Search Previous Year Questions

The correct answer is Variable resistance or rheostat.

Key Points

• A rheostat is an electrical component specifically designed to provide a variable resistance in a circuit, allowing for the precise manual control of current magnitude.
• The circuit symbol for this component is typically represented as a zigzag line (ANSI) or a rectangle (IEC) with an oblique arrow passing through it or a sliding contact arrow pointing towards it.
• Functionally, it operates based on Ohm's Law, where the relationship between voltage (V), current (I), and resistance (R) is expressed as I = V ÷ R; thus, increasing resistance directly reduces current for a constant voltage.
• The device is frequently constructed using Nichrome wire wound around an insulating ceramic core, utilizing a wiper to adjust the length of the conductor included in the circuit.
• It is widely used in real-world applications such as light dimmers, motor speed controllers, and fan regulators to adjust power levels without disconnecting the circuit.

 Additional Information

• Switch in the closed position:
• A closed switch indicates a completed conductive path, signifying that the circuit is in the ON state and electrons can flow.
• Its symbol is shown as a line connecting two terminal dots or a bridge making contact, preventing open-circuit conditions.
• A wire:
• Represented by a simple straight line, it serves as a conductor to connect various nodes within a schematic.
• In ideal circuit analysis, wires are assumed to have zero resistance, facilitating perfect energy transmission.
• A battery:
• A battery is a source of direct current (DC) consisting of multiple electrochemical cells connected in series to provide electromotive force (EMF).
• Its symbol features alternating long parallel lines (the positive terminal) and short, thicker lines (the negative terminal).

The correct answer is Calcium reacts less vigorously than sodium but more than magnesium, forming calcium hydroxide and hydrogen gas..

Key Points

• Calcium (Ca) is an alkaline earth metal located in Group 2 of the periodic table. Its reactivity with water is moderate compared to the highly explosive alkali metals like Sodium.
• When Calcium is added to cold water, it reacts to form Calcium Hydroxide [Ca(OH)₂] and Hydrogen gas (H₂). The chemical equation is represented as: Ca + 2H₂O → Ca(OH)₂ + H₂.
• The reaction is exothermic, but the heat evolved is not sufficient for the Hydrogen gas to catch fire, unlike the reaction of Sodium or Potassium with water.
• A distinct physical observation during this reaction is that the Calcium metal starts floating on the surface of the water because bubbles of Hydrogen gas formed stick to the surface of the metal pieces.
• In the reactivity series, Sodium is placed above Calcium, making it more reactive, while Magnesium is placed below Calcium, making it less reactive with cold water.

 Additional Information

• Sodium (Na):
• Belongs to Group 1 (Alkali metals).
• Reacts violently and explosively with cold water.
• The reaction is so exothermic that the produced Hydrogen gas catches fire immediately.
• Magnesium (Mg):
• Does not react with cold water at a significant rate.
• It reacts with hot water to form Magnesium Hydroxide and Hydrogen.
• When reacted with steam, it produces Magnesium Oxide (MgO) and Hydrogen gas.
• Calcium Hydroxide:
• Also known as slaked lime.
• It is used in white-washing and as a chemical reagent in various industrial processes.

The correct answer is Remain the same.

Key Points

• The mass percentage (w/w%) of a solution is a way of expressing its concentration by calculating the mass of the solute divided by the total mass of the solution, then multiplying by 100.
• The fundamental formula for mass percentage is: Concentration (%) = [Mass of Solute / (Mass of Solute + Mass of Solvent)] × 100.
• If we assume the initial mass of the solute is m and the initial mass of the solvent is M, the total initial mass of the solution is m + M.
• When both masses are doubled, the new mass of the solute becomes 2m and the new mass of the solvent becomes 2M. Consequently, the new total mass of the solution is 2m + 2M, which can be factored as 2(m + M).
• Substituting these new values into the formula gives: [2m / 2(m + M)] × 100. In this expression, the constant factor of 2 in the numerator and denominator cancels out completely.
• The resulting simplified formula is identical to the original one: [m / (m + M)] × 100. Therefore, the mass percentage remains unchanged despite the increase in the total quantity of the mixture.

 Additional Information

• Intensive Property: Concentration is considered an intensive property of matter, meaning it does not depend on the system size or the amount of material present in the system.
• Solute: The component of a solution that is dissolved and usually present in a smaller amount.
• Solvent: The medium, such as water, benzene, or alcohol, in which the solute is dissolved.
• Solution: A homogeneous mixture of two or more substances where the particles are distributed at the molecular level.
• Other Concentration Units:
• Molarity (M): Defined as the number of moles of solute per liter of solution; it is affected by temperature changes because volume changes with temperature.
• Molality (m): Defined as the number of moles of solute per kilogram of solvent; it is preferred in thermodynamics because it is independent of temperature.
• Mole Fraction: The ratio of the moles of one component to the total moles of all components in the mixture.

The correct answer is F/4.

Key Points

• Newton's Law of Universal Gravitation states that the force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
• The mathematical formula for this force is F = G (m₁ × m₂) / r², where F represents the gravitational force, G is the universal gravitational constant, m₁ and m₂ are the masses of the two bodies, and r is the distance between them.
• Initially, the force between the Earth and the Moon is given as F. If the initial distance is r, then F = G (M_e × M_m) / r².
• According to the problem, the distance is doubled, meaning the new distance r' is equal to 2r. All other parameters, including the masses and the gravitational constant, remain unchanged.
• Substituting the new distance into the formula, the new force F' becomes G (M_e × M_m) / (2r)², which simplifies to G (M_e × M_m) / 4r².
• Comparing the two equations, F' = (1/4) × [G (M_e × M_m) / r²], which simplifies to F' = F/4.

 Additional Information

• Inverse Square Law:
• This law is a fundamental principle in physics where a specified physical quantity or intensity is inversely proportional to the square of the distance from the source.
• In the context of gravity, if the distance is tripled, the force becomes F/9; if the distance is halved, the force increases to 4F.
• Universal Gravitational Constant (G):
• The value of G is approximately 6.674 × 10⁻¹¹ N m² kg⁻².
• It was first measured by Henry Cavendish in 1798.
• Properties of Gravitational Force:
• It is the weakest of the four fundamental forces in nature but has an infinite range.
• It is a central force, acting along the line joining the centers of the two interacting masses.
• It is independent of the medium between the two bodies.

The correct answer is Provide rigidity and protection.

Key Points

• The cell wall is a non-living, rigid, and semi-permeable outer layer found in plant cells, situated outside the cell membrane.
• Its primary chemical component in plants is cellulose, a complex polysaccharide that provides high tensile strength and structural durability.
• The main function is to provide structural support and rigidity, allowing plants to grow to significant heights and maintain a defined shape without an internal skeleton.
• It serves as a protective barrier that shields the cell from mechanical stress, physical injury, and infection by pathogens like bacteria or fungi.
• The cell wall helps the cell withstand turgor pressure; this internal pressure exerted by the central vacuole keeps the plant turgid and prevents the cell from bursting in hypotonic environments.
• It facilitates communication and transport between adjacent cells through plasmodesmata, which are narrow channels crossing the cell walls.

 Additional Information

• Cell Wall Composition:
• In fungi, the cell wall is primarily made of chitin, which is also found in the exoskeletons of arthropods.
• In bacteria, the wall is composed of peptidoglycan (murein), which is essential for survival in diverse osmotic conditions.
• Algal cell walls often contain cellulose along with other substances like galactans, mannans, and calcium carbonate.
• Cellular Respiration: This process is managed by the mitochondria, often called the powerhouse of the cell, where glucose is oxidized to produce ATP.
• Cell Division: This is a complex process regulated by the nucleus, which contains the genetic material (DNA), and involves structures like spindle fibers.
• Nutrient Transport: While the cell wall allows the passage of water and solutes, the plasma membrane is the structure responsible for selective permeability, controlling exactly which substances enter or leave the cell.

Shortcut Trick

Find the HCF of the given numbers: 1950, 1560, and 2340.

Divide by common divisor 10: 195, 156, 234.

Divide by common divisor 13: 15, 12, 18.

Divide by common divisor 3: 5, 4, 6.

Product of common divisors = 10 × 13 × 3 = 390.

Prime factors of 390 are 2, 3, 5, and 13. Their product is 390.

∴ The correct answer is 390.

Alternate Method

Given: Numbers are 1950, 1560, and 2340.

Formula Used: Prime factorization method to find common factors.

Perform prime factorization for each number:

⇒ 1950 = 2¹ × 3¹ × 5² × 13¹

⇒ 1560 = 2³ × 3¹ × 5¹ × 13¹

⇒ 2340 = 2² × 3² × 5¹ × 13¹

Identify the common prime factors present in all three numbers:

⇒ The common primes are 2, 3, 5, and 13.

Calculate the product of these common prime factors:

⇒ Product = 2 × 3 × 5 × 13

⇒ Product = 6 × 65 = 390

∴ The correct answer is 390.

Additional Information

Highest Common Factor (HCF)

The HCF is the product of the lowest powers of all common prime factors. In this case, HCF = 2¹ × 3¹ × 5¹ × 13¹ = 390.

Least Common Multiple (LCM)

The LCM is the product of the highest powers of all prime factors involved in the numbers. For these numbers, LCM = 2³ × 3² × 5² × 13¹ = 23400.

Prime Factorization

Every composite number can be expressed as a unique product of prime numbers. Common prime factors are those primes that appear in the factorization of all given numbers.

Shortcut Trick

Weighted average profit % = (Portion₁ × P₁ + Portion₂ × P₂ + Portion₃ × P₃)

Portion 1 = 50%; Portion 2 = 40% of 50% = 20%; Portion 3 = 100% − 50% − 20% = 30%

Net profit x = (0.50 × 40) + (0.20 × 13) + (0.30 × −32)

x = 20 + 2.6 − 9.6 = 13

∴ The correct answer is 13.

Alternate Method

Given:

Total goods = 100 units (Assumed CP = ₹1/unit, Total CP = ₹100)

First part = 50% of 100 = 50 units at 40% profit.

Second part = 40% of remaining goods (50) = 20 units at 13% profit.

Third part = still remaining goods = 100 − 50 − 20 = 30 units at 32% loss.

Calculations:

⇒ Profit from Part 1 = 40% of 50 = (40 ÷ 100) × 50 = ₹20

⇒ Profit from Part 2 = 13% of 20 = (13 ÷ 100) × 20 = ₹2.6

⇒ Loss from Part 3 = 32% of 30 = (32 ÷ 100) × 30 = ₹9.6

⇒ Total Net Profit = 20 + 2.6 − 9.6 = ₹13

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

⇒ x = (13 ÷ 100) × 100 = 13

∴ The correct answer is 13.

Additional Information

Weighted Average Profit Formula

When items are sold in different parts, the net profit/loss percentage is given by (n₁p₁ + n₂p₂ + ...) ÷ (n₁ + n₂ + ...), where n is quantity and p is profit%.

Successive Percentage of Remainder

If a% is removed, and then b% of the remaining is taken, the second part as a percentage of the whole is b × (100 − a) ÷ 100.

Profit and Loss Basics

Profit % = (SP − CP) ÷ CP × 100. A loss is treated as a negative profit in calculation of the overall net change.

Shortcut Trick

Let Cost Price (CP) = 100 units

List Price (MP) = 100 + 36% = 136 units

Selling Price (SP) = 136 − 25% of 136 = 136 − 34 = 102 units

Profit = SP − CP = 102 − 100 = 2 units

Given 2 units = ₹179 ⇒ 1 unit = ₹89.5

List Price = 136 units = 136 × 89.5 = ₹12172

∴ The correct answer is ₹12172.

Alternate Method

Given:

Mark-up Percentage = 36%

Discount Percentage = 25%

Actual Profit = ₹179

Formula Used:

Effective Profit % = Mark-up% − Discount% − [(Mark-up% × Discount%) ÷ 100]

Calculations:

⇒ Effective Profit % = 36 − 25 − [(36 × 25) ÷ 100]

⇒ Effective Profit % = 11 − [900 ÷ 100] = 11 − 9 = 2%

⇒ 2% of Cost Price = ₹179

⇒ 1% of CP = 179 ÷ 2 = ₹89.5

⇒ Cost Price (100%) = 89.5 × 100 = ₹8950

⇒ List Price (MP) = CP × (136 ÷ 100)

⇒ List Price = 8950 × 1.36

⇒ List Price = ₹12172

∴ The correct answer is ₹12172.

Additional Information

Relationship between CP and MP

The ratio of Cost Price to Marked Price is given by CP/MP = (100 − D%)/(100 + P%), where D is discount and P is profit.

Mark-up Percentage

Mark-up % = [(MP − CP) ÷ CP] × 100. It represents the percentage by which the list price is higher than the cost price.

Successive Percentage Change

When a value is increased by x% and then decreased by y%, the net change is [x − y − (xy/100)]%.

Shortcut Trick

If c is the third proportional to a and b, then c = b²/a.

Given x = y²/2 and y = 18²/x.

Substituting x: y = 324 ÷ (y²/2) ⇒ y = 648/y².

y³ = 648 ⇒ y = ³√(216 × 3) = 6³√3.

∴ The correct answer is 6³√3.

Alternate Method

Given:

First set: 2, y, and x are in continued proportion.

Second set: x, 18, and y are in continued proportion.

Formula Used:

If a : b = b : c, then b² = ac.

Calculations:

⇒ From the first condition: y² = 2 × x ⇒ x = y²/2

⇒ From the second condition: 18² = x × y ⇒ 324 = xy

⇒ Substituting the value of x in the second equation:

⇒ 324 = (y²/2) × y

⇒ 324 × 2 = y³

⇒ y³ = 648

⇒ y = ³√(216 × 3)

⇒ y = 6 × ³√3

∴ The correct answer is 6³√3.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is defined as √(ab).

Fourth Proportional

If a : b :: c : d, then d is the fourth proportional to a, b, c and is calculated as d = (b × c) / a.

Third Proportional

If a : b :: b : c, then c is the third proportional to a and b, calculated as c = b² / a.

Continued Proportion

Three numbers a, b, c are in continued proportion if the ratio of the first to the second is equal to the ratio of the second to the third (a/b = b/c).

Shortcut Trick

Directly apply the relation: 4r² = Surface Area ÷ π

4r² = 314 ÷ 3.14 = 100

r² = 100 ÷ 4 = 25

r = √25 = 5 cm

∴ The correct answer is 5 cm.

Alternate Method

Given:

Surface Area (SA) of the sphere = 314 cm²

Value of π = 3.14

Formula Used:

Surface Area of a sphere = 4 × π × r²

Calculations:

⇒ 314 = 4 × 3.14 × r²

⇒ 314 = 12.56 × r²

⇒ r² = 314 ÷ 12.56

⇒ r² = 25

⇒ r = √25

⇒ r = 5 cm

∴ The correct answer is 5 cm.

Additional Information

Volume of a Sphere

The total space occupied by a sphere is given by Volume = (4/3) × π × r³.

Hemisphere Formulas

For a hemisphere: Curved Surface Area = 2πr² and Total Surface Area = 3πr².

Volume of a Hemisphere

The volume of a hemisphere is exactly half of a sphere: Volume = (2/3) × π × r³.