

The logic followed here is:

Hence, "Option 4" is the correct answer.

The correct answer is Option - 1

Key Points

• In alternating current, the electric charge changes direction periodically means the direction varies from instant to instant.
• The voltage in the AC circuit also periodically reverses because the current changes direction.
• So, a change in both the direction and magnitude happens.

Important Points

• Alternating current (AC) is a type of electrical current that periodically reverses direction, in contrast to direct current (DC) which flows only in one direction.
• AC is the form in which electric power is delivered to businesses and residences.
• Alternating current is produced by most power stations and is used in homes and businesses. The AC in most homes and offices has a frequency of 60 hertz, which means it changes direction, or cycles, 60 times each second.
• The advantage of AC is that it can be transmitted over long distances due to its ability to be easily transformed to high voltage. High voltage transmission is more efficient because it reduces the energy lost to heat due to the resistance in wires over long distances*. Transformers are used to increase the voltage for transmission and decrease it for user-end applications.*
• Please note that AC can also be dangerous because it can stop the human heart due to the frequency similar to the heart's electrical signals. Therefore, careful precautions are always taken when working with AC.

Additional InformationDifference between AC and DC -

The correct answer is Twenty-Fourth Amendment Act.

Key Points

• The Twenty-Fourth Amendment of the Constitution of India was enacted in 1971.
• This amendment affirmed the power of Parliament to amend any part of the Constitution, including Part III which deals with Fundamental Rights.
• It was a response to the Supreme Court's ruling in Golaknath v. State of Punjab (1967) which held that Parliament could not curtail any of the Fundamental Rights.
• The amendment made it explicit that the Parliament has the power to amend any provision of the Constitution by way of addition, variation, or repeal.

Additional Information

• Golaknath v. State of Punjab (1967)
• This landmark case in Indian constitutional history held that Parliament could not amend Fundamental Rights.
• It placed restrictions on the Parliament's power to amend the Constitution under Article 368.
• The ruling prompted the government to seek ways to reassert parliamentary sovereignty, leading to the Twenty-Fourth Amendment.
• Kesavananda Bharati v. State of Kerala (1973)
• This case re-examined the scope of Parliament's power to amend the Constitution.
• The Supreme Court ruled that while Parliament could amend any part of the Constitution, it could not alter its 'basic structure'.
• The 'basic structure' doctrine emerged as a significant judicial innovation ensuring that certain fundamental principles remain inviolable.
• Forty-Fourth Amendment Act (1978)
• This amendment was enacted to restore certain provisions and checks that were altered during the Emergency (1975-77).
• It ensured that some of the rights and freedoms curtailed during the Emergency were reinstated.
• The amendment also provided that certain emergency powers and provisions would require a more stringent process to be invoked in the future.

The correct answer is Formation of calcium hydroxide.

Key Points

• Formation of calcium hydroxide involves the combination of calcium oxide (CaO) and water (H₂O) to form calcium hydroxide (Ca(OH)₂).
• It is an example of a combination reaction where two reactants combine to form a single product.
• The balanced chemical equation for this reaction is: CaO + H₂O → Ca(OH)₂.
• Calcium hydroxide is commonly known as slaked lime and is used in various applications such as water treatment, construction, and the production of mortar and plaster.

Additional Information

• Combination Reaction
• A combination reaction is a chemical reaction where two or more substances (reactants) combine to form a single new substance (product).
• These reactions are also known as synthesis reactions.
• Combination reactions can involve elements or compounds, and they usually release energy in the form of heat and light.
• Examples include the formation of water from hydrogen and oxygen (2H₂ + O₂ → 2H₂O) and the formation of carbon dioxide from carbon and oxygen (C + O₂ → CO₂).
• Calcium Hydroxide
• Calcium hydroxide, also known as slaked lime, is an inorganic compound with the chemical formula Ca(OH)₂.
• It is produced by adding water to calcium oxide (quicklime), a process called slaking.
• Calcium hydroxide is used in various industries, including construction (for making mortar and plaster), water treatment (to adjust pH levels), and in the food industry (for processing corn in nixtamalization).
• It appears as a white powdery solid and is slightly soluble in water, forming a solution known as lime water.
• Other Options Explained
• Formation of water: This is also a combination reaction but involves elements (hydrogen and oxygen) rather than compounds.
• Formation of carbon dioxide: This is a combination reaction involving an element (carbon) and a compound (oxygen).
• Formation of ammonia: This involves the combination of nitrogen and hydrogen, which are elements, not compounds.

The correct answer is a series circuit.

Key Points

• In a series circuit, all components are connected end-to-end, forming a single path for the current to flow.
• Festival lights or decorative lights are typically connected in series, meaning if one light fails, the entire circuit is interrupted, causing all lights to go out.
• This setup is beneficial for ensuring that the same current flows through each bulb, giving a uniform brightness.
• Series circuits are simple to design and implement but can be less reliable due to the "one-fault-all-fail" nature.

Additional Information

• Parallel Circuit
• In a parallel circuit, components are connected across common points or junctions, creating multiple paths for the current to flow.
• If one component in a parallel circuit fails, the current can still flow through the other paths, so other components remain operational.
• Parallel circuits are commonly used in household wiring to ensure that all devices receive the same voltage.
• Magnetic Effect
• Magnetic effect refers to the phenomenon where a current-carrying conductor generates a magnetic field around it.
• This principle is used in devices like electromagnets, electric motors, and transformers.
• Electromagnetic Induction
• Electromagnetic induction is the process of generating an electromotive force (EMF) by changing the magnetic flux through a coil.
• This principle is the working foundation for generators, inductors, and transformers.

Shortcut Trick

Average of two consecutive even numbers = 842 ÷ 2 = 421.

Since the numbers are consecutive even numbers, they must lie on either side of the average.

Numbers = 421 − 1 and 421 + 1.

Smaller number = 420.

∴ The correct answer is 420.

Alternate Method

Given: Sum of two consecutive even numbers = 842.

Let the smaller even number be x.

Then the next consecutive even number is x + 2.

⇒ x + (x + 2) = 842

⇒ 2x + 2 = 842

⇒ 2x = 842 − 2

⇒ 2x = 840

⇒ x = 840 ÷ 2

⇒ x = 420

∴ The correct answer is 420.

Additional Information

Consecutive Even Numbers

These are even numbers that follow each other in order, having a common difference of 2. Example: n, n+2, n+4.

Consecutive Odd Numbers

Similar to even numbers, consecutive odd numbers also have a difference of 2. Example: 1, 3, 5 or x, x+2.

Average Property

For any set of n consecutive numbers, the average is exactly the middle term (if n is odd) or the mean of the two middle terms (if n is even).

Given:

1. The interviews are on even dates.

2) There’s a 5-day gap between interviews.

3) None of the interviews are on 28th February.

The even dates in February (leap year) are:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28

Starting with the first date, each subsequent interview is on the 6th day (5-day gap). For example:

First date: 2nd

Next interview: 2nd + 6 = 8th

Next interview: 8th + 6 = 14th

Next interview: 14th + 6 = 20th

Next interview: 20th + 6 = 26th

So, the first person’s interview will be on 2nd February.

Hence, the correct answer is "Option (1)".

The correct answer is Option 1.

Key Points

• A concave mirror will diverge the rays of light if the object is placed between the pole and the focus.
• Convex mirrors always diverge light rays; they cannot converge them.
• In concave mirrors, when the object is placed between the pole and the focus, the image formed is virtual, erect, and magnified.
• Convex mirrors are used for rearview mirrors in vehicles because they provide a wider field of view as they diverge light rays.

Additional Information

• Spherical Mirrors:
• A spherical mirror is a mirror that has the shape of a piece cut out of a spherical surface. There are two types of spherical mirrors: concave and convex.
• Concave Mirrors: These mirrors are curved inward like a spoon. They can form real and virtual images depending on the position of the object.
• Convex Mirrors: These mirrors are curved outward. They always form virtual, erect, and diminished images regardless of the position of the object.
• Focus (F):
• It is the point where light rays parallel to the principal axis converge (concave mirror) or appear to diverge from (convex mirror) after reflection.
• Pole (P):
• It is the center of the spherical mirror.
• Principal Axis:
• It is the straight line passing through the pole and the center of curvature of the spherical mirror.
• Applications of Spherical Mirrors:
• Concave mirrors are used in torches, searchlights, and vehicle headlights to produce parallel beams of light.
• Convex mirrors are used as rearview mirrors in vehicles due to their wider field of view.

The correct answer is There are too many dams on it.

Key Points

• The construction of numerous dams on river Ganga has significantly altered its natural flow.
• These dams obstruct the migration patterns of aquatic species, impacting biodiversity.
• The dams have led to the reduction of water flow downstream, affecting the riverine ecosystem and local communities.
• These infrastructural interventions have contributed to the river being classified as endangered due to the ecological imbalances caused.

Additional Information

• Endangered River:
• A river is classified as endangered when it faces severe threats to its ecological health and biodiversity.
• Threats include pollution, over-extraction of water, dam construction, and climate change.
• Endangered rivers often suffer from reduced water quality, loss of aquatic life, and disruption of natural processes.
• Impact of Dams on Rivers:
• Dams can disrupt the natural flow of rivers, affecting sediment transport and deposition.
• They can lead to the creation of stagnant reservoirs, which can become hotspots for pollution and invasive species.
• Downstream ecosystems can be deprived of nutrients and sediments, affecting agriculture and natural habitats.
• Fish and other aquatic organisms often rely on free-flowing rivers for spawning and migration, which dams can obstruct.
• Biodiversity and Ecosystem Services:
• Biodiversity in rivers includes a variety of fish, plants, and microorganisms that contribute to the ecological balance.
• Rivers provide ecosystem services such as water filtration, nutrient cycling, and habitat for wildlife.
• Healthy river ecosystems support livelihoods, agriculture, and cultural practices of local communities.
• Conservation Efforts:
• Conservation efforts for endangered rivers include measures to reduce pollution, manage water extraction, and restore natural flow regimes.
• Environmental impact assessments are crucial before the construction of new dams or other infrastructural projects.
• Community involvement and sustainable practices are essential for the long-term health of river ecosystems.

The correct answer is Fe.

Key Points

• Fe, also known as Iron, is a chemical element with the symbol Fe and atomic number 26.
• It is a metal in the first transition series and is by mass the most common element on Earth, forming much of Earth's outer and inner core.
• Iron is used in construction, manufacturing, and various industrial applications due to its strength and durability.
• It is also a crucial element in biology, playing a key role in oxygen transport and storage in the form of hemoglobin and myoglobin.

Additional Information

• Boron (B)
• Boron is a metalloid with the atomic number 5.
• It is not a metal but has properties of both metals and non-metals.
• It is used in borosilicate glass, detergents, and as a semiconductor in electronics.
• Carbon (C)
• Carbon is a non-metal with the atomic number 6.
• It is a fundamental element in organic chemistry and is the basis of all known life forms.
• It exists in various forms, including graphite, diamond, and fullerenes.
• Silicon (Si)
• Silicon is a metalloid with the atomic number 14.
• It is widely used in electronics, particularly in semiconductors, and in the production of silicon-based materials like glass and ceramics.

Shortcut Trick

For pure recurring decimals, replace the bar with 9 in the denominator.

0.1‾ = 1/9 and 0.5‾ = 5/9

Sum = 1/9 + 5/9 = 6/9 = 2/3

∴ The correct answer is 2/3.

Alternate Method

Given:

Expression: 0.1‾ + 0.5‾

Formula Used:

A recurring decimal 0.a‾ can be written as the fraction a/9.

Calculations:

⇒ Let x = 0.111... ⇒ 10x = 1.111... ⇒ 9x = 1 ⇒ x = 1/9

⇒ Let y = 0.555... ⇒ 10y = 5.555... ⇒ 9y = 5 ⇒ y = 5/9

⇒ Total Value = 1/9 + 5/9

⇒ Total Value = (1 + 5) / 9

⇒ Total Value = 6 / 9

⇒ Total Value = 2 / 3

∴ The correct answer is 2/3.

Additional Information

Pure Recurring Decimal to Fraction

If the decimal is 0.ab‾, the fraction is ab/99. The number of 9s equals the number of repeating digits.

Mixed Recurring Decimal to Fraction

For 0.abc‾, the formula is (abc − ab) / 900. Use 9s for repeating digits and 0s for non-repeating digits after the decimal.

Rational Numbers

All recurring decimals are rational numbers because they can be expressed in the form p/q.

Given:

93 - 91 × 7 + 8 ÷ 3

Formula used:

Given the operations: '+' means '×', '×' means '÷', '÷' means '-', and '-' means '+'

Calculations:

We replace the operations as per the given meanings:

93 + 91 ÷ 7 × 8 - 3

Perform the operations step by step:

⇒ 93 + 13 × 8 - 3

⇒ 93 + 104 - 3

⇒ 197 - 3

⇒ 194

∴ The correct answer is option 2.

Shortcut Trick

Net time taken = (Filling time × Emptying time) ÷ (Emptying time − Filling time)

Net time = (3 × 5) ÷ (5 − 3)

Net time = 15 ÷ 2 = 7.5 hr

∴ The correct answer is 7.5 hr.

Alternate Method

Given: Filling Tap (A) = 3 hr, Emptying Hole (B) = 5 hr

⇒ Net efficiency of (A + B) = 5 − 3 = 2 units/hr

⇒ Total time to fill empty cistern = Total Work ÷ Net Efficiency

⇒ Time = 15 ÷ 2

⇒ Time = 7.5 hr

∴ The correct answer is 7.5 hr.

Additional Information

Pipes and Cisterns Efficiency

Efficiency of a filling pipe is taken as positive (+), while the efficiency of an emptying pipe (leak/outlet) is taken as negative (−).

Work Done Formula

Total Work = Time × Efficiency. In these problems, the capacity of the tank is generally assumed to be the LCM of the individual times.

Combined Rate

If one pipe fills in x hours and another empties in y hours (where y > x), the net work done per hour is (1/x − 1/y).

The correct answer is 1000 - 2000 mL.

Key Points

• A normal adult human being produces approximately 1000 - 2000 mL of urine per day.
• This range can vary based on factors such as fluid intake, diet, and overall health.
• Urine production is an essential bodily function for removing waste products and excess substances from the bloodstream.
• Maintaining this range of urine output helps ensure proper kidney function and overall fluid balance in the body.

Additional Information

• Urine Production:
• Urine is produced by the kidneys through a process called filtration.
• The kidneys filter waste products, excess substances, and fluids from the blood to form urine.
• Urine is then passed from the kidneys to the bladder through the ureters and eventually excreted from the body via the urethra.
• Factors Affecting Urine Output:
• Fluid intake: Increased fluid consumption typically results in higher urine output.
• Diet: Certain foods and beverages can influence urine production.
• Health conditions: Diseases such as diabetes and kidney disorders can affect urine output.
• Medications: Diuretics and other medications can increase urine production.
• Importance of Proper Hydration:
• Maintains electrolyte balance: Proper hydration helps maintain the balance of electrolytes in the body.
• Prevents kidney stones: Adequate fluid intake reduces the risk of kidney stones by diluting substances in urine that can form stones.
• Supports overall health: Proper hydration is crucial for bodily functions, including digestion, circulation, and temperature regulation.

Shortcut Trick

Let the cost price of X be x and Y be y.

From first condition: −0.10x + 0.15y = 7 ⇒ −10x + 15y = 700 ⇒ −2x + 3y = 140 --- (i)

From second condition: 0.12x + 0.05y = 10 ⇒ 12x + 5y = 1000 --- (ii)

Multiply (i) by 6: −12x + 18y = 840. Add to (ii): 23y = 1840 ⇒ y = 80.

Substitute y in (i): −2x + 240 = 140 ⇒ 2x = 100 ⇒ x = 50.

Total cost price = x + y = 50 + 80 = 130.

∴ The correct answer is ₹130.

Alternate Method

Given → Profit/Loss percentages and total profit values. Formulas: Profit = SP − CP | Loss = CP − SP | Total Profit = (Profit on Y) − (Loss on X).

⇒ Let CP of X = x and CP of Y = y. ⇒ Case 1: 0.15y − 0.10x = 7 ⇒ Case 2: 0.12x + 0.05y = 10 ⇒ Multiply Case 2 by 3: 0.36x + 0.15y = 30 ⇒ Subtract Case 1 from this: (0.36x + 0.15y) − (−0.10x + 0.15y) = 30 − 7 ⇒ 0.46x = 23 ⇒ x = 23 ÷ 0.46 = 50. ⇒ Substitute x = 50 in Case 1: 0.15y − 5 = 7 ⇒ 0.15y = 12 ⇒ y = 12 ÷ 0.15 = 80. ⇒ Total Cost Price = 50 + 80 = 130.

∴ The correct answer is ₹130.

Additional Information

Linear Equations in Profit and Loss

When profit or loss occurs on multiple items, the net profit is the algebraic sum of individual profits and losses (Profit is positive, Loss is negative).

Simultaneous Equations

To find two unknowns (CP of X and Y), we need two independent linear equations derived from the given conditions.

The logic followed here is:

Logic: (2nd number²× 2) - 2 = 1st number.

Now,

For, 48 : 5

⇒ (5² × 2) - 2 = 25 × 2 - 2 = 50 - 2 = 48.

For, 96 : 7

⇒ (7² × 2) - 2 = 49 × 2 - 2 = 98 - 2 = 96.

Similarly, for 6 : ?

⇒ (2² × 2) - 2 = 4 × 2 - 2 = 8 - 2 = 6.

Hence, the correct answer is "Option 1".

Given series:

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

Condition to be checked:

6s which are NOT immediately preceded by 3 but immediately followed by 3

Not 3 → 6 → 3

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

Thus there are two such patterns (8 6 3, 8 6 3) that are following the above conditions.

Hence,"2" is the correct answer.

Mistake Points

Immediately preceded by means immediately before or to come just before.

Immediately followed by means immediately after or to come just after.

The correct answer is Prominent light and dark bands are present.

Key Points

• Striated muscles are also known as skeletal muscles or voluntary muscles.
• They exhibit a pattern of light and dark bands, which are visible under a microscope.
• These muscles are attached to bones and are responsible for body movements.
• The cells of striated muscles are long, cylindrical, and multinucleated, which means they have multiple nuclei per cell.

Additional Information

• Striated Muscles:
• Striated muscles are named for their striped appearance due to the arrangement of actin and myosin filaments.
• These muscles are under conscious control, meaning we can control their movement voluntarily.
• They are responsible for locomotion, posture, and various voluntary movements.
• Non-Striated Muscles:
• Non-striated muscles, also known as smooth muscles, do not have the banded appearance seen in striated muscles.
• They are found in the walls of internal organs such as the stomach, intestines, and blood vessels.
• These muscles are involuntary and are controlled by the autonomic nervous system.
• Cardiac Muscles:
• Cardiac muscles are found only in the heart and have properties of both striated and non-striated muscles.
• They are striated like skeletal muscles but are involuntary like smooth muscles.
• Cardiac muscle cells are branched and connected at intercalated discs, which allow for coordinated contractions.

Shortcut Trick

Apply the successive percentage change formula: x + y + (xy/100).

Here, increase x = +10% and decrease y = −8%.

Net Change = 10 − 8 + [10 × (−8) / 100]

Net Change = 2 − 0.8 = 1.2%

Since the result is positive, it is an increase.

∴ The correct answer is 1.2% increase.

Alternate Method

Let the Initial Population be 100.

⇒ Population after 2020 increase = 100 + (10% of 100) = 110.

⇒ Population after 2021 decrease = 110 − (8% of 110) = 110 − 8.8 = 101.2.

⇒ Net Change = 101.2 − 100 = 1.2.

⇒ Percentage Change = (1.2 / 100) × 100 = 1.2%.

∴ The correct answer is 1.2% increase.

Additional Information

Successive Percentage Formula

For two successive changes of a% and b%, the net effective change is given by (a + b + ab/100)%.

Base Value Concept

In percentage change, the second change is always calculated on the modified value, not the original initial value.

Multiplying Factor

An increase of x% means multiplying by (1 + x/100) and a decrease of y% means multiplying by (1 − y/100).

Shortcut Trick

To find the simplest form, divide both numbers by their Highest Common Factor (HCF).

Check common factors: Both numbers are not even, so 2 is not common. Sum of digits (7+2+2=11, 1+0+8+3=12), so only 1083 is divisible by 3.

Try dividing by primes: 361 × 2 = 722 and 361 × 3 = 1083.

Since 361 is 19², the HCF is 361.

∴ The correct answer is 2 : 3.

Alternate Method

Given: Ratio = 722 : 1083

Formula Used: Simplest Form = (A ÷ HCF) : (B ÷ HCF)

⇒ Finding HCF of 722 and 1083 using Long Division Method:

⇒ 1083 = 722 × 1 + 361

⇒ 722 = 361 × 2 + 0

⇒ Therefore, HCF = 361

⇒ Divide both terms by 361:

⇒ 722 ÷ 361 = 2

⇒ 1083 ÷ 361 = 3

⇒ Simplest Form = 2 : 3

∴ The correct answer is 2 : 3.

Additional Information

Simplest Form of Ratio

A ratio a : b is in its simplest form if the Highest Common Factor (HCF) of a and b is 1.

Division Algorithm for HCF

For any two numbers, HCF can be found by dividing the larger number by the smaller number until the remainder is zero.

Properties of Ratios

Multiplying or dividing both terms of a ratio by the same non-zero constant does not change the value of the ratio.

The logic follows here:

The relationship is based on the product of consecutive integers.

For, 12 : 20

⇒ 12 = 3 × 4

⇒ 20 = 4 × 5

For, 56 : 72

⇒ 56 = 7 × 8

⇒ 72 = 8 × 9

Similarly, 30 : ?

⇒ 30 = 5 × 6

⇒ 42 = 6 × 7

Hence, the correct answer is "Option (4)".