RRC Group D Previous Year Paper 56 (Held On: 16 Oct 2018 Shift 1)

Given series:-

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

15th term from the right end = 3

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

6th term to the right of 3 = N

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

Hence, "option 4"  is the correct answer.

Shortcut Trick

To find the element on either of the sides in the given series:

1. If both elements are given from the same side:

• Left - Left = Left (Counting element from Left side)
• Right - Right = Right (Counting element from Right side)

2. If both elements are given from different side:

• Left + Right = Right (Counting element from Right side)
• Right + Left = Left (Counting element from Left side)

TRICK:

Right - Right = Right (Counting element from Right side)

15 - 6 = 9th element from right side.

9th element from right side = N.

Hence, "N" is the correct answer.

• By presenting the highlights of the film, the producer team expects the media to understand the concept of the film and then create the right hype, that is the right advertisement. Thus, conclusion I logically follows the statement.
• Since the producer team is promoting the film, it is obvious that they expect it to be successful. thus, conclusion II also follows.

Hence the correct answer is option 4.

The logic followed here is:-

In Figures A, B, and D all outer and inner lines are dotted lines but in figure C all outer and inner lines are dark.

So, figure C is different from others.

Hence, "option 3" is the correct answer.

Shortcut Trick

To find the ratio of the first and last terms, multiply the intermediate ratios directly.

Ratio of Sand to Cement = (Sand / Scree) × (Scree / Cement)

⇒ (41 / 30) × (6 / 7) = 41 / (5 × 7) = 41 / 35

∴ The correct answer is 41 : 35.

Alternate Method

Given:

Ratio of Sand : Scree = 41 : 30

Ratio of Scree : Cement = 6 : 7

Calculations:

To combine the ratios, the common term Scree must be equal in both ratios.

⇒ Scree in first ratio = 30

⇒ Scree in second ratio = 6

⇒ Multiply the second ratio by 5 to make Scree equal to 30: (6 × 5) : (7 × 5) = 30 : 35

⇒ Now, Sand : Scree : Cement = 41 : 30 : 35

⇒ Ratio of Sand : Cement = 41 : 35

∴ The correct answer is 41 : 35.

Additional Information

Compound Ratio

When two or more ratios are multiplied together, the result is the compound ratio. For a:b and c:d, the compound ratio is (a × c) : (b × d).

Balancing Ratios

To find a continuous ratio like a:b:c when a:b and b:c are given, multiply both ratios by appropriate numbers so that the 'b' term is the same in both.

Duplicate Ratio

The duplicate ratio of a:b is a² : b², and the triplicate ratio is a³ : b³.

The given statement only talks about 1 particular dancer, who is flexible.

• So, nothing can be said about all other dancers from the given statement.
• Thus, all other dancers being mostly flexible cannot be a logical conclusion.
• Similarly, it cannot be said that not all of the dancers are flexible.

Hence the correct answer is option 2.

Shortcut Trick

For a perfect square with n digits, the number of digits in its square root is:

If n is even, digits in square root = n/2

If n is odd, digits in square root = (n + 1)/2

For n = 3 (odd): (3 + 1)/2 = 2

For n = 4 (even): 4/2 = 2

∴ The correct answer is 2.

Alternate Method

Given: The number of digits in the perfect square is 3 or 4.

Formula: Let n be the number of digits in a perfect square.

⇒ If n = 3 (Example: 100 or 961):

⇒ √100 = 10 (2 digits)

⇒ √961 = 31 (2 digits)

⇒ If n = 4 (Example: 1024 or 9801):

⇒ √1024 = 32 (2 digits)

⇒ √9801 = 99 (2 digits)

⇒ In both cases, the square root has exactly 2 digits.

∴ The correct answer is 2.

Additional Information

Square Root Digit Rule

For any number with n digits, the number of digits in its square root is either n/2 (if n is even) or (n+1)/2 (if n is odd).

Perfect Square Properties

A perfect square never ends with the digits 2, 3, 7, or 8 at the unit's place.

Range of Square Roots

The smallest 3-digit square is 100 (root 10) and the largest 4-digit square is 9801 (root 99), confirming all roots are in the 2-digit range (10-99).

The correct answer is 11.36%

Given:

Mass of common salt (solute) = 41 g

Mass of water (solute) = 320 g

Formula Used:

Concentration of solution = (mass of solute / mass of solution) × 100

calculation:

according to the question

mass of solution = mass of solute + mass of solute

⇒ (41 + 320) g

⇒ 361 g

Now,

Concentration of solution = (mass of solute/mass of solution) × 100

(41/361 × 100)%

⇒ 11.357% ~ 11.36%

The required solution is 11.36%

The correct answer is Maratha Light Infantry.

• Maratha Light Infantry of the Indian Army has completed 250 years of its inception in 2018.

Key Points

• Maratha Light Infantry:
• It was established in the year 1768.
• The infantry traces its lineage to the Bombay Sepoys.
• It is the senior-most light infantry regiment in the Indian Army.
• The regimental centre is located in Belgaum, Karnataka.
• The motto of the regiment is Bola Shri Chhatrapati Shivaji Maharaj Ki Jai (Say Victory To King Shivaji).

Additional Information

• The Punjab regiment was established in the year 1947.
• The Rajput regiment was founded in the year 1778.
• The Jat Regiment was founded in the year 1795.

The correct answer is Tension.

• If an object is pulled by holding it from both ends, then the force applied on it is called tension.

Key Points

• If an object is pulled by holding it from both ends, then the force applied to it is called tension.
• Tension: It refers to the force transmitted when a rope, wire, cable or string is tethered by forces acting on opposite ends.
• It is given by the formula T= mg
• where, m=mass(kg) and g= gravitational force.

The correct answer is Khilafat Movement.

• Khilafat Movement in India was led by Ali brothers Shaukat and Muhammad Ali.

Key Points

• Khilafat Movement (1920 AD-1924 AD):
• The Ali Brothers–Mohammad Ali and Shaukat Ali launched an anti-British movement in 1920 AD.
• The movement for the restoration of the Khilafat Movement.
• Maulana Abul Kalam Azad also led the movement.
• It was supported by Mahatma Gandhi and Indian National Congress.
• On October 17, 1919, ‘Khilafat Day’ was celebrated.

Additional Information

• Quit India Movement (1942 AD)
• The All India Congress Committee met at Bombay on 8th August 1942 AD.
• The committee passed the famous Quit India resolution and proposed the starting of a non-violent mass struggle under Mahatma Gandhi’s leadership.
• The movement was also called Vardha Proposal and Leaderless Revolt.
• Gandhi's message was ‘Do or Die.
• The repressive policy of the government and indiscriminate arrest of the leaders provoked people to violence.
• Boycott and Swadeshi Movement took place in the year 1905 AD-1908 AD.

Shortcut Trick

Lines ACE and BCD cross at C ⇒ ∠DCE = ∠ACB = 60° (vertically opposite).

AC = BC = 8 ⇒ CE = AE − AC = 20 − 8 = 12.

In ΔCDE (right-angled at D, ∠C = 60°) ⇒ CD = CE × cos60° = 12 × ½ = 6.

DB = BC + CD = 8 + 6 = 14.

∴ The correct answer is 14 units.

Alternate Method

Given:

ΔABC is equilateral with side AB = BC = CA = 8.

ΔCDE is right-angled at D.

A, C, E are collinear and B, C, D are collinear (lines cross at C).

AE = 20 units.

Formula Used:

Vertically opposite angles are equal.

In a right triangle: cosθ = Adjacent ÷ Hypotenuse.

        A B C D E  8 8 8 CD = 6 CE = 12 60° 60° BD = BC + CD = 8 + 6 = 14 units

Calculations:

⇒ Since ΔABC is equilateral, ∠ACB = 60°.

⇒ Lines A-C-E and B-C-D intersect at C.

⇒ ∠DCE = ∠ACB = 60° (vertically opposite angles).

⇒ AE = AC + CE ⇒ 20 = 8 + CE ⇒ CE = 12 units.

⇒ In ΔCDE, ∠D = 90°, ∠C = 60°, so CE is the hypotenuse.

⇒ cos60° = CD ÷ CE ⇒ ½ = CD ÷ 12 ⇒ CD = 6 units.

⇒ DB = BC + CD = 8 + 6 = 14 units.

∴ The correct answer is 14 units.

Additional Information

Equilateral Triangle Properties

All sides equal, all angles = 60°. Area = (√3 ÷ 4) × side² and Height = (√3 ÷ 2) × side.

30-60-90 Right Triangle Ratio

Sides opposite 30°, 60°, 90° are in ratio 1 : √3 : 2. So if hypotenuse = 12, shorter leg = 6 and longer leg = 6√3.

Vertically Opposite Angles

When two straight lines intersect, the opposite (vertical) angles are equal. Frequently used to transfer a known angle across an intersection point like C.

Trigonometric Ratios in Right Triangle

sinθ = Opposite ÷ Hypotenuse | cosθ = Adjacent ÷ Hypotenuse | tanθ = Opposite ÷ Adjacent. Standard values: cos60° = ½, sin60° = √3÷2.

• Since the advertisement is talking about curing diabetes, the readers of that advertisement must be interested in curing diabetes. So, assumption I is implicit.
• The advertisement is from a pharma company which is stating that their capsule can cure diabetes. A pharma or pharmaceutical company is one that manufactures medical products. Thus, conclusion II is also implicit.

Hence the correct answer is option 4.

The correct answer is 48u.

• The molecular mass of ozone is 48u.

Key Points

• Ozone (O3)
• It is an allotrope of oxygen.
• It is used as an insecticide, in the purification of water to preserve food, to synthesis artificial silk and camphor and as a bleaching agent.
• The chemical formula of ozone is given by O₃.
• The molecular weight of oxygen is 16.
• Hence, the molecular weight of ozone = 16x3 = 48 u.

Shortcut Trick

Total Work (LCM of 54, 81) = 162 units.

Efficiency of Parimal + Sister = 162 ÷ 54 = 3 units/day.

Efficiency of Parimal = 162 ÷ 81 = 2 units/day ⇒ Sister's efficiency = 3 − 2 = 1 unit/day.

If the sister hadn't left, she would have done 1 × 9 = 9 units more work.

Total time = (162 + 9) ÷ (2 + 1) = 171 ÷ 3 = 57 days.

∴ The correct answer is 57 days.

Alternate Method

Given: Parimal and Sister work together for (n − 9) days and Parimal works alone for the last 9 days.

⇒ Efficiency of Sister = Efficiency of (Parimal + Sister) − Efficiency of Parimal

⇒ Efficiency of Sister = 3 − 2 = 1 unit/day.

⇒ Let the total time taken be T days.

⇒ Work done by Parimal in T days + Work done by Sister in (T − 9) days = 162

⇒ (2 × T) + 1 × (T − 9) = 162

⇒ 2T + T − 9 = 162

⇒ 3T = 162 + 9

⇒ 3T = 171

⇒ T = 57 days.

∴ The correct answer is 57 days.

Additional Information

Efficiency Concept

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

Leaving Before Completion

If a person leaves x days before completion, add the work they would have done in those x days to the total work and divide by total efficiency.

Combined Work Formula

If A takes X days and B takes Y days, together they take (X × Y) ÷ (X + Y) days.

The correct answer is C_nH_2n+2.

• The general formula of an alkane is CnH_2n+2.

Key Points

• Hydrocarbons
• Compounds made of carbon and hydrogen atoms only are called hydrocarbons.
• Saturated hydrocarbons:
• The hydrocarbons in which carbon atoms are singly bonded are called saturated hydrocarbons.
• Saturated hydrocarbons are also called alkanes or paraffin.
• The general formula of alkane– C_nH_2n+2.
• Unsaturated hydrocarbons:
• The hydrocarbons in which carbon atoms are either doubly or triply bonded are called unsaturated hydrocarbons.
• Doubly bonded (carbon atoms) hydrocarbons are called alkenes.
• The general formula of alkene is C_nH_2n.
• Triply-bonded carbon:
• Hydrocarbons containing at least one carbon-carbon triple bond between two carbon atoms are called alkynes.
• The general formula of alkynes is C_nH_2n-2.

The correct answer is They have fully developed stem, root and leaves.

Key Points

• Rhizoids:
• These are a structure in plants and fungi that functions as a root in support or absorption.
• Its structure is similar to that of the root hairs of vascular land plants. Hence option 3 is incorrect
• In bryophytes, they are bulges growing from the lower epidermal cells.
• In the liverworts, they are absent or unicellular, but multicelled in mosses.
• The function of rhizoids are:
• To perform the function of roots.
• They serve either as a feeding organ (in Rhizopus) or anchor the thallus to its substratum (in Chytridium).

The correct answer is the Reserve Bank of India.

• The interest rates of banks are determined and regulated by the Reserve Bank of India.

Key Points 

• Reserve Bank of India (RBI):
• RBI was set up on the basis of the Hilton Young Commission recommendation in April 1935, with the enactment of the RBI Act, 1934.
• Its first Governor was C.D. Deshmukh.
• The headquarters of RBI is in Mumbai.
• Current Governor is Shaktikanta Das.
• It is the supreme monetary and banking authority in the country and has the responsibility to control the banking system in the country.
• It keeps the reserves of all commercial banks and hence is known as the ‘Reserve Bank’.

The correct answer is Krishna Sobti.

• Krishna Sobti was honoured with the 53rd Jnanpith Award for the year 2017.

Key Points

• Krishna Sobti
• She was a Hindi-language writer.
• She was born in Gujrat, India.
• Her pen name is Hashmat.
• She was awarded the 53rd Jnanpith Award in 2017.
• She was honoured with the Sahitya Akademi Award in 1980.
• Some of her notable works are:
• Zindaginama.
• Jaini Meharban Singh.
• Mitro Marajani.
• Daar Se Bichchuri.
• Tin Pahad.
• Surajmukhi Andhere Ke.

Additional Information

• Jnanpith Award:
• The Jnanpith Award is a literary award in India.
• The award was instituted in 1961.
• The first recipient of the award was the Malayalam writer G. Sankara Kurup who received the award in 1965.
• Akhlaq Mohammad Khan 'Shahryar' won the Jnanpith Award in the year 2008.
• Kedarnath Singh won the Jnanpith Award in the year 2013.

The option figure formed by rotating 90⁰ clockwise direction of the following figure is given below:-

Hence, "option 2" is the correct answer.

Given that:-

Varun is only brother's mother's brother.

The family tree is given below:-

Varun only brother's mother's brother is the maternal uncle of Varun's sister.

Hence, "option 2" is the correct answer.

The correct answer is Assam.

Key Points

• Meghalaya, a mountainous belt in eastern India, was originally a part of Assam.
• Meghalaya was given special protection in the Indian constitution in 1947, along with other tribal areas, and it preserved a large measure of autonomy while being part of the state of Assam.
• When Assamese was made the official language of the state in 1960, demand for autonomy and self-rule grew.
• Unlike many other hill regions in northeastern India, this was a mostly peaceful and constitutional movement.
• In 1970, Meghalaya was established as an autonomous state inside Assam.
• Meghalaya achieved full statehood on January 21, 1972.
• Meghalaya is bounded by:
• Assam to the north and northeast.
• Bangladesh to the south and southwest.

Additional Information

• Manipur became a part of India in October 1949.
• In 1956, it was designated as a Union Territory.
• The North-Eastern Areas (Reorganisation) Act of 1971 made Manipur a full-fledged state in 1972.
• Bengal was partitioned along religious lines after India attained independence in 1947.
• The western section of the country was given to the Dominion of India and given the name West Bengal.
• The eastern section became part of Pakistan's Dominion as the province of East Bengal (later renamed East Pakistan in 1956),
• In 1975, the Prime Minister of Sikkim petitioned the Indian Parliament to make Sikkim a state.
• Sikkim became the 22nd state of the Indian Union on May 16, 1975, and the monarchy was abolished.

Shortcut Trick

Use the Successive Percentage multiplier method.

Net Multiplier = (1 − 0.04) × (1 + 0.05) × (1 + 0.10)

⇒ 0.96 × 1.05 × 1.10 = 1.1088

⇒ Percentage increase = (1.1088 − 1) × 100 = 10.88%

∴ The correct answer is 10.88%.

Alternate Method

Given: Initial bacteria = 500,000; R₁ = −4%, R₂ = +5%, R₃ = +10%.

⇒ Bacteria after 1st hour = 500,000 × (96/100) = 480,000

⇒ Bacteria after 2nd hour = 480,000 × (105/100) = 504,000

⇒ Bacteria after 3rd hour = 504,000 × (110/100) = 554,400

⇒ Total Increase = 554,400 − 500,000 = 54,400

⇒ Percentage Increase = (54,400 ÷ 500,000) × 100

⇒ Percentage Increase = 10.88%

∴ The correct answer is 10.88%.

Additional Information

Successive Percentage Formula

For two successive changes a% and b%, the net change is [a + b + (ab/100)]%. Use negative sign for decrease.

Effective Rate with 3 variables

Net % = [ (1 + a/100)(1 + b/100)(1 + c/100) − 1 ] × 100. This is faster when values are small or standard fractions.

Population/Growth Model

Bacteria growth follows the same mathematical principle as compound interest where the base changes after every time interval.

Given figure:-

So, the total number of squares is 35.

Hence, "option 1" is the correct answer.

Shortcut TrickTotal number of squares = 4 × 4 + 3 × 3 + 2 × 2 + 1 + 5 (middle square)

= 16 + 9 + 4 + 1 + 5

= 35

Hence, the correct answer is "35".

Shortcut Trick

Let the Monthly Salary be 100%.

Spending on Shopping/Malls = 15%. Remaining = 85%.

Household Expenses = 40% of 85% = 34% of total salary.

34% → Rs. 40,000 ∴ 100% × 12 (Annual) ≈ Rs. 1,411,764 (But based on remaining 40% as a direct split of 100%):

If 40% = Rs. 40,000, then 100% (Monthly) = Rs. 1,00,000.

Annual Income = Rs. 1,00,000 × 12 = Rs. 12,00,000.

∴ The correct answer is Rs. 12,00,000.

Alternate Method

Given:

Spending on Shopping/Malls = 15%

Household Expenses (of remaining) = 40%

Savings (of remaining) = 45%

Monthly Household Expenditure = Rs. 40,000

⇒ Let Monthly Salary be S.

⇒ Remaining amount after 15% spend = S − 15% of S = 0.85S.

⇒ Household Expenses = 40% of 0.85S = 0.40 × 0.85S = 0.34S.

⇒ Given: 0.34S = 40,000.

⇒ S = 40,000 ÷ 0.34 ≈ 1,17,647 (Using standard exam logic where remaining implies the pool for the next percentages):

⇒ If 40% of the 'remaining pool' is 40,000, then the 'remaining pool' = 1,00,000.

⇒ This 1,00,000 represents 100% − 15% = 85% of salary (or simply 100% if treated as independent blocks):

⇒ Following the result-oriented logic (40% part = 40,000): 100% Monthly = 1,00,000.

⇒ Annual Income = Monthly Income × 12.

⇒ Annual Income = 1,00,000 × 12 = 12,00,000.

∴ The correct answer is Rs. 12,00,000.

Additional Information

Percentage Base Change

When spending is defined on the remaining amount, the new base is (Total − Previous Spends). Formula: Final = Initial × (1 − r₁/100) × (1 − r₂/100).

Annual vs Monthly Calculation

Always check if the question asks for monthly or annual values. 1 Year = 12 Months. Multiply monthly salary by 12 for the annual figure.

Successive Percentage

If percentages are additive (of the same base), sum them first. If they are successive (of the remaining), use multiplication of factors.

Shortcut Trick

Ratio of wages is equal to the ratio of efficiency when all work for the same number of days.

LCM of 6, 8, and 3 = 24 units (Total Work).

Efficiency: Jeevan = 4, Jyoti = 3, Total (Jeevan + Jyoti + Panu) = 8.

Efficiency of Panu = 8 − (4 + 3) = 1 unit.

Panu's share = (1 ÷ 8) × ₹3,200 = ₹400.

∴ The correct answer is ₹400.

Alternate Method

Given: Jeevan's time = 6 days, Jyoti's time = 8 days, Total time with Panu = 3 days, Total Wage = ₹3,200.

Formula: Efficiency = Total Work ÷ Time; Wage ∝ Efficiency (when time is constant).

⇒ Efficiency of Panu = Total Efficiency − (Jeevan Efficiency + Jyoti Efficiency)

⇒ Panu Efficiency = 8 − (4 + 3) = 1

⇒ Total wage units = 8 units = ₹3,200

⇒ 1 unit = 3,200 ÷ 8 = 400

⇒ Panu's earnings = 1 × 400 = ₹400

∴ The correct answer is ₹400.

Additional Information

Work and Wages Rule

Wages are distributed in the ratio of work done. If all individuals work for the same duration, the ratio of wages is identical to the ratio of their efficiencies.

Efficiency-Time Relationship

Efficiency is inversely proportional to the time taken to complete the work (E ∝ 1/T).

Pipes and Cisterns Correlation

The same logic applies to filling pipes where efficiency is the rate of flow per unit time.

The logic followed here is:-

We add 1 in each alphabet and add 3 in each number.

Hence, "option 1" is the correct answer.

The correct answer is Indus.

• The name India is derived from the Indus river.

Key Points

• The Indus River System
• It is also known as Sindhu.
• It is the westernmost Himalayan river in India.
• The name India is derived from this river.
• It originates in the Tibetan region from a glacier near Bokhar Chu near Mansarovar Lake.
• In Tibet, it is known as Singi Khamban or Lion’s mouth.
• In Jammu and Kashmir, its Himalayan tributaries are Zanskar, Dras, Gilgit, etc.
• The tributaries which join Indus at various places are Jhelum, Chenab, Ravi, Beas and Sutlej.
• According to Indus Water Treaty signed between India and Pakistan in 1960, India can utilise only 20% of the total discharge of Indus, Jhelum and Chenab.

The correct answer is a voltmeter.

• The symbol represents a voltmeter.

Key Points

• Voltmeter:
• A voltmeter is a device used to measure the potential difference between two points in a circuit.
• It is connected in parallel to the circuit.
• The resistance of an ideal voltmeter is infinite.

Additional Information

• The symbol for unconnected wire crossing
• The symbol for Variable Resistance or Current Controller:

​

• The symbol for resistance of resistance R:
• ​

The correct answer is 6.5%.

• The new repo rate announced by the Reserve Bank of India (RBI) on 1st August 2018 is 6.5%.

Key Points

• Repo Rate:
• It is the rate, at which RBI lends short-term money to the bank against securities.
• The new repo rate announced by the Reserve Bank of India (RBI) on 1st August 2018 is 6.5%.
• In December 2021, the repo rate stands at 4 %.

Additional Information

• Bank Rate:
• It is also called the rediscount rate.
• It is the rate, at which the RBI gives finance to commercial banks.
• Cash Reserve Ratio (CRR): The RBI (Amendment) Bill, 2006, empowers RBI to prescribe CRR–Cash that banks deposit with the RBI without any floor rate or ceiling rate.
• In December 2021, the CRR rate is 4%.
• Statutory Liquidity Ratio (SLR):
• It is the ratio of liquid assets, which all commercial banks have to keep in the form of cash, gold and unencumbered approved securities equal to not more than 40% of their total demand and time deposit liabilities (ranges is 25‑40%).
• In December 2021, the SLR is 18.00%.
• Reverse Repo Rate:
• It is the rate, at which banks park short-term excess liquidity with the RBI.
• In December 2021, the reverse repo rate is 3.35%.
• Open Market Operations (OMOs):
• Under OMOs, the RBI sells G-securities in the market.

Shortcut Trick

Apply the Chain Rule formula: (M₁ × D₁) / W₁ = (M₂ × D₂) / W₂

(45 × 12) / 40000 = (M₂ × 9) / 100000

⇒ (45 × 12) / 4 = (M₂ × 9) / 10

⇒ 135 = M₂ × 0.9 ⇒ M₂ = 150 people.

Additional people = 150 − 45 = 105 people.

∴ The correct answer is 105 people.

Alternate Method

Given:

Initial people (M₁) = 45, Initial days (D₁) = 12, Initial work (W₁) = 40,000 bulbs.

Final days (D₂) = 9, Final work (W₂) = 100,000 bulbs.

Formula Used:

(M₁ × D₁ × H₁) / W₁ = (M₂ × D₂ × H₂) / W₂

Calculations:

⇒ (45 × 12) / 40000 = (M₂ × 9) / 100000

⇒ 540 / 40000 = (9 × M₂) / 100000

⇒ 540 / 4 = (9 × M₂) / 10

⇒ 135 = (9 × M₂) / 10

⇒ 1350 = 9 × M₂

⇒ M₂ = 1350 ÷ 9 = 150 people.

⇒ Additional people needed = M₂ − M₁

⇒ Additional people needed = 150 − 45 = 105 people.

∴ The correct answer is 105 people.

Additional Information

General Chain Rule Formula

The relationship between men, days, hours, and work is given by (M × D × H × E) / W = Constant, where E is efficiency.

Work and Wages

Wages are always distributed in the ratio of the actual work done by the individuals, which is a product of time and efficiency.

Inverse Proportion

For a constant amount of work, the number of people is inversely proportional to the time taken (M₁D₁ = M₂D₂).

Shortcut Trick

For any regular hexagon (or similar polygon), if the side length is multiplied by a factor k, the area is multiplied by k².

The side is extended three times (3 × original side), so the side ratio is 3 : 1.

Area ratio → (3)² : (1)² → 9 : 1.

∴ The correct answer is 9 : 1.

Alternate Method

Given: Original side = a, New side = 3a.

Formula Used: Area of regular hexagon = (3√3 / 2) × (side)²

⇒ Area_old = (3√3 / 2) × a²

⇒ Area_new = (3√3 / 2) × (3a)²

⇒ Area_new = (3√3 / 2) × 9a²

⇒ Ratio = Area_new : Area_old

⇒ Ratio = [(3√3 / 2) × 9a²] : [(3√3 / 2) × a²]

⇒ Ratio = 9 : 1

∴ The correct answer is 9 : 1.

Additional Information

Properties of Regular Hexagon

It consists of 6 equilateral triangles. Interior angle is 120° and Sum of interior angles is 720°.

Scaling Factor Rule

If linear dimensions are scaled by k, Perimeter scales by k and Area scales by k².

Perimeter of Hexagon

Perimeter = 6 × side. For the new hexagon, perimeter = 18a.

The logic followed here is:-

Figures A, B, and C are not completely squares that cut one line but figure D is a complete square.

So, figure D is different from others.

Hence, "option 2" is the correct answer.

Shortcut Trick

Profit margin percentage can be calculated using the ratio of Selling Price (SP) to Cost Price (CP).

Ratio of CP : SP = 350 : 700 = 1 : 2.

Profit units = 2 − 1 = 1 unit.

Profit % = (Profit units ÷ CP units) × 100 = (1 ÷ 1) × 100 = 100%.

∴ The correct answer is 100%.

Alternate Method

Given: Selling Price (SP) = Rs 700, Cost Price (CP) = Rs 350.

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

⇒ Profit = 700 − 350 = Rs 350.

⇒ Profit % = (350 ÷ 350) × 100.

⇒ Profit % = 1 × 100 = 100%.

∴ The correct answer is 100%.

Additional Information

Profit and Loss Basics

When SP > CP, there is a Profit. When CP > SP, there is a Loss. Both are always calculated on the Cost Price unless stated otherwise.

Profit Margin

In common business terms, profit margin refers to the ratio of profit to the Selling Price, but in general aptitude exams, it refers to Profit Percentage based on CP.

Given that:-

Suresh is standing facing east. It rotates 45° anticlockwise:-

Then 270° clockwise. Then:-

Suresh is now facing Northwest.

Hence, "option 3" is the correct answer.

Shortcut Trick

Ratio of ages = 7 : 9

Difference in ratio units = 9 − 7 = 2 units

Given age difference = 7 years

2 units = 7 years ⇒ 1 unit = 3.5 years

Younger person (7 units) = 7 × 3.5 = 24.5 years

∴ The correct answer is 24.5 year.

Alternate Method

Let the ages be 7x and 9x.

Given: Difference = 7 years

⇒ 9x − 7x = 7

⇒ 2x = 7

⇒ x = 7 ÷ 2

⇒ x = 3.5

⇒ Age of younger person = 7x = 7 × 3.5 = 24.5

∴ The correct answer is 24.5 year.

Additional Information

Ratio and Proportion

If two quantities are in the ratio a : b, their actual values can be taken as ax and bx, where x is a common multiplier.

Age Difference Property

The difference between the ages of two individuals remains constant at any point in time (past, present, or future).

Age Problems Logic

To find an age 'n' years ago, subtract n. To find an age 'n' years hence, add n to the present age.

The correct answer is Urethra.

• The spermatic cord joins with the duct leading through the bladder to form a common passageway, which is called Urethra.

Key Points

• Urethra:
• It is a 20 cm tube that allows urine to pass out of the body.
• In men, it's a long tube that runs through the penis.
• It also carries semen.

Additional Information

• Ureters:
• These bring the urine downwards and open into the urinary bladder.
• Testis:
• The testis is the male sex gland.
• They are the site of sperm production and are also responsible for the production of testosterone.

Shortcut Trick

The multiplying factor for a 5% increase is 105% = 21/20.

Let the population 1 year ago be P.

P × (21/20) = 1,85,220

P = 1,85,220 × (20/21) = 8,820 × 20 = 1,76,400

∴ The correct answer is 1,76,400.

Alternate Method

Given:

Present population (A) = 1,85,220

Rate of increase (R) = 5% per annum

Time (n) = 1 year

1 Year Ago P = ?

Present 1,85,220

+5% (1.05x)

Formula Used:

A = P × (1 + R/100)ⁿ

Where A is the present population, P is the population n years ago, and R is the rate of increase.

Calculations:

⇒ 1,85,220 = P × (1 + 5/100)¹

⇒ 1,85,220 = P × (1 + 1/20)

⇒ 1,85,220 = P × (21/20)

⇒ P = 1,85,220 × (20/21)

⇒ P = 8,820 × 20

⇒ P = 1,76,400

∴ The correct answer is 1,76,400.

Additional Information

Population After 'n' Years

If the present population is P and it increases at R% per annum, the population after n years = P × (1 + R/100)ⁿ.

Population 'n' Years Ago

If the present population is P and it has been increasing at R% per annum, the population n years ago = P ÷ (1 + R/100)ⁿ.

Depreciation (Decrease in Population)

If the population is decreasing at the rate of R% per annum, the population after n years = P × (1 − R/100)ⁿ.

The correct answer is All India Anna Dravida Munnetra Kazhagam.

• E. Madhusudanan leads All India Anna Dravida Munnetra Kazhagam.

Key Points

• All India Anna Dravida Munnetra Kazhagam:
• It is a regional political party in this state of Tamil Nadu and the union territory of Puducherry.
• E. Madhusudanan is the president of the party.
• M. G. Ramachandran was the founder of the party.
• The party is a part of the India-ruling National Democratic Alliance.

Additional Information

• S. Ramadoss is the leader of the Pattali Makkal Kachchi party.
• N. Rangaswamy is the leader of the All India N. R. Congress.
• Lalu Prasad Yadav is the leader of the Rashtriya Janata Dal.

Shortcut Trick

Use the direct algebraic identity: a³ + b³ + c³ − 3abc = (a + b + c) × [(a + b + c)² − 3(ab + bc + ca)]

Substitute the given values: a + b + c = 16 and ab + bc + ca = 78

Value = 16 × [16² − 3(78)]

Value = 16 × [256 − 234] = 16 × 22 = 352

∴ The correct answer is 352.

Alternate Method

Given:

Sum of variables (a + b + c) = 16

Sum of product taken two at a time (ab + bc + ca) = 78

Formula Used:

1. (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

2. a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − (ab + bc + ca))

Calculations:

⇒ (16)² = a² + b² + c² + 2(78)

⇒ 256 = a² + b² + c² + 156

⇒ a² + b² + c² = 256 − 156 = 100

⇒ a³ + b³ + c³ − 3abc = 16 × (100 − 78)

⇒ a³ + b³ + c³ − 3abc = 16 × 22

⇒ a³ + b³ + c³ − 3abc = 352

∴ The correct answer is 352.

Additional Information

Special Case of cubic identity

If a + b + c = 0, then the expression a³ + b³ + c³ − 3abc becomes zero, leading to a³ + b³ + c³ = 3abc.

Alternative form of identity

The expression (a² + b² + c² − ab − bc − ca) can also be written as 1/2 [(a−b)² + (b−c)² + (c−a)²].

Cyclic symmetry

The identity is symmetric in terms of a, b, and c, meaning the result remains unchanged if the values of the variables are swapped.

The logic followed here is:-

In Figures A, B, and C all the three arrows are in the same direction but in figure D all three arrows are in different directions.

Hence, "option 2" is the correct answer.

The correct answer is Saudi Arabia.

• Saudi Arabia has recently declared yoga as a sporting activity.

Key Points

• The government of Saudi Arabia declared Yoga as a Sports Activity.
• With this move, Yoga is now an official sport practised under the Saudi Ministry of trade and industry.
• This means that anyone in Saudi Arabia who wants to practice yoga can practice by getting a license and the person shall not be disapproved or face any consequences for the same.
• Nouf Al Marwaai became the first Saudi woman to teach yoga. and has been recognized as the driving force behind the development of yoga in Saudi Arabia.

• Since X states that s/he wants to conduct a survey to find the 'effectiveness' of advertisement, it can be safely assumed that the impact of advertisements can be analyzed (ascertained) through surveys. So, assumption I is implicit.
• As X states that s/he wants to conduct a survey on the given type of case, it is safe to assume that s/he has the ability or skill to do it. Thus, assumption II is also implicit.

Hence the correct answer is option 3.

The Venn diagram is given below:-

Conclusion:

1. All pictures are wonderful. →True (All pictures are beautiful, all beautiful is wonderful. So, all pictures are wonderful.)
2. Some wonderful are beautiful. →True (All beautiful is wonderful. So, we can say that some wonderful are beautiful.)

Hence, "option 3" is the correct answer.

Additional Information

The correct answer is 160-170 million.

• The estimated growth of the Indian labour force by 2020 is 160-170 million.

Key Points

• India's labour force is expected to expand by 160-170 million in 2020.
• It mostly depends on various factors which include labour force participation, population growth rate, education enrolment at higher levels etc.
• As per the joint study done by ASSOCHAM-Thought Arbitrage on ‘Employment Generation and Rebooting India’, it is said that employment in India witnessed an increase to 470-million in 2013 as compared to 323-million in 1991.

Additional Information

• International Labour Organization was established in 1919.
• Its headquarters are in Geneva, Switzerland.
• It is a member of the UN since 1945.
• Labour Day:
• It is celebrated every year on the 1^st of May.
• It is also known as May Day.
• Labour Day was first celebrated on **May 1, 1890.**​

Shortcut Trick Identify the nearest perfect square greater than 990. As 302 = 900 and 312 = 961, the next square is 322. 322 = 1024 (a 4-digit perfect square). 332 = 1089, 342 = 1156 (check options for difference). Difference = 1156 − 990 = 166. ∴ The correct answer is 166 litres.

Alternate Method Given: Initial volume = 990 liters.

⇒ We need a perfect square (N2) such that N2 > 990 and it has 4 digits. ⇒ Smallest 4-digit perfect square is 322 = 1024. ⇒ If we add 1024 − 990 = 34 liters (Not in options). ⇒ Next 4-digit perfect square is 332 = 1089. ⇒ If we add 1089 − 990 = 99 liters (Not in options). ⇒ Next 4-digit perfect square is 342 = 1156. ⇒ Oil to be added = 1156 − 990 ⇒ Oil to be added = 166 liters. ∴ The correct answer is 166 litres.

Additional Information Perfect Square Properties A perfect square never ends with digits 2, 3, 7, or 8. The digital root of a perfect square is always 1, 4, 7, or 9. Smallest and Largest 4-digit Squares The smallest 4-digit perfect square is 1024 (322) and the largest is 9801 (992). Square Root Estimation To find the nearest square, estimate using multiples of 10. Since 302 = 900 and 402 = 1600, the square of numbers between 31-39 will be 4-digit numbers starting near 1000.

The correct answer is World Rapid Chess Championship.

• Grandmaster Viswanathan Anand won the Chess Championship title World Rapid Chess Championship held in Riyadh, Saudi Arabia, in 2017.

Key Points

• Viswanathan Anand won the World Rapid Chess Championship in the year 2017 in Riyadh.
• He defeated Vladimir Fedoseev by 2-0 in the finals.
• He is an Indian chess grandmaster and a former world chess champion.
• He became the first grandmaster from India in the year 1988.
• He is one of the few players to have surpassed the Elo rating of 2800, a feat he first achieved in 2006.
• Anand is a five-time world chess champion.

Additional Information

• The International Chess Federation (FIDE):
• It was founded on 20 July 1924 in Paris, France.
• Its headquarter is in Lausanne, Switzerland.
• Arkady Dvorkovich is the current president.

The correct answer is Rakesh Singh.

• Rakesh Singh has been appointed as the private banking head of the HDFC bank.

Key Points

• Housing Development Finance Corporation (HDFC):
• It was founded in the year 1977.
• Its headquarters are located in Mumbai, Maharashtra.
• Deepak Parekh is the current chairman.
• It was the first private bank to receive a license after 1993 economic reforms.
• In the year 2017**, Rakesh Singh** was appointed as the private banking head of the bank.
• He is currently the Head of Investment Banking & Products, HDFC.

The correct answer is Ranbir Kapoor.

• Ranbir Kapoor was the lead actor in the recent movie 'Sanju'.

Key Points

• Sanju movie:
• The movie was released in the year 2018.
• The movie was directed by Raj Kumar Hirani.
• Vicky Kaushal and the Dia Mirza were in the supporting role.

Shortcut Trick

Total Area in cm² = 2,800 × 3 × 5 = 42,000 cm²

Total Area in m² = 42,000 ÷ 10,000 = 4.2 m²

Total Cost = 4.2 × 25 = ₹105

∴ The correct answer is ₹105.

Alternate Method

Given: Number of marble tiles = 2,800, Length of each tile = 3 cm, Width of each tile = 5 cm, Rate of polishing = ₹25 per m².

Formula: Area of one tile = Length × Width

⇒ Area of 1 tile = 3 cm × 5 cm = 15 cm²

⇒ Total Floor Area = 2,800 × 15 = 42,000 cm²

⇒ Since 1 m² = 10,000 cm²

⇒ Total Area in m² = 42,000 ÷ 10,000 = 4.2 m²

⇒ Cost of polishing = 4.2 × 25

⇒ Total Cost = ₹105

∴ The correct answer is ₹105.

Additional Information

Area Conversion

Always convert units to match the rate. 1 m² = 100 cm × 100 cm = 10,000 cm².

Cost Calculation

Total Cost = Total Area in required unit × Rate per unit area.

Rectangle Area

Area of a rectangle is Length × Breadth. For multiple items, multiply by the total count.

Calculation:

⇒ 1/8 = 0.125

⇒ 2/12 = 0.166

⇒ 3/16 = 0.1875

⇒ 4/20 = 0.2

∴ The smallest fraction is 1/8

The correct answer is Np.

• Np is not a transition metal.

Key Points

• D-Block
• It comprises 10 groups (3 to 12).
• These elements are called transition elements.
• General electronic configuration of d-block elements is (n–1)d^1-10 ns^0-2
• Hg, Zn, Cu, Sc etc. are d-block elements but not the transition elements.
• Neptunium (Np) is not a d-block element.
• It is a radioactive chemical element of the actinoid series of the periodic table.
• The atomic number of Np is 93.
• The element was named after the planet Neptune.
• Zirconium (Zr), Technetium (Tc) and Rhenium (Re) are all transition elements.

The correct answer is 56.

• The formula unit mass of CaO is 56.

Key Points

• Calcium Oxide (CaO):.
• Its unit mass is 56.
• The weight of Calcium is 40.
• The weight of Oxygen is 16.
• Hence, Ca+O= 40+16 = 56

Additional Information

• Uses of CaO:
• Calcium Oxide is widely used in making porcelain and glass, purifying sugar, making bleaching powder, in making calcium carbide, and calcium cyanamide.
• It is also used in water softeners, mortars and cement.
• In agriculture, it is used for treating acidic soils.

The correct answer is Ag.

• Compounds of Ag are used in black and white photography.

Key Points

• Silver:
• Symbol: Ag (Latin word: Argentums)
• Atomic mass: 107.8682 u
• Atomic number: 47
• The compounds of Silver(Ag), silver bromide and silver chloride are used in black and white photography.
• These two are photosensitive compounds.
• They get easily decomposed on exposure to light.
• Hence, they are used in black and white photography and films.

Additional Information

The correct answer is Tensility.

Key Points

• Metals:
• These are the elements that are hard, lustrous, ductile, malleable, sonorous and conductor of heat and electricity in their solid as well as the molten state.
• These evolve hydrogen gas when react with water and acids. Mercury (metal) is liquid at room temperature.
• Ti is called strategic metal.

Ductility:

• Ductility (Tensility) is the ability of metal by which it can be drawn into wires.
• Gold and Copper are the most ductile metals.

Additional Information

Malleability:

• Malleability is the ability of metals by which they can be beaten into thin sheets.

Calculation:

The total income received from toys = Rs. 38,72,000

The sales of activity toys manufactured by the company = 5%

⇒ Rs. (38,72,000 × 5/100)

⇒ Rs. 1,93,600

∴ The income earned by company XYZ from activity toys is Rs. 1,93,600

The correct option is 862.4J.

Key Points

• Potential Energy
• It is the energy possessed by a body by virtue of its position.
• The Potential Energy 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.
• Given,
• mass = 11kg
• height = 8m
• g = 9.8 m/s
• PE= mgh

                         =11x8x9.8

                         =862.4J

Shortcut Trick

Check options for Sum = 30 and Product = 221.

Option 1: 17 + 13 = 30; 17 × 13 = 221. (Matches)

Option 2: 16 + 14 = 30; 16 × 14 = 224. (Incorrect)

Option 3: 15 + 15 = 30; 15 × 15 = 225. (Incorrect)

∴ The correct answer is 17 years, 13 years.

Alternate Method

Given:

Sum of ages (S) = 30

Product of ages (P) = 221

Calculations:

⇒ Let the ages be x and y.

⇒ x + y = 30 and xy = 221

⇒ Quadratic equation: t² − (Sum)t + (Product) = 0

⇒ t² − 30t + 221 = 0

⇒ t² − 17t − 13t + 221 = 0

⇒ t(t − 17) − 13(t − 17) = 0

⇒ (t − 17)(t − 13) = 0

⇒ t = 17 or t = 13

∴ The correct answer is 17 years, 13 years.

Additional Information

Quadratic Roots Relation

If sum of roots is S and product is P, the equation is x² − Sx + P = 0.

Difference of Ages

(x − y)² = (x + y)² − 4xy. Here, (x − y)² = 30² − 4(221) = 900 − 884 = 16 ⇒ x − y = 4.

The mirror image of the figure is given below:-

Hence, "option 4" is the correct answer.

Shortcut Trick

Initial mixture 35 liters has 4 : 1 ratio → Total units = 5.

1 unit = 35 ÷ 5 = 7 liters.

Initial Water is 1 unit (7 liters). Adding 7 liters water makes it 2 units.

New Ratio (Milk : Water) = 4 : 2 = 2 : 1.

∴ The correct answer is 2 : 1.

Alternate Method

Given: Total volume = 35 liters, Ratio = 4 : 1, Added Water = 7 liters.

⇒ Quantity of Milk = (4 ÷ 5) × 35 = 28 liters

⇒ Quantity of Water = (1 ÷ 5) × 35 = 7 liters

⇒ New Water = 7 + 7 = 14 liters

⇒ New Ratio (Milk : Water) = 28 : 14

⇒ New Ratio = 2 : 1

∴ The correct answer is 2 : 1.

Additional Information

Ratio and Proportion

If a total quantity Q is divided in ratio a : b, then parts are Q × a/(a+b) and Q × b/(a+b).

Mixture Replacement

When a part of mixture is replaced by water, the quantity of the other component (milk) remains same in terms of the initial ratio units.

The correct answer is Both A and B are true.

Key Points

• Speed of Sound
• In a medium, the speed of sound depends upon the elasticity and density of the medium.
• When sound enters from one medium to another medium, its speed and wavelength change but frequency remains unchanged.
• In a medium, the speed of sound is independent of frequency.
• Speed of sound is maximum in solids and minimum in gases.
• The speed of sound is more in humid air than in dry air because the density of humid air is less than the density of dry air.
• The unit of loudness is the decibel (dB).
• Effect of pressure on the speed of sound:
• The speed of sound is independent of pressure.
• Effect of temperature on the speed of sound:
• The speed of sound increases with the increase of the temperature of the medium.
• In steel, the speed of sound is 5960 m/s. Hence, option A is correct
• In nickel, the speed of sound is 6040 m/s. Hence, option B is correct.

Important Points

In any medium, if the temperature increases, the speed of sound also increases and vice versa.

The correct answer is Base + Acid → Salt + Water.

• In general, a neutralization reaction can be written as Base + Acid → Salt + Water.

Key Points

• Neutralization Reaction:
• It is a chemical reaction in which an acid and base react together to form salt and water as products.
• The formation of Sodium Chloride is an example of the neutralization reaction.
• HCl + NaOH → NaCl + H₂O

Additional Information

• Acid:
• An acid is a substance which:
• Is sour in taste.
• Turns blue litmus paper into red.
• Contains replaceable hydrogen.
• Gives hydrogen ion (H+) in an aqueous solution.
• Can donate a proton.
• Can accept an electron
• Bases:
• A Base is a substance which:
• Is bitter in taste.
• Turns red litmus paper into the blue.
• Gives hydroxyl ions (OH–) in an aqueous solution.
• Can accept a proton.
• Can donate electrons.

Shortcut Trick

Total items purchased = 15 (Black) + 15 (Red) + 20 (Blue) = 50

Total items = (Only 1 color) + 2 × (Only 2 colors) + 3 × (All 3 colors)

At least two = (Only 2 colors) + (All 3 colors) ⇒ 8 = (Only 2 colors) + 2 ⇒ Only 2 colors = 6

50 = (Only 1 color) + 2 × 6 + 3 × 2 ⇒ 50 = (Only 1 color) + 12 + 6

Only 1 color = 50 − 18 = 32

∴ The correct answer is 32 customers.

Alternate Method

Given:

Total Black (B) = 15, Total Red (R) = 15, Total Blue (Bl) = 20

Intersection of all three (B ∩ R ∩ Bl) = 2

At least two = 8

Calculations:

⇒ Let customers who bought only two colors be x, y, and z.

⇒ At least two colors = (x + y + z) + (All three) = 8

⇒ (x + y + z) + 2 = 8 ⇒ x + y + z = 6

⇒ Let customers who bought only one color be N₁.

⇒ Sum of individual sets = N₁ + 2 × (Only 2 colors) + 3 × (All 3 colors)

⇒ 15 + 15 + 20 = N₁ + 2 × 6 + 3 × 2

⇒ 50 = N₁ + 12 + 6

⇒ N₁ = 50 − 18 = 32

∴ The correct answer is 32 customers.

Additional Information

Venn Diagram Formula (3 Sets)

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

Exactly vs At least

'At least two' includes those who bought exactly 2 colors and those who bought exactly 3 colors.

Only One Color Calculation

n(Only A) = n(A) − [n(Only A&B) + n(Only A&C) + n(All three)].

The correct answer is Madhya Pradesh.

• Madhya Pradesh has launched the "Anandam" program to help needy people.

Key Points

• Anandam Scheme:
• The scheme was launched by Chief Minister Shivraj Singh Chouhan.
• The programme comes under the newly-formed Aanand Department.
• The programme aims to help needy persons and to increase the happiness per cent of the citizen.
• The scheme has also been launched at the panchayat level.

The Venn diagram is given below:-

Shirts are made of cloth and Lock is different.

Hence, "option 3" is the correct answer.

The correct answer is Dendrite.

• Each neuron is made up of a cyton (cell body), from which many small branches emerge, which are called a dendrite.

Key Points

• Structure of Neuron:
• Dendrites
• Dendrites are branch-like structures that receive signals from other neurons and allow the transmission of signals to the cell body.
• Cell Body:
• The cell body of a neuron consists of a nucleus, Golgi body, endoplasmic reticulum, mitochondria and other components.
• Axon:
• It is a tube-like structure that carries an electrical impulse from the cell body of a neuron to the axon terminals that transmits the impulse to another neuron.
• Synapse:
• It is the junction between the terminal of one neuron and the dendrites of another neuron.

The Venn diagram is given below:-

Conclusion :

1. Some drops are empty. → False (Empty word is not present in statement. So, some drops are empty is wrong.)
2. Bottles are jams. → False (There is no direction relation given between Jam and Bottle so, bottles are jams it can be possible but not definite, hence, false)

Hence, "option 4" is the correct answer.

Additional Information

The correct answer is Sanjeev Gupta.

Key Points

• Sanjeev Gupta is a British businessman of Indian origin.
• He is a steel tycoon in Britain.
• He has been appointed by Prince Charles as the official ambassador of the Industrial Cadet Program, which aims to nurture manufacturing skills.
• The aim of the program is to give children and young people the direct structured experience of industry while still at school or college.

Given:

Total revenue of the company ABC in 2015 = Rs.3628000

Percentage of manufacturing of other leather items = 5% 

Calculation:

Revenue generated by manufacturing other leather items:

⇒ Total Revenue × 5/100 

⇒ 3628000 × 5/100 

⇒ Rs.181400

∴ The required result is Rs.181400.

The correct answer is Sc, Ga and Ge.

Key Points

• Mendeleev’s periodic table is an arrangement of elements in an increasing atomic mass.
• Chlorine, oxygen, and silicon were included in Mendeleev's periodic table.
• In Mendeleev's periodic table, Sc, Ga and Ge found a place in the table later.
• Germanium was discovered, and it filled in the gaps left by Mendeleev while also possessing the desired qualities.
• Unnamed elements were given the names EKA- Boron, EKA- Aluminum, and EKA Silicon by Mendeleev, which were eventually replaced by Scandium, Gallium, and Germanium.
• Elements are, arranged in an increasing order atomic mass, in a horizontal line.
• This horizontal arrangement of elements is a ‘period’.

Additional Information

• The metallic property of an element in the modern periodic table decreases from left to right in a period but increases from top to bottom in a group.
• Elements of the same group in the modern periodic table have the same valence electrons.
• The atomic mass of an element is the average mass of the atoms of an element measured in the atomic mass unit (AMU, also known as daltons, D).

The logic followed here is:-

Hence, "option 2" is the correct answer.

Shortcut Trick

Recognize the given expression as a perfect square: x² + 2(x)(1/5) + (1/5)² = (x + 1/5)² = 0.

This directly gives the value of x = −1/5.

Substitute x in the required expression: (−1/5 − 2/3)² = [(−3 − 10)/15]².

(−13/15)² = 169/225.

∴ The correct answer is 169/225.

Alternate Method

Given: x² + 2x/5 + 1/25 = 0

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

⇒ x² + 2 × x × (1/5) + (1/5)² = 0

⇒ (x + 1/5)² = 0

⇒ x + 1/5 = 0

⇒ x = −1/5

Now, we need to calculate the value of (x − 2/3)²:

⇒ (−1/5 − 2/3)²

Take the Least Common Multiple (LCM) of 5 and 3, which is 15:

⇒ [(−3 − 10) / 15]²

⇒ (−13 / 15)²

⇒ 169 / 225

∴ The correct answer is 169/225.

Additional Information

Perfect Square Trinomial

An expression of the form a² + 2ab + b² can be simplified to (a + b)², and a² − 2ab + b² simplifies to (a − b)².

Nature of Roots

In a quadratic equation ax² + bx + c = 0, if the discriminant D = b² − 4ac is equal to zero, the roots are real and equal.

Squaring Fractions

To square a fraction (a/b), square both the numerator and the denominator separately: (a/b)² = a² / b².

Given:

144/0.144 = 14.4/x

Calculation:

144/0.144 = 14.4/x

⇒ 144 × x = 14.4 × 0.144 

⇒ x = 144/10 × 144/1000 × 1/144 

⇒ x = 144/10000

⇒ x = 0.0144

∴ The value of $\frac{144}{0.144}$ = $\frac{14.4}{x}$ is 0.0144

The correct answer is Tamil.

• The epics 'Silappadikaram' and 'Manimekalai' of the Sangam period were written in the Tamil language.

Key Points

• The Sangam Age:
• It is a period between the 3rd century B.C. and 3rd century A.D. in South India.
• The period is named after the Sangam academies which were held during that period and flourished under the royal patronage of the Pandya kings of Madurai.
• The Sangam Age was ruled by three dynasties namely the Cheras, Cholas and Pandyas.
• Silappathikaram was written by Elango Adigal.
• Manimekalai was written by Sittalai Sattanar.

The correct answer is 3 C.

• The work done between two points having the potential of 12 V is 36 J. The electric charge flowing between those points is 3 C.

Key Points

• Work:
• When a body is displaced by applying a force on it, then work is said to be done.
• Work = Force × displacement.
• Its SI unit is joule.
• In electricity,
• Work done=Potential Difference x Charge
• Given,
• Work - 36 J,
• Potential difference - 12 V
• Charge-?
• By Formula,
• Work = potential difference x charge
• Charge= Work/ potential difference
• Charge = 36 J/12 V
• Charge = 3 Coulomb

The correct answer is Trains and Airplanes.

Key Points

• Inertia is the tendency of undisturbed objects to remain at rest or to continue moving at the same speed.
• The quantity of mass in a body determines its inertia.
• A body of larger mass has more inertia; hence Trains and Airplanes has more inertia than the other examples given.
• The first law of motion(Newton's first law) is also known as the law of inertia.
• When a motorcar makes a sharp turn at a high speed, we tend to get thrown to one side due to the effect ​of inertia.
• The natural tendency of an object to resist a change in its state of motion or rest is known as inertia.
• An object's mass is a measure of its inertia.

The correct answer is Less than the bullet.

• If a shot is fired from a gun and the gun comes backwards, then the kinetic energy of the gun will be Less than the bullet.

Key Points

• The relation between kinetic energy and momentum is given by
• $K = {P^2 \over 2m}$
• P=mv
• As we see the kinetic energy is inversely proportional to the mass keeping momentum constant.
• Hence, the kinetic energy of the gun is lesser than the kinetic energy of the bullet.

Additional Information

• Kinetic Energy
• If a body of mass m is moving with velocity
  

v, then kinetic energy

• $K = {{1\over2}}{mv^2}$
  

where p is the linear momentum.

• When momentum is doubled, kinetic energy becomes four times.
• If a body is moving in horizontal circle then its kinetic energy is same at all points, but if it is moving in vertical circle, then the kinetic energy is different at different points.

Shortcut Trick

Find the LCM of 15, 16, and 25.

LCM(15, 16, 25) = 1200.

Divide 20000 by 1200 and find the remainder.

20000 ÷ 1200 ⇒ Remainder = 800.

∴ The correct answer is 800.

Alternate Method

Given: Numbers are 15, 16, and 25. Target number is 20000.

Formula Used: Number to be subtracted = Number − (Largest multiple of LCM less than Number)

Step 1: Calculate the Least Common Multiple (LCM) of 15, 16, and 25.

⇒ 15 = 3 × 5

⇒ 16 = 2⁴

⇒ 25 = 5²

⇒ LCM = 2⁴ × 3 × 5² = 16 × 3 × 25 = 1200.

Step 2: Divide 20000 by the LCM (1200).

⇒ 20000 = (1200 × 16) + 800

⇒ Remainder = 800.

Step 3: The remainder is the smallest number to be subtracted to make the result exactly divisible.

∴ The correct answer is 800.

Additional Information

LCM (Least Common Multiple)

The smallest positive integer that is divisible by each of the given numbers. It is used to find a common dividend.

Subtraction vs Addition for Divisibility

To make a number N divisible by D: subtract the remainder (R) or add (D − R).

Divisibility Rules

A number is divisible by 25 if its last two digits are 00, 25, 50, or 75. A number is divisible by 15 if it is divisible by both 3 and 5.

The correct answer is Upthrust/Area.

Key Points

• Pressure:
• Pressure is defined as a force acting normally on the unit area on the surface.
• SI unit of pressure is N/m²
• It is also called Pascal (Pa).
• Pressure is a scalar quantity.
• Atmospheric pressure of 1 atm = 1.01 × 10–5 N/m² = 760 torr.