63rd BPSC Prelims 2018 Part 5 Question Paper with Answers and Solutions (Solved)

🔢 Concept: Euclidean Division and Remainders

According to the question, when a number is divided by 342, the remainder is 47. We have to find the remainder when the same number is divided by 19.

Step-by-Step Solution

Let the required number be N.

According to the division algorithm:

Dividend = Divisor × Quotient + Remainder

Therefore,

\[ N=342q+47 \]

where \(q\) is the quotient.

Now, we have to divide this number by 19.

Since,

\[ 342=19\times18 \]

Substituting this value:

\[ N=(19\times18)q+47 \]

\[ N=19(18q)+47 \]

The term \(19(18q)\) is completely divisible by 19. Therefore, only 47 will determine the remainder.

Now divide 47 by 19:

\[ 47=19\times2+9 \]

Hence, the remainder is 9.

📊 Quick Calculation Table

🧠 Important Mathematical Facts

• Division algorithm: For any integer \(a\) and positive integer \(b\), we can write \(a=bq+r\), where \(0\leq r<b\).
• Remainder property: If a number is expressed as a multiple of the divisor plus another number, the remainder is the remainder obtained by dividing that other number by the divisor.
• Divisibility: Since 342 is exactly divisible by 19, the multiple \(342q\) contributes zero remainder when divided by 19.
• Remainder range: A remainder must always be smaller than the divisor and cannot be negative.
• Useful shortcut: If \(a\) is divisible by \(b\), then the remainder of \(aq+r\) upon division by \(b\) is the same as the remainder of \(r\) upon division by \(b\).

Quick Revision: \(N=342q+47\); \(342=19\times18\); \(47=19\times2+9\). Required remainder = 9.

✔️ Final Answer: (B) 9

💰 Concept: Percentage of Income, Expenditure and Savings

According to the English question, a person spends 66⅔% of his income and saves ₹1,200 per month. We have to calculate his monthly expenditure.

Important: The Hindi question supplied here states 66%, whereas the English question states 66⅔%. The given answer options match the English figure of 66⅔%, so the calculation below uses 66⅔%.

Step-by-Step Solution

We know that:

\[ \text{Income}=\text{Expenditure}+\text{Savings} \]

Percentage of expenditure:

\[ 66\tfrac{2}{3}\%=\frac{200}{3}\% \]

Percentage of savings:

\[ 100\%-66\tfrac{2}{3}\%=33\tfrac{1}{3}\% \]

Therefore, savings represent one-third of the total income.

Given:

\[ \text{Savings}=1,200 \]

Let monthly income be \(I\).

\[ \frac{1}{3}I=1,200 \]

\[ I=1,200\times3=3,600 \]

Monthly expenditure:

\[ =\frac{2}{3}\times3,600 \]

\[ =2,400 \]

Hence, the monthly expenditure is ₹2,400.

📊 Income Distribution

🧠 Important Percentage Facts

• 66⅔%: Equivalent to the fraction \(\frac{2}{3}\).
• 33⅓%: Equivalent to the fraction \(\frac{1}{3}\).
• 50%: Equivalent to \(\frac{1}{2}\).
• 25%: Equivalent to \(\frac{1}{4}\).
• 20%: Equivalent to \(\frac{1}{5}\).
• Income relationship: Income is the sum of expenditure and savings. If two of these quantities are known, the third can be calculated.

⚡ Shortcut Method

If expenditure is 66⅔%, savings are 33⅓%. Therefore, the ratio of expenditure to savings is:

\[ \frac{2}{3}:\frac{1}{3}=2:1 \]

Savings = ₹1,200 = 1 part.

Expenditure = 2 parts:

\[ =2\times1,200=2,400 \]

⚠️ Hindi Wording Clarification

If the Hindi figure of 66% is taken literally, savings would be 34% of income. In that case:

\[ \text{Income}=\frac{1,200\times100}{34} =3,529.41\text{ (approximately)} \]

Expenditure would be approximately ₹2,329.41, which is not among the given options. Therefore, the intended percentage is clearly 66⅔%, consistent with the English question and option (A).

Quick Revision: Expenditure = 66⅔% = 2/3; Savings = 33⅓% = 1/3; Savings ₹1,200 → Income ₹3,600 → Expenditure ₹2,400.

✔️ Final Answer: (A) ₹2,400

📈 Concept: Profit and Loss Percentage

A man earns a profit of 20% by selling an article at a certain selling price. If he sells the same article at double that selling price, we have to calculate the new profit percentage.

Step-by-Step Solution

Let the cost price (CP) of the article be ₹100.

Profit = 20% of ₹100 = ₹20.

Therefore, the original selling price (SP) is:

\[ SP=CP+\text{Profit} \]

\[ =100+20=120 \]

According to the question, the article is now sold at double the original selling price.

New selling price:

\[ =2\times120=240 \]

New profit:

\[ =240-100=140 \]

Profit percentage:

\[ =\frac{\text{Profit}}{\text{Cost Price}}\times100 \]

\[ =\frac{140}{100}\times100=140\% \]

Hence, the new profit percentage is 140%.

📊 Comparison of Original and New Selling Prices

⚡ Shortcut Formula

When the original profit is \(x\%\) and the selling price is doubled, the new profit percentage is:

\[ \text{New Profit \%}=100+2x \]

Here, \(x=20\).

\[ =100+2(20)=140\% \]

Why does this formula work? If CP is ₹100, the original SP is \(100+x\). Doubling SP gives \(2(100+x)\). The new profit is \(2(100+x)-100=100+2x\), which is also the profit percentage because CP is ₹100.

🧠 Important Profit and Loss Facts

• Cost Price (CP): The price at which an article is purchased or produced.
• Selling Price (SP): The price at which an article is sold.
• Profit: When SP is greater than CP, Profit = SP − CP.
• Loss: When CP is greater than SP, Loss = CP − SP.
• Profit percentage: \(\frac{\text{Profit}}{CP}\times100\).
• Loss percentage: \(\frac{\text{Loss}}{CP}\times100\).
• Important rule: Profit and loss percentages are normally calculated on the cost price, not the selling price.

🔎 Common Examination Trap

Doubling the selling price does not mean that the profit percentage simply doubles. The original selling price includes both the cost price and the original profit. Therefore, the new profit must be calculated after subtracting the unchanged cost price from the doubled selling price.

Quick Revision: CP = ₹100 → Original SP = ₹120 → New SP = ₹240 → New Profit = ₹140 → Profit percentage = 140%.

✔️ Final Answer: (A) 140

👷 Concept: Time and Work

10 women can complete a work in 7 days, while 10 children can complete the same work in 14 days. We have to find the time taken by 5 women and 10 children working together.

Step-by-Step Solution

Step 1: Assume the total work.

Take the total work as the LCM of 7 and 14:

\[ \text{Total Work}=14\text{ units} \]

Step 2: Calculate the work done by 10 women.

10 women complete 14 units in 7 days.

\[ \text{Work done by 10 women in 1 day} =\frac{14}{7}=2\text{ units} \]

Therefore, work done by 1 woman in 1 day:

\[ =\frac{2}{10}=\frac{1}{5}\text{ unit} \]

Step 3: Calculate the work done by 10 children.

10 children complete 14 units in 14 days.

\[ \text{Work done by 10 children in 1 day} =\frac{14}{14}=1\text{ unit} \]

Therefore, work done by 1 child in 1 day:

\[ =\frac{1}{10}\text{ unit} \]

Step 4: Calculate the combined daily work.

Work done by 5 women in one day:

\[ =5\times\frac{1}{5}=1\text{ unit} \]

Work done by 10 children in one day:

\[ =10\times\frac{1}{10}=1\text{ unit} \]

Total work done by 5 women and 10 children in one day:

\[ =1+1=2\text{ units} \]

Step 5: Calculate the required time.

\[ \text{Time}=\frac{\text{Total Work}}{\text{Daily Work}} \]

\[ =\frac{14}{2}=7\text{ days} \]

Hence, 5 women and 10 children will complete the work in 7 days.

📊 Work and Efficiency Table

🧠 Important Time and Work Facts

• Basic formula: Work = Efficiency × Time.
• Efficiency: Work completed by a person or group in one unit of time.
• Inverse relationship: For the same work and constant efficiency, more workers mean fewer days, and fewer workers mean more days.
• Combined work: When workers work together, their individual daily efficiencies are added.
• LCM method: Taking total work as the LCM of the given completion times often makes calculations easier.
• Worker comparison: One woman works twice as fast as one child in this question, because the same number of women completes the work in half the time taken by the same number of children.

⚡ Shortcut Method

10 women complete the work in 7 days, so their daily work rate is \(\frac{1}{7}\).

10 children complete the work in 14 days, so their daily work rate is \(\frac{1}{14}\).

5 women do half the work of 10 women per day:

\[ \frac{1}{2}\times\frac{1}{7}=\frac{1}{14} \]

Therefore, combined daily work:

\[ \frac{1}{14}+\frac{1}{14}=\frac{1}{7} \]

Time required:

\[ =\frac{1}{1/7}=7\text{ days} \]

Quick Revision: 10 women → 1/7 work per day; 10 children → 1/14 work per day; 5 women → 1/14 work per day; combined rate → 1/7 work per day; time → 7 days.

✔️ Final Answer: (D) 7

🔢 Concept: Counting Multiples of a Number

We have to find how many integers strictly between 11 and 90 are divisible by 7. The first step is to identify the smallest and largest multiples of 7 within this range.

Step-by-Step Solution

Step 1: Find the first multiple of 7 greater than 11.

\[ 7\times1=7,\quad 7\times2=14 \]

Therefore, the first required multiple is 14.

Step 2: Find the last multiple of 7 less than 90.

\[ 7\times12=84,\quad 7\times13=91 \]

Therefore, the last required multiple is 84.

Step 3: List the multiples.

The required numbers are:

\[ 14,21,28,35,42,49,56,63,70,77,84 \]

There are 11 numbers.

⚡ Shortcut Method

The number of multiples of 7 from 1 to 90 is:

\[ \left\lfloor\frac{90}{7}\right\rfloor=12 \]

The number of multiples of 7 from 1 to 11 is:

\[ \left\lfloor\frac{11}{7}\right\rfloor=1 \]

Therefore, the number of multiples strictly between 11 and 90 is:

\[ 12-1=11 \]

Hence, the required count is 11.

📊 List of All Required Multiples

🧠 Important Mathematical Facts

• Multiple: A number is a multiple of another number if it can be expressed as their product with an integer.
• Smallest multiple greater than a number: Identify the next integer multiple after the given lower limit.
• Largest multiple below a number: Identify the greatest integer multiple that does not exceed the upper limit.
• Counting formula: The number of multiples of a positive integer \(d\) from 1 to \(n\) is \(\lfloor n/d\rfloor\).
• Strictly between two limits: For positive integers \(a<b\), the number of multiples of \(d\) strictly between them is \(\lfloor(b-1)/d\rfloor-\lfloor a/d\rfloor\), when \(a\) and \(b\) are integers.
• Arithmetic progression: Consecutive multiples of 7 form an arithmetic progression with first term 14 and common difference 7.

🔎 Arithmetic Progression Method

The multiples form an arithmetic progression:

\[ 14,21,28,\ldots,84 \]

Here, first term \(a=14\), last term \(l=84\), and common difference \(d=7\).

Number of terms:

\[ n=\frac{l-a}{d}+1 \]

\[ =\frac{84-14}{7}+1 =\frac{70}{7}+1 =10+1=11 \]

Quick Revision: First multiple = 14; last multiple = 84; common difference = 7; number of multiples = \((84-14)/7+1=11\).

✔️ Final Answer: (E) 11

🚣 Boats and Streams – Upstream and Downstream

The speed of the boat in still water is 7½ km/hour, and the speed of the river current given in the Hindi question is 1½ km/hour. The total time taken for the onward and return journeys is 50 minutes. We have to calculate the one-way distance.

📘 Important Formulae

• Downstream speed: Speed of boat in still water + Speed of stream.
• Upstream speed: Speed of boat in still water − Speed of stream.
• Time: Distance ÷ Speed.
• Distance: Speed × Time.

🧮 Step-by-Step Solution

Step 1: Calculate downstream speed.

Downstream speed = 7½ + 1½ = 9 km/hour.

Step 2: Calculate upstream speed.

Upstream speed = 7½ − 1½ = 6 km/hour.

Step 3: Convert the total time into hours.

50 minutes = 50/60 hour = 5/6 hour.

Step 4: Let the one-way distance be d km.

Time taken downstream = d/9 hour.

Time taken upstream = d/6 hour.

According to the question:

d/9 + d/6 = 5/6

Taking the LCM of 9 and 6, which is 18:

(2d + 3d)/18 = 5/6

5d/18 = 5/6

5d = 15

d = 3 km.

📊 Quick Calculation Table

⚠️ Important Note About the Question

The English version printed in the question states that the river is running at 12 km/hour, whereas the Hindi version states 1½ km/hour. A boat moving at 7½ km/hour in still water cannot travel upstream against a current of 12 km/hour. Therefore, the English figure appears to contain a printing or transcription error. The answer 3 km is obtained using the Hindi figure of 1½ km/hour.

🧠 Further Exam-Oriented Facts

• Still-water speed: The speed of a boat when the water is not flowing.
• Stream speed: The speed at which river water flows.
• Downstream: The boat moves in the direction of the current; its speed increases.
• Upstream: The boat moves against the current; its speed decreases.
• Average speed for equal distances: If a boat covers equal distances upstream and downstream, average speed is the harmonic mean of the two speeds: (2 × downstream speed × upstream speed) ÷ (downstream speed + upstream speed).
• Round-trip time: For a fixed distance, upstream and downstream times are different because their speeds are different.

Quick Revision: Downstream = Boat speed + Stream speed; Upstream = Boat speed − Stream speed; One-way distance in this question = 3 km.

✔️ Final Answer: (A) 3 km

💰 Compound Interest – Finding the Principal

Under compound interest, interest is added to the principal at the end of each compounding period. In this question, the amount after 2 years is ₹4,624 and the amount after 3 years is ₹4,913. We need to calculate the original principal.

📘 Important Formulae

Compound Amount:

A = P(1 + R/100)ⁿ

Where:

• A = Amount after n years.
• P = Principal or original sum.
• R = Annual rate of interest.
• n = Number of years.

When the amounts for two consecutive years are given, the interest rate can be found by dividing the later amount by the earlier amount.

🧮 Step-by-Step Solution

Step 1: Find the annual growth factor.

Amount after 2 years = ₹4,624.

Amount after 3 years = ₹4,913.

Therefore, the interest earned during the third year is:

₹4,913 − ₹4,624 = ₹289.

Step 2: Calculate the rate of compound interest.

Interest for the third year is calculated on the amount at the end of the second year.

Rate = (289 ÷ 4,624) × 100

= (289/4,624) × 100

= (1/16) × 100

= 6¼% per annum.

Step 3: Find the original principal.

Amount after 2 years = P × (1 + 6.25/100)²

4,624 = P × (17/16)²

4,624 = P × 289/256

P = 4,624 × 256/289

Since 4,624 ÷ 289 = 16:

P = 16 × 256

P = ₹4,096.

📊 Quick Calculation Table

🧠 Further Exam-Oriented Facts

• Simple Interest (SI): Interest is calculated only on the original principal throughout the period.
• Compound Interest (CI): Interest is calculated on the principal as well as previously accumulated interest.
• Annual compound interest: Amount = P(1 + R/100)ⁿ.
• Two consecutive years: If the amount after two years is A₂ and after three years is A₃, then the annual multiplication factor is A₃/A₂.
• Interest for the third year: It is calculated on the amount accumulated at the end of the second year, not merely on the original principal.
• Difference between CI and SI: For two years at an annual rate R%, the difference is P × (R/100)².

Quick Revision: Third-year interest = ₹289; annual compound interest rate = 6¼%; principal = ₹4,096.

✔️ Final Answer: (C) ₹4,096

📈 Shares and Dividends – Market Value of a Share

The question refers to shares with a face value of ₹20 each and a dividend rate of 9%. The investor wants an annual return of 12% on the amount invested. We have to calculate the market value of each share.

📘 Important Concepts and Formulae

• Face Value: The nominal value of a share mentioned by the issuing company.
• Dividend: The amount distributed by a company to shareholders, generally expressed as a percentage of face value.
• Market Value: The price at which a share is bought or sold in the market.
• Dividend per share: Face value × Dividend rate/100.
• Yield: (Annual dividend per share ÷ Market value per share) × 100.

🧮 Step-by-Step Solution

Step 1: Identify the face value and dividend rate.

Face value of each share = ₹20.

Dividend rate = 9%.

Step 2: Calculate the annual dividend per share.

Dividend = 20 × 9/100

= 180/100

= ₹1.80.

Step 3: Calculate the market value.

The investor wants a return of 12% on the amount invested.

Let the market value of each share be ₹x.

According to the yield formula:

(1.80/x) × 100 = 12

1.80 × 100 = 12x

x = 180/12

x = ₹15.

📊 Quick Calculation Table

🧠 Further Exam-Oriented Facts

• Face value and market value are different: Face value is the nominal value, whereas market value is determined by demand, supply and other market factors.
• Dividend is based on face value: A 9% dividend on a ₹20 share means ₹1.80 per share, not 9% of its market price.
• At par: When market value equals face value.
• At premium: When market value is greater than face value.
• At discount: When market value is lower than face value. Here, the share is purchased at a discount because ₹15 is less than its ₹20 face value.
• Yield increases when market price decreases: If the dividend remains fixed, a lower purchase price gives a higher percentage return.
• Total investment: For 20 shares at ₹15 each, total investment = 20 × 15 = ₹300; total annual dividend = 20 × 1.80 = ₹36; yield = (36/300) × 100 = 12%.

Quick Revision: Face value = ₹20; dividend = 9% = ₹1.80 per share; desired yield = 12%; market value = ₹15 per share.

✔️ Final Answer: (B) 15

📊 Data Interpretation – Pie Chart

The pie chart represents the expenditure of a country on different sports during a particular year. The central angle of each sector represents the proportion of total expenditure allocated to that sport. We have to calculate how much percent less is spent on football than on cricket.

📘 Important Concept and Formula

In a pie chart, the entire circle represents 100% of the total and measures 360°.

Therefore:

Percentage represented by a sector = (Central angle ÷ 360°) × 100.

When the question asks how much percent less one quantity is than another, the difference must be divided by the original comparison quantity.

Percentage decrease = [(Original value − New value) ÷ Original value] × 100.

📋 Information Given in the Pie Chart

🧮 Step-by-Step Solution

Step 1: Identify the angles for cricket and football.

Cricket = 81°.

Football = 54°.

Step 2: Calculate the difference between the two angles.

Difference = 81° − 54° = 27°.

Step 3: Calculate the percentage decrease with cricket as the base.

Percentage less = [(Cricket angle − Football angle) ÷ Cricket angle] × 100

= [(81 − 54) ÷ 81] × 100

= (27/81) × 100

= (1/3) × 100

= 33⅓%.

📊 Alternative Method Using Expenditure Percentages

Cricket’s share = (81/360) × 100 = 22.5%.

Football’s share = (54/360) × 100 = 15%.

Difference = 22.5 − 15 = 7.5 percentage points.

Percentage less than cricket = (7.5/22.5) × 100 = 33⅓%.

🧠 Further Exam-Oriented Facts

• Total angle of a pie chart: Always 360°.
• Percentage conversion: 1° represents 100/360 = 5/18% of the total.
• Cricket: 81° represents 22.5% of the total expenditure.
• Football: 54° represents 15% of the total expenditure.
• Difference: The difference is 27° or 7.5 percentage points of the total expenditure.
• Percentage less is not the same as percentage-point difference: The percentage-point difference is 7.5, but the percentage by which football expenditure is less than cricket expenditure is 33⅓%.
• Base value matters: To calculate how much football is less than cricket, cricket is the denominator. If the question asked how much cricket is more than football, football would be the denominator.

⚠️ Common Examination Trap

Do not calculate (81 − 54)/360 × 100 and select 7.5% as the answer. That gives the difference as a percentage of the entire country’s expenditure. The question asks the percentage by which football expenditure is less than cricket expenditure, so the difference must be divided by the cricket value, 81°.

Quick Revision: Cricket = 81°; Football = 54°; Difference = 27°; Percentage less = (27/81) × 100 = 33⅓%.

✔️ Final Answer: (E) 33⅓%

🤝 Partnership – Distribution of Profit

In a partnership, profit is generally distributed in proportion to the product of each partner’s capital invested and the time for which it remains invested. A invests ₹76,000 at the beginning of the year. B joins after some months with ₹57,000. At the end of the year, their profit-sharing ratio is 2:1. We have to calculate the number of months after which B joined.

📘 Important Formula

Profit-sharing ratio = (Capital of A × Time of A) : (Capital of B × Time of B).

In other words:

Profit share ∝ Capital × Time.

🧮 Step-by-Step Solution

Step 1: Write the given information.

• A’s capital = ₹76,000.
• B’s capital = ₹57,000.
• Total business period = 12 months.
• Profit-sharing ratio of A and B = 2:1.

Step 2: Let B invest for x months.

Since B joins after the beginning of the year, A’s investment period is 12 months and B’s investment period is x months.

Step 3: Apply the partnership formula.

(76,000 × 12) : (57,000 × x) = 2 : 1

Therefore:

(76,000 × 12)/(57,000 × x) = 2/1

912,000/(57,000x) = 2

912,000 = 114,000x

x = 912,000/114,000

x = 8 months.

Step 4: Calculate when B joined.

Total business period = 12 months.

B’s investment period = 8 months.

Therefore, B joined after = 12 − 8 = 4 months.

📊 Quick Calculation Table

🧠 Further Exam-Oriented Facts

• Partnership: A business arrangement in which two or more persons agree to share profits and, as provided by their agreement and applicable law, business responsibilities.
• Capital and time: When partners invest different amounts for different periods, profit is divided according to capital multiplied by time, unless a different valid agreement applies.
• Equal capital: If two partners invest equal capital for different periods, their profit ratio depends on their investment periods.
• Equal time: If partners invest for the same period, their profit ratio depends on their respective capitals.
• Working partner: A partner who actively participates in the management of the business.
• Sleeping partner: A partner who contributes capital but does not actively participate in daily management.
• Important distinction: The question asks when B joined, not how long B invested. B invested for 8 months and therefore joined 4 months after the business began.

Quick Revision: A’s capital-time product = 76,000 × 12; B’s capital-time product = 57,000 × 8; profit ratio = 2:1; B invested for 8 months and joined after 4 months.

✔️ Final Answer: (B) 4 months

⏱️ Quartz Crystals and Their Use in Clocks

Quartz crystals used in clocks are made of silicon dioxide (SiO₂). Quartz is a naturally occurring crystalline form of silica. It is widely used in electronic clocks and watches because of its piezoelectric property, which means that it produces an electric charge when mechanical pressure is applied and can also vibrate mechanically when an electric field is applied.

In a quartz clock, an electronic circuit applies an alternating voltage to a small quartz crystal. The crystal vibrates at a highly stable natural frequency. These vibrations are converted into regular electrical pulses, which are counted by the clock’s electronic circuit to measure time accurately.

⚡ Piezoelectric Effect

The piezoelectric effect is the ability of certain materials to generate an electrical potential when mechanical stress is applied. The reverse piezoelectric effect occurs when such materials undergo mechanical deformation under an applied electric field. Quartz is an important natural piezoelectric material.

📊 Important Properties of Quartz

🔬 Other Important Forms of Silicon Dioxide

• Quartz: A crystalline form of silicon dioxide commonly found in rocks and sand.
• Amethyst: A purple variety of quartz used as a gemstone.
• Agate: A banded variety of microcrystalline silica.
• Opal: A hydrated amorphous form of silica, unlike ordinary crystalline quartz.

🧠 Further Exam-Oriented Facts

• Silicon (Si): Atomic number 14; widely used as a semiconductor in electronic devices.
• Germanium (Ge): Atomic number 32; also used as a semiconductor.
• Titanium dioxide (TiO₂): Used in paints, pigments and sunscreens.
• Sodium silicate: Commonly known as water glass; used in adhesives, detergents and other industrial applications.
• Quartz clock: Its accuracy depends on the stable frequency of the quartz oscillator.
• Quartz versus silicon: Quartz is silicon dioxide (SiO₂), whereas elemental silicon has the chemical symbol Si.

Quick Revision: Quartz → SiO₂ → Piezoelectric effect → Stable vibrations → Accurate timekeeping.

✔️ Final Answer: (B) Silicon dioxide (SiO₂)

🧪 Bromine: A Reddish-Brown Liquid Halogen

Bromine (Br) is a non-metallic chemical element belonging to Group 17 of the periodic table. At ordinary room temperature, it exists as a reddish-brown, volatile liquid. It is one of the very few elements that are liquid at room temperature. Its molecules exist as diatomic molecules, represented by the formula Br₂.

The correct option is (D) red liquid, although the scientifically more precise description is reddish-brown liquid. Bromine gives off reddish-brown vapours and has a strong, unpleasant odour. It is corrosive and toxic, so it must be handled with appropriate laboratory safety precautions.

📊 Important Physical and Chemical Properties

🧬 Physical States of Halogens

Halogens belong to Group 17 of the periodic table. Their physical states change as atomic size and intermolecular forces increase down the group.

🔬 Important Uses of Bromine

• Flame retardants: Certain brominated compounds are used in materials to reduce flammability, although several uses are restricted because of environmental and health concerns.
• Water treatment: Bromine-based compounds are used as disinfectants in some swimming pools and industrial water systems.
• Photography: Silver bromide (AgBr) was historically important in photographic films and papers because it is light-sensitive.
• Pharmaceuticals: Certain bromine-containing compounds are used in the manufacture of medicines.
• Chemical industry: Bromine compounds are used in various chemical synthesis processes.

🧠 Further Exam-Oriented Facts

• Liquid non-metals: Bromine is the only non-metallic element that is liquid at ordinary room temperature.
• Other liquid element: Mercury (Hg) is a metal that is liquid at ordinary room temperature.
• Halogens: The name means salt-forming elements. They have seven electrons in their outermost shell.
• Reactivity: Halogen reactivity generally decreases down Group 17: fluorine is the most reactive halogen.
• Bromine water: It is used in laboratory tests for unsaturation; alkenes can decolourise bromine water through an addition reaction.
• Safety: Bromine is toxic, corrosive and harmful by inhalation or skin contact. It should only be handled under suitable laboratory safety conditions.

Quick Revision: Bromine → Br → Atomic number 35 → Group 17 → Reddish-brown liquid → Br₂.

✔️ Final Answer: (D) Red liquid (more precisely, reddish-brown liquid)

🔥 Gases Used in Welding: Oxy-Acetylene Welding

The commonly used gases in oxy-acetylene welding are oxygen (O₂) and acetylene (C₂H₂). Acetylene is a highly combustible fuel gas, while oxygen supports combustion. When acetylene burns in oxygen, it produces a very high-temperature flame capable of melting and joining metals.

The temperature of an oxy-acetylene flame can reach approximately 3,100–3,200°C, depending on operating conditions. This makes it suitable for welding and cutting many metals. The process is widely used in metal fabrication, repair work and engineering workshops.

⚙️ How Does Oxy-Acetylene Welding Work?

• Fuel gas: Acetylene provides the combustible fuel.
• Oxidising gas: Oxygen supports the combustion of acetylene.
• Flame: The gases are mixed in a welding torch and ignited to produce a high-temperature flame.
• Joining: The heat melts the edges of the metal pieces; filler metal may be added when required.
• Welding versus cutting: Welding joins metal pieces, whereas oxy-fuel cutting uses a high-temperature flame and an oxygen jet to cut suitable metals.

🧪 Chemical Reaction

The complete combustion of acetylene in oxygen can be represented by the balanced equation:

2C₂H₂ + 5O₂ → 4CO₂ + 2H₂O + Heat

In practical oxy-acetylene welding, the flame is adjusted to obtain the required characteristics. A neutral flame is commonly used for general welding applications. Carburising and oxidising flames are also used for specific materials and purposes.

📊 Types of Oxy-Acetylene Flames

🔧 Other Welding Processes and Their Gases

🧠 Further Exam-Oriented Facts

• Acetylene: Chemical formula C₂H₂; it is the simplest alkyne and is also called ethyne.
• Oxygen: Chemical formula O₂; it supports combustion but is not itself a fuel.
• Nitrogen: It is generally not used as the fuel gas in oxy-acetylene welding.
• Oxy-fuel cutting: Uses oxygen and a fuel gas; the oxygen jet oxidises and removes heated metal.
• Safety: Acetylene is highly flammable and can form explosive mixtures with air. Welding cylinders, regulators, hoses and flashback arrestors must be handled according to safety standards.
• Modern welding: Electric arc welding, MIG, MAG and TIG are widely used in industrial manufacturing alongside gas welding.

Quick Revision: Oxy-acetylene welding → Oxygen (O₂) + Acetylene (C₂H₂) → High-temperature flame → Metal joining.

✔️ Final Answer: (C) Oxygen and acetylene

🛡️ Galvanization: Zinc Coating on Iron and Steel

Galvanized iron (GI) pipes are iron or steel pipes coated with a thin protective layer of zinc (Zn). This coating protects the underlying metal from corrosion and rusting. The most common industrial method is hot-dip galvanization, in which cleaned iron or steel is immersed in molten zinc.

Zinc protects iron not only by acting as a physical barrier against air and moisture but also through sacrificial protection. Zinc is more reactive than iron and preferentially corrodes when the coating is damaged, thereby helping protect the exposed iron or steel.

⚙️ How Is Galvanization Done?

1. Cleaning: Oil, grease and dirt are removed from the iron or steel surface.
2. Pickling: The surface is treated with an appropriate acid solution to remove rust and scale.
3. Fluxing: A flux treatment helps prepare the surface for zinc coating and reduces oxidation before immersion.
4. Hot-dip coating: The cleaned material is immersed in molten zinc.
5. Cooling and inspection: The coated material is cooled and inspected for coating quality and uniformity.

📊 Important Methods of Corrosion Protection

🧪 Why Does Zinc Protect Iron?

Zinc is more electrochemically active than iron. When both metals are electrically connected in the presence of an electrolyte, zinc generally acts as the anode and corrodes preferentially. Iron acts as the cathode and is protected. This mechanism is called sacrificial anode protection.

Even if a small part of the zinc coating is scratched, the surrounding zinc can continue to provide sacrificial protection to the exposed iron, provided sufficient zinc remains and the electrochemical conditions allow it.

🧠 Further Exam-Oriented Facts

• Galvanization: Coating iron or steel with zinc to prevent corrosion.
• Zinc symbol: Zn; atomic number 30.
• Iron symbol: Fe; atomic number 26.
• Rust: Mainly hydrated iron(III) oxide, often represented as Fe₂O₃·xH₂O.
• Tinning versus galvanization: Tinning uses tin, whereas galvanization uses zinc.
• Stainless steel: Its corrosion resistance is mainly due to chromium, which forms a thin protective chromium oxide layer.
• Important distinction: Galvanized iron is zinc-coated iron or steel; it is not chromium-plated iron.
• Applications: GI pipes, fencing, roofing sheets, structural components and other outdoor steel products.

Quick Revision: Galvanization → Zinc coating → Sacrificial protection → Reduced rusting of iron and steel.

✔️ Final Answer: (A) Zinc

🌈 Visible Spectrum and Wavelength of Light

The visible spectrum is the portion of the electromagnetic spectrum that can be detected by the human eye. Its approximate wavelength range is commonly given as 380–750 nanometres (nm), although the limits vary slightly depending on the observer and the reference used.

The given option (B) 3900 Å–7600 Å is the expected answer in this question. Since 1 nanometre = 10 ångströms, this range corresponds to 390–760 nm, which lies within the commonly accepted approximate visible-light range used in many traditional textbooks.

📏 Understanding the Units

• Nanometre (nm): One billionth of a metre, or 10⁻⁹ m.
• Ångström (Å): One ten-billionth of a metre, or 10⁻¹⁰ m.
• Conversion: 1 nm = 10 Å.
• Visible light: Approximately 380–750 nm, or 3800–7500 Å; some conventional textbook ranges extend approximately from 3900 Å to 7600 Å.

🌈 Colours of the Visible Spectrum

White light can be dispersed into different colours by a prism. In the conventional sequence, the colours are violet, indigo, blue, green, yellow, orange and red (VIBGYOR). Wavelength increases from violet towards red.

📡 Electromagnetic Spectrum: Important Regions

The electromagnetic spectrum includes waves with different wavelengths and frequencies. The visible region is only a small part of this spectrum.

⚡ Important Scientific Principles

• Wavelength and frequency: They are inversely proportional for electromagnetic waves travelling in the same medium. A shorter wavelength corresponds to a higher frequency.
• Speed of light: In vacuum, electromagnetic waves travel at approximately 3 × 10⁸ metres per second.
• Dispersion: Splitting white light into its constituent colours is called dispersion.
• Rainbow: It is formed mainly due to refraction, dispersion and internal reflection of sunlight in water droplets.
• Infrared radiation: It is commonly associated with thermal radiation and is used in thermal cameras.
• Ultraviolet radiation: It has a shorter wavelength than visible violet light and can cause skin damage with excessive exposure.

🧠 Further Exam-Oriented Facts

• VIBGYOR: Violet, Indigo, Blue, Green, Yellow, Orange and Red.
• Shortest wavelength in visible light: Violet.
• Longest wavelength in visible light: Red.
• Highest frequency in visible light: Violet.
• Lowest frequency in visible light: Red.
• Ultraviolet: Lies beyond the violet end of the visible spectrum.
• Infrared: Lies beyond the red end of the visible spectrum.
• Important distinction: The visible wavelength limits are approximate, not absolute boundaries; different scientific references may use slightly different values.

Quick Revision: Visible light → Approximately 380–750 nm → 3800–7500 Å; traditional textbook range in this question → 3900–7600 Å; violet → shortest wavelength; red → longest wavelength.

✔️ Final Answer: (B) 3900 Å–7600 Å

🧼 Detergents and Their Chemical Composition

Many synthetic detergents used for washing clothes contain sulfonate-based surfactants, particularly alkylbenzene sulfonates. These compounds reduce the surface tension of water and help remove dirt, grease and oily stains from fabrics. Therefore, the correct answer is (D) Sulfonates.

🧪 What Are Sulfonates?

Sulfonates are salts or derivatives of sulfonic acids. Many detergent surfactants contain a hydrophobic (water-repelling) hydrocarbon chain and a hydrophilic (water-attracting) sulfonate group. This dual nature enables them to interact with both oily dirt and water, making cleaning more effective.

⚙️ How Do Detergents Remove Dirt?

• Wetting: Detergents reduce the surface tension of water, allowing it to spread more easily over the fabric.
• Emulsification: Their molecules help disperse oily substances into tiny droplets in water.
• Micelle formation: Surfactant molecules can form structures called micelles, in which their hydrophobic portions surround oily dirt while their hydrophilic portions remain in contact with water.
• Suspension and removal: Dirt remains dispersed in the washing water and is removed during rinsing.

📊 Important Types of Cleaning Agents

🧠 Further Exam-Oriented Facts

• Surfactant: A substance that reduces surface tension between liquids or between a liquid and a solid.
• Anionic detergents: Their active surfactant groups carry a negative charge in aqueous solution.
• Hard water: Detergents generally work better than ordinary soaps in hard water because they do not readily form insoluble scum with calcium and magnesium ions.
• Soap: Ordinary soap is generally made from fats or oils through saponification using an alkali.
• Biodegradability: The environmental impact of detergents depends on their chemical structure and formulation. Many modern formulations are designed to improve biodegradability.
• Important distinction: Not every detergent is a sulfonate; detergents may contain different classes of surfactants, builders, enzymes, fragrances and other ingredients.

Quick Revision: Laundry detergents → commonly contain sulfonate-based surfactants; surfactants → reduce surface tension; micelles → help remove oily dirt.

✔️ Final Answer: (D) Sulfonates

💧 Sweat and Excretion of Minerals

Human sweat is produced mainly by the sweat glands present in the skin. It consists primarily of water, along with dissolved salts, electrolytes and small quantities of other substances. Sweat helps regulate body temperature through evaporation and also contributes to the elimination of certain metabolic substances and minerals.

Among the elements listed in the question, magnesium, zinc and iron can be detected in human sweat in varying and generally small quantities. Therefore, the scientifically appropriate choice is (E) More than one of the above. The exact amount of each mineral varies with the individual, diet, physical activity, environment and rate of sweating.

🧪 Important Minerals Found in Sweat

🌡️ Functions of Sweat

• Thermoregulation: Evaporation of sweat from the skin removes heat and helps maintain normal body temperature.
• Water and electrolyte balance: Sweating causes the loss of water and electrolytes, particularly sodium and chloride.
• Minor excretory role: Sweat carries small quantities of urea, ammonia and certain minerals out of the body.
• Skin protection: Sweat contributes to the skin’s surface environment and works alongside other skin secretions.

🧠 Further Exam-Oriented Facts

• Main component: Water is the major component of human sweat.
• Major electrolytes: Sodium and chloride are among the principal electrolytes lost during sweating.
• Sweat glands: Eccrine glands are widely distributed and play a major role in temperature regulation.
• Apocrine glands: These are concentrated in certain body regions, such as the armpits, and their secretions differ from those of eccrine glands.
• Body odour: Fresh eccrine sweat is generally nearly odourless. Body odour can develop when skin bacteria break down components of sweat and other skin secretions.
• Dehydration: Excessive sweating without adequate fluid replacement can cause dehydration and electrolyte imbalance.
• Important scientific caution: The presence of a mineral in sweat does not mean that sweat is its principal route of elimination. The kidneys are the major organs responsible for regulating the body’s water and mineral balance.

Quick Revision: Sweat → mainly water; major electrolytes → sodium and chloride; other minerals → potassium, magnesium, calcium, zinc and trace iron; major function → temperature regulation.

✔️ Final Answer: (E) More than one of the above

🔵 Blue Vitriol — Copper Sulphate

Blue vitriol is the common name for copper(II) sulphate pentahydrate, whose chemical formula is CuSO₄·5H₂O. It is a blue crystalline solid because of the presence of water molecules in its crystal structure. Therefore, the correct answer is (C) Copper sulfate.

Strictly speaking, anhydrous copper(II) sulphate (CuSO₄) is white, whereas the common blue crystalline form is the pentahydrate. On heating, blue copper sulphate pentahydrate loses its water of crystallisation and becomes white anhydrous copper sulphate.

🧪 Important Chemical Properties

• Name: Copper(II) sulphate pentahydrate.
• Formula: CuSO₄·5H₂O.
• Appearance: Blue crystalline solid.
• Solubility: Soluble in water.
• On heating: Loses water of crystallisation and changes from blue to white anhydrous copper sulphate.
• On adding water: Anhydrous copper sulphate becomes hydrated and turns blue again.

🔥 Heating of Blue Vitriol

The dehydration process can be represented as:

CuSO₄·5H₂O → CuSO₄ + 5H₂O

Blue copper sulphate pentahydrate loses its five water molecules on heating and forms white anhydrous copper sulphate. This colour change is a familiar demonstration of water of crystallisation in school chemistry.

📊 Important Vitriols and Their Chemical Names

🌱 Uses of Copper Sulphate

• Agriculture: Used in certain formulations to control fungal diseases in plants.
• Fungicide: It is an ingredient in Bordeaux mixture, traditionally prepared using copper sulphate and lime.
• Laboratory: Used in chemistry experiments to demonstrate crystallisation and water of crystallisation.
• Electrochemistry: Used in copper electroplating and in laboratory electrochemical cells.
• Analytical chemistry: Used in certain chemical tests and laboratory procedures.

🧠 Further Exam-Oriented Facts

• Vitriol: The term is historically used for certain hydrated metal sulphates.
• Water of crystallisation: Water molecules chemically incorporated into the crystal structure of a salt.
• Blue colour: The blue colour of hydrated copper sulphate is associated with hydrated copper(II) ions.
• Iron sulphate: Green vitriol is ferrous sulphate, not copper sulphate.
• Zinc sulphate: White vitriol is zinc sulphate.
• Safety: Copper sulphate is harmful if swallowed and can be hazardous to aquatic organisms; it should be handled with appropriate precautions.

Quick Revision: Blue vitriol → CuSO₄·5H₂O; Green vitriol → FeSO₄·7H₂O; White vitriol → ZnSO₄·7H₂O.

✔️ Final Answer: (C) Copper sulfate

⚛️ Atomic Structure — The Nucleus

The nucleus is the small, dense central region of an atom. It contains positively charged protons and electrically neutral neutrons. Since protons carry positive charges and neutrons have no charge, the nucleus has an overall positive charge. Therefore, the correct answer is (D) Nucleus.

A proton is a positively charged particle present inside the nucleus, but the question asks for the entire positively charged central part of the atom. Hence, the answer is nucleus, not proton.

🔬 Three Main Subatomic Particles

⚖️ Important Parts of an Atom

• Nucleus: The central region containing protons and neutrons; it is positively charged and contains almost all the mass of an atom.
• Protons: Positively charged particles. The number of protons determines the atomic number and identifies the element.
• Neutrons: Electrically neutral particles that contribute to nuclear mass and help influence nuclear stability.
• Electrons: Negatively charged particles found in atomic orbitals around the nucleus.
• Atomic number (Z): Equal to the number of protons in the nucleus.
• Mass number (A): The total number of protons and neutrons in the nucleus.

📐 Important Atomic Relationships

Mass number = Number of protons + Number of neutrons

Atomic number = Number of protons

For a neutral atom:

Number of protons = Number of electrons

🧠 Further Exam-Oriented Facts

• Electron: Discovered by J. J. Thomson in 1897 through cathode-ray experiments.
• Nucleus: Discovered by Ernest Rutherford through the gold foil experiment, reported in 1911.
• Proton: Its identification is associated with Rutherford’s nuclear research.
• Neutron: Discovered by James Chadwick in 1932.
• Isotopes: Atoms of the same element having the same atomic number but different mass numbers.
• Isobars: Atoms of different elements having the same mass number but different atomic numbers.
• Isotones: Atoms having the same number of neutrons but different numbers of protons.
• Neutral atom: An atom is electrically neutral when its total positive and negative charges balance each other.

Quick Revision: Nucleus → central and positively charged; proton → +1; neutron → 0; electron → −1; atomic number → number of protons; mass number → protons + neutrons.

✔️ Final Answer: (D) Nucleus

❄️ Sublimation — Direct Conversion of Solid into Gas

Sublimation is the process in which a substance changes directly from the solid state into the gaseous state without passing through the liquid state. This process occurs under suitable temperature and pressure conditions. Therefore, the correct answer is (A) Sublimation.

During sublimation, particles of a solid gain sufficient energy to escape directly into the gaseous state. The reverse process, in which a gas changes directly into a solid without becoming liquid, is called deposition or desublimation.

🧊 Common Examples of Sublimation

• Camphor: Solid camphor gradually changes into vapour at ordinary conditions.
• Naphthalene: Naphthalene balls slowly disappear because the solid changes directly into vapour.
• Ammonium chloride: It is commonly demonstrated in school laboratories as a substance that sublimes on heating, although its vapour-phase chemistry involves dissociation.
• Dry ice: Solid carbon dioxide changes directly into carbon dioxide gas under ordinary atmospheric pressure.
• Iodine: On heating, solid iodine produces violet vapours.

📊 Changes of State of Matter

🌡️ Sublimation versus Other Processes

• Sublimation: Solid changes directly into gas without becoming liquid.
• Evaporation: A liquid changes into vapour from its surface; it can occur below the boiling point.
• Boiling: A liquid changes into vapour throughout the liquid at its boiling point under a given pressure.
• Condensation: A gas or vapour changes into liquid.
• Melting: A solid changes into liquid.
• Deposition: A gas changes directly into solid without passing through the liquid state.

🧠 Further Exam-Oriented Facts

• Dry ice: It is the solid form of carbon dioxide (CO₂), not frozen water.
• Atmospheric pressure: At ordinary atmospheric pressure, dry ice sublimes at approximately −78.5°C.
• Cooling effect: Sublimation absorbs heat from the surroundings, so it is an endothermic process.
• Deposition: It is the reverse of sublimation and releases heat to the surroundings.
• Purification: Sublimation can be used to separate certain sublimable solids from non-sublimable impurities.
• Frost formation: Water vapour can change directly into ice crystals on very cold surfaces through deposition.
• Important distinction: Not every solid changes directly into gas under ordinary conditions. Sublimation depends on the substance and the surrounding temperature and pressure.

Quick Revision: Solid → Gas = Sublimation; Gas → Solid = Deposition; Solid → Liquid = Melting; Liquid → Gas = Vaporisation; Gas → Liquid = Condensation.

✔️ Final Answer: (A) Sublimation

🧬 Insulin and the Regulation of Blood Glucose

Insulin is a peptide hormone secreted by the beta (β) cells of the Islets of Langerhans in the pancreas. Its principal role is to regulate blood glucose levels and carbohydrate metabolism. It helps body cells take up glucose from the blood and promotes the storage of excess glucose as glycogen, especially in the liver and skeletal muscles. Therefore, the expected answer is carbohydrates (B).

🔬 How Does Insulin Work?

• After a meal: Blood glucose generally rises, stimulating pancreatic beta cells to release insulin.
• Glucose uptake: Insulin increases glucose uptake in skeletal muscle and adipose tissue by promoting the movement of GLUT4 transporters to the cell membrane.
• Glycogenesis: It promotes the conversion of glucose into glycogen in the liver and muscles.
• Gluconeogenesis: It suppresses the production of new glucose, particularly in the liver.
• Glycogenolysis: It reduces the breakdown of stored glycogen into glucose.

📊 Important Functions of Insulin

🩺 Diabetes Mellitus and Insulin

Diabetes mellitus is a metabolic disorder characterised by persistently elevated blood glucose levels (hyperglycaemia). It occurs when the body does not produce sufficient insulin or cannot use insulin effectively.

• Type 1 diabetes: Usually results from autoimmune destruction of pancreatic beta cells, causing severe insulin deficiency. Insulin treatment is essential.
• Type 2 diabetes: Mainly involves insulin resistance, often accompanied by progressive impairment of insulin secretion.
• Gestational diabetes: Diabetes first diagnosed during pregnancy, although it may persist or increase the future risk of type 2 diabetes.
• Hypoglycaemia: An abnormally low blood glucose level; it may occur when insulin or certain diabetes medicines exceed the body’s immediate requirements.

🧠 Further Exam-Oriented Facts

• Source of insulin: Beta cells of the Islets of Langerhans in the pancreas.
• Glucagon: Secreted by pancreatic alpha (α) cells; it generally increases blood glucose by promoting glycogen breakdown and glucose production in the liver.
• Insulin and glucagon: They act as major counter-regulatory hormones in blood-glucose regulation.
• Discovery of insulin: Associated with Frederick Banting, Charles Best, J. J. R. Macleod and James Collip in the early 1920s.
• Nobel Prize: Banting and Macleod received the 1923 Nobel Prize in Physiology or Medicine for the discovery of insulin.
• Important distinction: Although insulin is especially important in carbohydrate metabolism, it also regulates fat and protein metabolism. Thus, option (B) is the conventional answer to this question.

Quick Revision: Insulin → pancreatic beta cells → lowers blood glucose → promotes glucose uptake and glycogen formation; Glucagon → pancreatic alpha cells → generally raises blood glucose.

✔️ Final Answer: (B) carbohydrates

💊 Penicillin: An Important Antibiotic

Penicillin is an antibiotic originally obtained from the fungus Penicillium. It was discovered by Alexander Fleming in 1928. Penicillin acts against susceptible bacteria by interfering with the formation of their cell walls. It is therefore the conventional correct answer to this question.

🔬 How Does Penicillin Work?

Bacterial cells possess a protective cell wall containing peptidoglycan. Penicillin belongs to the beta-lactam group of antibiotics. It binds to penicillin-binding proteins (PBPs), including enzymes involved in cell-wall formation, and prevents proper cross-linking of peptidoglycan. This weakens the bacterial cell wall and can lead to bacterial cell death.

• Type: Beta-lactam antibiotic.
• Action: Inhibits bacterial cell-wall synthesis.
• Effect: Generally bactericidal against susceptible bacteria.
• Limitation: It does not work against viral infections such as the common cold or influenza.
• Resistance: Some bacteria produce beta-lactamase enzymes that can destroy or inactivate certain penicillins.

📊 Difference Between the Given Options

⚠️ Important Clarification About Sulfadiazine

Sulfadiazine is an antibacterial medicine belonging to the sulfonamide group. It inhibits bacterial folate synthesis and is often described broadly as an antimicrobial or antibacterial drug. However, in the conventional classification used in general science examination questions, it is distinguished from naturally derived antibiotics such as penicillin and is classified as a synthetic sulfonamide chemotherapeutic agent. Therefore, (A) Penicillin is the expected textbook answer. The distinction depends on the strict or broad use of the word “antibiotic”.

🧠 Further Exam-Oriented Facts

• Alexander Fleming: Discovered penicillin in 1928 while studying bacterial cultures.
• First clinical development: Howard Florey and Ernst Boris Chain played major roles in developing penicillin for medical use.
• Nobel Prize: Fleming, Florey and Chain shared the 1945 Nobel Prize in Physiology or Medicine.
• Penicillin allergy: Some people develop allergic reactions to penicillin; severe reactions can include anaphylaxis.
• Antibiotic resistance: Unnecessary or inappropriate use of antibiotics contributes to antimicrobial resistance (AMR).
• Antibiotics and viruses: Antibiotics treat susceptible bacterial infections; they do not directly cure viral diseases such as dengue, measles or influenza.
• Responsible use: Antibiotics should be used only when medically indicated and according to the advice of a qualified healthcare professional.

Quick Revision: Penicillin → Penicillium fungus → Alexander Fleming → 1928 → beta-lactam antibiotic → inhibits bacterial cell-wall synthesis.

✔️ Final Answer: (A) penicillin

🌾 Cereals: Major Sources of Carbohydrates

Wheat, barley, rice and maize are all cereal grains and are major dietary sources of carbohydrates. Their principal carbohydrate component is generally starch. Therefore, all four options (A), (B), (C) and (D) are correct in the broad nutritional sense. Since the question includes the combined option “None of the above/More than one of the above”, the correct choice is (E) More than one of the above.

🔬 Why Are Cereals Rich in Carbohydrates?

Cereal grains store energy mainly in the form of starch in their endosperm. Starch is a complex carbohydrate made up of glucose units. During digestion, enzymes break starch down into smaller sugars, ultimately producing glucose that the body can use for energy.

• Starch: The main carbohydrate in most cereal grains.
• Dietary fibre: Present particularly in whole grains and bran; it supports digestive health.
• Protein: Cereals also contain protein, although the amount and quality vary by grain.
• Fat: Generally present in smaller amounts than carbohydrates, with variation among cereals and their processing.

📊 Nutritional Comparison of the Four Cereals

The following figures are approximate carbohydrate values per 100 g of raw, dry grain. Actual values vary with variety, moisture content and processing.

🍚 Important Differences Between Cereals

• Wheat: Widely used to prepare flour, bread, chapati and other food products. Wheat contains gluten-forming proteins.
• Barley: Known for its beta-glucan content, which is a soluble dietary fibre associated with beneficial effects on blood cholesterol.
• Rice: A staple food in many Asian countries. Brown rice retains the bran and germ, while polishing removes much of these layers.
• Maize: Used as food, animal feed and an industrial raw material. It is also used to produce starch, corn oil and other products.

🧠 Further Exam-Oriented Facts

• Carbohydrates: They provide approximately 4 kilocalories of energy per gram.
• Starch: A storage polysaccharide in plants, composed of amylose and amylopectin.
• Cellulose: A structural carbohydrate present in plant cell walls; humans cannot digest it with their own digestive enzymes.
• Glycogen: The principal storage carbohydrate in humans and other animals; mainly stored in the liver and skeletal muscles.
• Glucose: A simple sugar that serves as an important energy source for body cells.
• Whole grains: They retain the bran, germ and endosperm, generally providing more fibre and micronutrients than refined grains.
• Balanced diet: Cereals provide energy, but a balanced diet should also include adequate protein, healthy fats, vitamins, minerals and dietary fibre.

Important Question Note: If the question had asked which cereal has the highest carbohydrate content, the answer would depend on the food-composition data and whether the grain is raw, cooked or processed. As worded, all four cereals are mainly carbohydrate-rich foods.

Quick Revision: Wheat, barley, rice and maize → cereals → starch is the principal carbohydrate → all four are carbohydrate-rich.

✔️ Final Answer: (E) More than one of the above

⚛️ Platinum: A Very Dense Metal

Among the given options, platinum is the heaviest metal when “heaviest” is interpreted in the usual general-science sense of having the highest density. Platinum has a density of approximately 21.45 g/cm³ at room temperature, which is greater than that of gold, mercury and silver. Therefore, the correct answer is (D) platinum.

📊 Density Comparison of the Given Metals

Density means mass per unit volume. The following are approximate densities at or near room temperature; values can vary slightly with temperature and purity.

🔬 Important Properties of Platinum

• Atomic number: 78.
• Symbol: Pt.
• Group: Group 10 of the modern periodic table.
• Period: Period 6.
• Appearance: Silvery-white, lustrous metal.
• Nature: A transition metal and a member of the platinum-group metals (PGMs).
• Chemical behaviour: It is relatively unreactive and resistant to corrosion and oxidation under ordinary conditions.
• Melting point: Approximately 1,768°C.

🏭 Uses of Platinum

• Catalytic converters: Used in vehicle exhaust systems to help convert harmful gases into less harmful substances.
• Jewellery: Used in rings, necklaces and other ornaments because of its lustre and resistance to corrosion.
• Laboratory equipment: Used in certain crucibles and specialised laboratory apparatus because of its high melting point and chemical resistance.
• Industrial catalysts: Used in chemical manufacturing, petroleum refining and several catalytic processes.
• Medical applications: Certain platinum-containing compounds, such as cisplatin, are used in cancer treatment under medical supervision.

🧠 Further Exam-Oriented Facts

• Density versus atomic mass: Density is mass per unit volume; atomic mass is the mass of an atom expressed in atomic mass units. The two concepts are different.
• Densest naturally occurring element: Osmium is generally recognised as the densest element, with a density of about 22.59 g/cm³; iridium is very close to it. Neither is included in the given options.
• Platinum-group metals: The six commonly recognised PGMs are platinum, palladium, rhodium, ruthenium, iridium and osmium.
• Mercury: It is a metal that is liquid at ordinary room temperature, unlike platinum, gold and silver.
• Gold: Its chemical symbol is Au, derived from the Latin word *Aurum*.
• Silver: Its chemical symbol is Ag, derived from the Latin word *Argentum*; it has very high electrical and thermal conductivity.
• Important distinction: Platinum is the densest among the four metals listed, but it is not the densest known element.

Quick Revision: Platinum → Pt → Atomic number 78 → Density about 21.45 g/cm³ → highest density among the given options; Osmium → generally recognised as the densest element.

✔️ Final Answer: (D) platinum

🔩 Stainless Steel: An Alloy of Iron and Chromium

Stainless steel is an iron-based alloy that contains at least approximately 10.5% chromium by mass. Chromium forms a very thin, protective and self-repairing oxide layer on the steel surface, which provides resistance to corrosion and rusting. Therefore, the conventional answer is (B) iron and chromium.

🔬 Why Does Stainless Steel Resist Rusting?

When chromium in stainless steel reacts with oxygen, it forms a thin, adherent layer of chromium oxide (Cr₂O₃) on the surface. This passive film acts as a protective barrier and reduces further oxidation and corrosion. If the surface is scratched, the protective layer can reform in the presence of oxygen, provided suitable conditions are available.

• Iron: The main base metal of stainless steel.
• Chromium: The essential alloying element responsible for stainless or corrosion-resistant properties.
• Nickel: Added to many stainless-steel grades to improve ductility, toughness and corrosion resistance; it is not present in every grade.
• Molybdenum: Added to certain grades to improve resistance to pitting and crevice corrosion, particularly in chloride-containing environments.
• Carbon: Present in controlled amounts; its level influences hardness, strength and other properties.

📊 Common Types of Stainless Steel

🏭 Uses of Stainless Steel

• Household: Cooking utensils, sinks, refrigerators and kitchen appliances.
• Medical: Surgical instruments and certain medical equipment because of its durability and suitability for sterilisation.
• Construction: Railings, structural components, cladding and architectural fittings.
• Transport: Railway coaches, vehicle components and specialised transport equipment.
• Industry: Food-processing plants, chemical industries, tanks, pipes and heat exchangers.

🧠 Further Exam-Oriented Facts

• Alloy: A material formed by combining two or more elements, at least one of which is a metal, to obtain useful properties.
• Brass: An alloy of copper and zinc.
• Bronze: Traditionally an alloy of copper and tin.
• Solder: Traditionally made from tin and lead, although lead-free solder compositions are now widely used.
• German silver: An alloy of copper, zinc and nickel; despite its name, it contains no silver.
• Duralumin: An aluminium-based alloy containing copper, magnesium and manganese, among other elements.
• Galvanisation: The process of coating iron or steel with zinc to protect it from corrosion.
• Important distinction: Stainless steel is not simply iron mixed with nickel. Chromium is the essential element that gives it its characteristic corrosion resistance; nickel is an additional alloying element in many common grades.

Quick Revision: Stainless steel → iron + at least about 10.5% chromium → protective chromium oxide layer → corrosion resistance; 304 and 316 are common grades.

✔️ Final Answer: (B) iron and chromium

🦴 Plaster of Paris (POP) and Its Chemical Composition

Plaster of Paris (POP) is chemically known as calcium sulphate hemihydrate, with the formula CaSO₄·½H₂O. It is prepared by heating gypsum (calcium sulphate dihydrate, CaSO₄·2H₂O) at approximately 120–130°C under controlled conditions. When water is added to POP, it changes back into gypsum and forms a hard mass. This property makes it useful for preparing casts to support and immobilise fractured bones.

🧪 Preparation and Setting Reaction

Gypsum loses part of its water of crystallisation when heated and forms Plaster of Paris. On adding water, POP rehydrates and forms hard gypsum crystals.

Chemical reaction:

CaSO₄·½H₂O + 1½H₂O → CaSO₄·2H₂O + Heat

This reaction is responsible for the hardening of Plaster of Paris. The setting process releases heat and produces a rigid structure.

📊 Important Chemical Compounds

🏥 Uses of Plaster of Paris

• Medical use: Traditionally used to prepare casts that immobilise fractured bones and support healing.
• Sculptures and moulds: Used for making statues, decorative articles, toys and moulds.
• Construction: Used for false ceilings, wall finishing and decorative architectural work.
• Educational models: Used to prepare anatomical and scientific models.

🧠 Further Exam-Oriented Facts

• Gypsum: A naturally occurring mineral containing calcium sulphate dihydrate.
• POP: Calcium sulphate hemihydrate, produced by controlled heating of gypsum.
• Crystallisation water: Water chemically associated with a crystalline substance is called water of crystallisation.
• Hardening: POP hardens because it reacts with water and forms gypsum again.
• Important distinction: Gypsum is the raw material for making Plaster of Paris; the two substances have different chemical formulae.
• Safety: Medical casts must be applied appropriately because excessive tightness or heat during setting can cause complications.

Quick Revision: Gypsum → CaSO₄·2H₂O; Plaster of Paris → CaSO₄·½H₂O; adding water to POP → gypsum; common use → casts for fractured bones.

✔️ Final Answer: (D) gypsum

🧪 Alkenes: Hydrocarbons Containing a Carbon–Carbon Double Bond

A hydrocarbon containing at least one carbon–carbon double bond (C=C) is called an alkene. Alkenes are unsaturated hydrocarbons because they do not contain the maximum possible number of hydrogen atoms. For an open-chain alkene containing one double bond, the general molecular formula is C_nH_2n, where n is the number of carbon atoms.

📊 Comparison of Hydrocarbon Families

*Note: These formulae apply to open-chain hydrocarbons containing one relevant type of bond and no additional rings or multiple bonds.

🔬 Important Examples of Alkenes

• Ethene (C₂H₄): The simplest alkene, containing two carbon atoms joined by a double bond.
• Propene (C₃H₆): An important raw material for producing polypropylene.
• Butene (C₄H₈): An alkene with four carbon atoms; it has structural isomers.

⚗️ Important Chemical Properties and Reactions

• Addition reaction: Alkenes commonly undergo addition reactions because the double bond can open and attach new atoms or groups.
• Hydrogenation: Addition of hydrogen converts an alkene into an alkane in the presence of a suitable catalyst such as nickel.
• Bromine test: Alkenes generally decolourise reddish-brown bromine solution because bromine adds across the double bond.
• Polymerisation: Ethene molecules can join together to form polyethene (polythene), an important plastic.
• Combustion: Alkenes burn in oxygen to produce carbon dioxide and water under complete combustion conditions.

🧠 Further Exam-Oriented Facts

• Saturated hydrocarbons: Alkanes contain only carbon–carbon single bonds.
• Unsaturated hydrocarbons: Alkenes contain at least one C=C bond, while alkynes contain at least one C≡C bond.
• Suffix: The names of alkenes generally end in “-ene”, such as ethene and propene.
• Ethene: Also called ethylene; it is used in the manufacture of plastics and as a plant hormone for fruit ripening.
• Bond strength: A carbon–carbon double bond consists of one sigma (σ) bond and one pi (π) bond.
• Geometrical isomerism: Some alkenes, such as but-2-ene, show cis-trans or E/Z isomerism because rotation around the double bond is restricted.

Quick Revision: Alkane → single bond → C_nH_2n+2; Alkene → double bond → C_nH_2n; Alkyne → triple bond → C_nH_2n−2.

✔️ Final Answer: (B) alkene

🍶 Acetic Acid: The Main Acid in Vinegar

The chemical name commonly associated with vinegar is acetic acid (ethanoic acid), whose molecular formula is CH₃COOH. Vinegar is not pure acetic acid; it is a dilute aqueous solution containing acetic acid, generally around 4–8% by volume or concentration depending on the product and standard. It is produced when ethanol is oxidised by acetic-acid bacteria in the presence of oxygen.

🧪 Formation of Acetic Acid

During vinegar production, ethanol is converted into acetic acid through biological oxidation.

Chemical reaction:

CH₃CH₂OH + O₂ → CH₃COOH + H₂O

This process is carried out by bacteria such as Acetobacter. It is different from alcoholic fermentation, in which sugars are converted into ethanol by yeast.

📊 Important Facts About Acetic Acid

🔬 Important Chemical Properties and Uses

• Acidic nature: Acetic acid turns blue litmus paper red and reacts with bases to form salts and water.
• Reaction with sodium bicarbonate: It releases carbon dioxide gas, producing visible effervescence.
• Food preservation: Vinegar is used in pickling and food preservation because its acidity inhibits the growth of many microorganisms.
• Industrial use: Acetic acid is used in the manufacture of vinyl acetate, acetate esters, solvents and other chemicals.
• Glacial acetic acid: Nearly pure acetic acid is called glacial acetic acid because it freezes at approximately 16.6°C.

🧠 Further Exam-Oriented Facts

• Methanol: CH₃OH; also called methyl alcohol, and highly toxic if ingested.
• Ethanol: C₂H₅OH; also called ethyl alcohol, used in alcoholic beverages, solvents and sanitising products.
• Ethyl acetate: CH₃COOC₂H₅; an ester commonly used as a solvent.
• Carboxylic acids: Organic compounds containing the –COOH functional group.
• Acetic acid strength: It is a weak acid because it ionises only partially in water.
• Food safety: Ordinary food vinegar and concentrated laboratory acetic acid are not interchangeable; concentrated acid can cause serious chemical burns.

Quick Revision: Vinegar → dilute acetic acid; IUPAC name → ethanoic acid; formula → CH₃COOH; functional group → –COOH; glacial acetic acid freezes at approximately 16.6°C.

✔️ Final Answer: (C) acetic acid

🔋 Sulfuric Acid in a Lead-Acid Car Battery

The acid used in a conventional automobile lead-acid battery is dilute sulfuric acid (H₂SO₄). A lead-acid battery contains lead dioxide (PbO₂) as the positive plate, spongy lead (Pb) as the negative plate and dilute sulfuric acid as the electrolyte. The acid participates in the electrochemical reactions that produce electrical energy.

⚡ Working Principle of a Lead-Acid Battery

During discharge, both electrodes are gradually converted into lead sulphate (PbSO₄), while sulfuric acid is consumed and water is formed. During charging, an external electrical supply reverses the reaction and restores the original electrode materials and electrolyte concentration.

Overall discharge reaction:

Pb + PbO₂ + 2H₂SO₄ → 2PbSO₄ + 2H₂O

📊 Main Components of a Lead-Acid Battery

🔌 Important Facts About Car Batteries

• Cell voltage: A fully charged lead-acid cell has a nominal voltage of approximately 2 volts.
• 12-volt battery: A conventional 12 V car battery normally contains six lead-acid cells connected in series.
• Rechargeable: Lead-acid batteries are secondary batteries because they can be recharged.
• Specific gravity: The density of the electrolyte changes with its state of charge and can be used as an indicator in serviceable flooded batteries.
• Battery function: It supplies power to start the engine and supports electrical systems when required.

🌱 Modern Battery Technology

• Lead-acid: Commonly used in conventional vehicles for starting, lighting and ignition (SLI).
• Lithium-ion: Widely used in electric vehicles and portable electronic devices because of its high energy density.
• AGM battery: Absorbent Glass Mat batteries are a type of valve-regulated lead-acid battery in which the electrolyte is held in a glass-fibre mat.
• Recycling: Lead-acid batteries are highly recyclable, but improper disposal can cause serious lead and acid pollution.

⚠️ Safety Facts

• Sulfuric acid is highly corrosive and can cause severe skin and eye burns.
• A battery may release hydrogen and oxygen during charging; hydrogen is highly flammable.
• Never add ordinary tap water to a battery that requires distilled water; follow the manufacturer’s instructions.
• Never open or handle a sealed battery in an attempt to add acid or water.

Quick Revision: Car battery → lead-acid battery; electrolyte → dilute H₂SO₄; positive plate → PbO₂; negative plate → Pb; nominal cell voltage → approximately 2 V; six cells → 12 V battery.

✔️ Final Answer: (D) sulfuric acid

🥤 Carbon Dioxide in Soda Water

The gas released when a soda-water bottle is opened is carbon dioxide (CO₂). Soda water is water in which carbon dioxide has been dissolved under pressure. While the bottle remains sealed, the high pressure helps keep a relatively large amount of CO₂ dissolved in the water. When the cap is opened, the pressure decreases and dissolved carbon dioxide escapes as bubbles.

🧪 Dissolution of Carbon Dioxide in Water

Some dissolved carbon dioxide reacts reversibly with water to form carbonic acid (H₂CO₃). This contributes to the slightly acidic nature of carbonated water.

Chemical equilibrium:

CO₂ + H₂O ⇌ H₂CO₃

Most dissolved carbon dioxide remains physically dissolved as CO₂; only a small fraction forms true carbonic acid. When the pressure is reduced, CO₂ leaves the solution, producing the familiar fizzing sound and bubbles.

📊 Important Facts About Common Gases

🌍 Further Exam-Oriented Facts

• Carbonation: The process of dissolving carbon dioxide in water under pressure is called carbonation.
• Fizzy drinks: Carbon dioxide produces bubbles and contributes to the characteristic sharp sensation of carbonated beverages.
• Carbonic acid: It is a weak acid formed when CO₂ reacts with water; it can lower the pH of the drink.
• Fire extinguishers: Carbon dioxide is used in certain fire extinguishers because it does not support combustion and can displace oxygen around a fire.
• Greenhouse gas: CO₂ is an important greenhouse gas that contributes to global warming when its atmospheric concentration increases.
• Dry ice: Solid carbon dioxide is called dry ice. At normal atmospheric pressure, it changes directly from solid to gas by sublimation.
• Limewater test: Carbon dioxide turns limewater milky due to the formation of calcium carbonate.

Quick Revision: Soda water → CO₂ dissolved under pressure; opening the bottle → pressure falls; CO₂ escapes as bubbles; CO₂ + H₂O ⇌ H₂CO₃; dry ice → solid CO₂.

✔️ Final Answer: (A) carbon dioxide