RRC Group D Previous Year Paper 35 (Held On: 8 Oct 2018 Shift 2)

The correct answer is option 3, i.e., four-chambered heart.

• Birds(aves) have four-chambered heart.
• Chordates have closed circulatory system i.e., heart and blood vessels are found in them, and Heart in is divided into chambers like atriums (auricles) and ventricles.
• Pisces have two-chambered heart, i.e., one auricle and one ventricle.
• Amphibians and Reptile have three-chambered heart, i.e., two auricles and one ventricle.
• Aves and Mammals have four-chambered heart, i.e., two auricles and two ventricles.
• This kind of system prevents mixing of the oxygenated and de-oxygenated blood.

The correct answer is option 2, i.e., doubled.

• If the resistance is halved the current gets doubled.
• Electrical resistance is the obstruction in the flow of current.
• This means that when resistance will be less, the current will be more.
• Also, the formula for the current is, I = V / R, where I = Current, V = Voltage, R = Resistance.
• According to question, Resistance (R) is halved. Now, if the resistance is halved and the voltage remains the same, the new value of current becomes**, I′ = 2V/R, I′ = 2(V/R)** = 2I. Hence, the current will become double.

• The correct answer is Option 1, i.e., Supriya Sahu.
• As of September 2018, Supriya Sahu was the Director-General of Doordarshan.
• Doordarshan is one of the two divisions of the Prasar Bharti.
• It was founded by the Government of India on 15 September 1959 and is one of the largest broadcasting organizations of India in studio and transmitter infrastructure.
• Supriya Sahu is an IAS officer and currently serving as the Principal Secretary-cum-Managing Director of The Tamil Nadu Small Tea Growers’ Industrial Cooperative Tea Factories’ Federation Limited (INDCOSERVE) in Coonoor.
• A. Surya Prakash is currently serving as the chairperson of Doordarshan.

The correct answer is option 1, i.e., ears.

• Pinna is the external part of the ears.
• In mammals, an ear has 3 parts, namely external ear, middle ear, and inner ear.
• The external ear is the outermost part of the ear which is divided into ear pinna and auditory canal.
• The ear pinna is the main part and occurs only in mammals. It is due to this fact mammals are regarded to have true external ears.
• The muscles of ear pinna are vestigial parts of the human body.
• The parts of human eyes include: cornea, sclera, pupil, iris, lens, retina, choroid, etc.

Concept Used:

Rules to determine the number of significant figures:

• All non-zero numbers are significant.
• The Zeros between two non-zero digits are significant.
• Leading zeros are not significant.

Calculation:

Considering the given value 0.008594

Now, Correct to three significant figures can be written as 0.00859

• Significant figures of a number in notation are digits in the number.
• That is absolutely necessary to indicate the quantity of something in an accurate manner.
• This mainly uses to precise a number.
• For example:

The correct answer is option 2, i.e., Cricket.

• Angha Deshpande is related to Cricket.
• Angha Deshpande was a wicket-keeper and right-handed batswoman.
• She made her ODI debut in the year 2008 and played her last ODI in the year 2013.
• She made her T20 debut in the year 2011 and played her last T20 in the year 2014.

The correct answer is option 4, i.e., - 2.0 ms-1.

• The recoil velocity is the velocity by which pistol bounces back when a bullet is fired.
• In this case, the momentum of the bullet is equal to the momentum of the pistol.
• Hence, m_bv_b = m_pv_p (where m_b and m_p are the masses of bullet and pistol respectively and v_b and v_p are the velocities of bullet and pistol respectively).
• 3 x v_p = 40 x 10^-3 x 150
• v_p = 40 x 10-3 x 50
• v_p = 2000 x 10-3
• v_p = 2 m/s
• Here, the velocity of pistol is taken with negative sign because, it is in the opposite direction to that of the velocity of the bullet, i.e., bullet moves forward and pistol moves backwards.

The figure which can be formed from the given shapes is,

Hence, option 4 is the correct answer.

The correct answer is option 1, i.e., Pratyush.

• Pratyush is India's fastest and first multi-petaflops (PF) supercomputer unveiled at the Pune-based Indian Institute of Tropical Meteorology (IITM).
• The meaning of the word 'Pratyush' is 'rising sun' and the maximum speed of the supercomputer is 4.0 PetaFlops.
• It was inaugurated on 8 January 2018 by the Union Minister of Science and Technology, Dr. Harsh Vardhan.
• Pratyush is used for weather forecasting and climate monitoring.
• After Japan, the USA, and the UK, India has become the fourth country in the world to have a High-Performance Computing (HPC) facility meant for climate and weather research.
• The team of engineers that built Pratyush was led by Suryachandra A Rao at the IITM, Pune.
• Mihir is another supercomputer unveiled at the National Center for Medium Range Weather Forecast (NCMRWF), Noida. The maximum speed of this supercomputer is 2.8 PetaFlops. Together they provide a combined output of 6.8 PetaFlops.
• The purpose of the Mihir supercomputer is the same as that of Pratyush.

According to the given information,

Assumption I: This is implicit, because there are other oils available in the market.

Assumption II: This is also implicit, because health is definitely a priority for every individual and their family.

Hence, “both I and II” are implicit.

Shortcut Trick

If x + 1/x = k, then x² + 1/x² = k² − 2.

Given: tan f + cot f = 5 (Note: cot f = 1/tan f).

Let tan f = x, then x + 1/x = 5.

Value = 5² − 2 = 25 − 2 = 23.

∴ The correct answer is 23.

Alternate Method

Given: tan f + cot f = 5

Formula Used: (a + b)² = a² + b² + 2ab

⇒ (tan f + cot f)² = 5²

⇒ tan² f + cot² f + 2 × tan f × cot f = 25

⇒ tan² f + cot² f + 2 × tan f × (1/tan f) = 25

⇒ tan² f + cot² f + 2 = 25

⇒ tan² f + cot² f = 25 − 2

⇒ tan² f + cot² f = 23

∴ The correct answer is 23.

Additional Information

Reciprocal Identities

In trigonometry, tan f × cot f = 1 because cot f is the reciprocal of tan f.

Algebraic Power Rule

If x + 1/x = a, then x⁴ + 1/x⁴ = (a² − 2)² − 2.

Pythagorean Identities

Related identities include 1 + tan² f = sec² f and 1 + cot² f = cosec² f.

The correct answer is option 1, i.e., Fullerenes.

• In Fullerenes, carbon atoms are arranged in the shape of a football.
• Fullerenes are one of the allotropes of carbon.
• In fullerenes, carbon atoms are bonded by single and double bonds so as to form a closed or partially closed mesh, with fused rings of five to seven atoms.
• The most famous member of the Fullerenes is Buckminster Fullerenes. The molecule has 60 carbon atoms.
• It is named after Buckminster Fuller, because the structure of the molecule is similar to geodesic spheres made by this American architect, and is also known as 'Buckyball' as its shape is similar to that of 'soccer balls'.
• The accidental synthesis in the year 1985 led to the discovery of fullerenes.
• Methane (CH₄) is a hydrocarbon belonging to the family of alkanes and is the first member of the alkane family.
• Benzene is an aromatic hydrocarbon with the formula C₆H₆.
• Ethane (C₂H₆) is the second member of the alkane family after Methane.

The correct answer is option 3, i.e., Kalidas.

• 'Raghuvansham' is compiled by Kalidas.
• 'Raghuvansham' known as 'Raghuvamsa' is a Sanskrit epic poem compiled by Kalidas.
• The poem speaks in 19 sargas, about the Raghu dynasty, which included Raghu, Dasaratha, Rama, etc.
• Kalidas is assumed to be a 5th-century poet and writer. His famous works include Abhijanasakuntalam, Meghaduta, etc.
• Surdas was a 16th-century blind poet whose works were dedicated to the devotion towards Lord Krishna. He used to write in Braj Basha and 'Sur Sagar' is his most famous composition.
• Kabirdas was a 15th-century saint and poet, whose writings were influential in the Bhakti movement. He also wrote in Braj and his works were concerned with devotion, mysticism, and discipline. 'Kabir ke dohe' is still very popular.
• Tulsidas a devotee of Lord Rama was a saint and a renowned poet. He is best known for 'Ramcharitmanas'.

The correct answer is option 2, i.e., 273 K.

Key Points

• The melting point of ice is 273 K.
• Water can exist in all three forms, i.e., solid, liquid, and gas.
• Solid in the form of ice, liquid in the form of water, and gas in the form of water vapours.
• The melting point is the temperature at which a substance changes its state from solid into liquid.
• For ice, the temperature in degree Celcius is 0 and in kelvin, it is 273.
• Kelvin is the SI unit of temperature and 0ºC = 273 K
• The formula for converting ºC into K is: K = 273 + temperature in ºC
• The temperature at which a liquid transforms into gas is termed as its boiling point.
• For water, the boiling point is 100ºC, i.e., 373 K.

The correct answer is  250.

Key Points

• The maximum permissible strength of the Rajya Sabha is 250.
• As per Article 80 of the Indian Constitution, the maximum permissible strength of the Upper House of the Parliament, i.e., Rajya Sabha is 250.
• Out of the total 250, 238 are representatives from the States and Union Territories and 12 are nominated by the President.
• Currently, the maximum strength for Rajya Sabha is 245, of which 233 are elected by the legislatures of the states and union territories and the remaining 12 are nominated by the President.
• The Vice-President of India is the ex-officio Chairman of the Rajya Sabha, i.e., whosoever holds the office of Vice-President will automatically become the Chairman of the Rajya Sabha.

According to the given statement,

Course of action 1: This follows, because the footpath is filled with beggars.

Course of action 2: This also follows, because the social status of the beggars should be increased.

Hence, “both 1 and 2” follow.

Given

49 × 17 = 833

Calculation

0.0833 ÷ 4.9

= 833/10000 ÷ 49/10

= (833/10000) × (10/49)

= (49 × 17)/(1000 × 49)

= 17/1000

= 0.017

The correct answer is option 2, i.e., Tasman Sea.

• Tasman Sea separates Australia from New Zealand.
• The Tasman Sea is a section of the Southwestern Pacific Ocean and it is 2800 km long and 2000 km wide.
• Between the southeast coast of Australia and Tasmania to the west and New Zealand to the east.
• The sea was first navigated by Dutch explorer Abel Janszoon Tasman, hence the name the Tasman Sea.

Shortcut Trick

In Δ formed by depression angle 30°, the ratio of Height : Base is 1 : √3. Since Height = 150 m, then Base = 150√3 m.

In Δ formed by elevation angle 45°, the ratio of Height : Base is 1 : 1.

Since the Base is the same (150√3 m), the additional height is also 150√3 m.

Total Height of Building B = 150 + 150√3 = 150(1 + √3) m.

∴ The correct answer is 150 (1 + √3) m.

Alternate Method

Given: Height of Building A = 150 m. Angle of elevation = 45°. Angle of depression = 30°.

Formula Used: tan(θ) = Perpendicular ÷ Base

⇒ In bottom triangle: tan(30°) = 150 ÷ Distance between buildings

⇒ 1/√3 = 150 ÷ Distance

⇒ Distance = 150√3 m

⇒ In top triangle: tan(45°) = Extra height of B ÷ 150√3

⇒ 1 = Extra height ÷ 150√3

⇒ Extra height = 150√3 m

⇒ Total Height of Building B = 150 + 150√3

∴ The correct answer is 150 (1 + √3) m.

Additional Information

Angle of Elevation and Depression

The angle of elevation is measured upwards from the horizontal, while the angle of depression is measured downwards from the horizontal.

Trigonometric Ratios for Standard Angles

tan(30°) = 1/√3, tan(45°) = 1, and tan(60°) = √3. These are essential for solving Height and Distance problems.

The correct answer is option 4, i.e., 90 degrees.

• If the work done is zero, then the angle between the force and displacement is 900.
• Work is a scalar quantity, i.e., it only has magnitude and no direction.
• Work done is a scalar product of force and displacement, i.e., W = F.s or W = F s cosθ
• The value of cos 90° is 0, and as we know when anything is multiplied with 0 the product is 0.
• It is due to this, we say that the work done when the angle between force and displacement is 90º.

Shortcut Trick

Use the direct formula for distance when speed and time differences are given.

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

Difference in time = (1 minute early) − (−3 minutes late) = 4 minutes = 4/60 hours.

Distance = [ (42 × 36) ÷ (42 − 36) ] × [4/60]

Distance = [1512 ÷ 6] × [1/15] = 252 ÷ 15 = 16.8 km.

∴ The correct answer is 16.8 km.

Alternate Method

Given:

Speed₁ (S₁) = 42 km/h, Time₁ = T − 1 min

Speed₂ (S₂) = 36 km/h, Time₂ = T + 3 min

Formula Used:

Distance = S₁ × T₁ = S₂ × T₂

Calculations:

⇒ Let Distance be D.

⇒ Difference in time = 1 − (−3) = 4 minutes = 4/60 hour.

⇒ (D/36) − (D/42) = 4/60

⇒ [(7D − 6D) / 252] = 1/15

⇒ D / 252 = 1/15

⇒ D = 252 ÷ 15

⇒ D = 16.8 km

∴ The correct answer is 16.8 km.

Additional Information

Ratio Method for Distance

When distance is constant, speed is inversely proportional to time. Speed ratio 42:36 (7:6) implies time ratio 6:7. Difference 1 unit = 4 mins.

Relative Speed

In the same direction, relative speed is the difference (S₁ − S₂). In opposite directions, it is the sum (S₁ + S₂).

Average Speed

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

Drawing the Venn diagram,

Conclusion 1: Some parrots are NOT wolves.  → False (This is definitely false)

Conclusion 2: Some wolves are parrots → True (This is definitely true)

Hence, “only conclusion 2” follows.

Shortcut Trick

Efficiency ratio of Expert (E) to Trainee (T): 15E = 25T ⇒ 3E = 5T.

Work required: 8E + 15T. Since 15T = 9E, Work = 8E + 9E = 17E.

New team: 11E + xT must equal 17E ⇒ xT = 6E.

Since 3E = 5T, then 6E = 10T.

∴ The correct answer is 10 trainees.

Alternate Method

Given: 15 experts = 25 trainees (in terms of work done).

Formula Used: Total Work = Efficiency × Time

⇒ 15 Expert (E) = 25 Trainee (T)

⇒ 1 E = 25/15 T = 5/3 T

⇒ Case 1 Total Work = (8E + 15T) × Time

⇒ Case 2 Total Work = (11E + xT) × Time

⇒ 8E + 15T = 11E + xT

⇒ 15T − xT = 11E − 8E

⇒ (15 − x)T = 3E

⇒ Substitute 3E = 5T:

⇒ (15 − x)T = 5T

⇒ 15 − x = 5

⇒ x = 10

∴ The correct answer is 10 trainees.

Additional Information

Efficiency Equivalence

When M₁ men can do as much work as M₂ women, the efficiency ratio is E₁/E₂ = M₂/M₁.

Total Work Formula

Total Work = (Number of People × Individual Efficiency) × Time. For the same duration, work is directly proportional to total efficiency.

The correct answer is option 2, i.e. A and B are both true.

• Rigidity: It is the property of matter to maintain its shape even if external force works on it and solids show this property.
• The property exhibited by the solids by virtue of which they maintain their shape is termed as Rigidity.
• This is so because in solids the particles are closely packed with very little or no space between the particles and also the force of attraction between the particles is very high.
• Fluidity: It is the property of a substance to easily flow and allow a change in its shape under external forces and this property is exhibited both by liquids and gasses. 
• Fluidity in simple terms can be defined as the ability to flow.
• The ability of liquids and gases to take the shape of the container in which they are kept is because of their fluidity.

The correct answer is option 4, i.e., CaCO₃.

• While whitewashing, Ca(OH)2 reacts slowly with CO2 in the air to form a thin layer of CaCO3 on the walls.
• Ca(OH)2 is Calcium hydroxide, CO₂ is Carbon dioxide, and CaCO3 is Calcium carbonate.
• Calcium carbonate is formed 2-3 days after whitewashing, and thus we get a shiny finish on the wall.
• Following reaction takes place in the given case:
• Ca(OH)₂ + CO₂ → CaCO₃ + H₂O
• The common name of Calcium hydroxide is 'slaked lime' and the saturated solution of Calcium hydroxide is known as 'limewater'.
• Calcium carbonate is commonly known as 'limestone'.
• CaO is Calcium oxide.
• CaSO₄ is Calcium sulphate.
• CaCl₂ is Calcium chloride.

The correct answer is option 4, i.e., Jwala Gutta.

• Jwala Gutta was included in the Badminton Association of India's coach panel in 2017.
• The Badminton Association of India (BAI) has formed a new panel of 19 coaches which include former players like Jwala Gutta, Arvind Bhat, Chetan Anand, etc. Pullela Gopichand will still remain the Chief National Coach.
• Jwala Gutta is a renowned badminton player. She represented India in both mixed doubles and women's doubles at the international stage. She won the bronze medal in the 2011 World Championship.
• Other than Jwala Gutta, the other 3 women players included in the panel are Madhumita Bisht, Pradnya Gadre, and Oli Deka.
• Saina Nehwal is a former world no. 1 badminton player and has been honored with Rajiv Gandhi Khel Ratna Award and Arjuna Award.
• PV Sindhu is also a very famous badminton player and has won silver in the 2016 Summer Olympics and has been felicitated with awards like Rajiv Gandhi Khel Ratna Award, Padma Shri, and Padma Vibhushan.

The correct answer is option 2, i.e., Li Keqiang.

• Li Keqiang is the current Prime Minister of China.
• Li Keqiang, the incumbent Premier of the People's Republic of China, assumed his office on 15 March 2013.
• Li Keqiang is not only the head of the government but also one of the leading figures behind China's Financial and Economic Affairs, National Security, Foreign Affairs, etc.
• Xi Jinping is the President of the People's Republic of China.
• Hu Jintao was the President of the People's Republic of China before Xi Jinping.
• Wang Qishan is the Vice-President of the People's Republic of China.

Flowers, fruits and leaves are different elements that we get from plants and they are represented separately.

The correct Venn diagram is,

Hence, option 1 is the correct answer.

Shortcut Trick Condition for equal roots in x2 + kx + 9 = 0 is b2 = 4ac. k2 = 4 × 1 × 9 k2 = 36 k = ± √36 = ± 6 ∴ The correct answer is ± 6.

Alternate Method Given: Quadratic Equation: x2 + kx + 9 = 0 Formula Used: A quadratic equation ax2 + bx + c = 0 has equal roots if its Discriminant (D) is zero. ⇒ D = b2 − 4ac = 0 Calculations: ⇒ Comparing the given equation with ax2 + bx + c = 0, we get: ⇒ a = 1, b = k, c = 9 ⇒ Substitute values in the condition D = 0: ⇒ k2 − 4 × 1 × 9 = 0 ⇒ k2 − 36 = 0 ⇒ k2 = 36 ⇒ k = ± √36 ⇒ k = ± 6 ∴ The correct answer is ± 6.

Additional Information Nature of Roots For a quadratic equation, if D > 0, the roots are real and distinct; if D = 0, the roots are real and equal; if D < 0, the roots are imaginary. Discriminant Formula The discriminant (D) of the quadratic equation ax2 + bx + c = 0 is calculated using the formula D = b2 − 4ac. Perfect Square Condition A quadratic expression ax2 + bx + c is a perfect square if and only if its discriminant is zero (b2 − 4ac = 0). Roots of Quadratic Equation The roots are found using the quadratic formula: x = (−b ± √D) / 2a.

The correct answer is option 3, i.e., diamond.

• In diamond, each carbon atom is bonded to four other carbon atoms forming a rigid three-dimensional structure.
• Diamond is an allotrope of carbon, in which atoms are arranged in a crystal structure called diamond cubic.
• Diamond is the hardest and has the highest thermal conductivity of any natural material. These properties make it very useful for industrial purposes.
• Graphite is also an allotrope of carbon in which atoms are arranged in the hexagonal arrangement. Graphite is the most stable form of carbon under the STP (standard temperature and pressure). It is used in pencils and electrodes.
• Ethane (C₂H₆) is a hydrocarbon and second member of the alkane family after methane.
• Methane (CH4) is the first member of the alkane family having only one carbon atom.

The correct answer is option 2, i.e., Dronacharya Award.

• Dronacharya Award is bestowed upon coaches for producing medal winners at prestigious international sport events.
• Dronacharya Award is officially known as Dronacharya Award for Outstanding Coaches in Sports and Games.
• The award has been named after "Guru Dronacharya" who was the teacher of Kauravas and Pandavas in the Mahabharata and is given for producing medal winners at prestigious international sport events.
• The award is presented annually by the Ministry of Youth Affairs and Sports and was first presented in the year 1985.
• A bronze statue of Dronacharya, a certificate, ceremonial dress, and a cash prize of Rs. 5 lakhs is given to the awardee.
• The most recent recipients of the award in the year 2019 are: Mohinder Singh Dhillon, Rambir Singh Khokar, U. Vimal Kumar, Sandip Gupta, Sanjay Bhardwaj, and Merzban Patel.
• Arjuna Award is also presented by the Ministry of Youth Affairs and Sports to the players for their outstanding achievements in sports.
• Rajiv Gandhi Khel Ratna Award is the highest honour given to a sportsperson in India. It is also presented by the Ministry of Youth Affairs and Sports.
• Dhyan Chand Award is officially known as the Dhyan Chand Award for Lifetime Achievement in Sports and Games, is the award given for the contribution to the sport during the active career and also after the retirement.

Shortcut Trick

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

Given Rate (r) = 15% and Difference = ₹180.

180 = P × (15/100) × (15/100)

180 = P × (3/20) × (3/20) ⇒ 180 = P × (9/400)

P = (180 × 400) ÷ 9 = 20 × 400 = 8000.

∴ The correct answer is ₹8000.

Alternate Method

Given:

Time (n) = 2 years

Rate of Interest (r) = 15% per annum

Difference (CI − SI) = ₹180

Formula Used:

Difference for 2 years = P × (r/100)²

Calculations:

⇒ Let the Principal be P.

⇒ Simple Interest for 2 years = (P × 15 × 2) ÷ 100 = 0.30P

⇒ Compound Interest for 2 years = P × [ (1 + 15/100)² − 1 ]

⇒ CI = P × [ (1.15)² − 1 ] = P × [ 1.3225 − 1 ] = 0.3225P

⇒ Difference = CI − SI = 0.3225P − 0.30P = 0.0225P

⇒ 0.0225P = 180

⇒ P = 180 ÷ 0.0225

⇒ P = (180 × 10000) ÷ 225

⇒ P = 1800000 ÷ 225 = 8000

∴ The correct answer is ₹8000.

Additional Information

Difference for 3 Years

For a period of 3 years, the difference between CI and SI is calculated as: D = P(r/100)² × (3 + r/100).

Effective Interest Rate (CI)

For 2 years at rate r%, the effective compound interest rate is r + r + (r × r / 100)%.

Successive Percentage Change

The difference between CI and SI for 2 years is always equal to the interest calculated on the first year's interest: (r% of r)% of Principal.

The correct answer is option 3, i.e., In vitro fertilization.

• In some females, due to some problem, fertilization cannot take place. In such cases, freshly released egg and sperms are kept together for few hours for fertilization to occur outside the body. This is called: In vitro fertilization.
• The word "in vitro" means "in glass", the artificial fertilization that takes place outside the body in a glass test-tube is known as In vitro fertilization.
• In this process, the ovulation cycle of the woman is administered and the egg is taken from the body of the female and it is fertilized with the sperm of the male in the artificial environment.
• Regeneration is an asexual mode of reproduction in which a part of the body detaches from the parent to become an independent individual. This generally takes place in lower animals like hydra, sponges, earthworms, starfish, etc.
• Vegetative reproduction is also an asexual mode of reproduction in which a plant is grown from a specialized tissue of the parent plant body.
• Fertilization is a process of fusion of male and female gametes.

The correct answer is option 4, i.e., altitude.

• The value of 'g' decreases with altitude.
• 'g' is the acceleration due to gravity.
• The acceleration due to gravity is the acceleration gained by an object due to the force of gravitation. The SI unit for the same is m/s².
• Its standard value is 9.8 m/s² on the surface of the earth at the sea level.
• The formula of 'g' is: g = GM / R² (where G is 'gravitational constant', M is the mass of the earth, and R is the radius of the earth)
• The other formula for 'g' is: g = 4/3 πρRG
• The value of 'g' depends on the following:
• altitude above the surface of Earth
• shape of the Earth
• depth below the surface of Earth
• rotational motion of the Earth
• The value of 'g' decreases with altitude because g_h = g (1 + h/R)^-2  [where g_h is the acceleration due to gravity at height h]. This formula suggests that 'g' decreases with altitude.

Shortcut Trick

Direct identity: Difference of squares = (Sum of numbers) × (Difference of numbers)

Sum of numbers = (Difference of squares) ÷ (Difference of numbers)

Sum = 100 ÷ 2

Sum = 50

∴ The correct answer is 50.

Alternate Method

Given:

Let the two numbers be x and y.

Difference between numbers (x − y) = 2

Difference of squares (x² − y²) = 100

Formula Used:

Algebraic Identity: a² − b² = (a + b)(a − b)

Calculations:

⇒ x² − y² = 100

⇒ (x + y)(x − y) = 100

⇒ (x + y) × 2 = 100

⇒ x + y = 100 ÷ 2

⇒ x + y = 50

∴ The correct answer is 50.

Additional Information

Square of Sum Identity

The expansion of the square of the sum of two numbers is given by: (a + b)² = a² + b² + 2ab.

Square of Difference Identity

The expansion of the square of the difference of two numbers is given by: (a − b)² = a² + b² − 2ab.

Relation between Squares

A useful combined identity is: (a + b)² − (a − b)² = 4ab.

From the given graph we can say that,

In 1995 concentration of CO₂ = 360

In 2000 concentration of CO₂ = 370

In 2005 concentration of CO₂ = 380

In 2010 concentration of CO₂ = 385

In 2015 concentration of CO₂ = 400

Every year concentration of CO₂ is increasing.

∴ we can say that option (i) is the right answer

Shortcut Trick

Initial Ratio = 3 : 4 (Difference = 1 unit)

Final Ratio = 10 : 13 (Difference = 3 units)

To equate the differences, multiply initial ratio by 3 → 9 : 12

Change in each part = 10 − 9 = 1 unit → 1 unit = 3

Original numbers → 9 × 3 = 27 and 12 × 3 = 36

∴ The correct answer is 27, 36.

Alternate Method

Let the original numbers be 3x and 4x.

As per the condition, 3 is added to each number:

⇒ (3x + 3) / (4x + 3) = 10 / 13

⇒ 13 × (3x + 3) = 10 × (4x + 3)

⇒ 39x + 39 = 40x + 30

⇒ 40x − 39x = 39 − 30

⇒ x = 9

⇒ First Number = 3 × 9 = 27

⇒ Second Number = 4 × 9 = 36

∴ The correct answer is 27, 36.

Additional Information

Ratio and Proportion

A ratio compares two quantities by division. If a : b = c : d, then the product of extremes equals the product of means (ad = bc).

Cross Multiplication Method

For ratio problems involving additions or subtractions, the cross-product of the ratios can quickly determine the value of one unit.

Shortcut Trick

Net efficiency = 1/6 + 1/8 − 1/10

LCM of 6, 8, 10 = 120

Net efficiency = (20 + 15 − 12) / 120 = 23 / 120

Time taken = 120 / 23 = 5(5/23) hours

∴ The correct answer is 5(5/23) hr.

Alternate Method

Given: Inlet A fills in 6 hr, Inlet B fills in 8 hr, Outlet C empties in 10 hr.

Formula Used: Total Work = LCM of individual times; Efficiency = Total Work ÷ Time

⇒ Total Efficiency when all opened = 20 + 15 − 12

⇒ Total Efficiency = 23 L/hr

⇒ Total Time = Total Work ÷ Total Efficiency

⇒ Total Time = 120 ÷ 23 = 5(5/23) hours

∴ The correct answer is 5(5/23) hr.

Additional Information

Inlet and Outlet Logic

An inlet pipe does positive work (filling), while an outlet pipe does negative work (emptying) relative to the tank capacity.

Combined Efficiency

If pipe A fills in x hours and pipe B empties in y hours, net work in 1 hour = (1/x) − (1/y). If the result is positive, the tank fills; if negative, it empties.

Pipes and Cisterns vs Time and Work

The concepts are identical to Time and Work, where the tank capacity is the total work and the filling/emptying rates are the efficiencies.

The correct answer is  Voltmeter.

Key Points

• A voltmeter is an instrument used to measure the potential difference.
• A voltmeter is used between two points in an electric circuit to measure the potential difference between those two points.
• Voltmeter was invented in 1819 by Hans Oersted.
• The symbol for the voltmeter is shown below:

Additional Information

• The ammeter is the instrument used for measuring current in the electrical circuit.
• The galvanometer is the instrument that detects current in the electrical circuit.

The correct answer is option 4, i.e., lead.

• Lead is not a compound.
• Lead is an element and the symbol for lead is Pb.
• The atomic number of lead is 82 and belongs to group 14 of the periodic table and thus is a post transitional metal.
• Lead is a heavy metal that is soft and malleable, has low melting point, and is amphoteric in nature i.e., can react with both acids and bases.
• Compound is formed by the combination of two or more elements.
• Hydrogen sulfide (H₂S) is a gas that smells like rotten eggs.
• Chalk is a form of calcium carbonate i.e. CaCO₃.
• Sulphur dioxide (SO₂) is a toxic gas.

Here except E, the mirror image of M, W, and T will be same as they appear originally.

Hence, option C is the odd one out.

The correct answer is option 4, i.e., 1.5 ms-2.

Concept:

• Velocity: The rate of change of displacement of a body is called as the velocity of that body.
• It is a vector quantity which has both magnitude as well as direction.

$Velocity\left( V \right) = \frac{{Change;in;displacement}}{{Time;taken}} = \frac{{{S_2} - {S_1}}}{{{t_2} - {t_1}}};or;\frac{{dS}}{{dt}};$

Where S2 is final displacement at time t2 and S1 is initial displacement at time t1.गतीच्या 

• Acceleration: The rate of change of velocity is called as acceleration of the body.

$a = \frac{{v2 - v1}}{{t2 - t1}};or;\frac{{dv}}{{dt}}$

Where v2= Final velocity and v1= Initial velocity of an object at time t2, t1 respectively

Explanation:​

In the above question, we are given the initial and final velocities and change in the time period.

Since the answer must be in m/s² so, we need to convert

• Conversion of km/hr to m/s and vice versa-

18 km/hr converted to 18 × (5/18) = 5m/s

72 km/hr converted to 72 × (5/18) = 20 m/s

Change in velocity = 20 m/s - 5 m/s = 15 m/s

Time to change in velocity = 10 s

So, acceleration = (15 m/s) / 10 = 1.5 m/s²

The correct answer is 1.5 m/s²

Shortcut Trick

Let the side of the carpet be x m.

Cost Equation: 15x² + 6.50(100 − x²) = 1338.50

8.50x² + 650 = 1338.50 ⇒ 8.50x² = 688.50 ⇒ x² = 81 ⇒ x = 9 m.

Width of border = (Room side − Carpet side) ÷ 2 = (10 − 9) ÷ 2 = 0.5 m.

∴ The correct answer is 1/2 m.

Alternate Method

Given: Side of square room = 10 m, Total area = 100 m².

Formula Used: Area = Side²; Total Cost = (Area₁ × Rate₁) + (Area₂ × Rate₂).

⇒ Let the side of the square carpet be x meters.

⇒ Area of carpet = x² and Area of oil cloth = 100 − x².

⇒ Total Cost = (x² × 15) + [(100 − x²) × 6.50] = 1338.50

⇒ 15x² + 650 − 6.50x² = 1338.50

⇒ 8.50x² = 1338.50 − 650 = 688.50

⇒ x² = 688.50 ÷ 8.50 = 81

⇒ x = √81 = 9 m.

⇒ Width of oil cloth border (w) = (10 − 9) ÷ 2 = 0.5 m.

∴ The correct answer is 1/2 m.

Additional Information

Border Area Calculation

For a square/rectangular path inside a boundary, the inner side = Outer side − 2 × Width.

Area of Path

Area of square path = (Outer Side)² − (Inner Side)² or 4w(S − w) where S is outer side and w is width.

Costing Problems

Always ensure units for area (m²) and rate (per m²) are consistent before performing addition.

The pattern followed is,

In the third figure there is a single diagram and in the fourth figure the same diagram is represented twice and they are joined.

Similarly,

In the second figure, there are two triangles joined.

And,

In the first figure, there should be a single triangle.

Hence, option 4 is the correct answer.

Blankets, Sheets and Pillows are generally used for covering the Cot.

Whereas,

Cot is a small bed.

Hence, “cot” does not belong to the group.

Shortcut Trick

Remaining work in terms of man-days = 18 workers × (12 − 4) days = 144 units.

New number of workers = 18 − 2 = 16 workers.

Days required = Remaining Work ÷ Current Workers = 144 ÷ 16 = 9 days.

∴ The correct answer is 9 days.

Alternate Method

Given: Initial workers (M₁) = 18, Initial days (D₁) = 12, Days worked = 4, Workers left = 2.

Formula Used: Total Work = M × D; Remaining Work = M₁ × (D₁ − days lapsed) = M₂ × D₂

⇒ Total work = 18 × 12 = 216 units.

⇒ Work completed in 4 days = 18 × 4 = 72 units.

⇒ Remaining work = 216 − 72 = 144 units.

⇒ New strength of workers = 18 − 2 = 16 people.

⇒ Time taken by 16 people = 144 ÷ 16 = 9 days.

∴ The correct answer is 9 days.

Additional Information

Chain Rule Formula

For work problems involving variations in men, days, and hours: (M₁ × D₁ × H₁) / W₁ = (M₂ × D₂ × H₂) / W₂.

Man-Days Concept

Total work is often expressed as the product of the number of men and the number of days they work (M × D), assuming constant efficiency.

Efficiency Relation

The number of people is inversely proportional to the time taken to complete a fixed amount of work.

The correct answer is option 1, i.e., Melting of ice.

• The melting of ice is a physical change.
• The change that does not lead to changes in the chemical composition of a substance is termed as physical change.
• Physical changes lead to changes in the physical properties and are generally reversible in nature.
• Examples of physical changes are: melting of ice, transition into gas, textural changes, changes in size, shape, color, etc.

Additional Information

• In the case of the melting of ice, only a phase transition takes place, the chemical composition of ice does not change.
• Chemical changes lead to the transformation in the chemical composition of the substance. Either a new substance is synthesized or a substance is decomposed.
• The setting of milk into curd, the ripening of fruits, and fermentation of grapes all are examples of chemical changes since the chemical properties of each are changed.

The correct is option 3, i.e., wrinkled seed.

• The wrinkled seed character is recessive in garden pea plants.
• Gregor John Mendel, known as 'father of genetics', chose garden pea (Pisum sativum) for his experiments.
• Mendel coined terms 'dominant' and 'recessive' in terms of the characters studied by him.
• A dominant trait is one that expresses itself in the presence of other contrasting trait and dominates it. eg: tallness.
• A recessive trait is one that is not expressed when present along with the contrasting trait in the hybrid. eg: dwarfness.

The mirror image for the given figure is,

Hence, option 3 is the correct answer.

The correct answer is  Hydrogen.

Key Points 

• Hydrogen is the only non-metal placed with alkali metals.
• Hydrogen and alkali metals are placed in group 1 of the periodic table.
• This is so because Hydrogen and alkali metals both have only one electron in their valence shell.
• Alkali metals include Lithium (³Li), Sodium (¹¹Na), Potassium (¹⁹K), Rubidium (³⁷Rb), Caesium (⁵⁵Cs), and Francium (⁸⁷Fr).
• Alkali metals along with Alkaline Earth metals form the s-block elements since the last electron enters the s-orbital.
• Alkali metals are highly reactive, shiny, and soft metals. They readily lose their valence electron to become cations with a +1 charge.
• These react with acids to form salt and hydrogen gas. For eg:
• 2Na + 2HCl → 2NaCl + H₂

Shortcut Trick

For any n-sided polygon, the number of diagonals is given by the formula:

Number of diagonals = [n × (n − 3)] ÷ 2

Here, n = 19 (for a 19-gon).

Number of diagonals = [19 × (19 − 3)] ÷ 2

Number of diagonals = [19 × 16] ÷ 2 = 19 × 8 = 152

∴ The correct answer is 152.

Alternate Method

Given:

Number of vertices (n) = 19

Formula Used:

Number of diagonals = ⁿC₂ − n

Calculations:

⇒ Total number of lines that can be drawn using 19 vertices = ¹⁹C₂

The correct answer is option 4, i.e., Sania Mirza.

Key Points

• The author of the book "Ace against Odds" is Sania Mirza.
• The book is an autobiography, i.e., Sania Mirza has written about her own life.
• The book was released by Indian actor Shahrukh Khan in July 2016.
• Sania Mirza is a renowned Indian Tennis player. She is a former world number 1 and has won 6 Grand Slams. She took retirement from singles in the year 2013.
• Rohan Bopanna is also a professional tennis player from India and has won the 2017 French Open mixed double title with Gabriela Dabrowski.
• Leander Paes is a world-renowned Indian tennis player, with the greatest number of doubles win in the Davis Cup.
• Yuki Bhambri is an Indian tennis player and represents India in Davis Cup and is a former junior number 1.

The pattern followed here is,

Hence, “MU” is the correct answer.

Shortcut Trick

Total pearls can be taken as LCM of denominators (8, 4, 5) = 40 units.

Floor = 5 units, Chair = 10 units, Sofa = 16 units → Total distributed = 31 units.

Remaining on strand = 40 − 31 = 9 units.

Given 9 units = 18 pearls ⇒ 1 unit = 2 pearls.

Pearls on floor = 5 units = 5 × 2 = 10.

∴ The correct answer is 10.

Alternate Method

Given:

Let total pearls be x.

Floor = x/8, Chair = x/4, Sofa = 2x/5, Strand = 18.

Calculations:

⇒ x = x/8 + x/4 + 2x/5 + 18

⇒ x − (x/8 + x/4 + 2x/5) = 18

⇒ x − [(5x + 10x + 16x) / 40] = 18

⇒ x − 31x/40 = 18

⇒ 9x/40 = 18

⇒ x = (18 × 40) / 9 = 80

⇒ Pearls on floor = 80 / 8 = 10

∴ The correct answer is 10.

Additional Information

Fractional Summation

To find the remaining part, subtract the sum of all given fractions from 1: Remaining = 1 − (Σ Fractions).

LCM Method for Fractions

When dealing with multiple fractions, assuming the total as the LCM of denominators avoids complex decimal calculations.

Base Change in Percentage

Fractions can be converted to percentages (1/8 = 12.5%, 1/4 = 25%, 2/5 = 40%) to solve using the 100% base method.

Shortcut Trick

Side of cube (a) = ³√343 = 7 cm.

When two cubes are joined, total surface area = 2 × (6a²) − 2 × (common face area).

TSA = 12a² − 2a² = 10a².

TSA = 10 × 7² = 10 × 49 = 490 sq cm.

∴ The correct answer is 490 sq cm.

Alternate Method

Given: Volume of each cube = 343 cm³.

Formula Used: Volume of cube = a³; TSA of cuboid = 2(lb + bh + hl).

⇒ Side of cube (a) = ³√343 = 7 cm.

⇒ For the resulting cuboid:

⇒ Length (l) = 7 + 7 = 14 cm.

⇒ Breadth (b) = 7 cm.

⇒ Height (h) = 7 cm.

⇒ TSA = 2(14×7 + 7×7 + 7×14)

⇒ TSA = 2(98 + 49 + 98) = 2(245) = 490 sq cm.

∴ The correct answer is 490 sq cm.

Additional Information

Cube Properties

Lateral Surface Area = 4a² and diagonal of a cube = a√3.

Cuboid Diagonal

Length of the longest rod that can be placed in a cuboid = √(l² + b² + h²).

Volume of Cuboid

The amount of space inside the cuboid is calculated as V = l × b × h.

The correct answer is option 2, i.e., Ministry of Agriculture & Farmers, Welfare.

• Ministry of Agriculture & Farmers, Welfare has launched 'Mission Fingerling' in March 2017 to achieve the Blue Revolution.
• Mission Fingerling is a programme that aims to enable holistic development and management of the fisheries sector.
• The expected expenditure for the programme is Rs. 52000 lakhs.
• The target set for the programme is to raise the fisheries production from 10.79 mmt (2014-2015) to 15 mmt by 2020-21.
• 20 states have been identified by the government based on their potential to boost the Fish Fingerling production and Fish Seed Infrastructure in the country.
• Fingerling rearing ponds and hatcheries would be developed and the programme will converge in the production of 20 lakh tonnes fish annually, which will benefit approx. 4 million families.
• Blue Revolution aims to boost the fisheries sector in the country.

A group of players is called a team.

Similarly,

A group of ministers represent a Council.

“Council” relates to the third term in the same way that the second term relates to the first term.

Hence, “council” is the correct answer.

According to the given information,

Argument 1: This is strong, since alcohol is bad for health, government should not promote it.

Argument 2: This is not strong, because there are other forms also for revenue generation.

Hence, “only argument 1” is strong.

The correct answer is option 3, i.e., Chief Justice Indira Banerjee.

• Chief Justice Indira Banerjee became the Chief Justice of the Madras High court in March 2017.
• She assumed the office as the Chief Justice of the Madras High court on 5th April 2017 and remained at the post till 6th Aug 2018.
• Presently she is serving as a Judge of Supreme Court.
• She is the 8th female judge and the 3rd female judge of the Supreme Court in the Indian history.
• Justice Ashok Kumar Ganguly is a former Indian jurist. He retired as a Supreme court judge in 2012. He held the positions of Chief Justice of Madras High Court and Orissa High Court.
• Justice Sanjay Kaul is a Supreme Court judge and has earlier served as Chief Justice of Madras High Court and Punjab and Haryana High Court.
• Justice Rajesh Kumar Agrawal is currently serving as the President of the National Consumer Disputes Redressal Commission (NCDRC) and has earlier served as judge of the Supreme Court.

The correct answer is option 3, i.e., Gauri Lankesh.

• Gauri Lankesh was awarded the prestigious Reach All Women in WAR (RAW in WAR) Anna Politkovskaya Award on 7th October 2017.
• Anna Politkovskaya Award is given to honour women who are human rights defender from a conflict zone, who stand up for the victims of conflict.
• Anna Politkovskaya, a Russian journalist, lived her life bravely and stood for truth in the face of grave danger. She was murdered on 7th October 2006.
• To mark her death anniversary this award is presented annually.
• The RAW in WAR was founded by Mariana Katzarova, a friend and a human rights colleague of Politkovskaya, in the year 2006.
• Natalia Estemirova was the first recipient of the award.
• Gauri Lankesh was an Indian journalist-turned-activist from Bangalore who was murdered on 5 September 2017. She was given the Anna Politkovskaya Award for campaigning for women's rights and opposing caste-based discrimination.
• Kusum Nair was also a journalist who used to give her views on the agricultural policies.
• Sucheta Dalal is a business journalist who was awarded the Padma Shri in the year 2006.
• Malini Parthasarathy is the co-chairperson of The Hindu Group's Publishing Company, THG Publishing Private Limited.

The correct answer is option 2, i.e., the United States.

• The Yellowstone National Park is situated in the United States.
• The National Park is situated in the western part of the US and was established on March 1, 1872.
• It is the first National Park of the US and is known for its rich flora and fauna.
• The Yellowstone National Park is a UNESCO World Heritage Site.

The correct answer is option 4, i.e., 22000 Hz.

• A frequency of 22000n Hz is not audible to human beings.
• The frequency range of sound that a normal human adult can detect is from 20 Hz to 20000 Hz.
• The human infants can hear frequencies slightly higher than 20 kHz.
• Most small mammals have the capability of hearing higher frequencies but are however insensitive to lower frequencies.
• For eg. : In some species of bats, the frequency range of sound is 20 kHz to 200kHz.
• The frequencies above the audible range for humans, i.e., above 20 kHz, are termed as ultrasonic.
• The frequencies below the audible range for humans, i.e., below 20 Hz, are termed as infrasonic.
• Ultrasonic and infrasonic frequencies of sound are inaudible to humans.
• 22000 Hz comes under ultrasonic range, hence it is inaudible to human beings.

The correct answer is option 4, i.e., Mass of the falling object 'm'.

• The value of acceleration due to gravity does not depend upon: Mass of the falling object 'm'.
• The acceleration that is gained by an object due to the force of gravitation, is known as acceleration due to gravity (g).
• The formula of calculating acceleration due to gravity is: g = GM / r²  [where 'G' is gravitational constant, 'M' is the mass of the earth, and 'r' is the radius of the earth.
• The above formula suggests that acceleration due to gravity depends on Mass of the earth 'M', Constant of gravitation 'G', and Radius of the earth 'R'. Since all these are constant, therefore the value of 'g' is on the surface of the earth at the sea level is constant, i.e., 9.8 m/s².
• The formula does not contain the mass of the object, it means that acceleration due to gravity works equally on every object irrespective of its mass.

Given:

21 + [5 of {15 + (18 – 17)}]

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

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now

21 + [5 of {15 + (18 – 17)}]

⇒ 21 + [5 of {15 + 1}]

⇒ 21 + [5 of 16]

⇒ 21 + 80

⇒ 101

The number of triangles in the given figure are,

Hence, “40“ is the correct answer.

Given:

Earning of 2012 = 2,50,000

Earning of 2013 = 3,00,000

Earning of 2014 = 3,00,000

Earning of 2015 = 2,50,000

Earning of 2016 = 4,00,000

Calculation:

Varied cost of 2012 = 10% of 2,50,000 = 25000

Varied cost of 2013 = 10% of 3,00,000 = 30000

Varied cost of 2014 = 10% of 3,00,000 = 30000

Varied cost of 2015 = 10% of 2,50,000 = 25000

Varied cost of 2016 = 10% of 4,00,000 = 40000

 Total varied cost of all five years = (25000 + 30000 + 30000 + 25000 + 40000) = 1,50,000

∴ Average varied cost of five years = 150000/5 = 30000

The correct answer is option 2, i.e., Chennai.

• Chennai was recently included in the United Nations Educational, Scientific, and Cultural Organization's (UNESCO's) Creative Cities Network for contribution to Music.
• Chennai is the capital city of the Indian state of Tamil Nadu.
• Chennai is one amongst the 64 cities chosen from the 44 nations of the world.
• The number tally has now gone up to 180 cities of the 72 nations.
• Chennai is the third Indian city to get the designation of UNESCO's Creative Cities. The other cities are:
• Varanasi (City of Music)
• Jaipur (City of Crafts and Folk Arts)
• Mumbai has been designated a Creative city of film.
• Hyderabad a Creative city of gastronomy
• UNESCO's Creative Cities Network launched in the year 2004 includes cities in the below mentioned seven creative fields:
• Crafts and Folk Art
• Design
• Film
• Gastronomy
• Literature
• Media Arts
• Music

Given

31 × 23 = 713

Calculation

3100 × 0.00023

= 3100 × 23/100000

= (31 × 23)/1000

= 713/1000

= 0.713.

The pattern followed is,

In all the given figures, except in figure D the bigger and smaller version of same figure is shown.

Whereas,

In figure D, both figures are different.

Hence, option 4 is the odd one.

The correct answer is Vishnu Sharma.

Key Points

• Vishnu Sharma is the author of 'Panchatantra'.
• Panchatantra refers to the ancient Indian collection of interrelated animal fables and was originally written in the Sanskrit language.
• It was written around 200 BCE and is one of the oldest surviving texts.
• Panchatantra was translated into other languages like Persian, Syrian, and Arabic languages.
• Vishnu Sharma was an Indian scholar.

Additional Information

• Kalidas was a Sanskrit writer whose famous works include Abhijnanasakuntalam, Meghaduta, Raghuvamsa, etc.
• Valmiki was one of the most celebrated writers and his most famous works include Ramayana.
• Sri Harsha was a Sanskrit poet and philosopher of the 12th century and his famous works include Naishadha Charita, etc.

The correct answer is four, eight.

Important Points

• The foundation of Buddhism is the four noble truths and the eight-fold path.
• The four Noble Truths are:
• The Truth of Suffering (Dukkha)
• The Truth of the Cause of Suffering (Samudhya)
• The Truth of the Cessation of Suffering (Nirodha)
• The Truth of the Path Cessation of Suffering (Magga)
• The eight-fold path is Ashtangika Marga - 
• Right View or Right Understanding
• Right Thoughts
• Right Speech
• Right Conduct
• Right Livelihood
• Right Effort
• Right Mindfulness
• Right Meditation or Right Contemplation​

Additional Information

• Mahayana Buddhism:
• After the death of Buddha, a group evolved who believed that compassion for all humanity was an important part of the path, and that teaching is fully available to all.
• Those who followed the newly expanded ideals called themselves Mahayana meaning the big raft.
• In Mahayana Buddhism, all practicing Buddhists are apprentice Bodhisattvas.
• In Mahayana countries, images of the Buddha are set up in the temples and homes as an object of worship.
• Hinayana Buddhism:
• From about 100 years after the death of the Buddha, there had been a movement towards embracing the style of Buddhism.
• The early monks concentrated on personal enlightenment, seeking spiritual answers for themselves, and teaching others the way of enlightenment.
• But the information was severely limited to the lay community as it was assumed only monks could achieve Buddhahood.
• This section came to be known as Hinayana or also known as Theravada.
• Theravada means the way of elders.
• Milindapanha:
• The Milindapanha, or "Milinda's Questions," is an important early Buddhist text that usually is not included in the Pali Canon.
• Even so, the Milindapanha is cherished because it addresses many of Buddhism's most difficult doctrines with wit and clarity.
• The Milindapanha presents a dialogue between King Menander I (Milinda in Pali) and an enlightened Buddhist monk named Nagasena.
• Menander- I was an Indo-Greek king thought to have ruled from about 160 to 130 BCE.
• He was a king of Bactria, an ancient kingdom that took in what is now Turkmenistan, Afghanistan, Uzbekistan, and Tajikistan, plus a small part of Pakistan.

Shortcut TrickLet Total Capacity be the LCM of 2, 8, and 4 = 8 units.Efficiency of Tap A = 8 ÷ 2 = +4 units/hrEfficiency of Tap B = 8 ÷ 8 = +1 units/hrEfficiency of Tap C (Emptying) = 8 ÷ 4 = −2 units/hrCombined Efficiency = 4 + 1 − 2 = 3 units/hrTime taken = Total Capacity ÷ Combined Efficiency = 8 ÷ 3 hours.∴ The correct answer is 8/3 hr.Alternate MethodGiven: Filling time for Tap A = 2 hours, Tap B = 8 hours. Emptying time for Tap C = 4 hours.Formula Used: Net Work Done per hour = (1/A + 1/B − 1/C)PersonDaysTotal Work(LCM of 2, 8, 4)EfficiencyTap A (Fill)2 hr8 ÷ 2 = 4Tap B (Fill)8 hr88 ÷ 8 = 1Tap C (Empty)4 hr8 ÷ 4 = −2⇒ Total Efficiency of (A + B + C) = 4 + 1 − 2⇒ Total Efficiency = 3 units/hr⇒ Time required to fill the tank = Total Work ÷ Total Efficiency⇒ Time = 8/3 hours∴ The correct answer is 8/3 hr.Additional InformationPipes and Cisterns LogicAn inlet pipe is considered positive work (+), while an outlet pipe (leak) is considered negative work (−).Net Efficiency RuleIf a tank is filled in 'x' hours and emptied in 'y' hours, the net part filled in 1 hour is (1/x − 1/y) if x < y.

Drawing the diagram according to the given information,

When playing carrom, one faces opposite the other.

If Prakash is facing South – east, then Sunder will face North – west.

Hence, “north – west” is the correct answer.

The correct answer is option 3, i.e., A raised hammer.

• A raised hammer does NOT possess kinetic energy.
• The word "kinesis" means "motion", hence the kinetic energy is possessed by an object in motion.
• A rolling stone, a falling coconut, and a speeding car all are in some kind of motion and hence all these possess Kinetic energy.
• Kinetic energy is calculated using the formula: K.E. = ½ mv² [where 'm' is the mass of the object and 'v' is the velocity of the object]
• A raised hammer is in the stationary position and hence possess the Potential Energy.
• A raised hammer possesses Gravitational Potential Energy by virtue of its height.
• The formula of Gravitational Potential Energy is: U_g = mgh [where 'm' is the mass of the object, 'g' is the acceleration due to gravity and 'h' is the height above the ground]

The pattern followed here is,

Hence, “H - 225” is the correct answer.

The correct answer is option 3, i.e., 89-103.

• Atomic numbers of Actinoides are from 89-103.
• Actinides start from Actinium and go till the Lawrencium, i.e., there are 15 elements.
• Actinium (atomic no. 89) is often included in group 3, and the f-block actinides start from Thorium (atomic no. 90) thus reducing the elements to 14.
• The term Actinide means "actinium-like" and the elements included are: Ac, Th, Pa, U, Np, Pu, Am, Cm, Bk, Cf, Es, Fm, Md, No, and Lr.
• Actinides have variable valency, very large atomic and ionic radii, and exhibit an unusually large range of physical properties.
• All actinides are radioactive in nature, Uranium, and Thorium being the naturally occurring radioactive elements.
• 58-71 atomic numbers belong to the first series of the f-block i.e., the lanthanides.
• Lanthanides start from Lanthanum and the last lanthanide is Lutetium.
• But, similar to Actinium, Lanthanum (atomic no. 57) is not included in the f-block and belongs to the group 3.
• Hence, the f-block lanthanides are from atomic number 58-71.
• The Lanthanide series include:  Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu.

Shortcut Trick Total bulbs needed = 300 for 4 colors ⇒ 75 bulbs per color. Bulbs to buy: Red = 43, Green = 49, Yellow = 66, Blue = 75. Discounts: Red/Green (0%), Yellow (20% as 50 ≤ 66 < 70), Blue (30% as 75 ≥ 70). Total Cost = (43 + 49) × 15 + 66 × 15 × 0.80 + 75 × 15 × 0.70. Total Cost = 1380 + 792 + 787.50 = Rs. 2959.50. ∴ The correct answer is Rs. 2959.50.

Alternate Method Given: Total bulbs = 300, Colors = 4, Price/bulb = Rs. 15. Formulas: Required Bulbs = (Total ÷ 4) − Existing | Discounted SP = Price × (100 − D)% ÷ 100

⇒ Required per color = 300 ÷ 4 = 75 bulbs. ⇒ Red bulbs to buy = 75 − 32 = 43 (Cost = 43 × 15 = 645). ⇒ Green bulbs to buy = 75 − 26 = 49 (Cost = 49 × 15 = 735). ⇒ Yellow bulbs to buy = 75 − 9 = 66. Since 66 ≥ 50, Price = 15 × 0.80 = 12 (Cost = 66 × 12 = 792). ⇒ Blue bulbs to buy = 75 − 0 = 75. Since 75 ≥ 70, Price = 15 × 0.70 = 10.5 (Cost = 75 × 10.5 = 787.5). ⇒ Total Spend = 645 + 735 + 792 + 787.50 = 2959.50. ∴ The correct answer is Rs. 2959.50.

Additional Information Quantity-Based Discounting Discounts are often applied based on slabs. In this problem, purchasing 50-69 bulbs yields one rate, while 70+ bulbs yields a higher discount rate. Fixed vs Variable Costing Calculating requirements first (Target − Inventory) is essential before applying the pricing logic based on the purchase volume per item.

Given:

Satin% = 5%

Total production of fabric (of all type) = 1,50,000

Calculation:

⇒ 5% of 1,50,000

⇒ (5/100) × 150000

⇒ 5 × 1500

⇒ 7500

∴ Fabric produced in the year 2015 = 7500 tons

Embroidery is the activity of beautifully decorating a piece of cloth with stitches sewn into it.

Similarly,

Moonlight is the pale, cool light of the moon at night.

Beautiful is the word used for Embroidery and Cool is the word used for Moonlight.

‘Cool’ is related to the third word on the same basis as the second word is related to the first word.

Hence, “cool” is the correct answer.

The correct answer is option 3, i.e., Pune.

• Pune was ranked first in the 2018 Ease of Living Index prepared by the Ministry of Housing and Urban Affairs.
• The 2018 Ease of Living Index was released by the then Minister for Housing and Urban Affairs, Hardeep Singh Puri.
• Pune got the top spot out of the total 111 cities taken into consideration for the index.
• Navi Mumbai was successful in achieving the second spot.
• The national capital Delhi got the 65th position.
• Chennai was ranked 14th in the index.
• The last position was given to Rampur, a city in Uttar Pradesh.
• The Ease of Living Index aims to capture the state of the livability of the cities against the national and international benchmarks and it also encourages cities to move towards an 'outcome-based' approach to urban planning and management.
• The four parameters taken into consideration are:
• institutional factors (governance)
• social factors (education, health, etc.)
• economic factors (economy, employment)
• physical factors (pollution, water supply, etc.)

The pattern followed here is,

The circles in the figure inside keeps on increasing by one.

And,

The circles outside the figure keeps on decreasing by one.

The first figure should have one circle inside it.

The complete pattern is,

Hence, option 1 is the correct answer.

The correct answer is option 4, i.e., Rs. 50,000 crore.

• The Government of India has launched the Pradhan Mantri Krishi Sinchai Yojana (PMKSY) with an investment of Rs. 50,000 crore aiming at the development of irrigation sources for providing a permanent solution form drought.
• The scheme has been formulated keeping in view the visions "Har Khet Ko Pani" and "More Crop Per Drop".
• The scheme was launched on 1 July 2015, and it is an amalgamation of schemes like Accelerated Irrigation Benefit Irrigation (AIBP), Integrated Watershed Management Programme (IWMP), and On-Farm Water Management (OFWM).
• Rs 50,000 crores have been approved for the Pradhan Mantri Krishi Sinchai Yojana for a duration of 5 years.
• The major objectives of the scheme include:
• Confluence of investment in irrigation at the field level.
• Improvement in the efficiency of water usage so as to reduce the wastage of water
• Expansion in the cultivable land under irrigation (Har Khet Ko Pani)
• Intensifying the initiatives of being precise in irrigation and other water-saving technologies (more crop per drop)

The pattern followed here is,

The figure is rotated anti clock – wise direction by one place.

The figure which will come next in the pattern is,

Hence, option 2 is the correct answer.

The correct answer is option 1, i.e., Good Governance Day.

• The Union Ministry of Personnel, Public Grievances and Pensions launched the electronic - Human Resource Management System (e - HRMS) on the occasion of Good Governance Day on 25th December.
• The e-HRMS is an online platform and has been launched to take forward the goal of 'minimum government, maximum governance'.
• 25 applications of the 5 modules of the system were simultaneously launched.
• The e-HRMS will help central government employees in applying for leaves and in accessing their service-related information.
• The system will enable people to obtain all management-related inputs and reports through its dashboard.
• The launch of e-HRMS is in the line of fully automating the human resource management system with the target to bring all government employees on the employee portal.
• The Good Governance Day in India was established in the year 2014 on the birth anniversary of former PM Late Atal Bihari Vajpayee to honour him for his contributions.
• As per the government orders, the Good Governance day observed annually on 25th December will be a working day for the employees.

The pattern followed is,

All the figures except, figure D are formed with the help of lines.

Whereas,

Figure D is a circle.

Hence, option 2 is the odd one.

The pattern followed here is,

All the figures, except figure A are joined with the other figure.

Whereas,

In figure D, the figures given are represented separately, and are not joined.

Hence, option 2 is the odd one.

The correct answer is Option 3, i.e Thallophyta.

• Plants are divided into five groups: Thallophytes, Bryophytes, Pteridophytes, Gymnosperms and Angiosperms.
• Thallophyta do not have a well-differentiated body design and are the simplest of plants.
• Bryophyta are often called amphibians of the plant kingdom.
• Gymnosperms are flowerless plants that produce cones and seeds. The term gymnosperm literally means "naked seed," as gymnosperm seeds are not encased within an ovary.
• Pteridophytes include horsetails and ferns. Pteridophytes are used for medicinal purposes and as soil-binders
• Plantae and Animalia are further divided into subdivisions on the basis of increasing complexity of body organisation.

From statement 1:

From statement 2:

Combining both the statements,

We get the relationship by combining both statements.

Hence, “both 1 and 2 together” are sufficient.

The least possible Venn diagram is as follows,

Conclusion 1: Some brown are tables → False (This is definitely false)

Conclusion 2: Some woods are tables → True (This is definitely true)

Hence, “conclusion 2 alone” follow.

Shortcut Trick

Profit difference in percentage = 14% − 10% = 4%.

The value of this 4% difference is given as Rs. 27.

Ratio-unitary method: 4% ⇒ 27.

Therefore, 100% (Cost Price) = (27 ÷ 4) × 100.

CP = 27 × 25 = 675.

∴ The correct answer is Rs. 675.

Alternate Method

Given: Profit₁ = 10%, Profit₂ = 14%, Difference in Selling Price = Rs. 27. Formulas: SP = CP × (100 + Profit%) ÷ 100 | Difference in SP = SP₂ − SP₁.

⇒ Let the Cost Price (CP) be x.

⇒ SP₁ = x × (110 ÷ 100) = 1.10x.

⇒ SP₂ = x × (114 ÷ 100) = 1.14x.

⇒ Difference = 1.14x − 1.10x = 0.04x.

⇒ 0.04x = 27.

⇒ x = 27 ÷ 0.04 = 675.

∴ The correct answer is Rs. 675.

Additional Information

Cost Price & Selling Price Relationship

When an article is sold at a profit, SP = CP + Profit. If two different profit percentages are given for the same CP, the difference in SP is directly proportional to the difference in profit percentages.

Profit and Loss Basics

Profit % is always calculated on the Cost Price unless stated otherwise. Formula: Profit% = (Profit ÷ CP) × 100.

Shortcut Trick

Make the quantity of pencils equal for both buying and selling.

L.C.M. of 12 and 5 is 60.

CP of 60 pencils = (25 ÷ 12) × 60 = 125.

SP of 60 pencils = (12 ÷ 5) × 60 = 144.

Profit% = (SP − CP) ÷ CP × 100 = (144 − 125) ÷ 125 × 100 = 19 ÷ 125 × 100 = 15.2%.

∴ The correct answer is 15.2% gain.

Alternate Method

Given: CP = 25 per dozen (12 pencils); SP = 12 for 5 pencils. Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100.

⇒ Cost Price (CP) of 1 pencil = 25 ÷ 12 = Rs. 2.0833 ⇒ Selling Price (SP) of 1 pencil = 12 ÷ 5 = Rs. 2.4 ⇒ Profit = SP − CP = 2.4 − 2.0833 = 0.3167 ⇒ Profit% = (0.3167 ÷ 2.0833) × 100 ⇒ Profit% = 15.2%

∴ The correct answer is 15.2% gain.

Additional Information

Profit and Loss Calculation

To calculate Gain% or Loss%, always compare the CP and SP of the same number of items.

Unitary Method

Find the price of a single unit by dividing the total price by the total quantity before comparing.

Shortcut Trick

Prime numbers have only two factors: 1 and the number itself.

By definition, any two distinct prime numbers are co-prime.

The Highest Common Factor (HCF) of any set of co-prime numbers is always 1.

∴ The correct answer is 1.

Alternate Method

Given: x and y are two prime numbers.

⇒ Factors of x = 1 × x

⇒ Factors of y = 1 × y

⇒ Common Factor between x and y is only 1.

⇒ HCF (Highest Common Factor) = 1