RRC Group D Previous Year Paper 53 (Held On: 5 Oct 2018 Shift 2)

The correct answer is Raised hammer.

 Key Points

• Raised hammer doesn't possess kinetic energy.
• The kinetic energy of a body is the energy possessed by the body due to its motion. Since every point of the hammer is at rest. The kinetic energy of the hammer is zero.
• The gravitational potential energy of a body is the energy that varies depending on the height or position of the body. Since hammers are at non-zero height from the ground, its P.E. is non-zero.

Additional Information

• Kinetic energy, a form of energy that an object or a particle has by reason of its motion.
• If work, which transfers energy, is done on an object by applying a net force, the object speeds up and thereby gains kinetic energy.
• Kinetic energy is a property of a moving object or particle and depends not only on its motion but also on its mass.
• Potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.

The correct answer is CaO..

Key Points

• CaO reacts vigorously with water to form slaked lime.
• Calcium hydroxide, also called slaked lime, Ca(OH)₂, is obtained by the action of water on calcium oxide.
• When mixed with water, a small proportion of it dissolves, forming a solution known as limewater, the rest remaining as a suspension called milk of lime(Calcium hydroxide).

Additional Information

• Calcium hydroxide (traditionally called slaked lime) is an inorganic compound with the chemical formula Ca(OH)₂.
• It is a colorless crystal or white powder and is produced when quicklime (calcium oxide) is mixed or slaked with water.
• It has many names including hydrated lime, caustic lime, builders' lime, slaked lime, cal, and pickling lime.
• Calcium hydroxide is used in many applications, including food preparation.
• Limewater, also called milk of lime, is the common name for a saturated solution of calcium hydroxide.

The correct answer is Resistivity.

Key Points

• Ohm-m is the unit of resistivity.
• Ohm-Meter (ohm-m) is a unit in the category of Electric resistivity.
• It is also known as the ohm meter.
• This unit is commonly used in the SI unit system.
• Ohm-Meter (ohm-m) has a dimension of MLT^-3I^-2 where M is mass, L is length, T is time, and I is electric current.

Additional Information

• Resistance is the opposition that a substance offers to the flow of electric current. 

• It is represented by the uppercase letter R.

• The standard unit of resistance is the ohm, sometimes written out as a word, and sometimes symbolized by the uppercase Greek letter omega: 

• When an electric current of one ampere passes through a component across which a potential difference (voltage) of one volt exists, then the resistance of that component is one ohm.

• The resistance of a conductor is directly proportional to length.

• The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area.

• Resistance also depends on the material of the conductor.

The correct answer is 1529.

Key Points

• 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.

Additional Information

• 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 (1527) 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.

Given:

$18 \div \frac{1}{8} ;of;{ 11 + 16 - (10 + 7 - \overline{6+8} ) } = ?$

Concept used:

This is the concept of VBODMAS

V – Viniculum or Bar (–) i.e first you have to perform the mathematical operation under a bar, then go for removing brackets

B – Brackets (order to remove brackets for simplification: 1st ( ) circular / smaller brackets, 2nd { } Curly or flower brackets and finally [ ] square brackets.

O – Of  (After removing brackets, then go for operation having ‘Of”.in complex expression

D – Next do Division

M – Multiplication

A – then Addition follows finally

S – Subtraction.

Calculation:

$18 \div \frac{1}{8} ;of;{ 11 + 16 - (10 + 7 - \overline{6+8} ) } = ?$

⇒  $18 ÷ \frac{1}{8}; of;{ { 11 + 16 - (10 + 7 - 14 )}} =\ ?$

⇒ $18 ÷ \frac{1}{8};of;{ { 11 + 16 - 3}} =\ ?$

⇒ $18 ÷ \frac{1}{8} \times 24 =\ ?$

⇒ 18 ÷ 3

⇒ 6

∴ Answer is 6

According to the question,

Total units sold was 120 million

Unit sold in Karnataka = 120 × 2/5

⇒ 48

∴ 48 million were sold in the Karnataka region

The number of circles in the above figure is as follows:-

There is a total of 5 circles in the above figure which are labelled as 1, 2, 3, 4, and 5.

Hence, "option 1" is the correct answer.

The correct answer is Ankit Kavanna.

Key Points

• Ankit Kavanna is an Indian anti-hunger activist and he was awarded the Queen's Young Award in England in 2017.
• Anti-hunger activist Ankit Kawatra was awarded the Queen’s Young Leaders Award for 2017 at a ceremony in the Buckingham Palace here.
• The award recognizing the 25-year-old’s exceptional work towards solving hunger and malnutrition in India was presented to him by Queen Elizabeth II.

Additional Information

• Mr. Kawatra is the founder of Feeding India, an organization that aims to eradicate hunger and food wastage in India.
• Kawatra started Feeding India in 2014 with just 5 people, which now works in 43 cities across India with 4,500 volunteers.
• The foundation is currently serving 80 lakh meals to the needy.
• Queen's Young Award Launched in 2014, The Queen's Young Leader Award recognizes and honors exceptional people aged 18-29 across the Commonwealth, who are leading in their communities and using their skills to transform lives. are using it.

Given:

11:14, 17:21, 5:7, 2:3

Concept used:

Lowest Common Multiple

Calculation:

By writing the ratios in fraction form, we get

11/14, 17/21, 5/7, 2/3 

LCM of denominators of fractions (3, 21, 14, 7) 

⇒ LCM(3, 21, 14, 7) = 42 

By converting the given ratio as equivalent, we get 

11/14 × 3/3 = 33/42 

17/21 × 2/2 = 34/42

5/7 × 6/6 = 30/42 

2/3 × 14/14 = 28/42 

From above, writing the above fractions in descending order, 

34/42, 33/42, 30/42, 28/42

                       or 

17/21, 11/14, 5/7, 2/3 

∴ The last ratio will be 2/3 or 2 : 3.

Shortcut Trick

Total ways = (3 Boys × 2 Girls) + (4 Boys × 1 Girl) + (5 Boys × 0 Girls)

= (⁷C₃ × ⁶C₂) + (⁷C₄ × ⁶C₁) + (⁷C₅ × ⁶C₀)

= (35 × 15) + (35 × 6) + (21 × 1)

= 525 + 210 + 21 = 756

∴ The correct answer is 756 ways.

Alternate Method

Given: 7 boys and 6 girls. Total 13 students. Select 5 students with at least 3 boys.

Formula: ⁿC_r = n! / [r!(n − r)!]

⇒ Case 1 (3 Boys, 2 Girls): ⁷C₃ × ⁶C₂ = [(7 × 6 × 5) / (3 × 2 × 1)] × [(6 × 5) / (2 × 1)] = 35 × 15 = 525

⇒ Case 2 (4 Boys, 1 Girl): ⁷C₄ × ⁶C₁ = ⁷C₃ × 6 = 35 × 6 = 210

⇒ Case 3 (5 Boys, 0 Girls): ⁷C₅ × ⁶C₀ = ⁷C₂ × 1 = [(7 × 6) / (2 × 1)] × 1 = 21 ×

The correct answer is MS Dhoni.

Key Points

• MS Dhoni was conferred with the Padma Bhushan award in the 2018 Sports (Cricket) category.
• Dhoni has been the recipient of many awards, including the ICC ODI Player of the Year award in 2008 and 2009 (the first player to win the award twice), the Rajiv Gandhi Khel Ratna award in 2007, and the Padma Shri, India's fourth-highest civilian honour in 2009.
• Dhoni-led India to two World Cup triumphs in the inaugural ICC World Twenty20 held in South Africa in September 2007 and the 2011 ICC ODI World Cup.

Additional Information

• The Padma Awards are conferred on the recommendations made by the Padma Awards Committee, which is constituted by the Prime Minister every year.
• The nomination process is open to the public.
• Even self-nomination can be made.
• These awards are presented by the President of India at a ceremonial function held at Rashtrapati Bhawan.

The correct answer is Atmospheric Pressure.

Key Points

• Air pressure can be called atmospheric pressure.
• The air around us has weight, and it presses against everything it touches.
• That pressure is called atmospheric pressure, or air pressure.
• It is the force exerted on a surface by the air above it as gravity pulls it to Earth.

Additional Information

• Atmospheric pressure is commonly measured with a barometer.
• In a barometer, a column of mercury in a glass tube rises or falls as the weight of the atmosphere changes.
• An atmosphere (atm) is a unit of measurement equal to the average air pressure at sea level at a temperature of 15 degrees Celsius (59 degrees Fahrenheit).
• One atmosphere is 1,013 millibars or 760 millimeters (29.92 inches) of mercury.
• Condensation is the process where water vapor becomes liquid.
• It is the reverse of evaporation, where liquid water becomes a vapor.
• Condensation happens one of two ways:
• Either the air is cooled to its dew point or it becomes so saturated with water vapor that it cannot hold any more water or it becomes so saturated with water vapor that it cannot hold any more water.

Shortcut Trick

Apply M₁D₁ = M₂D₂

40 × 6 = 36 × D₂

D₂ = (40 × 6) ÷ 36 = 40 ÷ 6 = 20 ÷ 3

D₂ = 6 (2)/(3) days

∴ The correct answer is 6 (2)/(3) days.

Alternate Method

Given:

Initial men (M₁) = 40 men

Initial days (D₁) = 6 days

Final men (M₂) = 36 men

Formula Used:

Total Work = Men × Days

Calculations:

⇒ Total Work = 40 × 6 = 240 units

⇒ Required Days (D₂) = Total Work ÷ M₂

⇒ D₂ = 240 ÷ 36

⇒ D₂ = 20 ÷ 3

⇒ D₂ = 6 (2)/(3) days

∴ The correct answer is 6 (2)/(3) days.

Additional Information

Chain Rule Formula

For work involving efficiency and hours: (M₁×D₁×H₁×E₁)/W₁ = (M₂×D₂×H₂×E₂)/W₂.

Inverse Proportion

In Time and Work, the number of men is inversely proportional to the number of days taken to complete the work.

Work and Wages

Wages are distributed in the ratio of the work done by each individual, which is Efficiency × Time.

The correct answer is West Bengal, Uttar Pradesh and Jharkhand.

Key Points

• The National Mission for Clean Ganga (NMCG) has approved five 'Namami Gange' programs worth ₹295.01 crores for the states West Bengal, Uttar Pradesh, and Jharkhand.
• The National Ganga River Basin Authority (NGRBA) has taken a convergent and comprehensive approach to meet the challenges faced by the Ganga through four distinct areas, namely, wastewater management, solid waste management, industrial pollution, and riverfront development.

Additional Information

• ‘Namami Gange Programme’, is an Integrated Conservation Mission, approved as ‘Flagship Programme’ by the Union Government in June 2014 with a budget outlay of Rs. 20,000 Crore to accomplish the twin objectives of effective abatement of pollution, conservation, and rejuvenation of National River Ganga.
• Its implementation has been divided into Entry-Level Activities (for immediate visible impact), Medium-Term Activities (to be implemented within 5 years of time frame), and Long-Term Activities (to be implemented within 10 years).

The correct answer is Rabindranath Tagore.

Key Points

• Rabindranath Tagore was the first Indian to win the Nobel Prize.
• Rabindranath Tagore was the first Indian to get a Nobel Prize in 1913 for his work in Literature.
• He won the award for "his profoundly sensitive, fresh and beautiful verse, by which, with consummate skill, he has made his poetic thought, expressed in his own English words, a part of the literature of the West".

Additional Information

• Esther Duflo, Abhijit Banerjee, and Michael Kremer were awarded the Nobel Prize in Economics in 2019.
• They were awarded "for their experimental approach to alleviating global poverty".
• Esther Duflo is the youngest person to be awarded the Nobel prize in economics.
• Gerty Theresa Cori was the third woman to win a Nobel Prize in science.
• She is the first woman to be awarded the Nobel Prize in Physiology or Medicine for her vital role in the "discovery of the course of the catalytic conversion of glycogen".
• Maria Goeppert Mayer got the Nobel prize in Physics for proposing the nuclear shell model of the atomic nucleus.
• She was the second woman to win a Nobel Prize in physics.
• The first was Marie Curie.

Important Points

• The Nobel Prize in Physics for the year 2020 was awarded to three astrophysicists Roger Penrose from the UK, Reinhard Genzel from Germany, and Andrea Ghez from the USA.
• Emmanuelle Charpentier of France and Jennifer A Doudna of the USA have been awarded the 2020 Nobel Prize in Chemistry for developing CRISPR/Cas9 genetic scissors, one of gene technology’s sharpest tools.
• The 2020 Nobel Peace Prize has been awarded to the World Food Programme (WFP), a United Nations (UN) agency, for its efforts to combat hunger, bettering conditions for peace in conflict-affected areas, and preventing the use of hunger as a weapon of war and conflict.
• American economists, Paul Milgrom, and Robert Wilson have been awarded the Sveriges Riksbank Prize in Economic Sciences, 2020 for their work on commercial auctions.
• The Nobel Prize in Literature 2020 has been awarded to the USA poet Louise Glück "for her unmistakable poetic voice that with austere beauty makes individual existence universal."

The correct answer is Raja Chola.

Key Points

• Raja Chola got the Brihadeshwara temple built at Thanjavur.
• This South Indian style is most fully realized both in scale and detail in the Brihadeshwara temple built between 1003 and 1010 by the Chola king Rajaraja I.
• Built by Tamil king Raja Raja Chola I between 1003 and 1010 AD, the temple is a part of the UNESCO World Heritage Site known as the "Great Living Chola Temples", along with the Chola dynasty era Gangaikonda Cholapuram temple and Airavatesvara temple.

Additional Information

• Rajaraja I, born Arulmoli Varman, often described as Rajaraja the Great, was a Chola emperor and was the most powerful king in the south at his time chiefly remembered for reinstating the Chola power and ensuring its supremacy in south India and the Indian Ocean.
• Brihadishvara Temple locally known as Thanjai Periya Kovil, and also called Rajarajeswaram, is a Hindu temple dedicated to Shiva located on the South Bank of the Cauvery river in Thanjavur, Tamil Nadu.

Concept-

• Mendel proposed two general rules to consolidate his understanding of inheritance in monohybrid crosses.
• Today these rules are called the Principles or Laws of Inheritance the First Law or Law of Dominance and the Second Law or Law of Segregation.
• According to the law of dominance.
• Characters are controlled by discrete units called factors.
• Factors occur in pairs.
• In a dissimilar pair of factors, one member of the pair dominates the other.

Explanation-

• The dihybrid cross involves two characters in a single plant.
• The parent pea plants are of two types.
• Tall plants with violet flowers.
• Short plants with white flowers.
• So, the genotype of the parents could be-
• Tall plants with violet flowers: TTWW or TtWw
• Short plants with white flowers: ttww
• Since all the progeny bore violet flowers, it implies that the tall plant with violet flowers has genotype 'WW' for violet flower color.
• Since the progeny acquired is both tall and short, the parent plant was not a pure tall plant and carry genes that determine the short height of the plant.
• Therefore, the genotype of the plant with respect to height would be 'Tt'.

So, if a cross is carried out between a tall parent with violet flowers (TtWW) and a short parent with white flowers (ttww), the progeny obtained is TtWw (8) : ttWw (8).

Mistake Points

• Please note that in pea plants violet colour of flowers is dominant over white colour.
• Also, the violet colour character has been denoted here by "W" and not "V" (which is the initial letter of the dominant character).
• It is important to remember which character is dominant over which, irrespective of the letters that are used to denote it in the cross.

Additional Information

• Law of Segregation 
• This law is based on the fact that the alleles do not show any blending and that both the characters are recovered as such in the F2 generation though one of these is not seen at the F1 stage.
• Though the parents contain two alleles during gamete formation, the factors or alleles of a pair segregate from each other such that a gamete receives only one of the two factors.
• Of course, a homozygous parent produces all gametes that are similar while a heterozygous one produces two kinds of gametes each having one allele with equal proportion.

Shortcut Trick

Let Chetna's present age be C and Mahim's be M.

From option 1: If C = 65, then 5 years ago, C = 60. Mahim was (1/3 × 60) − 1 = 19.

So, M present = 19 + 5 = 24. After 17 years, C = 82 and M = 41.

Since 82 is exactly twice of 41, the condition is satisfied.

∴ The correct answer is 65 years.

Alternate Method

Given:

Let C = Chetna's present age and M = Mahim's present age.

Equation 1 (17 years later): C + 17 = 2(M + 17)

⇒ C + 17 = 2M + 34

⇒ C − 2M = 17 → (i)

Equation 2 (5 years ago): M − 5 = 1/3(C − 5) − 1

⇒ M − 5 = (C − 5 − 3) / 3

⇒ 3M − 15 = C − 8

⇒ 3M − C = 7 → (ii)

Adding (i) and (ii):

⇒ (C − 2M) + (3M − C) = 17 + 7

⇒ M = 24 years

Substitute M = 24 in (i):

⇒ C − 2(24) = 17

⇒ C − 48 = 17

⇒ C = 65 years

∴ The correct answer is 65 years.

Additional Information

Linear Equations in Ages

Problems involving ages are solved by translating "years ago" as subtraction and "hence/later" as addition to the present age variables.

Age Ratio Method

If the difference between ages is constant, the ratio of ages changes over time. Always ensure the absolute difference between two people's ages remains the same across all time periods.

The correct answer is 15.

Key Points

• If the electron configuration of an element is 2, 8, 5, then the number of protons is 15.
• Total no. of electrons = 2 + 8 + 5 = 15
• No. of electrons in an atom = No. of protons = Atomic No. = 15

Additional Information

• The atomic number or proton number (symbol Z) of a chemical element is the number of protons found in the nucleus of every atom of that element.
• The atomic number uniquely identifies a chemical element.
• It is identical to the charge number of the nucleus.

Given:

The sum of a fraction and its reciprocal is $2 \frac{25}{66}$

Calculation:

Let the fraction be (x/y) (Denote this by ‘a’)

Sum of the fraction (a) and its reciprocal (1/a) = $2 \frac{25}{66}$

a + (1/a) = 157/66

⇒ (a² + 1)/a = 157/66

⇒ 66a² - 157a + 66 = 0

⇒ 66a² - 121a - 36a + 66 = 0

⇒ 11a(6a - 11) - 6(6a - 11) = 0

⇒ (11a - 6) (6a - 11) = 0

⇒ a = 11/6 or 6/11

Greater is 11/6 = $1 \frac{5}{6}$

∴ Required answer is $1 \frac{5}{6}$

The correct answer is Nisha Dutt.

Key Points

• Nisha Dutt was honored with the 'Social Entrepreneur of the Year' award at the 7th Asian Awards in London.
• Nisha Dutt, the CEO of Intellecap, has been honoured with the “Social Entrepreneur of the Year” award at The 7th Asian Awards in London in recognition of her work in making Intellecap a globally known enterprise that focuses on social capital. With this.
• Dutt has become the first Indian woman leader to be honoured with this award.
• Her key contribution has been integrating technology with challenges of healthcare, financial services, incubation, and conceptualizing programs such as Innovations Labs and Credit-tree.

Additional Information

• The Asian Awards is an annual awards ceremony for the global Asian community that takes place in the United Kingdom, in 14 categories including business, philanthropy, entertainment, culture and sport.
• In 2010 and 2011, the awards were open only to those born in or directly from India, Sri Lanka, Pakistan or Bangladesh. From 2013, they were expanded to include all people of South, East and Southeast Asian descent.
• The tenth edition of the awards will take place in 2022 due to the COVID-19 pandemic.
• Awarded for Honouring Asian Excellence
• Presented by Paul Sagoo
• First awarded in 2010

The correct answer is Venezuela.

Key Points

• Angel Falls is located in Venezuela.
• Angel Fall is the world's tallest uninterrupted waterfall, with a height of 979 meters (3,212 ft) and a plunge of 807 m (2,648 ft).
• The waterfall drops over the edge of the Auyán-tepui mountain in the Canaima National Park a UNESCO World Heritage site.
• The height figure, 979 m (3,212 ft), mostly consists of the main plunge but also includes about 400 meters (1,300 ft) of sloped cascade and rapids below the drop and a 30-meter (98 ft) high plunge downstream of the talus rapids.
• The falls are along a fork of the Río Kerepacupai Merú which flows into the Churún River, a tributary of the Carrao River, itself a tributary of the Orinoco River.

Additional Information

The least possible Venn diagram is as follows:

Conclusion:

1. All glass is earth. → Follows (as shown in the above Venn diagram, the entire part of glass is inside earth)
2. Some earth are sand.→ Follows (as shown in the above Venn diagram, some part inside earth is sand)

Hence, the correct answer is "Both 1 and 2 follow."

Shortcut Trick

Identify the conjugate of the denominator: (5 + 3√2) → (5 − 3√2).

Calculate the denominator value using the difference of squares: 5² − (3√2)².

Denominator = 25 − 18 = 7.

Place the conjugate over the calculated denominator.

∴ The correct answer is (5 − 3√2)/7.

Alternate Method

Given: Fraction = 1 / (5 + 3√2)

Formula Used: Rationalization involves multiplying the numerator and denominator by the conjugate (a − b) of the denominator (a + b), utilizing the identity (a + b)(a − b) = a² − b².

Calculations:

⇒ [1 × (5 − 3√2)] / [(5 + 3√2) × (5 − 3√2)]

⇒ (5 − 3√2) / [(5)² − (3√2)²]

⇒ (5 − 3√2) / (25 − 18)

⇒ (5 − 3√2) / 7

∴ The correct answer is (5 − 3√2)/7.

Additional Information

Rationalizing Factor (Conjugate)

For a denominator of the form (a + √b), the rationalizing factor is (a − √b). Multiplying these results in a rational number a² − b.

Difference of Squares Identity

The identity (a + b)(a − b) = a² − b² is the fundamental tool used to eliminate surds from the denominator of a fraction.

Handling Coefficients in Surds

When squaring a term like (3√2), remember to square both parts: (3√2)² = 3² × (√2)² = 9 × 2 = 18.

The correct answer is Thallophyta.

 Key Points

• Lichen Plant belongs to Thallophyta Division.
• Thallophyta is a division of the plant kingdom including primitive forms of plant life showing a simple plant body.
• Including unicellular to large algae, fungi, lichens.
• The first ten phyla are referred to as thallophytes.
• They are simple plants without roots stems or leaves.

Additional Information

• Bryophytes are called "amphibians of the plant kingdom" because they are terrestrial plants but require water to end their life cycle at the time of sexual reproduction.
• Pteridophytes are the first terrestrial vascular plants. Carolus Linnaeus classified them under the group cryptogamae. The word ‘pteridophytes’ comes from Greek word Pteron meaning feather and phyton meaning plants.
• Angiosperms are a type of vascular plant that bears both flowers and fruits. These types of plants also have spores enclosed in the ovary. The ovule, once fertilized, develops into a seed that later matures into a fruit.

Shortcut Trick

Efficiency ratio of pipes A : B = 1.5 : 1 = 3 : 2. Combined efficiency = 5 units.

Net filling rate = (Combined A+B) − Discharge pipe = Total Work / 28.

Let Total Work be 84 units (LCM of 12 and 28). Discharge efficiency = 84 ÷ 12 = 7 units/hr.

Net efficiency = 84 ÷ 28 = 3 units/hr. ⇒ (A+B) − 7 = 3 ⇒ A+B = 10 units/hr.

Ratio 3:2 implies A = 6, B = 4. Less efficient B fills tank in 84 ÷ 4 = 21 hours.

∴ The correct answer is 21 hours.

Alternate Method

Given: Efficiency of Pipe 1 = 1.5 × Efficiency of Pipe 2. Discharge pipe (C) empties in 12 hours. Combined filling time (A+B+C) = 28 hours.

Formula Used: 1/T_net = 1/T_A + 1/T_B − 1/T_C; Efficiency ∝ 1/Time.

Calculations:

⇒ Efficiency of (A + B) − Efficiency of C = 3

⇒ Efficiency of (A + B) − 7 = 3

⇒ Total Efficiency of A + B = 10 units/hr.

⇒ Given ratio of efficiency A : B = 1.5 : 1 = 3 : 2.

⇒ Efficiency of less efficient pipe (B) = [2 / (3 + 2)] × 10 = 4 units/hr.

⇒ Time taken by pipe B alone = Total Work ÷ Efficiency of B = 84 ÷ 4 = 21 hours.

∴ The correct answer is 21 hours.

Additional Information

Pipes & Cisterns Efficiency

Efficiency is inversely proportional to time. If Pipe A is 'k' times efficient as Pipe B, then Time taken by A = (Time taken by B) / k.

Net Work Done

When filling and emptying pipes work together, the net rate is the difference: Net Rate = (Sum of Filling Rates) − (Sum of Emptying Rates).

The correct answer is $1 \over 16$.

Key Points 

• Gravitational force is inversely proportional to the square of the distance between two bodies**.**
• $F = {1 \over {d}^2}$
• $F = {1 \over {4}^2}$
• If the factor of 4 in 'd' is increased, then F becomes $1 \over 16$ times smaller.

Additional Information 

• Newton's law says that F = mg, where F is the weight and M is the mass, and G, is the acceleration due to gravity but since the gravity on Moon is much less than Earth.
• The weight of an object will be Different.
• The formula that links mass and the gravitational field strength is:
• gravity force = mass × gravitational field strength (g)
• This is when:
• gravity force is measured in newtons (N)
• mass is measured in kilograms (kg)
• gravitational field strength (g) is measured in newtons per kilogram (N/kg).

Shortcut Trick

Identify the highest power of prime factors in the given numbers.

Numbers: 5, 180 (36 × 5), 24 (8 × 3)

Highest powers: 2³ (from 24), 3² (from 180), 5¹ (from 5 or 180)

LCM = 8 × 9 × 5 = 360

∴ The correct answer is 360.

Alternate Method

Given: Numbers 5, 180, and 24.

Formula Used: LCM is the product of the highest powers of all prime factors involved in the numbers.

Prime Factorization:

⇒ 5 = 5¹

⇒ 180 = 2 × 2 × 3 × 3 × 5 = 2² × 3² × 5¹

⇒ 24 = 2 × 2 × 2 × 3 = 2³ × 3¹

Calculations:

⇒ List all prime factors: 2, 3, 5

⇒ Take highest power of 2: 2³ = 8

⇒ Take highest power of 3: 3² = 9

⇒ Take highest power of 5: 5¹ = 5

⇒ LCM = 8 × 9 × 5

⇒ LCM = 72 × 5 = 360

∴ The correct answer is 360.

Additional Information

LCM and HCF Relationship

For any two numbers 'a' and 'b', HCF(a, b) × LCM(a, b) = a × b.

HCF (Highest Common Factor)

HCF is the product of the lowest powers of common prime factors. For 5, 180, and 24, the HCF is 1 as there is no common factor for all three.

LCM of Fractions

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

The possible Venn diagram is given below:-

Conclusion:

1. Some hot are peas. → True (All the peas are hot, then some hot are peas is also correct.)
2. Some hot are tomatoes. → True (Some tomatoes are hot, then some hots are tomatoes is also correct.)

Hence, "option 2" is the correct answer.

The correct answer is Will be very stormy.

Key Points

• When the barometric readings suddenly decrease, it indicates that the weather will be very stormy.
• A sudden fall in the barometric reading is an indication of a storm.
• As the barometer measures changes in air pressure, therefore at the onset of a storm, low pressure occurs, which in turn would lead to rapid or violent movement of air from the high-pressure areas.

Additional Information

• Atmospheric pressure is commonly measured with a barometer.
• In a barometer, a column of mercury in a glass tube rises or falls as the weight of the atmosphere changes.
• An atmosphere (atm) is a unit of measurement equal to the average air pressure at sea level at a temperature of 15 degrees Celsius (59 degrees Fahrenheit).
• Condensation is the process where water vapor becomes liquid.
• It is the reverse of evaporation, where liquid water becomes a vapor.

Shortcut Trick

For any regular polygon with n sides, each exterior angle is calculated as 360° ÷ n.

For a pentagon, n = 5. Therefore, each exterior angle = 360° ÷ 5 = 72°.

Since the interior angle and exterior angle at a vertex are supplementary, their sum is 180°.

Each interior angle = 180° − 72° = 108°.

∴ The correct answer is 108°.

Alternate Method

Given: A normal (regular) pentagon.

Formula Used: Each interior angle of a regular polygon = [(n − 2) × 180°] ÷ n, where n is the number of sides.

⇒ For a pentagon, the number of sides n = 5.

⇒ Sum of all interior angles = (5 − 2) × 180°

⇒ Sum = 3 × 180° = 540°

⇒ Since it is a regular pentagon, all interior angles are equal.

⇒ Measure of each interior angle = 540° ÷ 5

⇒ Each interior angle = 108°

∴ The correct answer is 108°.

Additional Information

Sum of Interior Angles

The sum of the interior angles of a polygon with n sides is given by the formula (n − 2) × 180°.

Exterior Angle Property

For any convex polygon, the sum of all exterior angles (one at each vertex) is always 360°.

Regular Polygon Definition

A regular polygon is both equilateral (all sides are equal) and equiangular (all angles are equal).

Supplementary Angles

The interior angle and its corresponding exterior angle at any vertex of a polygon always add up to 180°.

The correct answer is Ramnath Kovind.

 Key Points

• Ramnath Kovind inaugurated the 'World Hindi Secretariat' in Mauritius in 2018.
• President Ram Nath Kovind inaugurated the World Hindi Secretariat building in Mauritius on the third day of his visit to the country.
• He also launched the World Hindi Secretariat's logo, an Early Digital Learning Programme as well unveiled foundation stones of a social housing project and a large ENT hospital being built with Indian assistance.

Additional Information

• The World Hindi Secretariat is fully financed by the Government of India and provided a grant of Rs. 33 crore.
• Land for it was given by the Government of Mauritius.
• Prime Minister Narendra Modi had laid the foundation stone of this building during his visit in 2015.
• The aim of the secretariat is to present Hindi as the common man’s language, Janbhasha, in front of the world.
• Hindi as a language has played an important role in culture and society building in both India and Mauritius.
• Indian diaspora in Mauritius has played a huge role in the spread of Hindi.

Shortcut Trick

Since Distance is constant, Speed is inversely proportional to Time.

Time ratio = 7 : 5

Speed ratio = 5 : 7

Given: 5 units = 40 km/h ⇒ 1 unit = 8 km/h

Required speed (7 units) = 7 × 8 = 56 km/h

∴ The correct answer is 56 km/h.

Alternate Method

Given:

Initial Speed (S₁) = 40 km/h

Initial Time (T₁) = 7 hours

New Time (T₂) = 5 hours

Formula Used:

Distance = Speed × Time

Calculations:

⇒ Total Distance = S₁ × T₁

⇒ Total Distance = 40 × 7 = 280 km

⇒ Required Speed (S₂) = Total Distance ÷ T₂

⇒ Required Speed = 280 ÷ 5

⇒ Required Speed = 56 km/h

∴ The correct answer is 56 km/h.

Additional Information

Inverse Variation

When distance is constant, speed and time are inversely proportional: S₁ × T₁ = S₂ × T₂.

Average Speed

For the same distance covered at two different speeds x and y, Average Speed = 2xy ÷ (x + y).

Unit Conversion

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

The pattern followed is,

In figures A, B, and D there are same figures present on the upper and lower sides.

Whereas,

In figure C, upper figure is a rhombus while lower figure is a trapezium

Hence, "option 3" is the correct answer.

Shortcut Trick

Effective Rate of Interest for 3.75 years = 6% × 3.75 = 22.5%

Total Amount in percentage = 100% (Principal) + 22.5% (Interest) = 122.5%

According to the question, 122.5% = ₹2,940

Principal (100%) = (2940 ÷ 122.5) × 100 = 24 × 100 = ₹2,400

∴ The correct answer is ₹2,400.

Alternate Method

Given:

Total Amount (A) = ₹2,940

Rate of Interest (R) = 6% per annum

Time (T) = 3³/₄ years = 15/4 years = 3.75 years

Formula Used:

Amount (A) = P + SI = P + (P × R × T) ÷ 100

Calculations:

⇒ 2940 = P + (P × 6 × 3.75) ÷ 100

⇒ 2940 = P + (P × 22.5) ÷ 100

⇒ 2940 = P + 0.225P

⇒ 2940 = 1.225P

⇒ P = 2940 ÷ 1.225

⇒ P = (2940 × 1000) ÷ 1225

⇒ P = 2400

∴ The correct answer is ₹2,400.

Additional Information

Simple Interest Formula

The basic formula for Simple Interest (SI) is (P × R × T) ÷ 100, where P is the Principal, R is the rate, and T is the time in years.

Relationship between Amount and Principal

The Total Amount (A) is the sum of the Principal and Interest earned: A = P × [1 + (R × T) ÷ 100].

Direct Principal Calculation

When the Amount is given, the Principal can be directly calculated as P = (100 × A) ÷ (100 + R × T).

The Venn diagram is given below:-

The shaded part is the total number of students who played only one game.

From game M students who played only one game = 11

From game N students who played only one game = 41

From game L students who played only one game = 18

Then the total number of students who played only one game = 11 + 41 + 18 = 70

So, 70 students played only one game.

Hence, "option 3" is the correct answer.

The correct answer is Al & P.

Key Points

• In the modern periodic table, Silicon (Z = 14) is placed between Al and P.
• Silicon has an atomic number 14 and the outer electronic configuration is 3s² 3ps².
• It is placed at the 3rd Period and 14th Group number.

Additional Information

• Silicon, the second most abundant element on earth, is an essential part of the mineral world.
• Its stable tetrahedral configuration makes it incredibly versatile and is used in various ways in our everyday lives.
• Found in everything from spaceships to synthetic body parts, silicon can be found all around us, and sometimes even in us.
• Silicon is a crystalline semi-metal or metalloid.
• ​It is a group 14 element in the same periodic group as carbon but chemically behaves distinctly from all of its group counterparts.
• Silicon shares the bonding versatility of carbon, with its four valence electrons, but is otherwise a relatively inert element.

Shortcut Trick

Net depreciation for 2 years at 10% per annum = 10 + 10 − (10 × 10) / 100 = 19%.

Remaining value = 100% − 19% = 81% of initial value.

Value after 2 years = 16000 × 81 / 100 = 160 × 81 = 12960.

∴ The correct answer is ₹12960.

Alternate Method

Given:

Initial Value (P) = ₹16,000

Depreciation Rate (R) = 10%

Time (n) = 2 years

Formula Used:

Value after n years = P × (1 − R / 100)ⁿ

Calculations:

⇒ Value after 1st year = 16000 − (10 / 100) × 16000

⇒ Value after 1st year = 16000 − 1600 = ₹14,400

⇒ Value after 2nd year = 14400 − (10 / 100) × 14400

⇒ Value after 2nd year = 14400 − 1440 = ₹12,960

∴ The correct answer is ₹12960.

Additional Information

Successive Depreciation

For two successive depreciation rates a% and b%, the effective rate is [a + b − (ab / 100)]%.

Appreciation Formula

If the value of an item increases annually, use A = P(1 + R / 100)ⁿ.

Scrap Value

The value of an asset at the end of its useful life after continuous depreciation is known as its Scrap Value.

The family tree is given below:-

• Manohar's father's sister's daughter is the cousin of Manohar.
• Hence, "option 4" is the correct answer.

Key Points

• Manohar's father's sister's daughter related to him as cousin.
• Manohar's father's sister is Manohar's Aunt.
• Therefore Manohar's Aunt's daughter is Manohar's cousin.

The correct answer is Oviparous.

Key Points

• Oviparous animals are called Hatching animals.
• Oviparous animals are born by hatching out of an egg.
• Oviparous animals are those that reproduce by laying eggs.
• They include animals like birds, most reptiles, most amphibians, fish, and the majority of arthropods.

Additional Information

• Viviparous Animals 
• The Latin term for viviparous is also known as 'viviparous'. It means 'to give life' or 'to bring alive'. Animals that can give birth to young are called viviparous animals.
• Examples: Marine animals such as whales, dolphins, dogs, cats and humans.
• Oviparous Animals
• In the case of oviparous animals, the primary process of fertilization takes place internally. The mothering parent produces the eggs. The eggs are not retained inside the mother’s body throughout embryonic development.
• Examples: Mostly amphibians, reptiles, birds, insects, molluscs, arachnids, and monotremes are examples of oviparous animals.

Given:

$110 ÷ [53 - {4^3 - (37 - 136 ÷ \overline{17 \times 2)} }] = ?$

Concept:

Follow BODMAS rule to solve this question, as per the order given below, 

Calculation:

$110 ÷ [53 - {4^3 - (37 - 136 ÷ \overline{17 \times 2)} }] = ?$

⇒110 ÷ [53 - {64 - (37 - 136 ÷ 34)}] = ?

⇒110 ÷ [53 - {64 - (37 - 4)}] = ? 

⇒110 ÷ [53 - {64 - (37 - 4)}] = ?

⇒110 ÷ [53 - {64 - 33}] = ?

⇒110 ÷ [53 - 31] = ?

⇒110 ÷ 22 = ?

⇒ 5 = ?

∴ The value of ? is 5.

The logic followed here is:

Repair is the synonym of edit.

Similarly,

Modify is the synonym of change.

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

The correct mirror image of the given figure when the mirror is held at the side is:-

Hence, "option 1" is the correct answer.

The correct answer is  150 J.

Key Points

• Given,
• Mass(m) = 15 kg
• Gravity (g) = 10 ms^-2
• Height (h) = 1 m
• \(Work = mgh \)
• $Work = 15 * 10 *1$
• Work = 150 J

Additional Information

• Newton's law says that F=mg, where F is the weight and M is the mass, and G, is the acceleration due to gravity but since the gravity on Moon is much less than Earth.
• The weight of an object will be Different.
• The formula that links mass and the gravitational field strength is:
• gravity force = mass × gravitational field strength (g)
• This is when:
• gravity force is measured in newtons (N)
• mass is measured in kilograms (kg)
• gravitational field strength (g) is measured in newtons per kilogram (N/kg)

The correct answer is Both A and B are false.

• Both A and B are false.

Key Points

• Hardness is a material's resistance to localized plastic deformation.
• From ultra-hard materials like diamond and boron-carbide to various ceramics and hard metals, to soft metals, polymers, and soft tissues, hardness is measured.
• Hardness is only one mechanical property to consider; other properties such as toughness and strength must also be taken into account, as hard materials have poor toughness and are readily fractured.
• In contrast to other attributes such as colour, texture, or material type, a shape is an object's external boundary, contour, or external surface.
• The volume and shape of a solid are both defined.
• Although a liquid has a defined volume, it lacks a defined shape.
• Gas doesn't have a defined volume or shape.

Important Points

• Fluidity is the property of a substance to easily flow and allow a change in its shape under external forces and this property is exhibited by both liquids and gases.
• Compressibility is the property of matter to allow compression under high pressure and the gases show this property.

Given series -

The pattern followed here is:

• In each row, there are three pairs of arrows.

• First pair: 2 upward-facing arrows

• Second pair: 2 downward-facing arrows.

• Third pair: First arrow facing upward and second arrow facing downward.

• In the given figure, the pair of downward-facing arrows is missing in the third row.

Hence, "option 1" is the correct answer.

Note:

• A discrepancy was found in this question in the original exam of 2018. Therefore, we have altered the question figure to create a correct one.

The alphabet template is given below:-

The logic followed here is:

Hence, "option 3" is the correct answer.

The correct answer is Acetic acid.

Key Points

• Acetic acid has the highest temperature of liquefaction and boiling.
• Acetic acid has a higher boiling point based on molecular weight and lower Surface tension due to its higher polarity related to the water; since its higher intermolecular force.
• In general boiling point increases with compound molecular weight.
• So, acetic acid has a higher boiling point based on molecular weight and lower Surface tension due to its higher polarity related to the water; since its higher intermolecular force.
• ethanol has one oxygen atom and acetic acid contains two oxygen atom so therefore acetic acid forms more H-bonds (hydrogen bonds) then that of ethanol with its neighboring molecules and a network of more and strong Hydrogen bonding is present in acetic acid.

Additional Information

• Liquefaction of gases is a physical conversion of a gas into a liquid state (condensation).
• The liquefaction of gases is a complicated process that uses various compressions and expansions to achieve high pressures and very low temperatures, using, for example, turboexpanders.
• Liquefaction processes are used for scientific, industrial and commercial purposes.
• The boiling point of a liquid varies according to the applied pressure; the normal boiling point is the temperature at which the vapour pressure is equal to the standard sea-level atmospheric pressure.
• At sea level, water boils at 100° C (212° F).

HintChloroform do not has H-Bond. So boiling point of Chloroform is lower.

The logic followed here is:

• Figure (X) has four triangles.
• Therefore, we can create figure X using figure (c).

Hence, "option 3" is the correct answer.

Shortcut Trick

Total population = 400

Working population = 80% of 400 = 320

Employees in Company A = 45% of Working population

Employees in Company A = 0.45 × 320 = 144

∴ The correct answer is 144.

Alternate Method

Given:

Total population = 400

Non-working population = 20%

Percentage of working population = 100% − 20% = 80%

Calculations:

⇒ Total number of working employees = 80% of 400

⇒ Total working employees = (80/100) × 400 = 320

⇒ Percentage of employees in Company A = 45% (of the working group)

⇒ Number of employees in Company A = 45% of 320

⇒ Number of employees in Company A = (45/100) × 320

⇒ Number of employees in Company A = 0.45 × 320 = 144

∴ The correct answer is 144.

Additional Information

Venn Diagram for Sets

For two sets A and B, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). This represents the total individuals in either group.

Percentage Calculations

To find x% of a value Y, use the formula (x/100) × Y. Always identify the correct base value before applying the percentage.

Complementary Percentage

If p% of a population does not belong to a category, then (100 − p)% belongs to that category.

The correct answer is Mangolia.

Key Points

• The Gobi Desert is a large desert or brushland region in East Asia.
• It covers parts of Northern and Northeastern China and of Southern Mongolia.
• The desert basins of the Gobi are bounded by the Altai Mountains and the grasslands and steppes of Mongolia on the north, by the Taklamakan Desert to the west, by the Hexi Corridor and Tibetan Plateau to the southwest and by the North China Plain to the southeast.
• The Gobi is notable in history as the location of several important cities along the Silk Road.
• The Gobi is a rain shadow desert, formed by the Tibetan Plateau blocking precipitation from the Indian Ocean from reaching the Gobi territory.
• It is the sixth-largest desert in the world and the second-largest in Asia after the Arabian Desert.

Additional Information

​

The correct answer is Prasoon Joshi.

Key Points

• Prasoon Joshi replaced Pahlaj Nihalani as Censor Board Chief in 2017.
• Pahlaj Nihalani, who turned the censor board into a precinct of serial controversy, has been sacked as the organisation's chairman.
• His successor is famous lyricist-adman Prasoon Joshi, while actor Vidya Balan joins the board.

Additional Information

• Colleagues of Mr Nihalani had accused him of treating the Central Board of Film Certification (CBFC) like his personal fiefdom, while filmmakers and critics accused him of demanding irrational cuts and moral policing.
• The Central Board of Film Certification is a statutory film-certification body in the Ministry of Information and Broadcasting of the Government of India.
• It is tasked with "regulating the public exhibition of films under the provisions of the Cinematograph Act 1952."

Shortcut Trick

Priyal's deficit in 12 exams = 12 × (25 − 23) = 24 marks.

This deficit of 24 marks must be recovered in the remaining 4 exams.

Extra marks needed per exam = 24 ÷ 4 = 6 marks.

Required average marks for Priyal = Target Average + Extra = 25 + 6 = 31.

∴ The correct answer is 31 marks.

Alternate Method

Given:

Sneha's average in 16 exams = 25 marks

Priyal's average in 12 exams = 23 marks

Formula Used:

Total Marks = Average × Number of Exams

Calculations:

⇒ Total marks obtained by Sneha = 16 × 25 = 400 marks

⇒ Current total marks of Priyal = 12 × 23 = 276 marks

⇒ Marks required by Priyal to equal Sneha = 400 − 276 = 124 marks

⇒ Number of remaining examinations for Priyal = 16 − 12 = 4

⇒ Required average for remaining exams = 124 ÷ 4 = 31 marks

∴ The correct answer is 31 marks.

Additional Information

Weighted Average Formula

Used when two groups are combined: Average_total = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Sum of Observations

Total Sum = Average × Number of items. If the average increases, the new item added must be greater than the original average.

Net Deviation Concept

The sum of deviations from the average is always zero. Total Deficit = Total Surplus relative to the mean.

The logic followed here is:

Dispur is the capital of Assam.

Similarly,

Amravati is the capital of Andhra Pradesh.

Trivandrum is the capital of Kerala, Kolkata is the capital of West Bengal, and Mumbai is the capital of Maharashtra.

Hence, "option 1" is the correct answer.

The correct answer is Anoxic respiration.

Key Points

• The incomplete dissolution of a substrate in the absence of oxygen is called anoxic respiration.
• Anoxic conditions involve environments in which molecular or free oxygen (O2) is absent, though bound oxygen may be present.
• “Anoxic” refers to the state of the environment rather than microorganisms and their processes.

Additional Information

• Anaerobic respiration is the type of respiration through which cells can break down sugars to generate energy in the absence of oxygen.
• This is in contrast to the highly efficient process of aerobic respiration, which relies on oxygen to produce energy.
• Anaerobic respiration is respiration using electron acceptors other than molecular oxygen.
• Although oxygen is not the final electron acceptor, the process still uses a respiratory electron transport chain.

The correct answer is Au.

Key Points

• Au is the most ductile metal.
• Ductility is the property of being drawn into wire.
• It is a permanent strain that accompanied fracture in a tension test.
• It is a desirable property in machine components that are subjected to unanticipated overloads or impact loads.
• The ductility of the metals decreases as the temperature increases because metals become weak at increasing temperatures.

Additional Information

• Aluminium is called green metal because it is a very environmentally friendly metal.
• Recycling this material saves 95% of the energy required to produce aluminium from raw materials.
• It is called as green metal as it is environment friendly because of its properties like :
• High durability
• Lightweight
• Malleability strength
• Corrosion-free
• Do not catch fire
• It can be easily recycled

Five friends:- L, M, N, O, and P

Facing:- Centre

N suddenly sits to the left of P.

L sits between O and P.

Therefore, O is sitting between M and L

Hence, "option 3" is the correct answer.

The correct answer is ICICI Bank.

Key Points 

• ICICI Bank became the first bank in India to offer an instant PPF account facility.
• ICICI Bank says it is the first lender in the country to introduce a fully digital and paperless procedure for opening a PPF account.
• Private lender ICICI Bank has launched a digital service to allow customers to open a PPF account online, eliminating the need for furnishing paper documents.
• The digital service will enable customers to open a public provident fund (PPF) account instantly and in a completely online and paperless manner.

Additional Information

• ICICI Bank Limited is an Indian multinational bank and financial services company with its corporate office in Mumbai, Maharashtra.
• It offers a wide range of banking products and financial services for corporate and retail customers through a variety of delivery channels and specialized subsidiaries in the areas of investment banking, life, non-life insurance, venture capital, and asset management.
• The bank has a network of 5,275 branches and 15,589 ATMs across India and has a presence in 17 countries.
• The bank has subsidiaries in the United Kingdom and Canada; branches in the United States, Singapore, Bahrain, Hong Kong, Qatar, Oman, Dubai International Finance Centre, China, and South Africa as well as representative offices in United Arab Emirates, Bangladesh, Malaysia, and Indonesia.

The correct answer is 240 C.

Key Points

• A current of 0.8 A is drawn by a filament of an electric bulb in 5 minutes.
• Let us assume the amount of electric charge flowing through the circuit as 'q'.
• 1 min = 60 sec
• 5 min = 5 × 60 = 300 sec
• We know that,
• ​$I = {q \over t}$, where I stands for the current, q stands for the amount of electric charge flowing, and t stands for time.
• $q = I \times t$
• $q = 0.8 \times 300$
• $q = 240 C$
• Hence the amount of electric charge flowing through the circuit is 240 C.

Shortcut Trick

Identify the standard algebraic identity: (a + b)² − (a − b)² = 4ab.

Here, a = 469 and b = 144.

The given expression is (4ab) ÷ (2ab).

By simplification, the ratio is 4 ÷ 2 = 2.

∴ The correct answer is 2.

Alternate Method

Given:

First term (a) = 469

Second term (b) = 144

Formula Used:

(a + b)² = a² + b² + 2ab

(a − b)² = a² + b² − 2ab

Calculations:

⇒ Numerator = (469 + 144)² − (469 − 144)²

⇒ Numerator = (469² + 144² + 2 × 469 × 144) − (469² + 144² − 2 × 469 × 144)

⇒ Numerator = 469² + 144² + 2 × 469 × 144 − 469² − 144² + 2 × 469 × 144

⇒ Numerator = 4 × 469 × 144

⇒ Denominator = 2 × (469 × 144)

⇒ Expression = (4 × 469 × 144) ÷ (2 × 469 × 144)

⇒ Value = 4 ÷ 2 = 2

∴ The correct answer is 2.

Additional Information

Sum of Squares Identity

(a + b)² + (a − b)² = 2(a² + b²). This is used when the middle sign is positive.

Difference of Squares

a² − b² = (a + b)(a − b). This identity is fundamental for factoring quadratic expressions.

Cubic Identities

a³ + b³ = (a + b)(a² − ab + b²) and a³ − b³ = (a − b)(a² + ab + b²).

The correct answer is Swami Vivekananda Airport, Raipur.

Key Points

• Swami Vivekananda Airport, Raipur ranked first in the Customer Satisfaction Index (CSI) Survey 2017.
• Swami Vivekananda Airport, Raipur, Chhattisgarh, has topped the charts in the Customer Satisfaction Index Survey among 49 airports in India.
• The airport achieved 4.84 scores in a five-point scale index in the latest CSI survey conducted by an independent agency for the period of Jan- June 2017 followed by Udaipur, Amritsar, and Dehradun airports which have scored 4.75, 4.74 and 4.73 respectively.

Additional Information

• The Customer Satisfaction Index (CSI) is a versatile analytical tool for measuring customer satisfaction with a product, service, or company.
• It stands that only the satisfied customer tends to repeatedly return to their favourite brand and also convey their positive experience to others
• Raipur airport is the 28th busiest airport in India by passenger traffic and 31st busiest by aircraft movement.
• High-level maintenance of infrastructure and passenger facilities, the green ambience, state-of-the-art technology, and courteous staff ensuring passenger satisfaction have resulted in Raipur getting the recognition for the third consecutive time in the past two years.

Given that:-

Pranitha goes in the north direction, then takes a right turn, again takes a right turn, and then takes a left turn.

The figure is given below:-

Pranitha going east direction now.

Hence, "option 1" is the correct answer.

The correct answer is 80 J.

Key Points 

• Given, 
• Force (f) =20 N
• displacement (s) = 4 m
• $Work=Force×Displacement$
• $Work = 20N×4m$
• Work = 80 J

Additional Information

• Work is done whenever a force moves something over a distance.
• Energy transferred = work done
• = force x distance moved in the direction of the force.
• Displacement is an example of a vector quantity.
• Distance is an example of a scalar quantity.
• A vector is any quantity with both magnitude and direction.

When it is folded on the dotted line, then the pattern will be the same as the sheet given below:-

Hence, "option 1" is the correct answer.

The correct answer is Kotak Mahindra Bank.

Key Points

• Kotak Mahindra bank is currently using Ranveer Singh as his celebrity endorser to open a bank account named '811'.
• Kotak Mahindra Bank has signed Ranveer Singh as its brand ambassador.
• It also had signed Vinay Pathak, as the brand mascot of the company.
• The process of opening 811 accounts was a five-minute task sitting at home since everything is done online.
• It also provided the Kotak 811 account holder with a virtual debit card.

Additional Information​

• Kotak Mahindra Bank Limited is an Indian banking and financial services company headquartered in the city of Mumbai, India.
• It is India's third-largest private sector bank by assets and by market capitalization as of November 2021.
• It offers banking products and financial services for corporate and retail customers in the areas of personal finance, investment banking, life insurance, and wealth management.
• As of February 2021, the bank has 1600 branches and 2519 ATMs.

• Assumption 1 says that the vacation spot should be cool and pleasant which is out of the context. The description only talks about the place being good for holidays.
• Assumption 2 suggests that Ram is the husband of Anita which implies that Ram has to be a male.
• Thus Assumption II is correct.

Hence, option 1 is the correct answer.

The family tree is given below:-

Naveen is the uncle of Kirthana.

Hence, "option 3" is the correct answer.

The alphabet template is given below:-

The logic followed here is:

Hence, "option 2" is the correct answer.

The correct answer is Shivering.

Key Points

• The sound of the human voice is produced from the vocal cord by shivering. 
• The vocal folds (vocal cords) are attached within the larynx to the largest of the laryngeal cartilages known as the thyroid cartilage or "Adam's apple".
• The vocal folds produce sound when they come together and then vibrate or shiver as air passes through them during the exhalation of air from the lungs.
• This vibration produces a sound wave for your voice.

Additional Information

• In order for the sound to be clear and not raspy or hoarse, the vocal folds must vibrate together symmetrically and regularly. 
• The rate of vibration determines the pitch of the voice.
• When the voice is hoarse, the vocal folds may not be closing fully, or may not be vibrating symmetrically.
• The larynx, or voice box, is located in the neck and performs several important functions in the body.
• The larynx is involved in swallowing, breathing, and voice production.
• Sound is produced when the air which passes through the vocal cords causes them to vibrate and create sound waves in the pharynx, nose and mouth.

The question talks about a way to avoid chaos in the vegetable market.

• Argument I suggests that if people are polite and they make way for each other, the chaos can be avoided which is logically correct. If people are mutually giving space to others, there won't be any chaos happening.
• Argument II suggests that avoiding chaos won't be possible because the roads there are narrow and cannot be kept clean. It is not logical to claim that roads cannot be cleaned daily. Municipal workers can be appointed to maintain basic cleanliness. Also, the problem of narrow roads can be resolved if they are widened. Traffic management can help reduce chaos caused by traffic. So, argument II does not sound logical.

Hence the correct answer is option 4.

Given that:-

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

• If the first and second, third, and fourth terms of the sequence are interchanged, then:-

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

There are two (5 8 6, 7 8 3) 8s that will not be divisible by the numbers on their left and right number.

Hence, "option 4" is the correct answer.

The correct answer is Thursday.

• The year 2018 is not a leap year.
• So, 15th February 2019 will be a Friday.
• The year 2019 is not a leap year so there are 28 days in February.
• So the number of days after 15th February 2019 to 18th April 2019 are 13 + 31 + 18 = 62
• Number of odd days in 62 days = 6
• Thus, on 18th April 2019, the day will be Friday + 6 days = Thursday.
• Hence, "option 4" is the correct answer.

The correct answer is Tuesday.

• The year 2003 is not a leap year.
• So, 18th October 2003 will be a Saturday.
• The year 2004 is a leap year so there are 29 days in February.
• The year 2005 is not a leap year so there are 28 days in February.
• So the number of days from 18th October 2003 to 18th October 2005 is 366 + 365 = 731
• Number of odd days in 731 days = 3
• Thus, on October 18, 2003, the day will be Saturday + 3 days = Tuesday.
• Hence, "option 4" is the correct answer.

Concept used:

Recurring decimal - When a digit starts repeating itself after the decimal.

Calculation:

⇒ 10/30 = 0.333333.....

⇒ 12/30 = 0.4

⇒ 14/30 = 0.466666.....

⇒ 8/30 = 0.266666....

∴ 12/30 is not a recurring decimal

The correct answer is India is a secular country.

Key Points

• India is a secular state which means that it is not based on any religion.
• India is called a secular state because it does not have any state religion and people are free to practice any religion of their choice.
• ​Hence statement 2 is correct.
• Religion in India is characterized by a diversity of religious beliefs and practices.
• The Indian subcontinent is the birthplace of four of the world's major religions: namely Hinduism, Buddhism, Jainism, and Sikhism.
• Religious diversity and religious tolerance are established by the law; the Constitution of India defines freedom of religion as a fundamental right and holds India to be a secular state.
• So India has not had a fixed state religion and India is not a divine country.
• Hence option 1 and option 3 are not correct.
• As per the Indian constitution, everyone is equal in front of the law and Indian law applies equally to all citizens of the country irrespective of their race, caste, religion, gender etc.
• Hence statement 4 is incorrect.

The correct answer is CaO.

Key Points

• Calcium oxide (CaO), commonly known as quicklime or burnt lime, is a widely used chemical compound.
• It is a white, caustic, alkaline, crystalline solid at room temperature.
• Formula: CaO
• IUPAC ID: Oxocalcium
• Molar mass: 56.0774 g/mol
• Melting point: 2,572 °C
• Density: 3.34 g/cm³​
• Soluble in: Water, Glycerol

Additional Information

• Calcium oxide appears as an odourless, white or grey-white solid in the form of hard lumps.
• A strong irritant to skin, eyes and mucous membranes.
• Used in insecticides and fertilizers.
• Calcium oxide is a member of the class of calcium oxides of calcium and oxygen in a 1:1 ratio.
• It has a role as a fertilizer.

The family tree is given below:-

1. Y has two sisters U and V.

• Here, there is no information given about X. Therefore, statement 1 alone is not sufficient.

2. X's mother is the sister of U's father.

• No information is given about Y. Therefore, statement 2 alone is not sufficient.

From statements 1 and 2 together then:-

• Here, statements 1 and 2 together are sufficient.
• X is the cousin of Y.

Hence, "option 2" is the correct answer.

Shortcut Trick

Area of a parallelogram is calculated as Base × Height.

From the figure, the base is 20 and the corresponding height is 12.

Area = 20 × 12 = 240.

∴ The correct answer is 240.

Alternate Method

Given:

Base (b) = 20

Height (h) = 12

Formula Used:

Area of Parallelogram = Base × Height

Calculations:

⇒ Area = b × h

⇒ Area = 20 × 12

⇒ Area = 240

∴ The correct answer is 240.

Additional Information

Properties of Parallelogram

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

Perimeter of Parallelogram

The perimeter is 2 × (sum of adjacent sides), similar to a rectangle.

Area using Sine of Angle

If two adjacent sides are 'a' and 'b' with an included angle θ, Area = a × b × sin(θ).

The correct answer is hard tissue.

Key Points

• The hard tissue of plant tissue does not hold living protoplasm at maturity.
• The protoplasm is the living part of a cell that is surrounded by a plasma membrane.
• In cell biology, the cytoplasm is all of the material within a eukaryotic cell, enclosed by the cell membrane, except for the cell nucleus.
• The material inside the nucleus and contained within the nuclear membrane is termed the nucleoplasm.

Additional Information

• Mature sclerenchyma cells are usually dead cells that have heavily thickened secondary walls containing lignin.
• The cells are rigid and nonstretchable and are usually found in nongrowing regions of plant bodies, such as the bark or mature stems.
• Sclerenchyma is one of the three types of ground, or fundamental, tissue in plants; the other two types are parenchyma (living thin-walled tissue) and collenchyma (living support tissue with irregular walls).
• Sclerenchyma cells occur in many different shapes and sizes, but two main types occur:
• fibres and sclereids.

Shortcut Trick

To find Asha's total income, we need both her basic income and additional allowance.

From Statement I and II: Asha's basic = ₹1,550 + ₹100 = ₹1,650.

From Statement III: Asha's allowance = ₹2,000 + ₹50 = ₹2,050.

Total Income = Basic + Allowance = ₹1,650 + ₹2,050 = ₹3,700.

Since components from all statements are required, all are sufficient together.

∴ The correct answer is All I, II and III are sufficient.

Alternate Method

Given:

Mala's Basic Income = ₹1,550 (from Statement II)

Asha's Basic Income = Mala's Basic + ₹100 (from Statement I)

Mala's Allowance = ₹2,000 (from Statement III)

Asha's Allowance = Mala's Allowance + ₹50 (from Statement III)

Formula Used:

Total Monthly Income = Basic Income + Additional Allowance

Calculations:

⇒ Using Statement II: Mala's Basic = ₹1,550

⇒ Using Statement I and II: Asha's Basic = 1,550 + 100 = ₹1,650

⇒ Using Statement III: Mala's Allowance = ₹2,000

⇒ Since Mala's allowance (2,000) is ₹50 less than Asha's, Asha's Allowance = 2,000 + 50 = ₹2,050

⇒ Total Monthly Income of Asha = 1,650 + 2,050 = ₹3,700

⇒ All statements are mandatory to reach the final sum.

∴ The correct answer is All I, II and III are sufficient.

Additional Information

Data Sufficiency Rules

In data sufficiency, you must determine if the information provided in the statements is enough to answer the question uniquely, without necessarily calculating the final value.

Salary Components

Gross Monthly Income is generally the sum of Basic Pay, Dearness Allowance (DA), House Rent Allowance (HRA), and other miscellaneous allowances.

Logical Connectives

Phrases like 'more than' or 'less than' indicate a comparison between two entities, requiring the value of the reference entity (in this case, Mala) to find the target (Asha).

• The statement only tells us that a proposal was made by the government at some point in time to reduce the present syllabus of NCERT. This is understood due to the usage of the words "had proposed".
• However, the final status of the proposal is not discussed in the statement.
• Therefore, neither of the conclusions follow.

Hence, option 4 is the correct answer.

Note: The official question had a discrepancy. We have rephrased the question to make it logically correct.

The correct answer is Kapil Dev.

Key Points

• Kapil Dev has written the book 'Cricket My Style'.
• Kapil Dev has written three autobiographical works.
• By God's Decree came out in 1985 and Cricket my style in 1987.
• He released his most recent autobiography, titled Straight from the Heart in 2004.
• Kapil Dev Ramlal Nikhanj born 6 January 1959) is a former Indian cricketer.
• He was a fast-medium bowler and a hard-hitting middle-order batsman.
• He led India to win its first Cricket World Cup title in 1983. He was named by Wisden as the Indian Cricketer of the Century in 2002.

Important Points

Additional Information

• Books by  Arundhati Roy
• The Algebra of Infinite Justice
• The God of Small Things
• The Ministry of Utmost Happiness
• The book 'Lockdown Liaisons' authored by Shobhaa De and Published by Simon and Schuster.
• Lockdown Liaisons is a collection of short stories, from the varying perspectives of both men and women, young and old, brave and cowardly, cheerful and weighed down.
• Books by Anil Kumble
• Wide Angle: Candid Moments from My Playing Days.

The correct answer is Cylindrical, branched and single-nuclei.

Key Points

• Heart muscles are Cylindrical, branched and single-nuclei.
• Cardiac muscle fibres are long, branched cells, shaped like cylinders joined end-to-end, with one or two nuclei located centrally.
• The fibres are separated by collagenous tissue that supports the capillary network of cardiac tissue.

Additional Information

• The myofilaments of cardiac muscle are arranged in a similar pattern to skeletal muscle, resulting in cross-striations.
• The fibres are crossed by linear bands called intercalated discs.
• These structures have two important roles.
• Firstly, they provide attachment points that provide the tissue with a characteristic branched pattern.
• Secondly, they allow cardiac muscle tissue to function as a functional syncytium.
• Essentially, the contractile stimuli are propagated from one cell to the next one, resulting in a synchronous contraction of the entire tissue section.