SSC CPO Tier- I Previous Year Paper (Held on: 4th July 2017 Shift 2)

1. Reaction : PRECIPITATION, hence word can be formed.

2. Patient : PRECIPITATION, hence word can be formed.

3. Reacts : ‘S’ is not present in PRECIPITATION, hence word cannot be formed.

4. Petition : PRECIPITATION, Hence word can be formed.

Hence, Reacts cannot be formed from the given word.

Clearly, when the paper sheet is unfolded it will appear as shown below:

Thus, fig.2 is the correct answer.

The least possible Venn diagram for the given statements is as follows,

Conclusion:

I. Some pencils are cups → it is true

II. No pencil is cup → it is false

III. Some cups are pens → it is possible but not definite, hence false

Hence, Only conclusion (I) follows

On close observation, we find that question figure is embedded in fig.1, as shown below:

Thus, figure 4 is the correct answer.

Here the relation between the quantity and their S.I unit is given,

for example, S.I unit of Time is second,

S.I. unit of Electric current is Ampere,

And S.I. unit of Temperature is Kelvin.

Similarly, S.I unit of Speed is Meter per Second.

Hence, Speed: Km/hr is the odd one out.

The least possible Venn diagram for the given statements is as follows,

Conclusion:

I) All boys are thin. → As all boys are smart and all smart are thin, definitely all boys will be thin, hence true.

II) All smart are boys. → It is possible but not definite, hence false.

Hence, Only conclusion (I) follows.

The pattern so followed is,

1 × 3 + 1 = 4;

4 × 3 + 1 = 13;

13 × 3 + 1 = 40;

40 × 3 + 1 = 121

121 × 3 + 1 = 364

Hence, 364 is the correct answer.

The given pairs of numbers except 83 - 97, are consecutive pairs of prime numbers,

Hence, 83 - 97 is the odd one out.

As per given figure,

Hence, are there (11 + 17 + 19 = 47) wooden plates.

1. Six games are in row from top to bottom.

2. Uno is just above Snakes & Ladders.

 Snakes & Ladders < Uno

2. The Monopoly is between Ludo and Chess

 Ludo > Monopoly > Chess or Chess > Monopoly > Ludo

3. Carrom is between Uno and Ludo

 Snakes & Ladders > Uno > Carrom > Ludo > Monopoly > Chess

Hence, Ludo is between Carrom and Monopoly.

1. Prison : IMPRISONMENT, hence a word can be formed.

2. Sonnet : IMPRISONMENT, hence a word can be formed.

3. Impression : Only a single ‘S’ is present in IMPRISONMENT, hence the word cannot be formed.

4. Moment : IMPRISONMENT, hence a word can be formed.

Hence, Impression cannot be formed from the given word.

As scissors is used for cutting the clothes,

Similarly,

Axe is used for cutting wood.

Hence, the correct answer is wood.

Clearly, when paper sheet is unfolded it will appear as shown below:

Thus, fig.4 is the correct answer.

If we rotate first dice such that, A comes at the TOP,

then, we can say that F is opposite to B.

Hence, F is the correct answer.

The figure may be labeled as:

Thus, the total number of triangles is 7.

The pattern follow is,

84 ÷ 2 = 42;

42 + 2 = 44;

44 ÷ 2 = 22;

22 + 2 = 24;

24 ÷ 2 = 12;

12 + 2 = 14

Hence, 14 is the correct answer.

Here Almonds, Cashew nut, Walnut comes under the category of dry fruits,

Whereas potato comes under the category of vegetables,

Hence, Potato is the odd one out.

The pattern followed is,

The sum of each column is 14,

1^st column = 2 + 4 + 3 + 5 = 14;

2^nd column = 7 + 1 + 2 + 4 = 14;

Similarly,

3^rd column = 14 - (6 + 4 + 3)

= 1

Hence, 1 is the correct answer.

The opposite pair are as follows :

(N - O), (Q - P) and (S - R) are the opposite pairs. so they will not appear adjacently in the folded cube figure.

Option 1, 3 and 4 contain opposite pairs which is wrong.

Thus option 2 figure  

 is possible.

Hence, option 2 is the correct answer.

The pattern followed here is,

A + 3 = D; D + 3 = G; G + 3 = J;

B + 4 = F; F + 4 = J; J + 4 = N;

According to alphabetical positions of the letters,

1. (A + B)² + 1 = (1 + 2)² + 1 = 10;

2. (D + F)² + 1 = (4 + 6)² + 1 = 101;

3. (G + J)² + 1 = (7 + 10)² + 1 = 290;

4. (J + N)² + 1 = (10 + 14)² + 1 = 577

Hence, correct answer is JN577.

As per the given diagram,

Hence, 12 is the correct answer.

Putting the symbols in the options we get,

1. 7 + 4 + 5 ÷ 165 = 5

= 7 + 4 + 0.030

= 11.030 ≠ 5

2. 7 × 4 × 5 = 165 + 5

= 224 ≠ 170

3. 7 × 4 ÷ 5 = 165 ÷ 5

= 5.6 ≠ 33

4. 7 × 4 + 5 = 165 ÷ 5

= 7 × 4 + 5 = 33

= 33 = 33

Hence, option (4) is the correct answer.

Clearly, fig.4 shows the correct right image of question figure.

Hence, figure 4 is the correct answer.

Let Amit's age at the time of his sister’s marriage be X.

So his present age will be 5X/4.

Also, Amit's age 5 years ago = X; so, present age will be 5 + X.

According to question,

5X/4 = 5 + X;

5X = 20 + 4X;

X = 20

His father's age at the time of marriage = 2X

so, present age of his father = 2X + 5= 2 × 20 + 5 = 45 years.

Hence, present age of father is 45 years.

The pattern follow is,

(First number - third number)² = middle number

(21 - 14)² = (7)² = 49

(159 - 146)² = (13)² = 169

Similarly,

(56 - 44)² = (12)² = 144

Hence, 144 is the correct answer.

1. 2³ + 4³ - 3³ = 45;

= 8 + 64 - 27

= 45;

2. 3³ + 5³ - 4³ = 88

= 27 + 125 - 64

= 88;

Similarly,

4³ + 2³ - 1³ = ?

= 64 + 8 - 1

= 71

Hence, 71 is the correct answer.

The pattern followed here is,

1. 214 = 2 + 1 + 4 = 7 (Sum of the number is divisible by 7)

2. 124 = 1 + 2 + 4 = 7 (sum of the number is divisible by 7)

3. 782 = 7 + 8 + 2 = 17 (sum of the number is not divisible by 7)

4. 554 = 5 + 5 + 4 = 14(sum of the number is divisible by 7)

Hence, 782 is odd one out.

The pattern followed here is of the type,

R + 3 = U

E + 3 = H

K + 3 = N

M + 3 = P

Similarly,

P + 3 = S

K + 3 = N

D + 3 = G

L + 3 = O

Hence the correct answer is SNGO.

As per the given figure,

Hence, there are 43 sour fruits.

As tailor uses needle for stitching clothes,

Similarly,

Woodcutter uses Axe for cutting the trees or the wood.

Hence, axe is the correct answer.

According to the given coding language,

Similarly,

Hence, 257314 is the correct answer.

The pattern follow is,

A + 3 = D;

D + 3 = G;

G + 3 = J;

J + 3 = M

Hence, M is the correct answer.

The figure may be labelled as:

Thus, the total number of quadrilaterals is 17.

The pattern followed here is,

P + 1 = Q

Q + 2 = S

R + 3 = U

S + 4 = W

Similarly,

A + 1 = B

B + 2 = D

C + 3 = F

D + 4 = H

Hence, the correct answer is BDFH.

As per the dictionary order,

5. Walk

6. West

7. Wind

8. Write

9. Wrong

Hence, 53421 is the correct dictionary order.

Present age of a father is 3 times that of his son, let son’s age be ‘X’

Then, father’s age will be ‘3X’.

Raman celebrated his 3^rd birthday 2 years ago,

That means his present age is 3 + 2 = 5 years

After 10 years the son’s age will be 5 times of Raman’s present age

Hence, son’s age after 10 years = 5 × 5 = 25

Hence, son’s present age = 25 - 10 = 15

Hence, present age of father (3X) = 3 × 15 = 45

Hence, father’s present age is 45 years.

1. 24 × 8 - 9 + 9 ÷ 10 = 26

= 19.2 ≠ 26

2. 24 ÷ 8 × 9 + 9 - 10 = 26

= 27 + 9 - 10

= 26

3. 24 - 8 ÷ 9 + 9 × 10 = 26

= 24 - 0.88 + 90

= 23.12 + 90

= 113.12 ≠ 26

4. 24 + 8 ÷ 9 × 9 - 10 = 26

= 24 + 8 - 10

= 32 - 10

= 22 ≠ 26

Hence, option (2) is the correct answer.

The pattern follow is,

B + 2 = D + 3 = G + 4 = K

X + 2 = Z + 3 = C + 4 = G

T + 2 = V + 3 = Y + 3 = B

N + 2 = P + 3 = S + 4 = W

Hence, TVYB is odd one out.

As per the dictionary order,

3. Beep

4. Boxed

5. Boxer

6. Brain

7. Brand

Hence, 35412 is the correct dictionary order.

The pattern followed here is,

Second number = (first number)³

125 = (5)³

= 125

Similarly,

? = (11)³

= 1331

Hence the correct answer is 1331.

On close observation, we find that question figure is embedded in fig.1, as shown below:

Thus, figure 2 is the correct answer.

According to the given information:

1. 2² + 4² + 6 = 26

2. 5² + 3² + 1= 35

Similarly,

23 – (2² + 3²) = 10

Hence, 10 is the correct answer.

Let us check each option according to given Matrix,

1. 20, 01, 57, 68, 58 → T R U M N

2. 42, 44, 89, 99, 88 → T R U M P

3. 03, 23, 96, 67, 69 → T R U O P

4. 31, 10, 65, 76, 79 → T R U M N

Hence, ‘42, 44, 89, 99, 88’ is the correct answer.

The pattern follow is,

R + 1 = S

V + 1 = W

C + 1 = D

T + 2 = V

Hence, TV is odd one out.

Let us check each option according to given Matrix,

1. 12, 42, 57, 95 → S O L L

2. 00, 30, 68, 58 → S O I A

3. 43, 04, 87, 69 → S O I L

4. 24, 11, 98, 76 → S O T L

Hence, ‘43, 04, 87, 69’ is the correct answer.

Clearly, fig.3 will complete the pattern when placed in the blank space of question figure as shown below:

Thus, Figure 3 is the correct answer.

Clearly, fig.4 shows the correct right image of question figure.

Hence, figure 4 is the correct answer.

Clearly, fig.4 will complete the pattern when placed in the blank space of question figure as shown below:

Thus, Figure 4 is the correct answer.

The pattern followed here is,

Second number = (first number) ² +1

26 = (5) ² + 1

= 25 + 1

= 26

Similarly,

? = (8) ² + 1

= 64 + 1

= 65

Hence the correct answer is 65.

The pattern follow is,

BALL = 2 + 1 + 12 + 12 = 27

CANE = 3 + 1 + 14 + 5 = 23

YELL = 25 + 5 + 12 + 12 = 54

Hence, 54 is correct answer.

Life On My Terms: From the Grassroots to the Corridors of Power, an autobiography of Sharad Pawar was released by Prime Minister Narendra Modi on 10 December 2015.

Graphite is used as a neutron moderator in nuclear reactors or atomic pile. Graphite was used to slow the neutrons down to energies more likely to support absorption and to reflect the neutrons back into the core to minimize loss.

The Royal Swedish Academy of Sciences has awarded Brown University Professor John Michael Kosterlitz the Nobel Prize in Physics “for theoretical discoveries of topological phase transitions and topological phases of matter.”

Article 18 relates to Abolition of titles

Prohibition of titles except Military and Academic titles. No citizen of India shall accept any title from any foreign state.

Solar-powered photovoltaic (PV) panels convert the sun's rays into electricity by exciting electrons in silicon cells using the photons of light from the sun. This electricity can then be used to supply renewable energy to your home or business.

A rhizome ("mass of roots”) is a modified stem that grows horizontally underground. It has nodes and internodes. Vertical shoots may arise from the buds on the rhizome of some plants, such as turmeric or ginger.

Fa-Hien is the famous Chinese pilgrim who visited India during the rule of Chandra Gupta II.

• The femur is by far the longest bone in the human body.
• It is commonly known as the thigh bone.
• It actually runs the distance from your hip down to around your knee area.

Snooker – Cue: A game played with cues on a billiard table in which the players use a cue ball (white) to pocket the other balls (fifteen red and six coloured) in a set order.

• Chinook wind is also known as 'Snow Eater’ as these winds move east, they rise over the western slopes of the mountains and then descend, becoming extremely dry and much warmer.
• Air naturally warms as it sinks, but dry air warms almost twice as fast as moist air.
• The winds can also spread fires easily because of the extremely dry air.

• Near coastal areas, the temperature on land in night time gets reduced due to Land breeze.
• Land breezes usually occur at night. At night, the temperature of the land cools quickly without the insolation from the sun.
• Heat is rapidly re-radiated back to the surrounding air. The water along the shore will then be warmer than the coastal land, creating a net movement of air from the land surfaces towards the ocean.

There are a total of 12 Schedules in the Indian Constitution.

The summer solstice is the longest day of the year. Solstices are opposite on either side of the equator, so the summer solstice in the Northern Hemisphere is the winter solstice in the Southern Hemisphere, and vice versa. Summer solstice in Northern Hemisphere was on 21 June.

A hydraulic brake is an arrangement of braking mechanism which uses brake fluid, typically containing glycol ethers or diethylene glycol, to transfer pressure from the controlling mechanism to the braking mechanism.Pascal's law basically states that any pressure applied to a fluid inside a closed system will transmit that pressure equally in all directions throughout the fluid. This law is the basic principle that causes hydraulic power in heavy construction machines to work.

White blood cells (WBCs), also called leukocytes or leucocytes, are the cells of the immune system that are involved in protecting the body against both infectious disease and foreign invaders.

President can declare a national emergency on three grounds: War, External aggression, armed rebellion.

• National Emergency - Article 352
• State Emergency – Article 356
• Financial Emergency – Article 360
• Learning Tip: The articles of emergency have a gap of +4 starting from 352.

The correct answer is option 2 i.e Longitudes

Longitude refers to the imaginary lines that bisect the globe through the North and South Poles (the ones that run vertically, as opposed to the lines of latitude that run horizontally, parallel to the equator).

• Longitude is measured by imaginary lines that run around the Earth vertically (up and down) and meet at the North and South Poles.
• These lines are known as meridians.
• Each meridian measures one arcdegree of longitude. The distance around the Earth measures 360 degrees.

The meridian that runs through Greenwich, England, is internationally accepted as the line of 0 degrees longitude, or prime meridian. The antimeridian is halfway around the world, at 180 degrees. It is the basis for the International Date Line.

Half of the world, the Eastern Hemisphere, is measured in degrees east of the prime meridian. The other half, the Western Hemisphere, in degrees west of the prime meridian.

• Degrees of longitude is divided into 60 minutes.
• Each minute of longitude can be further divided into 60 seconds.
• For example, the longitude of Paris, France, is 2° 29' E (2 degrees, 29 minutes east).
• The longitude for Brasilia, Brazil, is 47° 55' W (47 degrees, 55 minutes west).

Keyboard: A computer keyboard is an input device that allows a person to enter letters, numbers, and other symbols (these are called characters) into a computer.

Scanner: A scanner is an input device that scans documents such as photographs and pages of text. 

Joy-stick: A joystick is an input device consisting of a stick that pivots on a base and reports its angle or direction to the device it is controlling.

• Sulphuric acid or H₂SO₄ was called "oil of vitriol" because it was prepared by roasting "green vitriol" in an iron retort.
• It is a colourless, odourless, and syrupy liquid that is soluble in water.

Newton's first law is also known as the "law of inertia." This law states that if an object is at rest, then it will stay at rest until it is acted upon by another object. Then, the law states that an object in motion will stay in motion unless it is acted upon by an unbalanced force.

Nitrogen, Potassium, Phosphorus elements are commonly found in most fertilizers as

• Nitrogen is used by plants for lots of leaf growth and good green colour.
• Phosphorous is used by plants to help form new roots, make seeds, fruit and flowers. It's also used by plants to help fight disease.
• Potassium helps plants make strong stems and keep growing fast.

The Ministry of Women and Child Development in collaboration with the Ministry of Panchayati Raj has launched a nationwide programme for capacity building of Elected Women Representatives (EWRs) of Panchayats and a training program for Trainers of women panchayat leaders at Ranchi, Jharkhand.

Onam-Kerela:

Onam is the biggest and the most important festival of the state of Kerala. It is a harvest festival and is celebrated with joy and enthusiasm all over the state by people of all communities.

Kuchipudi-Andhra Pradesh:

Kuchipudi an established dance form originated in Andhra Pradesh.

Pongal-Tamil Nadu:

Pongal is a major Hindu festival that is celebrated in the fourteenth day of January every year. It is celebrated in the state of Tamil Nadu. 

Gudipadwda-Maharashtra:

GudiPadwa is an Indian festival that marks the beginning of the New Year and the harvest season for the people of Maharashtra.

The computer was invented in 1837 by Charles Babbage in the form of the Analytical Engine.

The correct answer is Third.

Green Revolution

• The Green revolution started in the year 1965 and the 3^rd five-year plan was between 1961-66.
• The green revolution started Under the Ministery of Food and Agriculture C. Subramaniam.
• In 1965, Lal Bahadur Shastri was the prime minister of India.
• Father of the Green revolution**(India)M.S.Swaminathan**
• The word Green revolution was first used by William S. Gaud, Administrator of the U.S Agency for International Development**(USAID).**
• World Father of the Green revolution Norman Borlaug.
• It's referring to the great increase in the production of wheat and rice Due to the introduction of high yielding seeds. Mainly  Mexican wheat seeds.
• The green revolution aims to make the country self-sufficient in food grains.
• It was introduced in North-India especially in Punjab, Haryana, and Uttar Pradesh.

Five-year Plan

• It was launched by The first Indian prime minister, Jawaharlal Nehru, In 1951.

The arrangement of leaves on a stem is known as phyllotaxy. Leaves can be classified as either alternate, spiral, opposite, or whorled.

The Prime Minister is the Ex-officio chairman of NITI Aayog in India.

Per capita income or average income measures the average income earned per person in a given area in a specified year. It is calculated by dividing the area's total income by its total population.

The per capita GDP is especially useful when comparing one country to another, because it shows the relative performance of the countries.

The Maitree Express or Moitree Express is the name of the first modern international passenger train service connecting Bangladesh to the the Indian state of West Bengal. The name Maitree Express means the Friendship Express, denoting the significance of the train service to the foreign relations between India and Bangladesh.

The minimum age for becoming a candidate for Lok Sabha election shall be 25 years. 

There are 59 Miniratna companies in Category – I.

CATEGORY I:

This tag is applies to only those PSEs who can made a profits consistently from the period of last three years or can holds an average of profit of Rs. 30 crore or more.

Confederations are voluntary union of sovereign and associations of independent states to secure some common purpose, agree to certain limitations on their freedom of action and establish some joint machinery of consultation or deliberation.

A scanner is a device that captures images from photographic prints, posters, magazine pages, and similar sources for computer editing and display. Scanners come in hand-held, feed-in, and flatbed types and for scanning black-and-white only, or colour.

Gautam Buddha is called “Light of Asia”. It is the title of a book written by Sir Edwin Arnold about the life of Buddha.

Key Points

• Mahatma Buddha was born on the day of Vaishakh Purnima in 563 BC in Lumbini, located in the lowlands of Nepal.
• It is well known that in his youth he saw the miseries of human life like sick person, old age and death. On the contrary, influenced by a happy sannyasin, Buddha at the age of 29 renounced worldly life and set out in search of truth.
• Mahatma Buddha attained self-realization while meditating under a Peepal tree in Bodh Gaya on the day of Vaishakh Purnima in 528 BC.
• On the day of Vaishakh Purnima, in 483 BC, Mahatma Buddha attained Nirvana at a place called Kushinara.
• After his death, his disciples called a council at Rajagriha, where the main teachings of Buddhism were codified.
• Four Buddhist councils were organized to synergize these teachings in the form of pitakas, after which three main pitakas were formed.
• The Vinaya Pitaka (the rules of order for Buddhists), the Sutta Pitaka (the teaching principles of the Buddha) and the Abhidhamma Pitaka (Buddhist philosophy), are collectively referred to as the Tripitaka. All these have been written in Pali language.

President nominates 2 members of the Anglo-Indian Community to Lok Sabha.

The correct answer is Existence of both public and private sectors in national economy

• The main feature of a mixed economy is the co-existence of both public and private enterprises.
• They work together. The industries in the private sector are managed and operated completely by private entrepreneurs.
• On the other-hand there is the public sector in which the enterprises are owned and managed by the State.

Democracies resolve conflicts in a better way and some of the reasons are:

1. Democracy gives equal chances to two different groups.
2. It does not protect a group from the view of superiority.
3. It judiciously gives its decisions.
4. It listens to every individual without any intention of opposition.

The 'One belt, One road' summit was held in Beijing - China. The project One Belt, One Road is planning to set up an intercontinental infrastructure network between Europe, Africa, Asia and China. “

• The temperature of water at the bottom of the lake will be 4°centigrade. As the water density increases, there is a decrease in freezing point.
• Hence the ice cannot be seen at the bottom of the lakes or oceans as the water at the bottom of the lake has more density than the top level.

• Xerophytes plants can survive in very less water as it adapted for living in extremely dry conditions with little access to water.
• They have deep root structures, thin or small leaves, and waxy surfaces to retain moisture.

Explanation:

Composting is one of the options for treatment of solid waste. In the composting process, the organic matter breaks down under bacterial action resulting in the formation of humus like material called compost.

• Vermicomposting: It involves the use of earthworms for composting organic solid waste. It is a resourceful way to recycle your food waste into compost. It takes about 2-3 months.
• Vermicompost (worm manure) is the end-product of the breakdown of organic matter by earthworms.
• This process of increasing fertility of soil by earthworms is known as vermicomposting.

Hence, Vermicompost is an organic fertilizer.

Birth and Death Rates are natural increase. Birth Rate is the term used to define the number of babies born every year per 1000 people in a population. Death Rate is the term used to define the number of deaths every year per 1000 people in a population.

Solar-powered photovoltaic (PV) panels convert the sun's rays into electricity by exciting electrons in silicon cells using the photons of light from the sun. This electricity can then be used to supply renewable energy to your home or business.

English philosopher and social reformer Jeremy Bentham is the father of 'Utilitarian School of Thought'.

Idol of dancing girl is a prehistoric bronze sculpture made in approximately 2500 BCE in the Indus Valley Civilisation city of Mohenjo-Daro.

Key Points

• Structurally, plant and animal cells are very similar because they are both eukaryotic cells.
• They both contain membrane-bound organelles such as the nucleus, mitochondria, endoplasmic reticulum, Golgi apparatus, lysosomes, and peroxisomes.
• Cell walls made of cellulose are only found around plant cells.

The correct answer is Semi-Permeable.

Key Points

• A Semi-permeable cell membrane is one that allows certain molecules or ions to pass through it by means of active or passive transport.
• Active transport processes require the cell to expend energy to move the materials, while passive transport can be done without using cellular energy.
• Surrounding the cell membrane in most plants, fungi, algae, and bacteria, the cell wall is a semi-permeable layer.
• It is responsible for providing structure, support, and protection to the cell.

Its composition varies among different organisms-

The 49^th parallel of north latitude forms part of the international boundary between Canada and the United States.

Samvad Kaumudi was a Bengali weekly newspaper published from Kolkata, India in the year 1821 by writer Raja Ram Mohan Roy. Its language was Bengali.

Amuktamalyada is an epic poem in Telugu composed by Krishnadevaraya of the Vijayanagar Dynasty. Amuktamalyada translates to one who wears and gives away garlands.

Let radius of the sphere be x.

⇒ radius of hemisphere = 3

Total surface area of sphere = 4πx²

Total surface area of hemisphere = 3π(3x)² = 27πx²

Ratio = 27 : 4

For same distance,

Time is inversely proportional to velocity.

Ratio of time taken = 1/10 : 1/12 : 1/15 

LCM of 10, 12 and 15 = 60

The required ratio = 60 × 1/10 : 60 × 1/12 : 60 × 1/15

⇒ 6 ∶ 5 ∶ 4

∴ The required ratio is 6 ∶ 5 ∶ 4.

Calculation:

(x + y)³ = x³ + y³ + 3xy(x + y)

⇒ x³ + y³ + 3xy × 4 = x³ + y³ + 12xy

⇒ x³ + y³ + 12xy

⇒ 4³

⇒ 64

Total marks obtained = 432

Average marks per subject = 432/5 = 86.4

86.4 marks will form (86.4 ⨯ 360/432 = 72°) at the center.

Central angle greater than 72° have marks more than average marks per subject.

⇒ English and maths marks is more than average marks per subject.

Shortcut Trick

Prime factorization of 24 = 2³ × 3¹

Total positive factors = (Power of 2 + 1) × (Power of 3 + 1)

⇒ (3 + 1) × (1 + 1)

⇒ 4 × 2 = 8

∴ The correct answer is 8.

Alternate Method

Given:

The number is 24.

Concept Used:

The positive factors of a number are all the integers that divide the number completely without leaving a remainder.

Calculation:

⇒ Let us list the pairs of positive integers whose product is 24.

⇒ 1 × 24 = 24

⇒ 2 × 12 = 24

⇒ 3 × 8 = 24

⇒ 4 × 6 = 24

⇒ The positive factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

⇒ Counting them gives exactly 8 factors.

∴ The correct answer is 8.

Additional Information

Total Number of Factors

If a number N = p^a × q^b × r^c (where p, q, r are prime factors), then the total number of factors = (a + 1)(b + 1)(c + 1).

Number of Odd Factors

To find odd factors, ignore the powers of 2. For N = 2^a × p^b × q^c (where p, q are odd primes), odd factors = (b + 1)(c + 1).

Number of Even Factors

Subtract the number of odd factors from the total factors, or calculate directly using a × (b + 1)(c + 1).

Sum of Factors

For N = p^a × q^b, the sum of all factors is [(p^a+1 − 1) ÷ (p − 1)] × [(q^b+1 − 1) ÷ (q − 1)].