Key Concept: Map Types

a) Physical map
[Solution Description]
According to the syllabus, physical maps mainly show natural features such as mountains, oceans, and rivers. Political maps show boundaries and cities, while thematic maps provide specific information.

Key Concept: Scale, Direction, Map Components

c) 875 km, northeast
[Solution Description]
To solve this question, we will break it into two parts:
1. Calculate the actual distance between the two cities using the scale provided.
2. Determine the intermediate direction for travel.
Step 1: The scale is given as 1 cm = 250 km. The distance between the two cities on the map is 3.5 cm.
Therefore, the actual distance = 3.5 cm * 250 km/cm = 875 km.
Step 2: If one city lies to the northeast (NE) of the other, to travel from the first city to the second, you would move in the northeast direction.
Combining both answers, the actual distance is 875 km, and the travel direction is northeast.

Key Concept: Map Interpretation, Symbols, Distance

c) 1000 meters
[Solution Description]
First, note that the scale of the map is $1 \text{ cm} = 200 \text{ m}$. The distance between the railway station and the school on the map is 5 cm. To find the actual distance, multiply the map distance by the scale factor:
$5 \text{ cm} \times 200 \text{ m/cm} = 1000 \text{ m}.$
This is the actual distance you will walk.

Key Concept: Types of Maps

c) Political map
[Solution Description]
Political maps show details of countries or states including their boundaries and cities, while physical maps show natural features and thematic maps focus on specific information.

Key Concept: Map Components

d) Assertion is false, but Reason is true.
[Solution Description]
The assertion states that a map always shows the exact size of places as they are in reality. This is false because maps use a scale to represent distances, which means they shrink large areas to fit on paper while maintaining proportional accuracy, not exact size. The reason explains that maps use a scale for accurate distance representation but cannot show exact sizes due to space limitations, which is true and directly counters the false assertion. Therefore, the correct answer is the option where the assertion is false, but the reason is true.

Key Concept: Map Components, Scale, Direction

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the scale of a map is essential for accurately determining the actual distance between two points. This is true because the scale provides the ratio between the distance on the map and the actual distance on the ground. The reason explains why the scale is necessary: without it, converting the map distance to real-world distance would not be possible. Both statements are true, and the reason correctly explains the assertion.

Key Concept: Maps and Their Components

b) Displays natural features like mountains and rivers
[Solution Description]
A physical map primarily shows natural features such as mountains, rivers, and oceans. It does not focus on political boundaries or human-made structures. From the syllabus, it is clear that physical maps are distinct from political and thematic maps.

Key Concept: Components of Maps

d) Scale
[Solution Description]
The three fundamental components of maps are distance, direction, and symbols. Scale is often used in conjunction with these components but is not listed as one of the primary three.

Key Concept: Political Maps

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that political maps show boundaries between countries and states, which is true. The reason explains that these boundaries are defined by governments and international agreements, which is also true and correctly explains why political maps display such boundaries.

Key Concept: Map Symbols

c) Provisional boundaries
[Solution Description]
On political maps, dotted lines are commonly used to denote provisional or disputed boundaries between regions or countries. These are not permanent and may change over time due to geopolitical agreements or conflicts.

Key Concept: Components of Maps

c) Scale
[Solution Description]
The three important components of maps highlighted in the syllabus are distance, direction, and symbols. Scale is often associated with maps but is not listed among these three primary components here. A legend explains symbols but is not classified as a fundamental component in this context.

Key Concept: Thematic Maps

c) Thematic map
[Solution Description]
Thematic maps are designed to show specific kinds of information, such as rainfall distribution, population density, or economic activity, rather than general geographic features.

Key Concept: Scale Application

c) 56 m
[Solution Description]
The scale is $1 \text{ cm} = 8 \text{ m}$. The map length is 7 cm. Actual length = Map length $\times$ Scale factor = $7 \text{ cm} \times 8 \text{ m/cm} = 56 \text{ m}$.

Key Concept: Scale Calculation

c) 20 km
[Solution Description]
The scale given is $1 \text{ cm} = 5 \text{ km}$. The map distance between the two cities is 4 cm. To find the actual distance, multiply the map distance by the scale factor: $4 \text{ cm} \times 5 \text{ km/cm} = 20 \text{ km}$.

Key Concept: Map Components

d) Colors
[Solution Description]
The three main components of maps mentioned in the syllabus are distance, direction, and symbols. Colors, while often used in maps for various purposes, are not listed as one of the primary components.

Key Concept: Direction – Cardinal \& Intermediate

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the direction between North and East is called Northeast. This is correct because Northeast is indeed the direction lying midway between North and East. The reason given is that Northeast is an intermediate direction as it lies between two cardinal directions. This is also true, and it correctly explains why the direction is named Northeast. Therefore, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

Key Concept: Symbol Identification

c) $PO$
[Solution Description]
The symbol for a Post Office as fixed by the Survey of India is $PO$. This is mentioned in the syllabus under symbols commonly used in maps.

Key Concept: Symbols in Maps

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to the syllabus, the Survey of India has fixed a set of symbols for maps of India, and $RS$ is indeed the symbol for a railway station. The reason correctly explains that standardization is done by the Survey of India to ensure uniformity. Therefore, both assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: Longitudes, Prime Meridian, Indian Astronomy

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The Assertion states that the Ujjayinī meridian was used as a prime meridian in Indian astronomy because it passed through Ujjain, a historically significant center for astronomical studies. This is true, as Indian astronomers like Varāhamihira used this meridian for calculations. The Reason claims that the Greenwich Meridian is the only globally accepted prime meridian today due to its accuracy in standardizing time zones. While the Greenwich Meridian is indeed the current global standard, this does not explain why the Ujjayinī meridian was historically significant. Thus, both statements are true, but the Reason does not correctly explain the Assertion.

Key Concept: Globes and Maps

d) Globes accurately represent the Earth’s spherical shape without distortion.
[Solution Description]
A globe is spherical, just like the Earth, which allows it to represent locations, distances, directions, and shapes more accurately without distortion. Flat maps, on the other hand, cannot perfectly represent a spherical surface due to distortions caused by projection methods.

Key Concept: Types of Maps

c) Physical map
[Solution Description]
Physical maps are designed to show natural features of the Earth such as mountains, oceans, and rivers. They focus on the physical landscape rather than political or thematic information.

Key Concept: Map Components

b) Distance, direction, and symbols
[Solution Description]
The three main components of a map are distance, direction, and symbols. These components help in understanding and interpreting the information presented on a map.

Key Concept: Globe vs Flat Map, Practical implications

b) Flat maps exaggerate distances near the poles
[Solution Description]
A globe represents the Earth’s curvature accurately, preserving distances and directions along great circles (shortest paths). A flat map distorts these properties unless specifically designed for navigation (e.g., Mercator projection), leading to incorrect distance calculations or directional errors.

Key Concept: Shape of the Earth, Representation on Maps

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a globe provides a more accurate representation of the Earth’s geography than a flat map. This is true because a globe mimics the Earth’s spherical shape, preserving relative sizes and distances without distortion. The reason explains that the spherical nature of the globe matches the Earth, while flat maps suffer from distortions when projecting a 3D surface onto a 2D plane. Since both statements are factually correct and the reason logically justifies the assertion, the correct answer is option (a).

Key Concept: Globe vs. Map

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
A globe is indeed a more accurate representation of the Earth because it maintains the correct proportions and shapes of landmasses and oceans, being a three-dimensional model. The reason given explains why globes are better—it’s due to their spherical shape, which avoids distortions present in flat maps. Therefore, both the assertion and the reason are true, and the reason correctly explains the assertion.

Key Concept: Map Components

d) Color schemes
[Solution Description]
Maps generally require distance, direction, and symbols as essential components for accurate representation. “Color schemes” enhance readability but are not fundamental to the structure of maps like distance, direction, or symbols.

Key Concept: Grid Lines

b) To locate places accurately using coordinates
[Solution Description]
Grid lines on a globe help in locating places accurately by providing a reference system similar to coordinates on a chessboard or rows in a market.

Key Concept: Maps, Globe, Representation

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a globe provides a more accurate representation of the Earth’s geography than a flat map. This is true because a globe mimics the actual shape of the Earth, which is nearly spherical. On the other hand, flat maps introduce distortions in area, shape, distance, or direction due to the challenge of projecting a 3D object (Earth) onto a 2D surface (map).
The reason states that the spherical shape of a globe eliminates distortions present in flat maps. This is also true, as the spherical shape ensures proportional distances and areas, unlike flat maps where distortions are inevitable (e.g., Mercator projection exaggerates polar regions).
Moreover, the reason correctly explains why the globe is superior to flat maps—because its spherical nature avoids the inherent distortions of flattening the Earth’s surface. Hence, both the assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: Market coordinates, Multi-step solution

a) Bookstore
[Solution Description]
To determine the type of shop at (M, 25):
1. Identify if 25 is divisible by 5: $25 \div 5 = 5$ with no remainder.
2. Since 25 is exactly divisible by 5, the shop at (M, 25) is a bookstore.

Key Concept: Understanding Coordinates

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the chess coordinate system uses letters and numbers to identify squares, which is true as per the syllabus. The reason given is that this system helps in recording moves, which is also correct. Moreover, the reason correctly explains why the assertion is valid since the uniqueness of each square’s coordinates enables precise move recording.

Key Concept: Locating Places on the Earth, Market Grid System

b) 3
[Solution Description]
The shops are in the same row (row 3). The number of shops between column 5 and column 9 is calculated as follows: $(9 – 5) – 1 = 3$ shops. This is because the positions $6$, $7$, and $8$ lie between $5$ and $9$.

Key Concept: Chessboard Coordinates, Locating Places on the Earth

b) b5
[Solution Description]
From $g1$, the knight’s first possible L-moves are to $e2$, $f3$, or $h3$. For example, starting at $g1$:
1st move to $e2$, 2nd move to $c3$, 3rd move to $a4$.
Alternatively: 1st move to $f3$, 2nd move to $d4$, 3rd move to $b5$.
However, $d5$ is not reachable in exactly three standard L-shaped moves.

Key Concept: Shop rows analogy

b) c2
[Solution Description]
Rows are labeled alphabetically starting from $a$. The 3rd row is $c$ (since $a$ is 1st, $b$ is 2nd, $c$ is 3rd). The position is given as 2. Thus, the coordinate is $c2$.

Key Concept: Chessboard analogy

a) g7 to g5
[Solution Description]
In chess, when white moves a pawn forward two squares (e.g., $g2$ to $g4$), black can respond by moving their pawn symmetrically from $g7$ to $g5$. This follows the standard opening move symmetry.

Key Concept: Market Coordinates

b) $(3, 4)$
[Solution Description]
Using the market analogy, the first number represents the row, and the second number represents the shop in that row. Therefore, “3rd row, 4th shop” translates to the coordinate $(3, 4)$.

Key Concept: Chessboard Notation

b) Letters for columns (A-H) and numbers for rows (1-8)
[Solution Description]
Chess notation uses letters from $a$ to $h$ for columns and numbers from 1 to 8 for rows. Each square is uniquely identified by a letter-number pair, such as $a1$ or $h8$.

Key Concept: Historical Prime Meridian, Latitude-Climate Relationship

c) Temperate Zone (moderate latitudes)
[Solution Description]
The shortest day duration (10 hours) indicates Ujjain receives moderate sunlight variation, typical of temperate zones (latitudes between $23.5°$ and $66.5°$). At $23.5°N$ (Tropic of Cancer), Ujjain is near the boundary of the Torrid Zone but falls under the Temperate Zone due to its measurable seasonal changes.

Key Concept: International Date Line

c) One day is subtracted
[Solution Description]
Crossing the International Date Line eastward subtracts one day from the current date, while crossing westward adds one day. This adjustment ensures consistency with global time zones.

Key Concept: Latitude and Climate

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the climate becomes colder towards the poles, which is true because solar radiation is spread over a larger area and at an oblique angle near the poles, reducing heat intensity. The reason correctly explains this by stating that latitude measures distance from the Equator; higher latitudes receive less direct sunlight, leading to colder temperatures. Therefore, both are true, and the reason correctly explains the assertion.

Key Concept: Climate Zones

c) Torrid
[Solution Description]
The syllabus mentions that around the Equator (latitude $0°$), the climate is generally hot and is called ‘torrid’. This is in contrast to temperate and frigid zones further from the Equator.

Key Concept: Climate Relation

d) Hot
[Solution Description]
According to the syllabus, the climate around the Equator is generally hot and is also called ‘torrid’. The other climates (temperate and frigid) are found as you move away from the Equator towards the poles.

Key Concept: Latitude and Climate

c) Hot (Torrid)
[Solution Description]
The Equator is located at $0°$ latitude. According to the syllabus, the climate around the Equator is generally hot (also called ‘torrid’). As one moves away from the Equator towards higher latitudes, the climate becomes more temperate or frigid.

Key Concept: Parallels of Latitude

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The assertion states that the length of a parallel of latitude decreases as we move from the Equator towards the poles. This is correct because parallels of latitude are circles running east-west, parallel to the Equator, and their circumference reduces as latitude increases towards the poles. The reason given is that the Earth is an oblate spheroid, which is true. However, this shape does not directly explain why the length of parallels decreases; it is due to the spherical geometry where circles of latitude become smaller towards the poles, regardless of the Earth’s slight oblateness. Thus, while both statements are true, the Reason is not the correct explanation for the Assertion.

Key Concept: Latitude Measurement, Historical Context

c) Declination of $30°N$
[Solution Description]
In modern terms, *madhya rekhā* corresponds to a prime meridian (longitude reference). The angle of elevation ($30°$) from this reference would describe celestial latitude (declination), similar to how terrestrial latitude measures angular distance north/south of the Equator. Thus, $30°$ represents a declination, not longitude or altitude.

Key Concept: Latitude Basics

d) $90°S$
[Solution Description]
The South Pole is located at the southernmost point on Earth. According to the syllabus, latitudes are expressed in degrees, with the Equator at $0°$ and the poles at $90°$ North and $90°$ South. Therefore, the South Pole’s latitude is $90°S$.

Key Concept: Latitude and Climate

c) $80°N$
[Solution Description]
According to the syllabus, as latitude increases towards the poles ($90°N$ or $90°S$), the climate becomes colder (frigid). The Equator ($0°$) has a hot climate, while mid-latitudes have temperate climates. Therefore, frigid climates are found near the poles.

Key Concept: Latitude and Climate Zones

b) Temperate (Moderate)
[Solution Description]
At the Equator ($0°$ latitude), the climate is torrid (hot). Moving towards the poles, the climate becomes temperate (moderate) between $23.5°$ and $66.5°$ latitudes, and frigid (cold) beyond $66.5°$. City 1 is at $30°N$, which falls in the temperate zone. City 2 at $60°N$ also lies within the temperate zone but closer to the upper boundary ($66.5°N$). However, given its proximity to the Arctic Circle ($66.5°N$), it may exhibit colder characteristics, but officially, it remains in the temperate zone.

Key Concept: Latitudes, Climate zones

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Assertion states that the climate near the poles is frigid due to their high latitudes, which is correct since higher latitudes ($60°N/S$ to $90°N/S$) experience colder climates as they receive less direct sunlight. Reason explains that higher latitudes receive less direct sunlight compared to lower latitudes, which is scientifically accurate. Sunlight strikes the Earth at oblique angles near the poles, spreading energy over a larger area and thus reducing intensity. This directly causes frigid conditions. Therefore, both statements are true, and Reason correctly explains Assertion.

Key Concept: Historical astronomy, Indian meridian

c) Both latitude and longitude are needed for precise location
[Solution Description]
The establishment of a reference meridian through Ujjain ($23.5°N$) acknowledged the need for both latitude (angular distance from Equator) and longitude (angular distance from prime meridian) to precisely locate places, forming a complete grid system.

Key Concept: Latitude and Climate

c) Torrid Zone
[Solution Description]
The Torrid Zone lies between $0°$ (Equator) and approximately $23.5°$ North and South latitudes. Since $15°S$ falls within this range, it belongs to the Torrid Zone, characterized by a hot climate.

Key Concept: International Date Line, Time Zones

b) 9:20 PM Monday
[Solution Description]
Tokyo is at $140^\circ E$, which falls in the GMT+9 time zone. Los Angeles is at $120^\circ W$, falling in GMT-8 (Pacific Time Zone). First, calculate the time difference: From $140^\circ E$ to $180^\circ$ (International Date Line) is $40^\circ$ westward, equivalent to $40/15 \approx 2.67$ hours (2 hours 40 minutes). Crossing the Date Line adds a day when traveling westward. The flight duration is 10 hours. Total time elapsed: 12 hours 40 minutes. Subtract this from departure time (10 AM Monday) gives 9:20 PM Sunday. But crossing the Date Line adds a day, making it 9:20 PM Monday.

Key Concept: Latitude and Climate

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The temperate zone is defined as the region lying between the Tropic of Cancer ($23.5°N$) and the Arctic Circle ($66.5°N$) in the Northern Hemisphere, and between the Tropic of Capricorn ($23.5°S$) and the Antarctic Circle ($66.5°S$) in the Southern Hemisphere. The assertion correctly identifies this range.
The reason states that as latitude increases, the angle of incidence of sunlight decreases. This is true because sunlight spreads over a larger area at higher latitudes due to Earth’s curvature. Less concentrated solar energy means lower temperatures, making the climate moderate. Therefore, the reason correctly explains why the temperate zone has moderate temperatures.

Key Concept: Latitude, Climate Zones

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion correctly states that the Frigid Zone has extremely cold temperatures due to its location near the poles and the low angle of sunlight. This aligns with the fact that higher latitudes receive less direct sunlight. The Reason accurately explains why this happens: as latitude increases, the angle at which sunlight strikes the Earth becomes more oblique, spreading the same amount of solar energy over a larger area. Thus, both Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: Latitude Range

c) 80°N
[Solution Description]
The Frigid Zone is characterized by extremely cold temperatures due to its proximity to the poles, specifically at latitudes close to $90°N$ and $90°S$. Among the given options, the latitude closest to the poles would have the coldest climate.

Key Concept: Measuring Longitude

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
First, let’s analyze Assertion (A): Longitude is indeed measured as the angular distance east or west from the Prime Meridian (Greenwich Meridian) along the Equator. This is correct according to the syllabus.
Now, Reason (R): It states that the Earth’s rotation causes different longitudes to have different local times, which is also true because time zones are based on longitude.
However, while both statements are true, Reason (R) does not explain why longitude is measured as an angle from the Greenwich Meridian. Hence, Reason (R) is not the correct explanation of Assertion (A).

Key Concept: Prime Meridian

a) $0°E$
[Solution Description]
The Prime Meridian is defined as the reference line for measuring longitudes and has a value of $0°$ longitude.

Key Concept: Time and Longitude

c) Because the Earth’s rotation affects exposure to sunlight
[Solution Description]
Local time varies with longitude because the Earth’s rotation causes different longitudes to experience sunlight at different times.

Key Concept: International Date Line, Longitude Crossing

b) Next date, 12:00 AM
[Solution Description]
The International Date Line is located at $180°$ longitude. Crossing it westward requires adding one day. If the ship crosses at 12:00 AM, the new date becomes the next calendar day at the same time. For example, if it was January 1 at 12:00 AM before crossing, it becomes January 2 at 12:00 AM immediately after crossing.

Key Concept: Prime Meridian, Historical Context

c) 76°
[Solution Description]
The angular distance between two meridians is calculated by finding the difference in their longitudes. Since Ujjain lies at \$76°E\$ and Greenwich is at \$0°E\$, the difference is \$76° – 0° = 76°\$. This measures the angle between the two meridians when measured along the Equator.

Key Concept: Prime Meridian and Historical Context

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The Assertion states that the Greenwich Meridian was accepted in 1884 due to its alignment with an astronomical center. This is partially true, as it was chosen for practical reasons (navigation and timekeeping) rather than purely astronomical significance. However, the Reason correctly notes that India historically had its own prime meridian (madhya rekhā) centered in Ujjayinī, a hub for astronomical studies. While both statements are factually accurate, the Reason does not directly explain why Greenwich was adopted in 1884; it instead provides historical context. Thus, they are independently true but not causally linked.

Key Concept: Longitude and Latitude Coordinates

d) No other coordinate pair represents the same location
[Solution Description]
Latitude ranges from $0°$ to $90°N$ or $90°S$, while longitude ranges from $0°$ to $180°E$ or $180°W$.
For a given location at $60°N$ and $90°W$, the equivalent coordinates in terms of degrees are:
– Latitude remains $60°$ but changes to $60°S$ in the southern hemisphere, but this would represent a different location.
– Longitude can also be represented as $270°$ (since $360° – 90° = 270°$), but standard practice is to keep it within $180°E/W$.
However, there is no other valid coordinate pair that represents the exact same location on Earth since changing the sign or hemisphere would shift the position entirely. Thus, the only correct representation here is the original one.
Therefore, no other coordinate pair represents the same location.

Key Concept: Time Zones

b) 9 PM (previous day)
[Solution Description]
The Prime Meridian ($0°$) is the reference point for calculating time differences based on longitude.
Given: Local time at $120°E$ = 8 AM.
Step 1: Calculate the time difference between $120°E$ and $0°$.
– $120°E$ is $120°$ east of $0°$.
– Time difference = $120° / 15°$ per hour = 8 hours ahead of GMT.
Step 2: Find GMT.
– Since $120°E$ is 8 AM and is 8 hours ahead of GMT, GMT = 8 AM – 8 hours = 12 AM (midnight).
Step 3: Calculate local time at $45°W$.
– $45°W$ is $45°$ west of $0°$.
– Time difference = $45° / 15°$ per hour = 3 hours behind GMT.
– Local time at $45°W$ = GMT – 3 hours = 12 AM – 3 hours = 9 PM (previous day).
Therefore, the local time at $45°W$ is 9 PM of the previous day.

Key Concept: Ujjayinī Prime Meridian

c) Astronomical calculations and timekeeping
[Solution Description]
The Ujjayinī meridian (madhya rekhā) was a reference line in ancient Indian astronomy. It passed through Ujjain and was used for astronomical calculations, as mentioned in various Indian astronomical texts.

Key Concept: Ujjayinī Prime Meridian

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion (A) states that the Ujjayinī meridian, known as madhya rekhā, was historically used as the prime meridian in ancient Indian astronomy. This is true because Indian astronomers like Varāhamihira referenced this line for their astronomical calculations.
The reason (R) explains that it passed through Ujjain, which was indeed a prominent hub for astronomy, reinforcing its use as a reference point. Both statements are correct, and the reason logically justifies the assertion since Ujjain’s prominence made it suitable as the prime meridian location.

Key Concept: Latitude and Climate

b) The climate becomes colder as latitude increases from the Equator.
[Solution Description]
The Equator is at $0°$ latitude and has a hot (torrid) climate. As we move toward the poles, the latitude increases ($90°N$ or $90°S$), and the climate becomes colder (frigid). Between these extremes, the climate is moderate (temperate). This relationship shows that as latitude increases from the Equator to the poles, the climate transitions from hot to cold.

Key Concept: Longitude, Time Zones

d) 8:00 PM
[Solution Description]
First, calculate the total change in longitude: $60°W$ to $30°E$ is a movement of $90°$ eastward ($60° + 30° = 90°$). Each $15°$ corresponds to 1 hour, so the time difference between departure and arrival locations is $90° \div 15° = 6$ hours. Since the airplane is moving eastward, time increases. The departure time at $60°W$ is 8:00 AM, so the local time at $30°E$ at departure would be 8:00 AM + 6 hours = 2:00 PM. Adding the flight duration of 6 hours, the local time at arrival will be 2:00 PM + 6 hours = 8:00 PM.

Key Concept: Indian Latitudes and Longitudes

b) $29^\circ$
[Solution Description]
The longitudinal extent of India is given as $68^\circ E$ to $97^\circ E$. To find the span, subtract the smaller longitude from the larger one: $97^\circ – 68^\circ = 29^\circ$.

Key Concept: Intersections of Latitudes and Longitudes

d) Assertion is false, but Reason is true.
[Solution Description]
The Assertion states that the Prime Meridian is the only meridian dividing the Earth into Eastern and Western Hemispheres. This is false because any meridian could theoretically divide the Earth into these hemispheres, but the Prime Meridian is internationally recognized as the standard ($0°$ longitude). The Reason correctly describes the Prime Meridian’s location and its role in defining longitudes globally. Thus, the Assertion is incorrect, but the Reason is true.

Key Concept: Latitude, Time Zones, International Date Line

b) Previous day, 8:00 PM
[Solution Description]
Tokyo is at 140$^\circ$E, so its time zone is UTC+9. Flying westward decreases longitude and crosses the International Date Line (180$^\circ$), subtracting a day. The flight duration is 8 hours, so the local time at departure was 12:00 PM. After 8 hours, local time would be 8:00 PM, but crossing the date line subtracts a day. Thus, the date goes back by one day, and the time remains 8:00 PM.

Key Concept: Latitude and Longitude

d) 23°N, 82°E
[Solution Description]
Latitude measures how far north or south a point is from the Equator, while longitude measures how far east or west it is from the Prime Meridian. In this case, the point is 23° north of the Equator and 82° east of the Prime Meridian. Therefore, its coordinates are written as 23°N, 82°E.

Key Concept: Hemispheres, Historical Prime Meridians

b) 3
[Solution Description]
First, analyze using Greenwich Meridian (0°):
15°W puts it in Western Hemisphere.
10°S puts it in Southern Hemisphere – so 2 hemispheres here.
Now using Ujjain’s Madhya Rekha (76°E):
Longitude difference = 76°E to 15°W = 91° west of Ujjain.
Since 180° is max, this is still western side but according to Indian system.
Latitude remains Southern – so 2 more classifications.
However, the Northern/Southern classification doesn’t change between systems.
Therefore total unique hemisphere classifications:
Western (Greenwich), Southern, Western (Ujjain) – total 3 unique classifications.

Key Concept: Historical Context, Hemisphere Concepts

c) Converting recorded longitudinal positions between the two systems
[Solution Description]
The key challenge arises from the different prime meridians:
– Star positions relative to zenith would remain largely unchanged as latitude is absolute
– Local time calculations would adjust based on longitude but follow same principles
– Celestial pole height depends only on latitude
– However, converting between the two systems requires accounting for the 76° offset between their prime meridians when recording longitudinal positions
The most complex aspect is maintaining consistency when translating star charts and navigation records between two systems with different fundamental references.

Key Concept: Latitude and Longitude

c) Latitude and Longitude
[Solution Description]
Latitude and Longitude together form a grid system that allows us to locate any place on the Earth’s surface precisely.

Key Concept: Grid System, Longitude, Indian Prime Meridian

b) $60.78°E$
[Solution Description]
The Earth rotates $15°$ per hour. If the Sun is overhead at Ujjain ($75.78°E$) at noon, one hour later it will be overhead at a location $15°$ west of Ujjain because the Earth rotates eastward. Subtract $15°$ from $75.78°E$ to get $60.78°E$.

Key Concept: Latitude, Longitude, Hemispheres

b) $45°S, 60°E$
[Solution Description]
The Southern Hemisphere is defined as having a latitude south of the Equator ($0°$ to $-90°S$), and the Eastern Hemisphere has longitudes from $0°$ to $180°E$. Among the options, only $45°S, 60°E$ satisfies both conditions: it is south of the Equator and east of the Prime Meridian.

Key Concept: Prime Meridian, Longitude, Historical Context

b) 5:08 PM
[Solution Description]
Since the Earth rotates $360°$ in 24 hours, it rotates $15°$ per hour ($360° / 24 = 15°$). The city is at $77°E$, which means it is $77°$ east of the Prime Meridian. To find the time difference, divide the longitude by $15°$ per hour: $77° / 15° \approx 5.133$ hours. Convert the decimal part to minutes: $0.133 \times 60 \approx 8$ minutes. Thus, the time difference is 5 hours and 8 minutes ahead of Greenwich. Adding this to 12:00 PM gives 5:08 PM.

Key Concept: Latitude and Climate

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion is true because regions near the Equator receive direct sunlight throughout the year, leading to higher temperatures (hot climate). As we move towards higher latitudes (North or South), the sunlight strikes at an angle, reducing its intensity and resulting in cooler climates (temperate or frigid).
The Reason is also correct as it accurately explains why the climate changes with latitude: the angle of sunlight reduces the intensity of solar radiation received at higher latitudes. Thus, the Reason correctly explains the Assertion.

Key Concept: Latitude Basics

b) $0°$
[Solution Description]
The Equator is the reference line for measuring latitudes. By definition, its latitude is $0°$. This is a fundamental concept in geography.

Key Concept: Northern and Southern Hemispheres

a) It is the longest parallel of latitude.
[Solution Description]
The Equator divides the Earth into Northern and Southern Hemispheres. It is the line of $0°$ latitude, halfway between the North and South Poles. All parallels of latitude are measured north or south of the Equator.

Key Concept: Time and Longitude

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Earth completes one full rotation of $360°$ in 24 hours. Therefore, the Earth rotates at a rate of $15°$ per hour ($360° / 24 = 15°$ per hour). This means that for every $15°$ of longitude eastward from the Prime Meridian, the local time increases by 1 hour. Hence, the assertion is true. The reason correctly explains this relationship as it describes how the Earth’s rotation causes the time difference based on longitude. Both the assertion and reason are true, and the reason is the correct explanation of the assertion.

Key Concept: International Date Line, Time Zone Crossing

b) Tuesday 12:00 PM
[Solution Description]
Crossing the International Date Line westward adds one day to the current date. Thus, if it’s Monday 12:00 PM before crossing, it becomes Tuesday 12:00 PM immediately after crossing.

Key Concept: Time Zones, International Date Line

c) Assertion is true, but Reason is false.
[Solution Description]
First, calculate the longitude difference between $15°E$ and $180°W$. Moving west from $15°E$ to $180°W$ covers a total of $195°$ ($15° + 180°$). Convert this to time difference: $195° \times 4\,\text{minutes/degree} = 780\,\text{minutes} = 13\,\text{hours}$. Subtract 13 hours from 12 pm at $15°E$, which gives 11 pm of the previous day. Assertion is true. The reason states crossing eastward subtracts a day, but we crossed westward. Hence, while the assertion is correct, the reason misrepresents the direction of crossing. Thus, Reason is false.

Key Concept: Earth’s rotation and time difference

c) 12 PM
[Solution Description]
To find the local time at $15^\circ W$, we first calculate the total longitude difference between $30^\circ E$ and $15^\circ W$. Moving westward from $30^\circ E$ to $0^\circ$ covers $30^\circ$, and then another $15^\circ$ to reach $15^\circ W$, totaling $45^\circ$ difference. Since $15^\circ$ equals 1 hour of time difference, $45^\circ$ corresponds to $\frac{45}{15}=3$ hours. Because we’re moving westward, time decreases. So, subtracting 3 hours from 3 PM gives 12 PM.

Key Concept: Time zones

c) 1:00 PM
[Solution Description]
The Earth rotates $15°$ per hour. The difference in longitude between $0°$ and $30°W$ is $30°$. Since each $15°$ corresponds to 1 hour, the time difference is $\frac{30}{15} = 2$ hours. Moving westward subtracts time, so local time at $30°W$ = 3:00 PM – 2 hours = 1:00 PM.

Key Concept: Time zone overlap, Earth rotation principles

a) 1:00 PM (same day)
[Solution Description]
Calculate the total longitude difference: $105°E$ to $180°$ is $75°$, plus $180°$ to $150°W$ is $330°$ total difference. Time difference is $330°/15°$ per hour = 22 hours. Crossing the International Date Line adds or subtracts a day. Moving eastward from $105°E$ to $150°W$ crosses the date line once (westward), adding a day. Subtract 22 hours from 11:00 AM to get 1:00 PM of the previous day, then add 1 day due to crossing the date line. Final time is 1:00 PM on the same day as the original date.

Key Concept: Local Time Calculation

d) Assertion is false, but Reason is true.
[Solution Description]
The Assertion states that if it’s 3:00 pm at $45°E$, then at $60°E$, the time will be 5:00 pm. We can verify this as follows:
1) Find the longitude difference between the two locations: $60°E – 45°E = 15°$.
2) Since the Earth rotates at $15°$ per hour, the time difference is $\frac{15°}{15°/\text{hour}} = 1 \text{ hour}$.
3) Because $60°E$ is east of $45°E$, the local time increases by 1 hour. Thus, $3:00 \text{ pm} + 1 \text{ hour} = 4:00 \text{ pm}$, not 5:00 pm. Therefore, the Assertion is false.
The Reason correctly states that the Earth rotates at $15°$ per hour, meaning each $15°$ longitude difference equals a 1-hour time difference. This part is true.
Hence, the Assertion is false, but the Reason is true.

Key Concept: Time Zone Calculation

c) 4:00 PM
[Solution Description]
The Earth rotates $360°$ in 24 hours, so each $15°$ of longitude corresponds to a 1-hour time difference. At $60°\text{E}$, the time difference from Greenwich is $\frac{60}{15} = 4$ hours. Since $60°\text{E}$ is east of Greenwich, the local time will be ahead by 4 hours. Therefore, the local time at $60°\text{E}$ will be $12:00\,\text{PM} + 4\,\text{hours} = 4:00\,\text{PM}$.

Key Concept: IST vs GMT, Time Zone Conversion

b) 9:30 AM
[Solution Description]
IST is 5 hours 30 minutes ahead of GMT.
To find GMT, subtract 5 hours 30 minutes from IST.
$3:00 \text{ PM} – 5 \text{ hours} = 10:00 \text{ AM}$.
$10:00 \text{ AM} – 30 \text{ minutes} = 9:30 \text{ AM}$.
Therefore, GMT is 9:30 AM.

Key Concept: Standard Time Calculation

c) 2:00 PM
[Solution Description]
The Earth rotates 15° per hour. At 30°E, the time difference from GMT (0°) can be calculated as follows:
30° / 15° per hour = 2 hours.
Since the country is east of Greenwich, the local time will be ahead of GMT. Therefore, add the time difference to GMT:
12:00 PM + 2 hours = 2:00 PM.
Thus, the standard time in the country will be 2:00 PM.

Key Concept: Time zones, International Date Line

b) Sunday 2:28 pm
[Solution Description]
First calculate longitude difference between Tokyo and San Francisco: $140°E$ to $180°E$ is $40°$, then $180°W$ to $122°W$ is $58°$. Total difference = $40° + 58° = 98°$. Time difference = $98° / 15°$ per hour = 6.533 hours ≈ 6 hours 32 minutes. Since flying eastward subtracts time: Departure time + Flight duration – Time difference = 10:00 + 11:00 – 6:32 = 14:28 (2:28 pm) same day. But crossing IDL eastward means subtracting a day → Sunday 2:28 pm.

Key Concept: Time Zones and Standard Time

a) 11:00 AM
[Solution Description]
The Earth rotates 360° in 24 hours, so each 15° represents a difference of 1 hour. To find the local time at 15°W when it’s 3:00 PM at 45°E, first calculate the longitudinal difference between the two locations.
45°E to 15°W involves moving westward. Total degrees from 45°E to 15°W:
From 45°E to 0° = 45°
From 0° to 15°W = 15°
Total = 45° + 15° = 60°
Now, convert degrees to time difference: 60° / 15° per hour = 4 hours.
Since we’re moving westward, subtract the time difference:
3:00 PM – 4 hours = 11:00 AM.

Key Concept: Time and Longitude

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that IST is 5 hours 30 minutes ahead of GMT, which is correct as per the syllabus. The Reason explains that a longitude difference of $82.5^\circ$ corresponds to a time difference of 5 hours 30 minutes because $15^\circ$ equals 1 hour (as given in the syllabus). Calculating: $82.5^\circ / 15^\circ = 5.5$ hours. Therefore, both Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: Local Time Difference

c) 3:00 pm
[Solution Description]
The Earth rotates $360^{\circ}$ in 24 hours, so each hour corresponds to $15^{\circ}$ of longitude. To find the time difference between Greenwich ($0^{\circ}$) and $45^{\circ}E$, divide the longitude difference by $15^{\circ}$ per hour:
$\text{Time difference} = \frac{45^{\circ}}{15^{\circ}\text{/hour}} = 3 \text{ hours ahead}$
Since it is 12:00 pm at Greenwich, the local time at $45^{\circ}E$ will be 12:00 pm + 3 hours = 3:00 pm.

Key Concept: IST Calculation

c) 1:30 pm
[Solution Description]
IST is 5 hours and 30 minutes ahead of GMT. To convert 8:00 am GMT to IST, simply add 5 hours and 30 minutes:
$8:00 \text{ am} + 5 \text{ hours} = 1:00 \text{ pm}$
$1:00 \text{ pm} + 30 \text{ minutes} = 1:30 \text{ pm}$
So, the IST will be 1:30 pm.

Key Concept: Standard Time vs. Local Time

c) Due to their large longitudinal extent
[Solution Description]
Large countries span many degrees of longitude, causing significant variations in local solar time. To maintain uniform standard times within regions while accounting for Earth’s rotation, these countries adopt multiple time zones.

Key Concept: Time zones, International Date Line

c) 5:00 AM on Tuesday
[Solution Description]
First, find the departure time of Tokyo in UTC. Since Tokyo is UTC+9, subtract 9 hours from 10:00 AM Tokyo time: 10:00 AM – 9 hours = 1:00 AM UTC on Monday. The flight duration is 12 hours, so the arrival time in UTC is 1:00 AM + 12 hours = 1:00 PM UTC on Monday. Now, convert this to Los Angeles time (UTC-8): 1:00 PM UTC – 8 hours = 5:00 AM on Monday. However, since the flight crosses the International Date Line westward, we add one day: 5:00 AM on Tuesday.

Key Concept: International Date Line, Time Zones

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The Assertion states that crossing the International Date Line east to west at 10:00 AM on Monday changes the local time to 10:00 AM on Tuesday. This is correct because crossing westward adds a day. The Reason explains that this adjustment compensates for the Earth’s rotation and maintains time consistency. However, while the Reason correctly describes the effect of adding a day, it inaccurately attributes it to “compensating for the Earth’s rotation.” The actual reason is to align with global timekeeping conventions as one moves across longitudes. Thus, both Assertion and Reason are true, but the Reason does not correctly explain the Assertion.

Key Concept: Time zone, International Date Line

b) Sunday 8:00 AM
[Solution Description]
The International Date Line is approximately at 180° longitude. Crossing the date line changes the date by one day but keeps the time the same (ignoring time zone adjustments for simplicity). Since 180°E and 180°W are the same line (the International Date Line), crossing it from east to west subtracts a day. Therefore, if it is Monday 8:00 AM at 180°E, it will be Sunday 8:00 AM at 180°W.

Key Concept: Time Zones and Local Time

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Earth completes a full rotation of 360 degrees in 24 hours, which means it rotates at a rate of $15^\circ$ per hour ($360^\circ / 24 = 15^\circ/\text{hour}$). Therefore, for every $15^\circ$ of longitude difference between two places, there will be a one-hour time difference. This explains why the local time changes with longitude. The assertion states that the difference in local time depends on the difference in longitudes, which is correct because the Earth’s rotation rate links longitude directly to time. The reason correctly explains this relationship by stating the $15^\circ$ per hour rotation rate.

Key Concept: Local Time and Standard Time

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Earth completes a full rotation of 360° in 24 hours, so it rotates at a rate of $360^\circ / 24 = 15^\circ$ per hour. This means for every 15° difference in longitude, there will be a 1-hour difference in local time. Given that the longitude difference between Porbandar and Tinsukia is 30°, the local time difference will be $30^\circ / 15^\circ = 2$ hours. Both the Assertion and Reason are true, and the Reason correctly explains the Assertion.