General Science and Ability · CSS 2024
CSS 2024 General Science and Ability - solved subjective questions
This set carries the seven subjective questions of the CSS 2024 General Science and Ability paper, Q2 through Q8, each solved and written from scratch for this platform. Q2 to Q5 are the Section A science questions, 16 parts in all; Q6 to Q8 are the Section B ability questions, 12 parts in all. The objective part of the paper is not covered here.
The science answers are kept to the length a five-mark part earns, and each one leads with the definition or mechanism an examiner is looking for rather than with background. The ability answers show the method without a calculator: what is given, the formula or reasoning used, the substitution, the working line by line, the units, and the final answer, with a check where one is available.
Three parts of this paper are ambiguous as printed. Each is solved on a stated reading rather than silently, so you can see the assumption and disagree with it if your examiner reads it differently.
New to solved papers? How to actually use CSS past papers explains the difference between reading them and working them.
Section A: General Science
Q2 Tuberculosis and hepatitis, the mechanism and construction of fibre optic cable, middle latitude cyclones and tornadoes, and ionic and covalent bonding
This question tests four distinct scientific skills: explaining diseases without confusing causes and symptoms, describing how a communication technology works, comparing two atmospheric systems, and distinguishing two forms of chemical bonding. Each part carries five marks, so the best answer is compact but structured. Define the terms first, explain the mechanism or distinction, and then add examples or applications.
(a) What is the Tuberculosis and Hepatitis? Explain briefly.
Tuberculosis
Tuberculosis, or TB, is an infectious disease caused mainly by the bacterium Mycobacterium tuberculosis. It usually affects the lungs, although it may also involve lymph nodes, bones, kidneys, the brain and other organs. Pulmonary TB spreads through airborne droplets released when a person with active disease coughs, sneezes or speaks.
TB infection and TB disease are not the same. A person with TB infection carries the bacteria but has no symptoms and does not transmit the disease. In active TB disease, the bacteria multiply and may cause a persistent cough, chest pain, fever, night sweats, fatigue, weight loss and sometimes blood in the sputum. Diagnosis commonly combines clinical assessment, chest imaging and laboratory testing of sputum.
TB is preventable and curable. The BCG vaccine gives children useful protection against severe forms such as TB meningitis, but it does not reliably prevent all pulmonary infection. Active drug-susceptible TB is treated with a prescribed combination of antibiotics for several months. Completing the full regimen is essential because irregular treatment encourages drug resistance.
Hepatitis
Hepatitis means inflammation of the liver. It may result from viruses, alcohol, certain medicines, toxins, autoimmune disease or metabolic disorders. The principal viral forms are hepatitis A, B, C, D and E. Hepatitis A and E usually spread through contaminated food or water and are commonly acute. Hepatitis B, C and D are primarily blood-borne; B and C may become chronic and cause cirrhosis or liver cancer.
Symptoms may include fatigue, nausea, abdominal discomfort, dark urine, pale stools and jaundice, although many infections initially produce no obvious symptoms. Prevention depends on the type. Safe vaccines are widely used against hepatitis A and B, and hepatitis B vaccination also prevents hepatitis D because D requires hepatitis B infection. There is no vaccine for hepatitis C. Safe water, screened blood, sterile needles and infection-control practices reduce transmission. Treatment ranges from supportive care for many acute cases to antiviral therapy for chronic hepatitis B or curative direct-acting antivirals for most hepatitis C infections.
(b) Explain the mechanism of Fiber Optic Cable for signal. Explain its construction.
An optical-fibre cable carries information as pulses of light rather than as electric current. Its central core is a very clear strand of glass or plastic. The core is surrounded by cladding whose refractive index is slightly lower. A protective buffer coating, strengthening material and outer jacket guard the delicate fibre against moisture, bending and mechanical damage.
At the transmitting end, a laser diode or light-emitting diode converts an encoded electrical signal into rapid light pulses. The pulses enter the core at a suitable angle. When they reach the core-cladding boundary, they undergo total internal reflection because they are travelling from the optically denser core towards the lower-index cladding and strike beyond the critical angle. Repeated reflections keep most of the light confined within the core as it travels along the cable.
At the receiving end, a photodiode detects the arriving pulses and converts them back into an electrical signal. The equipment then amplifies and decodes that signal into sound, data or video. Long links may use optical amplifiers or repeaters to compensate for attenuation. Fibre carries large amounts of data, suffers little electromagnetic interference and loses less signal over distance than ordinary copper cable.
(c) Explain the difference between Middle Latitude Cyclones and Tornadoes.
A middle-latitude cyclone, also called an extratropical cyclone, is a large low-pressure weather system that develops mainly between about 30° and 60° latitude. It forms where contrasting warm and cold air masses meet along fronts. A tornado is a much smaller, violently rotating column of air extending from a thunderstorm cloud to the ground.
- Formation: A middle-latitude cyclone draws energy from horizontal temperature contrasts and develops warm and cold fronts. A tornado usually develops within a severe thunderstorm when instability, moisture and vertical wind shear produce a rotating updraft.
- Scale: A cyclone may extend over hundreds or more than a thousand kilometres and influence several regions. A tornado is normally tens to hundreds of metres wide, although exceptional tornadoes can be wider.
- Duration: A cyclone commonly persists for several days. Most tornadoes last minutes, though some remain on the ground much longer.
- Weather: A cyclone brings widespread cloud, changing winds and prolonged rain or snow. A tornado produces a narrow path of extremely intense winds and concentrated damage.
- Observation: Cyclones are tracked through pressure maps, satellites and weather models. Tornado intensity is assessed with the Enhanced Fujita scale from observed damage. The Saffir-Simpson scale applies to hurricanes, not middle-latitude cyclones.
Both systems rotate around low pressure, counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere at cyclone scale. Tornado rotation is strongly shaped by its parent storm and local wind shear.
(d) What is difference between the Ionic and Covalent bonding? Give examples.
Chemical bonds hold atoms together by involving their valence electrons. In ionic bonding, one atom transfers one or more electrons to another. The transfer creates positively charged cations and negatively charged anions, which remain together because opposite charges attract. Ionic bonding is common between a metal and a non-metal. Sodium chloride is formed when sodium transfers an electron to chlorine, producing Na+ and Cl- ions. Magnesium oxide, MgO, is another example.
In covalent bonding, atoms share one or more pairs of electrons. It is common between non-metals whose attraction for electrons is similar enough to favour sharing rather than complete transfer. Two hydrogen atoms share electrons with oxygen in water, H2O. Methane, CH4, oxygen, O2, and carbon dioxide, CO2, also contain covalent bonds.
The resulting properties differ. Ionic compounds usually form crystalline solids with relatively high melting points. They conduct electricity when molten or dissolved in water because their ions can move, but they generally do not conduct as solids. Covalent substances may be gases, liquids or solids and often have lower melting points, although giant covalent structures such as diamond are major exceptions. Most simple covalent substances do not conduct electricity because they lack mobile charged particles.
Q3 Plastics and elastics, the role of remote sensing and GIS in environmental science, Kepler laws of planetary motion, and preservatives and antioxidants
This question moves from material science to environmental technology, astronomy and food science. The examiner expects accurate distinctions rather than long descriptions. For each part, identify the defining principle, explain how it works, and support it with carefully chosen examples. The printed word “Elastics” in part (a) is best understood as elastomers.
(a) What is difference between Plastics and Elastics? Explain briefly.
The printed term “Elastics” is not the usual technical category. In polymer science, the intended comparison is between plastics and elastomers. Both consist of long-chain polymers, but their molecular structures and mechanical behaviour differ.
Plastics can be moulded into a desired shape and normally retain that shape after the applied force is removed. Their polymer chains have limited freedom to move. Thermoplastics such as polyethylene and PVC soften on heating and can be remoulded. Thermosetting plastics such as Bakelite form dense cross-links during curing and cannot be reshaped by reheating. Plastics are used for containers, pipes, electrical insulation, furniture and machine parts.
Elastomers can be stretched, compressed or bent considerably and then recover most of their original shape. Their chains are flexible and coiled, with a small number of cross-links that prevent permanent sliding while allowing temporary extension. Natural rubber, silicone rubber and neoprene are common examples. They are used in tyres, seals, gloves, hoses and shock absorbers.
Thus, the central distinction is not simply that one material is hard and the other is soft. Plastics are designed mainly for shape retention and mouldability, whereas elastomers are designed for large reversible deformation and resilience.
(b) What is role of Remote sensing and GIS in environmental Science? Discuss briefly.
Remote sensing obtains information about the Earth without direct contact, usually through sensors on satellites, aircraft or drones. These sensors record reflected or emitted energy in visible, infrared, microwave and other bands. Geographic Information Systems, or GIS, store, combine, analyse and display data linked to location.
Remote sensing provides repeated coverage of large or inaccessible areas. It can identify changes in forests, crops, glaciers, wetlands, coastlines and urban land. Thermal data help map heat islands and wildfires, while multispectral observations can indicate vegetation stress, sediment, algal blooms or changes in surface water. Radar can acquire information through clouds and can help map floods or ground deformation.
GIS gives these observations analytical meaning. A researcher can overlay satellite imagery with elevation, rainfall, soil, population, roads and administrative boundaries. Spatial analysis then reveals patterns, exposure and change through time. It supports watershed management, habitat protection, pollution mapping, environmental-impact assessment and disaster planning.
The two tools are strongest when integrated. Remote sensing supplies timely observations; GIS connects them with field measurements and human information. Ground verification remains important because a remotely sensed signal may have more than one interpretation.
(c) What are Kepler laws related to the motion of planets?
Johannes Kepler formulated three laws that describe planetary motion around the Sun.
- Law of orbits: Every planet moves in an elliptical orbit with the Sun at one focus. The Sun is therefore not necessarily at the geometrical centre of the orbit. A planet’s distance from the Sun changes between perihelion, its nearest point, and aphelion, its farthest point.
- Law of areas: A line joining a planet to the Sun sweeps out equal areas in equal intervals of time. To sweep the same area, the planet moves faster when it is near the Sun and more slowly when it is farther away. Its orbital speed is therefore not constant.
- Law of periods: The square of a planet’s orbital period is proportional to the cube of the semi-major axis of its orbit: T² ∝ a³. For bodies orbiting the same central mass, T²/a³ is constant. Planets with larger orbits consequently require much more time to complete one revolution.
Kepler derived these laws from precise astronomical observations, especially those collected by Tycho Brahe. The laws described how planets move, while Newton’s law of gravitation later explained why. They remain useful for planets, moons, artificial satellites and many other two-body orbital systems.
(d) What is difference between preservatives and antioxidants? Discuss briefly with examples.
Preservatives are substances or processes used to delay food spoilage and extend safe shelf life. The category includes antimicrobial agents that inhibit bacteria, yeasts or moulds, as well as substances that slow chemical or enzymatic deterioration. Salt, sugar, vinegar, sodium benzoate, potassium sorbate and nitrites are familiar examples. Their suitability and permitted concentration depend on the food and applicable safety rules.
Antioxidants specifically slow oxidation. Oxidation can make fats rancid, destroy sensitive vitamins, alter colour and produce undesirable flavours. Antioxidants work by donating electrons or hydrogen, binding metal catalysts, removing oxygen or interrupting free-radical chain reactions. Ascorbic acid, tocopherols, rosemary extract, butylated hydroxyanisole and butylated hydroxytoluene are examples.
The categories overlap. An antioxidant used to delay oxidative spoilage is functioning as a preservative, but not every preservative is an antioxidant. Sodium benzoate mainly restrains microbial growth in acidic foods and is not used chiefly for antioxidant action. Tocopherol mainly protects oils against oxidation and therefore preserves quality through a different mechanism.
The clearest distinction is purpose and mechanism: “preservative” is the broader functional category, while “antioxidant” identifies substances that preserve by controlling oxidation. Neither category makes poor handling safe; hygiene, temperature control and suitable packaging remain essential.
Q4 The role of carbohydrates and vitamins, the functioning of liver and pancreas, drinking water standards and heavy metals, and radioactivity and its laws
This question covers nutrition, human physiology, water safety and nuclear science. A strong answer links structure with function and separates related concepts that are often mixed together. Part (c) requires categories of drinking-water quality rather than a random list of chemicals, while part (d) needs the mathematical laws of radioactive decay as well as a definition.
(a) What is role of Carbohydrates and Vitamins in the body? Discuss briefly.
Carbohydrates
Carbohydrates are sugars, starches and fibre composed mainly of carbon, hydrogen and oxygen. Their primary role is to provide energy. Digested carbohydrate is converted largely into glucose, which cells use to produce ATP. The brain and red blood cells rely heavily on glucose under ordinary conditions. Excess glucose can be stored as glycogen in the liver and muscles for later use; prolonged excess may be converted into fat.
Carbohydrates also spare protein from being used as fuel and help normal fat metabolism. Dietary fibre is not digested like starch, but it supports bowel movement, helps regulate blood glucose, contributes to satiety and provides substrate for beneficial gut microbes. Whole grains, pulses, fruit and vegetables provide carbohydrate together with fibre and micronutrients.
Vitamins
Vitamins are organic micronutrients needed in small quantities for normal metabolism, growth and maintenance. They do not supply energy directly. Many act as coenzymes: B vitamins assist energy metabolism, vitamin C supports collagen synthesis and antioxidant defence, and folate is essential for DNA formation. Fat-soluble vitamins have specialised roles: vitamin A supports vision and epithelial tissues, D regulates calcium and bone health, E protects cell membranes, and K is required for normal blood clotting.
Deficiency causes characteristic disorders, but excessive supplementation may also be harmful, particularly for fat-soluble vitamins that can accumulate in the body.
(b) Discuss the functioning of Liver and Pancreas.
Liver
The liver is the body’s largest internal gland and a central processing organ. Blood from the digestive tract reaches it through the hepatic portal vein, allowing absorbed nutrients and many chemicals to be processed before entering general circulation. The liver regulates blood glucose by storing glucose as glycogen and releasing or producing glucose when needed. It converts amino acids, forms urea from toxic ammonia, synthesises cholesterol and packages lipids.
It also produces plasma proteins, including albumin and several clotting factors. Liver cells modify medicines, alcohol and metabolic wastes so they can be eliminated. Kupffer cells help remove microbes and damaged blood cells. The liver produces bile, which carries waste products such as bilirubin and helps the small intestine digest and absorb fats. It also stores glycogen, iron and several vitamins.
Pancreas
The pancreas has exocrine and endocrine functions. Its exocrine cells release digestive enzymes into the small intestine. Amylase digests carbohydrates, lipase digests fats, and proteases digest proteins. Bicarbonate-rich fluid neutralises acidic material arriving from the stomach, creating a suitable environment for intestinal enzymes.
Its endocrine islets release hormones into the blood. Beta cells secrete insulin, which lowers blood glucose by promoting uptake and storage. Alpha cells secrete glucagon, which raises blood glucose by stimulating the liver. Together, these functions make the pancreas essential for digestion and glucose control.
(c) What are the standards of drinking water? How Heavy Metals in the water affect the living organisms?
Safe drinking water is judged through several linked standards rather than appearance alone.
- Microbiological quality: Water intended for drinking should not contain faecal indicator organisms such as E. coli in a 100 mL sample. Microbial contamination can cause diarrhoea, cholera, typhoid and other infections.
- Physical acceptability: Turbidity, colour, taste and odour should remain acceptable. High turbidity can shield microorganisms and reduce the effectiveness of disinfection.
- Chemical quality: Salts, nutrients, pesticides and toxic elements must remain within health-based national limits. As examples of widely used WHO guideline values, arsenic should not exceed 0.01 mg/L and lead should not exceed 0.01 mg/L. Local regulators may adopt different or more stringent standards.
- Radiological quality: Natural or artificial radionuclides should remain below screening and guidance levels established by the competent authority.
Heavy metals are persistent and cannot be destroyed biologically. Lead damages the nervous system, especially in children, and can impair learning, blood formation and kidney function. Arsenic exposure is associated with skin lesions, cardiovascular effects and increased cancer risk. Mercury can damage the brain and kidneys; methylmercury also biomagnifies in aquatic food chains. Cadmium accumulates in the kidneys and can weaken bones.
Plants and aquatic organisms may absorb these elements from contaminated water or sediment. Bioaccumulation in individuals and biomagnification through food webs can then expose fish, wildlife and humans even when the water concentration appears modest.
(d) What is radioactivity? Discuss the laws of radioactivity. Name two radioactive elements.
Radioactivity is the spontaneous transformation of an unstable atomic nucleus into a more stable state with the emission of particles or electromagnetic energy. The common emissions are alpha particles, beta particles and gamma rays. Individual nuclear decays are random, but a large sample follows precise statistical laws.
- Exponential decay law: The number of undecayed nuclei decreases at a rate proportional to the number still present. If N₀ is the initial number, then N = N₀ exp(-λt), where λ is the decay constant.
- Activity law: Activity is the number of decays per unit time and is given by A = λN. Its SI unit is the becquerel, equal to one decay per second.
- Half-life relation: Half-life is the time required for half the original radioactive nuclei to decay. It is constant for a given radionuclide and is related to the decay constant by t½ = 0.693/λ.
- Independence from ordinary conditions: Nuclear decay is generally unaffected by temperature, pressure, chemical combination or external physical state because it occurs within the nucleus.
Examples of naturally radioactive elements include uranium and radium. Uranium-238 undergoes a series of decays that eventually forms stable lead, while radium-226 decays principally by alpha emission to radon-222. Radioactivity is used in medicine, industry, research and age determination, but uncontrolled exposure can damage living tissue.
Q5 Plant nutrition elements, the difference between software and hardware with five examples of each, the types of earthquake waves, and longitudinal, electromagnetic and gamma radiations
This question tests classification and function across plant biology, computing and wave science. The answer should show the hierarchy clearly: essential plant elements are grouped by source and required quantity, a computer system combines physical components with instructions, and earthquake waves are divided into body and surface waves. Gamma radiation must be identified as part of the electromagnetic spectrum, not treated as an unrelated category.
(a) What are the Plant nutrition elements? Enumerate them.
An element is considered essential to a plant when the plant cannot complete its life cycle without it, its function cannot be fully replaced by another element, and it participates directly in plant metabolism or structure. The modern standard list contains 17 essential elements.
Plants obtain three non-mineral elements mainly from air and water:
- Carbon, C
- Hydrogen, H
- Oxygen, O
They require the following mineral macronutrients in comparatively large quantities:
- Nitrogen, N
- Phosphorus, P
- Potassium, K
- Calcium, Ca
- Magnesium, Mg
- Sulfur, S
They require these micronutrients in much smaller amounts:
- Iron, Fe
- Manganese, Mn
- Boron, B
- Zinc, Zn
- Copper, Cu
- Molybdenum, Mo
- Chlorine, Cl
- Nickel, Ni
Quantity does not indicate importance. A micronutrient is just as essential, but the plant needs less of it. Nitrogen is central to amino acids and chlorophyll; phosphorus contributes to ATP and nucleic acids; potassium regulates enzymes and water balance. Magnesium lies at the centre of chlorophyll, while iron supports electron transfer. Nickel is included because it activates urease, an enzyme needed for normal nitrogen metabolism. Deficiency or excess of any nutrient can restrict plant growth.
(b) What is difference between software and hardware? Give five examples of each.
Hardware consists of the physical, tangible components of a computer system. These parts perform input, processing, storage, communication and output operations. Hardware can be seen and handled, although many components are housed inside the computer. It is manufactured from electronic, magnetic and mechanical materials and is subject to physical wear or damage.
Five examples of hardware are:
- Central processing unit
- Random-access memory
- Solid-state drive or hard disk
- Keyboard
- Monitor
Software is the organised set of programs, instructions and related data that tells hardware what operations to perform. It is intangible. System software manages the computer and provides a platform, while application software helps the user perform particular tasks. Software does not wear out physically, but it may contain errors, become incompatible or require security updates.
Five examples of software are:
- Microsoft Windows
- Linux
- Microsoft Word
- Google Chrome
- Adobe Photoshop
Hardware and software are interdependent. A word processor cannot operate without a processor, memory, storage and display. The same hardware becomes useful for different tasks when it runs different software. Firmware occupies an intermediate practical position: it is software stored in non-volatile memory that directly controls hardware devices.
(c) What are the types of earthquake waves? Discuss them.
An earthquake releases stored elastic energy from its focus as seismic waves. These are divided into body waves, which travel through the Earth, and surface waves, which move along or near its surface.
Body waves
- Primary or P waves: These are compressional, longitudinal waves. Particles vibrate parallel to the direction of travel, producing alternate compression and expansion. P waves are the fastest seismic waves, arrive first at a station, and travel through solids, liquids and gases.
- Secondary or S waves: These are shear, transverse waves. Particles move perpendicular to the direction of propagation. S waves are slower than P waves and travel only through solids because fluids cannot support sustained shear stress. Their absence through the Earth’s outer core helped demonstrate that the outer core is liquid.
Surface waves
- Love waves: These move the ground horizontally from side to side, perpendicular to their direction of travel, with little vertical movement. They can cause severe damage to foundations.
- Rayleigh waves: These produce a rolling, elliptical motion with both vertical and horizontal components, rather like waves on water. They are generally slower than Love waves but can persist for long periods.
Surface waves usually have larger amplitudes and cause much of the damage near the surface. Seismologists use the different arrival times and paths of these waves to locate earthquakes and study the Earth’s interior.
(d) What are longitudinal waves, electromagnetic and Gamma radiations? Discuss them.
Longitudinal waves
In a longitudinal wave, particles of the medium vibrate parallel to the direction in which the wave travels. The motion produces alternating compressions, where particles are close together, and rarefactions, where they are farther apart. Longitudinal mechanical waves require a material medium. Sound in air, ultrasound and seismic P waves are examples. The particles oscillate locally; they do not travel with the disturbance from source to receiver.
Electromagnetic radiation
Electromagnetic radiation consists of coupled oscillating electric and magnetic fields. The two fields are perpendicular to each other and to the direction of propagation, so electromagnetic waves are transverse. They do not require a material medium and travel through a vacuum at the speed of light. The electromagnetic spectrum includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. All have the same basic nature but differ in frequency, wavelength and photon energy.
Gamma radiation
Gamma radiation is the highest-frequency, shortest-wavelength region of the electromagnetic spectrum. Gamma photons are commonly emitted when an excited atomic nucleus loses energy during radioactive decay or nuclear reactions. They have no mass and no electric charge. Their strong penetrating ability makes dense shielding such as lead or thick concrete necessary. Gamma rays are used in cancer radiotherapy, sterilisation, industrial inspection and nuclear medicine, but ionisation from excessive exposure can damage DNA and tissue.
The key relationship is that gamma radiation is not separate from electromagnetic radiation. It is one particularly energetic form of it.
Section B: General Ability
Q6 Four numbers whose sum is 105, five jumbled spellings, five number series, and a three digit number from its digit sums
This question examines algebraic translation, vocabulary, pattern recognition and place value. The safest method is to turn each sentence into a precise equation before calculating. Two printed parts require caution: series (c)(iv) does not establish a unique mathematical rule, and part (d) uses “10th digit” where “tens digit” is intended.
(a) If the sum of four numbers is 105. When 03 is added to a number, twice of another number, five times of third number and fourth number become equal to each other. What are these numbers in ascending order?
Let the four numbers be A, B, C and D. The conditions give:
A + B + C + D = 105
and
A + 3 = 2B = 5C = D
Let their common value be k. Then:
- A = k - 3
- B = k/2
- C = k/5
- D = k
Substitute these expressions into the sum:
(k - 3) + k/2 + k/5 + k = 105
Multiply throughout by 10:
10k - 30 + 5k + 2k + 10k = 1050
27k = 1080
k = 40
Therefore:
- A = 40 - 3 = 37
- B = 40/2 = 20
- C = 40/5 = 8
- D = 40
Check: 37 + 20 + 8 + 40 = 105, while 37 + 3 = 2(20) = 5(8) = 40.
Answer in ascending order: 8, 20, 37, 40.
(b) Find out the correct word from the given jumbled spellings.
- UCTREUTRS = STRUCTURE
- LOVONAC = VOLCANO
- CIHPROSTATAC = CATASTROPHIC
- YNTIAUMH = HUMANITY
- NNTHORER = NORTHERN
Each answer uses every supplied letter once. For example, CIHPROSTATAC rearranges into CATASTROPHIC, while NNTHORER rearranges into NORTHERN.
(c) Find the missing numbers in the series below
(i) 121, 11, 81, 9, ?, 7
The terms occur in square-root pairs:
- 121 = 11²
- 81 = 9²
- 49 = 7²
Missing number: 49.
(ii) 100, 50, 25, ?, 6.25
Each term is half the preceding term:
100 ÷ 2 = 50 ÷ 2 = 25 ÷ 2 = 12.5 ÷ 2 = 6.25
Missing number: 12.5.
(iii) 4, 9, 64, 125, 1296, ?
The bases rise from 2 to 7, while each exponent is used twice:
- 2² = 4 and 3² = 9
- 4³ = 64 and 5³ = 125
- 6⁴ = 1296 and 7⁴ = 2401
Missing number: 2401.
(iv) 2, 5, 12, 24, 48, ?
The printed terms do not determine one unique rule. The clearest intended continuation is repeated doubling from 12 onward:
12 × 2 = 24, 24 × 2 = 48, 48 × 2 = 96
Probable intended answer: 96. This should be presented with the ambiguity noted, rather than claiming that 96 is mathematically forced by the whole sequence.
(v) 44, 22, 66, 33, 132, ?
The operations alternate between division by 2 and multiplication by an increasing integer:
- 44 ÷ 2 = 22
- 22 × 3 = 66
- 66 ÷ 2 = 33
- 33 × 4 = 132
- 132 ÷ 2 = 66
Missing number: 66.
(d) If the sum of three digit number is 15 and sum of 10th and unit digit is 12. The difference of unit digit from 10th digit is equal to 02. What is the three digit number?
The printed “10th digit” means the tens digit. Let H, T and U represent the hundreds, tens and units digits.
The conditions are:
H + T + U = 15
T + U = 12
T - U = 2
Add the last two equations:
2T = 14
T = 7
Then:
U = 12 - 7 = 5
and:
H = 15 - 7 - 5 = 3
Place the digits in their stated positions: H = 3, T = 7 and U = 5.
Answer: 375.
Correction note: The answer 573 is inconsistent with the derived place values. It reverses the roles of the hundreds and units digits. The correct three-digit number is 375.
Q7 A journey around a right angle triangle, pocket money shared among five classmates, the surface area and volume of a sphere, and distributing Rs. 4,320 in parts
This question combines geometry, ratios and mensuration. Draw the relationships before substituting values. Part (b) is grammatically awkward, so its stated relationships must be translated explicitly. The coherent interpretation is that Shahbaz receives an amount equal to the sum of Nasir’s and Ali’s amounts.
(a) A man travels over the path of a right-angle triangle having base and hypotenuse 4 and 5 kilometers, respectively. After a complete round he continues in the same direction for 6 km and then turns at 90 degree and continues for another 8 km. How long he has travelled and how far he is from his starting point?
The right-angled triangle has base 4 km and hypotenuse 5 km. Let its third side be p.
By the Pythagorean theorem:
p² + 4² = 5²
p² = 25 - 16 = 9
p = 3 km
One complete round of the triangle therefore covers:
3 + 4 + 5 = 12 km
He then travels another 6 km, turns through 90°, and travels 8 km:
Total distance = 12 + 6 + 8 = 26 km
After completing the triangle, he has returned to his starting point. His last two movements are perpendicular displacements of 6 km and 8 km. His straight-line distance from the start is:
Displacement = √(6² + 8²)
= √100 = 10 km
Answer: He travels 26 km in total and finishes 10 km from his starting point.
(b) Hassan, Ali, Akbar, Nasir and Shahbaz are classmates having different pocket money. Hassan's pocket money is one third as much as of Ali and Ali has five times as much as Akbar. Akbar has thrice as much as Nasir and Shahbaz gets equal to Nasir and that of Ali. If they get Rs. 8000 then find the pocket money of each.
The last relationship is awkwardly printed. The coherent intended reading is:
Shahbaz = Nasir + Ali
Let Nasir receive x.
- Nasir = x
- Akbar = 3x
- Ali = 5(3x) = 15x
- Hassan = (1/3)(15x) = 5x
- Shahbaz = x + 15x = 16x
Their total is Rs. 8,000:
x + 3x + 15x + 5x + 16x = 8000
40x = 8000
x = 200
Therefore:
- Nasir = Rs. 200
- Akbar = Rs. 600
- Hassan = Rs. 1,000
- Ali = Rs. 3,000
- Shahbaz = Rs. 3,200
Check: 200 + 600 + 1,000 + 3,000 + 3,200 = 8,000.
(c) What will be the surface area and volume of a sphere if it has a radius of 7 m?
Given radius:
r = 7 m
Using π = 22/7, the surface area is:
Surface area = 4πr²
= 4 × 22/7 × 7²
= 616 m²
The volume is:
Volume = (4/3)πr³
= 4/3 × 22/7 × 7³
= 4312/3 m³
= 1,437 1/3 m³ ≈ 1,437.33 m³
Answer: Surface area = 616 m²; volume = 4,312/3 m³, approximately 1,437.33 m³.
(d) Distribute Rs. 4320 among Zain, Aslam and Ashraf in such a way that if zain gets 2 parts then Aslam gets three parts, whereas Ashraf gets seven parts.
The required ratio is:
Zain : Aslam : Ashraf = 2 : 3 : 7
Total parts:
2 + 3 + 7 = 12
Value of one part:
Rs. 4,320 ÷ 12 = Rs. 360
Therefore:
- Zain = 2 × 360 = Rs. 720
- Aslam = 3 × 360 = Rs. 1,080
- Ashraf = 7 × 360 = Rs. 2,520
Check: 720 + 1,080 + 2,520 = 4,320.
Q8 The original price of a car and the profit on it, twelve men and a job after four quit, a tree shadow thrown on a building, and distances between three moving cars
This question tests percentages, work rates, similar triangles and relative positions. Keep units visible and distinguish a remaining duration from total elapsed time. In the final part, convert 15 minutes to one-quarter of an hour before using the three speeds.
(a) A man purchases a car in an amount of Rs. 2400,000 in which he pays one-fourth extra as profit. Find the original amount of car and the amount of profit.
Interpret the printed amount Rs. 2400,000 as Rs. 2,400,000.
Let the original price be x. The profit is one-fourth of the original price:
Profit = x/4
The total price paid is:
x + x/4 = 2,400,000
5x/4 = 2,400,000
x = 2,400,000 × 4/5
x = Rs. 1,920,000
Profit:
Rs. 2,400,000 - Rs. 1,920,000 = Rs. 480,000
Check: one-fourth of Rs. 1,920,000 is Rs. 480,000, and their sum is Rs. 2,400,000.
Answer: Original price = Rs. 1,920,000; profit = Rs. 480,000.
(b) Twelve men can complete a job in twenty-four days. After four days four person quit. In how many days this job will be completed by the remaining persons.
Total work in man-days:
12 × 24 = 288 man-days
Work completed during the first four days:
12 × 4 = 48 man-days
Remaining work:
288 - 48 = 240 man-days
After four men leave, eight men remain. The additional time they require is:
240 ÷ 8 = 30 days
The phrase “by the remaining persons” asks for the time required by those eight workers after the four have left. That answer is 30 additional days. If total elapsed time from the beginning is required, add the first four days:
4 + 30 = 34 days
Answer: The remaining eight men complete the unfinished work in 30 more days, so the job finishes on day 34 from the original start.
(c) The shadow of a 10 m tall tree is falling on a high rise building and its height is 100 m. If the tree is 20 m away from the wall, at what distance from the wall is the light source?
Let x be the ground distance from the light source to the tree. The light source, tree and wall form two similar right triangles:
- Small triangle: height 10 m and base x
- Large triangle: height 100 m and base x + 20
By similarity:
10/x = 100/(x + 20)
Cross-multiply:
10(x + 20) = 100x
10x + 200 = 100x
90x = 200
x = 20/9 m ≈ 2.22 m
This is the distance from the light source to the tree. The question asks for the distance from the source to the wall:
x + 20 = 20/9 + 20
= 200/9 m ≈ 22.22 m
Answer: The light source is approximately 22.22 m from the wall.
(d) There are three cars and start moving in such a way that car A and B are moving opposite with speed 60 and 100 km/h. Car C is moving perpendicularly to both with speed 80 km/h. What is distance after 15 minutes between (i) A and B (ii) A and C (iii) B and C?
Convert the time:
15 minutes = 15/60 hour = 1/4 hour
Distances travelled in one-quarter hour:
- Car A: 60 × 1/4 = 15 km
- Car B: 100 × 1/4 = 25 km
- Car C: 80 × 1/4 = 20 km
(i) Distance between A and B
A and B move in opposite directions along the same line:
A-B distance = 15 + 25 = 40 km
(ii) Distance between A and C
Their paths are perpendicular:
A-C distance = √(15² + 20²)
= √625 = 25 km
(iii) Distance between B and C
Their paths are also perpendicular:
B-C distance = √(25² + 20²)
= √1025 = 5√41 km
≈ 32.02 km
Answers: A-B = 40 km; A-C = 25 km; B-C = 5√41 km, approximately 32.02 km.
Q1 of this paper is objective and is deliberately not part of this set. What is solved here is the subjective half, Q2 through Q8.
In the examination hall you do not attempt all seven. The paper's own instruction for Part-II is to attempt only four questions, two from each section, and all questions carry equal marks. Each of the seven is solved here anyway, because this is a study resource and you cannot know in advance which four you will want.
The questions are reproduced from the Federal Public Service Commission's CSS 2024 General Knowledge-I (General Science & Ability) paper for study purposes. Every answer was written from scratch for this platform and is offered as one good attempt, not as an official key. Verify any figure against a primary source before reproducing it in an examination.