SSC CPO Tier- I Previous Year Paper (Held on: 7th July 2017 Shift 1)

The pattern followed is:

Logic: (First Number × Last Number) ÷ 4 = Middle Number

(26 × 8) ÷ 4 = 52

(48 × 16) ÷ 4 = 192

Similarly,

(A × 14) ÷ 4 = 175

A × 14 = 175 × 4 

A = (175 × 4) ÷ 14 

∴ A = 50

Hence, 50 is correct.

Logic: (FIrst number ÷ 2) × (Third number ÷ 2) = Second Number

Formula used for equal number of rows and column:

Total number of rectangle ⇒ n³ + (n-1)³ + (n-2)³

n → number of rows/column

Formula used for unequal number of rows and column:

Total number of rectangle ⇒ (1 + 2 +......+ R) x (1 + 2 + .....+ C)

R → number of rows.

C → number of columns.

In this problem, the number of rows and column are not equal.

R → 3, C → 4

So, the number of rectangle in this figure = (1 + 2 +......+ R) x (1 + 2 + .....+ C) 

⇒ (1 + 2 + 3) x (1 + 2 + 3 + 4)

⇒ 6 x 10 = 60

The number of rectangles are:

Hence, ‘60’ is the correct answer.

The given figure is embedded in

Hence, option 2 is correct.

The pattern followed is:

All the options hai “- 4 ” and “ + 4 ” in them, except option 3.

Hence, option 3 is odd among them.

The representation for GLOW is:

G → 56, 68, 79, 87, 95

L → 57, 65, 78, 89, 96

O → 00, 13, 21, 34, 42

W → 04, 12, 20, 33, 41

GLOW → 95, 57, 13, 33

Hence, option 4 is correct

The mirror image along the line AB is

Hence, option 4 is correct.

The pattern followed is:

And,

Similarly, 

Hence, option 1 is correct

There are two positions of the same dice is given.

In both the positions 8 is same.

So, when one element is the same in both the dices then rotate it either clockwise or anti-clockwise to find the opposite faces.

Here, in 1st position rotate clockwise from 8 so we get:

⇒ 8 ⇔ 7 ⇔ 9

In position 2, rotate clockwise from 8, we get:

⇒ 8 ⇔ 6 ⇔ 4

So, 7 is opposite to 6 and 9 is opposite to 4.

Hence, 4 is opposite to 9.

The logic followed is:

1^st row → (8 × 6) + (6 × 12) + (12 × 8) = 48 + 72 + 96 = 216

3^rd row → (7 × 13) + (13 × 5) + (7 × 5) = 91 + 65 + 35 = 191

Similarly,

2^nd row → (4 × 22) + (22 × 3) + (4 × 3) = 88 + 66 + 12 = 166

Hence, ‘166’ is the correct answer.

In the first row,

4 × 6 + 1 = 25

25 × 5 = 125

In the second row,

8 × 7 + 1 = 57

57 × 9 = 513

In the third row,

11 × 6 + 1 = 67

67 × ? = 536

67 × 8 = 536

Hence, option 4 is correct

By decoding:

Using BODMAS rule

Option 1:

30 - 8 ÷ 4 +6 × 1 = 32

30 - 2 + 6 = 32

36 - 2 is not equal to 32

Option 2:

8 × 5 + 20 ÷ 4 - 6 = 41

8 × 5 + 5 - 6 = 41

40 + 5 - 6 =41

• 6 ≠ 41

Option 3:

12 - 12 ÷ 6 × 6 + 3 = 21

12 + 12 - 6 ÷ 6 × 3 = 21

12 + 12 - 1 × 3 =21

12 + 12 - 3 = 21

24 - 3 = 21 is correct

Option 4:

6 + 7 × 3 - 4 ÷ 6 = 26

6 × 7 ÷ 3 + 4 - 6 = 26

6 × 2.3 + 4 - 6 = 26

13.8 + 4 - 6 =26

11.8 is not equal to 26

Hence, option 3 is correct

Conclusion 1: Some cars are shining → False (This is definitely false)

Conclusion 2: No car is shining → True (This is definitely true)

Conclusion 3: No shining is car → True (This is definitely true)

Hence, Conclusion 2 and Conclusion 3 follow.

The figure which we get after cutting the paper is folded and punched is:

Hence, option 2 is correct.

Sea, River and Ocean are large water bodies.

Whereas, Swimming pool is a small water body

Hence, Option 4 is odd one out

The mirror image along line AB is:

Hence, option 2 is correct

Using BODMAS rule

Option 1:

35 ÷ 5 + 10 = 15 × 4

7 + 10 = 60

17 is not equal to 60

Option 2:

35 × 5 ÷ 10 > 15 × 4

35 × 1/2 > 60

17.5 is not greater than 60

Option 3:

35 ÷ 5 × 10 > 15 × 4

7 × 10 > 60

70 > 60 is correct

Option 4:

35 ÷ 5 × 10 < 15 + 4

7 × 10 < 15 + 4

70 < 17 is not true

Hence, option 3 is correct

Through Options

Option 1:

If Amit’s present age 56,

Ratio of ages of Sumit and Amit is 3 : 4

14* 4 = 56

Similarly,

Sumit’s age is 14 * 3 = 42

42 : 56 = 3 : 4

And Sumit’s age after 20 years = 42 + 20 = 62

Condition is satisfied

Hence, option 1 is correct.

By drawing Venn diagram:

Conclusion 1. Some green are grapes → True (This is definitely true)

Conclusion 2: Some hard are grapes → False (This is possible but not definite)

Conclusion 3: No grape is hard → False (This is definitely False)

Hence, only Conclusion 1 follows.

The diagrammatic representation is

Maximum number of boys is 36

Hence, option 2 is correct

The pattern followed is:

And,

Similarly,

Hence, option 4 is correct.

All the members are facing north

P and Q cannot sit at first and second places

R does not have S to his right

So, option 4 is correct.

The dictionary order of the given words is:

Dictionary → Dracula → Drink → Drinking → Drive

Hence, option 1 is correct

will be:

Broom which is wood but not long is represented by ‘f’

Hence, option 3 is correct

61 is a prime number

97 is a prime number

89 is a prime number

51 is not a prime number, it is divisible by 3 and 17

BALD cannot be formed using the given word.

Hence, option 2 is correct.

Hence, option 2 is correct.

Logical venn diagram:

Shirts and Trousers are types in Clothes

Hence, option 1 is correct

Similarly,

Hence, option 1 is correct.

Pen is used for writing.

Similarly,

Knife is used for cutting.

Hence, Option 4 is correct

Logical Venn diagram:

Branches and roots are part of a tree

Hence, option 2 is correct Venn diagram

The pattern followed is:

Hence, option 2 is correct.

The pattern followed is:

Hence, option 4 is correct.

The figure which will complete the pattern is:

Hence, option 2 is correct

62 : 145

8² = 64, 64 – 2 = 62

12² = 144, 144 + 1 = 145

So, 62 : 145

Similarly,

119 : 226

11² = 121, 121 – 2 = 119

15² = 225, 225 + 1 = 226

So, 119 : 226

Hence, option 2 is correct

From diagram we can see that ‘θ’ and ‘β’ are adjacent to ‘α’

Hence’ γ ‘will be opposite to ‘α’

Hence, option 1 is correct

The series followed is:

Hence, option 1 is correct

The figure which will complete the pattern is:

Hence, option 1 is correct.

The given figure is embedded in

Hence, option 1 is right.

Option 1: 13³ = 2197

13² = 169

2197 – 169 = 2028

Option 2: 11³ = 1331

11² = 121

1331 - 121 = 1210

Option 3: 7³ = 343

7² = 49

343 – 49 is not equal to 336

Option 4: 9³ = 729

9² = 81

729 – 81 = 648

Hence, option 3 is odd one out

NATIONAL cannot be formed using TRADITIONAL since it does not have 2 N’s.

Hence, option 1 is correct

The representation for HALT is

H → 04, 12, 21, 33, 40

A → 03, 14, 20, 32, 41

L → 55, 68, 77, 86, 99

T → 00, 13, 24, 31, 42

HALT → 21, 41, 68, 13

Hence, option 2 is correct

34 × 15 = 510

510 - 15 = 495

43 × 12 = 516

516 - 12 = 504

98 × 17 = 1666

1666- 17 = 1649

Hence, option 1 is correct

The figure which we get after cutting the paper is folded and punched is:

Hence, option 4 is correct.

Similarly,

Hence, option 4 is correct.

23 : 72

23 × 3 = 69

69 + 3 = 72

So, 23: 72

Similarly,

38 × 3 = 114

114 + 3 = 117

So, 38 : 117

Hence, option 2 is correct

The series followed is:

Hence, option 3 is correct

Counting number of triangles:

The triangles in the above figure are,

BGD, BGE, BGA, CGD, CGE, CGA, BDC, BEC, BAC, ABD, ABE, ACD, ACE, BED and CED

The number of triangles in the given figure is 15.

Hence, option 4 is correct

The dictionary order of the given words is:

Mandarin → Mandate → Master → Mobile → Monkey

Hence, option 1 is correct

In the given analogy, Create and destroy are given which are Antonyms

Option 1: Thin and Small are not antonyms

Option 2: Long and Short are antonyms

Option 3: Fat and huge are not antonyms

Option 4: Long and Topmost are not antonyms

Hence, option 2 is correct

VIBGYOR is the representation of colours after splitting of white light

VIBGYOR stands for Violet, Indigo, Blue, Green, Yellow, Orange and Red

Yellow, Blue and Red are colours in VIBGYOR, whereas White is not, since these colours are obtained from White

Hence, White is odd one out.

Post Office Protocol version 3 (POP - 3) is a standard mail protocol used to receive emails from a remote server to a local email client. POP - 3 allows you to download email messages on your local computer and read them even when you are offline.

*Note : From Germany- suspension of  Fundamental Rights(FR) are done during Emergency situation. Not emergency provisions taken.

Pakistani human-rights and education advocate Malala Yousafzai has just become the youngest person ever to be named a U.N. Messenger of Peace, an honorary title conferred by the body's Secretary General Antonio Guterres.

 Key Points

• Prime minister can be called as the most important institution in India because Prime Minister is the real executive head of the state as compare to the President who is the nominal head of the state.
• He heads the Party in power in Parliament.

Cellulose fibers are fibers made with ether or esters of cellulose, which can be obtained from the bark, wood or leaves of plants, or from a plant-based material.

In a periodic table atomic size gradually decreases from left to right across a period of elements. This is because, within a period or family of elements, all electrons are added to the same shell.

Friction is a force exerted by a surface against the motion of a body across its surface. Friction is a type of contact force only which is applied to an object by another object.

The correct answer is Plastids.

Key Points

• The plastids are the cell organelles found in all the plant cells.
• They bear some specific pigments, thus imparting specific colors to the plants.
• Three types of plastids are:
• Chloroplast - contains Chlorophyll(Green pigment)
• Chromoplast - contains Carotenoid(Red, Yellow, and orange pigment)
• Leucoplast - contains colorless plastid, mainly stores foodstuff in a plant cell.

Additional Information

• Nominated Members of the Parliament do not take part in the election of the President of India.
• President is elected by an electoral college consisting of elected members of parliament and Elected members of all State legislative assembly and Delhi and Pondicherry.
• He must have completed the age of 35 years to contest for Presidential elections. He must be a citizen of India.
• Article 54 and 55 provides for the election of the President.

• Hieun Tsang, the Chinese pilgrim, visited India during the reign of Harshavardhana with an aim of securing authentic Buddhist scripts.
• The Kannauj assembly (643 AD) was held in the honour of Hieun Tsang and to popularise Mahayana sect of Buddhism.

Groundnut is a legume, Kharif crop grown mainly for its edible seeds. It is widely grown in the tropics and subtropics, It is important to both small and large commercial producers.

• Calcium hypochlorite is an inorganic compound with formula CaOCl₂.
• As a mixture with lime and calcium chloride, it is marketed as chlorine powder or bleach powder for water treatment and as a bleaching agent.

Every one-degree shift of longitude corresponds to 4 minute time difference.

So a time difference of 1 hour (60 minutes) will have:

1 degree = 4 minutes

So, 60/4 = 15 and 15 × 1° = 15°

Now for 2 hours (120 min)

1 degree = 4 minutes

120/4 = 30 and 30 × 1° = 30°

So a time lag of 2 hours corresponds to 30 degrees of longitudinal change.

This follows from a simple fact that 360∘ ⇒ 24 hours.

Which is same as 360° ⇒ 1440 min. So 1° ⇒ 1440/360 = 4 minutes.

Concept:

Reflection: 

• The phenomena in which light ray is sent back into the same medium from which it is coming, on interaction with boundary, is called reflection.
• Laws of reflection: it states that angle of incident will be equal to angle of reflection for a ray of light reflected from plain polished surface

 i.e., The angle of incidence (θ i ) = Angle of reflection (θ r )

Note:

The incident ray, the reflected ray, and normal to the surface of incidence always lies in the same plane as shown above.

Explanation:

According to the law of reflection, the angle of reflection must equal the angle of incidence for each ray.

The correct answer is Tendon.

Tendons:

• Tendons are fibrous connective tissue.
• Tendon connects muscle to bone.

Additional Information

• Cartilages:
• It is a type of connective tissue in the body.
• It is a strong, flexible tissue that is the main type of connective tissue in the body.
• Due to the presence of Cartilages in our ears, the ears can be folded.
• Elastic cartilage is a type of cartilage present in the outer ear.
• It doesn’t have blood vessels or nerves.
• This tissue is present in joints, ears, nose, rib cage, and in many other areas of the body.
• Bones:
• Bones in our bodies are living tissues that make up the skeleton.
• It provides shape and support to the body, as well as protection for some organs in the body.
• The Femur is the strongest bones of the human body.
• Ligaments:
• It is a short, fibrous, and elastic connective tissue.
• It attaches bone to bone, gives support to the joints.
• Adipose is a connective tissue that stores energy in the form of fat.

Martial law is the imposition of direct military control of normal civilian functions of government, especially in response to a temporary emergency such as invasion or major disaster, or in an occupied territory. Martial law can be used by governments to enforce their rule over the public.

Relative density = Density of the substance/Density of water at 4°C. As both the numerator and the denominator on the RHS of the above formula has the same unit (i.e. kg/m³) they get cancelled.

Finance Ministry of India presents the Economic Survey in the parliament every year, just before the Budget. It is prepared under the guidance of the Chief Economic Adviser, Finance Ministry.

The Government has launched the ‘Test and Treat Policy for HIV patients’ in April 2017. As per this policy all people living with HIV (PLHIV) are to be treated with Antiretro Viral Therapy regardless of CD4 count, clinical stage, age or population.

Vasco da Gama reached India:

Vasco de Gama becomes the first European to reach India via the Atlantic Ocean when he arrives at Calicut on the Malabar Coast on 20 May 1498.

Babur started Mughal dynasty:

Babur, who laid down the foundation of the rule of a new dynasty in India in 1526 A.D.

Sepoy mutiny:

A revolt of the sepoy troops in British India (1857-59), resulting in the transfer of the administration of India from the East India Company to the crown known as Sepoy Mutiny.

Acquisition of Indian citizenship by Registration:

Loss of Indian citizenship by Deprivation:

Fundamental Right equality before law and equal:

Equality before the law is the principle that each independent being must be treated equally by the law and that all are subject to the same laws of justice.

The tertiary sector includes service industry and it holds the highest importance among all sector. The Tertiary sector of economy involves the provision of services to business as well as final consumers. Services may involve the transport, distribution and sale of goods from producer to consumers.

Under Section 22 of the Reserve Bank of India Act, RBI has sole right to issue currency notes of various denominations except one rupee notes.

The One Rupee note is issued by Ministry of Finance and it bears the signatures of Finance Secretary, while other notes bear the signature of RBI Governor.

The correct answer is On, in, or near the seabed.

• Benthos is all about those creatures which live on, in, or near the seabed like sea stars, sea squirts, sea slugs, corals, crabs, clams, whelks (sea snails), worms, sponges, urchins, and anemones.
• At the very beginning of the edge of the ocean, benthos can find out easily.
• It is very similar to the creatures of our rock pools and beaches at home so you can accept readily that The Antarctic creatures are similar to your rock pool.
• Macrophytic angiosperms like mangrove trees, marsh grasses, and seagrasses are known as Benthos plants.
• Macrophytic algae have green, red, and brown seaweeds, and the long-stemmed kelps, a type of brown algae.
• Microphytic algae also include benthic species like diatoms, Cyanobacteria, and dinoflagellates.
• The various kinds of Benthos are:

1. ​Hyperbenthos
2. Epibenthos
3. Endobenthos

Rhizome-Banana: The rhizome is the banana plant's stem.

Bulb-Onion: Onion is also known as the bulb onion or common onion. It is a vegetable that is the most widely cultivated species of the genus Allium.

Tuber- Potato: A tuber is the thickened part of an underground stem of a plant potato.

Female gametes are called ova or egg cells. Gametes are haploid cells, and each cell carries only one copy of each chromosome.

In a socialist society, the government decides what goods are to be produced in accordance with the needs of society. It is assumed that the government knows what is good for the people of the country and so the desires of individual consumers are not given much importance.

Concept-

• A neuron is a microscopic structure composed of three major parts, namely, the cell body, dendrites, and axons.

• A neuron is a cell that carries electrical impulses.
• Neurons are the basic units of the nervous system and its most important part is the brain.
• Every neuron is made of a cell body (also called a soma), dendrites and an axon.

China has hosted the 9^th BRICS summit in Xiamen on 1 September 2017.

The plotter is a computer printer for printing vector graphics. A plotter gives a hard copy of the output. It draws pictures on a paper using a pen.

To show good and careful judgment when handling practical matters, it can be described as Prudent. Similarly, a wise and well-thought-through decision or action can be called Prudent.

Calcium oxide (CaO), commonly known as quicklime or burnt lime, is a widely used chemical compound. It is a white, caustic, alkaline, crystalline solid at room temperature.

The food vacuole digests the food in Amoeba. Wastes and excess water are transported outside the cell by contractile vacuoles.

Madhubani art is practiced in the Mithila region of Bihar in India and Nepal. Painting is done with fingers, twigs, brushes, nib-pens, and matchsticks, using natural dyes and pigments, and is characterised by eye-catching geometrical patterns.

Tartaric acid is a white crystalline diprotic organic acid. The compound occurs naturally in many plants, particularly in grapes, bananas, and tamarinds. It is also one of the main acids found in wine. Oxalic acid is a natural product found in spinach.

• The concept of Directive Principles of State Policy was borrowed from the Irish constitution.
• This is an important feature of the constitution.
• Although the Directive Principles are asserted to be fundamental in the governance of the country they are not legally enforceable. Instead, they are guidelines for creating a social order characterized by social, economic, and political justice, liberty, equality, and fraternity as enunciated in the constitution's preamble.

The First Battle of Panipat, on 21 April 1526, was fought between the invading forces of Babur and the Lodi Kingdom. It took place in north India and marked the beginning of the Mughal Empire.

Trick: Babar ne 1526 mein Pani peeya (Battle of PaniPat) (1526)

Jog Falls is created by the Sharavathi River dropping 253 m (830 ft.) making it the third-highest plunge waterfall in India.

'The Red Sari' is written by Javier Moro which is a dramatized version of Sonia Gandhi's life, ran into some controversy in India.

Abiotic component of environment include water, light, radiation, temperature, humidity, atmosphere and soil.

There is no maximum time limit for the financial emergency (Article 360) in India unlike the State Emergency or the President rule. Once proclaimed (financial emergency) which means must be approved by both Houses of Parliament, it can continue for any duration if needed.

Trick: Emergency articles starts from (352 and then add + 4 + 4 that is 352, 356, 360)

Neptune planet is farthest from Sun among the above options.

The Great Dividing Range is located in Australia. It is so called because it forms a watershed. Rivers on the east side flow from the highlands toward the Pacific Ocean; on the west side they flow toward the central lowlands. In southern New South Wales and Eastern Victoria are the Australian Alps, the continent's tallest mountains.

Afghanistan is not a member of Indian Ocean Rim Association (IORA).

Theodore Maiman, American Engineer made the first laser operate on 16 May 1960 at the Hughes Research Laboratory in California.

The correct answer is Akbar.

Key Points

• Agra Fort, also known as the Red Fort of Agra, due to the extensive use of red sandstone in its construction.
• It was built predominantly by Emperor Akbar in 1565 AD, with subsequent additions by Shah Jahan and Aurangzeb, the Agra Fort is not just a fort but more of a walled city.
• It covers an area of approximately 94 acres, complete with palaces, mosques, and gardens.
• The fort combines different architectural styles, with a blend of Hindu and Islamic elements.
• Its notable structures include the Jahangir Palace, Diwan-i-Am, Diwan-i-Khas, and the Moti Masjid.
• Of particular historical interest is the fact that Shah Jahan, who added ornate white marble structures to the fort was imprisoned here by his son, Aurangzeb.
• He spent his final seven years in a tower with a view of the Taj Mahal, which he built in memory of his wife, Mumtaz Mahal.
• Today, Agra Fort is a UNESCO World Heritage site, open for tourists who want to experience India's rich history.

Additional Information

CONCEPT:

• Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid.

EXPLANATION:

• From the above definition, option 3 is correct.

• Laws of Floatation: The three conditions required for the body to float on water are:

1. The weight of the body in the figure is equal to the buoyant force. (c) (d)
2. The weight of the body is greater than the weight of the fluid displaced i.e. buoyant force.  (b)
3. The weight of the body is less than the weight of the fluid displaced i.e. buoyant force. (a)

Key Points

• Iron was not used in the Harappan cities.
• Harappan cities are part of Indus Valley Civilizations, which was held after the Chalcolithic period of stone-age.
• During the Chalcolithic period, copper was first used to make tools, utensils, and other objects.

Additional Information

• The Indus civilization, also known as the Indus Valley Civilization or the Harappan Civilization, is the oldest known urban culture of the Indian subcontinent.
• The atomic dates of civilization appear to be around 2500 to 1700 BCE, although the southern sites later moved into the second millennium BCE.
• The civilization was first identified in 1921 in Harappa in the Punjab region and then in 1922 in Mohenjo-Daro (Mohenjodaro) near the Indus River in the Indus (Sindh) region.
• Both sites are in the provinces of Pakistan, Punjab, and Sindh respectively.
• The ruins of Mohenjo-Daro were designated as a UNESCO World Heritage Site in 1980.

The correct answer is the Eighth Five Year plan.

• The Eighth five-year plan was launched after the inflation during 1990-91. It ran for a period of 5 years from 1992-1997.
• The main objective was to create employment, curb population growth, and to achieve overall human development.
• The major highlight of this plan was the modernisation of industries.
• The country achieved a growth of 6.8% against the target growth of 5.6%.

Twiddling in table tennis is the act of flipping your paddle so that the ball is played with the rubber on the other side to gain a competitive advantage.

Radius of base tent = r and area of its base is 38.5 cm² = πr²

Then r = √(12.25) = 3.5

Also conical volume = 1/3 π r² h=154

h = 12 and

l = √ h² + r²

l = √12² + 3.5²

 l = 12.5

Curved surface area = πrl = 137.50 cm²

Curved surface area of conical tent = Area of canvas = length × width = 137.50 cm²

Length = 137.50/width = 137.50/2 = 68.75

Let assume, A's 1 day's work = x and B's 1 day's work = y.

(A + B)'s 1 day's work = (x + y) = 1/15

∴ A + B in 5 days, completes 100/3% of work and remaining work i.e. 200/3% will be completed by B in 15 days.

So, No. of days for 100% of work completed by B = 45/2

∴ B's 1 day's work = y = 2/45

(A + B)'s 1 day's work = (x + y) =

⇒ x = 1/15 - 2/45 = 1/45

Days to complete the entire work for A = 45

Let monthly salary (in Rs.) = t

According to given information monthly spends (in %) on Clothing = 20% of income = 20t/100

Monthly spends (in %) on Education = 14% of income = 14t/100

Since the difference in monthly expenditure on Clothing and Education is Rs 9000 = (20t/100) - (14t/100)

t = 150000 = monthly salary (in Rs).

Now, saving = 10% of income = 15000

And expenditure on Bills = 8% of income = 12000

Difference (in Rs.) in monthly saving and monthly expenditure on Bills = 15000 - 12000 = 3000

Difference (in Rs.) in yearly saving and yearly expenditure on Bills = 12 × 3000 = 36000

$\frac{a}{2} = \frac{b}{3} = \frac{c}{4}$

a/b = 2/3 and c/b = 4/3

(a + b + c)/b = a/b + 1 + c/b = 2/3 + 1 + 4/3 = 3

Option A is correct answer.

Given:

In a mixture, milk and water are in ratio of 2 : 3. Some milk is added to the mixture because of which ratio of milk and water becomes 2 : 1.

Concept used:

Basic concept of addition and subtraction of quantity in the mixture.

Calculation:

Let quantity of total mixture = k

Quantity of milk = 2k/5 and Quantity of water in it = k - 2k/5

⇒ 3k/5

New ratio = 2 : 1

Let quantity of milk to be added further be x litres

Then, milk : water = (2k/5 + x) / (3k/5)

Now, = (2k/5 + x) / (3k/5) = 2/1

X = 4k/5

Quantity milk that was added as a percentage of initial mixture = (x/k) × 100 = 80%

∴ 80% of milk was added as a percentage of initial mixture.

Let the initial length, breadth respectively = l_1, b₁

Final length, breadth respectively = l_2, b₂

Length of a rectangle is increased by 50% we have l₁ = 1.5 l₂

To keeping the area the same,

l₁ × b₁ = l₂ × b₂

b₁ = 1.5 b₂

Percent its breadth should be reduced = [(b₂ - b₁) × 100]/ b₁ = $33\frac{1}{3}$

Total people for newspaper E = 20000 × 22% = 4400

From given ratio of male : female = 4 : 7

Let the no. of Male = 4e and No. of Female = 7e

4e + 7e = 4400

e = 400

 No. of Female reading newspaper E = 7e = 7 × 400 = 2800

Total people reading newspaper C = 20000 × 16% = 3200

From given ratio of male : female = 3 : 5

Let the no. of Male = 3c and No. of Female = 5c

3c + 5c = 3200

c = 400

 No. of Males for newspaper C = 3c = 3 × 400 = 1200

Difference of no. of Females for both newspaper E and C = 2800 - 1200 = 1600

 Required percent = (1600/1200) × 100 = 133.33

Calculation:

The distance traveled by each of them is to be made equal.

Distance traveled walking = Distance covered cycling.

Let after 8 hours of walking, A walk for x hours more before B catches up with him.

 Distance = Speed × Time

(8 + x)8 = 24x

x = 4

∴ B take 4 hours to catch up with A. Distance:

4 x 24 = 96 km.

Let monthly salary (in Rs.) = y

According to given information monthly spends (in %) on Fuel = 20% of income = 20y/100

Monthly spends (in %) on Bills = 8% of income = 8y/100

Since the difference in monthly expenditure on Fuel and Bills is Rs. 4800 = (20y/100) - (8y/100)

y = 400000 = monthly salary (in Rs).

Annual salary = Rs. 480000

Let total amount of income = x

Spends on:

Food = 3x/10, children's education = 2x/10

Remaining amount = x = 3x/10 - 2x/10 = x/2

∴ Expenditure on house rent = (x/2) × 60% = 3x/10

Now income left with him = 2x/10

∴ % income = 20%

∴ Option A is correct answer

According to solutions of above questions, No. of Female reading newspaper A and B are 2a = 2400 and 3b = 2400 which means both are equal (a = 1200 and b = 800)

∴ Option C is correct answer.

Formula used:

(a + b)² - (a-c)² = b² - c² + 2a (b + c)

Calculation:

Now, replacing the values with a= 1000, b = 4 and c = 2

We have, (1004)² - (998)² = 12012

Since given triangle is equilateral

So, the ratio of centroid on median 2 : 1 or PG : GA = 2 : 1

 (PG + GA) : (PG - GA) = 2 + 1/2 - 1 = 3 : 1

According to given information we have,

(A + B)/2 = (B + C)/2 - 15

A/2 = C/2 - 15

C = 65,

∴ A = 35

(sin y + cos y)/ (sin y - cos y) = 3

= (tan y + 1)/ (tan y - 1) = 3

tan y + 1 = 3tan y - 3

tan y = 2

Let monthly salary (in Rs) = x

According to given information monthly spends (in %) on saving = 10% of income

Also, monthly spends (in Rs.) on saving = 2400 = 10% of x

x = 24000

Let P₁ = x and P₂ = 3100 - x

Simple Interest =(P × R × T)/100

Where P is Principle amount, R is rate of interest, T is time in years.

Total annual interest = I₁ + I₂ = (8 × x × 1)/100 + [(3100 - x) × 6 × 1]/100

x = Rs. 1300

Given monthly spends on Fuel = 20% of monthly income = $\frac{{20; \times ;50000}}{{100}} = 10000$

∴ Option B is correct answer.

Let initial volume = l₁b₁h₁ and final volume = l₂b₂h₂

According to information, after increasing 20%

l₂ = 1.2 l₁ and b₂ = 1.2b₁

For the same volume we have,

l₁b₁h₁ = l₂b₂h₂ = (1.44) l₁b₁h₂

h₁ = (1.44) h₂

Percent of height reduced = (h₁ – h₂)/h₁ = 275/9% = $30\frac{5}{9}$%

Given:

If tan A = 5/9

Calculation:

[5 sin A + 9 cos A]/[5 sin A - 9 cos A]

Divide by cos A in numerator and dinominator 

= [5 tan A + 9]/[5 tan A - 9]

Also tan A = 5/9

⇒ [5(5/9) + 9]/(5(5/9) - 9]

⇒ 106/(- 56)

⇒ - 53/28

∴ [5 sin A + 9 cos A]/[5 sin A - 9 cos A] = -53/28

Let market price = 6x and cost price = 5x.

Discount = 15% = 6x × (15/100) = 18x/20

Selling Price = 6x - 18x/20 = 102x/20

Profit = S.P - C.P = 102x/20 - 5x = 2x/20

Profit% = [(Profit × 100)/Cost Price] = 2%

∴ Option C is correct answer.

Let radius of sphere = r and radius of conical bullet = R and height of bullet = h.

According to given information:

R = 2h and R= r/2        ----(i)

Also volume of sphere = 4/3 πr³and volume of Conical bullet = 1/3 πR²h

Let the total no. of bullets = y

Now we have, (volume of sphere) = y (volume of each conical bullet)

4/3 πr³= y 1/3 πR²h        ----(ii)

On equating and solving equations (i) and (ii) we get y = 64

∴ Option D is correct answer.

Let the O is the centre of the rectangle.

Area of ΔPQR is 48 cm² = 1/2 × PQ × QR

Area of ΔBCO = $\frac{1}{2} \times \frac{{PQ}}{2} \times \frac{{QR}}{2}$

Area of ΔBCD = 2 (area of ΔBCO)

Area of ΔBCD = $2\left( {\frac{1}{2} \times \frac{{PQ}}{2} \times \frac{{QR}}{2}} \right)$

Area of ΔBCD = 24 cm²

On putting the value of

√5 + √5 = 4.472, √2 + √8 = 4.242

√3 + √7 = 4.372, √2 + √8 = 4.242

√5 + √5 = 4.72, √3 + √7 = 4.372

Now we can see that all expressions are true for the above values.

∴ Option D is correct answer.

Given:

Copper by weight = 18% by weight of the total mixture

Calculation:

Let’s assume to total weight of the given mixture = 100 kg

⇒ Weight of copper = 18 kg

According to the unitary method,

For 18 kg of copper, we require 100 kg of mixture

⇒ 81 kg of copper is obtained from (100 × 81)/18 = 450 kg of mixture

∴ Option C is the correct answer

To check any no. P is prime or not we follow some steps as below:

Find a whole no. nearly greater the square root of P. And test weather P is divisible by any prime no. Less than K (Square root of that whole no.). If yes, P is not prime no otherwise P is a prime no.

Now, Square root of whole no. nearly greater than 337 is 19 and also the prime no. less 19 is 2,3,5,11,13,17. But here 337 is not divisible by any of them so, 337 is a prime no.

Factors of 12 are 1,2,3,4,6 and 12.

∴ 12 has has 6 positive factors.

32724 is divisible by 9, it’s true statement by divisibility rule of 9 (3 + 2 + 7 + 2 + 4) should also be Divisible by 9.

∴ Option D is correct answer.

108 = 2 × 2 × 3 × 3 × 3

Here we have two numbers (2 and 3) that are also prime number

∴ Option A is correct answer.

x + 1/x = 3

(x² + 1)/x = 3

(x2 + 1) = 3x      ----(i)

On putting the value from eq (i) in (x² - x + 1)/5x we get:

(x² - x + 1)/5x = (3x - x)/5x = 2/5

Given:

15 cos2θ + 17 sin2θ

Concept Used:

Minimum value of a sin2θ + b cos2 θ is b if b < a

Calculation:

Minimum value of 15 cos2θ + 17 sin2θ = 15

∴ The minimum value of 15 cos2θ + 17 sin2θ is 15.

a/4 = 1 + 3/a

a² = 4a + 12

a² - 4a - 12 = 0 

a = 6, -2

a³ = 216 or -8

Expenditure on Household items = 28% of 65000= 18200

And Clothing = 20% of 65000 = 13000

Now the difference (in Rs) between expenditure on Household items and Clothing

18200 - 13000 = 5200

∴ Option A is correct answer.

The formula of simple interest is as below.

SI = (P × R × T)/100

Where SI is simple interest.

P is Principle amount, R is rate of interest, T is time in years.

From question, money becomes 3 times, it means, interest itself is Twice of P here. So,

2P = (P × R × 50)/100

R = 4%

Given:

x3 + 6x2 + 12x = 19

Concept used:

Ax² + 2x = 5

Coefficient of x² = A, x = 2

Calculation:

x3 + 6x2 + 12x = 19

According to the question,

The coefficient of x³ = 1

∴ The value of x³ is 1.

Since given triangle is equilateral

So, the centroid median in ratio as 2 : 1 or PG : GD = 2 : 1

Let GD = x

Then PG = 2x = 24

x = 12

∴ 2x + x = PD

3x = PD = 36cm

cos 37° = a/b

sin 37° = √(b² - a²)/b        ----(i)

cosec37° - cos53° = 1/sin 37° - sin 37°

(1 - sin² 37˚)/ sin 37= a²/b√(b² - a²) (from (i)

GIVEN:

CP : SP = 13 : 9

Loss = Rs. 320

CALCULATION:

Let assume C.P = 13x and S.P. = 9x

The sum of C.P and S.P. = 13x + 9x = 22x      ----(i)

Also given loss incurred on article = 320 Rs. = 13x - 9x

⇒ x = 80

From eq. (i)

The sum (in Rs) of cost and selling prices = 1760 Rs.

∴ Option D is correct answer

Selling price of one apple = 60/64

now cost price of 1 apple = S.P.× (100/125) = 3/4 

for loss 40% new selling price = C.P.× (60/100) = 9/20

Apples sold for Rs. 36 = (20/9)×36 = 80

sin (A + B) - cos (A -B) = sinA.cosB + cosA.sinB - cosA.cosB - sinA.sinB

On putting these values we get sin (30 + x) - cos (60 - x) = 0

Since, $\sqrt[3]{8} = 2,\sqrt 4 = 2,;\sqrt[6]{{64}} = 2$

∴ Option D is correct answer.

Total people reading newspaper A = 20000 × 30% = 6000

From given ratio of male : female = 3 : 2

Let the no. of Male = 3a and No. of Female = 2a

3a + 2a = 6000

a = 1200

∴ Number of Female reading newspaper A = 2a = 2 × 1200 = 2400

∴ Option C is correct answer.

Q takes 10 days to complete the total amount of work

∴ In 1 day the amount of work completed by Q would be = 1/10

Also, according to information If Q complete the work with 100% efficiency then P complete that same work with (100 + 20 = 120)% (Note : P is 20% more efficient than Q )

Now, if Q complete 1/10 amount of work in 1 day then the amount of work done by P = 100/12

Number of days to complete that work for P is 100/12 = 25/3 days

Since a + b = 6x

a = 6x - b

[x/(3x - b)] - [x/(b - 3x)] = 0

∴ option 2 is correct.

Total people reading newspaper B = 20000 × 20% = 4000

From given ratio of male : female = 2 : 3

Let the number of male = 2b and Number of Female = 3b

2b + 3b = 4000

b = 800

No. of Male for newspaper B = 2b = 2 × 800 = 1600

Total people reading newspaper D = 20000 × 12% = 2400

From given ratio of male : female = 1 : 2

Let the no. of Male = d and No. of Female = 2d

d + 2d = 2400

d = 800

 No. of Male for newspaper D = d = 800

Now, required difference = 1600 - 800 = 800

minimum distance between the chords = (a - b)/2 = (32 - 24)/2 = 4  

x² + 16 = -4x

x² + 16 + 4x = 0

x³ + 16x + 4x² = 0

Adding 64 to both sides

x³ + 16x + 4x² + 64 = 64

x³ - 64 = -(16x + 4x² + 64)      ----(1)

Now from given condition

x² + 16 = -4x

16x + 4x² + 64 = 0        ----(2)

From (1) and (2)

We have x³ - 64 = 0

Note: This question is asked in the SSC previous year exam and solution is given accordingly.

Given:

first 10 natural numbers.

Concept used:

Sum of squares of first n natural Number = [n (n + 1) (2n + 1)]/6

Calculation:

Sum of squares of first n natural Number = [10(10 + 1)(2 × 10 + 1)]/6 = 385

∴ Average of squares of first 10 natural numbers = sum of squares/10 = 385/10 

Average of squares of first 10 natural numbers = 38.5

∴ The average of squares of first 10 natural numbers is 38.5.

**

Let we draw two perpendicular lines on BC from point A and D and meet at points E and F respectively.

FC = BE = (18 - 10)/2 = 4

Area of ABE = Area of DCF = ½ × FC × h (h = height)

Area of ABCD = Area AEFD + 2(Area of DCF)

70 = 10 × h + 2(½ × 4 × h) (FC = 4)

H = 5 cm

Now applying Pythagoras theorem in triangle DCF

h = 5, and FC = 4 then CD = √41

Alternate Method Area of trapezium = 1/2 (sum of the parallel side)× (distance between them)

70 = 1/2(10 +18) (H)

H = 5cm

Now applying Pythagoras theorem in triangle DCF

h = 5, and FC = 4

CD = √41cm

Since we have tangents on points P and Q, ∠APO = 90 and ∠OQA = 90°

And ∠POQ = 120° given.

In quadrilateral POQA,

∠POQ + ∠PAQ + ∠APO + ∠OQA = 360°

∠PAQ = 60°

Similarly in triangle POA,

We have ∠PAO = 30°

i.e. ∠PAQ = 2∠PAO

Time required to cover 90 km distance with rate 36km/hr = 90/36 = 2 hr 30 min

Also, if vehicle stops for 12 min. at the end of every 14^th km then, then vehicle has to stop total 6

time for 12 min. Total stopping time = 6 × 12 = 72 min(s) = 1 hr 12min(s)

Total time required = 3 hours 42 minutes

Since, here discount is in % value

Let assume the selling price = x

According to Option

I) final price = 0.25x

II) final price = 0.24x

III) final price = 0.21x

IV) final price = 0.225x

Then, we have lesser final price or best discount in option III only.

∴ Option D is correct answer.

The one word for the given sentence is 'Horizon'.

Key Points

• Let's have a look at the meaning of the marked option: 
• Horizon- "the line at the farthest place that you can see, where the sky seems to touch the land or sea". (सबसे दूर की रेखा जो आप देख सकते हैं, जहाँ आकाश भूमि या समुद्र को छूता हुआ प्रतीत होता है)
• Let's have a look at the meaning of the other given options:
• Nadir- "the worst moment, or the moment of least hope and least achievement". (सबसे बुरा क्षण, या कम से कम आशा और कम से कम उपलब्धि का क्षण)
• Zenith- "the highest point reached by a heavenly body (= any object existing in space, especially a planet, or the sun) as it travels around, or appears to travel around, another body" (एक स्वर्गीय पिंड द्वारा पहुँचा गया उच्चतम बिंदु, जब वह चारों ओर यात्रा करता है, या किसी अन्य पिंड के चारों ओर यात्रा करता प्रतीत होता है)
• Trivet- "a metal stand that you put on a table to protect its surface from hot dishes or pans". (एक धातु स्टैंड जिसे आप मेज पर रख देते हैं ताकि उसकी सतह को गर्म बर्तन या धूपदान से बचाया जा सके)
• Hence, we find that Horizon is the correct one-word substitute for the given meanings.
• Therefore, the correct answer is Option 3).

The meanings of the words are:

Quadragenarian => a person who is between 40 and 49 years old.

Quadilateral=> a four-sided figure.

Quadrangle=> a square or rectangular space or courtyard enclosed by buildings.

Quadruped=> an animal which has four feet, especially an ungulate mammal.

Thus option 3 is the correct answer.

The meanings of the words are:

Carnivorous=> one who feeds on flesh

Baccivorous=> feeding on berries

Aurivorous=> gold-devouring

Piscivorous=> One who lives on fish

Thus option 4 is the correct answer.

The meanings of the words are:

Euthanasia=> the painless killing of a patient suffering from an incurable and painful disease or in an irreversible coma.

Sty=> pigsty

Canicide=> the killing of a dog

Suicide=> killing of one ownself

Thus option 1 is the correct answer.

The meanings of the words are:

Amateur=> not well experienced

Inanimate=> lifeless

Alien=> unfamiliar and disturbing or distasteful.

Amnesty=> pardon

Thus option 2 is the correct answer.

The word here should be such that is created or comes into existence with time and not born. ‘Nuance’ which means ‘a subtle difference in or shade of meaning, expression, or sound; does not fit here. The word ‘coinage’ means ‘coins collectively or the invention of a new word or phrase.’ The word ‘cliché’ means ‘a phrase or opinion that is overused and betrays a lack of original thought’ and fits here conveying the meaning that it is made or deliberately used and not comes on its own. The word ‘current’ means ‘ongoing’ and makes no sense here. Thus option 3 is the correct answer

The meanings of the words are:

Epigram=> a short saying or poem that expresses an idea in a clever, funny way

Epitaph=> a phrase or form of words written in memory of a person who has died, especially as an inscription on a tombstone

Epilogue=> a section or speech at the end of a book or play that serves as a comment on or a conclusion to what has happened

Epicenter=> the point on the earth's surface vertically above the focus of an earthquake

Thus option 1 is the correct answer as it states what the remark should be like.

The saying receives a wide circulation thus the word ‘vague’ which means ‘unclear’ cannot fit here. The word ‘apt’ means ‘appropriate’ and justifies how the saying receives circulation. The word ‘ingenuine’ means ‘unreal’ and ‘emotional’ which means ‘relating to a person's emotions‘ do not fit here.