CSS Past Paper 2020 General Science and Ability Descriptive (Part 2)
CSS | Past Paper | Compulsory | 2020 | Part 2 | Descriptive
Below is the solution to PART-II (COMPULSORY) of the CSS Past Paper 2020 General Science and Ability Descriptive (Part 2).
Question 2
(a) On 7th April 2012 an Avalanche hit a Pakistan military base in Gayari sector trapping 140 soldiers and civilians under deep snow. What is Avalanche; describe its four types with focus on most dangerous type?
An avalanche is a rapid, downhill flow of a large mass of snow, ice, rock, and debris. It is a significant natural hazard in mountainous regions, triggered by factors like heavy snowfall, earthquakes, temperature changes, or human activity.
Four Main Types of Avalanches
- Loose Snow Avalanche: This starts from a single point and gathers more snow as it descends, forming a characteristic fan-shaped deposit. They are common in dry, powdery snow and are usually relatively small.
- Slab Avalanche: This is the most dangerous and deadly type. It occurs when a cohesive plate (or slab) of snow breaks away from the surrounding snowpack and slides downhill as a single unit. They are often triggered by the victim themselves and can be massive, traveling at high speeds and destroying everything in their path.
- Powder Snow Avalanche: This is a type of avalanche that consists of a cloud of powdered snow that can travel at extremely high speeds (over 300 km/h). It is often accompanied by a powerful air blast that can cause destruction beyond the snow deposit zone.
- Wet Snow Avalanche: These occur when liquid water weakens the bond between snow layers, typically in spring or during warming periods. They are slower than dry snow avalanches but are denser and can carry heavy debris, making them very destructive.
(b) What do you understand by Global Wind and Pressure patterns? Also explain wind and pressure features at higher altitude.
Global Wind and Pressure Patterns refer to the large-scale atmospheric circulation systems driven by the unequal heating of the Earth’s surface (equator vs. poles) and the planet’s rotation (Coriolis effect). This circulation redistributes heat and moisture around the globe.
The fundamental model is the Tri-Cellular Model, which consists of:
- Hadley Cell: Located between the equator and ~30°N/S. Warm air rises at the equator (Low Pressure – ITCZ), flows poleward aloft, cools, and sinks at the subtropics (High Pressure – Horse Latitudes), then returns as trade winds towards the equator.
- Ferrel Cell: A mid-latitude cell (30°-60°N/S) driven by the other two cells. Air descends at the subtropics, flows poleward at the surface (Westerlies), and rises at the sub-polar low-pressure zone.
- Polar Cell: Air descends at the poles (High Pressure), flows equatorward at the surface (Polar Easterlies), and rises at the polar front (Low Pressure).
Features at Higher Altitudes (Upper Troposphere)
- Pressure: Pressure decreases exponentially with altitude. The high-altitude pressure pattern is a mirror image of the surface, with low pressure over poles and high pressure over the equator.
- Wind: The dominant feature is the Jet Streams—narrow, fast-flowing, meandering air currents found at the tropopause. The most important are the Polar Jet Stream (at ~60°N/S, marking the polar front) and the Subtropical Jet Stream (at ~30°N/S). These winds greatly influence surface weather patterns and are crucial for aviation.
(c) World largest earthquake was assigned a magnitude of 9.5 by the United States Geological Survey on 22 May 1960 in southern Chile Valdivia. What do you know about earthquake? Also explain shallow-focus and deep-focus earthquakes.
An earthquake is a sudden and violent shaking of the ground caused by the abrupt release of energy in the Earth’s lithosphere. This energy release creates seismic waves. Most earthquakes occur along fault lines due to the movement of tectonic plates.
Earthquakes are classified based on the depth of their focus (hypocenter), the point where the rupture originates:
Shallow-focus Earthquakes
- Depth: 0 – 70 km below the Earth’s surface.
- Characteristics: They are the most common and by far the most destructive type of earthquake. Because the energy is released closer to the surface, the seismic waves have less distance to travel before reaching structures, resulting in more intense shaking and greater damage. The 2005 Kashmir and 2008 Sichuan earthquakes are tragic examples.
Deep-focus Earthquakes
- Depth: 300 – 700 km below the surface.
- Characteristics: These occur within subducting tectonic plates. While they can release enormous amounts of energy (like the 1994 Bolivia earthquake, Mw 8.2, depth 631 km), the seismic waves attenuate (weaken) significantly as they travel upward to the surface. Consequently, they are felt over a much wider area but generally cause less damage at any single point on the surface compared to a shallow quake of similar magnitude.
(d) Differentiate between the renewable and non renewable energy sources. Briefly explain Geothermal Energy and Hydro Electricity.
| Feature | Renewable Energy Sources | Non-Renewable Energy Sources |
| Definition | Sources that are naturally replenished on a human timescale. | Sources that exist in finite quantities and cannot be replenished once exhausted. |
| Sustainability | Sustainable and virtually inexhaustible. | Not sustainable; will eventually deplete. |
| Environmental Impact | Generally have a low carbon footprint and cause less pollution. | Major contributors to air and water pollution and greenhouse gas emissions. |
| Examples | Solar, Wind, Geothermal, Hydroelectric, Biomass. | Coal, Petroleum, Natural Gas, Nuclear (Uranium). |
Geothermal Energy
This energy harnesses the immense heat from the Earth’s interior. Wells are drilled into underground reservoirs to tap steam and hot water, which can then be used to drive turbines connected to electricity generators. It provides a reliable, baseload power source with very low emissions. Countries like Iceland and the Philippines utilize it extensively.
Hydro Electricity
This is the most developed and largest source of renewable electricity globally. It uses the kinetic energy of flowing water (often stored in dams) to spin turbines and generate power. It is a mature, efficient, and low-cost technology that also provides flood control and irrigation. However, large-scale hydro projects can have significant ecological and social impacts, including habitat destruction and population displacement.
Question 3
(a) What are Pesticides? Explain their different types; why persistent pesticides are more lethal for mankind?
Pesticides
Pesticides are chemical or biological substances used to prevent, destroy, repel, or mitigate pests such as insects, weeds, rodents, fungi, and bacteria.
Different Types
- Insecticides: Target insects.
- Herbicides: Target weeds and unwanted vegetation.
- Fungicides: Target fungi and molds.
- Rodenticides: Target rodents.
- Nematicides: Target nematodes (roundworms).
Why Persistent Pesticides are More Lethal?
Persistent pesticides, like the now-banned DDT, are organic compounds that do not break down easily in the environment. Their lethality stems from:
- Bioaccumulation: They accumulate in the fatty tissues of organisms.
- Biomagnification: Their concentration increases at each successive trophic level in the food chain. Top predators, including humans, accumulate the highest and most toxic concentrations.
- Long-Term Health Effects: This chronic exposure is linked to cancer, birth defects, neurological disorders, and disruption of the endocrine (hormone) system.
- Environmental Persistence: They remain in soil and water for decades, causing continuous damage to ecosystems and entering the human food supply.
(b) What are carbohydrates? Classify and give detail of each class along with examples.
Carbohydrates
Carbohydrates are organic compounds composed of carbon, hydrogen, and oxygen, serving as the primary source of energy for the body. They are commonly known as sugars, starches, and fibers.
Classification
- Monosaccharides (Simple Sugars): The simplest form of carbohydrates; they cannot be hydrolyzed into smaller sugars.
- Examples: Glucose (blood sugar), Fructose (fruit sugar), Galactose.
- Disaccharides: Composed of two monosaccharide units joined together.
- Examples: Sucrose (glucose + fructose; table sugar), Lactose (glucose + galactose; milk sugar), Maltose (glucose + glucose; malt sugar).
- Polysaccharides (Complex Carbohydrates): Long chains of monosaccharide units. They function as energy storage or structural materials.
- Examples:
- Starch (energy storage in plants; found in grains, potatoes).
- Glycogen (energy storage in animals and humans; stored in liver and muscles).
- Cellulose (structural component of plant cell walls; dietary fiber).
- Chitin (structural component in fungi and exoskeletons of insects).
- Examples:
(c) Discuss different methods of Food preservation.
Food preservation aims to prevent spoilage caused by microorganisms, enzymes, and oxidation, thereby extending shelf life and ensuring safety.
Different Methods
- Heat Treatment:
- Pasteurization: Heating food (like milk) to a specific temperature for a set time to kill pathogenic microorganisms without significantly altering taste.
- Canning: Sealing food in airtight containers and heating it to destroy all microorganisms.
- Removal of Moisture (Dehydration): Microorganisms require water to grow. Methods include sun-drying, spray-drying (milk powder), and freeze-drying.
- Temperature Control:
- Refrigeration: Slows down microbial growth and enzyme activity.
- Freezing: Halts microbial growth and chemical reactions entirely.
- Chemical Preservation: Adding substances that inhibit microbial growth.
- Examples: Salt (in curing meat), Sugar (in jams), Vinegar (pickling), and synthetic preservatives like sodium benzoate.
- Fermentation: Using beneficial microorganisms (e.g., bacteria, yeast) to produce acids or alcohol that preserve the food (e.g., yogurt, cheese, sauerkraut).
- Irradiation: Exposing food to ionizing radiation (like gamma rays) to kill bacteria, parasites, and insects.
(d) Where and how Fiber Optics are used? Also write down their advantages and disadvantages.
Uses of Fiber Optics
- Telecommunications: The backbone of the internet and modern telephone systems for long-distance and high-data-rate transmission.
- Medical Imaging: Used in endoscopes and laparoscopes to see inside the human body without invasive surgery.
- Networking: Connecting computers and servers within buildings and across campuses (LANs, MANs).
- Sensing: Used in sensors to measure temperature, pressure, strain, and other parameters in harsh environments.
- Lighting: Used for decorative lighting, signage, and illuminating hard-to-reach places.
Advantages
- High Bandwidth: Can carry vast amounts of data (e.g., voice, video) simultaneously.
- Low Attenuation: Signals can travel long distances (50-100 km) with minimal loss.
- Immunity to EMI: Unaffected by electromagnetic interference from power lines or other cables.
- Security: Difficult to tap into a fiber cable without detection.
- Size and Weight: Thinner, lighter, and more flexible than copper cables.
Disadvantages
- Cost: Higher initial installation cost compared to copper wiring.
- Fragility: Glass fibers can be more fragile and require careful handling and installation.
- Specialized Skills: Installation and splicing require specially trained technicians and expensive equipment.
Question 4
(a) Briefly describe the various segments of atmosphere. How these segments are maintaining the Earth Radiation Balance?
The atmosphere is divided into layers based on temperature gradients:
- Troposphere: The lowest layer (0-12 km), where weather occurs. Temperature decreases with altitude.
- Stratosphere: Extends up to 50 km. Contains the Ozone Layer which absorbs UV radiation, causing temperature to increase with altitude.
- Mesosphere: Extends up to 85 km. Temperature decreases with altitude; meteors burn up here.
- Thermosphere: Extends up to 600 km. Temperature increases dramatically due to absorption of high-energy solar radiation. Auroras occur here.
- Exosphere: The outermost layer, merging into space.
Maintaining Radiation Balance
The Earth’s energy balance is a state where the incoming solar energy is equal to the outgoing energy radiated back to space. The atmosphere plays a crucial role through:
- The Greenhouse Effect: Certain gases (e.g., CO₂, H₂O, CH₄) in the troposphere are transparent to incoming shortwave solar radiation but absorb and re-radiate the outgoing longwave infrared radiation from the Earth’s surface. This natural process traps heat, keeping the planet warm enough for life (~15°C average instead of -18°C).
- The Ozone Layer: Located in the stratosphere, it absorbs 97-99% of the sun’s harmful ultraviolet (UV) radiation, protecting life and preventing excessive heating.
(b) How the organic particulate matter enters in the atmosphere. Also describe the sources?
Organic particulate matter (OM) is a complex mixture of particles containing carbon compounds suspended in the air. It enters the atmosphere through:
Sources
- Primary Sources (Direct Emission):
- Combustion: Incomplete burning of biomass (forest fires, agricultural burning) and fossil fuels (diesel engines, coal combustion).
- Biological Particles: Direct emission of pollen, spores, plant fragments, and microbes.
- Secondary Sources (Formed in the Atmosphere):
- This is the dominant source. Volatile Organic Compounds (VOCs) are released from both natural sources (trees) and anthropogenic sources (vehicles, industrial solvents). These VOCs undergo photochemical reactions in the atmosphere, oxidizing to form low-volatility compounds that condense to form secondary organic aerosols (SOA).
(c) What is natural radioactivity? How it is different from the artificial radioactivity?
Natural Radioactivity
Natural radioactivity is the spontaneous disintegration of unstable atomic nuclei found in nature, emitting radiation to achieve stability. It originates from:
- Primordial Radionuclides: Left over from the formation of the solar system (e.g., Uranium-238, Thorium-232, Potassium-40).
- Cosmogenic Radionuclides: Formed by the interaction of cosmic rays with atmospheric gases (e.g., Carbon-14).
Difference from Artificial Radioactivity
| Feature | Natural Radioactivity | Artificial Radioactivity |
| Origin | Occurs spontaneously in nature. | Man-made; induced by nuclear reactions (e.g., bombarding stable nuclei with particles in a reactor or accelerator). |
| Elements | Typically involves heavy elements (Z>83) and some light isotopes like C-14. | Can be created in any element (e.g., Cobalt-60, Iodine-131). |
| Control | Uncontrollable process. | Can be controlled and produced on demand. |
| Application | Used in radiometric dating (C-14, U-238). | Used in medicine (radiotherapy, diagnostics), industry (tracers), and nuclear power. |
(d) What are the Fossils? Discuss the importance of paleontology.
Fossils
Fossils are the preserved remains, impressions, or traces of ancient organisms (plants, animals, microbes) from a past geological age. They are typically preserved in sedimentary rock.
Importance of Paleontology (The Study of Fossils)
- Evidence for Evolution: Fossils provide the most direct evidence for the history of life on Earth, showing how species have changed and evolved over millions of years (e.g., the evolution of whales from land mammals).
- Understanding Extinction Events: The fossil record documents past mass extinctions (e.g., the K-T event that wiped out dinosaurs), helping scientists understand the causes and consequences of biodiversity loss.
- Reconstructing Past Environments: Fossils are used to interpret past climates, geography, and ecosystems (paleoecology). For example, coal deposits indicate ancient swamp forests.
- Biostratigraphy: Fossils are used to date rock layers and correlate strata across different geographical regions. Index fossils are crucial for this.
- Resource Exploration: Paleontological data helps geologists locate fossil fuel reserves like oil and natural gas, which are often found in rocks of specific ages with certain fossil assemblages.
Question 5
(a) What do you know about Hepatitis? Describe its types and write down preventive measures.
Hepatitis
Hepatitis is an inflammatory condition of the liver. It can be self-limiting or can progress to fibrosis (scarring), cirrhosis, or liver cancer.
Main Types
- Hepatitis A (HAV): Spread through ingestion of contaminated food or water (fecal-oral route). It causes an acute infection but does not lead to chronic disease.
Prevention: Vaccination, improved sanitation, and safe food/water practices. - Hepatitis B (HBV): Spread through contact with infectious body fluids (blood, semen, etc.). It can be acute or chronic.
Prevention: Vaccination (highly effective), safe sex practices, screening of blood donations, and not sharing needles. - Hepatitis C (HCV): Primarily spread through direct blood-to-blood contact. Often becomes chronic.
Prevention: No vaccine exists. Prevention involves screening blood supplies, safe injection practices, and avoiding sharing personal items like razors. - Hepatitis D (HDV): Only occurs in people who are already infected with HBV.
Prevention: Hepatitis B vaccination prevents HDV coinfection. - Hepatitis E (HEV): Similar to HAV, spread through the fecal-oral route, mainly via contaminated water.
Prevention: Ensuring safe drinking water and improved sanitation.
(b) Differentiate between Middle Latitude Cyclones and Tornadoes.
| Feature | Middle Latitude Cyclones (Wave Cyclones) | Tornadoes |
| Scale | Synoptic-scale weather system, 1000-2500 km in diameter. | Mesoscale phenomenon, very small, rarely over 2 km wide. |
| Duration | Can last from several days to a week. | Very short-lived, typically minutes to a few hours. |
| Formation | Forms along the polar front due to the interaction of cold and warm air masses. | Forms from powerful thunderstorms (supercells), associated with intense wind shear and instability. |
| Pressure | Central low pressure, but the gradient is relatively gentle. | Extremely intense low pressure at the center, creating a massive pressure gradient. |
| Wind Speed | High winds, but generally less than 120 km/h. | The most violent winds on Earth, can exceed 480 km/h. |
| Impact | Causes widespread weather: cloudiness, precipitation over a large area. | Causes extremely localized but catastrophic destruction along a narrow path. |
(c) What is Open System Interconnections (OSI) and describe its layers?
The Open Systems Interconnection (OSI) model is a conceptual framework used to understand and standardize the functions of a telecommunication or computing system without regard to its underlying internal structure and technology. It divides the communication process into seven abstraction layers.
The Seven OSI Layers (from top to bottom)
- Application Layer (Layer 7): Provides network services directly to user applications (e.g., HTTP, FTP, SMTP).
- Presentation Layer (Layer 6): Translates, encrypts, and compresses data for the application layer (e.g., SSL/TLS).
- Session Layer (Layer 5): Establishes, manages, and terminates connections between applications (sessions).
- Transport Layer (Layer 4): Ensures complete data transfer. Provides flow control, error recovery, and segmentation (e.g., TCP, UDP).
- Network Layer (Layer 3): Provides logical addressing and Path determination (routing) between hosts on different networks (e.g., IP, routers).
- Data Link Layer (Layer 2): Provides node-to-node data transfer, error detection/correction, and MAC addressing. Divides into LLC and MAC sub-layers (e.g., Ethernet, switches).
- Physical Layer (Layer 1): Transmits raw bit stream over the physical medium. Defines electrical, mechanical, and functional specifications (e.g., cables, hubs, NICs).
(d) What is GPS? How does it work?
GPS
GPS (Global Positioning System) is a satellite-based radio-navigation system that provides geolocation and time information to a GPS receiver anywhere on or near the Earth.
How it Works?
- Satellite Constellation: The system consists of a network of at least 24 satellites orbiting the Earth, broadcasting precise microwave signals.
- Trilateration: A GPS receiver on the ground calculates its position by precisely measuring the distance from itself to four or more GPS satellites.
- Measuring Distance: The receiver measures the time delay between the transmission of the signal from the satellite and its reception. Since the signal travels at the speed of light, the distance to each satellite is calculated as: Distance = Speed of Light × Time.
- Pinpointing Location: With the known distances to at least three satellites and their precise locations in space (from their ephemeris data), the receiver can determine its own three-dimensional position (latitude, longitude, and altitude) through a mathematical process called trilateration. A fourth satellite is used to correct for clock errors in the receiver.
Question 6
(a) Tariq can do a tailoring job in 6 hours. Sajid does the same job in 4 hours. Irfan does it in 8 hours. Tariq and Sajid start doing the work. Sajid leaves after two hours and Irfan replaces him. How long would it take to complete the work?
Solution
First, find the work rates (fraction of the job per hour).
- Tariq’s rate: 1661 job/hour
- Sajid’s rate: 1441 job/hour
- Irfan’s rate: 1881 job/hour
Work done by Tariq and Sajid together in the first 2 hours:
Combined rate = 16+14=212+312=51261+41=122+123=125 job/hour
Work done in 2 hours = 2×512=1012=562×125=1210=65 of the job.
Work remaining: 1−56=161−65=61 of the job.
Now, Irfan replaces Sajid. New team: Tariq and Irfan.
Combined rate of Tariq and Irfan = 16+18=424+324=72461+81=244+243=247 job/hour
Time to complete the remaining 1661 job:
Time = Work / Rate = 16÷724=16×247=4761÷247=61×724=74 hours.
Total time to complete the work: First 2 hours + 4774 hours = 247274 hours.
Answer: It will take 247274 hours to complete the work.
(b) Find the missing number to complete each sum.
i. 9 + 8 – 5 = 2 × (————-)
9+8−5=2×(6)9+8−5=2×(6)
12=2×612=2×6
ii. 3 × 9 – 14 = 24 – (————-)
3×9−14=24−(11)3×9−14=24−(11)
27−14=1327−14=13, so 24−11=1324−11=13
iii. 15 ÷ 3 × 12 = 41 + (————-)
15÷3×12=41+(19)15÷3×12=41+(19)
5×12=605×12=60, so 41+19=6041+19=60
iv. 24 ÷ 4 + 5 = 66 ÷ (————-)
24÷4+5=66÷(6)24÷4+5=66÷(6)
6+5=116+5=11, so 66÷6=1166÷6=11
v. 8 × 6 – 13 + 3 = 7 × 6 – (————-)
8×6−13+3=7×6−(4)8×6−13+3=7×6−(4)
Left: 48−13+3=3848−13+3=38
Right: 42−4=3842−4=38
(c) There are seven students in a group having ages 17,17,18,18,18,19,19. Calculate mean, median, mode and range of their ages. Also define these mentioned terms.
Dataset
17, 17, 18, 18, 18, 19, 19
- Mean: The average. Sum of all values divided by the number of values.
Sum = 17+17+18+18+18+19+19 = 126
Number of values = 7
Mean = 126 / 7 = 18 - Median: The middle value when the data is ordered. For 7 values (odd), the 4th value is the median.
Ordered data: 17, 17, 18, 18, 18, 19, 19
Median = 18 - Mode: The value that appears most frequently. The number 18 appears three times.
Mode = 18 - Range: The difference between the highest and lowest values.
Highest = 19, Lowest = 17
Range = 19 – 17 = 2
Definitions
- Mean: The arithmetic average of a set of numbers.
- Median: The middle value in an ordered list of numbers.
- Mode: The value that occurs most frequently in a data set.
- Range: A measure of statistical dispersion, calculated as the difference between the maximum and minimum values.
(d) How does mental ability scales differ from IQ test?
Mental Ability Scales and IQ Tests are related but distinct concepts:
Mental Ability Scales (or Aptitude Tests)
These are designed to measure specific, often narrow, cognitive capabilities or potentials. They assess a person’s ability to learn and perform in a particular area in the future. Examples include tests for mechanical reasoning, verbal aptitude, or spatial visualization. They are often used for educational tracking and career counseling.
IQ Tests (Intelligence Quotient Tests)
These are designed to provide a general measure of overall cognitive functioning and intellectual potential. They aim to assess a broader range of mental capabilities (e.g., verbal comprehension, working memory, perceptual reasoning, processing speed) to yield a single score that represents general intelligence (the ‘g’ factor). The Stanford-Binet and Wechsler scales are classic examples.
Key Difference
The scope. Mental ability scales are typically domain-specific (measuring one specific ability), while IQ tests are comprehensive and aim to measure global intellectual functioning to produce a general IQ score.
Question 7
(a) Mushtaq, Pervaiz, Ehsan, Umair and Saleem are friends having different heights and weights. Mushtaq weighs four times as much as Pervaiz and Pervaiz weighs double than Ehsan, Ehsan weighs half as much as Umair and Umair weighs half as much as Saleem.
i. Who is the heaviest among five friends?
ii. Who is the second heaviest?
iii. Who has lowest weight?
iv. Who are equal in weight?
v. Mention the descending order.
Solution
Let’s decode the weight relationships step by step. Let Ehsan’s weight be E.
- Pervaiz weighs double than Ehsan: P = 2E
- Mushtaq weighs four times as much as Pervaiz: M = 4P = 4*(2E) = 8E
- Ehsan weighs half as much as Umair: So, Umair weighs double Ehsan: U = 2E
- Umair weighs half as much as Saleem: So, Saleem weighs double Umair: S = 2U = 2*(2E) = 4E
Now, express all weights in terms of E:
- Mushtaq (M) = 8E
- Pervaiz (P) = 2E
- Ehsan (E) = E
- Umair (U) = 2E
- Saleem (S) = 4E
Answers:
(i) Mushtaq is the heaviest (8E).
(ii) Saleem is the second heaviest (4E).
(iii) Ehsan has the lowest weight (E).
(iv) No one is equal in weight. (Pervaiz and Umair are both 2E? Wait: Pervaiz = 2E, Umair = 2E. So Pervaiz and Umair are equal).
(v) Descending order: Mushtaq > Saleem > Pervaiz = Umair > Ehsan
(b) A farmer needs to build a boundary wall around his farm. If the area of farm is 484 m2, what will be the total area of the wall if it is two meters high on three sides and three meters high on one side?
Solution
The farm is a square (implied by the area being a perfect square).
Area of square = side² = 484 m²
Therefore, side length = √484 = 22 meters
Perimeter of square = 4 × side = 4 × 22 = 88 meters
The wall is built on the perimeter. Its area is the perimeter multiplied by the height, but the height is not uniform.
- Length of three sides with 2m height = 3 × 22 = 66 meters
- Length of one side with 3m height = 1 × 22 = 22 meters
Total Area of the wall:
= (Area of three sides) + (Area of one side)
= (66 m × 2 m) + (22 m × 3 m)
= (132 m²) + (66 m²)
= 198 m²
(c) Five girls A,B,C,D,E and four boys W,X,Y,Z have to go to a trip in three cars, car-1,car-2 and car-3. The following restrictions for seating in car are to be observed:
i. Only three persons can sit in one car
ii. At least one boy and one girl must be in each car
iii. A and D should remain together
iv. Z cannot sit with B or C in the same car
Distribute boys and girls in three cars.
Restrictions
- Only three persons per car.
- At least one boy and one girl in each car.
- A and D must be together.
- Z cannot sit with B or C.
Distribution
Total people: 5 girls + 4 boys = 9 people. 3 cars × 3 people = 9 spots. Perfect.
- Car 1: Place A and D together (restriction iii). To satisfy restriction ii, this car needs at least one boy. Let’s put boy W with them. Car1: A, D, W
- Remaining: Girls: B, C, E. Boys: X, Y, Z.
- Restriction (iv): Z cannot be with B or C. Therefore, Z must be with E.
- Car 2: Let’s put Z and E together. They need one more person, and it must be a boy to satisfy the boy/girl rule. Let’s put X with them. Car2: E, Z, X
- Remaining: Girls: B, C. Boys: Y.
- Car 3: The last three: B, C, Y. This satisfies all rules: has one boy (Y) and two girls (B, C). Z is not with B or C.
Final Distribution
- Car 1: A, D, W
- Car 2: E, Z, X
- Car 3: B, C, Y
(d) What are social skills? Describe four causes of weak social skills.
Social Skills
Social skills are the skills we use to communicate and interact with each other, both verbally and non-verbally, through gestures, body language, and our personal appearance. They include abilities like effective communication, empathy, conflict resolution, and active listening.
Causes of Weak Social Skills
- Lack of Socialization: Limited exposure to social situations and interactions, especially during critical developmental periods in childhood and adolescence, can hinder the learning of social cues and norms.
- Technology Overuse: Excessive use of smartphones, social media, and video games can replace face-to-face interaction, reducing opportunities to practice and develop real-world social skills.
- Underlying Psychological Conditions: Conditions like Social Anxiety Disorder, Autism Spectrum Disorder (ASD), Attention Deficit Hyperactivity Disorder (ADHD), and depression can significantly impair an individual’s ability to perceive social cues and engage appropriately.
- Negative Past Experiences: Trauma, bullying, rejection, or growing up in a dysfunctional family environment can lead to fear of social interaction, low self-esteem, and the development of maladaptive social behaviors as defense mechanisms.
Question 8
(a) What do you understand by systematic sampling Discuss its types.
Systematic Sampling
Systematic sampling is a probability sampling method where researchers select members of the population at a regular interval (or kth term). After a random start, every kth element is chosen from the sampling frame, where k = Population Size (N) / Sample Size (n).
Types
- Linear Systematic Sampling: The most common type. The sampling interval (k) is calculated, a random start is chosen between 1 and k, and then every kth element is selected in a linear fashion until the desired sample size is reached.
- Circular Systematic Sampling: Used when the population size (N) is not a multiple of the sample size (n), making k a fraction. The sample list is treated as circular (the end is connected to the beginning). A random start is chosen, and elements are selected at a fixed interval until n elements are chosen.
(b) Blood groups of inhabitants of a village were checked. It was found that 600 people possessed blood group A, 650 possessed blood group B, 550 had blood group AB and 200 have blood group O.
i. Calculate the probability of having blood group B.
Total inhabitants = 600 (A) + 650 (B) + 550 (AB) + 200 (O) = 2000
Probability of having blood group B:
P(B) = Number with B / Total = 650 / 2000 = 13/40 or 0.325
ii. Calculate the probability of having blood group O.
Total inhabitants = 600 (A) + 650 (B) + 550 (AB) + 200 (O) = 2000
Probability of having blood group O:
P(O) = Number with O / Total = 200 / 2000 = 1/10 or 0.1
(c) A group of 50 men can construct 20 kilometer road in 40 days. How long will 70 men take to complete same length of road?
Solution
This is an inverse proportionality problem. More men means less time.
Let the required time be D days.
The relationship is: Men × Days = Constant (for the same work)
So, M1×D1=M2×D2
50×40=70×D2
2000=70×D2
D2=2000/70
D2=200/7=2847 days
Answer: 70 men will take 28472874 days.
(d) Zahid left a property worth Rs 1750,000/. His family had to pay off a debt of Rs 150,000/. The rest of money was distributed between a son and a daughter. How much did each child receive if share of a son was double than that of a daughter?
Solution
Net distributable estate = Total Property – Debt
= 1,750,000 – 150,000 = Rs 1,600,000
Let the daughter’s share be x. Therefore, the son’s share is 2x.
Total distribution: x+2x=3x
This equals the net estate: 3x=1,600,000
x=1,600,000/3=533,333.3 (This is the daughter’s share)
Son’s share = 2×533,333.3=1,066,666.6
Answer:
- Son receives Rs. 1,066,666.67 (approximately)
- Daughter receives Rs. 533,333.33 (approximately)
(Note: In Islamic law, the son receives double the share of the daughter, so this distribution is correct.)
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