RRC Group D Previous Year Paper 62 (Held On: 9 Oct 2018 Shift 1)

The correct answer is Football.

• Bembem Devi is associated with the sport of Football.

Key Points

• Oinam Bembem Devi:
• She is a football player.
• She plays as the Midfielder in the Women's Football Team of India.
• She is also called the Durga of Indian Football.
• She was awarded the Arjuna Award in the year 2017.
• She was given the Padma Shri award in 2020.
• =

 

Additional Information

• Football:
• The first football club in the world ‘Sheffield Football Club’ was founded in the year 1857 in England.
• The first Football club in India was ‘Dalhousie Club’.
• The apex institution of football is the ‘Federation of International Football Association’ (FIFA) was formed on May 21, 1904.
• The headquarters of FIFA is in Zürich, Switzerland.
• Football was included as a competitive game in Olympic Games officially in 1908.
• India took part in the World Olympic Football Competition in 1948 in London.
• The first World Cup was organised in Uruguay in 1930.
• In India, Indian Football Association (IFA) organises National Football Championship.
• The trophy awarded in their competition is called Santosh Trophy.

Shortcut Trick

For any expression of the form x + 1/x = 2, the only possible real value is x = 1.

Since cosecθ = 1/sinθ, the given equation is sinθ + 1/sinθ = 2, which implies sinθ = 1.

Therefore, sinⁿθ + cosecⁿθ = 1ⁿ + 1ⁿ = 1 + 1 = 2 for any power n.

Here n = 2018, so the value remains 2.

∴ The correct answer is 2.

Alternate Method

Given: sinθ + cosecθ = 2

Formula Used: cosecθ = 1/sinθ

⇒ sinθ + 1/sinθ = 2

⇒ (sin²θ + 1) / sinθ = 2

⇒ sin²θ − 2sinθ + 1 = 0

⇒ (sinθ − 1)² = 0

⇒ sinθ = 1

⇒ cosecθ = 1/1 = 1

⇒ sin²⁰¹⁸θ + cosec²⁰¹⁸θ = (1)²⁰¹⁸ + (1)²⁰¹⁸

⇒ 1 + 1 = 2

∴ The correct answer is 2.

Additional Information

Reciprocal Trigonometric Relations

Standard pairs like (sinθ, cosecθ), (cosθ, secθ), and (tanθ, cotθ) follow the property that if their sum is 2, then each individual ratio must be 1.

General Power Rule

If x + 1/x = 2, then xⁿ + 1/xⁿ = 2 for all natural numbers n. This is frequently used in Algebra and Trigonometry.

Minimum Value Property

For positive real numbers, the sum of a number and its reciprocal (x + 1/x) is always ≥ 2 (Arithmetic Mean ≥ Geometric Mean).

Shortcut Trick

Work left after 6 days = Work of 48 men for (30 − 6) = 24 days.

Remaining men = 48 − 12 = 36 men.

Using M₁D₁ = M₂D₂: 48 × 24 = 36 × Days.

Days = (48 × 24) ÷ 36 = 4 × 8 = 32 days.

∴ The correct answer is 32 days.

Alternate Method

Total Work = Men × Days

⇒ Total Work = 48 × 30 = 1440 units

⇒ Work done in 6 days = 48 × 6 = 288 units

⇒ Remaining Work = 1440 − 288 = 1152 units

⇒ Remaining Men = 48 − 12 = 36 men

⇒ Time taken = Remaining Work ÷ Remaining Men

⇒ Time taken = 1152 ÷ 36 = 32 days

∴ The correct answer is 32 days.

Additional Information

Chain Rule Formula

The fundamental relation is M₁D₁H₁/W₁ = M₂D₂H₂/W₂, where M is men, D is days, H is hours, and W is work.

Inverse Variation

For a constant amount of work, the number of men is inversely proportional to the time taken (M ∝ 1/D).

Work & Wages

Wages are always distributed in the ratio of the actual work done by each individual or their efficiencies.

Given,

Statements:

• No paper is a book.
• All books are bag.

Conclusions:

I. No bag is a paper.

II. Some bags are paper.

The least possible Venn diagram for the given statements is as follows:

Conclusions:

I. No bag is a paper. → False (It is possible but not definite)

II. Some bags are paper. → False (It is possible but not definite)

• Here, conclusions I and II form a complementary pair.
• Therefore, either I or II follows.

Hence, the correct answer is "Either I or II follows." 

Note: The official answer key is "Neither I nor II follows." However, this is incorrect. Because this is an either-or case. So, we have changed the answer accordingly.

Shortcut Trick To find the range of a number rounded to n decimal places, the lower bound is value − 0.5 × 10−n and the upper bound is value + 0.5 × 10−n. For 15.84 (2 decimal places), the error interval is ± 0.005. Lower Limit = 15.84 − 0.005 = 15.835 (inclusive). Upper Limit = 15.84 + 0.005 = 15.845 (exclusive). ∴ The correct answer is 15.835 ≤ x < 15.845.

Alternate Method Given: Number x = 15.84 (rounded to 2 decimal places). Formula Used: For a value rounded to the nearest unit of precision (d), the error interval is x − d/2 ≤ x < x + d/2.

⇒ Precision (d) = 0.01 (since it is 2 decimal places). ⇒ Lower Bound = 15.84 − (0.01 ÷ 2) = 15.84 − 0.005 = 15.835. ⇒ Upper Bound = 15.84 + (0.01 ÷ 2) = 15.84 + 0.005 = 15.845. ⇒ According to rounding rules, any value from 15.835 up to but not including 15.845 rounds to 15.84. ∴ The correct answer is 15.835 ≤ x < 15.845.

Additional Information Degree of Accuracy The degree of accuracy is half the unit to which the number is rounded. For rounding to 1 decimal place, accuracy is ±0.05. Error Intervals An error interval is written as Lower Bound ≤ x < Upper Bound. The upper bound is excluded because 15.845 would normally round up to 15.85. Significant Figures Similar rules apply to significant figures. If 16 is correct to 2 sig figs, the range is 15.5 ≤ x < 16.5.

The correct answer is Wrinkled seed.

• Wrinkled seed is a recessive characteristic in a pea plant.

Key Points

• Mendel experiments of inheritance:
• Pea plant was used by Mendel for this experiment.
• It was chosen because this plant has many contrasting characters like a dwarf and tall or wrinkled or round seeds.
• Gregor Mendel, through his experiments on pea plants, discovered the fundamental laws of inheritance.
• His breeding experiments in pea plants revealed that hereditary characteristics are determined by discrete factors (genes) that are transmitted to the next generation.
• He deduced three laws from his experiments and these laws are applicable when parents are pure breeding.
• The three laws of inheritance proposed by Mendel include:
• Law of Dominance
• Law of Segregation
• Law of Independent Assortment
• 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.​

Shortcut Trick

The sum of all interior angles of any quadrilateral is always 360°.

Since all four angles are equal, let each angle be x.

⇒ 4 × x = 360°

⇒ x = 360° ÷ 4 = 90°

∴ The correct answer is 90°.

Alternate Method

Given:

A quadrilateral where all four angles are equal.

Formula Used:

Sum of interior angles of a polygon = (n − 2) × 180°, where n is the number of sides.

Calculations:

For a quadrilateral, n = 4.

⇒ Sum of angles = (4 − 2) × 180°

⇒ Sum of angles = 2 × 180° = 360°

The correct answer is Ankit Kawatra.

• Ankit Kawatra won the Queen's Young Leader Award for 2017 at a ceremony held at Buckingham Palace.

Key Points

• Ankit Kawatra:
• He is an activist, fighting hunger and malnutrition.
• ​He is the founder of Feeding India.
• He received the award from Queen Elizabeth II for doing exceptional work solving hunger and malnutrition in India.

Additional Information

• Palbinder Kaur Shergill is the first turbaned Sikh woman to be appointed Canada SC judge.
• Srinivas Gokulnath is the first solo Indian to complete Race Around Austria.
• Tanmanjeet Singh Dhesi is a Member of the Parliament of the United Kingdom.

The correct answer is Any pair of objects.

• The universal law of gravitation applies to any pair of objects.

Key Points

• Gravitational Force:
• Mathematically, it is represented as:
• $F = {GMm\over r^2}$
• Where,
• F is the gravitational force
• G is gravitational constant
• M is the mass of the first particle
• m is the mass of the second particle
• r is the distance between them
• This is called Newton’s universal law of gravitation.
• The value of G is 6.67 × 10^-11 N m²/kg².

Additional Information 

• 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 $g = {GM_e \over R_e^2}$
• 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.
• 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 6th.

Key Points

• The rise of Jainism and Buddhism saw religious unrest in India in the 6th century BC.
• Jainism:
• It was founded by Rishabhnath.
• According to Jain tradition, there were 24 Tirthankaras, the first being Rishabhadeva/Adinatha and the last being Mahavira.
• The Vishnu Purana and the Bhagavat Purana describes Rishabh as an incarnation of Narayana.
• The name of two Jain Tirthankaras– Rishabha and Arishtanemi is found in Rigveda.
• Parshvnath: His four main teachings (Chaturthi) were:
• Ahimsa (non-injury);
• Satya (non-lying);
• Asteya (non-stealing);
• Aparigraha (non-possession).
• Mahavira adopted all these four teachings and added one more, i.e., Brahmacharya (chastity) to it.
• Buddhism:
• Gautama Buddha was the founder of Buddhism, was born in 563 BC.
• He renounced home at the age of 29, this was his Mahabhiniskramana.
• At the age of 35, under a peepal tree at Uruvell (Bodh Gaya) on the bank of river Niranjana, he attained Nirvana (enlightenment) after 49 days of continuous meditation.
• Buddha delivered his first sermon at Sarnath to his five disciples.
• It is known as Dharmachaka Pravartana (turning of the wheel of law).
• He died at the age of 80 in 483 BC at Kushinagar.
• This is known as Mahaparinirvana (final blowing out).

Shortcut Trick Net filling rate = (A × B) ÷ (B − A) where A is filling time and B is emptying time. Time taken = (8 × 10) ÷ (10 − 8) Time taken = 80 ÷ 2 = 40 hours. ∴ The correct answer is 40 hours. Alternate Method Given: Filling Tap (A) = 8 hours, Emptying Tap (B) = 10 hours. Formula Used: Total Work = LCM of time durations; Efficiency = Total Work ÷ Time.

Tap Time (hr) Total Capacity (LCM) Efficiency

Tap A (Fill) 8 40 units +5

Tap B (Empty) 10 −4

⇒ Net efficiency of (A + B) = 5 − 4 = 1 unit/hour. ⇒ Total time required = Total Capacity ÷ Net Efficiency ⇒ Total time = 40 ÷ 1 = 40 hours. ∴ The correct answer is 40 hours. Additional Information Pipes and Cisterns Convention An inlet pipe (filling) is always considered to have positive efficiency, while an outlet pipe (emptying) has negative efficiency. Net Work Formula If pipe A fills in 'x' hours and pipe B empties in 'y' hours (where y > x), net work per hour = (1/x − 1/y). Total Capacity The Least Common Multiple (LCM) of individual times is taken as the total volume or capacity of the tank for easier calculation.

The correct answer is –3.2 ms–1.

Key Points

• Given, 
• Mass of bullet, m₁ = 40g (= 0.04 kg)
• Mass of pistol, m₂ = 2 kg
• The initial velocity of the bullet (u₁) and pistol (u₂) = 0
• Final velocity of the bullet, v₁ = +160m s^-1
• Let, v₂ be the recoil velocity of the pistol.
• The total momentum of the pistol and bullet is zero before the fire because both are at rest.
• The total momentum of the pistol and bullet after it is fired is

                     = (0.0 kg 4x 160 m s^-1) + (2 kg x v₂ m s^-1)

                     = (6.4 + 2v₂) kg m s^-1

• Total momentum after the fire = Total momentum before the fire
• 6.4 + 2v₂ = 0
• →v₂ = 3.2 m/s
• Thus, the recoil velocity of the pistol is 3.2 m/s.

The correct answer is CaO.

• The chemical formula of unextinguished lime is CaO.

Key Points

• Lime:
• It is also known as unextinguished lime, quick lime or burnt lime.
• It is chemically calcium oxide.
• It is a white, caustic, alkaline, crystalline solid at room temperature.
• It is used in the manufacture of glass, cement, etc. and for drying ammonia and alcohol.

Additional Information

• CaCO₃ is the chemical formula of calcium carbonate.
• CaSO₄ is the chemical formula of calcium sulfate.
• CaCl₂ is the chemical formula of Calcium chloride.

Shortcut Trick

Convert mixed fraction 1(3/11) to improper fraction → (11×1 + 3)/11 = 14/11.

Square the fraction → (14/11)² = 14² / 11².

Result → 196 / 121.

∴ The correct answer is 196/121.

Alternate Method

Given: Mixed fraction = 1(3/11)

Formula: (a/b)² = a² / b²

⇒ 1(3/11) = (11 × 1 + 3) / 11

⇒ 14 / 11

⇒ (14 / 11)² = (14 × 14) / (11 × 11)

⇒ 196 / 121

∴ The correct answer is 196/121.

Additional Information

Fraction Squaring Rule

To square any fraction, square the numerator and the denominator separately: (x/y)ⁿ = xⁿ / yⁿ.

Mixed to Improper Conversion

For a mixed fraction A(b/c), the improper form is (A × c + b) / c.

Square Table Reference

Knowing squares up to 25 is vital: 11² = 121, 12² = 144, 13² = 169, 14² = 196, 15² = 225.

The correct answer is Sharda Sinha.

• Sharda Sinha was honoured with the 2018 Padma Bhushan award in the field of art-music.

Key Points

• Sharda Sinha:
• ​She is a Maithili-language folk-singer.
• She sings in Bhojpuri and Magahi languages too.
• She was honoured with the Padma Bhushan award in the year 2018 in the field of art-music.
• She was honoured with the Padma Shri in the year 1991.
• Padma Bhushan:
• The award is given for distinguished service of a high order in any field, including service rendered by government servants.
• It is the third-highest civilian honour in India.
• It was first awarded in 1954.

Additional Information

• Kaifi Azmi was an urdu poet.
• Gulzar was a lyricist, poet, author, screenwriter, and film director.
• His real name was Sampooran Singh Kalra.
• He was awarded the Padma Bhushan award in the year 2004.
• Javed Akhtar is a poet, lyricist, screenwriter and political activist. 
• He was awarded the Padma Bhushan award in the year 2007.

The logic followed here is as follows:

• The option figure D is the odd one out as it represents two perpendicular lines.
• Option figure A, option figure B and option figure C represents two parallel lines.

Hence, option figure D is the correct answer.

Shortcut Trick

To find the ratio A : C, directly multiply the given ratios (A/B) and (B/C).

A/C = (A/B) × (B/C)

A/C = (5/8) × (18/25)

A/C = (1 × 9) / (4 × 5) = 9/20

∴ The correct answer is 9 : 20.

Alternate Method

Given: A : B = 5 : 8 and B : C = 18 : 25

To combine the ratios, make the value of B common by taking the LCM of 8 and 18.

⇒ LCM(8, 18) = 72

⇒ A : B = (5 × 9) : (8 × 9) = 45 : 72

⇒ B : C = (18 × 4) : (25 × 4) = 72 : 100

⇒ A : B : C = 45 : 72 : 100

⇒ A : C = 45 : 100

⇒ A : C = 9 : 20 (Dividing by 5)

∴ The correct answer is 9 : 20.

Additional Information

Compound Ratio

The compound ratio of two ratios a:b and c:d is (ac) : (bd).

Duplicate and Triplicate Ratios

Duplicate ratio of a:b is a²:b² and Triplicate ratio is a³:b³.

Invertendo and Alternendo

If a:b = c:d, then Invertendo is b:a = d:c and Alternendo is a:c = b:d.

The correct answer is 4.

• The Indian Railways is ranked 4th among the world's largest railways.

Key Points

• Indian Railways:
• Indian Railway Board was established in March 1905.
• Indian Railway was nationalised in 1951.
• Railways have been divided into 18th zones.
• Southern Coast Railway was the 18th zone.
• The first Indian railway line in India was operated for public traffic in 1853 between Mumbai and Thane over a distance of 34 km.
• Ashwini Vaishnaw is the current Minister of Railways. (As per Jan 2022)
• The first electric train ran in India with the inauguration of services between Bombay VT and Kurla Harbour on 3rd Feb 1925 on ex-GIP Railway system.
• It is ranked 4th among the world's largest railways.

The correct answer is Bhartiya Janata Party.

• Bhartiya Janata Party has won a majority of seats in the Gujarat Assembly Election 2017.

Key Points

• Gujarat Assembly Election 2017:
• It has a total of 182 seats in the assembly.
• Out of these 182, BJP won 99 seats.
• Congress won 77 seats.
• 1 seat was won by NCP.
• Bhartiya Tribal Party and Independent won 2 and 3 seats respectively.

Additional Information

• Gujarat:
• Capital: Gandhinagar
• Governor: Acharya Devvrat
• Chief minister: Bhupendrabhai Patel
• Gujarat shares its borders with Madhya Pradesh,  Maharashtra and Rajasthan.
• It shares its international border with Pakistan.

Shortcut Trick

Check if the sides 12, 16, and 20 form a Pythagorean triplet:

12² + 16² = 144 + 256 = 400 = 20²

Since the condition is satisfied, it is a right-angled triangle where the longest side (20 m) is the hypotenuse.

Altitude to hypotenuse = (Product of legs) ÷ Hypotenuse

Altitude = (12 × 16) ÷ 20 = 192 ÷ 20 = 9.6 m.

∴ The correct answer is 9.6 m.

Alternate Method

Given: Sides of the triangle are a = 16 m, b = 12 m, and c = 20 m.

Formula Used: Area of triangle = (1/2) × Base × Height

⇒ Area of triangle = (1/2) × 16 × 12

⇒ Area = 96 m²

Given:

(–4)[20 $÷$ {(–2)$×$ (–8)}]

Concept used:

Calculation:

(-4)[20 ÷ {(–2) × (-8)}] 

⇒ (-4)[20 ÷ 16]

⇒ - 4 × 20/16

⇒ 20/- 4

⇒ - 5

∴ Required answer is - 5

The correct answer is Ebonite.​

Concept:

• Resistivity (ρ): The property of a conductor that opposes the flow of electric current through them and is independent of the shape and size of the materials but depends on the nature and temperature of the materials is called resistivity.
• The unit for resistivity is the ohm-meter (Ω-m).
• The resistivity of a material depends on its nature and the temperature of the conductor.
• The resistivity of a material doesn't depend on its shape and size (length and area).
• Materials that conduct electrical current easily are called conductors and have a low resistivity.
• Materials that do not conduct electricity easily are called insulators and these materials have a high resistivity.
• Resistivity is inversely proportional to the number of free electrons per unit volume of the conductor and to the average relaxation time of the free electrons in the conductor.

Resistivity is numerically equal to the resistance of a substance having a unit area of cross-section and unit length.

• The formula of resistivity is $\rho = \frac{m}{{n{e^2}\tau }}$
• Where, m = mass of an electron, n = number of electrons per unit volume of the conductor, τ = relaxation time.

Explanation:

Hence the correct answer is Ebonite.

Shortcut Trick

To find the square root of 519841, look at the last digit: 1. The square root must end in 1 or 9.

Ignore the last two digits (41) and find the largest square less than 5198.

Since 70² = 4900 and 80² = 6400, the first two digits are 72 (as 72² = 5184).

Check 721²: 518400 + 1440 + 1 = 519841.

∴ The correct answer is 721.

Alternate Method

Given: Number = 519841

Method: Long Division Method for finding square root.

⇒ Grouping the digits in pairs from right to left: 51, 98, 41.

⇒ Step 1: Find the largest square less than or equal to 51. 7 × 7 = 49. Remainder = 2.

⇒ Step 2: Bring down 98. New dividend = 298. Double the divisor (7 × 2 = 14).

⇒ Step 3: Find digit 'x' such that 14x × x ≤ 298. 142 × 2 = 284. Remainder = 14.

⇒ Step 4: Bring down 41. New dividend = 1441. Double the quotient (72 × 2 = 144).

⇒ Step 5: Find digit 'y' such that 144y × y = 1441. 1441 × 1 = 1441. Remainder = 0.

⇒ The quotient is 721.

∴ The correct answer is 721.

Additional Information

Unit Digit Property

A perfect square ending in 1 must have a square root ending in either 1 or 9.

Range Estimation

Always identify the nearest base (like 700² = 490,000) to quickly narrow down options in competitive exams.

The correct answer is chemical.

• To maintain the current in a given electrical circuit, the cell has to expend chemical energy stored in it.

Key Points

• When the cell is connected to a circuit, the potential difference sets the charges in motion and produces an electric current.
• In order to maintain the current in a given electric circuit, the cell has to expend the chemical energy stored in it.
• By this, the cell helps maintain a potential difference across the ends of a circuit and current starts to flow across the circuit from higher potential end to lower.
• Electrochemical Cell
• An electrochemical cell is a device that converts chemical energy into electrical energy.
• Primary Cell:
• In a primary cell, electrical energy is obtained from the irreversible chemical reaction taking place inside the cell.
• Examples: Voltaic Cell, Leclanche Cell, Daniel Cell, Dry Cell, etc.

Shortcut Trick Ratio of SP1 to SP2 in percentage terms: 105% → Rs. 420. Using unitary method: 1% → 420 ÷ 105 = Rs. 4. For SP2 = Rs. 380, the percentage value = 380 ÷ 4 = 95%. Net result = 95% − 100% = −5% (Loss). ∴ The correct answer is L = 5%.

Alternate Method Given: SP1 = Rs. 420, Profit1% = 5%, SP2 = Rs. 380. Formulas: CP = SP × 100 ÷ (100 + P%), Loss% = (CP − SP) ÷ CP × 100.

⇒ Cost Price (CP) = 420 × 100 ÷ (100 + 5) = 420 × 100 ÷ 105 = Rs. 400. ⇒ For New Selling Price (SP2) = Rs. 380. ⇒ Since CP > SP2, there is a Loss. ⇒ Loss Amount = 400 − 380 = Rs. 20. ⇒ Loss % = (20 ÷ 400) × 100 = 5%. ∴ The correct answer is L = 5%.

Additional Information Cost Price & Selling Price Relationship When SP > CP, it is a Profit. When SP < CP, it is a Loss. Both Profit% and Loss% are always calculated on the Cost Price unless stated otherwise. Percentage Change A 5% gain means the Selling Price is 105% of the Cost Price. A 5% loss means the Selling Price is 95% of the Cost Price.

The notice in the newspaper is inviting tenders from contractors for the building of the said bridge.

• Thus, it is clear that the municipality is planning to build a bridge. So, conclusion I follows.
• The invitation for tenders implies that the municipality is looking for a contractor who would be interested in building the bridge, it does not mean that the municipality wants to know how many people are interested. Thus, conclusion II does not follow.

Hence the correct answer is option 1.

The correct answer is Nikola Tesla.

• Alternating current was invented by Nikola Tesla.

Key Points

• Alternating current:
• It is an electric current that periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction.
• It was invented by Nikola Tesla.

Additional Information

• A rectifier is a device that converts alternating voltage (current) into direct voltage (current).
• An inverter is a device that converts direct voltage (current) into alternating voltage (current).

The logic followed here is:

• Ate is the past tense of Eat.

Similarly, 

• Bought is the past tense of Buy.

Hence, "Bought" is the correct answer.

At 9 am a general clock looks as follows:

The minute hand faces towards the north and the hour hand faces towards the west.

Hence, "west" is the correct answer.

The logic followed here is:

• The arrows in option figure A, option figure C and option figure D are moving in the clockwise direction
• The arrow in option figure B is moving in the anticlockwise direction.

Hence, "option figure B" is the correct answer.

Given,

Statements:

• Some lions are tigers.
• Some tigers are donkeys.

Conclusions:

1. Some lions are donkeys.
2. All tigers are donkeys.

The least possible Venn diagram for the given statements is as follows:

Conclusions:

I. Some lions are donkeys. → False (It is possible but not definite)

II. All tigers are donkeys. → False (It is possible but not definite)

Hence, the correct answer is "Neither I nor II follows."

In mirror images,

• The left side becomes the right side and vice versa.

So, the mirror image of the question figure will appear as follows:

Hence, "option figure A" is the correct answer.

Shortcut Trick

Identify the frequency of each number in the given data set.

The number 25 appears 2 times.

The number 45 appears 2 times.

All other numbers appear only once.

Since 25 and 45 have the highest frequency, both are modes.

∴ The correct answer is 45, 25.

Alternate Method

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

⇒ Arrange the data in ascending order: 12, 25, 25, 42, 45, 45, 54, 58, 59, 60, 65, 87

⇒ Frequency of 25 = 2

⇒ Frequency of 45 = 2

⇒ Frequency of all other numbers = 1

⇒ Mode is defined as the value that occurs with the highest frequency.

⇒ Since both 25 and 45 occur twice, the data is bimodal.

∴ The correct answer is 45, 25.

The correct answer is Cloning.

• In the process of cloning, the cell is involved in the generation of an exact copy of another living part of a complete organism.

Key Points

• Cloning:
• The process of generating a genetically identical copy of a cell or an organism.
• The cell is involved in the generation of an exact copy of another living part of a complete organism.
• Cloning happens often in nature—for example when a cell replicates itself asexually without any genetic alteration or recombination.

Additional Information

• IVF
• In vitro fertilization (IVF) is a type of assistive reproductive technology (ART).
• It involves recovering eggs from a woman's ovaries and fertilizing them with sperm.
• This fertilized egg is known as an embryo.
• Fructification is a process of fructifying.
• Regeneration is the process of restoring damaged or missing cells, tissues, organs sometimes even entire body parts to full function in plants and animals.

Shortcut Trick

Sum of remaining two fractions = 6 − 1¼ = 4.75

Ratio of these two fractions = 9 : 10 (Total parts = 19)

Value of 1 part = 4.75 ÷ 19 = 0.25

Largest fraction = 10 parts = 10 × 0.25 = 2.5

∴ The correct answer is 2½.

Alternate Method

Given: Sum = 6, Fraction₁ = 1¼ = 5/4, Ratio of others = 9 : 10

Formula: Sum of fractions = F₁ + F₂ + F₃

⇒ Let the other two fractions be 9x and 10x.

⇒ 5/4 + 9x + 10x = 6

⇒ 1.25 + 19x = 6

⇒ 19x = 6 − 1.25 = 4.75

⇒ x = 4.75 / 19 = 0.25 = 1/4

⇒ Fraction₂ = 9 × 1/4 = 2.25

⇒ Fraction₃ = 10 × 1/4 = 2.5 = 2½

⇒ Comparing 1.25, 2.25, and 2.5; the largest is 2.5.

∴ The correct answer is 2½.

Additional Information

Mixed Fractions to Improper

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

Ratio Distribution

If a sum S is divided in ratio a:b, then parts are [a/(a+b)]×S and [b/(a+b)]×S.

The logic followed here is:

• Smell(fragrance) comes from Rose.

Similarly, 

• Wisdom comes from experience.

Hence, "Experience" is the correct answer.

The logic followed here is:

All the elements are moving in a clockwise direction.

• The arrows are changing their direction alternately.
• The letters sF and Fs are changing their positions alternately.
• The signs ± + and ± are also changing their positions alternately.

Hence, option figure C is the correct answer.

The correct answer is Arthropoda.

• Arthropoda is probably the largest group of creatures.

Key Points

• ​Main features of Arthropoda:
• The body is divided into three parts– Head, Thorax and Abdomen.
• The body is covered with a thick chitinous exoskeleton.
• Jointed leg.
• The circulatory system is of open type.
• Its body cavities are called haemocoels.
• The trachea, book lungs, body surface are respiratory parts.
• These are mainly unisexual and fertilization takes place inside the body.
• Example: Cockroach and Prawn.

Total production of the year is 150000 tonnes

Woolen garments = 15%

So, 150000 × 15/100

⇒ 22500

∴ The production of woolen garments (in tonnes) in 2014 is 22500

Shortcut Trick

To find the LCM of 112, 24, and 48, observe that 48 is a multiple of 24, so we only need the LCM of 112 and 48.

Ratio of 112 : 48 → 7 : 3 (dividing by 16).

LCM = 112 × 3 = 336.

∴ The correct answer is 336.

Alternate Method

Given: Numbers are 112, 24, and 48.

Formula Used: Prime Factorization Method.

⇒ Prime factorization of 112 = 2 × 2 × 2 × 2 × 7 = 2⁴ × 7¹

⇒ Prime factorization of 24 = 2 × 2 × 2 × 3 = 2³ × 3¹

⇒ Prime factorization of 48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3¹

⇒ LCM = Product of highest powers of all prime factors involved.

⇒ LCM = 2⁴ × 3¹ × 7¹

⇒ LCM = 16 × 3 × 7

⇒ LCM = 48 × 7 = 336.

∴ The correct answer is 336.

Additional Information

LCM Definition

The Least Common Multiple (LCM) is the smallest positive integer that is divisible by each of the given numbers.

LCM and HCF Relationship

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

Division Method

LCM can also be found by dividing the numbers by common prime factors until all quotients become 1.

The correct answer is Prabodhankar Thackeray.

• The statue of Prabodhankar Thackeray was unveiled by Maharashtra Chief Minister Devendra Fadnavis at the headquarters of the Greater Mumbai Municipal Corporation.

Key Points

• Keshav Sitaram Thackeray:
• Prabodhankar Thackeray was his pen name .
• He rosed his voice against superstitions, untouchability, child marriage and dowry.
• He was the leader of Samyukta Maharashtra Samiti.
• He was the father of Bal Thackeray, the founder of Shiv Sena.
• His statue was unveiled by Maharashtra Chief Minister Devendra Fadnavis at the headquarters of the Greater Mumbai Municipal Corporation.

Additional Information

• Maharashtra:
• Chief Minister - Eknath Shinde
• Governor - Bhagat Singh Koshyari.
• Number of Districts - 36.
• Lok Sabha seats - 48.
• Rajya Sabha seats - 19.
• Founded: 1 May 1960

Shortcut Trick

Rate of 5% is equivalent to the fraction 1/20.

Since the population increases, the growth factor per year is (1 + 1/20) = 21/20.

To find the population 2 years ago, we multiply the current population by the reciprocal factor twice: (20/21)².

Population = 54000 × (20/21) × (20/21) ≈ 54000 × 0.907 ≈ 48979.59.

Rounding to the nearest whole number, we get 48980.

∴ The correct answer is 48980.

Alternate Method

Given:

Population in 2018 (A) = 54000

Annual growth rate (R) = 5%

Time period (n) = 2 years

Formula Used:

Future Population = Past Population × (1 + R/100)ⁿ

⇒ Past Population (P) = A ÷ (1 + R/100)ⁿ

Calculations:

⇒ P = 54000 ÷ (1 + 5/100)²

⇒ P = 54000 ÷ (1 + 1/20)²

⇒ P = 54000 ÷ (21/20)²

⇒ P = 54000 × (20/21) × (20/21)

⇒ P = 54000 × (400 / 441)

⇒ P = 21600000 ÷ 441

⇒ P ≈ 48979.59

⇒ P ≈ 48980 (approx.)

∴ The correct answer is 48980.

Additional Information

Compound Growth Formula

When a quantity increases at a constant rate, the value after n years is A = P(1 + R/100)ⁿ, where P is the initial value.

Effective Percentage Change

For two successive percentage changes of a% and b%, the net change is [a + b + (ab/100)]%.

Depreciation Rule

If a value decreases (like machinery or population decline), the formula becomes A = P(1 − R/100)ⁿ.

The parts given in the question figure can together make the options figure B as follows:

• Option figures A, C, and D have either additional parts or fewer parts as given in the question figure.

Hence, option figure B is the correct answer.

Note: This question was ignored in the official exam due to a discrepancy. We have modified the question to make it logical.

The correct answer is  625 J.

Key Points

• Given,
• Force, F = 125 N
• Displacement, S = 5m
• Work done = Force x Displacement
• = 125 x 5
• = 625 J.

The correct answer is graphite.

• In graphite, each carbon atom is bonded to three other carbon atoms in the same plane giving a hexagonal array.

Key Points

• Graphite:
• It is also known as plumbago or black lead.
• It is soft, greasy, dark greyish coloured crystalline solid.
• It is a good conductor of heat and electricity.
• It is chemically more reactive than diamond.
• Its layer structure is headed by weak van der Waal’s forces.
• Each carbon atom is bonded to three other carbon atoms in the same plane giving a hexagonal array.

 

Additional Information

• In the structure of a diamond, each carbon atom joins four other carbon atoms in regular tetrahedrons.
• In the structure of propene, each carbon atom joins four other carbon atoms.
• In the structure of Benzene, each carbon atom joins four other carbon atoms.

The correct answer is 1.25 m.

• Given,
• t = 0.5 sec
• g=a = 10m/s².
• u = 0 m/s
• Using first law of motion
• v = u+at
• v = 0+10x0.5
• v = 5 m/s
• By the second law of motion to compute distance travelled:
• $s =ut+ 1/2{ (at^2)}$
• s = 0+ 0.5x10x0.5²
• s = 1.25 m

Shortcut Trick

Let Radha's current age be 1 unit, then Sudha's is 2 units.

According to the condition: (2x + 4) = 4 × (x − 6).

Solving this: 2x + 4 = 4x − 24 ⇒ 2x = 28 ⇒ x = 14 years.

Current ages: Sudha = 28 years, Radha = 14 years.

Ages 2 years ago: 26 years and 12 years.

∴ The correct answer is 26 years and 12 years.

Alternate Method

Given: Sudha (S) = 2 × Radha (R).

Calculation:

⇒ Let current age of Radha = x

⇒ Current age of Sudha = 2x

⇒ (2x + 4) = 4(x − 6)

⇒ 2x + 4 = 4x − 24

⇒ 4x − 2x = 24 + 4

⇒ 2x = 28

⇒ x = 14 (Radha's current age)

⇒ 2x = 28 (Sudha's current age)

⇒ Ages 2 years ago: Sudha = 28 − 2 = 26 years; Radha = 14 − 2 = 12 years.

∴ The correct answer is 26 years and 12 years.

Additional Information

Ratio of Ages

When the age of two persons is given in a ratio, the difference between their ages remains constant throughout time.

Linear Equations in Ages

Always define variables based on the current age to simplify calculations for past or future conditions.

Verification Method

Back-substitution of options into the original conditions is often the fastest way to solve age-based multiple-choice questions.

Shortcut Trick

Let the speed of Jack be S₁ and Jill be S₂.

From given conditions: 4.5S₁ − 3S₂ = 6 and 5S₂ − 6S₁ = 5.

Multiply the first equation by 5 and the second by 3 to eliminate S₂: 22.5S₁ − 15S₂ = 30 and 15S₂ − 18S₁ = 15.

Adding these gives: 4.5S₁ = 45 ⇒ S₁ = 10 km/hr.

∴ The correct answer is 10 km/hr.

Alternate Method

Given: Time for Jack = 4.5 hrs, Time for Jill = 3 hrs, Diff = 6 km. Time for Jack = 6 hrs, Time for Jill = 5 hrs, Diff = −5 km.

Formula Used: Distance = Speed × Time

⇒ Let Jack speed = x and Jill speed = y.

⇒ 4.5x = 3y + 6 --- (Eq 1)

⇒ 6x = 5y − 5 --- (Eq 2)

⇒ From Eq 1: 3y = 4.5x − 6 ⇒ y = 1.5x − 2

⇒ Substitute y in Eq 2: 6x = 5(1.5x − 2) − 5

⇒ 6x = 7.5x − 10 − 5

⇒ 1.5x = 15

⇒ x = 10 km/hr

∴ The correct answer is 10 km/hr.

Additional Information

Average Speed

Total distance divided by total time. For two equal distances with speeds a and b, Average Speed = 2ab/(a+b).

Relative Speed

Speeds add up when moving in opposite directions (a+b) and subtract when moving in the same direction (a−b).

Unit Conversion

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

The correct answer is CO₂.​

Key Points

• Calcium hydroxide (Ca(OH)₂) reacts slowly with the carbon dioxide (CO₂) in the air to form a thin layer of calcium carbonate (CaCO₃).
• The layer is formed after two to three days of whitewashing and gives a shiny finish to the walls.
• Calcium carbonate is the chemical name of limestone.

The logic followed here is as follows:

Hence, "J" is the correct answer.

The correct answer is Actinide.

• Radioactive elements are placed in actinides.

Key Points

• Actinides:
• It is a series of 15 consecutive chemical elements in the periodic table from actinium (Ac) to lawrencium (Lr).
• From atomic numbers 89–103.
• All the elements are radioactive.
• Radioactivity
• Radioactivity was discovered by Henry Becquerel, Madame Curie and Pierre Curie for which they jointly won Nobel Prize.
• γ-rays are emitted after the emission of α and β rays.
• Alpha rays are positively charged helium nuclei (1/2 He), beta rays are negatively charged electrons and gamma rays are chargeless photons.
• The end product of all-natural radioactive elements after the emission of radioactive rays is lead.

Additional Information

• Lanthanides are a series of 15 naturally occurring metallic chemical elements.
• Their atomic numbers fall between 57 (Lanthanum) and 71 (Lutetium).

The correct answer is Sound.

• Sound cannot travel in a vacuum.

Key Points

• Sound Wave:
• It is a longitudinal mechanical wave.
• The longitudinal mechanical waves which lie in the range of 20 Hz to 20,000 Hz are called audible or sound waves.
• It cannot travel in a vacuum.
• The longitudinal mechanical waves having frequencies less than 20 Hz are called infrasonic. These are produced by earthquakes, volcanic, eruptions, Ocean waves, elephants, and whales.
• The longitudinal mechanical waves having frequencies greater than 20,000 Hz are called ultrasonic waves.

Additional Information

• Heat, Light and UV rays can travel in a vacuum.

The correct answer is 6.

• 6 atoms are present in the sodium carbonate molecule.

Key Points

• The formula of sodium-carbonate is Na₂CO₃.
• It contains 2 sodium atoms, 3 oxygen atoms and one carbon atom.
• Hence, the total number of atoms is 6.

Additional Information

• Uses of sodium carbonate:  
• It is used in the production of detergents and soaps.
• It is used in the manufacturing of glass.
• It is used in the production of rayon polymers.
• It is used in water softening.
• It is used as a raising agent, food additive as an anticaking agent, stabilizer etc.

The correct answer is 3.

• The maximum number of bonds a covalent bond can have between two atoms is 3.

Key Points

• Covalent bond:
• A bond formed between two same or different atoms by mutual contribution and sharing of electrons is called a covalent bond.
• Co-ordinate bond (or Dative bond): Coordinate bond is a special type of covalent bond in which one atom donates electrons to other atoms.
• The bonding between donor to acceptor atom is called co-ordinate bond.
• The maximum number of bonds a covalent bond can have between two atoms is 3.

The correct answer is South Africa.​

Key Points

• The Cape of Good Hope is located in South Africa.
• It is a rocky point on the Atlantic coast of the Cape Peninsula in South Africa.
• The Cape of Good Hope is a section of the Table Mountain National Park.
• It was earlier known as Cape Colony established by the Dutch in 1652.

 

Additional Information

• South Africa:
• Capitals: Cape Town, Pretoria, Bloemfontein
• President: Cyril Ramaphosa
• Currency: South African rand

Shortcut Trick

For a system of linear equations to have no solution, the lines must be parallel.

Condition: a₁/a₂ = b₁/b₂ ≠ c₁/c₂

From the equations: 8/20 = 5/(−k)

⇒ 2/5 = 5/(−k) ⇒ −2k = 25 ⇒ k = −12.5

∴ The correct answer is −12.5.

Alternate Method

Given Equations:

1. 8x + 5y + 11 = 0

2. 20x − ky − 9 = 0

Formula Used:

For a pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, the condition for No Solution (Inconsistent System) is:

a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Calculations:

Identify coefficients from the given equations:

a₁ = 8, b₁ = 5, c₁ = 11

a₂ = 20, b₂ = −k, c₂ = −9

Applying the condition a₁/a₂ = b₁/b₂:

⇒ 8/20 = 5/(−k)

Simplify the fraction 8/20 by dividing both by 4:

⇒ 2/5 = 5/(−k)

Cross-multiplying the terms:

⇒ 2 × (−k) = 5 × 5

⇒ −2k = 25

⇒ k = 25/(−2)

⇒ k = −12.5

Verify c₁/c₂ condition:

⇒ c₁/c₂ = 11/(−9) ≈ −1.22

⇒ Since 0.4 ≠ −1.22, the condition for no solution is strictly satisfied.

∴ The correct answer is −12.5.

Additional Information

Unique Solution (Intersecting Lines)

The system has a unique solution if the ratios of coefficients of x and y are not equal: a₁/a₂ ≠ b₁/b₂.

Infinite Solutions (Coincident Lines)

The system has infinitely many solutions if all ratios are equal: a₁/a₂ = b₁/b₂ = c₁/c₂.

Consistency of Equations

A system is Consistent if it has at least one solution (Unique or Infinite) and Inconsistent if it has no solution.

The correct answer is Bangladesh.

• Sheikh Hasina is the Prime Minister of Bangladesh.

Key Points

• Bangladesh:
• Capital: Dhaka.
• President: Abdul Hamid
• Prime Minister: Sheikh Hasina
• The Indian states of Assam, Mizoram, Tripura, Meghalaya, and West Bengal share their borders with Bangladesh.

Additional Information

• Ismail Sabri Yaakob is the Prime Minister of Malaysia.
• Salman bin Abdulaziz Al Saud is the King of Saudi Arabia.

To arrange the people from smallest to largest, we need all the four statements as follows:

Statement 1: G is the longest.

_ < _ < _ < _ < G

Statement 2. E is taller than F.

F < E

• Statements 1 and 2 when combined together are not sufficient to answer the question because there is no information about H and I.

Statement 3: H is the smallest.

H < _ < _ < _ < _

• Statements 1, 2, and 3 are not sufficient when taken together because there is no information about the size of I

Statement 4. F is taller than I.

I < F

• On combining statements 1, 2, 3, and 4, we get:
• H < I < F < E < G

Hence, "Statements 1, 2, 3 and 4 all together are sufficient" is the correct answer.

Confusion Points

• The fourth option "Every statement is sufficient" implies that we can determine the answer from any of the statements 1, 2, 3, and 4. Therefore, the fourth option is incorrect.

The correct answer is M. S. Swaminathan.

• M. S. Swaminathan has been awarded the 'Yeraringan Award'.

Key Points

• Green Revolution:
• It was launched in the year 1966 and was the brainchild of Norman Borlaug, though, in India, it was made successful by Dr M.S.
  

Swaminathan.

• The term ‘Green Revolution’ was coined by Dr William Gide.
• The achievements of the Green Revolution were the rise in cereal production especially wheat.
• Dr M.S. Swaminathan was awarded the 'Yeraringan Award' by the Vice President of India.
• Prof. M.S. Swaminathan was the first recipient of the Prize which was started by Norman Borlaug.

Given,

Statements:

I. No gates are sticks.

II. Some sticks are windows.

Conclusions:

1. All doors are windows. 2. Some sticks are gates.

The least possible Venn diagram for the given statements is as follows:

Conclusions:

I. All doors are windows. → False (It is not possible as the information about doors is not given)

II. Some sticks are gates. → False (It is not possible as no gates are sticks)

Hence, the correct answer is "Neither I nor II follows."

The correct answer is National Welfare Fund for Sportspersons.

• National Welfare Fund for Sportspersons was established in 1982 to support the outstanding sportspersons of the past year, sportspersons living in poverty conditions who brought glory to the country in sports.

Key Points

• National Welfare Fund for Sportspersons:
• It is also known as Pandit Deendayal Upadhyay National Welfare Fund For Sportspersons (PDUNWFS).
• It was set up in the year  1982.
• The motive of the scheme was to assist outstanding Sportspersons of past years, living in poverty circumstances who had brought glory to the country in sports.
• The scheme was revised in May 2016.
• The revised provisions contained to provide for lump sum ex-gratia assistance to outstanding Sportspersons of yesteryears.
• The scheme provides assistance for:
• injuries sustained during training for and participation in sports competitions.
• Assistance to Families of deceased Outstanding Sportspersons.
• Medical Treatment
• Assistance to coaches, support personnel, umpires, referees and match officials.

The logic used here is as follows:

Similarly,

Hence, "RGP" is the correct answer.

Shortcut Trick

Area of an equilateral triangle = 0.433 × (side)²

Given side = 19 cm

⇒ Area = 0.433 × 19²

⇒ Area = 0.433 × 361

⇒ Area = 156.313 cm²

∴ The correct answer is 156.31 cm².

Alternate Method

Given:

Side of the equilateral triangle (a) = 19 cm

Formula Used:

Area of equilateral triangle = (√3 / 4) × a²

Calculations:

⇒ Area = (√3 / 4) × (19)²

⇒ Area = (1.732 / 4) × 361

⇒ Area = 0.433 × 361

⇒ Area = 156.313 cm²

∴ The correct answer is 156.31 cm².

Additional Information

Height of Equilateral Triangle

The altitude or height (h) is given by the formula h = (√

The correct answer is Lake Titicaca.

• Lake Titicaca is the largest lake in South America.

Key Points

• Lake Titicaca:
• It is the largest lake in South America.
• It is also the world’s highest lake navigable to large vessels.
• The lake is situated 3,810 m above sea level.
• It is situated between Peru to the west and Bolivia to the east.

 

Additional Information

• Lake Poopo is a large saline water lake situated in Bolivia.
• Lake Valencia is the third largest lake in Venezuela
• Lake Janin is a lake in Quebec, Canada.

The correct answer is Four chambered hearts.

• Mammalian animals have four-chambered hearts.

Key Points

• Mammalia:
• Main features
• These are warm-blooded animals.
• There is no nucleus in their red blood cells (except in camel and lama).
• Mammalia is divided into three subclasses:
• Prototheria: It lays eggs, e.g., Echidna.
• Metatheria: It bears the immature child, e.g., Kangaroo.
• Eutheria: It bears the well-developed child, e.g., humans.
• They have a four-chambered heart.

Additional Information

• A fish has only a two-chambered heart.
• In amphibians, the heart is three-chambered.
• Crocodiles and birds' heart is also divided into four chambers.

The most appropriate Venn diagram for the word "Wool, Sweater, Hat"

 is as follows:

• Some sweaters and some hats are made up of wool.

Hence, option figure A is the correct answer.

Additional Information

• Sweaters were traditionally made from wool but can now be made of cotton, synthetic fibers, or any combination of these.

The correct answer is Mary Kom.

• Mary Kom won five-time gold medals in the Asian Women's Boxing Championship in the light flyweight (48kg) category.

Key Points

• MC Mary Kom:
• Her full name is Mangte Chungneijang Mary Kom.
• She is the only woman in the world to win the World Amateur Boxing Championship six times.
• She also won five-time gold medals in the Asian Women's Boxing Championship in the light flyweight (48kg) category.
• She is nicknamed Magnificent Mary.
• She is also a Member of Parliament, Rajya Sabha.

Important Points

• Karnam Malleswari is the first Indian woman to win a medal in an Olympic event.

The correct answer is Remains the same.

• If the potential difference and current through a circuit are doubled, then the resistance of the circuit remains the same.

Key Points

• Potential Difference:
• Work done in bringing a unit positive charge from one point to another point is the potential difference between the two points.
• Its SI unit is volt.
• It is a scalar quantity.
• Ohm’s Law
• The electric current flowing through a conductor is directly proportional to the potential difference across its ends.
• It is given by the formula:
• V=IR
• Given,
• V₁= 2V
• I₁= 2I
• hence, $R_1 = {V_1 \over I_1}$
• $R_1 = {2V\over 21}$
• Hence, the remains unchanged.

The correct answer is Only B is true.

Key Points

• Compressibility:
• It is the property by which a substance or matter can be reduced to a smaller space by pressure. Hence, statement A is false.
• Fluidity:
• It is a property of matter to flow easily and change shape under external force.
• This property is exhibited by both liquid and gas. Hence, statement B is true.

The correct answer is 57-71.

• The atomic number of lanthanide is in the 5-71 range.

Key Points

• Lanthanide:
• It is also called lanthanoid.
• It is any of the series of 14 consecutive chemical elements in the periodic table from lanthanum to lutetium i.e. atomic numbers 57–71 with 57 (Lanthanum) and 71 (Lutetium).
• Scandium and yttrium are rare-earth metals.

Additional Information

• Modern Periodic Table:
• It is a graphical representation of the Aufbau principle.
• It is based on the electronic configuration of elements and contains 118 elements.
• There are 7 periods and 18 groups.
• Modern periodic table is classified as:
  

i. s-block;

ii. p-block;

iii. d-block;

iv. f-block.

The correct answer is Tata Steel Ltd.

• Tata Steel Ltd won the Prime Minister's Trophy for Best Performing Integrated Steel Plant for the assessment years 2014-15 and 2015-16, on 8 December 2017.

Key Points

• Tata Steel Ltd.:
• It was earlier known as the Tata Iron and Steel Company Limited (TISCO).
• It was founded in the year 1907.
• Jamsetji Tata was the founder.
• Its headquarters are located in Mumbai, Maharashtra.

The logic used here is as follows:

• In option figures B, C, and D, the lines are equidistant.
• But in option A one of the lines is placed far from the remaining 3 lines.

Hence, option figure A is the correct answer.

The correct answer is 8 - 12 May 2017.​

Key Points

• From 8th - 12th May 2017, India organized the Cultural Festival in Egypt to mark the 156th birth anniversary of Rabindranath Tagore.
• The event was organised by the cultural wing Indian Embassy in Egypt.

Important Points

• Rabindranath Tagore:
• His first poem was published in the Amrita Bazar Patrika and then he wrote ‘Banaphul’ and ‘Bhanusinher Padavali’.
• He founded Shantiniketan near Bolpore in December 1901.
• He wrote Gitanjali, for which he was awarded the Nobel Prize in 1913.
• He also founded the Vishwa Bharati University.
• In 1919, he renounced the knighthood granted by the British crown after the Jallianwala Bagh Massacre.
• His composed National Anthem of two nations
• India–Jana Gana Mana
• Bangladesh–Amar Sonar Bangla

The correct answer is 44 times.​

Key Points

• The hands of a clock are 44 times perpendicular to each other in a day.
• After 1 hour, hour hands travels a space of 5 minutes or 30^o.
• On the clock, hands are 11 times opposite to each other in 12 hours and 22 times opposite in a day.
• The hands in the clock are perpendicular 22 times in 12 hours and 44 times in one day.

Given that,

X is taller than Y and Z is shorter than W.

⇒ X > Y and W > Z

We need to determine who is the shortest one.

Statement 1: Z is shorter than X.

⇒ X > Y and W > Z

⇒ X > Y, Z

• This statement alone is not sufficient as the shortest person can be Z or Y.

Statement 2: W is shorter than Y.

⇒ X > Y > W > Z

• Therefore, Z is the shortest person.
• Thus, statement 2 is sufficient to determine the shortest person.

Hence, "Only 2 is sufficient while only 1 is not sufficient" is the correct answer.

The triangles in the figure given below are as follows:

 

Hence, "19" is the correct answer.

The correct answer is Ajay Singh Bisht.

Key Points

• The birth name of Yogi Adityanath is Ajay Bisht.
• He is also the mahant of the Gorakhnath Math, Gorakhpur.
• He is the founder of Hindu Yuva Vahini.
• Uttar Pradesh:
• ​Capital: Lucknow
• Governor: Anandiben Patel
• Chief Minister: Yogi Adityanath.
• It shares its borders with the states of Rajasthan, Haryana, Delhi, Madhya Pradesh, Chattisgarh, Bihar, Jharkhand, Uttarakhand, Himachal Pradesh.
• It shares its international border with Nepal.

The correct answer is Tyagaraja.

• ​Tyagaraja is one of the Trinity of Carnatic Music.

Key Points

• Carnatic Music
• The Tamil classic of the 2nd century AD. titled ‘Silappadhikaram’ contains a vivid description of the music of that period.
• The Tolkappiyam, Kalladam and the contributions of the Saivite and Vaishnavite saints of the 7th and 8th centuries AD.
• It also serves as resource material for studying musical history.
• Trinity of Carnatic music:
• It is a trio of composer-musicians of Carnatic music in the 18th century.
• The trio consisted of Tyagaraja, Muthuswami Dikshitar and Shyama Sastri.
• Tyagaraja was a Telugu composer.
• He is known for Pancharatna Kritis.
• Muthuswami Dikshitar was a Sanskrit and Manipravalam composer.
• Shyama Sastri was a Telugu, Sanskrit composer.

In the figure above, the squares are as follows:

• ABED, BCFE, DEHG, EFIH, and ACIG

Hence, "5" is the correct answer.

According to the table,

In the month of November the least number of books were sold

∴ Required answer is November

The correct answer is Horticulture Farming.

• An estate where a cash crop is grown for sale is known as Horticulture Farming.

Key Points

• Horticulture farming is cultivating plants in an estate to produce food and medicinal ingredients as a cash crop.
• The horticulture includes a wide range of cash crops namely fruits, vegetables, flowers medicinal and aromatic plants mushrooms, plantation crops and spices.

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Additional Information

• A kitchen garden is a small farming garden growing fruits and vegetables in the backyard of the house by using kitchen wastewater.
• Slash and burn farming is a farming method that involves the cutting and burning of plants in a forest or woodland.
• Subsistence farming is the practice of growing crops and raising livestock adequate only for one's own use, without any excess for trade.

To find a year with the same calendar, we add 6 to the given year if the given year is a leap year + 1.

• 2004 is a leap year.
• 2005 = leap year + 1
• So we add 6.
• 2005 + 6 = 2011

Hence, "2005" is the correct answer.

Shortcut Trick

Effective rate for 2 years at 12% = 12 + 12 + (12 × 12) ÷ 100 = 24 + 1.44 = 25.44%

Total Amount = Principal × (100% + 25.44%) = 3,000 × 125.44%

Amount = 3,000 × 1.2544 = 3763.2

∴ The correct answer is Rs. 3,763.

Alternate Method

Given:

Principal (P) = Rs. 3,000

Rate (R) = 12% per annum

Time (T) = 2 years

Formula Used:

Amount (A) = P(1 + R/100)^T

Calculations:

⇒ A = 3000(1 + 12/100)²

⇒ A = 3000(1 + 3/25)²

⇒ A = 3000(28/25)²

⇒ A = 3000 × (784 ÷ 625)

⇒ A = 4.8 × 784

⇒ A = Rs. 3,763.2

Rounding off to the nearest integer, we get Rs. 3,763.

∴ The correct answer is Rs. 3,763.

Additional Information

Effective Rate for Compound Interest

For a 2-year period, the effective Compound Interest rate can be calculated using the successive percentage formula: R_eff = x + y + (xy/100).

Difference between CI and SI

The difference between Compound Interest and Simple Interest for 2 years is given by the formula: D = P(R/100)².

Amount with Different Compounding Frequencies

If interest is compounded half-yearly, the rate is taken as R/2 and time as 2n. Formula: A = P(1 + R/200)²ⁿ.

Shortcut Trick

Identify the algebraic form: ((a + b)² − (a − b)²) ÷ (2 × a × b).

Using the identity: (a + b)² − (a − b)² = 4ab.

Substituting the identity into the expression gives: 4ab ÷ 2ab.

The variables a and b cancel out completely: 4 ÷ 2 = 2.

The result is a constant regardless of the values 496 and 54.

∴ The correct answer is 2.

Alternate Method

Given:

Expression = ((496 + 54)² − (496 − 54)²) ÷ (2(496 × 54))

Formula Used:

(a + b)² − (a − b)² = 4ab

Calculations:

⇒ Let a = 496 and b = 54.

⇒ Numerator = (a + b)² − (a − b)²

⇒ Numerator = 4 × a × b = 4 × 496 × 54

⇒ Denominator = 2 × (496 × 54) = 2 × a × b

⇒ Expression = (4 × 496 × 54) ÷ (2 × 496 × 54)

⇒ Expression = 4 ÷ 2

⇒ Value = 2

∴ The correct answer is 2.

Additional Information

Sum of Squared Binomials

The identity (a + b)² + (a − b)² = 2(a² + b²) is used when the two squared terms are added.

Difference of Squares

The identity a² − b² = (a − b)(a + b) helps in factoring and simplifying quadratic differences.

Basic Expansion Rules

Expansion of (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b² are the building blocks of algebraic simplification.