The suggested solution provided is intended for guidance purposes and may not necessarily align with the answers and opinions of the students.
PART 1 (MCQS)
1) Apparently, the Solar System is moving around the galaxy with a speed of:
(A) 50 km/s
(B) 200 km/s
(C) 500 km/s
(D) Not moving at all
2) The image formation in the James Webb Space Telescope is due to:
(A) Gamma-Rays
(A) 50 km/s
(B) 200 km/s
(C) 500 km/s
(D) Not moving at all
2) The image formation in the James Webb Space Telescope is due to:
(A) Gamma-Rays
(B) X-Rays
(C) Visible Light
(D) Infra-Red Rays
3) In general, the cancer in a human body is caused by:
(A) Virus
(B) RNA
(C) DNA
(D) All of these
4) In a year, light travels a distance of:
(A) 9.4 x 10^2 km
(B) 9.4 x 10^5 km
(C) 9.4 x 10^12 km
(D) None of these
5) The location below the Earth’s surface where the Earthquake starts is called:
(A) Epicenter
(B) Hypocenter
(C) Seismic center
(D) All of these
6) During the combustion of gasoline in a vehicle engine, the energy used is:
(A) Chemical
(B) Mechanical
(C) Electrical
(D) All of these
7) A Bar System International unit to measure:
(A) Temperature
(B) Energy
(C) Pressure
(D) Force
8) One may define Renewable Energy as:
(A) Energy derived from non-traditional sources
(B) Energy derived from sources that do not use natural resources or harm the environment
(C) Energy from two ways that do not use up natural resources or harm the environment
(D) All of these
9) The sky looks blue due to:
(A) The scattering of sunlight by the Atmosphere
(B) The presence of water vapors in the air
(C) Absorption of blue light by the atmosphere
(D) Presence of CO₂ in the atmosphere
10) Soil pollution is caused by:
(A) Aerosol
(B) Ozone
(C) Acid rain
(D) All of these
Q.11) The correct full form of "AI" is:
(A) Artificially Intelligent
(B) Artificial Intelligence
(C) Artificially Intelligence
(D) Advanced Intelligence
12) "Cyclone" is generated due to:
(A) High Temperature
(B) High Humidity
(C) Low Pressure
(D) All of these
13) The Radioactive isotopes formed by neutrons bombardment on the Nucleus, these incident neutrons must have ________ to penetrate in the nucleus.
(A) Very high velocity
(B) Very low velocity
(C) Intermediate velocity
(D) All of these
14) An 'Enzyme' is a chemical substance that is found in living creatures; It is a:
(A) Protein
(B) Bacteria
(C) Virus
(D) All of these
15) An Antibiotic is a drug used to treat infections caused by:
(A) Protein
(B) Bacteria
(C) Virus
(D) All of these
16) In a covalent bonding, electron of two atoms:
(A) Share with each other
(B) Attract the other delocalized electrons
(C) Transfer from one atom to another
(D) None of these
17) The day and night are formed due to "Earth's" rotation on its own axis from:
(A) North to South
(B) South to North
(C) East to West
(D) West to East
18) The chemical formula for Methane gas is:
(A) CH₃
(B) CH₅
(C) CH₄
(D) CH₂
19) The Artificial Intelligence term was invented by:
(A) Geoffrey Hinton
(B) Albert Einstein
(C) Alan M. Turing
(D) John McCarthy
20) Disease-causing microorganisms are referred to as:
(A) Pathogens
(B) Coliform bacteria
(C) Viruses
(D) All of these
1) (B) 200 km/s
2) (D) Infra-Red Rays
3) (C) DNA
4) (C) 9.4 x 10^12 km
5) (B) Hypocenter
6) (A) Chemical
7) (C) Pressure
8) (D) All of these
9) (A) The scattering of sunlight by the Atmosphere
10) (D) All of these
11) (B) Artificial Intelligence
12) (D) All of these
13) (A) Very high velocity
14) (A) Protein
15) (B) Bacteria
16) (A) Share with each other
17) (D) West to East
18) (C) CH₄
19) (D) John McCarthy
20) (A) Pathogens
3) In general, the cancer in a human body is caused by:
(A) Virus
(B) RNA
(C) DNA
(D) All of these
4) In a year, light travels a distance of:
(A) 9.4 x 10^2 km
(B) 9.4 x 10^5 km
(C) 9.4 x 10^12 km
(D) None of these
5) The location below the Earth’s surface where the Earthquake starts is called:
(A) Epicenter
(B) Hypocenter
(C) Seismic center
(D) All of these
6) During the combustion of gasoline in a vehicle engine, the energy used is:
(A) Chemical
(B) Mechanical
(C) Electrical
(D) All of these
7) A Bar System International unit to measure:
(A) Temperature
(B) Energy
(C) Pressure
(D) Force
8) One may define Renewable Energy as:
(A) Energy derived from non-traditional sources
(B) Energy derived from sources that do not use natural resources or harm the environment
(C) Energy from two ways that do not use up natural resources or harm the environment
(D) All of these
9) The sky looks blue due to:
(A) The scattering of sunlight by the Atmosphere
(B) The presence of water vapors in the air
(C) Absorption of blue light by the atmosphere
(D) Presence of CO₂ in the atmosphere
10) Soil pollution is caused by:
(A) Aerosol
(B) Ozone
(C) Acid rain
(D) All of these
Q.11) The correct full form of "AI" is:
(A) Artificially Intelligent
(B) Artificial Intelligence
(C) Artificially Intelligence
(D) Advanced Intelligence
12) "Cyclone" is generated due to:
(A) High Temperature
(B) High Humidity
(C) Low Pressure
(D) All of these
13) The Radioactive isotopes formed by neutrons bombardment on the Nucleus, these incident neutrons must have ________ to penetrate in the nucleus.
(A) Very high velocity
(B) Very low velocity
(C) Intermediate velocity
(D) All of these
14) An 'Enzyme' is a chemical substance that is found in living creatures; It is a:
(A) Protein
(B) Bacteria
(C) Virus
(D) All of these
15) An Antibiotic is a drug used to treat infections caused by:
(A) Protein
(B) Bacteria
(C) Virus
(D) All of these
16) In a covalent bonding, electron of two atoms:
(A) Share with each other
(B) Attract the other delocalized electrons
(C) Transfer from one atom to another
(D) None of these
17) The day and night are formed due to "Earth's" rotation on its own axis from:
(A) North to South
(B) South to North
(C) East to West
(D) West to East
18) The chemical formula for Methane gas is:
(A) CH₃
(B) CH₅
(C) CH₄
(D) CH₂
19) The Artificial Intelligence term was invented by:
(A) Geoffrey Hinton
(B) Albert Einstein
(C) Alan M. Turing
(D) John McCarthy
20) Disease-causing microorganisms are referred to as:
(A) Pathogens
(B) Coliform bacteria
(C) Viruses
(D) All of these
SOLUTION:
1) (B) 200 km/s
2) (D) Infra-Red Rays
3) (C) DNA
4) (C) 9.4 x 10^12 km
5) (B) Hypocenter
6) (A) Chemical
7) (C) Pressure
8) (D) All of these
9) (A) The scattering of sunlight by the Atmosphere
10) (D) All of these
11) (B) Artificial Intelligence
12) (D) All of these
13) (A) Very high velocity
14) (A) Protein
15) (B) Bacteria
16) (A) Share with each other
17) (D) West to East
18) (C) CH₄
19) (D) John McCarthy
20) (A) Pathogens
PART 2
Q. 2.
(a) The age of the Universe is estimated to be 13.8 billion years. How was it estimated?
(b) Explain the phenomenon of Solar Eclipse.
(c) Describe the James Webb Space Telescope, its principle of operation, construction and its implementation.
(d) Describe Global Positioning System and its applications.
SOLUTION:
(a) Estimation of Universe's Age:
The age of the Universe, estimated to be around 13.8 billion years, is determined mainly through studying the Cosmic Microwave Background (CMB) radiation and observations of distant galaxies and their redshifts. By understanding the rate at which the universe is expanding (Hubble's constant) and the models of Big Bang cosmology, astronomers infer the time since the Big Bang, giving the age of the Universe.
(b) Solar Eclipse:
A solar eclipse occurs when the Moon comes between the Earth and the Sun, blocking all or part of the Sun's light. There are three types: total, partial, and annular. In a total solar eclipse, the Moon completely covers the Sun, as viewed from Earth. In a partial eclipse, only a portion of the Sun is obscured. In an annular eclipse, the Moon covers the Sun's center, leaving a ring-like appearance called the "ring of fire".
(c) James Webb Space Telescope (JWST):
The James Webb Space Telescope is a space observatory developed in collaboration between NASA, ESA, and CSA. Designed as the successor to the Hubble Space Telescope, JWST focuses on infrared astronomy. The primary mirror is 6.5 meters in diameter, made of gold-coated beryllium segments. JWST operates near the Earth-Sun L2 Lagrange point, about 1.5 million kilometers from Earth. Its primary missions involve studying the formation of stars and galaxies, the atmospheres of exoplanets, and other astrophysical phenomena.
(d) Global Positioning System (GPS):
GPS is a satellite-based navigation system consisting of a network of satellites placed into orbit by the U.S. Department of Defense. It allows users to pinpoint their precise location (latitude, longitude, and altitude) anywhere on Earth. GPS works by triangulating the signals from multiple satellites to determine a user's location. Applications of GPS include navigation for vehicles, planes, and ships; mapping and surveying; geolocation for mobile apps; and various scientific research purposes, among others.
Q. 3.
(a) What is a 'Weather Cycle'? Describe its causes and parts.(b) What is 'Air Pollution'? Discuss its causes and measurement methods. Name the countries which are highest and lowest to produce it.
(c) Write a comprehensive note on 'Pole Reversal' of Earth.
(d) Describe different Ocean Currents, their causes and effects on Climate.
SOLUTION:
(a) Weather Cycle:
The weather cycle, more commonly known as the water cycle, is the continuous movement of water on, above, and below the surface of the Earth. The process includes:
1. Evaporation: When water from oceans, lakes, and rivers turns into water vapor.
2. Condensation: Water vapor cools and forms clouds.
3. Precipitation: Water falls back to Earth as rain, snow, hail, or sleet.
4. Collection: Water gathers in oceans, lakes, and rivers, and the cycle begins again.
Causes include solar radiation (which causes evaporation) and gravity (which leads to precipitation and collection).
(b) Air Pollution:
Air pollution refers to the release of harmful substances into the Earth's atmosphere. Causes include:
1. Industrial activities releasing chemicals and pollutants.
2. Vehicle emissions.
3. Deforestation.
4. Burning of fossil fuels.
To measure air pollution, we use Air Quality Index (AQI) and various instruments like gas analyzers. As of my last update in January 2022, countries like China and India often record high levels of air pollution, while countries such as New Zealand and Canada have lower levels.
(c) Pole Reversal:
The Earth's magnetic poles are not fixed and can reverse. This is known as geomagnetic reversal or pole reversal. Over geological time scales, the North and South magnetic poles have switched places many times. Reasons for pole reversals are complex but are related to movements of molten iron within Earth's outer core. While pole reversals might have impacts on Earth's magnetosphere, they are not known to cause catastrophic events on Earth's surface.
(d) Ocean Currents:
Ocean currents are vast water movements in the ocean basins. They can be caused by:
1. Wind: Surface currents are driven by winds.
2. Temperature and salinity differences: This leads to density-driven or thermohaline circulation.
3. Gravity: Due to differences in seawater density.
4. Earth's rotation: The Coriolis effect.
Effects on Climate:
1. Warm currents, like the Gulf Stream, can warm adjacent land areas.
2. Cold currents can cool adjacent coastal lands.
3. They can influence rainfall patterns. For instance, areas with cold ocean currents often have deserts nearby.
4. Currents can also impact marine life and weather systems.
Ocean currents play a major role in distributing heat around the Earth, thereby playing a significant role in regulating the climate of coastal regions.
Q. 4.
(a) Write a note on data storage in a 'USB'. How is it different from the Hard disk?(b) Describe how a 'Solar Cell' converts light into electricity. Describe its construction, operation and applications.
(c) Write a comprehensive note on 'Food cycle in our body'.
(d) What is 'Artificial Intelligence'? How is it helpful for humanity?
SOLUTION:
(a) Data Storage in a USB vs Hard Disk:
USB (Universal Serial Bus) drives, commonly known as flash drives or thumb drives, use flash memory to store data. Flash memory is non-volatile, which means it retains data even when not powered. The data is stored in memory cells made of floating-gate transistors. USB drives are portable, compact, and have no moving parts.
Hard disks, on the other hand, store data on magnetic platters. They have a spinning disk and a moving read/write head, which can be more prone to mechanical failures. Hard disks have a larger storage capacity than USB drives and are typically used as the primary storage in computers.
Difference:
1. Portability: USB drives are much more portable than hard disks.
2. Durability: USB drives, with no moving parts, are less prone to mechanical failure.
3. Storage Capacity: Hard disks typically have a higher storage capacity.
4. Speed: Hard disks usually have faster read/write speeds compared to USBs.
5. Cost: USB drives tend to be cheaper for smaller storage capacities, but hard disks are more cost-effective for larger capacities.
(b) Solar Cell:
A solar cell, also known as a photovoltaic cell, converts light energy into electricity through the photovoltaic effect.
Construction: Solar cells are made of semiconductor materials, typically silicon. When light hits the cell, it knocks electrons loose from their atoms.
Operation: As the electrons flow through the cell, they produce an electric current. The cell has electric fields that drive the newly-freed electrons in a particular direction, creating an electric current.
Applications: Solar cells are used in a variety of applications, from powering small devices like calculators and road signs to large-scale energy production in solar power plants. They are also used in remote locations where it is challenging to access the main electricity grid.
(c) Food Cycle in our Body:
The food cycle in our body involves digestion, absorption, and assimilation of nutrients.
1. Ingestion: Taking food into the mouth.
2. Digestion: Breaking down complex food particles into simpler forms. This involves both mechanical (chewing, churning) and chemical processes (enzymes breaking down food).
3. Absorption: The simple molecules are absorbed into the bloodstream from the intestines.
4. Assimilation: Cells absorb these nutrients and use them for energy, growth, and repair.
5. Egestion: Undigested and unabsorbed substances are expelled from the body.
(d) Artificial Intelligence (AI):
Artificial Intelligence refers to the simulation of human intelligence in machines. These machines are programmed to think and learn like humans.
Benefits for Humanity:
1. Efficiency: AI can handle large datasets and perform tasks more efficiently and quickly than humans.
2. Automation: Routine tasks can be automated, leading to cost savings and freeing humans for more complex tasks.
3. Analysis: AI can analyze vast amounts of data and recognize patterns that humans might overlook.
4. Innovation: AI drives innovations in fields like medicine, astronomy, and finance.
5. Personalization: In areas like online shopping and streaming, AI offers personalized recommendations based on user behavior.
Q. 5.
(a) Explain the concept of diabetes, its causes and classifications in the human body.(b) Describe different sources of 'Renewable Energy'. How is it helpful for the environment?
(c) Define 'Enzymes'. Describe it types and functions within organisms.
(d) Describe the 'Cell Structure'. Elaborate 7 main functions of a cell in human beings.
SOLUTION:
(a) Diabetes is a metabolic disorder where the body does not produce enough insulin or does not use insulin properly. Insulin is a hormone that regulates the level of glucose in the blood. Causes include genetics, obesity, poor diet, and sedentary lifestyle. There are primarily two classifications:
1. Type 1 diabetes: Where the body does not produce insulin. It is usually diagnosed in children and young adults.
2. Type 2 diabetes: Where the body does not use insulin properly. It's the most common form and affects mostly adults, but is increasingly seen in children.
(b) Renewable Energy is derived from natural resources that replenish themselves over short periods of time. Sources include:
1. Solar energy
2. Wind energy
3. Geothermal energy
4. Hydroelectric energy
5. Biomass energy
6. Tidal and wave energy.
These sources reduce the carbon footprint and do not deplete natural resources, making them helpful for the environment by reducing greenhouse gas emissions and dependence on fossil fuels.
(c) Enzymes are biological catalysts that speed up chemical reactions in living organisms without being consumed in the process. Types include:
1. Hydrolases: Break chemical bonds through hydrolysis.
2. Isomerases: Convert molecules from one isomer to another.
3. Ligases: Join two molecules together.
4. Lyases: Break chemical bonds other than hydrolysis.
5. Oxidoreductases: Transfer electrons between molecules.
6. Transferases: Transfer functional groups between molecules.
Functions: They aid in digestion, DNA replication, energy production, and many other cellular functions.
(d) The cell is the basic structural and functional unit of all living organisms. Cell Structure comprises:
1. Cell Membrane: Protects the cell.
2. Cytoplasm: Contains cell organelles.
3. Nucleus: Directs cell activities and contains genetic material.
4. Mitochondria: Produces energy.
5. Endoplasmic Reticulum: Produces proteins and lipids.
6. Golgi Apparatus: Modifies and packages proteins.
7. Lysosomes: Digests waste materials.
Main functions of a cell in human beings are:
1. Provides structure to the body.
2. Facilitates growth through mitosis.
3. Facilitates movement in mobile organisms.
4. Produces energy to power cell functions.
5. Maintains a stable internal environment.
6. Aids in communication with other cells.
7. Performs metabolic reactions.
Q. 6.
(a) Find the area of a rectangular field whose length is 20 m and the length of its diagonal is 25m.(b) A Crow travels 5 km due South, 3 km due West, 4 km due North and 2 km toward South-East. How far is crow from its starting position?
(c) Three persons, Zain, Ali and Umar started a business with Rs. 150,000, Rs. 190,000 and Rs. 120,000 respectively. Zain manages the business and receives allowance of Rs. 160,000 for this management. After 5 months Ali withdraws Rs. 90,000 and business is closed after 9 months. What did each receive in the profit of Rs. 580,000?
(d) Mst. Razia Begum died leaving behind her property of Rs. 802,500 which was to be distributed among her husband, her mother and two daughters. The husband got 1/4, mother got 1/6 and remaining for 2 daughters. Rs. 7500 was spent on her burial. Find the share of each one.
SOLUTION:
(a) Using the Pythagoras theorem:
[ l^2 + b^2 = d^2 ]
Given:
[ l = 20m ]
[ d = 25m ]
Substitute in the equation:
[ 20^2 + b^2 = 25^2 ]
[ 400 + b^2 = 625 ]
[ b^2 = 225 ]
[ b = 15m ]
Area of the rectangle:
[ A = l times b ]
[ A = 20m times 15m = 300m^2 ]
Answer: The area of the rectangular field is 300m^2.
(b) The crow's north-south movement:
[ 5km (south) - 4km (north) = 1km (south) ]
The crow's east-west movement:
[ 3km (west) ]
To find the resultant displacement, combine the southward movement, westward movement, and southeastward movement. Using Pythagoras theorem:
[ R^2 = (1 + 2 times 0.7071)^2 + 3^2 ]
(Here, 0.7071 is the horizontal or vertical component of 2 km when it is moving southeast.)
[ R^2 = (1 + 1.4142)^2 + 9 ]
[ R^2 = 2.4142^2 + 9 ]
[ R^2 = 5.8276 + 9 ]
[ R^2 = 14.8276 ]
[ R approx 3.85km ]
Answer: The crow is approximately 3.85km from its starting position.
(c) Three persons, Zain, Ali, and Umar started a business with Rs. 150,000, Rs. 190,000, and Rs. 120,000 respectively...
Total investment:
[ 150,000 + 190,000 + 120,000 = 460,000 ]
Ali's effective capital:
[ 190,000 - 90,000 = 100,000 ]
For Ali, 5 months at 190,000 and 4 months at 100,000
[ Ali's capital for 9 months = 5 times 190,000 + 4 times 100,000 = 950,000 + 400,000 = 1,350,000 ]
For Zain and Umar, the capital remains the same for 9 months:
[ Zain's 9-month capital = 9 times 150,000 = 1,350,000 ]
[ Umar's 9-month capital = 9 times 120,000 = 1,080,000 ]
Total capital for 9 months:
[ 1,350,000 + 1,350,000 + 1,080,000 = 3,780,000 ]
Profit after Zain's allowance:
[ 580,000 - 160,000 = 420,000 ]
Zain's share:
[ (1,350,000/3,780,000) times 420,000 + 160,000 = 150,000 + 160,000 = 310,000 ]
Ali's share:
[ (1,350,000/3,780,000) times 420,000 = 150,000 ]
Umar's share:
[ (1,080,000/3,780,000) times 420,000 = 120,000 ]
Answer: Zain received 310,000, Ali received 150,000, and Umar received 120,000.
(d) Mst. Razia Begum died leaving behind her property of Rs. 802,500 which was to be distributed...
After burial expenses:
[ 802,500 - 7,500 = 795,000 ]
Husband's share:
[ 1/4 times 795,000 = 198,750 ]
Mother's share:
[ 1/6 times 795,000 = 132,500 ]
Remaining for 2 daughters:
[ 795,000 - (198,750 + 132,500) = 463,750 ]
Each daughter's share:
[ 463,750/2 = 231,875 ]
Answer: Husband received 198,750, mother received 132,500, and each daughter received 231,875.
(a) What percentage increase in daily average amount spent occurred between 2013 and 2014?
(b) How many visitors came to this country in 2013?
(c) What was the approximate percentage increase on the previous record number of visitors?
(d) If there are 30 people employed in this country's workforce, how many work in the tourism sector?
(a) Let the average daily expenditure in 2013 be ( x ). Given that it increased by 7% in 2014, the average expenditure in 2014 is ( 1.07x ). The expenditure in 2014 was $76.20. Hence, ( 1.07x = $76.20 ) which implies ( x = $71.21 ). Percentage increase from 2013 to 2014 is:
[ frac{76.20 - 71.21}{71.21} times 100% = 7% ]
(b) Given that the number of visitors in 2014 was 3% more than in 2013. If the number in 2013 was ( y ), then:
[ y + 0.03y = 24.4 text{ million} ]
[ implies 1.03y = 24.4 ]
[ implies y = 23.6893 text{ million} ]
So, there were approximately 23.6893 million visitors in 2013.
(c) The previous record number of visitors was set in 2011. Given that the 2014 numbers eclipsed this by 7%, we can say:
[ text{2011 visitors} times 1.07 = 24.4 text{ million} ]
[ text{2011 visitors} = 22.8037 text{ million} ]
Percentage increase from 2011 to 2014 is:
[ frac{24.4 - 22.8037}{22.8037} times 100% = 7% ]
(d) Given that 7% of the total workforce is employed in tourism and there are 30 people in the workforce, the number working in tourism is:
[ 0.07 times 30 = 2.1 ]
Since we can't have a fraction of a person, we can safely round down to 2 people working in tourism.
(b) Find out the correct word from the jumbled spellings given below:
IUPRNT, AERPSTEL, LLARIVTTOUE, DCAAOOV, ANAISSOTANTS
(c) A sphere of diameter 26 cm is half filled with honey. The honey is poured into a cylindrical breaker of diameter 16 cm. Find the depth of honey in the breaker.
(d) The breadth, length, and height of a room is 14 feet, 20 feet and 10 feet respectively. There is also a door of height 8 feet and width 5 feet. Two windows of height 5 feet are also there having a height of 8 feet and width 10 feet. Rs. 10.00 per square foot. How much will it cost to paint the inner walls and roof of the room?
(a) Let's start with the first part of the question:
Given, the sum of two numbers is 48.
Let's assume the larger number to be ( x ).
So, the smaller number is ( frac{x}{5} ).
Given, ( x + frac{x}{5} = 48 )
Multiplying each term by 5:
( 5x + x = 240 )
Combining like terms:
( 6x = 240 )
Divide each side by 6:
( x = 40 )
So, the larger number is 40 and the smaller number is ( frac{40}{5} = 8 ).
Answer: The two numbers are 40 and 8.
(b) Let's arrange the jumbled spellings:
IUPRNT = TURNIP
AERPSTEL = PLEASER
LLARIVTTOUE = VIRTUALLY
DCAAOOV = AVOCADO
ANAISSOTANTS = ANASTASIS
(c) Given sphere's diameter = 26 cm, so radius ( r_1 ) = 13 cm
Volume of the half sphere = ( frac{1}{2} times frac{4}{3} times pi times r_1^3 )
= ( frac{1}{2} times frac{4}{3} times pi times 13^3 )
= ( frac{1}{2} times frac{4}{3} times pi times 2197 )
= ( frac{1}{2} times frac{4}{3} times 3.1416 times 2197 )
≈ 11,656.95 cubic cm
Given diameter of the cylindrical breaker = 16 cm, so radius ( r_2 ) = 8 cm
After burial expenses:
[ 802,500 - 7,500 = 795,000 ]
Husband's share:
[ 1/4 times 795,000 = 198,750 ]
Mother's share:
[ 1/6 times 795,000 = 132,500 ]
Remaining for 2 daughters:
[ 795,000 - (198,750 + 132,500) = 463,750 ]
Each daughter's share:
[ 463,750/2 = 231,875 ]
Answer: Husband received 198,750, mother received 132,500, and each daughter received 231,875.
Q. 7.
In a certain country, 7% of the total workforce is employed in tourism. 24.4 million overseas visitors came to this country in 2014, which was a record year for inbound tourism. This level of visitors was 3% higher than in 2013. The average expenditure per visit of a US visitor was 7% higher in 2014 and it eclipsed the previous record set in 2011 by 7%. Previously, the peak in visitor expenditure was US$ 60 while in 2014 it was US$ 76.20.(a) What percentage increase in daily average amount spent occurred between 2013 and 2014?
(b) How many visitors came to this country in 2013?
(c) What was the approximate percentage increase on the previous record number of visitors?
(d) If there are 30 people employed in this country's workforce, how many work in the tourism sector?
SOLUTION:
(a) Let the average daily expenditure in 2013 be ( x ). Given that it increased by 7% in 2014, the average expenditure in 2014 is ( 1.07x ). The expenditure in 2014 was $76.20. Hence, ( 1.07x = $76.20 ) which implies ( x = $71.21 ). Percentage increase from 2013 to 2014 is:
[ frac{76.20 - 71.21}{71.21} times 100% = 7% ]
(b) Given that the number of visitors in 2014 was 3% more than in 2013. If the number in 2013 was ( y ), then:
[ y + 0.03y = 24.4 text{ million} ]
[ implies 1.03y = 24.4 ]
[ implies y = 23.6893 text{ million} ]
So, there were approximately 23.6893 million visitors in 2013.
(c) The previous record number of visitors was set in 2011. Given that the 2014 numbers eclipsed this by 7%, we can say:
[ text{2011 visitors} times 1.07 = 24.4 text{ million} ]
[ text{2011 visitors} = 22.8037 text{ million} ]
Percentage increase from 2011 to 2014 is:
[ frac{24.4 - 22.8037}{22.8037} times 100% = 7% ]
(d) Given that 7% of the total workforce is employed in tourism and there are 30 people in the workforce, the number working in tourism is:
[ 0.07 times 30 = 2.1 ]
Since we can't have a fraction of a person, we can safely round down to 2 people working in tourism.
Q. 8.
(a) The sum of two numbers is 48. If the smaller number is one-fifth of the larger number, find the two numbers.(b) Find out the correct word from the jumbled spellings given below:
IUPRNT, AERPSTEL, LLARIVTTOUE, DCAAOOV, ANAISSOTANTS
(c) A sphere of diameter 26 cm is half filled with honey. The honey is poured into a cylindrical breaker of diameter 16 cm. Find the depth of honey in the breaker.
(d) The breadth, length, and height of a room is 14 feet, 20 feet and 10 feet respectively. There is also a door of height 8 feet and width 5 feet. Two windows of height 5 feet are also there having a height of 8 feet and width 10 feet. Rs. 10.00 per square foot. How much will it cost to paint the inner walls and roof of the room?
SOLUTION:
(a) Let's start with the first part of the question:
Given, the sum of two numbers is 48.
Let's assume the larger number to be ( x ).
So, the smaller number is ( frac{x}{5} ).
Given, ( x + frac{x}{5} = 48 )
Multiplying each term by 5:
( 5x + x = 240 )
Combining like terms:
( 6x = 240 )
Divide each side by 6:
( x = 40 )
So, the larger number is 40 and the smaller number is ( frac{40}{5} = 8 ).
Answer: The two numbers are 40 and 8.
(b) Let's arrange the jumbled spellings:
IUPRNT = TURNIP
AERPSTEL = PLEASER
LLARIVTTOUE = VIRTUALLY
DCAAOOV = AVOCADO
ANAISSOTANTS = ANASTASIS
(c) Given sphere's diameter = 26 cm, so radius ( r_1 ) = 13 cm
Volume of the half sphere = ( frac{1}{2} times frac{4}{3} times pi times r_1^3 )
= ( frac{1}{2} times frac{4}{3} times pi times 13^3 )
= ( frac{1}{2} times frac{4}{3} times pi times 2197 )
= ( frac{1}{2} times frac{4}{3} times 3.1416 times 2197 )
≈ 11,656.95 cubic cm
Given diameter of the cylindrical breaker = 16 cm, so radius ( r_2 ) = 8 cm
Let the height (or depth) of honey in the breaker be ( h ) cm.
So, ( pi times r_2^2 times h = 11,656.95 )
=> ( 3.1416 times 8^2 times h = 11,656.95 )
=> ( 3.1416 times 64 times h = 11,656.95 )
=> ( h ) = 57.65 cm
Answer: The depth of honey in the breaker is 57.65 cm.
(d) Area of walls = 2(lh + bh) [2 times because walls are opposite to each other]
Given length, l = 20 feet, breadth, b = 14 feet, and height, h = 10 feet.
Area of walls = 2(20x10 + 14x10) = 2(200 + 140) = 2(340) = 680 square feet
Area of the door = 8x5 = 40 square feet
Area of two windows = 2(8x10) = 160 square feet
Total area to be painted = Area of walls + Area of the ceiling - Area of door - Area of windows
= 680 + (20x14) - 40 - 160
= 680 + 280 - 200
= 760 square feet
Cost = Rs. 10 per square foot
Total cost = 760 x 10 = Rs. 7600
Answer: It will cost Rs. 7600 to paint the inner walls and roof of the room.