RRB Group D Previous Year Paper (Held on: 30 Sept 2022 Shift 1)

Shortcut Trick

Use the Successive Multiplication method for price change and weight fraud.

Price Ratio (CP : SP) = 25 : 27.

Weight Ratio (Quantity given : Quantity charged) = 800 : 1000 = 4 : 5.

Effective Ratio = (25 × 4) : (27 × 5) = 100 : 135.

Gain% = (135 − 100) ÷ 100 × 100 = 35%.

∴ The correct answer is 35%.

Alternate Method

Given → CP per kg = ₹25, SP per kg = ₹27, True weight = 1000 g, Faulty weight = 800 g. Formulas: Gain% = (Total SP − Total CP) ÷ Total CP × 100 | Total CP = CP × (Actual weight ÷ 1000).

⇒ Cost of 1000 g = ₹25. Therefore, Actual Cost of 800 g = (25 ÷ 1000) × 800 = ₹20.

⇒ The shopkeeper sells 800 g (which cost him ₹20) for the price of 1 kg (₹27).

⇒ Selling Price obtained = ₹27.

⇒ Profit = SP − CP = 27 − 20 = ₹7.

⇒ Gain% = (7 ÷ 20) × 100 = 35%.

∴ The correct answer is 35%.

Additional Information

Dishonest Dealer Concept

When a dealer uses less weight, the Gain% = [Error ÷ (True Value − Error)] × 100 if he sells at cost price.

Effective Profit

If there is a profit on price (P%) and a profit due to weight fraud, the total profit is calculated by compounding the ratios of investment to returns.

Given Statements:

1. All flowers are white.
2. Some flowers are dark.
3. All darks are blue.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some whites are blue - True (Because, those parts of white which are flowers and part of dark, are also the part of is blue).

II. All darks are white - False (Because, only some parts of dark which are flowers, are also part of white, so this can be a possibility but not definite).

So, the only conclusion I follow.

Hence, the correct answer is "Option 4".

The correct answer is India.

Key Points

• India won its maiden Thomas Cup title on 15 May 2022, beating 14-time champion Indonesia 3-0 in the final in Bangkok.
• World championships bronze medallist Lakshya Sen defeated Indonesia's Anthony Sinisuka Ginting 8-21, 21-17, 21-16 in the first men's singles to give India a 1-0 lead.
• India had previously reached the semifinals of the Thomas Cup in 1952, 1955, and 1979.

Additional Information 

• ​The Thomas Cup, sometimes called the World Men's Team Championships, is an international badminton competition among teams representing member nations of the Badminton World Federation (BWF).
• The championships have been conducted every two years since 1982.
• The Uber Cup (first held in 1956–1957) is the world women's team championship.

Calculation:

$\left(\frac{-5}{7}\right)^{-6} \times\left(\frac{-5}{7}\right)^4$

⇒ $\left(\frac{-5}{7}\right)^{-2}$

⇒ $\left(\frac{-7}{5}\right)^{2}$

⇒ 49/25

∴ Option 3 is the correct answer.

The correct answer is Information Technology Act, Right to Information Act, Right to Education Act, Right to Person with Disabilities Act

Key Points

• The correct order is:
• Information Technology Act - 2000
• Right to Information Act - 2005
• Right to Education Act - 2009
• Right of Persons with Disabilities Act - 2016

Additional Information

• Information Technology Act (2000):
• The Information Technology Act, 2000 was one of the earliest significant legislations focusing on e-commerce, cyber laws, and the regulation of electronic transactions in India.
• It was enacted to provide legal recognition to electronic transactions and digital signatures.
• This Act forms the foundation for the legal framework surrounding the digital space in India.
• Right to Information Act (2005):
• The Right to Information Act, 2005 was introduced to ensure transparency and accountability in the functioning of government institutions.
• It empowers citizens to request information from public authorities and holds them accountable for their actions and decisions.
• This Act revolutionized citizen participation in governance.
• Right to Education Act (2009):
• The Right to Education Act, 2009 came into force to provide free and compulsory education to children aged 6-14 years.
• It guarantees the right of children to receive elementary education of a certain standard and promotes the involvement of children in schools.
• This Act was significant in promoting universal access to education.
• Right of Persons with Disabilities Act (2016):
• The Right of Persons with Disabilities Act, 2016 was enacted to ensure equal rights and opportunities for persons with disabilities in various spheres such as education, employment, healthcare, and social participation.
• It replaced the Persons with Disabilities (Equal Opportunities, Protection of Rights and Full Participation) Act, 1995, and broadened the scope of rights for differently-abled individuals.

The correct answer is 1.0 cm

Key Points

• Given values:
• Object size (h₀) = 3.0 cm
• Object distance (u) = -50 cm (negative because the object is on the left side of the lens)
• Focal length (f) = -25 cm (negative for a concave lens)
• Lens formula:
• 1/v = 1/f - 1/u
• Where 'v' is the image distance.
• 1/v = 1/(-25) - 1/(-50)
• 1/v = -1/25 + 1/50
• 1/v = (-2 + 1)/50
• 1/v = -1/50
• v = -50/3 cm = -16.67 cm
• Magnification formula:
• Magnification (M) = v/u = hᵢ/h₀
• Where 'hᵢ' is the image size.
• M = (-50/3) / (-50)
• M = 1/3
• Image size:
• hᵢ = M * h₀
• hᵢ = (1/3) * 3.0 cm
• hᵢ = 1.0 cm
• So, the size of the image formed is 1.0 cm.

Given Statement: S > W = T <  L < O ≤ R

Now,

Conclusions:

1. W < R → True (W = T <  L < O ≤ R It gives W < R)
2. S > L → False (S > W = T <  L No relation can be established between S and L)
3. W < O → True (W = T <  L < O It gives W < O)
4. T < S → True (S > W = T It gives S > T)

Here, Conclusion 2 NOT follows.

Hence, the correct answer is "Option 3".

The correct answer is Sodium chloride

Key Points

• Sodium chloride can conduct electricity, but glucose, kerosene, and alcohol cannot.
• Sodium chloride  is an ionic compound that conducts electricity when it's molten or dissolved in water.
• When dissolved in water, the sodium chloride dissociates into positively charged sodium ions and negatively charged chloride ions.
• These ions move freely in the solution, carrying a charge and allowing electricity to flow

Additional Information

• Ionic compounds have high melting and boiling points and conduct electricity in a molten state.
• Such a bond forms when the valence (outermost) electrons of one atom are transferred permanently to another atom. The atom that loses the electrons becomes a positively charged ion (cation), while the one that gains them becomes a negatively charged ion (anion).

The logic followed here is:

Given Sequence: F G _ C _ I Q _ S F _ S C A I Q _ S F _ S C _ I _ P S

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

Option 1) SAPGBGAP → F G S C A I Q P S / F G S C A I Q B S / F G S C A I P P S

Option 2) SAPGPGAQ → F G S C A I Q P S / F G S C A I Q P S / F G S C A I Q P S

Here, 'FGSCAIQPS' followed a pattern.

Option 3) SAPGPGBQ → F G S C A I Q P S / F G S C A I Q P S / F G S C B I Q P S

Option 4) SAPFBFAP → F G S C A I Q P S / F F S C A I Q B S / F F S C A I P P S

Hence, the correct answer is "Option 2".

The correct answer is 1998.

Key Points

• Maulana Azad National Urdu University (MANUU) was established by an Act of Parliament in 1998.
• It is a central university located in Hyderabad, Telangana.
• It was named after Maulana Abul Kalam Azad, who was a freedom fighter, an educationist, and the first Education Minister of independent India.
• The university is known for promoting Urdu language and literature.
• It has a dedicated Department of Urdu, which offers courses in Urdu language, literature, and culture.
• It has campuses in Hyderabad, Lucknow, and Srinagar.
• It also has centers in various cities across India.

Additional InformationMaulana Abul Kalam Azad:

• He was the nation's first minister of education from 1948 to 1958.
• He led the Khilafat movement from the front.
• He chose the pen name "Azad," which means "freedom," in order to distance himself from dogmatic religious beliefs.
• He fought for children's right to free education until the age of fourteen.
• He was also a pioneer in the establishment of India's higher education board, the University Grants Commission.

The correct answer is Sodium

Key Points

• Sodium reacts with chlorine to form sodium chloride (NaCl), which has a high melting point and is soluble in water.
• This reaction releases a large amount of heat and forms a stable ionic compound.
• Sodium chloride (NaCl) is highly soluble in water, which aligns with the compound described in the question.
• Sodium chloride has a relatively high melting point (~801°C), which matches the description of the compound having a high melting point.

Additional Information

• The melting point of a substance is the temperature at which it changes from a solid to a liquid.
• At this temperature, the solid and liquid phases of the substance exist in equilibrium
• The melting point of a substance depends on pressure and is usually specified at a standard pressure.
• During the melting process, the substance absorbs heat and the temperature remains constant.
• The melting point of a pure substance is a single temperature, but the melting point of a solution of two or more components is usually a range of temperatures.
• The melting point of a substance is a characteristic property of solid crystalline substances.
• The melting point of a substance is used to evaluate structural changes in organic compounds.

The correct answer is These elements belong to the second period of the modern periodic table.

• Atomic numbers 11 to 18 correspond to the elements:
• 11 - Sodium (Na), 12 - Magnesium (Mg), 13 - Aluminium (Al), 14 - Silicon (Si), 15 - Phosphorus (P), 16 - Sulfur (S), 17 - Chlorine (Cl), 18 - Argon (Ar).
• These elements all belong to the third period of the periodic table because their outermost electrons occupy the M shell (n=3).
• Hence The elements with atomic numbers 11 to 18 belong to the third period, not the second.
• The Modern periodic law & table was invented by Henry Moseley in 1913.
• The first who was able to arrange all the known elements was Mendeleev, he gave the law called the Mendeleev's periodic law.
• Dobereiner grouped the elements into triads.
• Newlands gave the law of octaves.
• Modern Periodic Table: 
• The defects of the periodic table of  Mendeleev were sorting out by Henry Moseley who invented the modern periodic law in 1913.
• The law of modern table states that - '' according to the increasing order of their atomic numbers if the elements are arranged, then the element's physical & chemical properties are repeated after regular intervals.
• Salient Features of the Modern Periodic Table: 
• The element's properties are the functions that are periodical according to their atomic numbers.
• On the basis of the Modern table, Scientist Bohr invented a long form of the periodic table that was created by Warner& Rang.
• The periodic table consists of 18 groups & 7 periods.
• Division structure of elements with respective periods: 
• According to the increasing order of their atomic numbers if the elements are arranged, then the element's physical & chemical properties are repeated after 2, 8, 18, and 32 intervals.
• There are 2 elements in the first period, 8 elements in second and third periods each respectively, 18 elements fourth and fifth periods each respectively, 32 elements in the sixth period, and 19 elements in the seventh period till now.
• Division structure of elements with respective periods( in Table format): 

We follow the given table and code the given combination:

Given combination: %$7#8

Here, Only the first condition followed in the given combination, none of the other conditions apply.

So, the first and the last elements are to be interchanged.

So, the code for '%$7#8' is → 'SPUHU'.

Hence, the correct answer is 'Option (4)'$.

The correct answer is A, B and D

Key Points

• The correct group of fundamental rights provided by the Constitution is:
• A. Right to equality
• B. Right to freedom of religion
• D. Right to constitutional remedies
• These rights are fundamental to safeguarding individual liberty and equality in India.

Additional Information

• A. Right to Equality
• This is a fundamental right guaranteed under Articles 14 to 18 of the Constitution. It includes:
• Equality before the law (Article 14).
• Prohibition of discrimination on grounds of religion, race, caste, sex, or place of birth (Article 15).
• Equality of opportunity in public employment (Article 16).
• Abolition of untouchability (Article 17).
• Abolition of titles (Article 18).
• B. Right to Freedom of Religion
• Guaranteed under Articles 25 to 28, this fundamental right ensures:
• Freedom of conscience and the right to freely profess, practice, and propagate religion (Article 25).
• Freedom to manage religious affairs (Article 26).
• Freedom from payment of taxes for promotion of any religion (Article 27).
• Freedom in attending religious instruction in educational institutions (Article 28).
• Right to Constitutional Remedies
• This is a crucial fundamental right under Article 32.
• It empowers individuals to approach the Supreme Court or High Courts to enforce other fundamental rights if they are violated.
• Dr. B.R. Ambedkar described this as the "heart and soul" of the Constitution.
• Remedies include writs such as habeas corpus, mandamus, prohibition, certiorari, and quo warranto.

We follow the given table and code the given combination:

Given combination: ψ62%85

Here, Only the first condition followed in the given combination, none of the other conditions apply.

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

So, the code for 'ψ62%85' is → 'SNMRKT'.

Hence, the correct answer is 'Option (2)'$.

The correct answer is Nylon

Key Points

• Nylon is non-biodegradable, while cotton and wool are biodegradable
• Nylon
• ​A synthetic fiber that is non-biodegradable and cannot be broken down.
• Synthetic products are usually non-biodegradable because they are man-made.
• Washing machines can release microplastics from nylon into the environment.

Additional Information

Shortcut Trick

Apply the divisibility rule of 9: A number is divisible by 9 if the sum of its digits is divisible by 9.

Check Option (2): 3132 → 3 + 1 + 3 + 2 = 9.

Since 9 is divisible by 9, the number 3132 is divisible by 9.

∴ The correct answer is 3132.

Alternate Method

Given: Four numbers to check for divisibility by 9.

Rule: Sum of digits must be a multiple of 9.

⇒ Option (1): 2 + 3 + 5 + 2 = 12 (Not divisible by 9)

⇒ Option (2): 3 + 1 + 3 + 2 = 9 (Divisible by 9)

⇒ Option (3): 2 + 1 + 2 + 1 = 6 (Not divisible by 9)

⇒ Option (4): 1 + 0 + 9 + 9 = 19 (Not divisible by 9)

⇒ Only 3132 satisfies the condition.

∴ The correct answer is 3132.

Additional Information

Divisibility by 3

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

Divisibility by 11

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

Divisibility by 6

The number must be even and the sum of its digits must be divisible by 3.

The correct answer is Kilowatt hour.

Key Points

• Kilowatt-hour
• Kilowatt-hour is the commercial unit of electric energy.
• kWh is a common unit of electrical energy (kilowatt-hour). It is defined as the amount of energy utilised for an hour by a 1kW appliance.
• The kilowatt-hour (abbreviated kWh) is a unit of energy that represents the energy used to generate one kilowatt of power for one hour.
• It is used to measure the amount of electricity consumed in homes, industries, and businesses.

Additional Information

• Although it is not a formal standard unit in any system, the kilowatt-hour is frequently employed in electrical applications.
• The unit of electrical energy is the kWh, which is the same for household and commercial use.
• Commercial units are charged at a separate rate than household units, which is higher.
• It is mostly used to reduce power usage in factories and other commercial settings.

Shortcut Trick

Ratio of Length to Width is 3 : 1.

Sum of ratio parts = 3 + 1 = 4 units (representing half of the perimeter).

8 units (Full Perimeter) = 64 cm.

1 unit (Width) = 64 ÷ 8 = 8 cm.

∴ The correct answer is 8 cm.

Alternate Method

Given:

Perimeter of Rectangle = 64 cm

Width (W) = 1/3 × Length (L)

Formula Used:

Perimeter = 2 × (Length + Width)

Calculations:

⇒ Let Length (L) = 3x and Width (W) = x

⇒ Perimeter = 2 × (3x + x) = 64

⇒ 2 × 4x = 64

⇒ 8x = 64

⇒ x = 64 ÷ 8 = 8

⇒ Width = x = 8 cm

∴ The correct answer is 8 cm.

Additional Information

Area of Rectangle

The total space occupied by the rectangle is given by Area = Length × Width.

Diagonal of Rectangle

The distance between opposite corners is d = √(L² + W²).

Properties of Rectangle

Opposite sides are equal and parallel, and each interior angle is exactly 90°.

Given: Seven boxes E, F, G, H, I, J and k are kept one over the other but not necessarily in the same order.

1. Only one box is kept above F.

2. Only three boxes kept between F and J.

3. K is kept immediately below of J.

4. Neither G nor I is kept at the top.

5. Only H is kept between G and I.

So, 'Two' are kept between H and K.

Hence, the correct answer is "Option 4".

Given: P, Q, R, S and T live on five 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 5 .

1) P lives on an odd numbered floor.

2) P lives immediately below T and immediately above S.

3. R is not on the lowermost floor.

So, 'T' lives on floor number 4.

Hence, the correct answer is "Option 4".

The correct answer is It is called upper house of parliament and it never dissolves.

Key Points

• Rajya Sabha:
• Rajya Sabha or the ‘Council of States’ is the second chamber of the Indian parliament, which traces its origin to the Montagu-Chelmsford Reforms, 1919.
• Rajya Sabha as the second chamber of the parliament intended to play certain roles as a permanent house.
• It never dissolves like Lok sabha.
• It is called upper house of parliament and it never dissolves.
• One-third of its members retire every two years, revisionary house (reconsidering bills passed by the Lok Sabha), and offers a degree of continuity in the underlying policies of laws passed by parliament. .
• Its member shall not be less than 30 years of age.

Additional Information

• Representing the Vulnerable Sections:
• Women, religious, ethnic, and linguistic minority groups are not adequately represented in the Lok Sabha (due to first past the post-election system).
• An indirect form of election (through propositional representation) to the Rajya Sabha, therefore, would give them a chance to get involved in the nation’s law-making process.
• Thus, Rajya Sabha can make a place for people who may not be able to win a popular mandate.
• Special Powers of Rajya Sabha:
• The Upper House also has some special powers, such as:
• Power to transfer a subject from the State List to Union List for a specified period (Article 249).
• To create additional All-India Services (Article 312).
• To endorse Emergency under Article 352 for a limited period when the Lok Sabha remains dissolved.

The correct answer is the Council of Scientific and Industrial Research (CSIR)

Key Points

• The Shanti Swarup Bhatnagar Prize for Science and Technology is awarded annually by the Council of Scientific and Industrial Research (CSIR).
• Dr. Shanti Swarup Bhatnagar, is one of the most prestigious science awards in India.
• The award is given to scientists below the age of 45.
• It honours exceptional research contributions made in India during the last five years.

Additional Information

The correct answer is Ammonia

Key Points

• Aquatic animals like fish excrete waste in the form of ammonia.
• Ammonia is a nitrogenous waste product that is excreted in a gaseous form
• Ammonia is a toxic waste product that is easily soluble in water.
• Aquatic animals excrete ammonia through their gills or across their body surface.
• Animals that excrete ammonia are called ammonotelic.

Additional Information

• Urea
• A nitrogenous waste product that's created when the liver converts ammonia.
• Urea is less toxic than ammonia and is eliminated in urine.
• Uric acid
• A nitrogenous waste product that's created when the body breaks down purines.
• Uric acid is found in blood and urine.
• High levels of uric acid can cause gout.
• Sweat salts
• Electrolytes like sodium, chloride, potassium, magnesium, and calcium that are found in sweat.
• Sweat is mostly water, but also contains salts.

The correct answer is Mayor is the head of the Municipal Corporation.

Key Points

• The Mayor is the ceremonial and administrative head of the Municipal Corporation
• He represents the city and presides over corporation meetings.
• The Mayor is the first citizen of the city.

Additional Information

• The number of member councilors in the municipal corporation varies from 40 to 85.
• Mayor and Councilor are elected directly.
• The number of Municipal Corporation is 16 in Madhya Pradesh.
• The Mayor in Council is the main committee of the Municipal Corporation.
• The Mayor of this committee is the ex-officio chairman.
• The Municipal Council consists of ex-officio members of the Lok Sabha Rajya Sabha, six expert members are appointed by the Governor.
• Mayors are usually elected by the elected members of the Municipal Corporation or directly by the people, depending on the rules of the respective state.
• In some states, the Mayor's tenure is one year, while in others, it can be five years.

According to the given Venn diagram:

The shaded area shows the "the number of sour tasting yellow fruits".

So, the total number of 'the number of sour tasting yellow fruits' is 2.

Hence, the correct answer is "Option 2".

The correct answer is ₹2.7 lakh crore

Key Points

• India's GDP in 1947 was ₹2.7 lakh crore.
• some other economic facts about India on the eve of independence:
• Low growth
• India's economy grew very little from 1900 to 1947, with national income increasing by 0.4% per year and per capita income increasing by 0.1% per year.
• Low share of global GDP
• India's GDP was 16% of the global GDP in 1820, but by 1947 it had fallen to 4%.
• Agriculture-based economy
• India's economy was 95% dependent on agriculture, and 85% of the population lived in villages.
• Poor economic condition
• India's economy was in poor condition, with low employment rates, poverty, and a lack of opportunities.
• Exploitation
• The British exploited India's economy, rural areas, manufacturing, and other sectors.
• Poor agricultural practices
• The British did not use proper technologies, fertilizers, or irrigation equipment for agriculture. ​

Additional Information

• GDP of India​
• According to the Press Information Bureau (PIB), here is some recent data on India's GDP: 
• 2024-25
• Nominal GDP is estimated to be ₹77.31 lakh crore, a 9.7% increase from Q1 of 2023-24. Real GVA is estimated to be ₹40.73 lakh crore, a 6.8% increase from 2023-24.
• India's real GDP is projected to grow between 6.5–7%. The IMF has upgraded its GDP forecast to 7% for FY24-25.
• 2023-24
• Real GDP is estimated to be ₹173.82 lakh crore, an 8.2% increase from 2022-23. Nominal GDP is estimated to be ₹295.36 lakh crore, a 9.6% increase from 2022-23.
• The Central Statistics Office (CSO) releases six estimates of India's annual GDP over a period of two years and 10 months.

The correct answer is Viktor Axelsen.

Key Points 

• Viktor Axelsen won the All England Open Badminton Championship Men’s Singles 2020 title.
• The championship was held in Birmingham, England.
• It was a part of the All England Open championships, which had been held since 1899.
• In the women's category,  Tai Tzu-Ying won the championship.
• Viktor Axelsen is a Danish badminton player. He is the 2017 World champion and the 2020 Olympic champion.
• He won the 2010 World Junior Championships, beating South Korea's Kang Ji-Wook in the final to become the first-ever European player to hold the title.

Additional Information

• Lakshya Sen
• ​Lakshya Sen  is an Indian badminton player.
• He's a former World Junior No. 1. Sen is a bronze medalist at the World Championships, a gold medalist at the Thomas Cup, a silver medalist at the Asian Games and a gold and silver medalist at the Commonwealth Games
• He has also won bronze medals at the Asia Team and Asia Mixed Team Championships. Sen won the Canada Open and was the runner-up at the All England Open.
• At the junior level, he has won a gold and silver medal at the Youth Olympic Games, a bronze medal at World Junior Championships and a gold and bronze medal at Asia Junior Championships.
• Kidambi Srikanth​
• Kidambi Srikanth is an Indian badminton player.
• He was ranked no. 1 player in men's singles in the world in April 2018
• He was conferred with Padma Shri award in 2018
• He was also conferred with Arjuna award in 2015.

The correct answer is a - 3, b - 4, c - 2, d - 1

Key Points

Hence the correct matching is a - 3, b - 4, c - 2, d - 1

Additional Information

• 1.Ahmedabad → Sabarmati
• Ahmedabad, a major city in Gujarat, is located on the banks of the Sabarmati River.
• The Sabarmati Riverfront project in Ahmedabad is a notable development along this river.
• 2. Kolkata → Hooghly
• Kolkata, the capital city of West Bengal, lies along the Hooghly River, which is a distributary of the Ganges.
• The iconic Howrah Bridge and Vidyasagar Setu span this river, making it integral to the city's identity.
• 3. Guwahati → Brahmaputra
• Guwahati, the largest city in Assam, is situated on the southern banks of the mighty Brahmaputra River.
• This river is one of the major rivers in India and is central to the culture and economy of Assam.
• 4. Nasik → Godavari
• Nasik, a city in Maharashtra, is located on the banks of the Godavari River, the second-longest river in India.
• It is also a significant pilgrimage site, known for hosting the Kumbh Mela on the riverbanks.

Given:

2.33 - 4.12 + 6.13 × 11.3 = ? 

Concept used:

Calculation:

2.33 - 4.12 + 6.13 × 11.3 = ? 

⇒ 2 - 4 + 6 × 11 = ? 

⇒ -2 + 66

⇒ 64

The closest approximate value is 64.

Given:

3.013 ÷ 2.99 × 6.01 = ?

Concept used:

Calculation:

3.013 ÷ 2.99 × 6.01 = ?

⇒ 3³ ÷ 3 × 6

⇒ 3² × 6

⇒ 9 × 6

⇒ 54

The closest approximate value is 54.

Given:

 216${\frac{2}{n}}$ = 36.

Calculation:

 216${\frac{2}{n}}$ = 36.

⇒  6$3\times {\frac{2}{n}}$ = 6²

⇒ 6/n = 2

⇒ n = 3

∴ Option 4 is the correct answer.

The correct answer is the direction of current

Key Points

• The polarity of an electromagnet can be reversed by changing the direction of the electric current passing through it.
• The strength of an electromagnet can be increased by increasing the number of turns of wire in the coil or by increasing the current in the coil.
• The direction of the current flowing through the electromagnet determines its polarity.
• Reversing the direction of the current reverses the polarity of the electromagnet.

Additional Information

• An electromagnet is a temporary magnet that should ideally have the property to behave as a magnet when current passes through it and lose magnetism as soon as the current is stopped.
• Soft iron is generally used for making electromagnets because it has high magnetic permeability, i.e. it can easily gain magnetic properties when current is passed around the core and quickly lose when the current is stopped.
• The soft iron inside the coil makes the magnetic field stronger because it becomes a magnet itself when the current is flowing

Calculation:

Expense of a family on fuel = 7%

Expense of a family on miscellaneous = 12%

Expense of a family on investment = 11%

Total expense = 7 + 12 + 11 = 30%

Central angle for total expenditure on fuel, miscellaneous and investment = 30/100 × 360 = 108° 

∴ Option 2 is the correct answer.

Given number: 705.0, 7.005, 7.500, 70.50, 7050, 7.050, 75

After arranging in ascending order:

7.005, 7.050, 7.500, 70.50, 75, 705.0, 7050

Hence, the correct answer is 'Option 3'.

The correct answer is Short-run Production

Key Points

• The production cycle in which at least one factor of production remains constant is called the short run.
• The law of returns to a factor explains such a production function
• A short-run production function refers to that period of time, in which the installation of new plant and machinery to increase the production level is not possible.
• The production function can be described as the operational relationship between the inputs and outputs, in the sense that the maximum amount of finished goods that can be produced with the given factors of production, under a particular state of technical knowledge.
• There are two kinds of the production function, short run production function and long run production function.
• The short run production function is one in which at least is one factor of production is thought to be fixed in supply, i.e. it cannot be increased or decreased, and the rest of the factors are variable in nature.

Additional Information

• Variable long term production
• It is a production process where all inputs are variable, meaning they can be adjusted.
• This allows companies to optimize their production process and maximize output.
• Long run production
• ​The long-run production function shows the most efficient way to produce any level of output.
• The long-run average total cost curve is also the long-run production cost curve.
• constant long term production
• ​Constant long-term production is a situation where a firm's output remains the same over a long period of time.
• This can happen when a firm's production function is such that it experiences constant returns to scale.

Shortcut Trick

Outer surface area of an open cuboid = Lateral Surface Area + Base Area.

Area = 2h(l + b) + lb = 2 × 1.5 × (4 + 3.6) + (4 × 3.6).

Area = 3 × 7.6 + 14.4 = 22.8 + 14.4 = 37.2 m².

Cost = 37.2 × 55 = ₹2046.

∴ The correct answer is ₹2,046.

Alternate Method

Given:

Length (l) = 4 m, Breadth (b) = 3.6 m, Depth (h) = 1.5 m

Rate of painting = ₹55 per m²

Calculations:

⇒ Surface area to be painted = Area of 4 walls + Area of base

⇒ Surface area = [2 × h × (l + b)] + [l × b]

⇒ Surface area = [2 × 1.5 × (4 + 3.6)] + [4 × 3.6]

⇒ Surface area = [3 × 7.6] + 14.4

⇒ Surface area = 22.8 + 14.4 = 37.2 m²

⇒ Total Cost = Total Area × Rate

⇒ Total Cost = 37.2 × 55 = ₹2046

∴ The correct answer is ₹2,046.

Additional Information

Total Surface Area of Cuboid

The total surface area of a closed cuboid is 2(lb + bh + hl).

Lateral Surface Area (Area of 4 walls)

The area of the vertical faces of a cuboid is 2h(l + b).

Volume of Cuboid

The capacity or space occupied by a cuboid is given by Length × Breadth × Height.

Shortcut Trick

Total Surface Area (TSA) of a cylinder is given by 2πr(r + h).

Given radius (r) = 2 cm and height (h) = 10 cm.

TSA = 2 × π × 2 × (2 + 10)

TSA = 4 × π × 12 = 48π cm².

∴ The correct answer is 48π cm².

Alternate Method

Given:

Radius (r) of the cylinder = 2 cm

Height (h) of the cylinder = 10 cm

Formula Used:

Total Surface Area = Curved Surface Area + 2 × Area of Base

Total Surface Area = 2πrh + 2πr² = 2πr(h + r)

Calculations:

⇒ Total Surface Area = 2 × π × 2 × (10 + 2)

⇒ Total Surface Area = 4π × 12

⇒ Total Surface Area = 48π cm²

∴ The correct answer is 48π cm².

Additional Information

Curved Surface Area of Cylinder

The area of the side surface excluding the top and bottom bases is given by 2πrh.

Volume of Cylinder

The total space occupied by the cylinder is calculated using the formula V = πr²h.

Area of Circular Base

Each base of a right circular cylinder is a circle with an area equal to πr².

Calculation:

The average ticket sold on Monday, Tuesday and Wednesday was 31.

The tickets sold on Monday were 28.

The tickets sold on Tuesday were 24.

Total tickets = 31 × 3 = 93

Tickets sold on Wednesday = 93 - (28 + 24) = 41.

Tickets sold on Wednesday were 41.

Shortcut Trick

Age difference remains constant throughout life.

5 years ago, Ratio of ages (Arun : Kiran) = 5 : 1

Difference in ratio parts = 5 − 1 = 4 units → 20 years

1 unit = 5 years ⇒ Arun's age 5 years ago = 5 × 5 = 25 years

Present age of Arun = 25 + 5 = 30 years.

∴ The correct answer is 30 years.

Alternate Method

Let the present age of Kiran be x years.

Since Arun is 20 years elder, Arun's present age = x + 20 years.

According to the problem, 5 years ago:

⇒ (Arun − 5) = 5 × (Kiran − 5)

⇒ (x + 20 − 5) = 5(x − 5)

⇒ x + 15 = 5x − 25

⇒ 4x = 40

⇒ x = 10 years (Kiran's age)

⇒ Arun's present age = x + 20 = 10 + 20 = 30 years.

∴ The correct answer is 30 years.

Additional Information

Constant Age Difference

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

Ratio of Ages

If the age ratio is given for different time periods, convert them to a common scale using the constant difference property.

Linear Equations in Ages

For 'n' years ago, subtract 'n' from present ages; for 'n' years hence, add 'n' to present ages.

Given statements:  P < Q ≤ R < S > T ≥ U > V

Now, 

Conclusions:

1. T > V → True (T ≥ U > V it gives T > V)

2. P < R → True (P < Q ≤ R it gives P < R)

3. S ≥ V → Not True (S > T ≥ U > V it give S > V, not S ≥ V)

4. Q < S → True (Q ≤ R < S it gives Q < S)

Here, Conclusion 3 follows.

Hence, the correct answer is "Option 1".

Given: Six boxes M, N, O, P, Q, and R are kept one above the other.

1) Only 2 boxes are kept below M.

__ > __ > __ > M > __ > __

2) Only one box is kept above Q.

__ > Q > __ > M > __ > __

3) O is kept at any of the positions above R but not at the topmost position.

4) R is not kept at the bottommost position.

__ > Q > O > M > R > __

5) N is kept at any of the positions below Q.

__ > Q > O > M > R > N

So, P will be kept at the topmost position.

P > Q > O > M > R > N

Hence, the correct answer is "Option 4".

The correct answer is un-deviated

Key Points

• The emergent ray from the optical center of a lens will be un-deviated.
• This means that the ray will pass through the lens without changing direction.
• The optical center is the center of the lens.
• A ray of light passing through the optical center of a lens will emerge without any deviation after refraction.
• This means that the path of the ray will not change

Additional Information CONCEPT:

• All the cases for the ray of light emanating from the source and refracting through a convex lens are shown in the table:

The correct answer is 11

Key Points

• In August 2022, 11 districts of West Bengal were included in the 'Combating Child Trafficking' campaign.
• These districts were chosen based on their higher prevalence of child trafficking cases and other socio-economic factors that contributed to the vulnerability of children to trafficking.
• The campaign was a collaborative effort involving multiple stakeholders, including government agencies, NGOs, and law enforcement, to strengthen child protection measures and ensure the safety and well-being of children.
• The 'Combating Child Trafficking' campaign in West Bengal, launched in August 2022,
• It aimed at addressing and preventing child trafficking in specific vulnerable districts.

Additional Information The 11 districts included were:

1. South 24 Parganas
2. East Midnapore
3. West Midnapore
4. North 24 Parganas
5. Cooch Behar
6. Darjeeling
7. Jalpaiguri
8. Malda
9. Murshidabad
10. Birbhum
11. Bankura

These districts were targeted to implement strategies like community engagement, better surveillance, legal interventions, and coordination among different stakeholders to combat child trafficking effectively.

The correct answer is Na2SO4 + BaCl2 → BaSO4 + 2NaCl

Key Points

• The reaction Na2SO4 (aq) + BaCl2 → BaSO4 (s) + 2 NaCl (aq) + 2 NaCl (aq) is the example of Double displacement reaction.
• The reaction between Na2SO4 + BaCl2  is an endothermic reaction.
• When barium chloride (BaCl2) and sodium sulfate (Na2SO4), which leads to the formation of sodium chloride and barium sulphate.
• As a result of the above-given reaction, a white colour precipitate is formed due to the formation of barium sulphate.
• Na2SO4 (aq) + BaCl2 → BaSO4 (s) + 2 NaCl (aq) + 2 NaCl (aq)
• As the white precipitate formed is cool, the given reaction is inferred to be an endothermic reaction.
• This reaction is also an example of a double displacement reaction as two elements in the reactants are displacing each other.

Additional Information Other types

• Addition reaction :
• An addition reaction occurs when two or more reactants combine to form a product without the loss of any atoms present in the reactants.
• Addition reaction is common in compounds that have unsaturated C-C bonds, like double (alkene) and triple (alkyne) bonds.
• The weaker π bond is converted into two new stronger bonds.
• Reduction reaction :
• Redox is a type of chemical reaction in which the oxidation states of atoms are changed.
• Redox reactions are characterized by the actual or formal transfer of electrons between chemical species, most often with one species undergoing oxidation while another species undergoes reduction.
• Decomposition reaction :
• A decomposition reaction is a reaction in which a compound breaks down into two or simpler substances.
• The general form of a decomposition reaction is:
• AB→A+B. Most decomposition reactions require an input of energy in the form of heat, light, or electricity.

The logic followed here is:

So, '84' is the missing number in the given series.

Hence, the correct answer is "Option 1".

Given series:

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

Condition to be checked:

Odd Number → Even Number → Odd Number

(Left) 9 2 3 5 7 8 6 3 2 1 5 6 7 9 4 3 6 3 5 8 2 (Right)

Thus, there are five such patterns that satisfy the given conditions: (9 2 3), (3 2 1), (5 6 7), (9 4 3) and (3 6 3)

Hence, the correct answer is "Option (3)".

Mistake Points

Immediately preceded by means to come just before.

Immediately followed by means to come just after.

Logic: (1^st numbers × 3) ÷ 5 = 2^nd number.

Now,

For, 25 ∶ 15

⇒ (25 × 3) ÷ 5

⇒ 75 ÷ 5 = 15

15 = Second Number.

Similarly, for 15 ∶ x

⇒ (15 × 3) ÷ 5

⇒ 45 ÷ 5 = 9.

⇒ x = 9.

So, 9 will be the value of x.

Hence, the correct answer is "Option 1".

Shortcut Trick

Difference in ages is constant: 48 − 32 = 16 years.

Ratio was 5 : 3, difference in ratio parts = 5 − 3 = 2 units.

2 units = 16 years ⇒ 1 unit = 8 years.

Roja age then: 3 units × 8 = 24 years.

Years ago = 32 − 24 = 8 years.

∴ The correct answer is 8 years.

Alternate Method

Given: Current age of Hema = 48 years, Current age of Roja = 32 years.

Let x years ago the ratio was 5 : 3.

⇒ (48 − x) / (32 − x) = 5 / 3

⇒ 3 × (48 − x) = 5 × (32 − x)

⇒ 144 − 3x = 160 − 5x

⇒ 5x − 3x = 160 − 144

⇒ 2x = 16

⇒ x = 8 years

∴ The correct answer is 8 years.

Additional Information

Age Difference Property

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

Ratio Balancing

To solve age ratios quickly, ensure the numerical difference between ratio parts matches the actual age difference.

Proportion Rule

If a/b = c/d, then cross-multiplication (ad = bc) is the standard algebraic way to find the unknown variable.

Given word: 'REASON'

After changing each vowel to the letter following it in the English alphabetical order and each consonant to the letter preceding it in the English alphabetical order: 

Now, after arranged in alphabetical order:

So 'P' will be fourth from the left.

Hence, the correct answer is "Option 2".

Given: Six students are sitting around a circular table facing the centre.

1. Taran is an immediate neighbour of Karam and Viraj. 2. Param is sitting second to the right of Taran. 3. Sunny is an immediate neighbour of Param and Manjit. 4. Karam is sitting second to the right of Sunny.

Here, Param is the immediate neighbour of Sunny and Viraj.

Hence, the correct answer is "Option 1".

The logic followed here is:

Thus, '4' will replace the question mark in the given series.

Hence, the correct answer is "Option 2".

Statements:

1. Some classical dancers are students.
2. Rama is a classical dancer.
3. Sohan is a student of class X.

Conclusion:

(I) Sohan is not a classical dancer - Doesn't follow (Because there are some students who are classical dancers but it is not clearly mentioned that the students are of X class).

(II) Rama is a student - Doesn't follow (Because it is clearly mentioned in the given statements that rama is a classical dancer but it is not definite that whether rama is a student or not).

Thus, none of the conclusions definitely follow.

Hence, the correct answer is "Option 3".

The correct answer is 4.0m

Key Points

• The radius of curvature (R) of a spherical mirror is related to its focal length (f) by the following equation:
• R = 2f
• In this case, the focal length (f) of the convex mirror is given as 2 m.
• Therefore, the radius of curvature (R) is:
• R = 2 * 2 m = 4 m
• So, the correct answer is 4.0 m.

Important Points

• Spherical Mirrors and Their Properties
• Concave Mirror: A concave mirror curves inwards, like the inside of a spoon. It can focus light rays to a single point.
• Convex Mirror: A convex mirror curves outwards, like the back of a spoon. It diverges light rays, making objects appear smaller and providing a wider field of view.
• Key Terms
• Focal Length (f): The distance between the mirror's surface and its focal point (the point where parallel light rays converge after reflection in a concave mirror, or appear to diverge from in a convex mirror).
• Radius of Curvature (R): The radius of the sphere from which the mirror is a part. It's the distance between the mirror's surface and the center of curvature (the center of that sphere).

The correct asnwer is By dialysis.

The correct answer is MRI scan

Key Points

• The process of obtaining images of different body parts by using a weak magnetic field produced inside the body is called Magnetic Resonance Imaging (MRI).
• MRI is a non-invasive medical imaging technique that uses radio waves and a strong magnetic field to create images of the body's internal structures.
• MRI scanners are large, tube-shaped magnets.
• MRI is often used to diagnose disease, plan treatment, and monitor the effectiveness of treatment.
• MRI is especially useful for imaging the brain, spinal cord, heart, blood vessels, bones, joints, and soft tissues.

Additional Information

• Ultrasound scan
• ​An ultrasound scan, also known as a sonogram, is a non-invasive procedure that uses high-frequency sound waves to create images of the inside of the body.
• It can be used to diagnose conditions, monitor fetal development, or guide surgeons during certain procedures.
• PET scan
• ​A PET (positron emission tomography) scan is a medical imaging procedure that uses a radioactive tracer to create 3D images of the inside of the body.
• PET scans involve radiation exposure.
• The amount of radiation is usually less than that received from natural sources like the sun.
• However, pregnant women shouldn't undergo a PET scan unless necessary.
• CT Scan
• ​A CT scan, or computed tomography scan, is a medical imaging procedure that uses X-rays and a computer to create detailed pictures of the inside of the body.
• CT scans can be used to diagnose disease, plan treatment, and evaluate how well treatment is working.

The correct answer is Odisha

Key Points

• The Mahanadi River is a major river in East Central India, predominantly flowing through the state of Odisha.
• It covers a total drainage area of 141,600 square kilometres and has a course of 858 kilometres.
• It is the third largest river in terms of water potential and drainage area in the Indian peninsula after the Godavari and the Krishna rivers.
• In Odisha, it's the largest river and holds great economic significance for the state as it supports agriculture, industry, and the daily lives of people.
• Some of the most significant rivers in the region include the Seonath, Hasdeo, Mand, Jonk, Telen, and Ib.
• The Mahanadi river system is known for the Hirakud Dam.
• This dam is one of the longest in the world and serves a critical purpose in flood control and providing irrigation water.

Additional Information

Given: 32 * 16 * 8 * 2 * 3 * 5 * 5

Checking the given options:

Option 1) -, +, ÷, =, ×, +

⇒ 32 - 16 + 8 ÷ 2 = 3 × 5 + 5

⇒ 32 - 16 + 4 = 15 + 5

⇒ 36 - 16 = 20

⇒ 20 = 20.

L.H.S = R.H.S

Here, the equation is satisfied.

Option 2) +, -, ÷, ×, =, +

⇒ 32 + 16 - 8 ÷ 2 × 3 = 5 + 5

⇒ 32 + 16 - 12 = 10

⇒ 48 - 12 = 10

⇒ 36 ≠ 10.

Here, the equation is not satisfied.

Option 3) -, +, ÷, ×, =, +

⇒ 32 - 16 + 8 ÷ 2 × 3 = 5 + 5

⇒ 32 - 16 + 12 = 10

⇒ 44 - 16 = 10

⇒ 28 ≠ 10.

Here, the equation is not satisfied.

Option 4) -, +, ×, =, ÷, +

⇒ 32 - 16 + 8 × 2 = 3 ÷ 5 + 5

⇒ 32 - 16 + 16 = 3 ÷ 5 + 5

⇒ 48 - 16 = 0.6 + 5

⇒ 32 ≠ 5.6.

Here, the equation is not satisfied.

Hence, the correct answer is "Option 1".

The correct answer is 17^th.

Key Points

• The Halogens are the elements belonging to Group 17 in the periodic table.
• A periodic table is an arrangement of elements based on their atomic numbers and chemical properties.
• It is divided into 18 groups and 7 periods running vertically and horizontally respectively.
• The periodic table accommodates a discrete combination of metal, non-metals, and metalloids.
• The elements in the periodic table are arranged horizontally in ascending order of their atomic numbers known as periods.
• Vertically the elements having identical chemical properties are clubbed together known as groups.
• The 18 groups are also known as columns and the 7 periods are also known as the rows.

Additional InformationPeriods:

• Elements are arranged in increasing the atomic number of elements in a period.
• One extra electron gets added to the outermost shell as we move along the periods from left to right.
• The electron gets added to the same shell or orbit and thus the electrons present for bonding increase by one unit.
• Thus, the shell number remains the same but the number of electrons present for bonding increases along a period.

Groups:

• Elements having the same number of outer electrons are put in the same group of the periodic table.
• When we move down a group, new shells get added.
• The outermost shell has electrons present for bonding.
• Though the number of shells increases as we go down in a group, the number of electrons in the outermost shell remains the same.
• For example, the Halogens F, Cl, Br, I, At all belong to group 17 and have 7 electrons in the outermost shell.
• Similarly, Group 16 elements have 6 electrons in the outermost shell, group 15 has 5 electrons in the outermost shell, and so on.

Hence, group 17 is called halogens.

Given:

Statement:

Kids should be allowed to use mobile phones from an early age.

Now,

Arguments:

I. Continuous use of mobile phone causes distraction for the kids - False (As the statement clearly mentioned that kids should be allowed to use mobile phone. So, any negative point will weaken the given statement).

II. A lot of educational apps encourage playful competition among kids while enhancing the way they learn new ideas - True (There are lots of educational app which can help the kids to enhance there learning ability from a very early age and this argument is strengthening the given statement).

Hence, the correct answer is "Option 1".

Given: The mirror image of a 12-hour clock is 3 ∶ 25.

Now, the actual time is:

Hence, the correct answer is "Option 1".

The correct answer is Carbon

Key Points

• Graphite is a non-metal which is a good conductor of both heat and electricity.
• It is an allotrope of carbon, other allotropic forms being diamond, amorphous carbon, etc.
• The conductive properties of graphite come from its unique structure.
• It is composed of layers of carbon atoms arranged in a hexagon lattice.
• These layers are weakly bonded so they can slide over one another, which is why graphite is also used as a lubricant.
• Furthermore, within these layers, each carbon atom is only bonded to three others.
• This leaves one free electron, which can move within the layer.
• This mobility of electrons allows for the conduction of electricity.

Additional Information

• Sulfur
• ​Sulfur is a chemical element; it has symbol S and atomic number 16.
• It is abundant, multivalent and nonmetallic.
• Under normal conditions, sulfur atoms form cyclic octatomic molecules with the chemical formula S₈.
• Elemental sulfur is a bright yellow, crystalline solid at room temperature.
• Phosphorus:
• Phosphorus is a non-metal, yet it does not conduct electricity or heat very well.
• Its atomic structure doesn't allow for the free movement of electrons which is essential for conductivity.

The correct answer is Sardar Sarovar Dam.

Key Points

• Narmada Bachao Andolan is the most powerful mass movement, started in 1985, against the construction of a huge dam on the Narmada river.
• Narmada Bachao Andolan (NBA) is an Indian social movement initiated by native tribals (Adivasis), farmers, environmentalists, and human rights activists. The river flows through the states of Gujarat, Madhya Pradesh, and Maharashtra.
• Sardar Sarovar is the project related to Narmada Bachao Andolan.
• Medha Patkar and Baba Amte are associated with Narmada Bachao Andolan.

Important Points

• Narmada is the largest west flowing peninsular river in India.
• Narmada river originates from Amarkantak Plateau, Madhya Pradesh.
• It drains into the Arabian Sea through the Gulf of Khambhat.
• Major tributaries of the Narmada river are:
• Hiran river.
• Tendoni river.
• Kolar river.
• Hatni river.
• Orsang river.
• Tawa river.
• Barna river.

Additional Information

Shortcut Trick

Difference in Present ratio (4 : 5) is 1. Difference in Past ratio (10 : 13) is 3.

Equalize differences by multiplying present ratio by 3 → 12 : 15.

Change in units: 12 − 10 = 2 units. Given: 2 units = 4 years ⇒ 1 unit = 2 years.

Present ages: 12 × 2 = 24 and 15 × 2 = 30. After 3 years: 27 : 33 = 9 : 11.

∴ The correct answer is 9 : 11.

Alternate Method

Given: Present ratio of Arjun and Dharma = 4 : 5. Ratio 4 years ago = 10 : 13.

Formula Used: Ratio = (Initial Value ± Change) / (Initial Value ± Change)

⇒ Let the present ages be 4x and 5x.

⇒ 4 years ago, ages were (4x − 4) and (5x − 4).

⇒ (4x − 4) / (5x − 4) = 10 / 13

⇒ 13 × (4x − 4) = 10 × (5x − 4)

⇒ 52x − 52 = 50x − 40

⇒ 2x = 12 ⇒ x = 6

⇒ Arjun's present age = 4 × 6 = 24 years.

⇒ Dharma's present age = 5 × 6 = 30 years.

⇒ After 3 years, Arjun's age = 24 + 3 = 27 years.

⇒ After 3 years, Dharma's age = 30 + 3 = 33 years.

⇒ Required Ratio = 27 : 33 = 9 : 11.

∴ The correct answer is 9 : 11.

Additional Information

Ratio Balancing Method

To solve age problems quickly, multiply the ratios so that the numerical difference between the parts of the two ratios becomes equal to the actual time gap.

Difference Invariance

The age difference between two people remains constant throughout their lives. If A is 5 years older than B now, A will be 5 years older than B after n years.

Cross-Multiplication Method

For two ratios A:B and C:D with a constant change k, use |(A×D) − (B×C)| units = |(C−D)| × k.

The correct answer is shown null deflection

Key Points

• In electromagnetic induction, a current is induced in a coil only when there is a relative motion between the coil and the magnetic field, causing a change in magnetic flux.
• If both the coil carrying current and the magnetic field are stationary,
• there is no change in magnetic flux, and thus the galvanometer shows no deflection (null deflection).
• Electromagnetic Induction: Electric current is induced in the closed conductor if the magnetic flux associated with it changes.
• Magnetic Flux: The product of magnetic field and area is called magnetic flux.
• The change in magnetic flux can be changed by change in field or associate area.

Additional Information

• The theory of Electromagnetic Induction by Faraday.
• He concluded that the rate of change in flux is gives the emf of the coil.

$E = \frac{\Delta \phi }{\Delta t}$

• Lenz law related this to the conservation of energy.
• According to this law, the emf will be induced in a coil due to a changing magnetic flux in such a way that it will oppose the cause which has produced it.
• This law states that the induced emf in a conductor due to a changing magnetic flux is such that the magnetic field created by the induced emf opposes the change in a magnetic field.

$\Rightarrow emf=-N\left ( \frac{d\phi}{dt} \right )$

where N = number of loops and dϕ =  Change in magnetic flux

• The above equation is given by Faraday's law, but the negative sign is a result of Lenz's law.

The correct answer is Reports of National Family Health Survey

Key Points

• Reports of the National Family Health Survey (NFHS) are not a source of formal data on unemployment in India.
• The NFHS is a survey that provides data on health and family welfare.
• It Primarily focuses on health, nutrition, and population metrics rather than employment or unemployment data
• A survey conducted by the Ministry of Statistics and Programme Implementation to collect data on unemployment

Additional Information

• The National Sample Survey Organisation (NSSO) and the Census of India are sources of formal data on unemployment in India.
• The NSSO conducts surveys to collect data on employment and unemployment.
• The Census of India also publishes data on employment and unemployment.

Given:

Town X is west of town Y.

 Town Q is north of X.

Town P is east of Q and north-west of Y.

Thus, Town P is north-east of Town X.

Hence, the correct answer is " Option 3".

Shortcut Trick

Assume the Mean is 11. Calculate the net deviation of the known numbers from 11.

Deviations: (11 − 11) + (15 − 11) + (13 − 11) + (10 − 11) = 0 + 4 + 2 − 1 = +5.

To maintain the Mean at 11, the deviation of p must be −5.

Value of p = 11 − 5 = 6.

∴ The correct answer is 6.

Alternate Method

Given: Observations = 11, 15, 13, p, 10 | Arithmetic Mean = 11 | Total count (n) = 5

Formula: Mean = (Sum of all observations) ÷ (Total number of observations)

⇒ 11 = (11 + 15 + 13 + p + 10) ÷ 5

⇒ 11 × 5 = 49 + p

⇒ 55 = 49 + p

⇒ p = 55 − 49

⇒ p = 6

∴ The correct answer is 6.

Additional Information

The correct answer is 4ohm.

Key PointsGiven: Known Resistence= 2ohm, let unknown resistance be: x

Formula: $\mathrm{R}_\mathrm{series}=R_1+R_2$, $R_1=2 ohm$ and $R_2=x$

$\Rightarrow \mathrm{R}_\mathrm{series} = 6 ohm$

$\Rightarrow \mathrm{R}_\mathrm{series} = 2+x$

$\Rightarrow 6= 2+x$

$\Rightarrow x=4$

Hence, unknown resistance is 4ohm

Additional Information

• Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them.
• The formula for Ohm's Law is given by: $V=IR$
• where, V is the voltage across the conductor (measured in volts, V).
• I is the current flowing through the conductor (measured in amperes, A).
• R is the resistance of the conductor (measured in ohms, Ω).
• Series Resistance
• In a series configuration, resistors are connected end-to-end, and the same current flows through each resistor in sequence.
• The total or equivalent resistance of resistors in series is the sum of their individual resistances.
• $\mathrm{R}_\mathrm{series}= R_1+R_2+R_3+......R_n$
• Parallel Resistance
• In a parallel configuration, resistors are connected such that each resistor is directly connected to the voltage source.
• This means that the voltage across each resistor in parallel is the same.
• The total or equivalent resistance of resistors in parallel is found by the reciprocal of the sum of the reciprocals of their individual resistances.
• $\frac{1}{\mathrm{R}_\mathrm{parallel}}=\frac{1}{ R_1}+\frac{1}{ R_2}+\frac{1}{ R_3}+......\frac{1}{ R_n}$

Shortcut Trick For any real value of x, the term x2 is always non-negative (x2 ≥ 0). Multiplying by 9, 9x2 ≥ 0. Adding 16 to both sides, 9x2 + 16 ≥ 16. Since the minimum value of y is 16, the graph stays entirely above the x-axis (where y = 0). ∴ The correct answer is neither intersects nor touches the x-axis. Alternate Method Given: Equation of the graph is y = 9x2 + 16. Formula Used: For a quadratic equation ax2 + bx + c = 0, the Discriminant (D) = b2 − 4ac. ⇒ To find if the graph touches or intersects the x-axis, we set y = 0. ⇒ 9x2 + 0x + 16 = 0 ⇒ Here, a = 9, b = 0, and c = 16. ⇒ D = (0)2 − 4 × 9 × 16 ⇒ D = 0 − 576 = −576 ⇒ Since D < 0, the equation has no real roots. ⇒ This means the graph does not have any x-intercepts and thus never meets the x-axis. ∴ The correct answer is neither intersects nor touches the x-axis. Additional Information Nature of Roots and Graph If D > 0, the graph intersects the x-axis at two distinct points. If D = 0, the graph touches the x-axis at exactly one point (the vertex). Parabola Orientation For y = ax2 + bx + c, if a > 0, the parabola opens upwards. If a < 0, it opens downwards. Vertex of a Parabola The vertex (minimum or maximum point) of the parabola is located at the coordinates (−b/2a, −D/4a).

Given:

1)  Exactly two boys sit between S and N, to the right of S.

2)  P is an immediate Neighbour of M and S. 

3) R is second to the right of P and to the immediate right of S.

4)  N is an immediate Neighbour of Q and O.

5)  O is third to the left of M, 

Here, Q is seated second to the left of P.

Hence, the correct answer is " Option 2 ".

The correct answer is 2016

Key Points

• On 4 September 2016, Mother Teresa was canonized as a saint by Pope Francis at a grand ceremony at the Vatican.
• Mother Teresa, a renowned and celebrated nun, who served thousands of diseased and destitute people in Kolkata was canonized by Pope Francis at a grand ceremony in the Vatican.
• The event saw lakhs of pilgrims, including those from India, reaching the venue to witness the ceremony.
• A 12-member delegation led by the Minister of External Affairs Sushma Swaraj and a delegation from West Bengal and New Delhi including Mamata Banerjee and Arvind Kejriwal also became a part of the event.

Additional Information

• Mother Mary Teresa Bojaxhiu, honoured in the Catholic Church as Saint Teresa of Calcutta, was an Albanian-Indian Roman Catholic nun and missionary.
• She was born in Skopje, then part of the Kosovo Vilayet of the Ottoman Empire.
• During her lifetime Mother Teresa became famous as the Catholic nun who dedicated her life to caring for the destitute and dying in the slums of Calcutta - now known as Kolkata.

The correct answer is 'She is a Changemaker'

Key Points

• In December 2021, the National Commission for Women (NCW) launched the pan-India capacity-building programme called "She is a Changemaker" to enhance the leadership skills of grassroots women political leaders.
• This initiative aimed to empower women in politics and governance by providing them with the necessary tools and training to strengthen their roles in decision-making.
• It is  to enhance the leadership abilities of women serving in Panchayati Raj Institutions and urban local bodies.
• It is to  To provide training on effective governance, policymaking, and understanding legal and constitutional frameworks.

Additional Information

• National Commission for Women:
• It is also one of the significant statutory bodies established by the Government of India.
• It was established in 1992 under the provisions of the National Commission for Women Act, 1990.
• The Central Government took the initiative to establish this Commission by keeping in view the provisions of India’s constitution to strengthen the women in the country through addressing plights, suppressions, and other types of violence they use to face.
• National Commission for Women also takes the initiatives for the overall development of the women community in the whole country.

The correct answer is Transportation in phloem uses GTP & CTP

Key Points

• The statement "Transportation in phloem uses GTP & CTP" is false.
• Phloem transport uses energy in the form of ATP to move materials like sucrose into the phloem tissue.
• Phloem transport is a process that moves food and other substances throughout a plant.
• The process of phloem transport is driven by osmotic pressure gradients and active transport processes.

Additional Information

• The primary sugar transported in phloem is sucrose, which is a non-reducing sugar.
• Phloem transport is bidirectional, meaning it can transport nutrients in both upward and downward directions.
• The increase in osmotic pressure due to sucrose causes water to move into the phloem tissue.
• The pressure moves the material in the phloem to tissues which have less pressure.
• Functions of plant tissues:
• Plant tissues have different functions depending upon their structure and location
• Help provide mechanical strength to organs.
• They help in providing elasticity and flexibility to the organs.
• They help the tissues to bend easily in various parts of a plant like- leaf, stem, and branches without damaging the plant
• The xylem and phloem tissues help in the transportation of material throughout the plants
• They divide to produce new cells and help in the growth of the plants.
• They help in various cellular metabolisms like photosynthesis, regeneration, respiration, etc.

Shortcut Trick

Gain is 1/5 of the Selling Price (SP).

Let SP = 5 units, then Gain = 1 unit.

Cost Price (CP) = SP − Gain = 5 − 1 = 4 units.

Gain% = (Gain ÷ CP) × 100 = (1 ÷ 4) × 100 = 25%.

∴ The correct answer is 25%.

Alternate Method

Given: Selling Price (SP) = ₹15,000 | Gain = 1/5 of SP. Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100.

⇒ Gain = 1/5 × 15,000 = ₹3,000. ⇒ Cost Price (CP) = SP − Gain = 15,000 − 3,000 = ₹12,000. ⇒ Gain% = (3,000 ÷ 12,000) × 100. ⇒ Gain% = 1/4 × 100 = 25%.

∴ The correct answer is 25%.

Additional Information

Profit and Loss on SP vs CP

Generally, profit percentage is calculated on Cost Price unless specified otherwise. If profit is given as a fraction of SP (1/n), the profit on CP is 1/(n−1).

Conversion Formula

Profit% on CP = [Profit% on SP ÷ (100 − Profit% on SP)] × 100.

Shortcut Trick

HCF of (5, 15, 20) → Smallest number (5) divides all, so HCF = 5.

LCM of (5, 15, 20) → Largest number is 20. Multiples of 20: 20, 40, 60. 60 is divisible by 5 and 15, so LCM = 60.

Required Ratio = 60 : 5 = 12 : 1.

∴ The correct answer is 12 : 1.

Alternate Method

Given: Numbers are 5, 15, and 20.

Prime Factorization:

⇒ 5 = 5¹

⇒ 15 = 3¹ × 5¹

⇒ 20 = 2² × 5¹

Calculations:

⇒ HCF = Product of lowest powers of common factors = 5¹ = 5.

⇒ LCM = Product of highest powers of all prime factors = 2² × 3¹ × 5¹

⇒ LCM = 4 × 3 × 5 = 60.

⇒ Required Ratio = LCM : HCF

⇒ Ratio = 60 : 5

⇒ Ratio = 12 : 1

∴ The correct answer is 12 : 1.

Additional Information

Product Rule

For two numbers a and b, Product of numbers = HCF(a, b) × LCM(a, b).

LCM and HCF of Fractions

LCM = LCM of Numerators ÷ HCF of Denominators; HCF = HCF of Numerators ÷ LCM of Denominators.

Co-prime Numbers

If two numbers are co-prime, their HCF is 1 and their LCM is their product.

Shortcut Trick

Multiplying factor for 25% interest = (1 + 25/100) = 1.25

Balance after 1^st year = (20,000 × 1.25) − 2,500 = 25,000 − 2,500 = ₹22,500

Balance after 2^nd year = (22,500 × 1.25) − 2,500 = 28,125 − 2,500 = ₹25,625

∴ The correct answer is ₹25,625.

Alternate Method

Given: Principal (P) = ₹20,000 | Rate (R) = 25% p.a. | Instalment (x) = ₹2,500

At the end of Year 1:

⇒ Interest = 20,000 × (25 / 100) = ₹5,000

⇒ Total Amount = 20,000 + 5,000 = ₹25,000

⇒ Balance after 1^st instalment = 25,000 − 2,500 = ₹22,500

At the end of Year 2:

⇒ Interest = 22,500 × (25 / 100) = ₹5,625

⇒ Total Amount = 22,500 + 5,625 = ₹28,125

⇒ Balance after 2^nd instalment = 28,125 − 2,500 = ₹25,625

∴ The correct answer is ₹25,625.

Additional Information

Compound Interest Formula

The amount A after n years is given by A = P(1 + R/100)ⁿ, where interest is added back to the principal.

Effective Rate with Part Payment

In cases of part payment, calculate the interest on the current balance first, then subtract the payment to find the new principal for the next period.

Simple vs Compound Interest

In Compound Interest, the debt grows faster because interest is charged on the accumulated interest of previous years.

Shortcut Trick

Let the initial population be 100%.

Successive reduction: 100% × 4/5 (after 20% loss) × 19/20 (after 5% loss) = 15,200.

Total reduction factor = 0.8 × 0.95 = 0.76.

Initial Population = 15,200 ÷ 0.76 = 20,000.

∴ The correct answer is 20,000.

Alternate Method

Given:

Reduction 1 (War) = 20%

Reduction 2 (Epidemic) = 5% of remaining

Present population = 15,200

Let the population before the war be x.

⇒ Population after war = x − (20% of x) = 0.8x

⇒ Population after epidemic = 0.8x − (5% of 0.8x)

⇒ 0.8x × (1 − 0.05) = 15,200

⇒ 0.8x × 0.95 = 15,200

⇒ 0.76x = 15,200

⇒ x = 15,200 ÷ 0.76

⇒ x = 20,000

∴ The correct answer is 20,000.

Additional Information

Successive Percentage Change

When a value is changed by a% and then by b%, the net effective change is (a + b + ab/100)%.

Base Change Property

If the population decreases by r%, the new population is P × (1 − r/100). For successive decreases, multiply the factors: P × (1 − r₁/100) × (1 − r₂/100).