RRC Group D Previous Year Paper 58 (Held On: 30 Oct 2018 Shift 2)

The logic followed here is:-

Words are formed with letters.

Similarly,

The necklace is formed with beads.

Hence, "option 3" is the correct answer.

Shortcut Trick

Net percentage change formula = x + y + (x × y)/100

Here, x = 30 and y = 30 (since all sides of a square are equal).

Percentage increase = 30 + 30 + (30 × 30)/100

Percentage increase = 60 + 9 = 69%

∴ The correct answer is 69%.

Alternate Method

Given: Increase in side = 30%

Formula Used: Area of square = side²

⇒ Let the initial side of the square be 10 units.

⇒ Initial Area = 10 × 10 = 100 sq. units.

⇒ New side after 30% increase = 10 + 30% of 10 = 13 units.

⇒ New Area = 13 × 13 = 169 sq. units.

⇒ Increase in area = 169 − 100 = 69 sq. units.

⇒ Percentage increase = (69/100) × 100 = 69%.

∴ The correct answer is 69%.

Additional Information

Successive Percentage Change

When a quantity is changed by x% and then by y%, the net change is given by [x + y + (xy/100)]%.

Area and Side Relation

If the side of a square is multiplied by a factor 'k', then the area is multiplied by k².

Percentage to Fraction

A 30% increase can be viewed as a multiplier of 1.3. New Area = (1.3 × old side)² = 1.69 × Old Area, which is a 69% increase.

The correct answer is Paphiopedilum.

Key Points

• Paphiopedilum is a monocot.
• Paphiopedilum is often called the venus slipper.
• It is a genus of the Lady slipper orchid subfamily Cypripedioideae of the flowering plant family Orchidaceae.
• The genus comprises some 80 accepted taxa including several natural hybrids.
• It is a monocot plant.
• It is an Angiosperm.

Additional Information

• Angiosperms, are also known as flowering plants and have seeds enclosed within their fruit.
• Gymnosperms have no flowers or fruits and have naked seeds on the surface of their leaves.
• Gymnosperm seeds are configured as cones.
• The leaves of angiosperm plants have two types of venation.
• The arrangement of veins and veinlets on the lamina of a leaf is called venation.
• There are two types of venation, reticulate and parallel venation.
• Reticulate venation: In some leaves, the veins and veinlets are irregularly distributed over the entire lamina, forming a network. Such leaves are said to have reticulated venation.
• Parallel venation: In some leaves, the veins and veinlets run parallel to each other. Such leaves are said to have parallel venation.

The correct answer is Assam.

Key Points

• N.C. Bordoloi Indoor Stadium is located in the state of Assam.
• Location : Guwahati, Assam
• Venue for Basketball and Handball

Additional Information

Important Points

• Assam is a state in northeastern India known for its wildlife, archeological sites, and tea plantations.
• In the west, Guwahati, Assam’s largest city, features silk bazaars and the hilltop Kamakhya Temple.
• Umananda Temple sits on Peacock Island in the Brahmaputra river.
• The state capital, Dispur, is a suburb of Guwahati.

Shortcut Trick Find the roots of the quadratic expression −5x2 + 2x + 7 by setting it to zero. The roots are x = −1 and x = 1.4. Since the coefficient of x2 is negative, the parabola opens downwards. The sign is positive between the roots (−1 < x < 1.4) and negative outside the roots (x < −1 or x > 1.4). The given condition x < 5 includes both regions where the expression is positive, negative, and even zero. ∴ The correct answer is Can't be said.

Alternate Method Given: Expression f(x) = −5x2 + 2x + 7 and condition x < 5. Factorizing the expression: ⇒ −5x2 + 7x − 5x + 7 = 0 ⇒ −5x(x − 1.4) − 5(x + 1) ... let's use splitting the middle term correctly: ⇒ −5x2 + 7x − 5x + 7 = 0 ⇒ −x(5x − 7) + 1(5x − 7) = 0 is wrong, let's re-split: ⇒ −5x2 − 5x + 7x + 7 = 0 ⇒ −5x(x + 1) + 7(x + 1) = 0 ⇒ (7 − 5x)(x + 1) = 0 ⇒ Roots are x = −1 and x = 7/5 = 1.4. Testing values for x < 5: ⇒ Case 1: x = 0 (which is < 5), f(0) = −5(0)2 + 2(0) + 7 = 7 (Positive). ⇒ Case 2: x = −2 (which is < 5), f(−2) = −5(−2)2 + 2(−2) + 7 = −20 − 4 + 7 = −17 (Negative). ⇒ Case 3: x = −1 (which is < 5), f(−1) = 0 (Neutral/Zero). ⇒ Since f(x) can be positive, negative, or zero within the domain x < 5, the sign is not constant. ∴ The correct answer is Can't be said.

Additional Information Sign of Quadratic Expression For ax2 + bx + c, if a < 0 and the roots are real (α, β), the expression is positive for α < x < β and negative for x < α or x > β. Parabola Direction If the leading coefficient 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards, indicating a maximum value at the vertex. Discriminant (D) The nature of roots is determined by D = b2 − 4ac. If D > 0, the quadratic will change signs at its two distinct real roots.

Medulla Oblongata is not correct.

Key Points

• Medulla Oblongata is not a part of the respiratory system.
• The medulla oblongata may be regarded as the “spinal cord of the head” when viewed from the perspective of its importance in the control of the head and facial musculature.
• The medulla oblongata is not an independent entity in the central nervous system.
• The medulla oblongata acts as a pipeline for ascending and descending pathways involved in a wide variety of nervous system functions and also as a processor of input from a diverse array of sources located within the periphery as well as from all levels of the nervous system.

Additional Information

• Parts of Respiratory system:
• Nose.
• Mouth.
• Throat (pharynx)
• Voicebox (larynx)
• Windpipe (trachea)
• Large airways (bronchi)
• Small airways (bronchioles)
• Lungs.
• Anaerobic respiration does not need oxygen.
• It is the release of a relatively small amount of energy in cells by the breakdown of food substances in the absence of oxygen.
• Anaerobic respiration happens in muscles during hard exercise.

The correct image for the blank space is given below:-

Hence, "option 4" is the correct answer.

The correct answer is Hydrogen.

• ​Hydrogen bonding is the third type of van der Waals' force.
• It is exactly the same as dipole-dipole interaction, it just gets a special name.
• A hydrogen bond is a dipole-dipole interaction that occurs between any molecule with a bond between a hydrogen atom and any of oxygen/fluorine/nitrogen.

Additional Information

• Van der Waals force is a general term used to define the attraction of intermolecular forces between molecules.
• There are two kinds of Van der Waals forces:
• Weak London Dispersion Forces and stronger dipole-dipole forces.
• Examples of van der Waals forces include hydrogen bonding, dispersion forces, and dipole-dipole interactions.

The statement highlights a problem that the top universities have been ruined because the government has appointed bureaucrats as vice-chancellors.

• Conclusion 1 clearly identifies the major reason behind the problem from the statement and suggests a solution by saying that the vice-chancellor should be appointed after checking his expertise. Thus, conclusion 1 logically follows the statement.
• On similar lines, conclusion 2 also suggests the qualities a vice-chancellor should have in order to resolve the problem given in the statement. Thus, it logically follows.

Hence the correct answer is option 2.

The transparent sheet resembles when folded along the dotted line then the pattern will be:-

• Inner all line right rotate 180⁰.

 

Hence, "option 4" is the correct answer.

The correct answer is Virtual, erect, small image between pole and focus.

• An object is placed in front of a convex mirror the virtual, erect, small image between pole and focus will be formed.

Key Points

• The convex mirror always forms an image that is smaller than the size of the object.
• When an object is placed in front of a convex mirror at a point between infinity and the pole of the mirror.
• The image formed is virtual and diminished.
• A convex mirror always produces a virtual image of the object, regardless of the distance between the object and the mirror.
• The size of the image is smaller than the object.
• The image formed is upright (erect) and horizontally flipped.

Additional Information

• Characteristics of Concave Mirrors
• Light converges at a point when it strikes and reflects back from the reflecting surface of the concave mirror.
• Hence, it is also known as a converging mirror.
• When the concave mirror is placed very close to the object, a magnified and virtual image is obtained.
• However, if we increase the distance between the object and the mirror then the size of the image reduces and a real image is formed.
• The image formed by the concave mirror can be small or large or can be real or virtual.​

The statement talks about an advertisement on a billboard that implies 'multiply your money'.

• From the given statement, nothing can be determined about the assurance of the tagline. So, assumption I is not implicit.
• Since the tagline is on a billboard, it is safe to assume that the readers are interested in multiplying their money, i.e. earn money fast. Thus, assumption II is implicit.

Hence the correct answer is option 4.

The pattern followed here is:

• From statement 3, it is clear that there are no intelligent men that are prosperous. So, the men that are not intelligent may be prosperous.
• Statement 2 says some layers are intelligent, which means some lawyers are not intelligent. From both these statements, it is evident that some lawyers are prosperous and some are not. Thus, conclusion 1 is a correct possibility, so it follows.
• Since it is clearly given that no intelligent man is prosperous, irrespective of being a lawyer or not, therefore conclusion II cannot follow.

Hence the correct answer is option 4.

The correct answer is Catenation.

• Carbon has the unique ability to form bonds with other atoms of carbon, giving rise to large molecules.
• This property is called catenation.
• Catenation is the binding of an element to itself through covalent bonds to form chain or ring molecules.
• Carbon is the most common element that exhibits catenation.

Important Points

• Catenation occurs most readily with carbon, which forms covalent bonds with other carbon atoms to form longer chains and structures.
• This is the reason for the presence of a vast number of organic compounds in nature. Carbon is best known for its catenation properties, with organic chemistry (essentially the study of catenation carbon structures (and known as catenations)).
• In biochemistry, the carbon chain links hydrogen, oxygen, and various other elements such as biometals on the carbon backbone.
• However, carbon is by no means the only element capable of forming such a catenation, and many other main-group elements are capable of forming a wide range of catenation, including hydrogen, boron, silicon, phosphorus, and sulfur.

The correct answer is 18th or zero group.

Key Points

• The noble gases (Group 18) are located in the far right of the periodic table and were previously referred to as the "inert gases" due to the fact that their filled valence shells (octets) make them extremely non-reactive.
• Noble gases are said to be zero group elements because they have zero valencies and they cannot combine with other elements to form compounds.
• The zero group elements are Helium, Neon, Argon, Krypton, Xenon, and Radon.

Additional Information

• The discoverers of noble gases are :

The correct answer is Railways.

Key Points

• Piyush Goyal is the Union Minister of railways as of August 2018.
• Piyush Goyal, who had been the Union minister for railways and coal in the first term of the Narendra Modi-led Bharatiya Janata Party (BJP) government at the Centre, has been given charge of the railways and commerce & industry ministries in the second term.
• ​He was the finance minister and corporate affairs minister from January 23 to February 15, 2019).
• He presented the Interim Budget for 2019-20.

Additional Information

• SEVA app was launched by Union Minister Piyush Goyal to monitor the coal-dispatch process.
• Union Minister of State for Power, Coal, New and Renewable Energy and Mines Piyush Goyal recently launched the Saral Eindhan Vitaran Application (SEVA) aiming to facilitate the industry's connection with the coal companies by proving information on coal dispatch.
• The application helps track coal dispatch to 118 power plants through Fuel Supply Agreement (FSA), dispatch through special forward E-Auction and Bridge Linkage from over 200 dispatch points.

1. B1 contains packaged food.

B₁ = food.

• Here, there is no information given about the weight of B₁, B₂, and B₃. Therefore, statement 1 alone is not sufficient.

2. The weight of B3 is one-fourth of the weight of all the other boxes added together.

B₃ = 1/4(B₁ + B₂)

• No information is given about the weight of B₁, B₂, and B₃. Therefore, statement 2 alone is not sufficient.
• Here, statements 1 and 2 both are not sufficient.

Hence, "option 4" is the correct answer.

The correct answer is Odisha.

 Key Points

• Bhushan Power & Steel Limited (BPSL) is a steel company that is engaged in the manufacturing and marketing of steel products.
• Bhushan Power & Steel Limited, Jharsuguda is in Odisha.
• It was established in 1970.
• In July 2019, BPSL was allegedly involved in fraud worth ₹3805.15 crore rupees (US$535.23 million), as detected by Punjab National Bank.
• It is one of India's most indebted companies and appears among the 12 companies referred by the Reserve Bank of India (RBI) to a bankruptcy court for the purpose of debt resolution.

Additional Information​

• Koyna Hydroelectric Power Project
• The Koyna Hydroelectric Project is one of the largest hydroelectric power plants in India.
• It is a complex project with four dams including the largest dam on the Koyna River, Maharashtra.
• The project site is in the Satara district near Patan.
• India’s first Geothermal Power Project will be established in Ladakh.
• Ladakh will get India’s first geothermal power project to tap the potential of natural geysers dotting the Puga area, 170 km east of Leh and not far from the China border, in Changthang plains.

The correct answer is 400 J.

Key Points

• Given,
• Mass, m=20 kg
• height, h= 2 m
• Acceleration due to gravity, g = 10 ms^-2
• The work done by the porter will be equal to the potential energy.
• Potential energy = mgh

                                                = 20 x 2 x 10

                                                = 400 J

Additional Information

• Potential Energy
• It is the energy possessed by a body by virtue of its position.
• PE of a body in the gravitational field of the earth is mgh.
• where m = mass, g = acceleration due to gravity, h = height of the body from the surface of the earth.
• When a body is falling downwards, then its potential energy goes on changing to kinetic energy.

The correct answer is Butane.

Key Points 

• Liquefied Petroleum Gas (LPG) is a blend of light hydrocarbon compounds.
• It mainly consists of butane or propane or a mixture of both.
• At room temperature, both gases are colourless and odourless.
• It is a mixture of 48% propane, 50% butane, and 2% pentane.

Additional Information

• Water Gas:
• Water-gas is a mixture of CO and H₂.
• However, by-products such as char, tar, soot, ash, and condensates are also produced.
• Natural gas is a naturally occurring hydrocarbon gas mixture consisting primarily of methane, but commonly including varying amounts of other higher alkanes, and sometimes a small percentage of carbon dioxide, nitrogen, hydrogen sulfide, or helium.
• Compressed natural gas is a fuel that can be used in place of petrol (gasoline), diesel fuel, and liquefied petroleum gas (LPG).
• CNG combustion produces fewer undesirable gases than the aforementioned fuels.
• In comparison to other fuels, natural gas poses less of a threat in the event of a spill, because it is lighter than air and disperses quickly when released.

The correct answer is Raja Raj Chola I.

Key Points

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

Additional Information 

• Rajaraja I often described as Rajaraja the Great, was a Chola emperor and in his time the most powerful king in the south who was primarily responsible for restoring Chola's power and establishing his control over South India and the Indian Ocean.
• Brihadishvara Temple locally known as Thanjai Periya Kovil, and also called Rajarajeswaram, is a Hindu temple dedicated to Shiva located on the South Bank of the Cauvery river in Thanjavur, Tamil Nadu.

Calculation:

The reciprocal of $1{\frac{2}{3}}$ = 5/3

∴ The reciprocal is 3/5

The correct answer is India.

Key Points

• In a historic first for Indian boxing, India will host the men's World Championship for the first time in 2021 besides next year's women's World Championship.
• AIBA made the announcement at the end of its two-day executive committee meeting in Moscow.
• The major men's boxing events hosted by India have been the 1990 World Cup in Mumbai and the 2010 Commonwealth Championships in New Delhi.
• "It is the first time ever that a country has been awarded two major Championships, that too back to back.

Additional Information

• The AIBA World Boxing Championships, and the AIBA Women's World Boxing Championships, are biennial amateur boxing competitions organized by the International Boxing Association (AIBA), which is the sport governing body.
• Alongside the Olympic boxing program, they are the highest level of competition for the sport.
• The championships were first held for men in 1974 and the first women's championships were held over 25 years later in 2001.

Shortcut Trick

In a right-angled triangle, the two acute angles are always complementary.

Sum of acute angles = 90°

Second acute angle = 90° − 58° = 32°

∴ The correct answer is 32°.

Alternate Method

Given:

One acute angle = 58°

One angle of a right-angled triangle = 90°

Formula Used:

Angle Sum Property of a triangle: Sum of all internal angles = 180°

Calculations:

⇒ Let the three angles be ∠A, ∠B, and ∠C.

⇒ ∠A + ∠B + ∠C = 180°

⇒ 90° + 58° + ∠C = 180°

⇒ 148° + ∠C = 180°

⇒ ∠C = 180° − 148°

⇒ ∠C = 32°

∴ The correct answer is 32°.

Additional Information

Complementary Angles

Two angles are complementary if their sum is exactly 90°.

Supplementary Angles

Two angles are supplementary if their sum is exactly 180°.

Types of Triangles by Angles

Acute (all < 90°), Right (one = 90°), and Obtuse (one > 90°).

Shortcut Trick

Total frequency N = 50, so N/2 = 25.

The Median Class is 145 − 150 (cumulative frequency 29 is just above 25).

Median = Lower Limit + [(N/2 − cf) ÷ f] × h

Median = 145 + [(25 − 11) ÷ 18] × 5 = 145 + 3.89 = 148.89 cm.

∴ The correct answer is 148.89 cm.

Alternate Method

Given: Total number of girls (N) = 50.

Formula Used: Median = l + [(N/2 − cf) ÷ f] × h

⇒ N/2 = 50 ÷ 2 = 25.

⇒ Median Class = 145 − 150 (Cumulative frequency 29 is just greater than 25).

⇒ Lower limit (l) = 145.

⇒ Frequency of median class (f) = 29 − 11 = 18.

⇒ Cumulative frequency of preceding class (cf) = 11.

⇒ Class size (h) = 5.

⇒ Median = 145 + [(25 − 11) ÷ 18] × 5

⇒ Median = 145 + [14 ÷ 18] × 5

⇒ Median = 145 + [7 ÷ 9] × 5

⇒ Median = 145 + 3.888...

⇒ Median ≈ 148.89 cm.

∴ The correct answer is 148.89 cm.

The alphabet table is given below:-

The logic followed here is:-

Hence, "option 4" is the correct answer.

The correct answer is State Bank Of India.

Key Points

• Recently (January 2018), the Finance Minister has announced Electoral Bonds, these Bonds can be purchased from State bank of India.
• State Bank of India had been authorized to sell and encash electoral bonds, the 13th such sale since the scheme started in 2018, from January 13 till January 22.
• Electoral Bonds shall be valid for 15 calendar days from the date of issue and no payment shall be made to any payee political party if the electoral bond is deposited after the expiry of the validity period.
• Under the scheme, which was notified on January 2, 2018, a person or company incorporated in India can buy electoral bonds and give them to political parties registered under the Representation of the People Act, 1951 and those that secured not less than 1% of the votes polled in the last Lok Sabha or State Assembly elections.

Additional Information

• State Bank Of India:
• Headquarters: Mumbai
• Founded: 1 July 1955
• ICICI Bank:
• Headquarters: Vadodara
• Founder: Industrial Credit and Investment Corporation of India
• Founded: 1994, Vadodara
• Punjab National Bank
• Headquarters: New Delhi
• Founded: 19 May 1894, Lahore, Pakistan

The number of triangles is:-

The total number of triangles is 17.

Hence, "option 4" is the correct answer.

The correct answer is Kasinathuni Viswanath.

Key Points

• The name of the director is Kasinathuni Vishwanath who changed the face of Telugu cinema, who was given the 'Dadasaheb Phalke Award' for 2016 on 3rd May 2017.
• Kasinadhuni Viswanath, the Telugu film director and actor, conferred Dadasaheb Phalke Award for 2016.​
• K Vishwanath would receive a golden lotus, a cash prize of Rs 10 lakhs, and a shawl as part of the Dadasaheb Phalke Award considered the highest recognition in Indian cinema, which was given by President Pranab Mukherjee at the 64th National Film Awards.

Additional Information

List of previous recipients of Dadasaheb Phalke Award 

Shortcut Trick

Cost Price (CP) of Weaver = 150 ÷ 1.25 = 120.

New Profit % = (Direct SP − CP) ÷ CP × 100 = (180 − 120) ÷ 120 × 100 = 50%.

Shopkeeper SP = 150 × 1.30 = 195.

Customer Profit (Saving) = Shopkeeper SP − Direct SP = 195 − 180 = 15.

∴ The correct answer is 50%, Rs. 15.

Alternate Method

Given: Weaver SP = 150, Weaver Profit = 25%, Shopkeeper Profit = 30%, Direct SP = 180. Formulas: CP = SP ÷ (1 + P%) | Profit% = (SP − CP) ÷ CP × 100 | Profit = SP − CP.

⇒ Cost Price (CP) of the saree for the Weaver = 150 × (100 ÷ 125) = 120.

⇒ Weaver's Profit % if sold at 180 = [(180 − 120) ÷ 120] × 100 = 50%.

⇒ Selling Price (SP) of the Shopkeeper to the Customer = 150 × (130 ÷ 100) = 195.

⇒ Customer's Profit (Money Saved) = 195 − 180 = 15.

∴ The correct answer is 50%, Rs. 15.

Additional Information

Chain Rule in Profit and Loss

When a product passes through multiple hands, the Final SP = Initial CP × (100 + P₁)% × (100 + P₂)%...

Customer Profit

In direct-selling scenarios, customer profit refers to the difference between the market retail price and the direct purchase price.

The correct answer is Article 164.

Key Points

• Article 164
• The Chief Minister shall be appointed by the Governor and the other Ministers shall be appointed by the Governor on the advice of the Chief Minister, and the Ministers shall hold office during the pleasure of the Governor:
• Provided that in the State of Bihar, Madhya Pradesh, and Orissa, there shall be a Minister in charge of tribal welfare who may, in addition, be in charge of the welfare of the Scheduled Castes and backward classes or any other work
• The Council of Ministers shall be collectively responsible to the Legislative Assembly of the State.
• Before a Minister enters upon his office, the Governor shall administer so him the oaths of office and of secrecy according to the forms set out for the purpose in the Third Schedule
• A Minister who for any period of six consecutive months is not a member of the Legislature of the State shall at the expiration of that period cease to be a Minister
• The salaries and allowances of Ministers shall be such as the Legislature of the State may from time to time by law determine and, until the Legislature of the State so determines, shall be as specified in the Second Schedule The Advocate General for the State.

Additional Information

• Article 130: Seat of Supreme Court
• Article 122: Courts not to inquire into proceedings of Parliament
• Article 162: Extent of executive power of State Subject

The correct answer is Odisha.

Key Points

• Biju Janata Dal is a regional political party of Odisha.
• The Biju Janata Dal is a regional political party in the Indian state of Odisha founded and led by Naveen Patnaik, the current Chief Minister of Odisha and the son of former Chief Minister of Odisha Biju Patnaik.
• It was founded on 26 December 1997.

Additional Information

• The BJD won nine seats in the 1998 general election and Naveen was named Minister for Mines.
• In the 1999 general elections, the BJD won 10 seats.
• The party won a majority of seats in the Odisha Legislative Assembly in the 2000 and 2004 elections in alliance with the Bharatiya Janata Party (BJP).
• The BJD won 11 Lok Sabha seats in the 2004 elections.
• In the aftermath of the 2008 Kandhamal riots, the BJD parted ways with the BJP in both the Lok Sabha and Assembly in the 2009 general election, citing communalism and differences in seat sharing.
• During the election, BJD won 14 seats and secured a strong 108 legislative seats out of 147 seats in the 2009 Odisha legislative elections.

The correct answer is Ag.

Key Points

• Ag (Silver) is found as a free element in nature.
• Its symbol (Ag) is derived from the Latin Argentum, meaning "white and shining," Because silver is easily reduced to pure metal from its ores by relatively low heat, and because it is occasionally found free in nature.

Additional Information

• Au (Gold), Pt (Platinum), Ag (Silver), etc. are found in the free state as these metals are chemically less reactive in nature and do not react with oxygen present in the atmosphere thus, are found in the free state.
• The metals like Na (Sodium), K (Potassium), Ca (Calcium) and Mg (Magnesium) are not found in their free state in nature because of the reason that all of these metals are high-up in the reactivity series.
• And just because they are so reactive, they are never found in nature as free elements.

The correct answer is Soumitra Chattopadhyay.

Key Points

• Soumitra Chattopadhyay was honored with France's highest honor 'Legion of Honour' at the 42nd International Kolkata Book Fair in 2018. 
• Veteran Bengali actor Soumitra Chatterjee received the Legion of Honour, the highest French civilian award, 30 years after his mentor and renowned filmmaker Satyajit Ray was conferred with the same.
• Ambassador of France to India Alexandre Ziegler conferred the insignia of Knight of the Legion of Honour the highest French civilian distinction, on Soumitra Chatterjee for his contribution to cinema.

Additional Information

• The National Order of the Legion of Honour, formerly the Royal Order of the Legion of Honour is the highest French order of merit, both military and civil.
• Established in 1802 by Napoleon Bonaparte, it has been retained by all later French governments and régimes.
• Motto: Honour and Fatherland
• Awarded for: Excellent civil or military conduct; delivered, upon official investigation
• Eligibility: Military and Civilians
• Grand Master: President of France

The logic followed here is:-

In figures A, B, and D inner shape (part) is shaded and outer shape (part) is not shaded but in figure C outer shape (part) is shaded and inner shape (part) is not shaded.

Figure C is different from others.

Hence, "option 2" is the correct answer.

Shortcut Trick

Total sum of individual amounts = (Sum of pairs) ÷ 2

Sum = (227 + 273 + 280) ÷ 2 = 780 ÷ 2 = ₹390

Malika amount = (Total Sum) − (Rani + Tamali)

Malika = 390 − 273 = ₹117

∴ The correct answer is ₹117.

Alternate Method

Given:

Malika (M) + Rani (R) = ₹227 --- (i)

Rani (R) + Tamali (T) = ₹273 --- (ii)

Tamali (T) + Malika (M) = ₹280 --- (iii)

Adding equations (i), (ii), and (iii):

⇒ 2(M + R + T) = 227 + 273 + 280

⇒ 2(M + R + T) = 780

⇒ M + R + T = 780 ÷ 2 = 390

To find Malika's share, subtract (R + T) from the total:

⇒ Malika = (M + R + T) − (R + T)

⇒ Malika = 390 − 273

⇒ Malika = 117

∴ The correct answer is ₹117.

Additional Information

Cyclic Equations

When equations are given in the form (x+y), (y+z), and (z+x), the sum of variables is always half the sum of the constant terms.

Ratio and Proportion

If the shares were needed in ratios, we would find individual values: M=117, R=110, T=163 and then simplify.

The logic followed here is:-

Hence, "option 4" is the correct answer.

The correct answer is Bhutan.

Key Points

• Archery is the national sport of Bhutan.
• Archery, the national sport of Bhutan, is a common feature of everyday life.
• It is played differently from the international game and is seen as a celebration of the country's way of life.

Additional Information

List of Countries and their National Games

The Venn diagram is given below:-

<br>

 

Conclusion:

1. All oriental rollers are doves. → False (All doves are oriental rollers but all oriental rollers are not doves.)
2. All pigeons are oriental rollers. → Ture (All pigeons are doves, all doves are oriental rollers. So, all pigeons are oriental rollers.)

Hence, "option 3" is the correct answer.

Additional Information

The logic followed here is:-

In figures A, B, and D 1, 2, 3, and 4 number inside the circle but in figure C 1, 3, 4, and 5 number inside the circle.

So, figure C is different from others.

Hence, "option C" is the correct answer.

The correct answer is A and B.

Key Points 

• Gravity:
• The acceleration due to gravity is the rate of increase of velocity of a body falling freely towards the earth.
• It is represented by $g = {GM_e \over R^2_e}$
• where M_e is the mass of the earth and R_e is the radius of the earth.
• The value of g at the surface of the earth is 9.8 m/s².
• The value of g on the Moon is 1/6th of that on the earth. But, according to the formula of g, the ratio of the earth and the moon will be 6:1. Hence, statement B is incorrect.
• The force due to gravity is given by the formula, F = mg
• The value of g does not depend on surrounding objects. Hence statement A is incorrect.
• In Newton's law of universal gravitation, the attractive force between two objects (F) is equal to G times the product of their masses divided by the square of the distance between them.
• ​$F = {GM_1*M_2\over R^2_e}$
• The SI unit of G is N m2/kg². Hence statement C is correct.

Additional Information

Variation in g:

• The value of g decreases with height or depth from the earth’s surface.
• g is maximum at poles. Hence, it will be maximum at the Camp in Antarctica
• g is minimum at the equator.
• g decreases due to the rotation of the earth.
• g decreases if the angular speed of the earth increases and increases if the angular speed of the earth decreases.

The correct answer is K.P. Sharma Oli.

Key Points

• K.P. Sharma Oli was sworn in as the 41st Prime Minister of Nepal.
• Khadga Prasad Sharma Oli, the leader of the Communist Party of Nepal (Unified Marxist-Leninist) was sworn in as the 41st Prime Minister of Nepal.
• His swearing-in follows the resignation of Sher Bahadur Deuba from the post earlier in the day.

Additional Information

• Nepal
• Capital: Kathmandu
• Currency: Nepalese rupee
• Prime minister: Sher Bahadur Deuba (Jan 2022)
• President: Bidhya Devi Bhandari​ (Jan 2022)

Shortcut Trick

The LCM (Least Common Multiple) of any set of numbers is maximum when the numbers are coprime to each other.

For three numbers a, b, and c, if HCF(a, b) = HCF(b, c) = HCF(a, c) = 1, then LCM = a × b × c.

Since the question asks for the maximum optimal value, we assume the case where no factors are shared.

∴ The correct answer is Product of all three numbers.

Alternate Method

Given: Three numbers (say n₁, n₂, and n₃).

Property: The LCM of a set of numbers is always less than or equal to their product.

⇒ LCM(n₁, n₂, n₃) ≤ n₁ × n₂ × n₃.

⇒ The equality holds true if and only if the numbers are pairwise coprime (i.e., they share no common factors other than 1).

⇒ Therefore, the maximum possible (optimal) value for the LCM is reached when we multiply all the given numbers together.

∴ The correct answer is Product of all three numbers.

Additional Information

Coprime Numbers

Numbers whose HCF is 1. Their LCM is always equal to their product.

Relation between HCF and LCM

For two numbers a and b: HCF(a, b) × LCM(a, b) = a × b. This direct product rule specifically applies to two numbers.

LCM Property

The LCM is the smallest positive integer that is divisible by all numbers in the set. It can never be smaller than the largest number in the set.

The correct answer is Monohybrid cross.

Key Points

• Mendel gives the law of purity of gametes on the basis of monohybrid crosses.
• To understand the idea of the purity of gametes, a monohybrid cross is taken.
• A monohybrid cross between pea plant-bearing axial flowers (AA) and plant-bearing terminal flowers (aa). In hybrid F1, two types of male and female gametes are formed in equal quantity.
• On separation, these factors are randomly united in pairs at the time of fertilization and transferred to offspring.
• In pure homozygous forms both factors being alike, only one type of gametes is formed.
• In F2 generation, two varieties appear in ratio 3:1.
• That is why law can also be defined as allele pairs separate during gamete formation and the paired condition is restored by random fusion of gametes during fertilization.

Additional Information

• Backcrossing is the crossing of a hybrid with one of its parents, or an adult genetically identical to the parent, to obtain offspring with a genetic identity close to that of the parent.
• It is used in horticulture, animal breeding and gene knockout organism development.
• A dihybrid cross describes a mating experiment between two organisms that are equally hybrid for two traits.
• A hybrid organism is one that is heterozygous, meaning that it carries two different alleles at a particular genetic position or locus.
• In its simplest form, a test cross is an experimental cross of an individual organism of the dominant phenotype, but an organism with unknown genotype and a homozygous recessive genotype (and phenotype).

The alphabet table is given below:-

The logic followed here is:-

1. We add 1 in the place value of the first letter and we get new letter in the place of first value and add one more new letter in the place of second value.

2. Subtracted 1 in the place value of the second and third letters and get new third and fourth letters and add new third letter in the place of new fifth place and so on.

 

 

Hence, "option 3" is the correct answer.

The correct answer is Sodium.

• Sodium metal can be cut with a knife.
• Sodium is silver-white color metal with malleable and ductile properties.
• It is a metal that can easily be cut with a knife.
• It is a good conductor of heat and electricity.

Key Points

• Sodium and potassium can be cut with a knife.
• Sodium is a chemical element with the symbol Na and atomic number 11.
• It is a soft, silvery-white, highly reactive metal. Sodium is an alkali metal, being in group 1 of the periodic table.
• Its only stable isotope is ²³Na.
• The free metal does not occur in nature and must be prepared from compounds.

Additional Information

• Aluminum:
• Symbol: Al
• Atomic mass: 26.981539 u
• Atomic number: 13
• Platinum
• Symbol: Pt
• Atomic mass: 195.084 u
• Atomic number: 78
• Copper
• Symbol: Cu
• Atomic mass: 63.546 u
• Atomic number: 29

Given:

The given value = $√{183184}$

Calculation:

The given number = 183184

Factors of 183184 = 2 × 2 × 2 × 2 × 107 × 107

now, we make pairs of factors to obtain the square root.

So, √183184 = 2 × 2 × 107

⇒ 428

∴ The required value is 428

Shortcut Trick

Convert mixed fractions to improper fractions: 28 1/2 = 57/2 m and 8 3/4 = 35/4 m.

Cost of 57/2 m = ₹1254 ⇒ Cost of 1 m = (1254 × 2) ÷ 57 = 44.

Cost of 35/4 m = 44 × (35/4) = 11 × 35 = ₹385.

∴ The correct answer is ₹385.

Alternate Method

Given:

Initial length = 28 1/2 m = 57/2 m

Initial cost = ₹1254

Target length = 8 3/4 m = 35/4 m

Calculations:

⇒ Unit cost = Total Cost ÷ Total Length

⇒ Unit cost = 1254 ÷ (57/2) = 1254 × (2/57)

⇒ Unit cost = 22 × 2 = ₹44 per meter

⇒ Cost of 35/4 m = 44 × (35/4)

⇒ Cost = 11 × 35 = ₹385

∴ The correct answer is ₹385.

Additional Information

Unitary Method

It involves finding the value of a single unit first and then multiplying by the required quantity. Value = (Total Value / Total Units) × Required Units.

Mixed Fraction Conversion

To convert a b/c to an improper fraction, use the formula: (a × c + b) / c.

Direct Proportion

When one quantity increases as another increases, they are in direct proportion: x₁/y₁ = x₂/y₂.

The logic followed here is:-

Hence, "option 4" is the correct answer.

Given:

4.025

Concept used:

a.00b = a00b/1000

Calculation:

4.025 = 4025/1000

⇒ $\frac{161} {40}$

∴ Required answer is $\frac{161} {40}$

The correct answer is Milk.

Key Points

• Gujarat is one of the largest milk-producing states in India with the contribution of 7.75% share in the total milk production of India.
• Gujarat is the largest producer of major cash crops like cotton, groundnut, tobacco, cumin, sesamum, etc in India.
• Other major crops produced are Rice, Wheat, Jowar, Bajra, Maize, Tur, and Gram.
• Gujarat lies in a subtropical high-pressure zone towards west India.
• It is characterized by semi-arid & arid conditions.
• The coastal zone of the state remains dry during most of the year.
• Hence, salt production is high.

Additional Information

• Uttar Pradesh is the highest sugarcane-producing State in the subtropical zone having an area of about 22.77 Lakh hectares with the production of 135.64 Million Ton cane whereas Haryana has the highest productivity of sugarcane in the Subtropical Zone.
• Coffee production in India is dominated in the hill tracts of South Indian states, with Karnataka accounting for 71%, followed by Kerala with 21%, and Tamil Nadu (5% of overall production with 8,200 tonnes).
• Tea production in West Bengal was approximately 25 million kilograms in March 2021, the highest of any other region in the country.
• Assam came second that year with close to 20 million kilograms.

Shortcut Trick

For a period of 3 years, the difference between CI and SI is given by: P × (R/100)² × (3 + R/100).

Given Principal (P) = Rs. 8,000 and Rate (R) = 5%.

Difference = 8000 × (5/100)² × (3 + 5/100)

Difference = 8000 × (1/400) × (3.05) ⇒ 20 × 3.05 = 61.

∴ The correct answer is Rs. 61.

Alternate Method

Given: Principal (P) = Rs. 8,000, Rate (R) = 5%, Time (T) = 3 years.

Formula: Simple Interest (SI) = (P × R × T) / 100 | Compound Interest (CI) = P[(1 + R/100)^T − 1]

⇒ Simple Interest (SI) = (8000 × 5 × 3) / 100 = Rs. 1200

⇒ Compound Interest (CI) = 8000 × [(1 + 5/100)³ − 1]

⇒ CI = 8000 × [(1.05)³ − 1] = 8000 × [1.157625 − 1]

⇒ CI = 8000 × 0.157625 = Rs. 1261

⇒ Difference = CI − SI = 1261 − 1200 = Rs. 61

∴ The correct answer is Rs. 61.

Additional Information

Difference for 2 Years

The difference between CI and SI for 2 years is calculated as P(R/100)².

Compound Interest Formula

The amount after T years is A = P(1 + R/100)^T, and CI = A − P.

Effective Rate of Interest

For 3 years at 5%, the effective CI rate is 15.7625%, while the SI rate is 15%. The difference is 0.7625% of Principal.

A boy has five used crayons.

He is trying to arrange them in order from shortest to longest.

1. L is taller than G and D.

L > G and D

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

2. B is taller than L.

B > L

• No information is given about D, G, and X. Therefore, statement 2 alone is not sufficient.

3. X is smaller than G.

X < G

• No information is given about B, D, and L. Therefore, statement 3 alone is not sufficient.

From statements 1, 2, and 3 we get:-

B > L > G > X or D.

B is the longest among them.

• Here, statements 1, 2 and 3 are sufficient.

Hence, "option 2" is the correct answer.

Shortcut Trick

Sum of individual sets (n(P₁) + n(P₂) + n(P₃)) = 40 + 30 + 40 = 110.

Sum of elements in only two and all three = n(At least 2) + n(Exactly 2) + n(Exactly 3) logic.

Total individual count = (People liked only 1) + 2×(People liked exactly 2) + 3×(People liked exactly 3).

Given: At least 2 = 20, Exactly 3 = 10 ⇒ Exactly 2 = 20 − 10 = 10.

110 = (Only 1) + 2×(10) + 3×(10) ⇒ Only 1 = 110 − 50 = 60.

∴ The correct answer is 60 people.

Alternate Method

Given:

Customers liking Perfume 1 [n(P₁)] = 40

Customers liking Perfume 2 [n(P₂)] = 30

Customers liking Perfume 3 [n(P₃)] = 40

Customers liking all three [n(P₁ ∩ P₂ ∩ P₃)] = 10

Customers liking at least two = 20

Calculations:

⇒ Let a, b, c be people liking only one perfume, x, y, z liking exactly two, and g liking all three.

⇒ At least two = (x + y + z) + g = 20

⇒ Given g = 10, then (x + y + z) = 20 − 10 = 10

⇒ Total individual likes = n(P₁) + n(P₂) + n(P₃) = 110

⇒ Sum = (a + b + c) + 2×(x + y + z) + 3×g

⇒ 110 = (Only one) + 2×(10) + 3×(10)

⇒ 110 = (Only one) + 20 + 30

⇒ Only one = 110 − 50 = 60

∴ The correct answer is 60 people.

Additional Information

Venn Diagram Formulas for 3 Sets

Total n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − [n(A ∩ B) + n(B ∩ C) + n(C ∩ A)] + n(A ∩ B ∩ C).

Regions of Exactly N

Exactly one = Total − (Exactly two + Exactly three). Sum of n(A,B,C) counts Exactly 2 twice and Exactly 3 thrice.

At Least vs Exactly

At least two = (Exactly two) + (Exactly three). This is a common trap in set theory problems.

In an ordinary year, there are 365 days and on dividing 365 by 7,

we get remainder = 1, so this extra one day is taken as an odd day.

Similarly, in a leap year, there are 366 days and on dividing 366 by 7,

we get remainder = 2, so these extra days are taken as the odd days.

Thus, the remainder, which we get after dividing the number of days by 7 is considered as odd days.

2014 = we find out the odd days (the nearest leap year + completing year) = 2000 + 13

In 2000 years the odd days = 0

In 13 years the odd days = 13/4 = 3 leap years and 10 normal years.

In 3 leap years the odd days = 6, and 10 normal years = 10

So total = 6 + 10 = 16 odd days i.e. 16/7 = 2 odd days (remainder)

Odd days in January = 6 days i.e. 6 odd days.

Total  = 2 + 6 = 8/7 = 1 odd days.

 

Monday of the week was 6th January 2014.

Hence, "option 2" is the correct answer.

Shortcut Trick

Product-Difference Formula: Time taken by Meena = (Rita × Both) ÷ (Rita − Both)

Required Days = (15 × 10) ÷ (15 − 10)

Required Days = 150 ÷ 5 = 30 days

∴ The correct answer is 30 days.

Alternate Method

Given:

Time taken by Rita and Meena = 10 days

Time taken by Rita alone = 15 days

Calculations:

⇒ Total Work = LCM of 10 and 15 = 30 units

⇒ Efficiency of Rita + Meena = 30 ÷ 10 = 3 units/day

⇒ Efficiency of Rita = 30 ÷ 15 = 2 units/day

⇒ Efficiency of Meena = (Efficiency of Rita + Meena) − (Efficiency of Rita)

⇒ Efficiency of Meena = 3 − 2 = 1 unit/day

⇒ Days taken by Meena = Total Work ÷ Efficiency of Meena

⇒ Days taken by Meena = 30 ÷ 1 = 30 days

∴ The correct answer is 30 days.

Additional Information

Work and Efficiency Relationship

Efficiency is inversely proportional to the time taken to complete a work. Total Work = Efficiency × Time.

Combined Work Formula

If A takes 'x' days and B takes 'y' days, together they take (xy) ÷ (x + y) days.

Pipes and Cisterns

The same logic applies to pipes filling a tank, where efficiency represents the rate of flow per unit time.

The correct answer is 56.

Key Points

• Newland assumed that only 56 elements exist in nature.
• In 1866, John Newlands, an English scientist, arranged the then-known elements in order of increasing atomic mass.
• He started with the element with the lowest atomic mass (hydrogen) and ended with Thorium which was the 56th element.
• He found that every eighth element has the same properties as the first. He compared it to the octave found in music.
• That's why he called it the 'law of octaves'.
• This is known as 'Newlands' Law of Octaves'.
• The properties of lithium and sodium were found to be similar in Newlands' octave.

Additional Information

• Law of Octaves was applicable only up to calcium, as after calcium every eighth element did not possess properties similar to that of the first.
• It was assumed by Newlands that only 56 elements existed in nature and no more elements would be discovered in the future.
• But, later on, several new elements were discovered, whose properties did not fit into the Law of Octaves.
• In 1869, just five years after John Newlands put forward his Law of Octaves, a Russian chemist called Dmitri Mendeleev published a periodic table.
• Mendeleev also arranged the elements known at the time in order of relative atomic mass, but he did some other things that made his table much more successful.

Shortcut Trick

Total Selling Price (SP) of 12 units = Rs. 6,48,816

Selling Price (SP) per unit = 6,48,816 ÷ 12 = Rs. 54,068

Cost Price (CP) per unit = Rs. 52,283

Profit % = (SP − CP) ÷ CP × 100

Profit % = (54,068 − 52,283) ÷ 52,283 × 100 = 1,785 ÷ 52,283 × 100 ≈ 3.41%

Matching with closest option, the approximate profit percentage is 3.30%.

∴ The correct answer is 3.30%.

Alternate Method

Given: Total Selling Price for 12 units = Rs. 6,48,816; Cost Price per unit = Rs. 52,283

Formulas: Profit = SP − CP | Profit % = (Profit ÷ CP) × 100

⇒ Total Cost Price (CP) for 12 units = 12 × 52,283 = Rs. 6,27,396

⇒ Total Profit = Total SP − Total CP = 6,48,816 − 6,27,396 = Rs. 21,420

⇒ Profit % = (Total Profit ÷ Total CP) × 100

⇒ Profit % = (21,420 ÷ 6,27,396) × 100 ≈ 3.41%

⇒ Since 3.30% is the closest standard value among the given options, we select 3.30%.

∴ The correct answer is 3.30%.

Additional Information

Profit and Loss Percentage

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

Approximate Calculations

In examinations, when options are spread apart, values can be rounded to the nearest significant figure to speed up calculations.

Shortcut Trick

For an equilateral triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), the y-coordinate of the centroid is G_y = (y₁ + y₂ + y₃) ÷ 3.

In an equilateral triangle, the third vertex (x₃, y₃) is related to the others by symmetry. For a fixed base (0, 0) and (3, √3), the two possible third vertices (p, q₁) and (p, q₂) are reflections across the perpendicular bisector.

The sum of the y-coordinates of the two possible third vertices for an equilateral triangle based on points (x₁, y₁) and (x₂, y₂) is always y₁ + y₂.

∴ q₁ + q₂ = 0 + √3 = √3.

∴ The correct answer is √3.

Alternate Method

Given: Vertices A(0, 0), B(3, √3), and C(p, q).

Formula Used: Distance = √[(x₂−x₁)² + (y₂−y₁)²]

⇒ Side AB² = (3 − 0)² + (√3 − 0)² = 9 + 3 = 12.

⇒ Since it is equilateral, AC² = 12 and BC² = 12.

⇒ AC² = p² + q² = 12 ... (i)

⇒ BC² = (p − 3)² + (q − √3)² = 12.

⇒ p² + 9 − 6p + q² + 3 − 2√3q = 12.

⇒ (p² + q²) + 12 − 6p − 2√3q = 12.

⇒ 12 + 12 − 6p − 2√3q = 12 ⇒ 6p + 2√3q = 12 ⇒ 3p + √3q = 6.

⇒ p = (6 − √3q) ÷ 3. Substitute this into (i):

⇒ [(6 − √3q) ÷ 3]² + q² = 12.

⇒ (36 + 3q² − 12√3q) ÷ 9 + q² = 12.

⇒ 36 + 3q² − 12√3q + 9q² = 108.

⇒ 12q² − 12√3q − 72 = 0 ⇒ q² − √3q − 6 = 0.

⇒ This is a quadratic equation in q with roots q₁ and q₂.

⇒ Sum of roots (q₁ + q₂) = −b ÷ a = −(−√3) ÷ 1 = √3.

∴ The correct answer is √3.

Additional Information

Third Vertex of Equilateral Triangle

If two vertices are (x₁, y₁) and (x₂, y₂), the third vertex (x, y) is given by x = (x₁+x₂ ± √3(y₁−y₂))/2 and y = (y₁+y₂ ± √3(x₂−x₁))/2.

Area of Equilateral Triangle

Area = (√3 ÷ 4) × side². In this case, Area = (√3 ÷ 4) × 12 = 3√3 sq. units.

Centroid Property

For an equilateral triangle, the centroid, circumcenter, orthocenter, and incenter all coincide at the same point.

Shortcut Trick

Side of square (a) = 28 cm.

Radius of circle (r) = a ÷ 2 = 14 cm.

Area of middle portion = Area of square − 4 × (Area of quadrant).

Area = a² − πr² = 28² − (22/7 × 14 × 14) = 784 − 616 = 168 cm².

∴ The correct answer is 168 cm².

Alternate Method

Given: Side of square = 28 cm. Four circles touch each other on the square's corners.

Formula Used: Area of square = side²; Area of circle = πr².

⇒ Side of the square (a) = 28 cm

⇒ Since circles touch each other, radius (r) = 28 ÷ 2 = 14 cm

⇒ Area of square = 28 × 28 = 784 cm²

⇒ Area of 4 quadrants (one full circle) = (22/7) × 14 × 14

⇒ Area of circle = 22 × 2 × 14 = 616 cm²

⇒ Area outside circles (middle) = 784 − 616 = 168 cm²

∴ The correct answer is 168 cm².

Additional Information

Area of Shaded Region in Square

For a square of side 'a' with four quadrants at corners, the central area is a² − π(a/2)² ≈ 0.2146a².

Quadrant Properties

A quadrant is 1/4th of a circle with an angle of 90° at the center. Area = πr²/4 and Perimeter = πr/2 + 2r.

Circle Touching Concept

When circles of equal radii touch externally, the distance between their centers is equal to 2r.

The correct answer is Kerala Congress (M).

Key Points

• C.F. Thomas has led Kerela Congress (M) political party in the Indian state.
• One of the founding leaders of the Kerala Congress (Mani) regional party and a nine-time MLA from Changanassery, CF Thomas passed away.
• ​Thomas contested Assembly elections for the first time from Changanassery in Kottayam district in 1980 and went on to win a record nine consecutive times from the same seat till the latest election in 2016.

Additional Information

• Thomas remained an MLA for 40 years and is considered a modern architect of Changanassery, which grew into a major town in the Kottayam district.
• In the Congress-led UDF government between 2001 and 2006, Thomas served as the minister for rural development, registration, and khadi.
• Kerala Congress is a political party in Kerala, India founded In 1964. By the leadership of Mathachan Kuruvinakunnel, K. M. George, R. Balakrishna Pillai.

Shortcut Trick

The profit earned by Smita is the difference between Compound Interest (CI) and Simple Interest (SI) for 2 years.

Shortcut formula for 2-year difference: Profit = P × (R/100)²

⇒ Profit = 75,000 × (15/100) × (15/100)

⇒ Profit = 75,000 × 0.0225 = 1,687.5

∴ The correct answer is Rs. 1,687.5.

Alternate Method

Given:

Principal (P) = Rs. 75,000

Rate (R) = 15% per annum

Time (T) = 2 years

Step 1: Calculate Simple Interest (SI)

⇒ SI = (P × R × T) ÷ 100

⇒ SI = (75,000 × 15 × 2) ÷ 100

⇒ SI = 750 × 30 = 22,500

Step 2: Calculate Compound Interest (CI)

⇒ CI = P × [(1 + R/100)^T − 1]

⇒ CI = 75,000 × [(1 + 15/100)² − 1]

⇒ CI = 75,000 × [(1.15)² − 1]

⇒ CI = 75,000 × [1.3225 − 1]

⇒ CI = 75,000 × 0.3225 = 24,187.5

Step 3: Calculate Profit

⇒ Profit = CI − SI

⇒ Profit = 24,187.5 − 22,500 = 1,687.5

∴ The correct answer is Rs. 1,687.5.

Additional Information

Difference between CI and SI for 3 years

The formula to find the difference for a 3-year period is: Difference = P(R/100)² × (3 + R/100).

Relation between SI and CI for 2 years

For a 2-year period, Compound Interest can also be calculated as: CI = SI × (1 + R/200).

Effective Rate of Interest

For CI compounded annually for 2 years, the effective rate is R + R + (R × R)/100. Here, 15 + 15 + 2.25 = 32.25%.

Calculation:

Total expenditure = Rs. 50,000

Expenditure on transport cost  = 10%

Required angle at the centre of the area related to transport expenditure = (10/100 × 360°)

⇒ 36° 

∴ Required angle at the centre of the area related to transport expenditure is 36°

The logic followed here is:

 

 

Code for weekdays:

 

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

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

We will find the day on 1st July 2007 = (2000 years + Period from 1.1.2007 to 1.7.2007)

As mentioned above:

Odd days in 1600 years = 0

Odd days in 400 years = 0

Now number of odd days in:

Jan, Feb, March, April, May, June and July

(31 + 28 + 31 + 30 + 31 + 30 + 1) = 182 days = 0 odd days

Total number of odd days = (0 + 0 + 0) = 0

So on 1st July, 2007 it was Sunday. 

Next Friday 1st + 5 = 6 and so on.

In July, 2007 Friday falls on 6th, 13th, 20th and 27th. 

Hence, the correct answer is "Option 3".

The correct answer is Gas.

• Gases usually have low densities mainly because the intermolecular force of attraction is better, the gas molecules are much smaller.
• As a result, they move all over the space which further leads to the generation of larger intermolecular spaces.
• Furthermore, in comparison to solids and liquids, gases have a very small number of molecules per unit volume.
• Density = Mass / Volume
• They have the least mass/volume among gases. Thus, the increased volume is mostly due to the reduced density of the gases.

Key Points

• Solid – Particles are tightly packed in a regular structure. Sodium is a solid at room temperature.
• Liquid – Particles are tightly packed but free to move past each other. Mercury is the only metal that is liquid at standard conditions for temperature and pressure.
• Gas – Particles are spread out and move randomly.

Important Points

• ​Hydrogen is the element with the lowest density in the periodic table.
• Osmium is the element with the highest density.
• The density of a substance is its mass per unit volume.
• The symbol most often used for density is ρ.
• Specific gravity:
• It is defined as the density of material with respect to the density of water at 4°C. (DensityofsubstanceDensityofwater)
• It can be defined as the ratio of mass or weight of substance with respect to mass or weight of water at 4º C.

The mirror image of the given figure is given below:-

Hence, "option 3" is the correct answer.

Shortcut Trick

Total population increase = 8680 − 8000 = 680.

If all 8000 were males, increase = 8% of 8000 = 640.

Excess increase = 680 − 640 = 40.

This 40 represents the extra 4% (12% − 8%) of the females.

4% of females = 40 ⇒ Total females = (40 ÷ 4) × 100 = 1000.

∴ The correct answer is 1000.

Alternate Method

Given:

Initial population = 8000

Final population = 8680

Male growth rate = 8%

Female growth rate = 12%

Formula Used:

Total Increase = (Growth % of Males × Males) + (Growth % of Females × Females)

Calculations:

⇒ Total increase = 8680 − 8000 = 680

⇒ Overall increase percentage = (680 ÷ 8000) × 100 = 8.5%

⇒ Using alligation method:

⇒ Ratio of Males to Females = (12 − 8.5) : (8.5 − 8)

⇒ Ratio = 3.5 : 0.5 = 7 : 1

⇒ Total ratio parts = 7 + 1 = 8 units

⇒ 8 units = 8000

⇒ 1 unit = 1000

⇒ Number of females = 1 unit = 1000

∴ The correct answer is 1000.

Additional Information

Rule of Alligation

It is a shortcut to find the ratio in which two components are mixed to get a mean value: Ratio = (Higher Value − Mean) : (Mean − Lower Value).

Percentage Change

The percentage change is calculated as: (Final Value − Initial Value) ÷ Initial Value × 100.

Weighted Average

The net change in a population can be seen as a weighted average of the changes in its subgroups (males and females).

The correct answer is Joy Goswami.

Key Points

• Eminent Bengali poet Joy Goswami was conferred with the 31st Moortidevi Award for the year 2017.
• The committee, headed by poet and scholar Satya Vrat Shastri, unanimously decided to confer the award upon Goswami for his poetry collection titled 'Du Dondo Phowara Matro'.
• It is the first time the award will be given to a Bengali poet.
• 'Du Dondo Phowara Matro' is an autobiographical account of the poet's life featuring his close ones including a pet cat
• The work also echoes secret trysts, chance loves, and more of the fantastical quotidian which makes up the poet's consciousness.

Additional Information

• The Moortidevi Award is an Indian literary award annually presented by the Bharatiya Jnanpith, a literary and research organisation.
• Moortidevi Award
• Awarded for Literary award in India
• Sponsored by Bharatiya Jnanpith
• Reward(s) ₹4 lakh
• First winner - C. K. Nagaraja Rao (1983)
• Most recent winner Vishwanath Prasad Tiwari (2019)

We know that:

The diagram is given below:-

Mr. Z is North east from his starting position.

Hence, "option 4" is the correct answer.

The question in the statement asks if there is a need for pet daycare centres in the city.

• Argument 1 justly answers the question and elaborates the need of working people, and highlights that it will be a good option. Thus, argument I is strong.
• Argument 2 only states that it is not needed without justifying it. Veterinary clinics and pet care centres are different things. So, argument II is not strong.

Hence the correct answer is option 3.

The correct answer is 20 Hz to 20000 Hz.

Key Points

• The audible range of sound for human beings is 20 Hz to 20000 Hz.
• Humans can detect sounds in a frequency range from about 20 Hz to 20 kHz.
• (Human infants can actually hear frequencies slightly higher than 20 kHz, but lose some high-frequency sensitivity as they mature; the upper limit in average adults is often closer to 15–17 kHz.)

Additional Information

• The number of sound vibrations emitted per second is known as the frequency which is measured in hertz (Hz).
• The lower (or higher) the frequency, the lower (or higher) the pitch of the sound.
• The sensation of a frequency is commonly referred to as the pitch of a sound.
• A high pitch sound corresponds to a high-frequency sound wave and a low pitch sound corresponds to a low-frequency sound wave.

The correct answer is Be > Mg > Ca.

Key Points

• The group Be > Mg > Ca shows the correct order of first ionization potential.
• The ionization energy decreases down the group with an increase in size.
• These elements (Be> Mg>Ca) are 2nd group elements and the order correctly reflects a trend in ionization energy.

Additional Information

• The ionization energy decreases down the group with an increase in size.
• These elements( Be> Mg>Ca ) are 2nd group elements and the order correctly reflects a trend in ionization energy.
• Ionization energy is the quantity of energy that an isolated, gaseous atom in the ground electronic state must absorb to discharge an electron, resulting in a cation.
• H(g)→H+(g)+e⁻
• This energy is usually expressed in kJ/mol, or the amount of energy it takes for all the atoms in a mole to lose one electron each.

The Venn diagram is given below:-

 

Conclusion:

I. All women are trees. → True (As all women are flowers, all flowers are trees so all women are trees, hence, true)

II. All trees are women. → False (As all women are flowers, all flowers are trees then all trees are women, it can be possible but not definite, hence, false)

Hence, "option 4" is the correct answer.

Additional Information

The Venn diagram is given below:-

The total number of students playing the only two games 12 + 13 + 14 = 39.

Hence, "option 2" is the correct answer.

Given:

$√{30-√{30-√{30-√{30-√{.....}}}}}\space?\space$

Calculation:

Let x be the value of $√{30-√{30-√{30-√{30-√{.....}}}}}\space?\space$

Then,

⇒ x = √30 – x

squaring both sides we get,

⇒ x² = 30 – x

⇒ x² + x – 30 = 0

⇒ x² + 6x – 5x – 30 = 0

⇒ x(x + 6) – 5(x + 6) = 0

⇒ (x – 5) (x + 6) = 0

⇒ x = 5 or -6

∴ The required value is 5

The correct answer is Finance and Planning.

Key Points

• Sudhir Mungantiwar handles the ministry of finance and planning the state of Maharashtra (2018).
• Sudhir Sachchidanand Mungantiwar is a legislator from the state of Maharashtra, India.
• He served as the Cabinet Minister of Finance & Planning and Forests departments in the Government of Maharashtra.

Additional Information

• Ministry of Home Affairs Department Maharashtra is a Ministry of Government of Maharashtra.
• The Ministry of Cultural Affairs is a ministry in the Government of Maharashtra. Ministry is responsible for promoting regional culture.
• The Ministry is headed by a cabinet-level minister.

The family tree is given below:-

Brother of V is the paternal uncle of Y. Since V is the father of Y.

Hence, "option 1" is the correct answer.

The logic followed here is:

The bridges are built over the river.

Similarly,

The tunnel is built under the mountain (Tunnel is made in the mountain).

Hence, "option 1" is the correct answer.

The correct answer is Malayalam.

Key Points

• The award-winning film 'Little Magician' was shot in Malayalam.
• The little magician was made in Malayalam.
• Later it was dubbed in Tamil, Telugu, and Hindi, with the Hindi dubbed being 'Chota Jadugar'.
• It won the national film award for best special effects.
• 'The Waterfall', which captures the journey of a young city boy as he learns to appreciate the value of the environment as well as think critically about climate change and development, has been awarded the National Award for 'Best Educational Film'.

Additional Information

• The National Film Awards is the most prominent film award ceremony in India.
• Established in 1954, it has been administered, along with the International Film Festival of India and the Indian Panorama, by the Indian government's Directorate of Film Festivals since 1973.
• Every year, a national panel appointed by the government selects the winning entry, and the award ceremony is held in New Delhi, where the President of India presents the awards.
• This is followed by the inauguration of the National Film Festival, where the award-winning films are screened for the public.

The figure has the closest resembles the question figure is given below:-

Hence, "option 4" is the correct answer.

From option 1:-

b b c / d d d / b e c / b d e → don't follow a pattern.

From option 2:-

b b c / d d e / b b c / d d e → Follows a pattern and 'bbc / dde' remains the same.

From option 3:-

b c c / d d d / b b c / d d e → don't follow a pattern.

From option 4:-

b b c / d d e / b d c / b d e → don't follow a pattern.

Hence, "option 2" is the correct answer.

The correct answer is 450 C.

Key Points

• Given,
• Current, I = 0.75 A
• Time, T= 10 minutes⇒ 600 seconds
• Charge, Q = ?
• Q = I x T
• Q = 0.75 x 600
• Q = 450 C

Additional Information

• Charge:
• A charge is a property associated with the matter due to which it produces and experiences electric and magnetic effects.
• It is the energy that a body attains when it loses or gains the electrons.
• Its S.I. unit is coulomb C.

The correct answer is 9 : 3 : 3 : 1

Key Points

• The phenotypic ratio in the F2 generation is  9 : 3 : 3 : 1.
• In the F2 generation of Mendel's dihybrid cross, the phenotypic ratio is 9:3:3:1 but here 9 and 1 represent the parental types i.e., they show the parental phenotype but 3 and 3 represent the recombinants i.e., showing one character of one parent and the other character of another parent.
• So, the phenotypic ratio of recombinants is 3:3 i.e., 1:1.

Additional Information

• A monohybrid cross is a mating between individuals who have different alleles at one genetic locus of interest.
• In a monohybrid cross, the pure breed tall and dwarf homozygous plants were crossed.
• The result of F1 generation explains the Law of Dominance while that of F2 explains the Law of segregation.
• The F1 generation being all tall despite being heterozygous explains the dominant feature of the allele ‘T’ over ‘t’ of the gene T/t.
• The fact that none of the parents of the F2 were dwarf, yet the dwarf plant was obtained in F2 explains that in a heterozygous individual, both the different alleles segregate from each other while gamete formation.

The correct answer is Outside the earth's gravitational field.

Key Points

• The value of 'g' is less than the actual value of 'g' Outside the earth's gravitational field.
• The value of g at all places is not the same, it varies.
• The value of 'g' changes slightly from place to place but its value near the earth's surface is 9.8 m/s2.
• The value of g is more at the poles and less at the equator.
• Hence on the basis of altitude the value of g changes.
• The value of g is independent of the object’s mass and only depends upon location – the planet the object is on and the distance from the center of that planet.
• The value of acceleration due to gravity is maximum at poles and minimum at the equator.

Additional Information

• The value of 'g' is 9.8 m/s².
• The value of g is independent of the object’s mass and only depends upon location – the planet the object is on and the distance from the center of that planet.

The logic followed here is:-

Each letter of a single digit of the place value subtracted 1 and two-digit of the place value subtracted 1 and we take the second number.

Similarly,

Hence, "option 2" is the correct answer.

The correct answer is Only A is true.

Key Points 

• Irreversible chemical reactions can occur in only one direction.
• The reactants can change to the products, but the products cannot change back to the reactants.
• Reversible chemical reactions can occur in both directions.
• The reactants can change to the products, and the products can also change back to the reactants.​​
• Example
• N2(g) + 3H2(g) $\rightleftharpoons$  2NH3(g)
• Hence statement A is true.
• ​CaCO3(s) $\xrightarrow{heat}$  CaO(s) + CO2(g)
• It is a thermal decomposition reaction as Calcium carbonate undergoes decomposition and the carbon dioxide gas formed.
• The second product of the reaction, the calcium oxide.
• The chemical reaction in which two or more products are formed from a single reactant is called the ''Decomposition reaction”.
• Photodissociation, photolysis, or photodecomposition is a chemical reaction in which a chemical compound is broken down by photons.
• Hence statement B is not true.

Additional Information 

• A combination reaction is a reaction where two or more elements or compounds combine to form a single compound. Such reactions are represented by equations of the following form: X + Y → XY.
• The combination of two or more elements to form one compound is called a combination reaction.
• Other types of Chemical Reactions:
• Decomposition reaction: The opposite of a combination reaction, a complex molecule breaks down to make simpler ones.
• AB → A + B.
• Precipitation reaction: Two solutions of soluble salts are mixed resulting in an insoluble solid (precipitate) forming.
• A + Soluble salt B  → Precipitate + soluble salt C.
• Neutralization reaction: An acid and a base react with each other. Generally, the product of this reaction is salt and water.
• Acid + Base → Salt + Water.
• Combustion reaction: Oxygen combines with a compound to form carbon dioxide and water. These reactions are exothermic, meaning they give off heat. 
• A + O2 → H2O + CO2.
• Displacement reaction: One element takes place with another element in the compound. 
• A + BC → AC + B.

Shortcut Trick

Total Work (LCM of 18, 60) = 180 units. Efficiency: Ratna = 10, Sanju = 3.

Work cycle (8 days): (3 days × 10) + (5 days × 3) = 30 + 15 = 45 units.

Cycles needed: 180 ÷ 45 = 4 full cycles.

Total time = 4 cycles × 8 days = 32 days.

∴ The correct answer is 32 days.

Alternate Method

Given: Ratna takes 18 days, Sanju takes 60 days. Sequence: Ratna (3 days), Sanju (5 days).

⇒ Work done by Ratna in 3 days = 3 × 10 = 30 units

⇒ Work done by Sanju in 5 days = 5 × 3 = 15 units

⇒ Total work in one cycle (8 days) = 30 + 15 = 45 units

⇒ Total cycles required = 180 ÷ 45 = 4

⇒ Total days = 4 cycles × 8 days/cycle = 32 days

∴ The correct answer is 32 days.

Additional Information

LCM Method for Total Work

Total work is assumed as the Least Common Multiple of individual time periods to ensure efficiencies are whole numbers.

Alternate Day / Sequential Work

In cyclic work, calculate the total work done in one complete cycle (sum of time periods of each person) and then divide the total work by this value.