Search Previous Year Questions

The Correct answer is (A) - (iv), (B) - (iii), (C) - (i), (D) - (ii).

CONCEPT:

Convex mirror:

• If the outer surface of the spherical mirror is the reflecting surface then it is called a convex mirror. It is also called the diverging mirror.
• The nature of the image formed by a convex mirror does not depend on the distance of the object from the; mirror. These images are always virtual, smaller than the object, and situated behind the mirror.

Concave mirror:

 If the inner surface of the spherical mirror is the reflecting surface, then it is called a concave mirror. It is also called a focusing mirror/converging mirror.

• The size of the image produced by these mirrors can be larger or smaller than the object, depending upon the distance of the object from the mirror.
• The concave mirror can form both real as well as virtual images of any object.

Explanation:

• Convex mirror -used for rear view in vehicles: A concave mirror is a mirror with a reflecting surface that curves inward like the inside of a bowl.
• When used as a rear-view mirror in vehicles, it allows the driver to see a wider field of view. The mirror's curved shape converges the light rays, making objects appear smaller but also allowing a larger area to be visible in the reflection.
• Concave lens - used for near-sightedness: A concave lens is thinner at the center and thicker at the edges. It is used to correct near-sightedness or myopia. Near-sightedness occurs when light entering the eye is focused in front of the retina, causing distant objects to appear blurry.
• A concave lens diverges light rays, allowing them to focus properly on the retina, thus improving distant vision**.**
• Concave mirror - used in torch lights: A convex mirror is a mirror with a reflecting surface that curves outward.
• Convex mirrors have a wider field of view compared to flat mirrors and are often used in torch lights or flashlights to provide a broader spread of light. They scatter light rays, allowing a larger area to be illuminated.
• Convex lens -used in microscopes: A convex lens is thicker at the center and thinner at the edges. It converges light rays and is commonly used in microscopes to magnify small objects. When light passes through a convex lens, it converges and forms a real, enlarged, and inverted image of the object being observed, which allows for detailed examination in microscopes.

The correct answer is 9.8 m/s².

Key Points

• The mean value of 'g' on the surface of the Earth is 9.8 m/s².
• This value represents the average acceleration due to gravity experienced by objects in free fall near the Earth's surface.
• The value of 9.8 m/s² is a standard approximation used in scientific calculations.
• This gravitational acceleration is a result of the Earth's mass and radius and is vital for understanding motion and forces in physics.

Additional Information

• Newton's Law of Universal Gravitation
• This law states that every point mass attracts every other point mass by a force acting along the line intersecting both points.
• The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.
• Variation of 'g'
• The value of gravitational acceleration 'g' varies slightly over the Earth's surface due to factors like altitude, latitude, and local geological structures.
• Gravitational acceleration decreases with altitude and is slightly stronger at the poles compared to the equator.
• Free Fall
• Free fall is the motion of a body where gravity is the only force acting upon it.
• In a vacuum, all objects fall at the same rate regardless of their masses.
• Gravitational Constant (G)
• The gravitational constant (G) is approximately 6.674 × 10⁻¹¹ N(m/kg)².
• It is a key constant in the equation of Newton's Law of Universal Gravitation.

The correct answer is Barometer.

Key Points

• A barometer is an instrument used to measure atmospheric pressure.
• It is essential in weather forecasting and determining altitude.
• Barometers come in two main types: mercury barometers and aneroid barometers.
• Mercury barometers use mercury in a glass tube, while aneroid barometers use a small, flexible metal box called an aneroid cell.

Additional Information

• Atmospheric Pressure
• It is the force exerted onto a surface by the weight of the air above that surface in the atmosphere of Earth (or that of another planet).
• It is measured in units such as Pascals (Pa), millibars (mb), or inches of mercury (inHg).
• Mercury Barometer
• Invented by Evangelista Torricelli in 1643.
• Consists of a long glass tube filled with mercury, with one end open to the atmosphere.
• Aneroid Barometer
• Does not use liquid; instead, it uses a small, flexible metal box (aneroid cell).
• The cell expands or contracts with changes in atmospheric pressure, and this movement drives a mechanical pointer on a dial.
• Uses of Barometers
• Weather forecasting by measuring atmospheric pressure changes to predict short-term changes in the weather.
• Altitude determination, as atmospheric pressure decreases with an increase in altitude.

The correct answer is Wavelength.

Key Points

• The wavelength is the distance between two successive crests (or troughs) of a wave.
• It is usually denoted by the Greek letter lambda (λ).
• Wavelength is an important parameter in the study of wave phenomena, including sound waves, light waves, and water waves.
• It determines the spatial period of the wave, which is the distance over which the wave's shape repeats.

Additional Information

• Wave Period:
• The wave period is the time it takes for two successive crests (or troughs) to pass a fixed point.
• It is the reciprocal of the wave frequency.
• Wave Frequency:
• Wave frequency is the number of crests (or troughs) that pass a given point in one second.
• It is measured in hertz (Hz).
• Wave Amplitude:
• Wave amplitude is the maximum displacement of points on a wave, measured from the equilibrium position.
• It is a measure of the wave's energy.

The correct answer is Growth.

Key Points

• Growth refers to a quantitative process of change in terms of size, scale, number, or output.
• Since growth is quantitative, it can be measured using indicators such as population, income, production, or area.
• Growth is generally value-neutral, but it can be guided or aided by ethics, norms, and policies to ensure balanced and sustainable outcomes.
• Hence, the correct answer is Option 4 – Growth.

Additional Information

• Development:
• Refers to both quantitative and qualitative improvements in the quality of life.
• Includes economic, social, educational, and environmental aspects.
• Progress:
• Indicates movement towards a better or more advanced state.
• It is a qualitative concept and often involves value judgments.
• Evolution:
• Refers to a gradual process of change over time.
• Commonly used in biological and social sciences.

CONCEPT:

Neutral Oxides

• Neutral oxides are oxides that do not show acidic or basic behavior when dissolved in water.
• They do not react with acids or bases to form salts.
• Common examples of neutral oxides include carbon monoxide (CO), nitrous oxide (N₂O), and water (H₂O).

EXPLANATION:

• CO: Carbon monoxide is a neutral oxide. It does not react with acids or bases.
• CO₂: Carbon dioxide is an acidic oxide because it reacts with bases to form salts.
• Na₂O: Sodium oxide is a basic oxide because it reacts with acids to form salts.
• MgO: Magnesium oxide is also a basic oxide because it reacts with acids to form salts.

Since CO does not show acidic or basic behavior, it is classified as a neutral oxide.

Therefore, the correct answer is CO.

The correct answer is Nitrogen dioxide gas.

Key Points

• During the thermal decomposition of lead nitrate (Pb(NO₃)₂), brown fumes are observed due to the formation of nitrogen dioxide gas (NO₂).
• The reaction can be represented as: 2Pb(NO₃)₂ (s) → 2PbO (s) + 4NO₂ (g) + O₂ (g).
• Nitrogen dioxide is a reddish-brown gas and is one of the several nitrogen oxides.
• This gas is a significant air pollutant and has a sharp, biting odor.

Additional Information

• Lead Nitrate Decomposition
• Lead nitrate decomposes upon heating to produce lead oxide (PbO), nitrogen dioxide (NO₂), and oxygen (O₂).
• This is an example of a thermal decomposition reaction, where a compound breaks down into simpler substances when heated.
• Nitrogen Dioxide (NO₂)
• Nitrogen dioxide is a toxic gas and a prominent air pollutant.
• It is primarily produced from combustion processes, including vehicle emissions and industrial activities.
• Prolonged exposure to high levels of NO₂ can cause respiratory problems and other health issues.
• Thermal Decomposition
• Thermal decomposition is a chemical reaction in which a compound breaks down into two or more products upon heating.
• It is an endothermic process, meaning it requires the absorption of heat.
• Air Pollution
• Air pollution refers to the presence of harmful substances in the atmosphere, including gases like nitrogen dioxide, sulfur dioxide, and particulate matter.
• It can have significant adverse effects on human health, the environment, and the climate.

Shortcut Trick

Calculate semi-perimeter s = (12 + 14 + 16) ÷ 2 = 21 m.

Use Heron's Formula: Area = √[s(s−a)(s−b)(s−c)]

Area = √[21 × (21−12) × (21−14) × (21−16)] = √[21 × 9 × 7 × 5]

Area = √[7 × 3 × 3 × 3 × 7 × 5] = 7 × 3 × √[3 × 5] = 21√15 m².

∴ The correct answer is 21√15 m².

Alternate Method

Given:

Sides of the triangle: a = 12 m, b = 14 m, c = 16 m

Formula Used:

Area of triangle = √[s(s−a)(s−b)(s−c)], where s is the semi-perimeter.

⇒ Semi-perimeter (s) = (a + b + c) ÷ 2

⇒ s = (12 + 14 + 16) ÷ 2 = 42 ÷ 2 = 21 m

⇒ Area = √[21 × (21 − 12) × (21 − 14) × (21 − 16)]

⇒ Area = √[21 × 9 × 7 × 5]

⇒ Area = √[3 × 7 × 3 × 3 × 7 × 5]

⇒ Area = 3 × 7 × √[3 × 5]

⇒ Area = 21√15 m²

∴ The correct answer is 21√15 m².

Additional Information

Heron's Formula

It is used to find the area of any triangle when all three sides are known: Area = √[s(s−a)(s−b)(s−c)].

Right-Angled Triangle Area

Area = 1/2 × Base × Height. Applicable when the height is perpendicular to the base.

Equilateral Triangle Area

Area = (√3 / 4) × side². All sides must be of equal length.

Shortcut Trick

Ratio of males to females = 225000 : (360000 − 225000) = 225 : 135 = 5 : 3

Let the literate percentage of females be x%. Using weighted average:

(5 × 17) + (3 × x) = (5 + 3) × 35

85 + 3x = 280 ⇒ 3x = 195 ⇒ x = 65

∴ The correct answer is 65%.

Alternate Method

Given:

Total population = 360000

Total males = 225000

Total females = 360000 − 225000 = 135000

17% Males

x% Females

35% Overall

x − 35

18

Ratio = 5 Ratio = 3

3 parts = 18 → 5 parts = 30 ⇒ x − 35 = 30 ⇒ x = 65

Calculations:

⇒ Total literate population = 35% of 360000 = (35 ÷ 100) × 360000 = 126000

⇒ Total literate males = 17% of 225000 = (17 ÷ 100) × 225000 = 38250

⇒ Total literate females = Total literate population − Literate males

⇒ Total literate females = 126000 − 38250 = 87750

⇒ Percentage of literate females = (Literate females ÷ Total females) × 100

⇒ Percentage of literate females = (87750 ÷ 135000) × 100

⇒ Percentage of literate females = 65%

∴ The correct answer is 65%.

Additional Information

Alligation Rule

Used to find the ratio in which two components are mixed. Ratio = (Dearer − Mean) : (Mean − Cheaper).

Weighted Average Formula

When a group is divided into parts with varying averages, the combined average is: A = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Percentage Change and Base

The percentage of a part concerning a whole is calculated as (Part ÷ Whole) × 100.

GIVEN:

Time = 4 years

Interest rates = 2% p.a.

Principal = Rs. 50,000

FORMULA USED:

SI = (PTR)/100

Where, P = Principal Amount

             R = Interest rate

             T = Time for which interest is applied on the amount

CALCULATION:

SI = (50000 × 2 × 4)/100

⇒ SI = 4000

The answer is 4000.