RRC Group D Previous Year Paper 73 (Held On: 12 Nov 2018 Shift 3)

The logic followed here is:-

And,

And,

Similarly,

Hence, "option 3" is the correct answer.

Calculation:

Total sales in the year = Rs. 5000 crores

Total sales by Vivo company = 6%

Now,

⇒ (6% of 5000)

⇒ (6/100 × 5000)

⇒ 300 crores

∴ The sales made by Vivo company is 300 crores.

Shortcut Trick

Smallest 3-digit number divisible by 8: 104

Largest 3-digit number divisible by 8: 992

Number of terms (n) = [(Last term − First term) ÷ Common Difference] + 1

n = [(992 − 104) ÷ 8] + 1 = [888 ÷ 8] + 1 = 111 + 1 = 112

∴ The correct answer is 112.

Alternate Method

Given: Three-digit numbers divisible by 8.

Formula Used: Arithmetic Progression (AP) n^th term: a_n = a + (n − 1)d

⇒ Smallest 3-digit number = 100. 100 ÷ 8 leaves remainder 4. So, first term (a) = 100 + (8 − 4) = 104.

⇒ Largest 3-digit number = 999. 999 ÷ 8 leaves remainder 7. So, last term (a_n) = 999 − 7 = 992.

⇒ Common difference (d) = 8.

⇒ 992 = 104 + (n − 1) × 8

⇒ 992 − 104 = (n − 1) × 8

⇒ 888 = (n − 1) × 8

⇒ n − 1 = 888 ÷ 8

⇒ n − 1 = 111

⇒ n = 112

∴ The correct answer is 112.

Additional Information

Divisibility Rule of 8

A number is divisible by 8 if its last three digits are divisible by 8 or if the last three digits are zeros.

Sum of Arithmetic Progression

The sum of n terms of an AP is S_n = (n/2) × [2a + (n − 1)d] or S_n = (n/2) × [first term + last term].

Finding the Number of Multiples

To find multiples between X and Y, calculate ⌊Y/k⌋ − ⌊(X−1)/k⌋ where k is the divisor.

The correct answer is 1000 kg ms–1.

Key Points 

• Given that
• Mass of the body (m) = 50 kg
• Velocity of the body (v) = 20 m/s
• Momentum of the body (p) = $Mass (m) * Velocity (v)$
• =  50 * 20
• = 1000 m/s
• So the momentum of the body will be 1000 kgm/s.

The correct answer is (ii), (iii), and (iv).

Key points

• The term isotope mainly corresponds to the variation in the atomic mass or weight of an element.
• It may also refer to variations of a single element that have the same number of protons but vary in the number of neutrons in the atom.
• Isotopes of an element have different physical properties because they have different mass numbers.
• The chemical properties of different isotopes are almost similar.
• When it comes to the physical properties of isotopes including mass, melting or boiling point, density, and freezing point, they are all different.
• The physical properties of any isotope are largely determined by its mass.
• So statements (ii), (iii) and (iv) are correct.

Additional Information 

Two elements are said to be isobars of one another if they have different sets of electrons and the same number of nucleons.

• An example of a series of isobars would be the 40S, 40Cl, 40Ar, 40K, and 40Ca.
• The term nucleon is a collective term used for the combination of neutron and proton altogether inside the nucleus of an atom.

Isotopes are atoms of the same element with a different number of Neutrons.

• Isotopes are atoms with the same number of protons but that have a different number of neutrons.
• For example - Uranium-235 and Uranium-239 are two different isotopes of the element uranium.
• the atomic number is equal to the number of protons.
• the atomic mass is the sum of protons and neutrons.
• Isotopes are elements with the same atomic number but different mass numbers.

Shortcut Trick

Ratio of salt and acid = 5 : 7

Total ratio parts = 5 + 7 = 12 units

12 units = 360 g ⇒ 1 unit = 30 g

Mass of acid = 7 units = 7 × 30 g = 210 g

∴ The correct answer is 210 gm.

Alternate Method

Given:

Ratio of salt to acid = 5 : 7

Total weight of the mixture = 360 g

Formula Used:

Component Quantity = (Component Ratio / Total Ratio) × Total Quantity

Calculations:

⇒ Total ratio = 5 + 7 = 12

⇒ Quantity of acid = (7 / 12) × 360

⇒ Quantity of acid = 7 × 30

⇒ Quantity of acid = 210 g

∴ The correct answer is 210 gm.

Additional Information

Ratio and Proportion

If a total quantity Q is divided in the ratio a : b, then the parts are (a/(a+b))×Q and (b/(a+b))×Q respectively.

Percentage Composition

The percentage of a component in a mixture can be found by (Component Ratio / Total Ratio) × 100.

Compound Ratio

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

Shortcut Trick

Total value of assets = 40000 + 15000 = 55000

Effective premium rate on total value = 7.5% of 80%

⇒ Effective rate = (7.5 × 80) ÷ 100 = 6%

⇒ Total Premium = 6% of 55000 = (6 ÷ 100) × 55000 = 3300

∴ The correct answer is Rs. 3,300.

Alternate Method

Given:

Cost of house = Rs. 40,000

Cost of household articles = Rs. 15,000

Rate of premium = 7.5%

Insured coverage = 80% of total value

Calculations:

⇒ Total value of house and articles = 40,000 + 15,000 = Rs. 55,000

⇒ Insured amount = 80% of total value

⇒ Insured amount = (80 ÷ 100) × 55,000 = Rs. 44,000

⇒ Fire insurance premium = 7.5% of insured amount

⇒ Premium = (7.5 ÷ 100) × 44,000

⇒ Premium = 7.5 × 440 = Rs. 3,300

∴ The correct answer is Rs. 3,300.

Additional Information

Percentage Calculation

To find X% of Y, use the formula: (X ÷ 100) × Y. This fundamental concept is widely used to calculate premiums, discounts, and simple interest.

Successive Percentages

When applying consecutive percentages (like taking A% of B% of a value), the net effective fraction of the original base is (A × B) ÷ 100 %.

Insurance Policy Value

Premiums are strictly paid on the insured portion of an asset, which serves as the maximum liability the insurance company bears in case of damage.

The correct answer is Ahmedabad.

Key Points

• Ahmedabad is a city in Gujarat.
• Ahmedabad city is located on the banks of the River Sabarmati.
• The Sabarmati river is one of the major west-flowing rivers in India.
• It originates in the Aravalli Range of the Udaipur District of Rajasthan and meets the Gulf of Khambhat of the Arabian Sea after travelling 371 km in a south-westerly direction across Rajasthan and Gujarat.

Additional Information

• Valsad is a city and a municipality in the Valsad district of the Indian state of Gujarat.
• Surat is a city in the western Indian state of Gujarat.
• Located at the mouth of the Tapti River, it used to be a large seaport.
• Vapi is a city and municipality in the Valsad district in the state of Gujarat, India.
• It is situated near the banks of the Daman Ganga River.

Concept Used:         

Follow the BODMAS rule according to the table given below:

Calculation:

3$\frac{5}{8}$+ $\frac{6}{16}-\frac{5}{24}$ + 3$\frac{1}{2}$.

⇒ 29/8 + 6/16 – 5/24 + 7/2

⇒ (174 + 18 – 10 + 168)/48

⇒ (350/48)

⇒ 175/24

∴ The required value is 175/24

The correct answer is Water and Pine oil.

Key Points

• In the froth flotation method, ore powder is placed in a tank filled with a mixture of water and pine oil.
• Froth flotation is an important concentration process that can be used to selectively separate hydrophobic materials from hydrophilic waste gangue.
• Froth flotation is one of the most popular operational processes for mineral beneficiation.
• In ore/mineral beneficiation, froth flotation is a method by which commercially important minerals are separated from impurities and other minerals by collecting them on the surface of a froth layer.
• Flotation is the process of separation of beneficial minerals from a mixture by creating froth on which minerals separate out.
• This method of froth floatation is a method of mineral processing in which different minerals are separated selectively.
• Such ores containing multiple metals such as lead, copper, and zinc can be selectively extracted by using froth floatation.
• The minerals that do not float into the froth are called the flotation tailings or flotation tails.

Given that:

• 4_9_3_4 = 16
• Option 1: ÷, +, ×

4 ÷ 9 + 3 × 4 = 16

0.44 + 3 × 4 = 16

0.44 + 12 = 16

12.44 = 16, So LHS ≠ RHS, it is not correct.

• Option 2: ×, +, ÷

4 × 9 + 3 ÷ 4 = 16

4 × 9 + 0.75 = 16

36 + 0.75 = 16

36.75 = 16, So LHS ≠ RHS, it is not correct.

• Option 3: ×, ÷, +

4 × 9 ÷ 3 + 4 = 16

4 × 3 + 4 = 16

12 + 4 = 16

16 = 16, So LHS = RHS, it is correct.

• Option 4: ÷, ×, +

4 ÷ 9 × 3 + 4 = 16

0.44 × 3 + 4 = 16

1.33 + 4 = 16

4.33 = 16, So LHS ≠ RHS, it is not correct.

Hence, "option 3" is the correct answer.

The logic followed here is:-

Hence, "option 3" is the correct answer.

The logic followed here is:-

  - Two parallel lines. 2.   - Two parallel lines. 3.   - Two parallel lines. 4.   - Two intersecting lines.

So, figure D is different from others.

Hence, "option 3" is the correct answer.

Shortcut Trick

To minimize the total sections, the number of students per section must be maximum.

Maximum students per section = HCF of (188, 282, 423) = 47.

Total sections = (188 ÷ 47) + (282 ÷ 47) + (423 ÷ 47)

Total sections = 4 + 6 + 9 = 19

∴ The correct answer is 19 sections.

Alternate Method

Given:

Number of students in 4^th class = 188

Number of students in 5^th class = 282

Number of students in 6^th class = 423

Formula Used:

Minimum sections = Total students in each class ÷ Maximum capacity per section

Maximum capacity per section = HCF of the number of students in all given classes.

Class 4

188 students → 4 sec

Class 5

282 students → 6 sec

Class 6

423 students → 9 sec

Total Sections = 4 + 6 + 9 = 19

Calculations:

⇒ First, calculate the HCF of 188, 282, and 423 using the difference method.

⇒ Difference between 282 and 188 = 94

⇒ Difference between 423 and 282 = 141

⇒ The difference between these two results (141 − 94) = 47

⇒ Checking divisibility: 188 ÷ 47 = 4, 282 ÷ 47 = 6, 423 ÷ 47 = 9

⇒ Hence, the HCF is 47, which means each section has exactly 47 students.

⇒ Number of sections in class 4 = 188 ÷ 47 = 4

⇒ Number of sections in class 5 = 282 ÷ 47 = 6

⇒ Number of sections in class 6 = 423 ÷ 47 = 9

⇒ Total minimum number of sections = 4 + 6 + 9 = 19

∴ The correct answer is 19 sections.

Additional Information

Highest Common Factor (HCF)

HCF is the largest positive integer that divides all the given numbers without leaving a remainder. It is practically used when dividing items, groups, or lengths into the largest possible equal segments.

Difference Method for HCF

The HCF of given numbers is always a factor of the difference between any two of those numbers. Calculating differences helps skip long factorisations and quickly locates the HCF.

Least Common Multiple (LCM)

LCM is the smallest integer that is a multiple of all given numbers. Unlike HCF, which breaks down numbers into groups, LCM builds them up to find a common matching point.

The correct answer is Bharatiya Janata Party.

Key Points

• Bhartiya Janata Party won the Gujarat Assembly Elections, 2017.
• The 14th Gujarat Legislative Assembly election, 2017 was held on 9 December 2017 and 14 December 2017.
• The votes were counted on 18 December. All 182 members of the Gujarat Legislative Assembly were elected with the leader of the largest party or coalition expected to become the next Chief Minister.
• The incumbent Bharatiya Janata Party obtained a simple majority with an increase in the vote share.
• Despite suffering a decrease in the number of seats, the incumbent government retained its simple majority in the house.​

Additional Information

• The Indian National Congress, colloquially the Congress Party but often simply Congress is a political party in India with widespread roots.
• Founded in 1885, it was the first modern nationalist movement to emerge in the British Empire in Asia and Africa.
• Samajwadi Party is a socialist political party in India, headquartered in New Delhi.
• It is mainly based in Uttar Pradesh, with a significant presence in other states as well.
• The All India Trinamool Congress, colloquially the Trinamool Congress is an Indian political party that is predominantly active in West Bengal.
• The party is led by Mamata Banerjee, the current Chief Minister of West Bengal, who has led the state since 2011.

The logic followed here is:-

• A snake crawls from one place to another.

Similarly, 

• Honey bees fly from one place to another.

Hence, "option 4" is the correct answer.

The correct answer is Both A and B are true.

Key Points

• N₂₍g) + 3H₂₍g) ⇌ 2NH₃(g) 
• It is a reversile reaction.
• Ammonia (NH₃) can be decomposed by the action of light and platinum-loaded titanium oxide.
• Also, it can be noted from the equation that, reversible sign (⇌) has been used to indicate its reversibility.
• CaCO₃(s) $\rm \underrightarrow {heat}$ CaO(s) + CO2(g)  
• In the above reaction, calcium carbonate (CaCO3) is breaking to form two products.
• The decomposition is taking place due to heat.
• Hence, the above reaction is a thermal decomposition reaction.

The correct answer is Karnataka.

Key Points

• Kolar Gold Field is located in Karnataka.
• Kolar Gold Fields, mining area, southeastern Karnataka state, southern India.
• It lies on a Southern Railway spur that loops from Bangarapet to Bengaluru (Bangalore).
• Economic activities centred on the goldfields, which were the southern portion of a gold-bearing region that extends for 40 miles (65 km).

Additional Information

• The Bunder diamond mine in the Chhatarpur district of Madhya Pradesh has reserves of around 34.20 million carats of diamond, according to the mines ministry.
• Two gold blocks, the Chakariya mine at Singrauli and Imaliya gold block at Katni in Madhya Pradesh, are also among the 13 mines to be up for auction.
• Ramagiri goldfields are said to have about four tonnes of gold reserves, while the Boksampalli region has about two tonnes of yellow metal reserves in Karnataka.
• The Wayanad-Malabar Gold Mine is in Tamil Nadu, India.
• The site was first discovered in 1875.
• The Wayanad-Malabar Gold Mine was closed at the time of data entry with no known plans to re-open.

The Venn diagram is given below:-

The total number of students who play both F and H but not B is 12.

Hence, "option 3" is the correct answer.

The correct answer is Bharat Net.

Key Points

• Bharat Net is a flagship mission implemented by Bharat Broadband Network Ltd. (BBNL).
• It is a Special Purpose Vehicle (SPV) set up by the Government of India under the Companies Act, 1956 with an authorized capital of Rs 1000 crore.
• Currently, it is being implemented by the Department of Telecommunication under the Ministry of Communications.
• Aims and Objectives- 
• To facilitate the delivery of e-governance, e-health, e-education, e-banking, Internet, and other services to rural India.
• To connect all the 2,50,000 Gram panchayats in the country and provide 100 Mbps connectivity to all gram panchayats.
• To achieve this, the existing unused fibers (dark fiber) of public sector undertakings (PSUs) (BSNL, Railtel, and Power Grid) were utilized and incremental fiber was laid to connect to Gram Panchayats wherever necessary.

The correct answer is Kinetic energy is converted into light and sound energy.

Key Points

• Kinetic energy is converted into light and sound energy during the thunder of clouds.
• Lightning is a discharge of electricity.
• A single stroke of lightning can heat the air around it to 30,000°C (54,000°F)
• This extreme heating causes the air to expand explosively fast.
• The expansion creates a shock wave that turns into a booming sound wave, known as thunder.

Additional Information

• As ice crystals high within a thunderstorm cloud flow up and down in the turbulent air, they crash into each other.
• Small negatively charged particles called electrons are knocked off some ice and added to other ice as they crash past each other.
• This separates the positive (+) and negative (-) charges of the cloud.
• The top of the cloud becomes positively charged while the base of the cloud becomes negatively charged.

1. Weight of R is less than P.

⇒ R < P

• Here, there is no information about the weight of Q and S.
• Therefore, statement 1 alone is not sufficient.

2. Weight of R is less than Q and S.

⇒ R < Q and S

• Here, there is no information about the weight of P.
• Therefore, statement 2 alone is not sufficient.
• From statements 1 and 2, we get the following cases:
• Case 1: R < P < Q < S
• Case 2: R < P < S < Q
• Case 3: R < Q < P < S
• Case 4: R < Q < S < P
• Case 5: R < S < P < Q
• Case 6: R < S < Q < P
• Therefore, the least weight is R in all the above 6 cases.
• So, statements 1 and 2 together are sufficient.

Hence, "option 4" is the correct answer.

The correct answer is Hyderabad.

Key Points

• The Rajiv Gandhi International Cricket Stadium is a cricket stadium in Hyderabad, Telangana, India.
• Located in the eastern suburb of Uppal, it has a capacity of 40,000 and extends across 16 acres (65,000 m2) of land.
• It serves as the home ground for the Hyderabad Cricket Association and the Indian Premier League team Sunrisers Hyderabad.
• As of 3 March 2019, it has hosted 5 Tests, 6 ODIs, and 2 T20Is.
• This stadium hosted the opener and final of the 2017 Indian Premier League, and also the final of the 2019 Indian Premier League.

Additional Information

The correct answer is the Alkaline metal group.

Key Points

• Elements like Li, Na, and K are related to the alkali metal group. 
• The alkali metals consist of the chemical elements lithium (Li), sodium (Na), potassium (K), rubidium (Rb), caesium (Cs), and francium (Fr). Together with hydrogen, they constitute group 1, which lies in the s-block of the periodic table.
• The Group 1 elements are called the alkali metals.
• All the Group 1 elements are very reactive. They must be stored under oil to keep air and water away from them.
• Group 1 elements form alkaline solutions when they react with water, which is why they are called alkali metals. ​

Additional Information

• The halogens are a group in the periodic table consisting of five or six chemically related elements: fluorine, chlorine, bromine, iodine (I), and astatine.
• In the modern IUPAC nomenclature, this group is known as group 17.
• Noble gases are said to be zero group elements because they have zero valencies and they cannot combine with other elements to form compounds.
• The zero group elements are Helium, Neon, Argon, Krypton, Xenon, and Radon.
• The alkaline earth metals are six chemical elements in group 2 of the periodic table.
• They are beryllium, magnesium, calcium, strontium, barium, and radium.
• The elements have very similar properties.

Shortcut Trick

To find the HCF of decimals, first make the number of decimal places equal: 3.63, 5.28, 6.93.

Remove the decimal point and find the HCF of 363, 528, and 693.

The difference between 363 and 528 is 165. The difference between 528 and 693 is 165.

Factors of 165 are 1, 3, 5, 11, 15, 33... Check divisibility: 33 × 11 = 363, 33 × 16 = 528, 33 × 21 = 693.

HCF of integers is 33. Placing the decimal back for 2 places gives 0.33.

∴ The correct answer is 0.33.

Alternate Method

Given: Numbers are 3.63, 5.28, and 6.93.

Formula Used: HCF of Decimals = (HCF of numbers without decimal) ÷ (10ⁿ), where n is the number of decimal places.

⇒ Step 1: Express decimals as integers by multiplying by 100: 363, 528, 693.

⇒ Step 2: Factorize 363 = 3 × 11 × 11.

⇒ Step 3: Factorize 528 = 2⁴ × 3 × 11.

⇒ Step 4: Factorize 693 = 3² × 7 × 11.

⇒ Step 5: Common prime factors are 3 and 11.

⇒ Step 6: HCF (363, 528, 693) = 3 × 11 = 33.

⇒ Step 7: HCF of decimals = 33 ÷ 100 = 0.33.

∴ The correct answer is 0.33.

Additional Information

HCF of Fractions

HCF of Fractions = (HCF of Numerators) ÷ (LCM of Denominators).

LCM of Decimals

To find LCM of decimals, make the number of decimal places same, find LCM of resulting integers, and place the decimal back.

Property of HCF

The HCF of two or more numbers is the greatest number that divides each of them exactly without leaving a remainder.

The correct answer is Kidambi Srikanth.

Key Points

• Kidambi Srikanth won the title in the men's section of the Australian Open Badminton Championship competition held in 2017. 
• Srikanth Kidambi was the winner of the Australian Open Super Series badminton tournament in 2017.
• He won this title in Men's Singles category by beating Rio Olympics champion China's Chen Long. He was ranked world number 1 in the April 2018 BWF ranking.

Additional Information

• Son Won-ho is a South Korean badminton player.
• He reached a career-high as world number 1 in the men's singles in May 2017.
• He competed at the 2012 and 2016 Summer Olympics.
• Chen Long is a Chinese professional badminton player. He is the 2016 Olympic champion, two-time World champion, and an Asian champion.
• Chen was a former World number 1, occupying the top men's singles ranking for 76 consecutive weeks from December 2014 to June 2016.
• 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.

The correct answer is Anti-defection.

Key Points

• The 10th Schedule of the Indian Constitution is about Anti-defection.
• 10th Schedule of The Constitution of India is about anti-defection law.
• Anti defection law acts as a deterrent for those who hop parties from one to other.
• It is a type of control system against the members of any political party leaving the original party for another.

Additional Information

• The right to privacy is protected as an intrinsic part of the right to life and personal liberty under Article 21 and as a part of the freedoms guaranteed by Part III of the Constitution.
• Universal suffrage (also called universal franchise, general suffrage, and common suffrage of the common man) gives the right to vote to all adult citizens, regardless of wealth, income, gender, social status, race, ethnicity, political stance, or any other restriction, subject only to relatively minor exceptions.
• The Constitution (Eighty-sixth Amendment) Act, 2002 inserted Article 21-A in the Constitution of India to provide free and compulsory education of all children in the age group of six to fourteen years as a Fundamental Right in such a manner as the State may, by law, determine.

The correct answer is WPI (Wholesale Price Index).

Key Points

• Consumer price index (CPI):
• It is a price index, the price of a weighted average market basket of consumer goods and services purchased by households.
• Changes in measured CPI track changes in prices over time.
• The GDP deflator also called the implicit price deflator, is a measure of inflation.
• It is the ratio of the value of goods and services an economy produces in a particular year at current prices to that of prices that prevailed during the base year.
• The industrial production index (IPI) measures production and capacity levels in the manufacturing, mining, electric, and gas industries, relative to a base year.
• Wholesale Price Index (WPI):
• It is the year-on-year percentage change in the wholesale price index (WPI), which is used as an indicator of headline inflation. Hence option 2 is correct

Additional Information

• Difference between WPI and CPI: 
• WPI tracks inflation at the producer level and CPI captures changes in prices levels at the consumer level.
• WPI does not capture changes in the prices of services, which CPI does.

Hence, the Wholesale Price Index (WPI) is the year-on-year percentage change in the wholesale price index (WPI), which is used as an indicator of headline inflation.

Shortcut Trick

If a + 1/a = k, then a² + 1/a² = k² − 2.

Applying the trick once: 4² − 2 = 14.

Applying the trick again for the fourth power: 14² − 2 = 196 − 2 = 194.

∴ The correct answer is 194.

Alternate Method

Given: a + 1/a = 4

Formula Used: (x + y)² = x² + y² + 2xy

⇒ Squaring both sides: (a + 1/a)² = 4²

⇒ a² + (1/a)² + 2 × a × (1/a) = 16

⇒ a² + 1/a² + 2 = 16

⇒ a² + 1/a² = 14

⇒ Squaring both sides again: (a² + 1/a²)² = 14²

⇒ (a²)² + (1/a²)² + 2 × a² × (1/a²) = 196

⇒ a⁴ + 1/a⁴ + 2 = 196

⇒ a⁴ + 1/a⁴ = 196 − 2

⇒ a⁴ + 1/a⁴ = 194

∴ The correct answer is 194.

Additional Information

Negative Sign Identity

If a − 1/a = k, then a² + 1/a² = k² + 2. When moving from a negative sign to a square, the constant 2 is added.

Cubic Algebraic Identity

If a + 1/a = k, then a³ + 1/a³ = k³ − 3k. This shortcut avoids full expansion of the cube formula.

Power 5 Calculation

a⁵ + 1/a⁵ = (a² + 1/a²)(a³ + 1/a³) − (a + 1/a). This is a common higher-power identity used in competitive exams.

The least possible Venn diagram is given below:-

Conclusion:

1. No monkey is human. → False ( it is possible but not definite)
2. Some humans are apes. → True (As can be seen in the Venn diagram, some part of Human is ape)

Hence, "option 4" is the correct answer.

The correct answer is 1885.

Key Points

• 'Indian National Congress' was formed in the year 1885.
• On 28 December 1885, the Indian National Congress was founded at Gokuldas Tejpal Sanskrit College in Bombay, with 72 delegates in attendance.
• Hume assumed office as the General Secretary, and Womesh Chunder Bonnerjee of Calcutta was elected president.

Additional Information

• The INC was the first national movement of a political kind in India with the initial aim of getting more Indians involved in the governance of the country.
• Later on, its purpose upgraded to complete independence.
• And, post-independence, it emerged as a major political party in the country.
• For the first session, Hume obtained permission from the then Viceroy of India Lord Dufferin.
• It was initially supposed to be held in Poona but was moved to Bombay due to the outbreak of cholera in Poona.
• ​The first session was attended by 72 delegates from all the Indian provinces.
• There were 54 Hindus, 2 Muslims, and the rest were Jain and Parsi members.
• The president of the first session was Womesh Chandra Bonnerjee.
• Prominent attendees of the maiden session were Dadabhai Naoroji, Dinshaw Wacha, William Wedderburn, Pherozeshah Mehta, etc.

The correct answer is Both A and B are correct.

• The speed of sound depends on the properties of the medium through which it travels.
• In water (seawater), the speed of sound is 1531 m/s.
• In the air, the speed of sound is 346 m/s.
• So both the options are correct.
• The speed of sound in a medium depends on the temperature, density of the medium. The speed of sound decreases when we go from solid to the gaseous state.
• In any medium, as we increase the temperature the speed of sound increases.
• Speed of sound in different media at 25 ºC.

https://ncert.nic.in/ncerts/l/iesc112.pdf

Calculation:

Total grains produced by state A = (15 + 10 + 10) = 35

Total grain produced by state B = (5 + 20 + 15) = 40

Total grain produced by state C = (25 + 15 + 10) = 50

Total grain produced by state D = (15 + 25 + 5) = 45

∴ The maximum grains produced by state C

The correct answer is Telangana.

Key Points

• Mission Kakatiya is an irrigation project launched by the Telangana government.
• The objective of Mission Kakatiya is to enhance the development of agriculture-based income for small and marginal farmers, by accelerating the development of minor irrigation infrastructure, strengthening community-based irrigation management, and adopting a comprehensive program for restoration of tanks.
• The works of Mission Kakatiya Phase - I are completed by 31.05. 2017.

Additional Information

• Swachh Bharat Mission(SBM) is a country-wide campaign initiated by the Government of India in 2014 to eliminate open defecation and improve solid waste management.
• It was Initiated by the Government of India, the mission aimed to achieve an "open-defecation free" (ODF) India by 2 October 2019, the 150th anniversary of the birth of Mahatma Gandhi.

Shortcut Trick

When the Rate of Interest (R) and Time (T) are numerically equal, the shortcut formula is R = √(100 × SI/P).

Given SI/P = 1/36, we substitute the value into the formula.

R = √(100 × 1/36) = √(100/36) = 10/6.

On simplifying, R = 5/3 %.

∴ The correct answer is 5/3 %.

Alternate Method

Given:

Simple Interest (SI) = 1/36 of Principal (P)

Rate (R) = Time (T) = x

Formula Used:

SI = (P × R × T) ÷ 100

Calculations:

⇒ P/36 = (P × x × x) ÷ 100

⇒ 1/36 = x² ÷ 100

⇒ x² = 100 ÷ 36

⇒ x = √(100 ÷ 36)

⇒ x = 10/6

⇒ x = 5/3 %

∴ The correct answer is 5/3 %.

Additional Information

Simple Interest (SI)

The interest calculated only on the initial Principal amount for the entire period. Formula: SI = PRT/100.

Relation between R and T

When R and T are equal, the squared value R² is directly proportional to the ratio of interest to principal (SI/P).

Amount in SI

The total sum of money returned after interest is added. Formula: Amount (A) = P + SI or A = P[1 + (RT/100)].

The statement highlights the teacher's opinion that X is the most intelligent among the students in the said class.

• From the statement, we can understand that X is more intelligent than the rest of the students. However, this does not imply that she thinks that the remaining students are not intelligent at all. Thus, assumption I is not implicit.
• The teacher sees student X as an intelligent one, but that does not imply that the teacher expects him to become a teacher in the future. Thus, assumption II is also not implicit.

Hence the correct answer is option 4.

The correct answer is 2.

Key Points

• The maximum number of electrons that can be filled in the K shell of an atom is 2.
• Each subshell is constrained to hold 4ℓ + 2 electrons at most, namely:
• Each s subshell holds at most 2 electrons
• Each p subshell holds at most 6 electrons
• Each d subshell holds at most 10 electrons
• Each f subshell holds at most 14 electrons
• Each g subshell holds at most 18 electrons
• Therefore, the K shell, which contains only an s subshell, can hold up to 2 electrons.
• The L shell, which contains an s and a p, can hold up to 2 + 6 = 8 electrons, and so forth; in general, the nth shell can hold up to 2n² electrons.

The direction diagram will be as follows:

• As X takes a right turn from point F, then he will face the east direction at point G

Hence, "option 2" is the correct answer.

Shortcut Trick

Total Sales (2014) = 7 + 3 = 10 lakh

Total Sales (2016) = 18 + 7 = 25 lakh

Percentage Increase = [(25 − 10) ÷ 10] × 100

Percentage Increase = [15 ÷ 10] × 100 = 150%

∴ The correct answer is 150% increase.

Alternate Method

Given:

Sales in 2014 (Area 1) = 7 lakh, (Area 2) = 3 lakh

Sales in 2016 (Area 1) = 18 lakh, (Area 2) = 7 lakh

Formula: Percentage Difference = [(New Value − Old Value) ÷ Old Value] × 100

⇒ Total sales in 2014 = 7 + 3 = 10 lakh

⇒ Total sales in 2016 = 18 + 7 = 25 lakh

⇒ Difference in sales = 25 − 10 = 15 lakh

⇒ Percentage Change = (15 ÷ 10) × 100

⇒ Percentage Change = 1.5 × 100 = 150%

⇒ Since 25 > 10, it is an increase.

∴ The correct answer is 150% increase.

Additional Information

Percentage Increase/Decrease

Percentage change is calculated as (Difference ÷ Original Value) × 100. Always use the initial year/value as the base.

Data Interpretation (DI) Tabulation

In tabular DI, ensure you sum all categories (Area 1 + Area 2) if the question asks for the total sales of the company for a specific year.

Average Sales

Average Sales = (Total Sales over all years) ÷ (Number of years).

The logic followed here is:-

• Four lines are drawn inside the circle from figure A to figure B.

• Four lines are drawn inside the quadrilateral from figure C to figure D.

Hence, "option 4" is the correct answer.

The correct answer is Bifurcation.

Key Points

• The process of division of a cell into two identical daughter cells is called bifurcation. 
• Bifurcation theory describes how small changes in an input parameter can cause a bifurcation or qualitative change in the behaviour of the system.
• The ability to make a dramatic change in system output is often essential to organism function, and bifurcations are therefore ubiquitous in biological networks such as the switches of the cell cycle.

Additional Information

• Fragmentation occurs when an organism literally breaks off from itself.
• The broken fragments of the organism grow into individual separate organisms.
• On the other hand, regeneration is a form of asexual reproduction where the organism is capable of regrowing certain parts of its body when it loses them.
• Octopi, for instance, can regrow their arms when a predator bites them off.

Concept Used:         

Follow the BODMAS rule according to the table given below:

Calculation:

2 × 8 + (7 × 4) ÷ 2 – 24

⇒ 2 × 8 + 28 ÷ 2 – 24

⇒ 2 × 8 + 14 – 24

⇒ 16 + 14 – 24

⇒ 30 – 24

⇒ 6

∴ The required value is 6

 

 

Note: Multiple of 400 years i.e. 800, 1200, 1600, 2000 have 0 odd days.

Calculating leap year: For Finding the number of leap year (1 - 99) years, divide the number of years by 4 and the quotient will be the number of leap years.

Code for weekdays:

 

1950 = we find out the odd days (the nearest leap century year + the nearest century year + completing year) = 1600 + 300 + 49

• In 1600 year the odd days = 0
• In 300 year the odd days = 1
• In 49 years, odd days = 49/4 = 12 leap years and 37 ordinary years
• In 12 leap years, no. of odd days = 24
• In 37 ordinary years, no. of odd days = 37
• So total = 24 + 37 = 61 odd days i.e. 61/7 = 5 odd days (remainder)
• Odd days in January = 25 i.e. 4 odd days

Total = 0 + 1 + 5 + 4 = 10 days = 3 odd days i.e Wednesday.

As the code of Wednesday is 3.

Hence, Wednesday is the correct answer.

The family tree is given below:-

The daughter of M is the niece of V.

Hence, "option 3" is the correct answer.

The correct answer is Father.

Key Points

• The sex of the children is determined by the hereditary chromosome inherited from the father.
• Men determine the sex of a baby depending on whether their sperm is carrying an X or Y chromosome.
• An X chromosome combines with the mother's X chromosome to make a baby girl (XX) and a Y chromosome will combine with the mother's to make a boy (XY).

Additional Information

• A gene consists of two parts, known as alleles, one inherited from each parent.
• It is likely men carry two different types of allele, which results in three possible combinations in a gene that controls the ratio of X and Y sperm;
• Men with the first combination, known as mm, produce more Y sperm and have more sons.
• The second, known as mf, produce a roughly equal number of X and Y sperm and have an approximately equal number of sons and daughters.
• The third, known as ff produce more X sperm and have more daughters.

The logic followed here is:-

• the positional value of D is 4.
• the positional value of U is 21.
• the positional value of X is 24.
• the positional value of M is 13 and not 10.

Hence, "option 4" is the correct answer.

The correct answer is Pt.

Key Points

• The metal Platinum(Pt) is found in a free state.
• Gold, silver, platinum, etc occur in a free state.
• Since Gold, Platinum, and Silver are the least reactive metals, hence they are found in a free state in nature.

Additional Information

• Iron and zinc are quite reactive and hence they do not occur in the free state.
• The compounds of metals found in nature are their oxides carbonate and sulfides.
• Metals like Na, Ca, and Mg are very reactive metals, they react with oxygen even at room temperature therefore they are never found in the free state in nature.

The correct answer is Nissl Granules.

• Nissl's granules also known as nissl's body are large granular structures present in neurons.
• These are made up of rough endoplasmic reticulum and have a number of ribosomes present on them.
• Their primary function is the synthesis of proteins.
• Components of the nephron are
• Bowmans Capsule
• Glomerulus
• Proximal Convoluted tubule (PCT)
• Loop of Henle
• Distal convoluted tubule (DCT)
• So the Nissl's granules are part of the neuron and other options are part of Nephron.

Additional Information Image of the neuron:

Image of Nephron:

The triangles in the question figure are shown below:

• The total number of triangles is 23.

Hence, "option 3" is the correct answer.

The correct answer is sweet potato vine.

Key Points

• Sweet potato vine is a dicot plant.
• The sweet potato or sweet potato (Ipomoea batatas) is a dicotyledonous plant that belongs to the bindweed or morning glory family, Convolvulaceae.
• Its large, starchy, sweet-tasting (tasting similar to pumpkin), tuberous roots are used as a root vegetable.

Additional Information

• Paphiopedilum often called the Venus slipper, is a genus of the lady slipper orchid subfamily Cypripedioideae of the flowering plant family Orchidaceae.
• A pine is any conifer tree or shrub in the genus Pinus of the family Pinaceae.
• Pinus is the sole genus in the subfamily Pinoideae.
• Ficus is a genus of about 850 species of woody trees, shrubs, vines, epiphytes, and hemiepiphytes in the family Moraceae.

• Let the number of newspapers be X,
• If every newspaper is read by 60 students, then the number of students would be X × 60 = 60X.
• Since every student read 4 newspapers.
• Therefore, number of students = ${X × 60\over 4} = 480$

⇒ X = ${480 × 4\over 60}$

⇒ X = 8 × 4 = 32

• Thus, there are exactly 32 newspapers.

Hence, "option 4" is the correct answer.

The correct answer is Xylem.

Key Points

• Xylem is not normal permanent tissue.
• Xylem is a complex permanent, conducting tissue that conducts water and mineral nutrients in only an upward direction from root to leaves (unidirectional).
• The cells of the xylem have thick lignified walls, and many of them are dead.
• It is a heterogeneous tissue consisting of various elements.

Additional Information

• Sclerenchyma, in plants, supports tissue composed of any of various kinds of hard woody cells.
• Mature sclerenchyma cells are usually dead cells that have heavily thickened secondary walls containing lignin.
• Sclerenchyma, in plants, support tissue composed of any of various kinds of hard woody cells.
• Mature sclerenchyma cells are usually dead cells that have heavily thickened secondary walls containing lignin.
• Macrophage is a type of white blood cell that helps eliminate foreign substances by engulfing foreign materials and initiating an immune response.

The statement puts forward a question, whether or not rural women be given computer education without any cost.

• Argument I answers in affirmative with adequate reasoning that free computer education will empower and help women. So, argument I is strong.
• Argument II states that there is no need to make it mandatory, however, the statement does not mention making education mandatory, it only suggests making it free. Thus, argument II is incorrect and thereby not strong.

Hence the correct answer is option 3.

Shortcut Trick For an infinite Arithmetico-Geometric Progression (AGP) series where terms are 5/13, 55/132, 555/133..., rewrite terms as 5(1)/13 + 5(11)/132 + 5(111)/133... Let S = Σ (5/9)×(10n−1)/13n = (5/9) [Σ(10/13)n − Σ(1/13)n]. Sum of infinite GP = a / (1−r). S = (5/9) [(10/13)/(1−10/13) − (1/13)/(1−1/13)] = (5/9) [10/3 − 1/12] = (5/9) × (39/12) = 65/36. ∴ The correct answer is 65/36. Alternate Method Given: S = 5/13 + 55/132 + 555/133 + ... ∞ Formula: Sum of infinite GP = a / (1−r) where |r| < 1.

⇒ S = (5/9) [ (10−1)/13 + (100−1)/132 + (1000−1)/133 + ... ] ⇒ S = (5/9) [ (10/13 + 102/132 + 103/133 + ...) − (1/13 + 1/132 + 1/133 + ...) ] ⇒ S = (5/9) [ {(10/13) / (1 − 10/13)} − {(1/13) / (1 − 1/13)} ] ⇒ S = (5/9) [ {(10/13) / (3/13)} − {(1/13) / (12/13)} ] ⇒ S = (5/9) [ 10/3 − 1/12 ] ⇒ S = (5/9) [ (40 − 1) / 12 ] = (5/9) × (39/12) ⇒ S = (5 × 13) / (3 × 12) = 65/36 ∴ The correct answer is 65/36. Additional Information Sum of Infinite GP For a geometric progression a, ar, ar2..., the sum to infinity is S∞ = a / (1−r), provided |r| < 1. General Term for Repetitive Digits A sequence of digits like 5, 55, 555 can be represented as Tn = (5/9)(10n − 1). Arithmetico-Geometric Progression (AGP) An AGP is a series in which each term is the product of corresponding terms of an AP and a GP.

Shortcut Trick

When a certain distance is covered at speeds S₁ and S₂ and total time T is given:

Distance = [ (S₁ × S₂) ÷ (S₁ + S₂) ] × T

⇒ Total Time T = 5 hr 48 min = 5 + (48 ÷ 60) = 29 ÷ 5 hours

⇒ Distance = [ (25 × 4) ÷ (25 + 4) ] × (29 ÷ 5)

⇒ Distance = (100 ÷ 29) × (29 ÷ 5) = 100 ÷ 5 = 20

∴ The correct answer is 20 km.

Alternate Method

Given:

Speed by bus (S₁) = 25 km/h

Speed on foot (S₂) = 4 km/h

Total time (T) = 5 hours 48 minutes = 5 + (48 ÷ 60) = 5 + (4 ÷ 5) = 29 ÷ 5 hours

Formula Used:

Time = Distance ÷ Speed

Total Time = T₁ + T₂

Calculation:

⇒ Let the one-way distance be D km.

⇒ Time taken by bus = D ÷ 25 hours

⇒ Time taken on foot = D ÷ 4 hours

⇒ (D ÷ 25) + (D ÷ 4) = 29 ÷ 5

⇒ (4D + 25D) ÷ 100 = 29 ÷ 5

⇒ 29D ÷ 100 = 29 ÷ 5

⇒ D = (29 × 100) ÷ (29 × 5)

⇒ D = 100 ÷ 5 = 20

∴ The correct answer is 20 km.

Additional Information

Average Speed Formula

When equal distances are covered at speeds S₁ and S₂, the average speed for the entire journey is (2 × S₁ × S₂) ÷ (S₁ + S₂).

Time Difference Formula

If the difference in time taken to cover a distance D at two speeds S₁ and S₂ is Δt, then Distance D = [ (S₁ × S₂) ÷ |S₁ − S₂| ] × Δt.

Relative Speed Concept

When two objects move in the same direction, their relative speed is the difference of their individual speeds (|S₁ − S₂|). In opposite directions, it is the sum of their speeds (S₁ + S₂).

Shortcut Trick

Net change in Total Marks = Correct Marks − Incorrect Marks = 56 − 65 = −9.

Change in Average = Total Change ÷ Number of students = −9 ÷ 36 = −0.25.

Correct Mean = Original Mean + Change = 72.50 − 0.25 = 72.25.

∴ The correct answer is 72.25.

Alternate Method

Given:

Total number of students = 36

Original Mean of marks = 72.50

Incorrect value = 65, Correct value = 56

Calculations:

⇒ Original sum of marks = 36 × 72.50 = 2610

⇒ Corrected sum of marks = 2610 − 65 + 56

⇒ Corrected sum = 2601

⇒ Corrected mean = 2601 ÷ 36

⇒ Corrected mean = 72.25

∴ The correct answer is 72.25.

Additional Information

Correction in Mean

When values are misread, the correct mean is found using: New Mean = Old Mean + (Correct Value − Incorrect Value) ÷ n.

Property of Arithmetic Mean

The algebraic sum of the deviations of a set of observations from their arithmetic mean is always zero.

Change in Observations

If each observation in a data set is increased or decreased by a constant value k, the mean also increases or decreases by k.

Shortcut Trick

Use the direct formula for the difference between CI and SI for 3 years:

Difference (D) = P × (R/100)² × (3 + R/100)

D = 4500 × (8/100) × (8/100) × (3 + 0.08)

D = 4500 × 0.0064 × 3.08 = 28.8 × 3.08 = 88.704

∴ The correct answer is Rs. 88.704.

Alternate Method

Given:

⇒ Principal (P) = Rs. 4500

⇒ Rate (R) = 8% per annum

⇒ Time (T) = 3 years

⇒ Simple Interest (SI) for 3 years = (4500 × 8 × 3) ÷ 100 = Rs. 1080

⇒ Compound Interest (CI) can be calculated using the amount formula:

⇒ Amount (A) = P(1 + R/100)^T = 4500(1 + 8/100)³

⇒ A = 4500 × (1.08)³ = 4500 × 1.259712 = Rs. 5668.704

⇒ CI = A − P = 5668.704 − 4500 = Rs. 1168.704

⇒ Difference = CI − SI = 1168.704 − 1080 = Rs. 88.704

∴ The correct answer is Rs. 88.704.

Additional Information

Difference for 2 Years

The difference between CI and SI for 2 years is given by the formula: D = P × (R/100)².

Effective Rate of Interest

For a rate R, the effective CI rate for 3 years is 3R + 3R²/100 + R³/10000 percent.

Simple Interest Formula

Simple interest is calculated only on the principal: SI = (P × R × T) ÷ 100.

Shortcut Trick Make the denominators equal to 112 for all fractions. Lower limit: 1/8 × 14/14 = 14/112 Upper limit: 1/7 × 16/16 = 16/112 The fraction n/112 must lie between 14/112 and 16/112. The only integer n between 14 and 16 is 15. ∴ The correct answer is 15.

Alternate Method Given: 1/8 < n/112 < 1/7

Step 1: Convert the boundaries to fractions with denominator 112. ⇒ Lower Bound = 1/8 = (1 × 14) / (8 × 14) = 14/112 ⇒ Upper Bound = 1/7 = (1 × 16) / (7 × 16) = 16/112 Step 2: Set up the inequality. ⇒ 14/112 < n/112 < 16/112 Step 3: Solve for the integer n. ⇒ 14 < n < 16 ⇒ Since n is an integer, n = 15. ∴ The correct answer is 15.

Additional Information Comparison of Fractions To compare fractions, convert them to a common denominator by finding the LCM of the denominators. Decimal Conversion Another method is converting to decimals: 1/8 = 0.125 and 1/7 ≈ 0.1428. Thus, 0.125 < n/112 < 0.1428. Cross Multiplication Rule For two fractions a/b and c/d, if a × d > b × c, then a/b > c/d.

Shortcut Trick

• ​The half-circle in the question figure is different from that of option figures B, C, and D.
• Option figure B has a bigger part whereas option figures C and D have smaller parts.
• So, option figure A is the correct answer.

Detailed explanation:

• The circle with two lines and one small circle move 90⁰ clockwise direction. So, in the answer figure, the small circle will appear towards the right.
• Similarly, the half-circle with two lines inside it moves 900 anticlockwise.

Hence, "option 3" is the correct answer.

Shortcut Trick

Convert units to cm: Hall = 1600 cm × 1000 cm; Brick = 20 cm × 10 cm.

Number of bricks = (Area of hall) ÷ (Area of one brick)

Number of bricks = (1600 × 1000) ÷ (20 × 10) = 1600000 ÷ 200 = 8000.

∴ The correct answer is 8000 bricks.

Alternate Method

Given:

Length of hall (L) = 16 m = 1600 cm

Width of hall (W) = 10 m = 1000 cm

Brick dimensions = 20 cm × 10 cm

Formula Used:

Number of bricks = (Total Area) ÷ (Area of 1 brick)

⇒ Area of Hall = 1600 × 1000 = 16,00,000 cm²

⇒ Area of one Brick = 20 × 10 = 200 cm²

⇒ Required Bricks = 16,00,000 ÷ 200

⇒ Required Bricks = 8000

∴ The correct answer is 8000 bricks.

Additional Information

Unit Conversion

Always ensure all dimensions are in the same unit before calculation. 1 meter = 100 centimeters and 1 m² = 10,000 cm².

Area of Rectangle

The area of a rectangular surface is calculated as Length × Breadth.

Number of Tiles/Bricks

Required quantity = (Total Surface Area) ÷ (Area of a single unit). If there is a mortar thickness, it must be added to the brick dimensions first.

The correct answer is 270 C.

Formula Used:

• Charge = Current x time

here, Current = 0.75 A

Time in sec = 6 x 60 = 360 sec.

Amount of charge flow in 6 min = 0.75 x 6 x 60

                                                  = 270 Coulomb

Shortcut Trick

The foot of the perpendicular from any point (x, y) to the x-axis is always (x, 0).

Given point P = (−5, 2).

Here, the x-coordinate is −5 and the y-coordinate is 2.

Thus, the coordinates of the foot M on the x-axis are (−5, 0).

∴ The correct answer is −5, 0.

Alternate Method

Given: Point P(−5, 2) and its perpendicular foot M on the x-axis.

Formula Used: For any point (x, y), the foot of the perpendicular to the x-axis is (x, 0) and to the y-axis is (0, y).

⇒ The given point is P(−5, 2). ⇒ The x-coordinate of point P is −5. ⇒ The y-coordinate of point P is 2. ⇒ When a perpendicular is drawn from P to the x-axis, the x-coordinate of the foot M remains the same as that of P. ⇒ Since M lies on the x-axis, its y-coordinate must be 0. ⇒ Therefore, the coordinates of M are (−5, 0).

∴ The correct answer is −5, 0.

Additional Information

Foot of Perpendicular to Y-axis

For any point (x, y), the foot of the perpendicular drawn to the y-axis is (0, y).

Distance from Coordinate Axes

The perpendicular distance of a point (x, y) from the x-axis is |y| units and from the y-axis is |x| units.

Reflection of a Point

The reflection of point (x, y) in the x-axis is (x, −y), and its reflection in the y-axis is (−x, y).

The least possible Venn diagram is given below:-

Conclusion:

I) Some fruits are lions. → False (it is possible but not definite.)

II) Some cats are lions. → True (this is visible in the above Venn diagram, a part of cat is lion)

Hence, "option 4" is the correct answer.

The correct answer is Kannauj.

Key Points

• After the death of Harshavardhana, the kings of the Pratihara, Pala, and Rashtrakuta dynasties fought with each other to gain control over Kannauj. 
• The Tripartite Struggle for control of Northern India occurred in the 9th century.
• The battle was between the Pratihara Empire, the Pala Empire, and the Rashtrakuta Empire.

Additional Information

• After the death of Emperor Harsha Vardhana, his empire disintegrated and north India was parcelled out in many states.
• ​The glory of being the capital of north India was no more Pataliputra but Kannauj.

The correct answer is Balakrishna Doshi.

Key Points

• Balakrishna Doshi was awarded the first Pritzker Architecture Prize.
• Indian architect and reputed urban planner Balkrishna Doshi have been named this year's winner of the Pritzker Prize for being able to interpret architecture and transform it into buildings that respect Eastern culture.
• Balkrishna Doshi was born in Pune, India on August 26, 1927, into an extended Hindu family that had been involved in the furniture industry.

Additional Information

• Sheila Sri Prakash is an architect and urban designer of Indian origin.
• She is the founder of Shilpa Architects and is the first woman in India to have started and operated her own architectural practice.
• Satish Gujral was an Indian painter, sculptor, muralist, and writer of the post-independent era.
• He was awarded the Padma Vibhushan, the second-highest civilian award of the Republic of India, in 1999.
• Revathi S. Kamath was an Indian architect and planner based in Delhi.
• She is a pioneer of mud architecture in India.
• In addition to this, she is also credited with building the tallest stainless steel structure in India.

The correct answer is 20°C.

Key Points

• The temperature difference between upper layers and deeper layers of the ocean for setting up an OTEC power plant should be 20°C. 
• Since ocean thermal energy is generated due to a difference in temperatures, for an OTEC plant to be installed, a temperature difference of 20^oC is required.

Additional Information

• Ocean Thermal Energy Conversion (OTEC) is a process that can produce electricity by using the temperature difference between deep cold ocean water and warm tropical surface waters.
• OTEC plants pump large quantities of deep cold seawater and surface seawater to run a power cycle and produce electricity.

Shortcut Trick

Meena's present age = 26 − 6 = 20 years.

Ratio of Meena to Sina = 4 : 3.

4 units → 20 years.

1 unit → 5 years.

3 units → 3 × 5 = 15 years.

∴ The correct answer is 15 years.

Alternate Method

Given:

Ratio of Meena's age to Sina's age = 4 : 3

Meena's age after 6 years = 26 years

Let the present age of Meena be 4x and Sina be 3x.

⇒ 4x + 6 = 26

⇒ 4x = 26 − 6

⇒ 4x = 20

⇒ x = 5

Present age of Sina:

⇒ 3x = 3 × 5

⇒ 3x = 15 years

∴ The correct answer is 15 years.

Additional Information

Ratio and Proportion in Ages

If the ratio of ages is a:b, their actual ages can be taken as ax and bx, where x is a common multiplier.

Future and Past Ages

To find age after n years, add n (Age + n). To find age n years ago, subtract n (Age − n).

Age Difference

The difference between the ages of two persons remains constant throughout their lives.

The logic followed here is:-

• The first circle moves in 180⁰ clockwise direction and we get the second circle.

Similarly,

• The third circle moves in 180⁰ clockwise direction and we get the fourth circle.

Hence, "option 3" is the correct answer.

The argument states that the manager has made a request to the employees to avoid making long personal calls during working hours.

• Thus, it can be assumed that the manager is expecting the employees to listen to him and comply with his request and hence made the request. So, assumption I logically follows the argument.
• Assumption 2 contradicts assumption 1. So, only one of the assumptions can be implicit at a time. Since assumption 1 follows, assumption II will not follow the argument.

Hence the correct answer is option 1.

Additional Information

• When the argument has stated a request or an order, the assumption will have to be in favour of the request or order. In simple terms, no one makes a request expecting people to not follow it. Thus, the correct assumption will be in favour of the statement.

Shortcut Trick

To rationalize a fraction with a denominator like (a + √b), multiply both numerator and denominator by its conjugate (a − √b).

Given expression: 1 / (3 + √5)

Conjugate of the denominator is (3 − √5).

Simplified Result = (3 − √5) / (3² − (√5)²) = (3 − √5) / (9 − 5) = (3 − √5) / 4.

∴ The correct answer is (3 − √5) / 4.

Alternate Method

Given: 1 / (√5 + 3)

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

⇒ 1 / (3 + √5)

⇒ [1 × (3 − √5)] / [(3 + √5) × (3 − √5)]

⇒ (3 − √5) / [(3)² − (√5)²]

⇒ (3 − √5) / (9 − 5)

⇒ (3 − √5) / 4

∴ The correct answer is (3 − √5) / 4.

Additional Information

Rationalization of Surds

The process of converting a fraction with an irrational denominator into an equivalent fraction with a rational denominator is called rationalization.

Conjugate Pairs

Two binomial surds whose product is a rational number are called conjugates. For example, (x + √y) and (x − √y) are conjugate pairs.

Algebraic Identity

The identity (a + b)(a − b) = a² − b² is used to eliminate square roots from the denominator during simplification.

The least possible Venn diagram is given below:-

Conclusion:

I. Some buses are bikes. → False ( it is possible but not definite)

II. Some bikes are buses. → False (it is possible but not definite)

III. Some bikes are trains. → True (Some trains are bikes. So, some bikes are trains is also true. This is also visible in the above Venn diagram)

IV. Some trains are buses. → True (As shown in the Venn diagram, a part of train is bus.)

Hence, "option 3" is the correct answer.

The correct answer is a Sound wave.

Key Points 

• In longitudinal waves, the direction of vibration in the medium of the particle is parallel to the propagation of the wave.
• In longitudinal waves, the particles transfer energy from one point to another by vibrating in the line of direction of propagation of the wave.
• In longitudinal waves, the movement of particles is usually parallel to the movement of energy.
• Longitudinal waves travel in the form of compression and rarefaction.
• The best example of longitudinal waves is sound waves.

Additional Information 

• Transverse Waves:
• In transverse waves, the particles transfer energy from one point to another point by vibrating perpendicularly in the direction of the propagation of the wave.
• In a transverse wave, the particles are displaced perpendicular to the direction that the wave travels.
• Radio waves, water waves are a few examples of transverse waves.
• Waves produced in a string are a good example of a transverse wave.
• Waves produced in a string are standing waves.

The logic followed here is:-

 - the pink pencil is facing in a different direction in figure A.

• In figures B, C, and D, we can see the pink pencil facing the opposite direction 

• Thus, figure A is different from others.

Hence, "option 4" is the correct answer. 

Additional Information

• this is how the yellow pencil appears in all 4 option figures
• this is how the blue pencil appears in all 4 option figures
• this is how the green pencil appears in all 4 option figures

The correct answer is P/m.

Key Points

• Momentum refers to the quantity of motion that an object has.
• If an object is in motion (on the move) then it has momentum. Momentum can be defined as "mass in motion."
• All objects have mass.
• So if an object is moving, then it has momentum - it has its mass in motion.
• p = mv
• So $v = {p\over{m}}$
• p = momentum
• m = mass
• v = velocity

The logic followed here is:-

• When we rotate the question figure 90⁰ clockwise we get figure D.

Hence, "option 4" is the correct answer.

Shortcut Trick

Apply the Alligation method to find the ratio of members in the two groups.

Difference 1 (Group 1 − Combined) = 15 − 13.7 = 1.3

Difference 2 (Combined − Group 2) = 13.7 − 12 = 1.7

Ratio of members (Group 1 : Group 2) = 1.7 : 1.3 = 17 : 13

Since the number of members in Group 1 is given as 17, the value of n must be 13.

∴ The correct answer is 13.

Alternate Method

Given: Mean score of Group 1 = 15, Members = 17; Mean score of Group 2 = 12, Members = n; Combined mean = 13.7

Formula Used: Combined Mean = (n₁ × x̄₁ + n₂ × x̄₂) ÷ (n₁ + n₂)

⇒ 13.7 = (17 × 15 + n × 12) ÷ (17 + n)

⇒ 13.7 × (17 + n) = 255 + 12n

⇒ 232.9 + 13.7n = 255 + 12n

⇒ 13.7n − 12n = 255 − 232.9

⇒ 1.7n = 22.1

⇒ n = 22.1 ÷ 1.7

⇒ n = 13

∴ The correct answer is 13.

Additional Information

Arithmetic Mean

The Mean is the sum of all observations divided by the total number of observations. Total Sum = Mean × Total Count.

Weighted Average

When combining two groups with different sizes n₁ and n₂ and averages A₁ and A₂, the combined average is A_avg = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Alligation Rule in Averages

The ratio of the number of items in two groups is the inverse ratio of the deviations of their averages from the combined average.

 

• Given that:25 > 90 $ 9 < 8

Putting the value on above equation:-

25 + 90 ÷ 9 - 8

= 25 + 10 - 8

= 35 - 8

= 27

Hence, "option 3" is the correct answer.

The correct answer is more.

Key Points

• A compressed spring has more energy as compared to a normal spring.
• When we stretch or compress a spring we work against the restoring force of the spring.
• This work is stored as elastic potential energy in the spring.
• The more we stretch or compress the spring, the more work is done by you and more energy is stored.
• Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing.

The correct answer is Mamta Kalia.

Key Points

• Renowned Hindi scholar and writer Mamta Kalia (77) was chosen for Vyas Samman 2017 for her novel “Dukkham Sukkham”.
• She was selected by a selection committee headed by author Vishwanath Prasad Tiwari.
• Dukkha Sukkham published in 2009 is the saga of a lower-middle-class family of three generations.

Additional Information

• Sudha Murty is an Indian engineering teacher, author, and social worker.
• She is also the chairperson of the Infosys Foundation. She is married to the co-founder of Infosys, N. R. Narayana Murthy.
• Sushmita Banerjee, also known as Sushmita Bandhopadhyay and Sayeda Kamala, was a writer and activist from India.
• Her works include the memoir Kabuliwalar Bangali Bou based on her experience of marrying an Afghan and her time in Afghanistan during Taliban rule.
• Shweta Taneja is an Indian author of novels, short fiction, graphic novels, nonfiction, and comic books.

Shortcut Trick

Efficiency Ratio of Raju : Shaju = 2 : 1

Combined Efficiency = 2 + 1 = 3 units/day

Total Work = Combined Efficiency × Days = 3 × 12 = 36 units

Raju alone = Total Work ÷ Raju's Efficiency = 36 ÷ 2 = 18 days

∴ The correct answer is 18 days.

Alternate Method

Given:

Efficiency of Raju = 2 × Efficiency of Shaju

Time taken together = 12 days

Calculations:

⇒ Let Shaju's efficiency be 1 unit/day.

⇒ Raju's efficiency = 2 units/day.

⇒ Total efficiency of (Raju + Shaju) = 2 + 1 = 3 units/day.

⇒ Total Work = Total Efficiency × Total Time

⇒ Total Work = 3 × 12 = 36 units.

⇒ Time taken by Raju alone = Total Work ÷ Raju's Efficiency

⇒ Time taken = 36 ÷ 2 = 18 days.

∴ The correct answer is 18 days.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken to complete a work. If the ratio of efficiency is x : y, then the ratio of time taken is y : x.

Total Work Formula

Total Work = Efficiency × Time. This is the fundamental constant used to solve most Time and Work problems.

Combined Work

When multiple people work together, their individual efficiencies are added to find the net efficiency per day.

The straight lines required to make the question figure is shown below:-

• The minimum number of straight lines required to make the question figure is 7.

Hence, "option 2" is the correct answer.

The water image of the given number is given below:-

Hence, "option 2" is the correct answer.

The correct answer is 1761.

Key Points

• The third battle of Panipat was fought in the year 1761.
• The Third Battle of Panipat took place on 14 January 1761, at Panipat, about 60 miles (95.5 km) north of Delhi between a northern expeditionary force of the Maratha Empire and a coalition of the King of Afghanistan Ahmad Shah Durrani with two Indian Muslim allies—the Rohilla Afghans of the Doab and Shuja-ud-Daula,
• The battle of Panipat was fought to protect India from the raids that began with Nadir Shah in 1739 and to protect the effete Mughal dynasty.
• Bhau declared Shah Alam as the absentee Mughal Emperor and Shujauddaulah as the Wazir.

Additional Information

• The Battle of Ghaghra was fought in the year 1529.
• The Battle of Ghaghra, fought in 1529, was a major battle for the conquest of India by the Mughal Empire.
• It followed the first Battle of Panipat in 1526 and the Battle of Khanwa in 1527.
• The forces of now Emperor Zahir ud-Din Muhammad Babur of the emerging Mughal Empire were joined by Indian allies in the battle against the Eastern Afghan Confederates under Sultan Mahmud Lodi and Sultanate of Bengal under Sultan Nusrat Shah.
• Battle of Khatauli
• The Battle of Khatoli was fought in 1518 between the Lodi dynasty under Ibrahim Lodi and the Kingdom of Mewar under Rana Sanga, during which Mewar emerged victoriously.
• Battle of Gagron
• The Battle of Gagron was fought in 1519 between Sultan Mahmud Khalji II of Malwa and Rana Sanga of Mewar.
• The conflict took place in Gagron and resulted in Sanga's victory, with him taking Mahmud captive and annexing significant territory.
• Battle of Bayana
• The Battle of Bayana (1526) was a rare setback for Babur after his victory at Panipat on 21 April 1526.
• Although this victory gave Babur control of Delhi and Agra, many other fortified places refused to accede to his authority.

The correct answer is Arvind Adiga.

Key Points

• India's first-time novelist Aravind Adiga won the 50,000 pounds Man Booker Prize 2008 for his novel.
• The White Tiger. Young Indian writer Aravind Adiga is one of the two first-time novelists on the 2008 Man Booker's shortlists of six.
• The other is Australia's Steve Toltz.
• The White Tiger is a novel by Indian author Aravind Adiga.
• It was published in 2008 and won the 40th Man Booker Prize the same year.

Additional Information

• Amitav Ghosh is an Indian writer and the winner of the 54th Jnanpith award, India’s highest literary honour, best known for his work in English fiction.
• Anita Desai, born Anita Mazumdar is an Indian novelist and the Emerita John E. Burchard Professor of Humanities at the Massachusetts Institute of Technology.
• As a writer, she has been shortlisted for the Booker Prize three times.
• Suzanna Arundhati Roy is an Indian author best known for her novel The God of Small Things, which won the Man Booker Prize for Fiction in 1997 and became the best-selling book by a non-expatriate Indian author.
• She is also a political activist involved in human rights and environmental causes.

Shortcut Trick

Savings = 22% → Expenditure = 100% − 22% = 78%

78% of Income = ₹9,894.30

Total Income = 9,894.30 ÷ 0.78 = ₹12,685

∴ The correct answer is ₹12,685.

Alternate Method

Given:

Savings Percentage = 22%

Total Expenditure = ₹9,894.30

Formula: Income = Expenditure + Savings

⇒ Let Total Income be ₹X.

⇒ Expenditure Percentage = 100% − 22% = 78%

⇒ 78% of X = 9,894.30

⇒ (78 ÷ 100) × X = 9,894.30

⇒ X = (9,894.30 × 100) ÷ 78

⇒ X = 989,430 ÷ 78

⇒ X = 12,685

∴ The correct answer is ₹12,685.

Additional Information

Income-Expenditure Relation

Income is always the base (100%) in percentage-based salary problems. Income = Expenditure + Savings.

Percentage Change

If income increases by x% and expenditure increases by y%, the new savings are calculated using the updated absolute values.

Base Change Rule

To find the original value when a part is given: Original = (Part Value ÷ Part Percentage) × 100.