RRC Group D Previous Year Paper 40 (Held On: 15 Oct 2018 Shift 2)

The number of squares in the given figure is,

Hence, “38” is the correct answer.

The correct answer is the Nationalist Congress Party.

Nationalist Congress Party:

• Founded- 25 May 1999.
• Founder- Sharad Pawar, P.A. Sangma, and Tariq Anwar.
• Party Philosophy- Progressivism, Populism, Secular democracy, Gandhian secularism, Egalitarianism, Social justice, Federalism, Social conservatism, Nationalism.
• Election Symbol- Clock.
• Student wing- Nationalist Student Congress.

All India Trinamool Congress:

• Founded- January 1998
• Founder- Mamata Banerjee
• Party Philosophy- Secularism and populism.
• Election Symbol- Twin flowers in the grass.
• Student wing- Trinamool Chhatra Parishad.

Indian National Congress:

• Founded- 1885.
• Founder- Allan Octavian (A.O) Hume.
• Party Philosophy- Indian Nationalism (Liberal nationalism), Social democracy, Democratic socialism, Gandhian socialism, Progressivism.
• Student wing- National Students Union of India (NSUI).
• Election Symbol- The hand.

Bahujan Samaj Party:

• Founded- April 14, 1984.
• Founder- Kanshi Ram.
• Party Philosophy- Human rights, Social equality, Secularism, Social justice, Self-respect.
• Election Symbol- Elephant.

The correct answer is option 1.

• In Nickel speed of sound 6040 m/s.
• In Aluminium, the speed of sound is 6420 m/s.

Important Points

Speed of Sound in Different Media:

• The speed of sound in the air is 331 m/s^–1 at 0ºC and 344 m/s^–1 at 22ºC.
• It depends on the type of the medium through which it is traveling.
• It depends on the temperature and pressure of that medium.
• Speed of sound Decrease- when it passes from the solid to the gaseous state of a given medium.
• Speed of sound Increase- In any medium, when temperature and humidity increase.
• Speed of Sound- Solid > Liquid > Gases

Key Points

Speed of sound in different media at 25ºC

The correct answer is The motion of the sun around the planets.

• The universal law of Gravitation- Every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.
• Sir Isaac Newton discovered Gravity.

Key Points

The phenomenons explained by the universal law of gravitation:

• The force that binds us to the earth.
• The motion of the moon around the earth.
• The motion of planets around the Sun.
• The tides due to the moon and the Sun.

The correct answer is Al (Aluminum).

Key Points

• An amphoteric oxide is an oxide that can act as either an acid or base in a reaction to produce salt and water.
• Amphoterism depends on the oxidation states available to a chemical species. Because metals have multiple oxidation states, they form amphoteric oxides and hydroxides.
• Metals that display amphoterism include copper, zinc, lead, tin, beryllium, and aluminum.
• Al2O3 is an amphoteric oxide. When reacted with HCl, it acts as a base to form the salt AlCl3. When reacted with NaOH, it acts as an acid to form NaAlO2.

The correct answer is 6.

India is divided into 6 physiographical regions

• The Himalayan Mountains
• The Northern Plains
• The Peninsular Plateau
• The Indian Desert
• The Coastal Plains
• The Islands

Source: https://ncert.nic.in/textbook/pdf/iess102.pdf

Key Points

Some important facts:

• The folds of the Great Himalayas are asymmetrical in nature.
• The core of this part of Himalayas is composed of granite.
• The outermost range of the Himalayas is called the Shiwaliks.
• The Western Ghats are higher than the Eastern Ghats.
• The Eastern Ghats are discontinuous and irregular and dissected by rivers draining into the Bay of Bengal.

The correct answer is 686J.

Explanation: 

• At height (h) = 5m
• Mass of the object (m) = 14 kg
• Acceleration due to gravity (g)= 9.8 ms-2
• Potential Energy = mgh

                                        =1459.8 = 686J

• Joule (J) is the S.I unit of energy.

The pattern followed is,

The figure has four circles and a right-angle triangle inside it.

Similarly,

There are four circles and a right angle triangle in figure C.

Figure C resembles the given figure.

Hence, option 1 is the correct answer.

Shortcut Trick

Let Total Work (Capacity) = LCM(6, 8, 10) = 120 units.

Efficiencies: Inlet A = 20, Inlet B = 15, Outlet C = −12.

Work done in 1st hour by A & B = 20 + 15 = 35 units.

Remaining work = 120 − 35 = 85 units.

Combined efficiency (A + B + C) = 20 + 15 − 12 = 23 units/hr.

∴ The correct answer is 85/23 hr.

Alternate Method

⇒ Work done by Inlet A and Inlet B in 1 hour = 20 + 15 = 35 units.

⇒ Remaining Capacity of the tank = 120 − 35 = 85 units.

⇒ Combined efficiency when all three taps are opened = 20 + 15 − 12 = 23 units/hr.

⇒ Time required to fill the remaining tank = Remaining Capacity ÷ Combined Efficiency

⇒ Time = 85/23 hr.

∴ The correct answer is 85/23 hr.

Additional Information

Pipes and Cisterns Concept

Inlet efficiency is taken as positive, while outlet (leakage) efficiency is taken as negative. Total work is usually the LCM of individual times.

Work and Time Relation

Time = Total Work ÷ Net Efficiency. If the net efficiency is negative, the tank will be emptied.

Shortcut Trick

Let the total number of coins be 100 units.

Value = (20 × 5) + (25 × 10) + (15 × 2) + (40 × 1) = 100 + 250 + 30 + 40 = 420 units.

Given 420 units = ₹210 ⇒ 1 unit = 0.5.

Number of ₹1 coins = 40 units = 40 × 0.5 = 20.

∴ The correct answer is 20 coins.

Alternate Method

Given: Total amount = ₹210. Percentages of coins: ₹5 = 20%, ₹10 = 25%, ₹2 = 15%.

Step 1: Calculate the remaining percentage for ₹1 coins.

⇒ Remaining % = 100% − (20% + 25% + 15%) = 100% − 60% = 40%.

Step 2: Let the total number of coins be x.

⇒ Total Value = (0.20x × 5) + (0.25x × 10) + (0.15x × 2) + (0.40x × 1) = 210

⇒ 1.00x + 2.50x + 0.30x + 0.40x = 210

⇒ 4.20x = 210

⇒ x = 210 ÷ 4.2 = 50

Step 3: Find the number of ₹1 coins.

⇒ Number of ₹1 coins = 40% of 50 = 0.40 × 50 = 20

∴ The correct answer is 20 coins.

Additional Information

Ratio of Value

The total value is the sum of (Number of coins × Face value of each coin). If ratios are given, always multiply the coin ratio by the denomination value.

Denomination Conversion

Ensure all units are in the same currency (all in Rupees or all in Paise). ₹1 = 100 Paise.

The correct answer is Banabhatta.

Explanation:

• Banabhatta was the court poet of king Harshavardhana.
• Banabhatta wrote Harshvardhan's biography Harshacharita in Sanskrit.
• He describes his association with Thanesar in his biography.

About Banabhatta:

• A great poet of India, Banabhatta was born around the 7th century in a village in India.
• He was born in Pritikuta village, which was situated on the banks of Hiranyavahu.
• He was born to Chitrabhanu and Rajadevi and he was a family of Vatsyayana gotra.
• This poetic genius wrote one of the most famous and earliest novels, known as Kadambari. It is a biographical work of Harsha and Kadambari.

About other options:

• Bilhana:
• He was a Sanskrit writer and a well-known Kashmiri poet.
• He was born in Kavi Bilhana in the middle of the 11th century.
• Jayadeva:
• Jayadeva was born in the middle of the 12th century and his birthplace was Kendubilwa.
• He was the author of the Sanskrit poem 'Gita Govinda'. He is known for his epic poem 'Gita Govinda', which depicts the divine love of Krishna and his consort, Radha. This poem, which presents the view that Radha is greater than Hari, is considered an important text in the Bhakti movement of Hinduism.
• Sri Jayadeva was famous in Orissa, especially at Puri Dham for his composition of 'Gita Govinda'. His father's name was Bhojadeva and his mother's name was Radha Devi. His wife's name was Padmabati.
• Chand Bardai:
• Chand Bardai was an Indian poet. He composed Prithviraj Raso, an epic poem in Brajbhasa about the life of king Prithviraj Chauhan.

The correct answer is Bindusara.

Explanation:

• King Ashoka was the son of Bindusara, who belonged to the Maurya dynasty.
• Bindusara was the second Mauryan emperor of India.
• He was the son of Chandragupta Maurya, the founder of the Mauryan dynasty.

About other options:

• Chandragupta Maurya:
• Chandragupta Maurya, known as Sandrakottos to the Greeks, was the founder of the Maurya Dynasty (4th-2nd century BCE) and is credited with the setting up of the first pan-Indian empire.
• Aided by his mentor and later minister Chanakya or Kautilya (c. 4th century BCE), he set up a vast centralized empire, details of whose functioning, society, military, and economy are well preserved in Kautilya’s Arthashastra.
• Chandragupta II:
• He was the next great Gupta emperor after his father Samudragupta (335/350 - 370/380 CE).
• He came to be known by his title Vikramaditya (Sanskrit: "Sun of Power").
• He carried on the legacy of Samudragupta and contributed his share towards sustaining an extensive empire that carved out a place for itself in history.
• Bimbisara:
• He was a king of the Magadha Kingdom who is credited with establishing imperial dominance in the Indian subcontinent.
• Son of a minor king called Bhattiya, he belonged to the Haryanka Dynasty, which is said to be the second imperial dynasty of Magadha.

Shortcut Trick

Identify the highest common factor: All numbers are multiples of 47.

94 = 47 × 2, 188 = 47 × 4, 235 = 47 × 5.

LCM = 47 × LCM(2, 4, 5) = 47 × 20.

LCM = 940.

∴ The correct answer is 940.

Alternate Method

Given: Numbers are 94, 188, and 235.

Formula Used: Prime Factorization Method for LCM.

⇒ 94 = 2¹ × 47¹

⇒ 188 = 2² × 47¹

⇒ 235 = 5¹ × 47¹

⇒ LCM = 2² × 5¹ × 47¹

⇒ LCM = 4 × 5 × 47

⇒ LCM = 20 × 47 = 940.

∴ The correct answer is 940.

Additional Information

LCM (Least Common Multiple)

The smallest positive integer that is divisible by each of the given numbers. It is calculated by taking the highest power of every prime factor present.

HCF and LCM Relation

For two numbers a and b, the product of the numbers is equal to the product of their HCF and LCM: a × b = HCF(a, b) × LCM(a, b).

Prime Factorization

Expressing a number as a product of prime numbers to easily find common divisors or multiples.

The mirror image of the given figure is,

Hence, option 3 is the correct answer.

The pattern followed is,

In the first figure the circle is placed on top of a triangle and in the second figure the triangle is inside the circle.

Similarly,

In the third figure the circle is on top of rhombus.

And,

In the fourth figure the rhombus should be inside the circle.

The figure that will come next in the pattern is,

Hence, option 3 is the correct answer.

Shortcut Trick

Arrange the given 12 numbers in ascending order: 12, 25, 25, 42, 45, 45, 54, 58, 59, 60, 65, 87.

Since the total number of terms (N = 12) is even, the median is the average of the two middle terms (6^th and 7^th terms).

The 6^th term is 45 and the 7^th term is 54.

Median = (45 + 54) ÷ 2 = 49.5.

∴ The correct answer is 49.5.

Alternate Method

Given:

Data set: 42, 45, 58, 87, 45, 54, 65, 12, 25, 25, 59, 60

Total number of observations (N) = 12

Formula Used:

When the total number of observations (N) is even:

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

Calculations:

⇒ First, arrange the given data set in ascending order:

12, 25, 25, 42, 45, 45, 54, 58, 59, 60, 65, 87

⇒ Here, the total number of terms N = 12, which is even.

⇒ The 6^th term (N/2) = 45

⇒ The 7^th term (N/2 + 1) = 54

⇒ Median = (6^th term + 7^th term) ÷ 2

⇒ Median = (45 + 54) ÷ 2

⇒ Median = 99 ÷ 2 = 49.5

⇒ Thus, the median of the given data set is 49.5.

⇒ Option (1) is correct because the calculated median is 49.5.

⇒ Option (2) is incorrect because 59.5 does not represent the average of the two middle terms.

⇒ Option (3) is incorrect because 54 is only the 7^th term, not the average of the two middle terms.

⇒ Option (4) is incorrect because 45 is only the 6^th term, not the average of the two middle terms.

∴ The correct answer is 49.5.

Additional Information

Median for Odd Number of Terms

If the total number of observations (N) is odd, the median is the middlemost term, which is the ((N + 1)/2)^th term after arranging the data in ascending or descending order.

Mean (Arithmetic Average)

Mean is the sum of all observations divided by the total number of observations: Mean = (Sum of all terms) ÷ N.

Mode

Mode is the value that appears most frequently in a data set. A data set can have one mode, more than one mode, or no mode at all.

Empirical Relationship

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

Ratio of ages of father and son is 3 : 1.

Let their ages be measured in terms of x.

So, present age of father is 3x and that of son is x.

The product of their ages is 147.

(3x) × (x) = 147

→ 3x² = 147

→ x² = 49

→ x = 7

Sum of their ages = 3 × (7) + 7 = 28

Hence, ‘28’ is the correct answer.

Shortcut Trick

Distance = [Product of Speeds ÷ Difference of Speeds] × Total Time Difference

Product of Speeds = 66 × 54

Difference of Speeds = 66 − 54 = 12 km/h

Time Difference = 5 min early + 3 min late = 8 min = 8/60 hours

Distance = (66 × 54 / 12) × (8 / 60) = 39.6 km

∴ The correct answer is 39.6 km.

Alternate Method

Given:

Speed₁ (S₁) = 66 km/h, Speed₂ (S₂) = 54 km/h

Time Difference (Δt) = 5 + 3 = 8 minutes = 8/60 hours

Formula Used:

Distance (D) = (S₁ × S₂ × Δt) ÷ (S₁ − S₂)

Calculations:

⇒ D = (66 × 54 × 8/60) ÷ (66 − 54)

⇒ D = (66 × 54 × 2) ÷ (12 × 15)

⇒ D = (3564 × 2) ÷ 180

⇒ D = 7128 ÷ 180

⇒ D = 39.6 km

∴ The correct answer is 39.6 km.

Additional Information

Time Difference Calculation

When comparing early and late arrivals, the total time difference is the sum of both (Early + Late). If both cases are early or both are late, the difference is the subtraction of values.

Speed-Time Inversely Proportional

For a constant distance, the ratio of speeds is inversely proportional to the ratio of times taken: S₁/S₂ = T₂/T₁.

Average Speed Formula

For equal distances covered at different speeds S₁ and S₂, Average Speed = 2 × S₁ × S₂ ÷ (S₁ + S₂).

The pattern followed is,

Hence, “O” is the correct answer.

The correct answer is Charles Darwin.

Explanation:

• Theory of evolution by natural selection was proposed by Charles Darwin and Alfred Russel Wallace in the nineteenth century.
• The theory of evolution by natural selection, first formulated in Darwin's book "On the Origin of Species" in 1859.
• Charles Darwin was born on 12 February 1809, in Shrewsbury, and died 19 April 1882.

About other options:

• Johann Mendel:
• Gregor Mendel, in full Gregor Johann Mendel, was born on 22 July 1822 and died on 6 January 1884.
• He was botanist, teacher, and Augustinian prelate, the first person to lay the mathematical foundation of the science of genetics, in what came to be called Mendelism.
• Johann Dobereiner:
• Johann Wolfgang Döbereiner was born on 13 December 1780 and died on 24 March 1849.
• He was the German chemist whose observation of similarities among certain elements anticipated the development of the periodic system of elements.
• John Dalton:
• John Dalton was born on September 5 or 6, 1766, and died on 27 July 1844.
• He was an English meteorologist and chemist, a pioneer in the development of modern atomic theory.

Shortcut Trick

Efficiency of Rajan (R) = 4 units/day and Bhavesh (B) = 3 units/day (taking Total Work = 24).

Efficiency of Charan (C) = Efficiency of (R + B) = 4 + 3 = 7 units/day.

Efficiency of (B + C) = 3 + 7 = 10 units/day.

Time taken by (B + C) = Total Work ÷ Combined Efficiency = 24 ÷ 10 = 2.4 days.

∴ The correct answer is 2(2)/(5) days.

Alternate Method

Given:

Time taken by Rajan = 6 days

Time taken by Bhavesh = 8 days

Formula Used:

Total Work = LCM of individual days

Efficiency = Total Work ÷ Time

Calculations:

⇒ Total Work = LCM(6, 8) = 24 units

⇒ Efficiency of Rajan = 24 ÷ 6 = 4 units/day

⇒ Efficiency of Bhavesh = 24 ÷ 8 = 3 units/day

⇒ Efficiency of Charan = Efficiency of (Rajan + Bhavesh) = 4 + 3 = 7 units/day

⇒ Combined Efficiency of (Bhavesh + Charan) = 3 + 7 = 10 units/day

⇒ Time taken by (Bhavesh + Charan) = 24 ÷ 10 = 12/5 = 2(2/5) days

∴ The correct answer is 2(2)/(5) days.

Additional Information

Combined Efficiency Rule

When two people work together, their combined efficiency is the sum of their individual efficiencies. Efficiency is inversely proportional to time.

Work and Wages

Wages are distributed in the ratio of the work done by each individual, which is the same as the ratio of their efficiencies if they work for the same duration.

Pipes & Cisterns

Similar logic applies to pipes where an inlet pipe has positive efficiency and an outlet pipe has negative efficiency.

The correct answer is Pavan Kumar Chamling.

Key Points

• Explanation:
• Pawan Kumar Chamling was born on 22 September 1949 and he is an Indian politician.
• He was the Founder and President of the Sikkim Democratic Front, which governed the state for five successive terms since 1994.
• He was born in Yangang, in South Sikkim to a Nepali parent's Ash Bahadur Chamling and Ash Rani Chamling.

Important Points

• Incumbent CM of Sikkim Prem Singh Tamang since 27 May 2019.

Additional Information

• About Sikkim:
• Capital: Gangtok.
• State Animal: Red Panda.
• State Bird: Blood Pheasant.
• State Flower: Noble dendrobium.

The correct answer is Power.

• Power:- A Measure of the rate of doing work or transferring energy
• Power= Work/ Time= Force x Displacement/Time
• Its SI Unit is Watt.
• Watt:-Watt is Joule Per Second. (J/s).

Extra Facts:-

Force:- 

• A-Force is a push or pulls upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a Force upon each of the objects.
• F= m x a where F= Force, m= mass of object and a= acceleration
• SI Unit:- Newton

Work Done:- 

• It is a measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement.
• W= fd where W= Work, f= force and d= displacement
• SI Unit:- Joule.

Momentum:-

• Momentum is generally 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= m x v where P= Momentum, m= mass and V= velocity
• SI Unit:- Kg m/s.

The correct answer is PC Mustafa.

• PC Mustafa is an entrepreneur who is CEO and Cofounder of a Company called ID Special Foods Pvt. Ltd.
• The Company employed more than 2000 younger from ruler India to feed millions of Indians Healthy and preservative-free Idli and Dosa Batter including other foods on a daily basis.
• ID Special Foods Pvt. Ltd. is a leading food industry that is providing several flavors of Idli and Dosa.
• The company was established in 2006 by Mustafa and his cousins who started operating ID (Idli, Dosa) from 550 Square Feet.
• PC Mustafa did B.Tech in Computer Science from NIT.
• He got an MBA Degree from IIM Bangalore.

Extra Facts:-

Sunny Varkey:- 

• He is the founder and chairman of Global Advisory and Educational Management firm GEMS, Education.

RC Subramoniam:-

• He is the Managing Director at Tenneco Automotive Private Limited, Pune.

Shortcut Trick

Total Distance to travel = Initial height + Depth below ground = 35 + 430 = 465 m.

Time Taken = Total Distance ÷ Speed = 465 ÷ 7.5.

⇒ 4650 ÷ 75 = 62 minutes.

∴ The correct answer is 62 min.

Alternate Method

Given:

Initial position = +35 m (above ground level)

Final position = −430 m (below ground level)

Speed of descent = 7.5 m/min

Calculations:

⇒ Total vertical distance = |Initial position − Final position|

⇒ Distance = |35 − (−430)| = |35 + 430| = 465 m

⇒ Time = Distance ÷ Speed

⇒ Time = 465 ÷ 7.5

⇒ Time = 4650 ÷ 75

⇒ Time = 62 min

∴ The correct answer is 62 min.

Additional Information

Relative Position and Integers

In vertical movement, positions above a reference point (ground) are taken as positive integers, while positions below are taken as negative integers. The distance is the absolute difference between these values.

Time, Speed, and Distance Formula

The fundamental relation is Time = Distance ÷ Speed. Ensure all units are consistent (e.g., meters and meters per minute) before performing division.

The correct answer is 1 N x 1 m.

Key Points

• 1 Joule = 1 N x 1 m.
• 1 Joule is equal to the energy transferred to an object when a force of one Newton acts on that object in the direction of the force's motion through a distance of one meter.

​

Additional Information

Power:- 

• Power is the amount of energy transferred or converted per unit of time.
• SI Unit of Power is Watt.

Energy:- 

• It is defined as the capacity of doing work.
• It may exist in potential, kinetic, thermal, electrical, chemical, nuclear or other various forms.
• SI unit of Energy is Joule.

According to the given statement,

Assumption I: This is implicit, because the survey is being conducted on healthiest breakfast in India, and the healthiest can be found from the survey.

Assumption II: Since, X possesses such skills, only then he is ready to conduct a survey, so this is also implicit.

Hence, “both I and II” are implicit.

The least possible Venn diagram is,

Conclusion I: Some autos are cycles → True (This is definitely true)

Conclusion II: No scooter is auto → False (This is definitely false)

Hence, “only I” follows.

CALCULATION:

Considering the given values

3/15 = 1/5 = 0.2,

5/20 = 1/4 = 0.25

8/64 = 1/8 = 0.125

25/1000 = 1/40 = 0.025

So, 0.25 > 0.20 > 0.125 > 0.025

∴ 25/1000 is the smallest fraction.

Platinum, Silver and Gold are metals.

Whereas,

Oxygen is a gas, which is the life supporting component of the air.

Hence, “oxygen” is the odd one.

Shortcut Trick

Total Work = LCM(12, 18) = 36 units.

Efficiency of A = 3, Efficiency of B = 2.

If A leaves 3 days before, add A's 3-day work to total: 36 + (3 × 3) = 45.

Total time = 45 ÷ (3 + 2) = 9 days.

Together working time = Total time − Days A was absent = 9 − 3 = 6 days.

∴ The correct answer is 6 days.

Alternate Method

Given: Time taken by A = 12 days, Time taken by B = 18 days.

Formula Used: Efficiency = Total Work ÷ Time; Work Done = Efficiency × Time.

⇒ Let the total work be completed in x days.

⇒ A worked for (x − 3) days and B worked for x days.

⇒ Work by A + Work by B = 36

⇒ 3(x − 3) + 2x = 36

⇒ 3x − 9 + 2x = 36

⇒ 5x = 45 ⇒ x = 9 days.

⇒ Number of days they worked together = (x − 3) = 9 − 3 = 6 days.

∴ The correct answer is 6 days.

Additional Information

Leaving Before Completion

When a person leaves n days before completion, add their n days of work to the total work and divide by the sum of efficiencies of all people involved.

Work and Efficiency Relation

Efficiency is inversely proportional to the time taken to complete a task. Ratio of time A:B = x:y → Ratio of efficiency A:B = y:x.

Combined Work Formula

If two people can do a work in X and Y days respectively, they together take (X × Y) ÷ (X + Y) days to complete the work.

The number of squares in the given figure is,

Hence, “23” is the correct answer.

Shortcut Trick

Convert the mixed fraction to an improper fraction: 6 39/160 = (160 × 6 + 39) / 160 = 999/160.

The denominator 160 is the product of the numerator and denominator of the target fraction (x/y − y/x = (x²−y²)/xy).

Check options for product xy = 160: (1) 15 × 8 = 120; (2) 16 × 5 = 80; (3) 32 × 5 = 160.

Verify 32/5: (32/5) − (5/32) = (1024 − 25) / 160 = 999/160. This matches the given value.

∴ The correct answer is 32/5.

Alternate Method

Given: Difference between positive fraction and its reciprocal = 6 39/160.

Formula: Let the fraction be x. The equation is x − 1/x = 999/160.

⇒ (x² − 1) / x = 999 / 160 ⇒ 160x² − 160 = 999x ⇒ 160x² − 999x − 160 = 0 ⇒ 160x² − 1024x + 25x − 160 = 0 ⇒ 32x(5x − 32) + 5(5x − 32) = 0 ⇒ (32x + 5)(5x − 32) = 0 ⇒ Since x is a positive fraction, 5x − 32 = 0 ⇒ x = 32/5

∴ The correct answer is 32/5.

Additional Information

Reciprocal Property

If a fraction is defined as a/b, its reciprocal is b/a. The product of a fraction and its reciprocal is always 1.

Fraction Difference Formula

The difference between a fraction x/y and its reciprocal y/x is given by (x² − y²) / xy.

Quadratic Roots

For the equation ax² + bx + c = 0, roots can be found using factorisation or the quadratic formula x = (−b ± √(b² − 4ac)) / 2a.

Shortcut Trick

Let total people be 9 units.

Adults = 2 units | Children = 9 − 2 = 7 units.

Difference (7 − 2) = 5 units → 65 children.

1 unit = 13 children.

Children = 7 × 13 = 91.

∴ The correct answer is 91.

Alternate Method

Given:

Fraction of adults = 2/9

Difference between children and adults = 65

Calculations:

⇒ Let total people = x

⇒ Adults = 2x/9

⇒ Children = x − 2x/9 = 7x/9

⇒ 7x/9 − 2x/9 = 65

⇒ 5x/9 = 65

⇒ x = (65 × 9) ÷ 5 = 13 × 9 = 117

⇒ Number of children = 7/9 × 117 = 7 × 13 = 91

∴ The correct answer is 91.

Additional Information

Ratio and Proportion

When a fraction a/b is given, we can assume the total as 'b' units and the specific part as 'a' units to simplify calculations.

Percentage Change

To find the percentage of children, calculate (Children/Total) × 100. In this case, (7/9) × 100 ≈ 77.78%.

Unitary Method

Always equate the given absolute difference to the difference in parts/units to find the value of one unit.

According to the given information,

Statement 1: This statement alone is insufficient since we cannot determine the number of packets.

Statement 2: This statement alone is also insufficient since information of about big packets is only given in this statement.

Statement 3: This statement alone is also not sufficient, since information about smaller and larger packets is only given in this statement.

Combining the three,

From statement 2, there are 6 big packets.

From statement 3,

There are twice the amount of smaller packets than there are larger packets.

And,

From statement 1, it is mentioned that half of all packets are the medium packets.

Combining all the three, we can find the number of packets in the box.

Hence, “statement 1, 2 and 3 together” are sufficient.

The pattern followed is,

In the first figure, the square is inside the pentagon and in the second figure the square is on the pentagon.

Similarly,

In the third figure, the circle is inside the triangle.

And,

In the fourth figure, the circle should be on the triangle.

The figure which will come next in the pattern is,

Hence, option 3 is the correct answer.

The Correct Answer is Karnataka.

• The 7^th edition of the Rashtriya Sanskriti Mahotsav (RSM) under the Ek Bharat Shreshtha Bharat matrix, was held in Karnataka on January 14, 2018.
• The event organized by the Ministry of Culture continued till 20^th January.
• The state paired with Karnataka was Uttarakhand.
• The event was inaugurated by Minister of Parliamentary Affairs Ananth Kumar in the presence of Minister of State for Culture Mahesh Sharma.
• Rashtriya Sanskriti Mahotsav aims to celebrate national integration and the idea of unity in the diversity of the country. It celebrates the rich culture and heritage of India.
• It covers events including art forms from classical and folk, Music and Dance, theatre to literature, and Visual Arts.

Other Facts:-

Rashtriya Sanskriti Mahotsav held at different places:-

The correct answer is 18 Groups and 7 Periods.

• Modern Periodic Table has 18 Groups and 7 Periods.
• It has 118 Elements.
• Each of the tables has a vertical row is called groups. Elements in groups have similar chemical and physical properties because they have the same number of outer electrons.
• Each of the tables has horizontal rows is called periods. During a period, a gradual change in chemical properties occurs from one element to another.
• It was given by Dmitri Mendeleev.
• The Structure of it is like a bird Grid.
• The Modern Periodic table is used to organize all the known elements.
• Advantages of Modern Periodic Table:- 
• It is easier to remember the properties of an element if its position in the periodic table is known.
• It made the study of Chemistry Systematic and Easy.

Modern Periodic Table:-

CONCEPT:

• Uniform motion: The motion of an object in which the object travels in a straight line and its velocity remains constant along that line as it covers equal distances in equal intervals of time, irrespective of the duration of the time.
• Example: Ball moving on a frictionless surface with constant velocity.
• Non-uniform motion: The motion of an object in which the object travels with varied speed and it does not cover the same distance in equal time intervals, irrespective of the time interval duration.
• Example: The motion of a train

​EXPLANATION:

• During the uniform motion of an object along a straight line, the velocity remains constant with time. Hence option 4 is correct.

Additional Information

• In the uniform motion, the change in velocity of the object for any time interval is zero. This means in the case of uniform motion, the rate of change of velocity, i.e. acceleration is equal to zero.

Sublimation is the phase transition of a substance directly from the solid to the gas phase without passing through the intermediate liquid phase. Sublimation is an endothermic process that occurs at temperatures and pressures below a substance's triple point in its phase diagram.

Drawing the diagram according to the given information,

He is facing towards south now.

Hence, “south” is the correct answer.

1^st January 2017 – Monday

2^nd January 2017 – Tuesday

3^rd January 2017 – Wednesday

4^th January 2017 – Thursday

5^th January 2017 – Friday

6^th January 2017 – Saturday

7^th January 2017 – Sunday

Day + 7 days = same day.

Since 2017 is not a leap year, there will be 28 days in February.

In January leaves are = 5^th January (1^st Friday), 7^th January (Sunday), 14^th January (Sunday), 21^st January (Sunday), 28^th January (Sunday). Total = 5

In February leaves are = 2^nd February (1^st Friday), 4^th February, 11^th February, 18^th February, 25^th February. Total = 5

 In March leaves are = 2^nd March (1^st Friday), 4^th March, 11^th March, 18^th March, 25^th March. Total = 5.

In April leaves are = 1^st April, 6^th April (1^st Friday).

Hence, 17^th holiday will be on 6^th April 2017.

The pattern followed is,

In all the given figures, except figure A, the figure inside the square is formed with the help of lines.

Whereas,

In figure A, there is a circle immersed in a square.

Hence, option 2 is the odd one.

In marketing, product bundling is offering several products for sale as one combined product. It is a common feature in many imperfectly competitive product markets. Industries engaged in the practice include telecommunications, financial services, health care, and information

• Cutaneous respiration takes place in earthworms.
• Cutaneous respiration is Gas exchange that occurs via the skin or body surface of animals

According to the given statement,

Assumption I: Because of the higher fee in the schools some children drop out from schools and work as labour. If education is made free then child labour will be reduced. Hence, this is implicit.

Assumption II: This is not implicit, because education is the topic talked about in the statement, not about all free things.

Hence, “only assumption I” is implicit.

Drawing the family tree,

Rajan’s father’s only brother’s father is the paternal grandfather to Rajan.

Hence, “paternal grandfather” is the correct answer.

• Sarojini Naidu was the first female governor of Uttar Pradesh.
• Sarojini Naidu never took over as the Chief Minister of Uttar Pradesh.
• Sarojini Naidu is also called the Nightingale of India.
• Pandit Govind Ballabh Pant was the first Chief Minister of Uttar Pradesh.
• Narayan Dutt Tiwari was the former Chief Minister of Uttar Pradesh and Uttarakhand.
• Chandra bhanu Gupta was also the Chief Minister of Uttar Pradesh state three times.

From the given Bar Graph we can say that,

In the year 2015,

⇒ Ranks scored from institute “ABC” = 80

The correct answer is Acceleration.

• The change in the velocity with respect to time in a movable object is called Acceleration.
• Formulated by a = Velocity/ Time taken.
• It is a Vector Quantity.
• Unit of this is** (meter/ second²)**.

Momentum

• Momentum is determined by the product of the mass of the object and its velocity.
• It is a vector quantity.
• The formula is M = mass x velocity.
• SI unit is m/s (meter/ second).

Speed

• Distance covered in a unit time is called Speed.
• It is a Scaler quantity.
• SI unit is meter/second.
• The formula is v = Distance covered/ taken time.

Displacement

• When a body covered the distance from one position to another position, then the minimum distance between the initial and final position of the body is called displacement.
• It is a vector quantity.
• Its SI unit is meter.
• Displacement can be positive, negative or zero.
• Displacement can be zero but distance can never be zero.

From the given table, Arranging number of tourists in descending order:

3000 (April), 2500 (March), 2000 (January and May), 1500 (February) and 1000 (June)

The second least visited month was February with 1500 tourists

According to the given information,

Symbol should be immediately preceded by a letter, but immediately not followed by a number.

Number of times the condition satisfied is:

P 3 R I M J 3 Q % W @ / N $ E 5 X Y 1 # 8

Q %

W @

N $

Hence, “3” is the correct answer.

GIVEN:

Total revenue = Rs. 3,628,000

Sale of bag = 45%

Sale of shoes = 15%

CALCULATION:

From the given pie chart we can say that,

When manufacturing = 100%, Total revenue = Rs. 3,628,000

100% = Rs. 3,628,000

⇒ 1% = Rs. 36280

Total revenue by bag and shoes = 60%,

⇒ 60% = 60 × 36280

∴ Total revenue by bag and shoes = Rs. 2176800

The correct answer is AgCl and AgBr.

• AgCl, AgBr, AgF and AgI are known as Silver Halides.
• A silver halide is one of the chemical compounds that can form between the element silver and one of the halogens.
• Silver halides are light-sensitive chemicals.

Silver Nitrate (AgNO₃)

• Silver Nitrate is an inorganic chemical with antiseptic activity.
• It appears as a colourless or white crystalline solid becoming black on exposure to light or organic material.
• In its solid form, silver nitrate is coordinated in a trigonal planar arrangement.

Uses:

• Type of pesticide used to destroy or inhibit the growth of disease-causing mechanisms.
• Related to all forms of cleaning/washing, including cleaning products used in the home, laundry detergents.
• Drug product, or related to the manufacturing of drugs.

Key Points

Uses of Silver Halides.

The correct answer is ATP.

ATP(Adenosine Triphosphate):

• It is the organic compound composed of the phosphate groups, adenine, and the sugar ribose.
• These molecules provide energy for various biochemical processes in the body.
• That is why it is called Energy Currency of the Cell.
• The ATP molecule was discovered in the year 1929 by German chemist Karl Lohmann.
• These ATP molecules are synthesized by Mitochondria, therefore it is called the powerhouse of the cell.
• In the year 1948, Scottish biochemist Alexander Todd was the first person to synthesized the ATP molecule.

ADP(Adenosine diphosphate):

• Adenosine diphosphate (ADP), is an important organic compound in metabolism and is essential to the flow of energy in living cells.
• It is essential in photosynthesis and glycolysis.
• It is the end-product when adenosine triphosphate ATP loses one of its phosphate groups.
• The energy released in the process is used to power up many vital cellular processes.
• ADP reconverts to ATP by the addition of a phosphate group to ADP.

The correct answer is white.

• When a piece of magnesium ribbon is ignited, light and heat are produced.
• The oxidation or combustion of magnesium in the air has long been used as a source of intense light in photography and for other photochemical reactions.
• After burning magnesium, it gives some ash.
• The colour of the ash is white when it burns.

Shortcut Trick

For half-yearly compounding, the rate becomes half and time becomes double.

New Rate = 12% ÷ 2 = 6% per period; Periods (n) = 1 × 2 = 2.

Net Effective Interest Rate for 2 periods = x + y + (xy ÷ 100) ⇒ 6 + 6 + (6 × 6 ÷ 100) = 12.36%.

Compound Interest = 20,000 × 12.36% = ₹2,472.

∴ The correct answer is ₹2,472.

Alternate Method

Given: Principal (P) = ₹20,000 | Annual Rate (R) = 12% | Time (T) = 1 year.

Formula Used: Compound Interest (CI) = P[(1 + r/100)ⁿ − 1]

⇒ Interest rate for half-year (r) = 12% ÷ 2 = 6%

⇒ Number of conversion periods (n) = 1 × 2 = 2 periods

⇒ Amount (A) = 20,000 × (1 + 6/100)²

⇒ A = 20,000 × (1.06) × (1.06)

⇒ A = 20,000 × 1.1236 = ₹22,472

⇒ Compound Interest (CI) = Amount − Principal

⇒ CI = 22,472 − 20,000 = ₹2,472

∴ The correct answer is ₹2,472.

Additional Information

Half-Yearly Compounding Rule

When interest is compounded half-yearly, the annual rate is divided by 2 and the time in years is multiplied by 2.

Successive Percentage Formula

For two periods, the net interest rate can be found using the formula: Net % = r + r + (r² ÷ 100).

Difference between CI and SI

For 2 periods, the difference between CI and SI is given by: CI − SI = P(r/100)².

The correct answer is Manjot Kalra.

• Manjot Kalra made a century in the final match to help Indian team to clinch the title.
• He made 101 not out in 102 balls.
• He made this century against Australia.

Facts about U-19 World Cup 2018.

• It was organised in New Zealand.
• Won by India (4th time).
• Runner up was Australia.

Key Points

Titles in the U-19 World Cup:

$\frac{x}{{{x}^{2}}-1}=\frac{A}{x-1}+\frac{B}{x+1}$

⇒ $\frac{x}{{{x}^{2}}-1}=\frac{A\left( x+1 \right)+B\left( x-1 \right)}{{{x}^{2}}-1}$

⇒ x = Ax + A + Bx – B

⇒ x = x (A + B) + (A – B)

On comparing

A + B = 1      ---(1)

A – B = 0      ---(2)

From equation (1) and equation (2)

A = 1/2 and B = 1/2

Shortcut Trick

By the Remainder Theorem, if (x − 5) is a factor, then P(5) = 0.

Substitute x = 5 directly into the polynomial: 3(5)² + 5a + 4 = 0.

75 + 5a + 4 = 0 ⇒ 5a = −79.

a = −79 ÷ 5 = −15.8.

∴ The correct answer is −15.8.

Alternate Method

Given:

Polynomial P(x) = 3x² + ax + 4

Divisor = x − 5

Formula Used:

The Factor Theorem states that if a polynomial P(x) is perfectly divisible by (x − k), then the remainder P(k) must be equal to 0.

Calculations:

⇒ Let x − 5 = 0 ⇒ x = 5

⇒ P(5) = 3(5)² + a(5) + 4 = 0

⇒ 3(25) + 5a + 4 = 0

⇒ 75 + 5a + 4 = 0

⇒ 79 + 5a = 0

⇒ 5a = −79

⇒ a = −79 ÷ 5

⇒ a = −15.8

∴ The correct answer is −15.8.

Additional Information

Factor Theorem

A special case of the remainder theorem which states that a polynomial f(x) has a factor (x − a) if and only if f(a) = 0.

Remainder Theorem

When a polynomial f(x) is divided by a linear divisor (x − a), the remainder is given by the value f(a).

Synthetic Division

A shorthand method of polynomial division, especially when dividing by a linear factor, to quickly find quotients and remainders.

Shortcut Trick

The sum of roots for a quadratic equation x² − 12x + k = 0 is given by −b/a = −(−12)/1 = 12.

Let the roots be α and β, where α = 3.

α + β = 12 ⇒ 3 + β = 12.

β = 12 − 3 = 9.

∴ The correct answer is x = 9.

Alternate Method

Given: The quadratic equation is x² − 12x + k = 0 and one root is x = 3.

Formula Used: For any quadratic equation ax² + bx + c = 0, the Sum of Roots (α + β) = −b/a.

⇒ Comparing x² − 12x + k = 0 with ax² + bx + c = 0:

⇒ a = 1, b = −12, and c = k.

⇒ Sum of roots = −(−12) / 1 = 12.

⇒ Let the two roots be α and β.

⇒ Given that α = 3.

⇒ 3 + β = 12.

⇒ β = 12 − 3.

⇒ β = 9.

∴ The correct answer is x = 9.

Additional Information

Sum and Product of Roots

For a quadratic equation ax² + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a.

Nature of Roots

The nature is determined by the Discriminant (D) = b² − 4ac. If D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are imaginary.

Formation of Quadratic Equation

If the roots α and β are known, the equation is formed as x² − (α + β)x + (α × β) = 0.

The number of triangles in the given figure is,

Hence, “17” is the correct answer.

The pattern followed is:

1. The given figure is rotating 180° in clock wise direction in 1st figure to 2nd and 4^th to 5^th figure.

2) And 2^nd and 5^th figures are flipped vertically.

1st figure to 2^nd figure and 3^rd figure;

Similarly, 

4^th to 5^th and 5^th to 6^th figure;

But,

In the 3^rd figure it does not follow the pattern. 

Hence, option 2 is dissimilar from the given options.

The correct answer is MR Rajagopal.

Key Points

      MR Rajagopal

• Born- Trivantpuram, Kerla
• He is known as the father of palliative care in India.
• In 1993, he founded the Pain and Palliative Care Society (PPCS) in Medical College, Calicut, Northern Kerala.
• He has been working tirelessly since 1993 to integrate palliative care across medical health institutions.
• In 2018, he has been honored by Padma Shri.
• "Hippocratic"- A documentary film based on Dr. M R Rajagopal's life.

Additional Information

      Palliative Care

• It is an approach that improves the quality of life of patients and their families facing the problem associated with a life-threatening illness, through the prevention and relief of suffering by means of early identification and impeccable assessment and treatment of pain and other problems.

Bhakti Yadav

• She was the first female Doctor from Indore.
• She had been honored by Padam Shri.

Sanduk Ruit

• He is an ophthalmologist from Nepal.
• He is one of the founders of the Tilganga Institute of Ophthalmology.

Rani Bang

• She is a social activist and researcher working in the field of community health, in Maharastra.
• She has been honored by Padam Shri.

Shortcut Trick

Since the percentage values are multiples, use the inverse ratio property.

Ratio of percentages = 18.3 : 54.9 = 1 : 3

Therefore, the ratio of values must be 3 : 1

As 3 units = 60, then 1 unit = 20

∴ The correct answer is 20.

Alternate Method

Given: 18.3% of 60 = 54.9% of x

Formula Used: Percentage calculation (a% of b = c% of d)

⇒ (18.3 ÷ 100) × 60 = (54.9 ÷ 100) × x

⇒ 18.3 × 60 = 54.9 × x

⇒ x = (18.3 × 60) ÷ 54.9

⇒ x = 60 ÷ (54.9 ÷ 18.3)

⇒ x = 60 ÷ 3

⇒ x = 20

∴ The correct answer is 20.

Additional Information

Percentage Equality Rule

If a% of B = c% of D, then the product a × B must always equal c × D, allowing for quick cancellation of the denominator 100.

Commutative Property

Remember that x% of y is always equal to y% of x. This property can often simplify complex-looking decimal calculations.

The correct answer is Dr Harsh Vardhan.

National Wildlife Genetic Resource Bank :

• Increase the collection of genetic resources from wildlife through collaboration with zoos in India.
• Help in protecting inia's biodiversity and environment.

Others Facts:

Let, the age of son be x and the age of mother be y

It is given that the son's present age is two-fifths of his mother's age.

$x = \frac{2}{5}y$      ----(i)

After 8 Years, the son will be one half of his mother's age

$x + 8 = \frac{1}{2}(y + 8)$

$x = \frac{y}{2} + 4 - 8$

$x = \frac{y}{2} - 4$      ----(ii)

On solving eq (i) and eq(ii)

Hence, the age of the mother is 40 years now.

Given, A son's present age is two-fifths of his mother's age.

Then, we let the age of the mother = 5x, and the age of son = 2x

After 8 years, he will be one-half of his mother's age.

Then, Mother = 5x + 8 and Son = 2x + 8

(5x + 8) × (1 / 2) = 2x + 8

5x + 8 = 4x + 16

5x - 4x = 16 - 8

x = 8

So**, the age of son = x = 8 years**

The age of mother = 5x = 5 × 8 = 40 years

Shortcut Trick

Average Speed = Total Distance ÷ Total Time

Total Distance = 30 m + 70 m = 100 m

Total Time = 4 s + 6 s = 10 s

Average Speed = 100 ÷ 10 = 10 ms⁻¹

∴ The correct answer is 10 ms⁻¹.

Alternate Method

Given:

Distance 1 (d₁) = 30 m, Time 1 (t₁) = 4 s

Distance 2 (d₂) = 70 m, Time 2 (t₂) = 6 s

Formula Used:

Average Speed = (Total Distance Covered) ÷ (Total Time Taken)

Calculations:

⇒ Total Distance = d₁ + d₂ = 30 + 70 = 100 m

⇒ Total Time = t₁ + t₂ = 4 + 6 = 10 s

⇒ Average Speed = 100 / 10

⇒ Average Speed = 10 ms⁻¹

∴ The correct answer is 10 ms⁻¹.

Additional Information

Average Speed with Equal Distance

If an object covers two equal distances at speeds v₁ and v₂, the average speed is given by (2 × v₁ × v₂) ÷ (v₁ + v₂).

Units of Speed

To convert speed from km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Uniform Motion

In uniform motion, the average speed of an object is equal to its actual speed at any point in time.

Shortcut Trick

Let the total capacity be the LCM of denominators (5, 12) = 60 units.

Initial quantity = 3/5 × 60 = 36 units.

Final quantity = 7/12 × 60 = 35 units.

Difference = 36 − 35 = 1 unit → 20 litres.

Total capacity = 60 units = 60 × 20 = 1200 litres.

∴ The correct answer is 1200 litres.

Alternate Method

Given: Initial fraction = 3/5, Oil used = 20 litres, Final fraction = 7/12.

Formula: Capacity × (Initial fraction − Final fraction) = Quantity used.

⇒ Let the total capacity be 'C'.

⇒ (3/5)C − 20 = (7/12)C

⇒ (3/5)C − (7/12)C = 20

⇒ [(36 − 35) / 60]C = 20

⇒ (1/60)C = 20

⇒ C = 20 × 60

⇒ C = 1200

∴ The correct answer is 1200 litres.

Additional Information

Fraction Comparison

To find the difference between two fractions, always equate the denominators by taking their Least Common Multiple (LCM).

Capacity Calculation

The actual quantity of a substance in a container is the product of its fractional part and the total capacity.

Unitary Method

In ratio-based problems, if 1 unit represents a specific value, the total value is found by multiplying the total units by that specific value.

The correct answer is Kerala.

• Mohiniyattam is a dance form of Kerala.
• Mohiniyattam is one of the eight classical dance of India.

Key Points

Classical Dance of India:

Drawing the family tree,

Jay and Neel are cousins.

Hence, “cousins” is the correct answer.

The correct answer is Minsk.

• Minsk is the capital of Belarus.
• Belarus Currency- Belarusian ruble.

Key Points

Others Facts:

The correct answer is 40 J.

Explanation

• Moving Charge= 4 C (Q)
• Two points having a P.D (V)= 10 V
• Work= W

W= VQ

W=  10v  x 4C= 40 J

The correct answer is movements.

Explanation:

• Muscle tissue is a soft tissue that makes up most of the tissues in the muscles of the human muscular system.
• It is the only type of tissue that has cells with the ability to contract.
• This tissue can be used to move bones, compress chambers, or squeeze various organs.
• There are three major types of muscle tissues in the human body:
• Skeletal muscle tissue:
• ​Skeletal muscle is the most common type of muscle tissue in the human body. To move bones in opposite directions, skeletal muscles often consist of pairs of muscles that work in opposition to one another to move bones in different directions at joints.
• Skeletal muscle fibres are bundled together in units called muscle fascicles, which are bundled together to form individual skeletal muscles. Skeletal muscles also have connective tissue supporting and protecting the muscle tissue.
• Smooth muscle tissue:
• ​Smooth muscle is muscle tissue in the walls of internal organs and other internal structures such as blood vessels.
• When smooth muscles contract, they help the organs and vessels carry out their functions. When smooth muscles in the stomach wall contract, for example, they squeeze the food inside the stomach, helping to mix and churn the food and break it into smaller pieces. This is an important part of digestion.
• Contractions of smooth muscles are involuntary, so they are not under conscious control. Instead, they are controlled by the autonomic nervous system, hormones, neurotransmitters, and other physiological factors.
• Cardiac muscle tissues:
• Cardiac muscle is found only in the wall of the heart. It is also called myocardium.
• When cardiac muscle contracts, the heartbeats and pumps blood. Contractions of cardiac muscle are involuntary. They are controlled by electrical impulses from specialized cardiac muscle cells in an area of the heart muscle called the sinoatrial node.

The correct answer is India.

Explanation:

• World Environment Day is a UN Environment-led global event, the single largest celebration of our environment each year, which takes place on June 5 and is celebrated by thousands of communities worldwide.
• India is the global host of 2018 World Environment Day.
• The theme of World Environment Day is “Beat Plastic Pollution”.
• The theme “Beat Plastic Pollution”, urges governments, industry, communities, and individuals to come together and explore sustainable alternatives and urgently reduce the production and excessive use of single-use plastic polluting our oceans, damaging marine life, and threatening human health.

Additional Information

• Plastic Pollution facts:
• Every year the world uses up to 5 trillion plastic bags.
• Each year, at least 13 million tonnes of plastic end up in the oceans, the equivalent of a full garbage truck every minute.
• In the last decade, we produced more plastic than in the whole last century.
• 50 per cent of the plastic we use is single-use or disposable.
• We buy 1 million plastic bottles every minute.
• Plastic makes up 10% of all of the waste we generate.

Shortcut Trick

Identify the highest power of all prime factors present in 36, 40, and 660.

36 = 2² × 3²

40 = 2³ × 5

660 = 2² × 3 × 5 × 11

LCM = 2³ × 3² × 5 × 11 = 8 × 9 × 5 × 11 = 3960.

∴ The correct answer is 3960.

Alternate Method

Given: Numbers are 36, 40, and 660.

Formula Used: LCM (Least Common Multiple) using the Division Method.

⇒ Divide the numbers by the smallest prime factor (2): 18, 20, 330

⇒ Divide again by 2: 9, 10, 165

⇒ Divide again by 2: 9, 5, 165

⇒ Divide by 3: 3, 5, 55

⇒ Divide by 3: 1, 5, 55

⇒ Divide by 5: 1, 1, 11

⇒ Divide by 11: 1, 1, 1

⇒ LCM = 2 × 2 × 2 × 3 × 3 × 5 × 11

⇒ LCM = 8 × 9 × 55 = 72 × 55 = 3960

∴ The correct answer is 3960.

Additional Information

LCM and HCF Relationship

For two numbers A and B, Product of numbers = LCM × HCF.

LCM of Fractions

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

HCF of Fractions

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

The correct answer is Ga.

Explanation:

• Gallium has a very low melting point of 29.76°C.
• Gallium is a soft, silvery metal used primarily in electronic circuits, semiconductors, and light-emitting diodes (LEDs).
• It is also useful in high-temperature thermometers, barometers, pharmaceuticals, and nuclear medicine tests.
• The largest producers of gallium are Australia, Russia, France, and Germany.
• Atomic number (number of protons in the nucleus): 31
• Atomic symbol (on the periodic table of the elements): Ga
• Atomic weight (average mass of the atom): 69.723
• Phase at room temperature: solid
• Boiling point: 3,999 F (2,204 C)
• Number of isotopes (atoms of the same element with a different number of neutrons): 24 whose half-lives are known
• Most common isotopes: Two stable Ga-69 (natural abundance 60.1 per cent) and Ga-71 (natural abundance 39.9 per cent).

​

Key Points 

About other options:

The pattern followed is,

The figures A, B and C are open figures.

Whereas,

Figure D is a circle, which is a closed figure.

Hence, option 1 is the odd figure.

The pattern followed is,

The figures A, C and D have the same base figure which is surrounded by other symbols.

Whereas,

Figure B has one line missing.

Hence, option 4 does not belong to the group.

(Note: In original paper this question has discrepancy. The extra shaded triangle in the figure D in question are to be changed. The empty triangle will be as per the figure given above.)

Mistake Points

 Figure  D is not the odd one out. Figure B is the odd one out as figure B has one line missing.

Shortcut Trick

Directly substitute ∠A = 30° into the expression: sin² 30° − cos² 30° + tan² 30°.

Value substitution: (1/2)² − (√3/2)² + (1/√3)²

Calculation: 1/4 − 3/4 + 1/3 = − 2/4 + 1/3 = − 1/2 + 1/3 = − 1/6.

∴ The correct answer is − 1/6.

Alternate Method

Given: In triangle ABC, ∠B = 90° and ∠A = 30°.

Formula Used: Standard trigonometric values: sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3.

The expression to evaluate is sin² A − cos² A + tan² A.

⇒ Expression = (sin 30°)² − (cos 30°)² + (tan 30°)²

⇒ Expression = (1/2)² − (√3/2)² + (1/√3)²

⇒ Expression = 1/4 − 3/4 + 1/3

⇒ Expression = (1 − 3)/4 + 1/3

⇒ Expression = − 2/4 + 1/3

⇒ Expression = − 1/2 + 1/3

⇒ Expression = (− 3 + 2)/6

⇒ Expression = − 1/6

∴ The correct answer is − 1/6.

Additional Information

Trigonometric Identities

Fundamental identities include sin²θ + cos²θ = 1 and 1 + tan²θ = sec²θ.

Double Angle Relation

The term (sin²A − cos²A) is equal to − (cos²A − sin²A), which simplified is − cos 2A.

Standard Values at 30°

For θ = 30°: sin θ = 0.5, cos θ = 0.866, tan θ = 0.577.

The least possible Venn diagram is,

Conclusion 1: Some seats are pillows → False (This is definitely false)

Conclusion 2: Some cushions are seats → False (This is definitely false)

Hence, “neither 1 nor 2” follows.

Shortcut Trick

Let Total Work be 80 units (LCM of 40 and 80).

Efficiency of A = 2 units/min and Efficiency of B = 1 unit/min.

Pipe A worked for the entire 30 minutes, filling 30 × 2 = 60 units.

Remaining 80 − 60 = 20 units were filled by pipe B.

Time for pipe B = 20 ÷ 1 = 20 minutes.

∴ The correct answer is 20 min.

Alternate Method

Given: Total time taken to fill the tank = 30 minutes.

Calculations:

⇒ Pipe A was open for the entire duration of 30 minutes.

⇒ Work done by Pipe A = Efficiency × Time = 2 × 30 = 60 units.

⇒ Remaining work to be done by Pipe B = Total Work − Work by A = 80 − 60 = 20 units.

⇒ Time for which Pipe B was open = Remaining Work ÷ Efficiency of B

⇒ Time = 20 ÷ 1 = 20 minutes.

∴ The correct answer is 20 min.

Additional Information

Total Work Concept

Total work is usually taken as the LCM of the individual times to simplify calculations into integers.

Pipes and Cisterns

If a pipe fills a tank in x hours, its efficiency is 1/x. For outlet pipes, efficiency is taken as negative.

Efficiency Formula

Efficiency = Total Work ÷ Time Taken. Total Work = Efficiency × Total Time.

Shortcut Trick

Option Verification Method: Check the given options in the first condition (7 bats + 6 balls = ₹3,800).

For Option (3): (7 × 500) + (6 × 50) = 3500 + 300 = ₹3,800.

Check second condition: (3 × 500) + (5 × 50) = 1500 + 250 = ₹1,750.

Both conditions are satisfied by Option (3).

∴ The correct answer is Bat: ₹500, Ball: ₹50.

Alternate Method

Given: 7 bats + 6 balls = ₹3,800 and 3 bats + 5 balls = ₹1,750.

Formula Used: Linear Equations in two variables (Substitution or Elimination).

⇒ Let cost of 1 bat be x and cost of 1 ball be y.

⇒ 7x + 6y = 3800 --- (i)

⇒ 3x + 5y = 1750 --- (ii)

⇒ Multiply (i) by 5 and (ii) by 6:

⇒ 35x + 30y = 19000

⇒ 18x + 30y = 10500

⇒ Subtracting: 17x = 8500 ⇒ x = 500

⇒ Substitute x = 500 in (ii): 3(500) + 5y = 1750 ⇒ 1500 + 5y = 1750 ⇒ 5y = 250 ⇒ y = 50

∴ The correct answer is Bat: ₹500, Ball: ₹50.

Additional Information

Linear Equations in Two Variables

Equations of the form ax + by + c = 0 represent a straight line. Solving a pair of such equations finds the point of intersection.

Elimination Method

Make the coefficients of one variable equal by multiplying the equations with suitable constants, then add or subtract to eliminate that variable.

Unitary Cost Calculation

Total cost = (Quantity₁ × Price₁) + (Quantity₂ × Price₂). This forms the basis of business math word problems.

The correct answer is Pt.

Key Points

• Dobereiner made the first observation on platinum as a catalyst.
• Catalyst is the substance that increases the rate of a chemical reaction without itself undergoing any permanent chemical change.
• Each of Dobereiner's triads was a group of three elements.
• The appearance and reactions of the elements in a triad were similar to each other.
• He showed that in each triad the mean of the lightest and heaviest atomic weights approximated the atomic weight of the middle element.

Additional Information

• Dobereiner's triads grouped elements with similar chemical properties.
• Consider lithium, sodium, and potassium, for example.
• These elements all react with water at room temperature.
• They react with chlorine to form compounds with similar formulas: LiCl, NaCl, and KCl.
• They combine with hydrogen to form compounds with similar formulas: LiH, NaH, and KH.
• They form hydroxides with similar formulas: LiOH, NaOH, and KOH.

The correct answer is between F and C.

• When an object is placed beyond the centre of curvature of a concave mirror, the image will be formed between the focus and centre of curvature.

Additional Information

Centre of Curvature:- 

• The Centre of a circle which passes through a curve at a given point and has the same tangent and curvature at that point.

Focus:-

• In geometrical optics, a focus also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle.

Diagrams:-