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The correct answer is RER has ribosomes.

Key Points

• The Endoplasmic Reticulum (ER) is a large, membrane-bound network of sacs and tubules found in eukaryotic cells, serving as a primary site for molecular synthesis and transport.
• The Rough Endoplasmic Reticulum (RER) is physically distinguished by the presence of numerous ribosomes attached to its outer membrane surface, which give it a granular or rough appearance under electron microscopy.
• In contrast, the Smooth Endoplasmic Reticulum (SER) is characterized by a complete lack of ribosomes, resulting in a smooth, tubular structure.
• The presence of ribosomes on the RER facilitates its primary function: the translation and synthesis of proteins, particularly those intended for secretion or for use in lysosomes and the plasma membrane.
• The SER serves distinct roles, primarily focusing on lipid biosynthesis, steroid metabolism, and the detoxification of lipid-soluble drugs and metabolic wastes.

 Additional Information

• Rough Endoplasmic Reticulum (RER):
• It is often continuous with the nuclear envelope, allowing for efficient transport of mRNA.
• It contains chaperone proteins that assist in the proper folding of newly synthesized polypeptide chains.
• It is highly developed in cells that specialize in protein secretion, such as pancreatic cells (secreting insulin) and plasma cells (secreting antibodies).
• Smooth Endoplasmic Reticulum (SER):
• It is responsible for the synthesis of phospholipids and cholesterol, which are critical for membrane biogenesis.
• In the liver, SER enzymes like Cytochrome P450 are vital for detoxifying various chemicals.
• In striated muscle cells, a specialized form called the sarcoplasmic reticulum regulates calcium ion concentrations, which is essential for muscle contraction.

The correct answer is 1 km/h west.

Key Points

• Average velocity is defined as the total displacement of an object divided by the total time taken for the journey. Unlike speed, velocity is a vector quantity, meaning it possesses both magnitude and direction.
• To calculate net displacement, we must assign a sign convention to the directions. Usually, East is taken as positive (+) and West is taken as negative (−). Following this, the first displacement is +6 km and the second displacement is −8 km.
• The net displacement is the algebraic sum of individual displacements: 6 km + (−8 km) = −2 km. The negative sign indicates that the resultant displacement is 2 km towards the west from the starting point.
• The total time elapsed for the journey is the sum of the individual time intervals, which is 1 hr + 1 hr = 2 hrs.
• Applying the formula for average velocity:

Average Velocity = Net Displacement / Total Time

Average Velocity = −2 km / 2 hrs = −1 km/h.

The magnitude is 1 km/h and the direction is West.

 Additional Information

• Difference between Average Speed and Average Velocity:
• Average Speed is a scalar quantity calculated by dividing the total distance by the total time. In this case, total distance = 6 km + 8 km = 14 km. Thus, Average Speed = 14 km / 2 hrs = 7 km/h.
• Average Velocity can be zero or negative depending on the displacement, whereas average speed is always positive if the body is in motion.
• Vector Properties:
• Displacement is the shortest straight-line distance between the initial and final positions. If a body returns to its original position after any amount of travel, its displacement and consequently its average velocity will be zero.

The correct answer is Sodium acetate, carbon dioxide, and water.

Key Points

• Ethanoic acid, also known as acetic acid, is a weak organic acid represented by the chemical formula CH₃COOH.
• When ethanoic acid reacts with sodium carbonate (Na₂CO₃), it undergoes a characteristic acid-carbonate reaction, which is a type of neutralization.
• The reaction produces three distinct products: a salt called sodium acetate (CH₃COONa), carbon dioxide (CO₂) gas, and water (H₂O).
• The balanced chemical equation for this interaction is: 2CH₃COOH + Na₂CO₃ → 2CH₃COONa + H₂O + CO₂.
• This reaction is physically marked by brisk effervescence due to the rapid evolution of carbon dioxide gas.
• The formation of sodium acetate, a salt of a weak acid and a strong base, results in a solution that is slightly alkaline in nature.

 Additional Information

• Ethanoic Acid Properties:
• It is the main ingredient of vinegar, typically making up 5% to 8% of the solution by volume.
• Pure ethanoic acid is called glacial acetic acid because its melting point is 290 K (16.6 °C), causing it to freeze during cold climates.
• It belongs to the homologous series of carboxylic acids and is widely used as a preservative in pickles.
• Sodium Carbonate (Washing Soda):
• It is an inorganic compound with the formula Na₂CO₃ and is often used as a water softener in laundry and for manufacturing glass.
• Carbon Dioxide Testing:
• The presence of CO₂ produced in this reaction can be verified using the lime water test. When the gas is passed through lime water (calcium hydroxide), it turns milky due to the formation of insoluble calcium carbonate.
• Comparison with Sodium Bicarbonate:
• Ethanoic acid also reacts with sodium hydrogen carbonate (baking soda) to produce the same products: CH₃COOH + NaHCO₃ → CH₃COONa + H₂O + CO₂.

The correct answer is 6 V.

Key Points

• The electric potential difference between two points in an electric circuit is defined as the amount of work done (W) in moving a unit electric charge (Q) from one point to the other.
• The fundamental mathematical relationship for electric potential is expressed as: Potential Difference (V) = Work Done (W) / Charge (Q).
• According to the problem statement, the amount of work done to move the charge is 12 Joules (J).
• The magnitude of the electric charge being moved between the two specified points is given as 2 Coulombs (C).
• By substituting these values into the formula, we calculate the potential difference as: V = 12 / 2, which results in a value of 6.
• Since the units of measurement are in the International System of Units (SI), the resulting potential difference is expressed in Volts (V).

 Additional Information

• Electric Potential (Volt):
• The SI unit of electric potential difference is the Volt, named in honor of the Italian physicist Alessandro Volta.
• One Volt is defined as the potential difference between two points when one Joule of work is done to move a charge of one Coulomb from one point to the other (1 V = 1 J/C).
• It represents the electrical pressure or tension that drives the flow of electrons through a conductor.
• Measurement and Instrumentation:
• The potential difference is measured using a device called a Voltmeter.
• A voltmeter is always connected in parallel across the component or points where the potential difference is to be measured.
• It possesses a very high resistance so that it takes a negligible current from the circuit, ensuring accurate readings.
• Electric Charge and Energy:
• The Coulomb (C) is the SI unit of electric charge, equivalent to the charge transported by a constant current of one ampere in one second.
• The charge of a single electron is approximately 1.6 × 10⁻¹⁹ Coulombs, meaning one Coulomb consists of roughly 6.242 × 10¹⁸ electrons.

The correct answer is 900 J.

Key Points

• Power is defined as the rate at which work is done or energy is consumed per unit of time.
• The fundamental relationship between these physical quantities is given by the formula Power (P) = Work Done (W) / Time (t).
• To calculate the total work done by the electric bulb, the formula is rearranged to Work (W) = Power (P) × Time (t).
• The problem provides a Power rating of 90 W and a Time interval of 10 seconds.
• Substituting the given values into the equation results in: Work = 90 W × 10 s = 900 J.
• This calculation confirms that the bulb performs 900 Joules of work over the specified duration.

 Additional Information

• Units and Definitions:
• The Watt (W) is the SI unit of power and is equal to one Joule per second (1 J/s).
• The Joule (J) is the SI unit of energy and work, representing the energy transferred when a force of one Newton acts through a distance of one meter.
• The power rating of an appliance indicates how much electrical energy it converts into other forms (like light or heat) every second.
• Practical Applications:
• In domestic electricity billing, energy is often measured in kilowatt-hours (kWh) rather than Joules due to the large scale of consumption.
• One kilowatt-hour is equivalent to 3.6 × 10⁶ Joules.
• Efficiency in electric bulbs is measured by how much of the total work done is actually converted into visible light versus wasted thermal energy.

Shortcut Trick

Use the Weighted Average method by simplifying quantity ratios.

Ratio of goods: 40% : (25% of 60%) : (Remaining 45%) → 40 : 15 : 45 → 8 : 3 : 9

Net Profit % = [ (8 × 17) + (3 × 22) + (9 × −10) ] ÷ (8 + 3 + 9)

Net Profit % = [ 136 + 66 − 90 ] ÷ 20 = 112 ÷ 20 = 5.6%

∴ The correct answer is 5.6%.

Alternate Method

Given:

Total goods = 100%

Part 1: 40% of goods at 17% Profit.

Part 2: 25% of the remaining (100% − 40% = 60%) goods at 22% Profit.

Part 3: Rest of the goods at 10% Loss.

Calculations:

⇒ Quantity of Part 1 = 40%

⇒ Quantity of Part 2 = 25% × (100 − 40)% = 0.25 × 60% = 15%

⇒ Quantity of Part 3 = 100% − (40% + 15%) = 100% − 55% = 45%

⇒ Assume Cost Price (CP) of 1 unit = ₹1. Total CP = ₹100.

⇒ Profit from Part 1 = 40 × (17/100) = ₹6.8

⇒ Profit from Part 2 = 15 × (22/100) = ₹3.3

⇒ Loss from Part 3 = 45 × (10/100) = ₹4.5

⇒ Total Profit/Loss = 6.8 + 3.3 − 4.5 = ₹5.6

⇒ Overall Profit % = (Total Profit ÷ Total CP) × 100 = (5.6 ÷ 100) × 100 = 5.6%

∴ The correct answer is 5.6%.

Additional Information

Weighted Average Profit

When different quantities (q₁, q₂...) are sold at different profit rates (p₁, p₂...), the overall profit percentage is (q₁p₁ + q₂p₂ + ...) ÷ (q₁ + q₂ + ...).

Profit and Loss Basics

Profit % = (Profit ÷ CP) × 100, and Loss % = (Loss ÷ CP) × 100. Profit or Loss is always calculated on the Cost Price (CP) unless stated otherwise.

Effective Percentage Change

For two successive changes a% and b%, the effective change is [a + b + (ab/100)]%. This is useful in Successive Discounts or compound growth scenarios.

Shortcut Trick

For a number to be divisible by 4, the last two digits must be divisible by 4.

In the number 62A4, the last two digits are A4.

Checking the least value from options: If A = 0, the digits are 04.

Since 04 is divisible by 4 (4 × 1 = 4), the condition is satisfied.

∴ The correct answer is 0.

Alternate Method

Given: The number 62A4 is divisible by 4.

Property used: A number is divisible by 4 if and only if its last two digits are divisible by 4.

Calculations:

⇒ The last two digits of the number 62A4 are A4.

⇒ We need the smallest value of A (where A is a digit from 0 to 9) such that A4 is divisible by 4.

⇒ Let us test the possibilities for A:

⇒ If A = 0, number = 04. 04 ÷ 4 = 1. (Divisible)

⇒ If A = 1, number = 14. 14 ÷ 4 = 3.5. (Not divisible)

⇒ If A = 2, number = 24. 24 ÷ 4 = 6. (Divisible)

⇒ Since we need the least possible value of A, we compare the valid values: 0, 2, 4, 6, 8.

⇒ The smallest value among these is 0.

∴ The correct answer is 0.

Additional Information

Divisibility by 2

A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).

Divisibility by 8

A number is divisible by 8 if its last three digits are divisible by 8.

Divisibility by 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

Shortcut Trick

Let Total Work (LCM of 10, 12, 15) = 60 units.

Efficiencies: A = 6, B = 5, C = −4. Combined (A+B−C) = 7 units/hr.

Work done in 4 hr = 7 × 4 = 28 units. Remaining = 60 − 28 = 32 units.

Time for (A+B) to finish = 32 ÷ (6+5) = 32/11 = 2 ¹⁰/₁₁ hr.

Total time = 4 + 2 ¹⁰/₁₁ = 6 ¹⁰/₁₁ hr.

∴ The correct answer is 6 ¹⁰/₁₁ hr.

Alternate Method

Given:

Time taken by Pipe A = 10 hr

Time taken by Pipe B = 12 hr

Time taken by Pipe C = 15 hr (Emptying)

Formula Used:

Total Work = Time × Efficiency

Calculations:

⇒ All pipes work together for 4 hours.

⇒ Combined efficiency of (A + B − C) = 6 + 5 − 4 = 7 units/hr

⇒ Work done in 4 hours = 7 × 4 = 28 units

⇒ Remaining Work = 60 − 28 = 32 units

⇒ Now Pipe C is closed, only A and B work.

⇒ Combined efficiency of (A + B) = 6 + 5 = 11 units/hr

⇒ Time to fill remaining tank = 32 ÷ 11 = 2 ¹⁰/₁₁ hr

⇒ Total time taken = 4 + 2 ¹⁰/₁₁ = 6 ¹⁰/₁₁ hr

∴ The correct answer is 6 ¹⁰/₁₁ hr.

Additional Information

Negative Efficiency

When a pipe is used to empty a tank (outlet pipe), its efficiency is always subtracted from the total efficiency (treated as negative).

Pipes & Cisterns LCM Method

The capacity of the tank is usually assumed to be the LCM of the individual times taken by each pipe.

Fraction of Work Done

If a pipe fills a tank in 'x' hours, then the work done in 1 hour is 1/x.

Shortcut Trick

Apply the Empirical Relationship formula: Mode = 3 × Median − 2 × Mean.

Substitute the values: Mode = (3 × 51) − (2 × 19).

Mode = 153 − 38 = 115.

∴ The correct answer is 115.

Alternate Method

Given:

The Mean of the data = 19

The Median of the data = 51

Formula Used:

In statistics, for a moderately skewed distribution, the Empirical Relation is:

Mode = 3(Median) − 2(Mean)

Calculations:

⇒ Mode = 3 × 51 − 2 × 19 ⇒ Mode = 153 − 38 ⇒ Mode = 115

∴ The correct answer is 115.

Additional Information

Nature of Distribution

For a perfectly Symmetrical Distribution, the Mean, Median, and Mode are all equal (Mean = Median = Mode).

Skewness Rule

In a Negatively Skewed distribution (as seen here), the values generally follow the order: Mode > Median > Mean.

Karl Pearson Formula

The empirical relation can also be written as: (Mean − Mode) = 3 × (Mean − Median).

Shortcut Trick

Side of the Square = √225 = 15 cm.

Perimeter of the square = 4 × 15 = 60 cm.

Side of the Regular Hexagon = 60 ÷ 6 = 10 cm.

Area of Hexagon = 1.5 × √3 × (side)² = 1.5 × √3 × 100 = 150√3 cm².

∴ The correct answer is 150√3 cm².

Alternate Method

Given:

Area of Square = 225 cm²

Perimeter of Square = Perimeter of Regular Hexagon

Formula Used:

Area of Square = (side)²

Perimeter of Square = 4 × side

Perimeter of Regular Hexagon = 6 × side

Area of Regular Hexagon = [3√3 ÷ 2] × (side)²

Calculations:

⇒ Let the side of the square be s.

⇒ s² = 225 cm²

⇒ s = √225 = 15 cm

⇒ Perimeter of the square = 4 × 15 = 60 cm

⇒ Let the side of the regular hexagon be a.

⇒ Perimeter of the hexagon = 6 × a = 60 cm

⇒ a = 60 ÷ 6 = 10 cm

⇒ Area of the hexagon = [3√3 ÷ 2] × (10)²

⇒ Area = [3√3 ÷ 2] × 100

⇒ Area = 150√3 cm²

∴ The correct answer is 150√3 cm².

Additional Information

Properties of a Regular Hexagon

A regular hexagon consists of 6 equilateral triangles. Each internal angle is 120° and the sum of all interior angles is 720°.

Area of any Regular Polygon

Area = (n × s²) ÷ [4 × tan(180/n)], where n is the number of sides and s is the side length.

Perimeter-Area Relationship

For a fixed perimeter, the area increases as the number of sides of a regular polygon increases (a circle has the maximum area for a given perimeter).