CBSE Sample Papers for Class 10 Social Science Paper 7

CBSE Sample Papers for Class 10 Social Science Paper 7 are part of CBSE Sample Papers for Class 10 Social Science. Here we have given CBSE Sample Papers for Class 10 Social Science Paper 7.

CBSE Sample Papers for Class 10 Social Science Paper 7

BoardCBSE
ClassX
SubjectSocial Science
Sample Paper SetPaper 7
CategoryCBSE Sample Papers

Students who are going to appear for CBSE Class 10 Examinations are advised to practice the CBSE sample papers given here which is designed as per the latest Syllabus and marking scheme as prescribed by the CBSE is given here. Paper 7 of Solved CBSE Sample Paper for Class 10 Social Science is given below with free PDF download solutions.

Time: 3 Hours
Maximum Marks: 80

General Instructions

  1. The question paper has 27 questions in all. All questions are compulsory.
  2. Marks are indicated against each question.
  3. Questions from serial number 1 to 7 are very short answer questions. Each question carries 1 mark.
  4. Questions from serial number 8 to 18 are 3 marks questions. Answer of these questions should not exceed 80 words each.
  5. Questions from serial number 19 to 25 are 5 marks questions. Answer of these questions should not exceed 100 words each.
  6. Question number 26 and 27 are map questions of 2 marks from History and 3 marks from Geography. After completion, attach the maps inside the answer book.

QUESTIONS

Question 1.
What was ‘Hosay’?
OR
Who devised Spinning jenny? When?
OR
What do you mean by Chartism and the 10-hour movement?

Question 2.
What were the Biliotheque Bleue’?
OR
Name the earliest Marathi novel? Who wrote it?

Question 3.
Identify any two major alliances which contested in the 2004 Parliamentary Elections of India?

Question 4.
Name the local names of the alluvial soils found in the piedmont plains?

Question 5.
What are renewable resources? Give example.

Question 6.
Define GDP.

Question 7.
What are the functions of money?

Question 8.
Write short note on Rinderpest.
OR
Explain the role of the ‘gomasthas’ and ‘jobbers’ in the history of cotton textile industry of India.
OR
Narrate the information you could draw from the writings of Henry Mayhew on crime in London by the end of 19th century and state the steps taken by the government to check crime.

Question 9.
Why the Roman Catholic Church decide to maintain an Index of Prohibited Books from 1558?
OR
‘Stories in prose were not new to India’. Support your answer with three examples.

Question 10.
How do you differentiate federalism from a Unitary form of government?

Question 11.
“Every social difference does not lead to social division”. Explain with suitable example.

Question 12.
“The leaders of the Sinhala community sought to secure dominance over government by virtue of their majority”. Comment.

Question 13.
Why are dams referred to as multi-purpose river valley projects? Briefly explain these giving two examples of multi-purpose projects.

Question 14.
What is plantation farming? State two characteristics of plantation farming. Also mention two examples of plantation crops.

Question 15.
“Consumers are exploited in the marketplace in various ways”. Discuss with example.

Question 16.
Classify the countries according to the World Bank criterion.

Question 17.
Write a short note on Consumers International.

Question 18.
Define what is trade barrier? Why Indian government put various barriers in foreign trade and investments before 1991?

Question 19.
What marked the beginning of the Civil Disobedience Movement? How was this movement different from the Non-Cooperation Movement?

Question 20.
“The Habsburg Empire that ruled over Austria-Hungary, for example, was a patchwork of many different regions and peoples”. Justify.
OR
Describe any four steps taken by the French for the development of the Mekong Delta Region’.

Question 21.
“Ours is still a male dominated, Patriarchal society. Women face disadvantage, discrimination and oppression in various ways.” Discuss.

Question 22.
Suggest a few broad guidelines that should be kept in mind while devising ways and means for political reforms in India.

Question 23.
What are Golden Quadrilateral Super Highways? What is their major objective? Explain Golden Quadrilateral Super Highways.

Question 24.
When and where the first successful textile mill was established? Explain the three reasons that led to the location of cotton textile industry in Gujarat and Maharashtra initially.

Question 25.
Study the data given in the table and answer the questions that follow :

Sector Organised Unorganised Total (in million)
Primary 2   242
Secondary 9 54 63
Tertiary 17 76 93
Total 28    
Total in Percentage     100%
  1. Which is the most important sector that provides most jobs to the people?
  2. What is the number of persons engaged in the unorganised sector?
  3. Why is this unorganised sector more important? Give one reason.
  4. Which is the most important organised sector? Give one reason.

Question 26.
Two features A and B are marked on the given political outline map of India:

Identify these features with the help of the following information and write their correct names on the lines marked in the map :

A. The place where Gandhji led the cotton mill workers’ agitation.
B. The place where INC Session took place in 1927

OR

Locate and label on the same map given:

  1. Champaran-indigo planters’ agitation in 1916.
  2. Calcutta-INC Session September 1920.

Question 27.
On the given same political outline map of India locate and label/identify the type of soil the following with appropriate symbols:

  1. Identify the type of soil in the shaded area on map.
  2. Largest producer of ragi among Indian states,
  3. Hirakud Dam

ANSWERS

Answer 1.
In Trinidad the annual Muharram procession was transformed into a riotous carnival called ‘Hosay’ (for Imam Hussain) in which workers of all races and religions joined.
OR
Spinning Jenny was devised by James Hargreaves in 1764.
OR
Two political movements of London in the 19th Century were called Chartism (a movement demanding the vote for all adult males) and the 10-hour movement (limiting hours of work in factories).

Answer 2.
In France, were present the ‘Biliotheque Bleue’, which were low-priced small books printed on poor quality paper, and bound in cheap blue covers.
OR
The earliest novel in Marathi was Baba Padmanji’s Yamuna Paryatan (1857).

Answer 3.
Two major alliances in 2004 parliamentary elections- the National Democratic Alliance, the United Progressive Alliance and the Left Front.

Answer 4.
Duars, Chos and Terai.

Answer 5.
Groundwater is an example of renewable resources. These resources are replenished by nature as in the case of crops and plants.

Answer 6.
The value of final goods and services produced in each sector during a particular year provides the total production of the sector for that year. And the sum of production in the three sectors gives what is called the Gross Domestic Product (GDP) of a country. It is the value of all final goods and services produced within a country during a particular year. GDP shows how big the economy is.

Answer 7.

  1. Money acts as a medium of exchange in goods and services and in payment of debts.
  2. Money is used as a measure of value.
  3. It is a Standard of Demand Payments.
  4. It acts as store of value.

Answer 8.
(i) A devastating cattle disease, Rinderpest arrived in Africa in the late 1880s. It was carried by infected cattle imported from British Asia to feed the Italian soldiers invading Eritrea in East Africa.

(ii) Entering Africa in the east, rinderpest moved west Tike forest fire’, reaching Africa’s Atlantic coast in 1892. It reached the Cape (Africa’s southernmost tip) five years later. Along the way rinderpest killed 90 per cent of the cattle.

(iii) The loss of cattle destroyed African livelihoods. Planters, mine owners and colonial governments now successfully monopolised what scarce cattle resources remained, to strengthen their power and to force Africans into the labour market. Control over the scarce resource of cattle enabled European colonisers to conquer and subdue Africa.

OR

The ‘gomasthas’: The East India Company tried to eliminate the existing traders and brokers connected with the cloth trade, and establish a more direct control over the weaver. It appointed a paid servant called the gomastha to supervise weavers, collect supplies, and examine the quality of cloth.

Jobber:

(i) Getting jobs was always difficult, even when mills multiplied and the demand for workers increased. The numbers seeking work were always more than the jobs available. Entry into the mills was also restricted. Industrialists usually employed a jobber to get new recruits.

(ii) Very often the jobber was an old and trusted worker. He got people from his village, ensured them jobs, helped them settle in the city and provided them money in times of crisis. The jobber therefore became a person with some authority and power. He began demanding money and gifts for his favour and controlling the lives of workers.

OR
In the mid-nineteenth century, Henry Mayhew wrote about London labour, and compiled long lists of those who made a living from crime.

(i) He listed many of them as ‘criminals’ who were in fact poor people who lived by stealing lead from roofs, food from shops, lumps of coal, and clothes drying on hedges.

(ii) There were others who were more skilled at their trade, expert at their jobs. There were cheats and tricksters, pickpockets and petty thieves crowding the streets of London.

Steps taken:

(i) In an attempt to discipline the population, the authorities imposed high penalties for crime.

(ii) Offered work to those who were considered the ‘deserving poor’.

Answer 9.
(i) Print and popular religious literature stimulated many distinctive individual interpretations of faith even among little-educated working people.

(ii) In the sixteenth century, Menocchio, a miller in Italy, began to read books that were available in his locality. He reinterpreted the message of the Bible and formulated a view of God and Creation that enraged the Roman Catholic Church and began its inquisition to repress heretical ideas. Menocchio was hauled up twice and ultimately executed.

(iii) The Roman Church, troubled by such effects of popular readings and questionings of faith, imposed severe controls over publishers and booksellers and began to maintain an Index of Prohibited Books from 1558.

OR

(i) Banabhatta’s Kadambari, written in Sanskrit in the seventh century, is an early example.

(ii) The Panchatantra.

(iii) There was also a long tradition of prose tales of adventure and heroism in Persian and Urdu, known as ‘dastan’.

Answer 10.
Federalism:

  1. Is a system of government in which power is divided between the central authority and various constituent units of the country. Federation may have government for the entire nation and government at the levels of provinces or states.
  2. Both these levels of the government enjoy their power independent of the others. Powers of each level is specified in the Constitution.

A unitary government:

  1. Has one level of government or the sub-units are subordinate to the central government.
  2. The central government can pass orders to the provincial or the local government.

Answer 11.

  1. Every social difference does not lead to social division. Social differences divide similar people from one another, but they also unite very different people.
  2. People belonging to different social groups share differences and similarities cutting across the boundaries of their groups

Example: Carlos and Smith were similar in one way (both were African-American) and thus different from Norman who was white. But they were also all similar in other ways – they were all athletes who stood against racial discrimination.

Answer 12.

  1. The democratically elected government adopted a series of Majoritarian measures to establish Sinhala supremacy.
  2. In 1956, an Act was passed to recognize Sinhala as the only official language, thus disregarding Tamil.
  3. The governments followed preferential policies that favoured Sinhala applicants for university positions and government jobs.
  4. A new constitution stipulated that the state shall protect and foster Buddhism.
  5. All these government measures, coming one after the other, gradually increased the feeling of alienation among the Sri Lankan Tamils.

Answer 13.
Large dams are referred to as multipurpose river valley projects where the many uses of the impounded water are integrated with one another as:

Irrigation, electricity generation, water supply for domestic and industrial uses, flood control, recreation, inland navigation and fish breeding.

(a) In Sutlej-Beas river basin, the Bhakra-Nangal project water is being used both for hydel power production and irrigation.
(b) Similarly, Hirakund project in the Mahanadi basin integrates conservation of water with flood control.

Answer 14.
Plantation farming: In this type of farming, a single crop is grown on a large area.

Characteristics:

  1. The plantation has an interface of agriculture and industry
  2. Use large tracts of land and capital intensive inputs with manual labour.

Examples of plantation crops: Tea, coffee, rubber, sugarcane, banana etc.

Answer 15.
Sometimes traders indulge in unfair trade practices such as when shopkeepers weigh less than what they should or when traders add charges that were not mentioned before, or when adulterated/defective goods are sold.

Answer 16.
(i) In World Development Reports, brought out by the World Bank, this criterion is used in classifying countries.

(ii) Countries with per capita income of US$ 12616 per annum and above in 2012, are called rich countries and those with per capita income of US$ 1035 or less are called low-income countries.

(iii) India comes in the category of low middle income countries because its per capita income in 2012 was just US$ 1530 per annum. The rich countries, excluding countries of Middle East and certain other small countries are generally called developed countries.

Answer 17.
(i) In 1985 United Nations adopted the UN Guidelines for Consumer Protection. This was a tool for nations to adopt measures to protect consumers and for consumer advocacy groups to press their governments to do so.

(ii) At the international level, this has become the foundation for consumer movement.

(iii) Today, Consumers International has become an umbrella body to over 220 member organisations from over 115 countries.

Answer 18.
(i) Tax on imports is an example of trade barrier. It is called a barrier because some restriction has been set up.

(ii) Governments can use trade barriers to increase or decrease (regulate) foreign trade and to decide what kinds of goods and how much of each, should come into the country.

(iii) The Indian government, after Independence, had put barriers to foreign trade and foreign investment. This was considered necessary to protect the producers within from foreign competition.

(iv) Industries were just coming up in the 1950s and 1960s, and competition from imports at that stage would not have allowed these industries to come of only essential items such as machinery, fertilizers, petroleum etc.

Answer 19.
(i) On 6 April Gandhi reached Dandi, and ceremonially violated the law, by picking up a handful of salt. This marked the beginning of the Civil Disobedience Movement.

(ii) People were now asked not only to refuse cooperation with the British, as they had done in 1921-22, but also to break colonial laws. Thousands in different parts of the country broke the salt law, manufactured salt and demonstrated in front of government salt factories.

(iii) As the movement spread, foreign cloth was boycotted, and liquor shops were picketed. Peasants refused to pay revenue and chaukidari taxes, village officials resigned, and in many places forest people violated forest laws – going into Reserved Forests to collect wood and graze cattle.

Answer 20.
(i) It included the Alpine regions – the Tyrol, Austria and the Sudetenland – as well as Bohemia, where the aristocracy was predominantly German-speaking. It also included the Italian-speaking provinces of Lombardy and Venetia.

(ii) In Hungary, half of the population spoke Magyar while the other half spoke a variety of dialects. In Galicia, the aristocracy spoke Polish.

(iii) Besides these three dominant groups, there also lived within the boundaries of the empire, a mass of subject peasant peoples – Bohemians and Slovaks to the north, Slovenes in Camiola, Croats to the south, and Roumans to the east in Transylvania.

(iv) Such differences did not easily promote a sense of political unity. The only tie binding these diverse groups together was a common allegiance to the emperor.

OR

(i) The French began by building canals and draining lands in the Mekong delta to increase cultivation.

(ii) The vast system of irrigation works – canals and earthworks – built mainly with forced labour, increased rice production and allowed the export of rice to the international market.

(iii) Vietnam exported two-thirds of its rice production and by 1931 had become the third largest exporter of rice in the world.

(iv) This was followed by infrastructure projects to help transport goods for trade, move military garrisons and control the entire region. Construction of a trans-Indo-China rail network that would link the northern and southern parts of Vietnam and China was begun.

Answer 21.
(i) The literacy rate among women is only 54 per cent compared with 76 per cent among men. Similarly, a smaller proportion of girl students go for higher studies. But the girls drop out because parents prefer to spend their resources for their boys’ education rather than spending equally on their sons and daughters.

(ii) The proportion of women among the highly paid and valued jobs is still very small. On an average an Indian woman works one hour more than an average man every day. Yet much of her work is not paid and therefore often not valued.

(iii) The Equal Wages Act provides that equal wages should be paid to equal work. However in almost all areas of work, from sports and cinema, to factories and fields, women are paid less than men, even when both do exactly the same work.

(iv) In many parts of India, parents prefer to have sons and find ways to have the girl child aborted before she is bom. Such sex-selective abortion led to a decline in child sex ratio (number of girl children per thousand boys) in the country to merely 927. This ratio has fallen below 850 or even 800 in some places.

(v) There are reports of various kinds of harassment, exploitation and violence against women. They are not even safe even within their own home from beating, harassment and other forms of domestic violence.

Answer 22.
(i) Reforms through Legal Ways: Law has an important role to play in political reform. Carefully devised changes in law can help to discourage wrong political practices and encourage good ones. Example: A change in rules for LBW decisions helped to reduce negative batting tactics. But no one would ever think that the quality of cricket could be improved mainly through changes in the mles.

(ii) Any legal change must carefully look at what results it will have on politics. Sometimes the results may be counter-productive. Example: Many states have banned people who have more than two children from contesting panchayat elections. This has resulted in denial of democratic opportunity to many poor and women, which was not intended. Another example is RTI.

(iii) Reform through ‘Political Practices’: Democratic reforms are to be brought about principally through political practice. The most important concern should be to increase and improve the quality of political participation by ordinary citizens.

(iv) Reform measures that rely on democratic movements, citizens’ organisations and the media are likely to succeed in reforming political system. The main focus of political reforms should be on ways to strengthen democratic practices.

Answer 23.
(i) The government has launched a major road development project linking Delhi-Kolkata- Chennai-Mumbai and Delhi by six-lane Super Highways.

(ii) The North-South corridors linking Srinagar (Jammu & Kashmir) and Kanyakumari (Tamil Nadu), and East-West Corridor connecting Silcher (Assam) and Porbander (Gujarat) are part of this project.

(iii) The major objective of these Super Highways is to reduce the time and distance between the mega cities of India.

(iv) The National Highway Authority of India (NHAI) implements and maintains these super highways.

Answer 24.
Successful location: Mumbai, 1854

Factors responsible for location of cotton textile industry in Gujarat and Maharashtra:

(i) Availability of raw cotton: This region predominantly located in the black soil. Therefore, good quality of cotton was easily available.

(ii) Well developed transportation network: This region was well connected with efficient network of roads and railways. It got the benefit of port facilities also.

(iii) Market: There was a huge demand for cotton goods in and around this region. Therefore, this industry concentrated in and around Gujarat and Maharashtra.

Answer 25.
(i) Primary-Agricultural Sector

(ii) 370 million

(iii) Agricultural Sector is most important unorganised sector because the unorganised sector mostly comprises of landless agricultural labourers, small and marginal farmers. Nearly 80 per cent of rural households in India are in small and marginal farmer category. These farmers need to be supported through adequate facility for timely delivery of seeds, agricultural inputs, credit, storage facilities and marketing outlets. Employment is more production is less.

(iv) Tertiary Sector: Employment is less and production is less. Also it produces ‘services’ rather than ‘goods’.

Answer 26.

CBSE Sample Papers for Class 10 Social Science Paper 7 1

Answer 27.

CBSE Sample Papers for Class 10 Social Science Paper 7 2

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NCERT Solutions for Class 9 Maths Chapter 12 Constructions Ex 12.2

NCERT Solutions for Class 9 Maths Chapter 12 Constructions Ex 12.2 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 12 Constructions Ex 12.2.

Board CBSE
Textbook NCERT
Class Class 9
Subject Maths
Chapter Chapter 12
Chapter Name Constructions
Exercise Ex 12.2
Number of Questions Solved 5
Category NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 12 Constructions Ex 12.2

Question 1.
Construct a ∆ ABC in which BC = 7 cm, ∠B = 75° and AB + AC = 13 cm.
Solution:
Given that, in ∆ ABC, BC = 7 cm, ∠B = 75° and AS + AC = 13 cm
Steps of construction

  1. Draw the base BC = 7 cm
    NCERT Solutions for Class 9 Maths Chapter 12 Constructions Ex 12.2 img 1
  2. At the point 6 make an ∠XBC = 75°.
  3. Cut a line segment BD equal to AB + AC = 13 cm from the ray BX.
  4. Join DC.
  5. Make an ∠DCY = ∠BDC.
  6. Let CY intersect BX at A.
    Then, ABC is the required triangle.

Question 2.
Construct a ∆ ABC in which BC = 8 cm, ∠B = 45° and AB – AC = 35 cm.
Solution:
Given that, in ∆ ABC,
BC = 8 cm, ∠B = 45°and AB – AC = 3.5 cm
NCERT Solutions for Class 9 Maths Chapter 12 Constructions Ex 12.2 img 2
Steps of construction

  1. Draw the base BC = 8 cm
  2. At the point B make an ∠XBC = 45°.
  3. Cut the line segment BD equal to AB – AC = 3.5 cm from the ray BX.
  4. Join DC.
  5. Draw the perpendicular bisector, say PQ of DC.
  6. Let it intersect BX at a point A
  7. Join AC.

Question 3.
Construct a ∆ ABC in which QR = 6 cm, ∠Q = 60° and PR – PQ = 2 cm.
Solution:
Given that, in ∆ ABC, QR = 6 crn ∠Q = 60° and PR – PQ = 2 cm
Steps of construction

  1. Draw the base QR = 6 cm
  2. At the point Q make an ∠XQR = 60°.
  3. Cut line segment QS = PR- PQ (= 2 cm) from the line QX extended on opposite side of line segment QR.
  4. Join SR.
  5. Draw the perpendicular bisector LM of SR.
  6. Let LM intersect QX at P.
  7. Join PR.
    NCERT Solutions for Class 9 Maths Chapter 12 Constructions Ex 12.2 img 3

Question 4.
Construct a ∆ XYZ in which ∠Y = 30°, ∠Y = 90° and XY + YZ + ZX = 11 cm.
Solution:
Given that, in ∆XYZ ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11cm
NCERT Solutions for Class 9 Maths Chapter 12 Constructions Ex 12.2 img 4
Steps of construction

  1. Draw a line segment BC = XY + YZ + ZX = 11 cm
  2. Make ∠LBC = ∠Y = 30° and ∠MCB = ∠Z = 90°.
  3. Bisect ∠LBC and ∠MCB. Let these bisectors meet at a point X.
  4. Draw perpendicular bisectors DE of XB and FG of XC.
  5. Let DE intersect BC at Y and FC intersect BC at Z.
  6. Join XY and XZ.
    Then, XYZ is the required triangle.

Question 5.
Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm.
Solution:
Given that, in A ABC, base BC = 12 cm, ∠B = 90° and AB + BC= 18 cm.
Steps of construction

  1. Draw the base BC = 12 cm
  2. At the point 6, make an ∠XBC = 90°.
  3. Cut a line segment BD = AB+ AC = 18 cm from the ray BX.
  4. Join DC.
  5. Draw the perpendicular bisector PQ of CD to intersect SD at a point A

Join AC.
Then, ABC is the required right triangle.
NCERT Solutions for Class 9 Maths Chapter 12 Constructions Ex 12.2 img 5

NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6

NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6.

Board CBSE
Textbook NCERT
Class Class 9
Subject Maths
Chapter Chapter 11
Chapter Name Circles
Exercise Ex 11.6
Number of Questions Solved 10
Category NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6

Question 1.
Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.
Solution:
Given: Two circles with centres O and O’ which intersect each other at C and D.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6 img 1
To prove: ∠OCO’ = ∠ODO’
Construction: Join OC, OD, O’C and O’D
Proof: In ∆ OCO’and ∆ODO’, we have
OC = OD (Radii of the same circle)
O’C = O’D (Radii of the same circle)
OO’ = OO’ (Common)
∴ By SSS criterion, we get
∆ OCO’ ≅ ∆ ODO’
Hence, ∠OCO’ = ∠ODO’ (By CPCT)

Question 2.
Two chords AB and CD of lengths 5 cm and 11 cm, respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 cm, find the radius of the circle.
Solution:
Let O be the centre of the given circle and let its radius be cm.
Draw ON ⊥ AB and OM⊥ CD since, ON ⊥ AB, OM ⊥ CD and AB || CD, therefore points N, O, M are collinear.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6 img 2
Let ON = a cm
∴ OM = (6 – a) cm
Join OA and OC.
Then, OA = OC = b c m
Since, the perpendicular from the centre to a chord of the circle bisects the chord.
Therefore, AN = NB= 2.5 cm and OM = MD = 5.5 cm
In ∆OAN and ∆OCM, we get
OA2 = ON2 + AN2
OC2 = OM2 + CM2
⇒ b2 = a2 + (2.5)2
and, b2 = (6-a)2 + (5.5)2 …(i)
So, a2 + (2.5)2 = (6 – a)2 + (5.5)2
⇒ a2 + 6.25= 36-12a + a2 + 30.25
⇒ 12a = 60
⇒ a = 5
On putting a = 5 in Eq. (i), we get
b2 = (5)2 + (2.5)2
= 25 + 6.25 = 31.25
So, r = \( \sqrt{31.25} \) = 5.6cm (Approx.)

Question 3.
The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre ?
Solution:
Let PQ and RS be two parallel chords of a circle with centre O such that PQ = 6 cm and RS = 8 cm.
Let a be the radius of circle.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6 img 3
Draw ON ⊥ RS, OM ⊥ PQ. Since, PQ || RS and ON ⊥ RS, OM⊥ PQ, therefore points 0,N,M are collinear.
∵ OM = 4 cm and M and N are the mid-points of PQ and RS respectively.
PM = MQ = \(\frac { 1 }{ 2 }\) PQ = \(\frac { 6 }{ 2 }\) = 3 cm
and RN = NS = \(\frac { 1 }{ 2 }\) RS = \(\frac { 8 }{ 2 }\) = 4 cm
In ∆OPM, we have
OP2 = OM2 + PM2
⇒ a2 =42 + 32 = 16 + 9 = 25
⇒ a = 5
In ∆ORN, we have
⇒ OR2 = ON2 + RN2
⇒ a2 = ON2 + (4)2
⇒ 25 = ON2 + 16
⇒ ON2 = 9
⇒ ON = 3cm
Hence, the distance of the chord PS from the centre is 3 cm.

Question 4.
Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that ∠ABC is equal to half the difference of the angles subtended by the chords AC and DE at the centre.
Solution:
Since, an exterior angle of a triangle is equal to the sum of the interior opposite angles.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6 img 4
∴ In ∆BDC, we get
∠ADC = ∠DBC + ∠DCB …(i)
Since, angle at the centre is twice at a point on the remaining part of circle.
∴ ∠DCE = \(\frac { 1 }{ 2 }\) ∠DOE
⇒ ∠DCB = \(\frac { 1 }{ 2 }\) ∠DOE (∵ ∠DCE = ∠DCB)
∠ADC = \(\frac { 1 }{ 2 }\) ∠AOC
∴ \(\frac { 1 }{ 2 }\) ∠AOC = ∠ABC + \(\frac { 1 }{ 2 }\) ∠DOE (∵ ∠DBC = ∠ABC)
∴ ∠ABC = \(\frac { 1 }{ 2 }\) (∠AOC – ∠DOE)
Hence, ∠ABC is equal to half the difference of angles subtended by the chords AC and DE at the centre.

Question 5.
Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonals.
Solution:
Given: PQRS is a rhombus. PR and SQ are its two diagonals which bisect each other at right angles.
To prove: A circle drawn on PQ as diameter will pass through O.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6 img 5
Construction: Through O, draw MN || PS and EF || PQ.
Proof : ∵ PQ = SR ⇒ \(\frac { 1 }{ 2 }\) PQ = \(\frac { 1 }{ 2 }\) SR
So, PN = SM
Similarly, PE = ON
So, PN = ON = NQ
Therefore, a circle drawn with N as centre and radius PN passes through P, O, Q.

Question 6.
ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Prove that AE = AD.
Solution:
Since, ABCE is a cyclic quadrilateral, therefore
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6 img 6
∠AED+ ∠ABC= 180°
(∵ Sum of opposite angle of a cyclic quadrilateral is 180°) .. .(i)
∵ ∠ADE + ∠ADC = 180° (EDC is a straight line)
So, ∠ADE + ∠ABC = 180°
(∵ ∠ADC = ∠ABC opposite angle of a || gm).. .(ii)
From Eqs. (i) and (ii), we get
∠AED + ∠ABC = ∠ADE + ∠ABC
⇒ ∠AED = ∠ADE
∴ In ∆AED We have
∠AED = ∠ADE
So, AD = AE
(∵ Sides opposite to equal angles of a triangle are equal)

Question 7.
AC and BD are chords of a circle which bisect each other. Prove that
(i) AC and BD are diameters,
(ii) ABCD is a rectangle.
Solution:
(i) Let BD and AC be two chords of a circle bisect at P.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6 img 7
In ∆APB and ∆CPD, we get
PA = PC ( ∵ P is the mid-point of AC)
∠APB = ∠CPD (Vertically opposite angles)
and PB = PD (∵ P is the mid-point of BD)
∴ By SAS criterion
∆CPD ≅ ∆APB
∴ CD= AB (By CPCT) …(i)
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6 img 8
∴ BD divides the circle into two equal parts. So, BD is a diameter.
Similarly, AC is a diameter.
(ii) Now, BD and AC bisect each other.
So, ABCD is a parallelogram.
Also, AC = BD
∴ ABCD is a rectangle.

Question 8.
Bisectors of angles A, B and C of a ∆ABC intersect its circumcircle at D, E and F, respectively. Prove that the angles of the ∆DEF are 90° – \(\frac { 1 }{ 2 }\) A, 90° – \(\frac { 1 }{ 2 }\) B and 90° – \(\frac { 1 }{ 2 }\) C.
Solution:
∵ ∠EDF = ∠EDA + ∠ADF
∵ ∠EDA and ∠EBA are the angles in the same segment of the circle.
∴ ∠EDA = ∠EBA
and similarly ∠ADF and ∠FCA are the angles in the same segment and hence
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6 img 9

Question 9.
Two congruent circles intersect each other at points A and B. Through A any line segment PAQ is drawn so that P, Q lie on the two circles. Prove that BP = BQ.
Solution:
Let O’ and O be the centres of two congruent circles.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6 img 10
Since, AB is a common chord of these circles.
∴ ∠BPA = ∠BQA
(∵ Angle subtended by equal chords are equal)
⇒ BP = BQ

Question 10.
In any ∆ ABC, if the angle bisector of ∠A and perpendicular bisector of BC intersect, prove that they intersect on the circumcircle of the ∆ABC.
Solution:
(i) Let bisector of ∠A meet the circumcircle of ∆ABC at M.
Join BM and CM.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6 img 11
∴ ∠MBC = ∠MAC (Angles in same segment)
and ∠BCM = ∠BAM (Angles in same segment)
But ∠BAM = ∠CAM (∵ AM is bisector of ∠A)…. .(i)
∴ ∠MBC = ∠BCM
So, MB = MC (Sides opposite to equal angles are equal)
So, M must lie on the perpendicular bisector of BC
(ii) Let M be a point on the perpendicular bisector of BC which lies on circumcircle of ∆ ABC.
Join AM.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6 img 12
Since, M lies on perpendicular bisector of BC.
∴ BM = CM
∠MBC = ∠MCB
But ∠MBC = ∠MAC (Angles in same segment)
and ∠MCB = ∠BAM (Angles in same segment)
So, from Eq. (i),
∠BAM = ∠CAM
AM is the bisector of A.
Hence, bisector of ∠A and perpendicular bisector of BC at M which lies on circumcircle of ∆ABC.
We hope the NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6, help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.6, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5

NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5.

Board CBSE
Textbook NCERT
Class Class 9
Subject Maths
Chapter Chapter 11
Chapter Name Circles
Exercise Ex 11.5
Number of Questions Solved 12
Category NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5

Question 1.
In figure A,B and C are three points on a circle with centre 0 such that ∠BOC = 30° and ∠ AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ ADC.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5 img 1
Solution:
∴ ∠AOC = ∠AOB + ∠BOC = 60P + 30° = 90°
∴ Arc ABC makes 90° at the centre of the circle.
∴ ∠ADC = \(\frac { 1 }{ 2 }\) ∠AOC
(∵ The angle subtended by an arc at the centre is double the angle subtended by it any part of the circle.)
= \(\frac { 1 }{ 2 }\) x 90° = 45°

Question 2.
A chord of a circle is equal to the radius of the circle, find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.
Solution:
Let BC be chord, which is equal to the radius. Join OB and OC.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5 img 2
Given, BC=OB = OC
∴ ∆OBC is an equilateral triangle.
∠BOC =60°
∴ BAC = \(\frac { 1 }{ 2 }\) ∠BOC
= \(\frac { 1 }{ 2 }\) x 60° = 30°
(∵ The angle subtended by an arc at the centre is double the angle subtended by it any part of the circle.)
Here, ABMC is a cyclic quadrilateral.
∴ ∠BAC + ∠BMC = 180°
(∵ In a cyclic quadrilateral the sum of opposite angles is 180°)
⇒ ∠BMC= 180° – 30° =150°

Question 3.
In figure, ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5 img 3
Solution:
∴ ∠POR = 2∠PQR = 2 x 100° = 200°
(Since, the angle subtended by the centre is double the angle subtended by circumference.)
Since, in ∆OPR, ∠POR = 360° – 200° = 160° .. (i)
Again, ∆ OPR, OP = OR (Radii of the circle)
∴ ∠OPR = ∠ORP (By property of isosceles triangle)
In ∆POR, ∠OPR + ∠ORP + ∠POR = 180° …(ii)
From Eqs. (i) and (ii), we get
∠OPR + ∠OPR + 160° = 180°
∴ 2 ∠OPR = 180° – 160° = 20°
∴ ∠OPR = \(\frac { { 120 }^{ circ } }{ 2 }\) = 10°

Question 4.
In figure, ∠ABC = 69°,∠ACB = 31°, find ∠BDC.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5 img 4
Solution:
∵ ∠BDC = ∠BAC …(i)
(Since, the angles in the same segment are equal)
Now , in ∆ABC
∴ ∠A + ∠B+ ∠C= 180°
⇒ ∠A+ 69°+ 31° = 180°
⇒ ∠A + 100° = 180°
∴ ∠A = 180° – 100° = 80°
⇒ ∠BAC=80°
∴ From Eq.(i)∠BDC = 80°

Question 5.
In figure, A, B and C are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130° and ∠ ECD = 20°. Find ∠BAC.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5 img 5
Solution:
∴ ∠AEB = 180° – 130° = 50° (Linear Pair) …(i)
⇒ ∠CED = ∠AEB = 50° (Vertically opposite)
Again ∠ABD = ∠ACD (Since, the angles in the same segment are equal)
∠ABE = ∠ECD
⇒ ∠ABE = 180° …(ii)
∴ In ∆ CDE
∠A+ 20° + 50° = 180° [From Eqs. (i) and (ii)]
∠A + 70° = 180°
∴ ∠A = 180°- 70° =110°
Hence ∠BAC = 110°

Question 6.
ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC is 30°, find ∠BCD. Further, if AB = BC, find ∠ECD.
Solution:
Angles in the same segment are equal.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5 img 6
∴ ∠BDC = ∠BAC
∴ ∠BDC = 30°
In ∆ BCD, we have
∴ ∠BDC + ∠DBC + ∠BCD = 180° (Given, ∠DBC = 70° and ∠BDC = 30°)
∴ 30° + 70° + ∠BCD = 180°
∴ ∠BCD= 180°-30°-70° = 80°
If AB = BC, then ∠BCA = ∠BAC= 80° (Angles opposite to equal sides in a triangle are equal)
Now, ∠ECD = ∠BCD – ∠BCA = 80° – 30P = 50° (∵ ∠BCD = 80° and ∠BCA =30°)
Hence, ∠BCD = 80°
and ∠ECD = 50°

Question 7.
If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.
Solution:
Given: Diagonals NP and QM of a cyclic quadrilateral are diameters of the circle through the vertices M, P, Q and N of the quadrilateral NQPM.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5 img 7
To prove: Quadrilateral NQPM is a rectangle.
Proof: ∵ ON = OP = OQ = OM (Radii of circle)
Now, ON = OP = \(\frac { 1 }{ 2 }\) NP
and OM = OQ = \(\frac { 1 }{ 2 }\) MQ
∴ NP = MQ
Hence, the diagonals of the quadrilateral MPQN are equal and bisect each other. So, quadrilateral NQPM is a rectangle.

Question 8.
If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
Solution:
Given: Non-parallel sides PS and QR of a trapezium PQRS are equal.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5 img 8
To prove: ABCD is a cyclic trapezium.
Construction: Draw SM ⊥ PQ and RN ⊥ PQ.
Proof In ∆SMP and ∆RNQ, we get
SP = RQ (Given)
∠SMP = ∠RNQ (Each = 90°)
and SM = RN
(∵ Distance between two parallel lines is always equal)
∴ By RHS criterion, we get
∆ SMP ≅ ∆ RNQ
So, ∠P = ∠Q (By CPCT)
and ∠PSM = ∠QRN
Now, ∠PSM = ∠QRN
∴ 90° + ∠PSM = 90° + ∠QRN (Adding both sides 90°)
∴ ∠MSR + ∠PSM = ∠NRS + ∠QRN (∵∠MSR = ∠NRS = 90°)
So, ∠PSR = ∠QRS
i.e., ∠S = ∠R
Thus, ∠P = ∠Q and ∠R = ∠S …(i)
∴ ∠P+ ∠Q+ ∠R+ ∠S = 360° (∵ Sum of the angles of a quadrilateral is 360°)
∴ 2∠S + ∠Q = 360° [From Eq. (i)]
∠S+∠O = 180°
Hence, PQRS is a cyclic trape∠ium.

Question 9.
Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A,D and P, Q respectively (see figure). Prove that ∠ ACP = ∠QCD.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5 img 9
Solution:
Given: Two circles intersect at two points B and C. Through B two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q, respectively.
To prove: ∠ACP = ∠QCD
Proof: In circle I, ∠ACP = ∠ABP (Angles in the same segment) …(i)
In circle II, ∠QCD = ∠QBD{Angles in the same segment)…(ii)
∠ABP = ∠QBD (Vertically opposite angles)
From Eqs. (i) and (ii), we get ∠ACP = ∠QCD

Question 10.
If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.
Solution:
Given: Two circles are drawn with sides AC and AB of AABC as diameters . Both circles intersect each other at D.
To prove: D lies on BC.
Construction: Join AD.
Proof: Since, AC and AB are the diameters of the two circles.
∠ADB = 90° ( ∴ Angles in a semi-circle) …(i)
and ∠ADC = 90° (Angles in a semi-circle) …(ii)
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5 img 10
On adding Eqs. (i) and (ii), we get
∠ADB + ∠ADC = 90° + 90° = 180°
Hence, BCD is a straight line.
So, D lies on BC.

Question 11.
ABC and ADC are two right angled triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.
Solution:
Since, ∆ADC and ∆ABC are right angled triangles with common hypotenuse.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5 img 11
Draw a circle with AC as diameter passing through B and D. Join BD.
∵ Angles in the same segment are equal.
∴ ∠CBD = ∠CAD

Question 12.
Prove that a cyclic parallelogram is a rectangle.
Solution:
Given: PQRS is a parallelogram inscribed in a circle.
To prove: PQRS is a rectangle.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5 img 12
Proof: Since, PQRS is a cyclic quadrilateral.
∴ ∠P+∠R = 180°
(∵ Sum of opposite angles in a cyclic quadrilateral is 180°) …(i)
But ∠P = ∠R (∵ In a || gm opposite angles are equal) …(ii)
From Eqs. (i) and (ii), we get
∠P = ∠R = 90°
Similarly, ∠Q = ∠S = 90
∴ Each angle of PQRS is 90°.
Hence, PQRS is a rectangle.
We hope the NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5, help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.5, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4

NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4.

Board CBSE
Textbook NCERT
Class Class 9
Subject Maths
Chapter Chapter 11
Chapter Name Circles
Exercise Ex 11.4
Number of Questions Solved 6
Category NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4

Question 1.
Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.
Solution:
Let O and O’ be the centres of the circles of radii 5 cm and 3 cm, respectively.
Let AB be their common chord.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4 img 1
Given, OA = 5 cm, O’A = 3cm and OO’ = 4 cm
∴ AO’2 + OO’2 = 32 + 42 = 9 + 16- 25 = OA2
∴ OO’A is a right angled triangle and right angled at O’
Area of ∆OO’A = \(\frac { 1 }{ 2 }\) x O’A x OO’
= \(\frac { 1 }{ 2 }\) x 3x 4= 6sq units …(i)
Also, area of ∆OO’A = \(\frac { 1 }{ 2 }\) x OO’ x AM
= \(\frac { 1 }{ 2 }\) x 4 x AM =2 AM …(ii)
From Eqs. (i) and (ii), we get
2AM = 6 ⇒ AM = 3
Since, when two circles intersect at two points, then their centre lie on the perpendicular bisector of the common chord.
∴ AB = 2 x AM= 2 x 3 = 6 cm

Question 2.
If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.
Solution:
Given: MN and AS are two chords of a circle with centre O, AS and MN intersect at P and MN = AB
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4 img 2
To prove: MP = PB and PN = AP
Construction: Draw OD ⊥ MN and OC ⊥ AB.
Join OP
Proof : ∵ DM = DN = \(\frac { 1 }{ 2 }\) MN (Perpendicular from centre bisects the chord)
and AC = CB = \(\frac { 1 }{ 2 }\) AB (Perpendicular from centre bisects the chord)
MD = BC and DN = AC (∵ MN = AS)…(i)
in ∆ODP and ∆OPC
OD = OC (Equal chords of a circle are equidistant from the centre)
∠ ODP = ∠OCP
OP = OP (Common)
∴ RHS criterion of congruence,
∆ ODP ≅ ∆ OCP
∴ DP = PC (By CPCT)…(ii)
On adding Eqs. (i) and (ii), we get
MD + DP = BC + PC
MP = PB
On subtracting Eq. (ii) from Eq. (i), we get
DN – DP = AC – PC
PN = AP
Hence, MP = PB and PN = AP are proved.

Question 3.
If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.
Solution:
Given: RQ and MN are chords of a with centre O. MN and RQ intersect at P and MN = RQ
To prove: ∠ OPC = ∠ OPB
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4 img 3
Construction: Draw OC ⊥ RQ and OB ⊥ MN.
Join OP.
Proof: In ∆ OCP and ∆ OBP, we get
∠ OCP = ∠ OBP (Each = 90°)
OP = OP (Common)
OC = OB (Equal chords of a circle are equidistant from the centre)
∴ By RHS criterion of congruence, we get
∆ OCP ≅ ∆ OBP
∴ ∠ OPC = ∠ OPB (By CPCT)

Question 4.
If a line intersects two concentric circles (circles with the same centre) with centre 0 at A, B, C and D, prove that AB = CD (see figure).
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4 img 4
Solution:
Let OP be the perpendicular from O on line l. Since, the perpendicular from the centre of a circle to a chord
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4 img 5
Now, BC is the chord of the smaller circle and OP ⊥ BC.
∴ BP = PC ……(i)
Since, AD is a chord of the larger circle and OP ⊥ AD.
∴ AP = PD …(ii)
On subtracting Eq. (i) from Eq. (ii), we get
AP – BP = PD – PC
⇒ AB = CD
Hence proved.

Question 5.
Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6 m each, what is the distance between Reshma and Mandip?
Solution:
Let O be the centre of the circle and Reshma, Salma and Mandip are represented by the points Ft, S and M, respectively.
Let RP = xm.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4 img 6
From Eqs. (i) and (ii), we get
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4 img 7
Hence, the distance between Reshma and Mandip is 9.6 m.

Question 6.
A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.
Solution:
Let Ankur, Syed and David standing on the point P, Q and R.
Let PQ = QR = PR = x
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4 img 8
Therefore, ∆ PQR is an equilateral triangle. Drawn altitudes PC, QD and RN from vertices to the sides of a triangle and intersect these altitudes at the centre of a circle M.
As PQR is an equilateral, therefore these altitudes bisects their sides.
In ∆ PQC,
PQ2 = PC2 + QC2 (By Pythagoras theorem)
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4 img 9
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4 img 10

We hope the NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4, help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.4, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.3

NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.3 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.3.

Board CBSE
Textbook NCERT
Class Class 9
Subject Maths
Chapter Chapter 11
Chapter Name Circles
Exercise Ex 11.3
Number of Questions Solved 3
Category NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.3

Question 1.
Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?
Solution:
Different pairs of circles are
(i) Two points common
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.3 img 1
(ii) One point is common
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.3 img 2
(iii) No point is common
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.3 img 3
(iv) No point is common
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.3 img 4
(v) One point is common
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.3 img 5
From figures, it is obvious that these pairs many have 0 or 1 or 2 points in common.
Hence, a pair of circles cannot intersect each other at more than two points.

Question 2.
Suppose you are given a circle. Give a construction to find its centre.
Solution:
Steps of construction
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.3 img 6
Taking three points P,Q and R on the circle.
Join PQ and QR,
Draw MQ and NS, respectively the perpendicular bisectors of PQ and RQ, which intersect each other at O.
Hence, O is the centre of the circle.

Question 3.
If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.
Solution:
Given: Two circles with centres O and O’ intersect at two points M and N so that MN is the common chord of the two circles and OO’ is the line segment joining the centres of the two circles. Let OO’ intersect MN at P.
To prove: OO’ is the perpendicular bisector of MN.
NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.3 img 7
Construction: Draw line segments OM, ON, O’M and O’N.
Proof In ∆ OMO’ and ONO’, we get
OM = ON (Radii of the same circle)
O’M = O’N (Radii of the same circle)
OO’ = OO’ (Common)
∴ By SSS criterion, we get
∆ OMO’ ≅ ONO’
So, ∠ MOO’ = ∠ N00′ (By CPCT)
∴ ∠ MOP = ∠ NOP …(i)
(∵ ∠ MOO’ = ∠ MOP and ∠ NOO’ = ∠ NOP)
In ∆ MOP and ∆ NOP, we get
OM = ON (Radii of the same circle)
∠ MOP = ∠NOP [ From Eq(i)]
and OM = OM (Common)
∴ By SAS criterion, we get
∆ MOP ≅ ∆NOP
So, MP = NP (By CPCT)
and ∠ MPO = ∠ NPO
But ∠ MPO + ∠NPO = 180° ( ∵MPN is a straight line)
∴ 2 ∠ MPO = 180° ( ∵ ∠ MPO = ∠ NPO)
⇒ ∠ MPO = 90°
So, MP = PN
and ∠ MPO = ∠ NPO = 90°
Hence, OO’ is the perpendicular bisector of MN.

We hope the NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.3, help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.3, drop a comment below and we will get back to you at the earliest.

CBSE Sample Papers for Class 12 Informatics Practices Paper 4

CBSE Sample Papers for Class 12 Informatics Practices Paper 4 are part of CBSE Sample Papers for Class 12 Informatics Practices. Here we have given CBSE Sample Papers for Class 12 Informatics Practices Paper 4.

CBSE Sample Papers for Class 12 Informatics Practices Paper 4

Board CBSE
Class XII
Subject Informatics Practices
Sample Paper Set Paper 4
Category CBSE Sample Papers

Students who are going to appear for CBSE Class 12 Examinations are advised to practice the CBSE sample papers given here which is designed as per the latest Syllabus and marking scheme, as prescribed by the CBSE, is given here. Paper 4 of Solved CBSE Sample Paper for Class 12 Informatics Practices is given below with free PDF download solutions.

Time : 3 hrs
Maximum Marks : 70

General Instructions

  • All questions are compulsory.
  • Answer the’questions after carefully reading the text.

QUESTIONS

Question 1.
(a) There is a numbered address (four parts separated by periods) that identifies a Website uniquely. What is it?
(b) Name any of the two encodings used for Indian computing language.
(c) Two students in the same room have connected their laptop using bluetooth for working on a seminar presentation. Out of the following, what kind of network they have formed? LAN, MAN, PAN, WAN.
(d) Ketan has set-up a network of computers. Now, he wants to prevent unwanted networking connections according to some filtering/blocking rules. Suggest him the solution.
(e) Write the name of the following:
(i) It is a protocol/technology used to exchange files on Internet.
(ii) It provides a set of rules to transfer files, videos, images etc., over the World Wide Web.
(f) What do you understand by network security? Name any two common threats to it.
(g) Differentiate between star topology and bus topology of network.

Question 2.
(a) What would you write in Exit button’s Action Performed method, if you want to end the execution of your Java GUI application?
(b) In the code fragment given below, what happens when choice equals to 5?

int n = 0, m = 0 ;
int choice = Integer.parselnt (args[0]) ;
if (choice == 1)
{
n = 11 ;
m = 10 ;
}
else if (choice == 2)
{
n = 20 ;
m = 220 ;
}
j OptionPane.showMessageDialog(this,"n=" + n +, "m=" + m) ;

(c) Write a Java method that takes three digits integer as parameter and returns its middle digit.

(d) Predict the output of the following HTML code :

<UL>
<LI> A few new Students: </LI>
<UL type="Square">
<LI> Sohan </LI>
<LI> Mohan </LI>
<LI> Rohan </LI>
</UL>
</UL>

(e) (i) Rewrite the following code using switch case statement :

if (value==l)
j TextFieldl.setText( "Computer Books" ) ;
else if(value==2)
j TextFieldl.setText( "English Books" ) ;
else if(value==3)
j TextFieldl.setText ( "GS Books" ) ;
else
j TextFieldl.setText ( "Wrong Choice" ) ;

(ii) Write HTML tag to do the following:
I. Insert the picture in the Web page.
II. Insert the empty line in the Web page.

Question 3.
(a) Identify the output of the following code:

SELECT LCASE ("COMPUTER SCIENCE") ;

(b) Which keyword eliminates the redundant data from a query result?
(c) Consider the table :
CBSE Sample Papers for Class 12 Informatics Practices Paper 4 1

Identify error(s) in the following SQL statement. Rewrite the correct SQL statement.

SELECT Empid AS Total_emp, AVG(Total_Salary) AMOUNT FROM SALARY;

(d) Write SQL queries for the following:
(i) Add a NOT NULL constraint in table EMP1 in which a column Designation is declared as NULL.
(ii) Drop the table EMP1.

(e) Given below is the 'TRAIN' table :
CBSE Sample Papers for Class 12 Informatics Practices Paper 4 2
(i) SET AUTOCOMMIT = 1 ;
INSERT INTO TRAIN VALUES ('T03', 'Goa') ;
ROLLBACK ;
SELECT * FROM TRAIN ;

(ii) SET AUTOCOMMIT = 0 ;
INSERT INTO TRAIN VALUES ( 'T03' .'Goa’) ;
COMMIT;
INSERT INTO TRAIN VALUES ( 'T04’ '. 'RAJASTHAN’) ;
ROLLBACK ;
SELECT * FROM TRAIN ;

Is both query output is same if yes, state the reason?

Question 4.
(a) In a SWITCH statement, what is the purpose of ‘default’ section?
(b) (i) Find the output of the following Java code snippet :

String word = "Highrise" ;
String wordl c = word.toLowerCase ( ) ;
for ( int i = 0 ; i<wordlc.length ( ) ; i +=4)
{
String extstr=wordlc.substring (i, i+2) ;
j TextAreal.append!extstr+''\n") ;
}

(ii) Write the value that will be stored in variable num after execution of following code and also define working:

int num=0 ;
for ( int j=9 ; j>=6 ; j- -)
{
if (j%3==0)
num=num+j ;
else
num = num - j ;
}

(c) (i) The following code has some error(s). Rewrite the correct code underlining all the corrections made :

int i ;
i=10 ;
do;
i=i-4;
System.out.displayin ( i ) ;
Iwhile i>=4 ;

(ii) Write a Java code to find out whether a year is a leap year or not.
(d) Ravi is a programmer at Arora Book Store. He created the following GUI in NetBeans. Help him in writing code for the following :
CBSE Sample Papers for Class 12 Informatics Practices Paper 4 5

(i) Write the code for [Calculate Price] button. Total price should be displayed in jTextField5 on clicking the CommandButton1.
(ii) To clear all the text field on clicking of [Reset] button.
(iii) To terminate the application on the click of [Exit] button.
[Assume suitable names for the various controls on the Form].

Question 5.
(a) Mr. Khanna wants to remove all the rows from STOCK table to release the storage space, but he does not want to remove the structure of the table. What MYSQL statement should be used?
(b) Consider the following two tables :
CBSE Sample Papers for Class 12 Informatics Practices Paper 4 6

Give output of the following query :

SELECT CLASSES.Class_Name, SUBJECTS.Sub_Name
FROM CLASSES. SUBJECTS
WHERE CLASSES.S_No = SUBJECTS.S_No ;

(c) (i) What are the properties of transactions maintained by database system?
(ii) Write the output of the following SQL queries :

I. SELECT SUBSTRC EASYCALCULATION', 5,11) AS String ;
II. SELECT CHAR(77, 121, 83, 81, 76) AS V;

(d) Table “LAB” is shown below. Write commands in SQL for (i) and (ii) and output for (iii) and (iv).
CBSE Sample Papers for Class 12 Informatics Practices Paper 4 7
(i) Display the SurName, Fname and City of LAB students residing in New Delhi city.
(ii) Display the LAB Sid, City and Pincode of students in descending order of Pincode.

(iii) SELECT SurName FROM LAB WHERE Fee>=20000 ;
(iv) SELECT SUM(Fee) FROM LAB WHERE Gender = 'F' ;

Question 6.
(a) (i) Write SQL query to create a table ‘BANK’ with following structure :
CBSE Sample Papers for Class 12 Informatics Practices Paper 4 11
(ii) Consider the tables TEACHER and SUBJECT given below :
CBSE Sample Papers for Class 12 Informatics Practices Paper 4 12

I. Which column is used to relate both tables?
II. Is it possible to have a primary key and foreign key both in one table? Justify your answer with the help of tables given above.

(b) With reference to the above given tables (in Q6 (a)(ii)), write commands In SQL for (j) and. (ii) and output for (iii) below :

(i) To display Teacher ID, Naine of lèachei Subject Name, Contact Number of Teachers whose qualification is MCA.
(ii) lb display Teacher ID, Teacher Name, Subject ID, Subjects of all teachers with subject name starting with ‘S’. . .

(iii) SELECT T.TID,T.TName, T.TCity, S.SID,S.SName
FROM TEACHER T, SUBJECT S
WHERE T.TID = S.TID AND S.Fee BETWEEN 500 AND 875 ;

Question 7.
(a) How does E-Business improve customer satisfaction?
(b) Write down advantages of E-Govemance over society
(c) Ram works for the customer support executive. He wishes to create controls on a form for the following functions. Choose appropriate controls from TextBox, Label, RadioButton, CheckBox, ListBox, ComboBox, CommandButton and write in third column.
CBSE Sample Papers for Class 12 Informatics Practices Paper 4 14

ANSWERS

Answer 1.
(a) IP address
(b) Two encodings used for Indian computing language are as follows:
(i) UNICODE (Universal Code)
(ii) ISCII (Indian Standard Code for Information Interchange).
(c) PAN
(d) The suggested solution for him to given problem is Firewall.
(e) (i) FTP (File Transfer Protocol) (ii) HTTP (HyperText Transfer Protocol)
(f) Network security refers to the provisions and policies adopted by the administrators to protect data during data transmission and to guarantee that these transmissions are authentic.
Two common threats to network security are as follows: (i) Trojan Horses (ii) Worms
(g) Differences between star topology and bus topology are as follows :
CBSE Sample Papers for Class 12 Informatics Practices Paper 4 16

Answer 2.

(a) System.exit (0) ;

(b) The message dialog will show the value as n = 0, m = 0.

(c) private int retMid (int num)
{
int a = num%100 ;
int b = a/10 ;
return b ;
}

(d) Output

  • A few new Students :
  • Sohan « Mohan
  • Rohan
(e) (i) switch (value)
{
case 1: j TextFieldl.setText ( "Computer Books" ) ;
break;
case 2: j TextFieldl.setText ( "English Books" ) ;
break;
case 3: j TextFieldl.setText ( "GS Books") ;
break;
default: j TextFieldl.setText ( "Wrong Choice" ) ;
}
(ii) I. <IMG> tag II. <BR> tag

Answer 3.
CBSE Sample Papers for Class 12 Informatics Practices Paper 4 3
(b) DISTINCT keyword eliminates the redundant data from a query result.
(c) The correct code is :

SELECT COUNT (Empid) AS Total_emp, AVG (Total_Salary) AS AMOUNT FROM SALARY :
(d) (i) ALTER TABLE EMP1 MODIFY Designation CHAR!2) NOT NULL ;
(ii) DROP TABLE EMP1 ;
CBSE Sample Papers for Class 12 Informatics Practices Paper 4 4

Yes, both queries output is same because in (ii) query AUTOCOMMIT is 0. When AUTOCOMMIT is OFF, all transaction control commands will be affect and when AUTOCOMMIT mode is 1 it commits and terminates the current transaction.

Answer 4.
(a) In a SWITCH statement, the default section will be executed when no match is found with switch expression to case constant value.
(b)

(i) hi
ri
(ii) Working :
iteration 1 : j=9. 9>=6 True
if (9%3==0) True
num=0+9=9
iteration 2 : j=8, 8>=6 True
if(8%3==0) False
num=9-8=1
iteration 3 : j=7, 7>=6 True
if(7%3==0) False
num=1 - 7=-6
iteration 4: j=6, 6>=6 True
if(6%3==0) True
num= -6+6=0
iteration 5: j=5, 5>=6 False

Output
0 will be stored in num.

(c) (i) The correct code is

int i ;
i=10 ;
d0
i=i -4;
System.out.println ( i ) :
}while (i>=4) ;

(ii) if (year%4==0)
System.out.println(year+"is a leap year") ;
else
System.out.println(year+"is not a leap year") ;

(d) For 1st button, we have to specify the following code :

(i) private void jButtonlActionPerformed(java.awt.event.ActionEvent evt)
{
float price, total ;
int rioc ;
price = Float.parseFloat (j TextField3.getText ( ) ) ;
noc = Integer.parselnt (j TextField4.getText ( ) ) ;
total = price * noc ;
j TextField5.setText (Float.toString(total) ) ;

(ii) For 2nd button, we have to specify the following code :

private void jButton2ActionPerformed(java.awt.event.ActionEvent evt)
{
j TextField1.setText(” ") ;
j TextField2.setText(" ") ;
j TextField3.setText(" ") ;
j TextField4.setText(" ") ;
j TextField5.setText(" ") ;
}

(iii) For 3rd button, we have to specify the following code :

private void jButton3ActionPerformed(java.awt.event.ActionEvent evt)
{
System.exit (0) ;
}

Answer 5.
(a) The command to delete all rows from the STOCK table without deleting the structure of the table will be as follows :

DELETE FROM STOCK ;
CBSE Sample Papers for Class 12 Informatics Practices Paper 4 8

(c) (i) Properties of transactions maintained by database system are as follows :

I. Atomicity This property ensures that either all operations of the transactions are performed in completion or none of the operations are performed and reflected in database.

II. Consistency It ensures that the database before and after the transaction is in a consistent state.

III. Isolation It ensures that each transaction executing takes place in isolation.

IV. Durability It ensures that the changes made in the database remains in it, after the successful completion of a transaction.

CBSE Sample Papers for Class 12 Informatics Practices Paper 4 9

(d)

(i) SELECT SurName, Fname, City FROM LAB WHERE City ='New Delhi' ; 
(ii) SELECT,Sid, City, Pincode FROM LAB ORDER BY Pincode DESC ;
CBSE Sample Papers for Class 12 Informatics Practices Paper 4 10

Answer 6.
(a)

(i) CREATE TABLE BANK
(
BankID VARCHAR(5) PRIMARY KEY,
BankName CHAR(10) NOT NULL. Location CHAR (10),
No_of_Branch INTEGER
) ;

(ii) I. TID
II. Yes, it is possible to have primary key and foreign key column in one table. Primary key column is used to uniquely identify each record of the table while foreign key column is used to maintain referential integrity.

As in the given table ‘SUBJECT’, SID column is a primary key while TID may act as a foreign key.

(b) (i) SELECT T.TID, T.TName, S.SName, T.TContact_No 
FROM TEACHER T, SUBJECT S
WHERE T.TID = S.TID AND T.TQualification = 'MCA' ;

(ii) SELECT T.TID, T.TName, S.SID, S.SName
FROM TEACHER T,SUBJECT S
WHERE T.TID = S.TID AND S.SName LIKE 'S%' ;
CBSE Sample Papers for Class 12 Informatics Practices Paper 4 13

Answer 7.
(a) E-Business improves customer satisfaction by using are as follows :

  1. Customers can receive highly customisable services.
  2. Even remote area customers are reached in E-Business.

(b) The advantages of E-Governance over society are as follows :

  1. A lot of productivity time of government servants and general public is saved.
  2. Transparency has increased and therefore cheating cases have been reduced.
  3. E-Governance programs have resulted in increased public participation.
  4. People have also benefited from it in the form of reduced cost and availability of the services.

CBSE Sample Papers for Class 12 Informatics Practices Paper 4 15

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CBSE Sample Papers for Class 12 Informatics Practices Paper 3

CBSE Sample Papers for Class 12 Informatics Practices Paper 3 are part of CBSE Sample Papers for Class 12 Informatics Practices. Here we have given CBSE Sample Papers for Class 12 Informatics Practices Paper 3.

CBSE Sample Papers for Class 12 Informatics Practices Paper 3

Board CBSE
Class XII
Subject Informatics Practices
Sample Paper Set Paper 3
Category CBSE Sample Papers

Students who are going to appear for CBSE Class 12 Examinations are advised to practice the CBSE sample papers given here which is designed as per the latest Syllabus and marking scheme, as prescribed by the CBSE, is given here. Paper 3 of Solved CBSE Sample Paper for Class 12 Informatics Practices is given below with free PDF download solutions.

Time : 3 hrs
Maximum Marks : 70

General Instructions

  • All questions are compulsory.
  • Answer the questions after carefully reading the text.

QUESTIONS

Question 1.
(a) Name any two transmission medium for networking.
(b) How would you extract Manufacturer_Id and Card_No from a MAC address?
(c) What is the geological scope of LAN, MAN, and WAN?
(d) In how many ways can you type Indian scripts on a computer?
(e) Identify the type of topology from the following:
(i) In it, each node is connected with the help of a single coaxial cable.
(ii) In it, each node is connected with the help of independent cable and central switching (communication controller) node.
(f) Which of the following are open standards and which are proprietary standards?
(i) OGG
(ii) WMA
(iii) DOC
(iv) JPEG
(g) Repeaters are used over long network lines. Explain.

Question 2.
(a) Samarth created a program. He wants that variables used in the class can only be accessed by class’s subclass and not by unrelated classes. Help him by providing the solution.
(b) Write the output in jTextFieldl if stucode is 70.

switch(stucode)
{ 
case 30 :
Mark = 80;
break ; 
case 50 :
Mark = 40 ;
break ;
default :
Mark = 10 ;
}
j TextFieldl.set Text ("'+Mark) ;

(c) (i) Identify the error(s) in the following HTML code. Also, write the correct code.

<BODY color="yellow" text="white">

(ii) Consider the following XML document. Check this for well-formedness.

<name>Sahil</name>
<name>Dishu</name>

(d) What will be the content of the jTextAreal after executing the following code (assuming that the j TextAreal had no content before executing this code)?

for (int i=1;i<=4; i++)
{
j TextAreal.setText ( j TextAreal.getText ()+" "
+Integer. toString (i  + i )) ;
}

(e) (i) Rewrite the following code using SWITCH statement :

if (test = = 1)
System.out.println("Hello") ;
else if(test==2)
System.out.println("Hi i") ; 
else if(test= =3)
System.out.print1n("Good") ; 
else 
System.out.println("No Match Found") ;

(ii) Write a method in Java that takes two numbers as input from two text fields and display which is greater in another text field.

Question 3.
(a) A table named OFFICE has 6 rows and 10 columns and another table named STAFF has 3 rows and 5 columns. How many rows and columns will be there if we obtain the Cartesian product of these two tables?
(b) Give one difference between CEIL ( ) and FLOOR ( ) functions.
(c) Explain the use of UNIQUE constraint. How is it different from primary key constraint?
(d) Consider the table ‘COMPANY’.
CBSE Sample Papers for Class 12 Informatics Practices Paper 3 1
(e) (i) Aryan a student of class XII created a table ANNUAL. Grade is one of the column of this table. To find the details of students whose grades have not been entered, he wrote the following MySQL query, which did not give the desired result

SELECT * FROM ANNUAL WHERE GRADE = "NULL"

Help Aryan to run the query by removing the errors from the query and write the correct query.
(ii) Given below is the ‘STUDENT table:
CBSE Sample Papers for Class 12 Informatics Practices Paper 3 2

SET AUTOCOMMI T = 0 ;
INSERT INTO STUDENT VALUES (104,'Yash') ;
COMMIT:
INSERT INTO STUDENT VALUES (106,'Muskan') ;
SAVEPOINT A :
UPDATE STUDENT SET Name = 'Sahil' WHERE SId=102 ;
SAVEPOINT B ;
What will be the output of the following SQL query now?
SELECT * FROM STUDENT ;

Question 4.
(a) Sahil created a program using switch case. He used the data type double for selection variable. Is it correct to define selection variable as double? Give reason.
(b) (i) Consider the following code and given output:

String s1 = new String ("Aryan") ;
String s2 = new String ("Aryan") ; 
if (s1.equals (s2)) .
System.out.println ("si is equal to s2"); 
if (s1 == s2)
System.out.println ("s1 is equal to s2");

(ii) Find out tbe error (s) in the following code fragment:

interface Student 
{
public void method ( ) ;
}
public class extends Student
{
public void method ( ) :
}

(c) (i) “The variable/expression in the switch statement should either evaluate to an integer value or string value”. State Thie or False.
(ii) Write statement to increase the value assigned to variable K by 2 and then to display the value.
(iii) What will be displayed in jTextAreal after the execution of the following loop? Also, write that how many times this loop will be execute?

for (int K=4; K<=20; K+=4) 
j TextAreal . setText (j TextAreal.getText ( )+" "
+ Integer . to String (2 * K)) ;

(d) Ronit Roy is a programmer at LINC Enterprises. He created the following GUI in NetBeans. Help him to write code for the following:
(i) To display series of odd or even numbers (depending on starting number- j TextField 1 is even or odd) in the j TextArea 1 on click of command button [Display The Series].
e.g. If the start number is 5 and last number is 11.
CBSE Sample Papers for Class 12 Informatics Practices Paper 3 5

Then, TextArea content will be 5 7 9 11. If the start number is 2 and last number is 10. Then, Text Area content will be 2 46 8 10.
(ii) To clear both the text fields and text area, on clicking [Reset] button.
(iii) To terminate the application on the click of [Stop] button.

Question 5.
(a) By using which clause, you can specify a condition to specify the values that you want to view in a particular range?
(b) Table FURNITURE has 7 rows and 10 columns. What is the cardinality and degree of this table?
(c) Explain the following functions and give output of each of the statement.

(i) SELECT INSTR('Computer', ’ P') ; 
(ii) SELECT RIGHT( 'Computer'. 3) ;

(iii) How is left join different from a natural join?

(d) Table “BOOK” is shown below. Write commands in SQL for (i) and (ii) and output for (iii) and (iv)
CBSE Sample Papers for Class 12 Informatics Practices Paper 3 6

(i) Display the Book name, price and page of ‘BOOK table whose author name is Priyanka.
(ii) Display the Book_id and Author_Name of Book whose price above 150.

(iii) SELECT C0UNT(*), Price FROM BOOK WHERE Price = 350 ;
(iv) SELECT SUM(Price) FROM BOOK WHERE Page<200 ;

Question 6.
(a) (i) Create table CUSTOMER as per following Table structure :
CBSE Sample Papers for Class 12 Informatics Practices Paper 3 10
(ii) Consider the following tables PRODUCT and CLIENT :
CBSE Sample Papers for Class 12 Informatics Practices Paper 3 11

I. Which column is used to relate the two tables?
II. Is it possible to have a primary key and a foreign key both in one table? Justify your answer with the help of tables given above.

(b) With reference given to the above tables in Q 6 (a) (ii), write SQL commands for the statements (i) and (ii) and give output for SQL query (iii).
(i) To display the details of products whose Price is in range of 50 to 100 (both values included).
(ii) To display the ClientName, City from table CLIENT and ProductName, Price from table PRODUCT with their corresponding matching P_ID.

(iii) SELECT Manufacturer, MAX(Price), MIN (Price), C0UNT ( * )
FROM PRODUCT GROUP BY Manufacturer ;

Question 7.
(a) How is E-Commerce beneficial to businessmen? Write one point.
(b) What issues are still to be worked out for E-Governance to meet all its objectives?
(c) Ridhi is creating a form for registration of annual function. Help her to choose most appropriate controls out of ListBox, ComboBox, TextField, TextArea, RadioButton, CheckBox and CommandButton for the following entries :
CBSE Sample Papers for Class 12 Informatics Practices Paper 3 13

ANSWERS

Answer 1.
(a) Two transmission medium for networking are as follows :
(i) Co-axial cable
(ii) Radiowave

(b) The first three bytes of a MAC address represent Manufacturer Jd and the last three bytes of a MAC address represent Card_No.

(c) LAN is confined to relatively small areas such as a building or a group of buildings.
WAN spans a large area, possibly several continents. MAN is between LAN and WAN,
i.e. spanning a small city or town.

(d) Indian scripts can be entered in two different ways which are as follows:
(i) Using phonetic text entry
(ii) Using keymap based text entry

(e) (i) Bus topology (ii) Star topology

(f) Open Standards (i) OGG and (iv) JPEG
Proprietary Standards (ii) WMA and (iii) DOC

(g) When the transmitted data has to travel over a long distance, the signals start degrading after a certain distance. If the signals degrade too much, the data will be lost and it will fail to reach the destination. Therefore, repeaters are used. Repeater is a device that is used to replicate and amplify a signal over long distance transmission.

Answer 2.
(a) He should declare those variables.as protected in the superclass. Since, by declaring the variables as protected they can only be accessed by the subclasses of that class.

(b) j TextFieldl will contain 10.

(c) (i) color is not an attribute of <BODY> tag. To specify background color of the Web page, we use bgcolor attribute of the <BODY> tag. Correct code is:

<BODY bgcolor = "yellow" text = "white">

(ii) Given XML document is not well-formed, because it has a number of root elements. Whereas an XML document must have only one root element.
(d) j TextArea1 will contain 2 4 6 8
(e)

(i) switch(test)
{
case 1:
System.out.println("Hello") ; 
break ;
case 2 :
System.out.println("Hii");
break ; 
case 3 :
System.out.println("Good"); 
break ; 
default :
System.out.println ("No Match Found") ;
}


(ii) public void findGreater ()
{ 
int a = Integer . parselnt ( jTextField1 . get Text () ) ; 
int b = Integer . parselnt ( jTextField2 . getText () ) ; 
if (a > b)
j TextField3 . setText ("a is greater") ; 
else
jTextField3 . setText ("b is greater") ;
}

Answer 3.
(a) Number of rows = 6 × 3 = 18 and number of columns = 10 + 5 = 15
If we obtain Cartesian product of these two tables, we would get 18 rows and 15 columns.
(b) CEIL ( ) function returns the smallest integer value that is not less than passed numeric expression, while FLOOR ( ) function returns the largest integer value that is not greater than passed numeric expression, e.g.
CBSE Sample Papers for Class 12 Informatics Practices Paper 3 3
(c) The UNIQUE constraint on a column ensures that all values in a column are distinct, i.e. no two tuples/rows can have same value in that particular column. A column having UNIQUE constraint can have NULL (until explicitly mentioned as NOT NULL), whereas column having a PRIMARY KEY constraint, implicitly means that the field is required to be UNIQUE and NOT NULL

(d) SELECT DISTINCT C_City. SUM (Price) FROM COMPANY GROUP BY C_City ;

(e) (i) The correct query is :

SELECT * FROM ANNUAL WHERE GRADE IS NULL ;

CBSE Sample Papers for Class 12 Informatics Practices Paper 3 4

Answer 4.
(a) No, he cannot use double datatype as selection variable in switch as it is not good for exact comparisons. Generally, int, short, byte, or char are only used as selection variable in switch.

(b) (i) Here, only first, System.out.println will work because equals method compares the content of string object, where = = operator compares reference of string object. So output will be: s1 is equal to s2.
(ii) I. A class cannot extend an interface. It should only implement.
II. Definition of method should be given in class or it should be declared as abstract.

(c) (i) True

(ii) int K ;
K = K + 2 ;
System.out.println(K) ;

(iii) Output
j TextAreal will display = 8 16 24 32 40
Loop will be 5 times execute.

(d) (i) We have to double click at the Display The Series button (jButton 1) and type the following code:

int start = Integer . parselnt ( jTextFieldl.getText( ) ); 
int last = Integer.parselnt ( jTextField2.getText( ) ); 
for( int i=start; i<=last; i=i+2)
{
jTextAreal.append(" " + i):
}

(ii) We have to double click at the Reset button (jButton2) and type the following code :

jTextFieldl.setText (" ") ; 
jTextField2.setText(" ") ; 
jTextAreal.setText(" ") ;

(iii) We have to double click at the Stop button (jButton3) and type the following code :
System. exit (0) ;

Answer 5.
(a) BETWEEN clause.
(b) Cardinality = number of rows = 7
Degree = number of columns = 10

(c) (i) lNSTR (str,substr) function is used to return position of first occurrence of substr in str.

SELECT INSTR ('Computer'. 'p') ;

CBSE Sample Papers for Class 12 Informatics Practices Paper 3 7

(ii) RIGHT (str, len) function returns the specified Ten’ number of characters from the right of the string ‘str’.

SELECT RIGHT ('Computer' ,3) ;

CBSE Sample Papers for Class 12 Informatics Practices Paper 3 8

(iii) Left join is a form of join where all the rows(even non-matching ones) from the first table are returned in the result.
Whereas in natural join, the result consists of only the matched rows.

(d)

(i) SELECT BName, Price, Page FROM BOOK
WHERE Author_Name = 'Priyanka' :
(ii) SELECT B00K_id, Author_Name FROM BOOK WHERE Price >150 ;

CBSE Sample Papers for Class 12 Informatics Practices Paper 3 9

Answer 6.
(a)

(i) CREATE TABLE CUSTOMER
(
CId INTEGER PRIMARY KEY,
CName VARCHARC30) NOT NULL,
CAddress VARCHAR (20),
Pincode INTEGER,
Contact_No VARCHAR(10)
) ;
(i) I. P_ID

II. Yes, it is possible to have primary key and foreign key columns in one table.
Primary key column is used to uniquely identify each record of the table while foreign key column is used to maintain referential integrity.

As in the given table CLIENT, C_lD column is a primary key while P_lD may act as a foreign key.

(b) (i) SELECT * FROM PRODUCT WHERE Price BETWEEN 50 AND 100 ;
(ii) SELECT CLIENT. ClientName, CLIENT.City, PRODUCT. ProductName, 
PRODUCT.Price FROM CLIENT, PRODUCT 
WHERE CLIENT.P_ID = PRODUCT.P_ID ;
CBSE Sample Papers for Class 12 Informatics Practices Paper 3 12

Answer 7.
(a) E-Commerce advantage is acquisition of new customers and increased sales.

(b) The following issues need to be worked out in order to make E-Governance meet all its objectives:

  1. All the services of Government offices should be made available through online portals.
  2. Awareness programs should be conducted to make people aware about the availability of the services available online.
  3. Efforts should be made to remove E-literacy.
  4. The available technology in terms of hardware, software and broadband services should be made within reach of all the people.

CBSE Sample Papers for Class 12 Informatics Practices Paper 3 14

We hope the CBSE Sample Papers for Class 12 Informatics Practices Paper 3 help you. If you have any query regarding CBSE Sample Papers for Class 12 Informatics Practices Paper 3, drop a comment below and we will get back to you at the earliest.

CBSE Sample Papers for Class 12 Informatics Practices Paper 5

CBSE Sample Papers for Class 12 Informatics Practices Paper 5 are part of CBSE Sample Papers for Class 12 Informatics Practices. Here we have given CBSE Sample Papers for Class 12 Informatics Practices Paper 5.

CBSE Sample Papers for Class 12 Informatics Practices Paper 5

Board CBSE
Class XII
Subject Informatics Practices
Sample Paper Set Paper 5
Category CBSE Sample Papers

Students who are going to appear for CBSE Class 12 Examinations are advised to practice the CBSE sample papers given here which is designed as per the latest Syllabus and marking scheme, as prescribed by the CBSE, is given here. Paper 5 of Solved CBSE Sample Paper for Class 12 Informatics Practices is given below with free PDF download solutions.

Time : 3 hrs
Maximum Marks : 70

General Instructions

  • All questions are compulsory.
  • Answer the’questions after carefully reading the text.

QUESTIONS

Question 1.
(a) Define a network. What are the different types of networks?
(b) Two neighbourhood schools at a distance of 120 m from each other have decided to join their LkNs using UTP cable, so that they can share their E-Learning resources. But after joining their LANs, they are not able to share the resources due to loss of signal in between. Which device should they use so that signal is amplified in between?
(c) Write the difficulty to sell the software developed using open source software.
(d) What is the mechanism that obtains IP address using a URL of a website?
(e) Define the following terms: (i) Data channel (ii) Baud
(f) Discuss about MODEM. What is its function?
(g) Write down the various facilities provided by the server.

Question 2.
(a) Write HTML code to produce a TextArea with 20 rows and 10 columns.
(b) Identify invalid vanable naines out of the following. State reason if invalid.
(i) switch
(ii) sum 12
(ii) address
(iv) Name
(c) Briefly explain the different GUI output methods used in Java.
(d) Write code for the event handler of a radio button so that when it is selected/unselected, its text changes to “Selected” or “Unselected”.
(e) (i) Rewrite the following program code using if else statement:

int a=jComboBox1.getSelectedlndex ( ) ;
switch(a)
{
case 0 :
GrandTotal=0. 10 * BillAmt ;
break ;
case 1 :
GrandTotal=0 .9 * BillAmt ;
break ;
case 2 :
GrandTotal=O. 8 * Bill Amt ;
break ;
default :
GrandTotal=BillAmt ;

(ii) Neelam has to design two Web pages with following specffications write HTML tags for these :
I. One Web page should have ordered list.
II. Another Web page should have horizontal rule with color ‘Blue’.

Question 3.
(a) How would you display system date as the result of a query?
(b) Following are some statements :

CREATE TABLE EMPLOYEE
(
Emp_Id INT NOT NULL ,
OrderNo INT NOT NULL ,
Emp_rank INT ,
PRIMARY KEY(Emp_Id) ,
FOREIGN KEY(Emp_rank) REFERENCES Persons(Emp_rank)
) ;

Identify the number and types of constraints in the above table EMPLOYEE.

(c) Ahuja entered the following SQL statement to display all workers of the country “US” and “India” from the table “PROFIT”.
CBSE Sample Papers for Class 12 Informatics Practices Paper 5 1

SELECT*FROM PROFIT WHERE Country='US' AND Country-'India' ;

Rewrite the correct statement, if it is wrong.

(d) Consider the table :
CBSE Sample Papers for Class 12 Informatics Practices Paper 5 2
(i) Write query to display Emp_Name, Emp_Salary whose name starts from ‘S’.
(ii) Delete the record of employee Neeru from the table COMPANY.

(e) (i) Consider the CUSTOMER table.
CBSE Sample Papers for Class 12 Informatics Practices Paper 5 3

The following SQL queries are executed on the above table :

INSERT INTO CUSTOMER VALUES ('C106', ‘Aakash’) ;
COMMIT ;
UPDATE CUSTOMER SET Cust_Name='Abhishek' WHERE Cust_ID='C104'; SAVEPOINT P ;
INSERT INTO CUSTOMER VALUES ('C107','Chris') ;
SAVEPOINT Q ;
INSERT INTO CUSTOMER VALUES ('C108Gagan’) ;
SAVEPOINT R ;
ROLLBACK TO Q ;

What will be the output of the following SQL query now?

SELECT*FROM CUSTOMER ;

(ii) An attribute P of datatype VARCHAR (30) has the value “Rastogi”. The attribute Q of datatype CHAR(30) has value “Garg”. How many characters are occupied in attributes P and Q?

Question 4.
(a) What will be the value of variables’m’ and ‘n’ after the execution of the following code?

int m,n = 0 ;
for(m = 1; m <= 4; m++)
{
n+=m;
n- -;
}

(b) (i) Write the corresponding Java expressions for the following mathematical expressions :

CBSE Sample Papers for Class 12 Informatics Practices Paper 5 5

(c) (i) What is XML editor? Also, write Free XML editors.
(ii) The following code has some error(s). Rewrite the correct code underlining all the correction made.

float m=6, float n=1,p=1 ;
do ;
{
p==p*n ;
n++ ;
while (n<=m)
j TextFieldl.setText (" " +p) ;
}

(d) Read the following case study and answer the questions that follow :

Mr. Das is working as a Chief Information Officer in AMD constructions company. In the month of January, he received a letter from the management to store all his employees information in electronic form. He decided to develop a small software application form to store employee’s personal data. He instructed one of his juniors to make a form in Java swing to enter employees information. The junior presented the following form to Mr. Das.

CBSE Sample Papers for Class 12 Informatics Practices Paper 5 6

The form details are given in the following table :

CBSE Sample Papers for Class 12 Informatics Practices Paper 5 7

(i) Write a code snippet on Action Event of ClearFormBTN button to clear Text Field objects, set default choice in the Radio Buttons to Female and clearing all CheckBox controls.
(ii) Write a method ProCheckQualification to be called in the Submit Button’s Action Event. The procedure code will perform the following action:

If the Check Box PostGraduateCB is checked, then the procedure will automatically check the CheckBoxes GraduatcCB and lntermediateCB irrespective of their initial state. Similarly, if the CheckBox GraduateCB is checked then automatically check IntermethateCB, otherwise only IntermediateCB should be automatically checked.

(iii) Write a method ProConvertCase to convert all the employee details in NameTF, FatherNameTF, MotherNameTF and AddressTF to upper case characters.

Question 5.
(a) How do you select all rows from a table named “PRODUCT’ where the value of the column “Product_name” starts with “B”?
(b) What is null value in MySQL database?
(c) (i) Riya Pandey is the Manager of company named Royal, she wants to create a table ‘EMPLOYEE’ to store details of her company.

I. Which of the following can be the attribute(s) of ‘EMPLOYEE’ table?
i. EmpNo
ii. ”Rahul”
iii. Name
iv. 115

II. Name the primary key of the table ‘EMPLOYEE’. State reason for choosing it.

(ii) Write the output of the following SQL queries :

I. SELECT TRUNCATED.864,2) ;
II. SELECT RIGHT(CONCAT(’PUBLICATION', 'ARIHANT'), 4) ;

(d) Consider the following table named “BANK” with details of account holders.
Write commands in SQL for (i) and (ii) and outputs for (iii) and (iv).

CBSE Sample Papers for Class 12 Informatics Practices Paper 5 9

(i) To display all information of account holders whose transaction value is not mentioned.
(ii) To add another column Address with datatype VARCHAR and size (30).

(iii) SELECT Name, Balance FROM BANK WHERE Name LIKE '%i%' ;
(iv) SELECT ROUNDCBalance, -3) FROM BANK WHERE AccountNo = ’B2436’ ;

Question 6.
(a) (i) Write a MySQL command for creating a table ‘SUPPLIERS’

CBSE Sample Papers for Class 12 Informatics Practices Paper 5 12
(ii) In a database Bank, there are two tables CUSTOMER and TRANSACTION with the following contents :

CBSE Sample Papers for Class 12 Informatics Practices Paper 5 13
I. The Cust_ID column in the CUSTOMER table is the key.
The Cust_ID column in the TRANSACTION table is a key.

II. Identify the attributes, which can be chosen as candidate keys in the table CUSTOMER. Also, define candidate key.
(b) With reference to the above given tables (in Q.6 (a) (ii)), write SQL commands for (i) and (ii) and output for (iii).

(i) To add a column Tranjfype with datatype VARCHAR and size 15 in the table TRANSACTION.
(ii) To display Cust_ID, Cust_Name, Account_No, Tran lD, Amount where Amount is greater than 5000.00

(iii) SELECT Cust_ID, Cust_Name, Tran_ID, Amount 
FROM CUSTOMER, TRANSACTION
WHERE CUSTOMER.Cust_ID = TRANSACTION.Cust_ID
AND Account_Type = "Saving" ;

Question 7.
(a) Define front-end of an information system.
(b) E-Business is useful for both businessmen and customer. What benefits does an E-Business offer to the customer?
(c) Muskan works for a store. She wants to create controls on a form for the following functions. Which controls should she use? Choose appropriate controls from TextBox, Label, OptionButton, CheckBox, IistBox, ComboBox, CommandButton.

CBSE Sample Papers for Class 12 Informatics Practices Paper 5 15

ANSWERS

Answer 1.
(a) A network is an interconnected collection of autonomous computers and devices via same kind of transmission machine. Networks can be classified into three categories which are as follows:

  1. Local Area Network (LAN)
  2. Metropolitan Area Network (MAN)
  3. Wide Area Network (WAN)

(b) Repeater is a device used to amplify signals.

(c) Sometimes there is no commercial market for software. You cannot sell software using previous trademarks, which is developed by another person.

(d) Domain Name Resolution.

(e) (i) A data channel is the medium used to carry information or data from one point to another.
(ii) Baud is the unit of measurement for the information carrying capacity of a communicatton channel of analog type. It is synonymous with bps (bits per second) of digital type circuit.

(f) A modem is a computer peripheral device that connects a workstation to other workstations via telephone lines and facilitates communications. It is short form for MOdulation/DEModulation. Modem converts digital signals into analog signals and vice-versa.

(g) Facilities provided by the server in a network environment are as follows:

  1. Resource sharing
  2. Centralised database storage
  3. Internet sharing with authentication
  4. Account monitoring

Answer 2.

(a) <TEXTAREA rows= "20" cols= “10” name= "tar” > Enter detail</TEXTAREA>

(b) (i) switch is invalid because variable names must not be a keyword.
(c) For displaying an output in a Java program, we can use either of the two methods. which are as foIlows:

System.ouiprint ( ) This method displays the text and keeps the cursor in the same line.
System.out.printin ( ) This method displays the text and then moves the cursor to the next line.

(d) private void RdBtnStateChanged ( javax.swing.event.ChangeEvent evt )
{
//RdBtn is the name of Radio Button
if ( RdBtn.isSelected ( ) )
RdBtn.setText ("Selected") ;
else
RdBtn.setText ("Unselected") ;
}

(e) (i) The rewritten code with the use of if else Statement is as follows :
int a=j ComboBox1.getSelectedlndex( ) ;
if (a==0)
GrandTotal=0.10*Bill Amt :
else if(a==1) .
GrandTotal=0.9*BllAmt ;
else if(a==2)
GrandTotal=0.8*BillAmt;
else
GrandTotal=BillAmt ;
(ii) I. <0L> <LI>
II. <HR color='blue'>

Answer 3.
(a) To obtain current system date :

SELECT CURDATE ( ) ;

(b) There are three constraints defined in EMPLOYEE table, are as follows :
(i) Two NOT NULL constraints for column Empjd and OrderNo.
(ii) One PRIMARY KEY constraint for column Empjd.
(iii) One FOREIGN KEY constraint for column Emp_rank.

(c) The correct code is,

SELECT*FROM PROFIT WHERE Country='US' OR Country-'India' ;

(d)

(i) SELECT Emp_Name, Emp_Salary FROM COMPANY WHERE Emp_Name LIKE'S%' ;
(ii) DELETE FROM COMPANY WHERE Emp_Name='Neeru' ;

(ii) The number of characters occupied in attribute P has value Rastogi are 7 and in attribute Q has value Garg are 4.

CBSE Sample Papers for Class 12 Informatics Practices Paper 5 4

Answer 4.
(a) Value of m 5 and n = 5

(b) (i) I. float A = (((b + f) / c ) - d) ; 
II. float z = x * x * x + y * y - (sqrt(x*y))/2 ;

(ii) Java code is ;
float price=Float.parseFloat ( j TextField1.getText ( ) ) ;
int quantity=Integer.parselnt ( j TextFleld2.getjext ( ) ) ;
float tot=price*quantity ;
float tax=tot*10/100 ;
j TextFleld3.setText(” “+tot) ;
j TextField4.setText(” “+tax) ;

(c)
(i) XML editor allow you to create and manipulate XML documents. The basic features which you need are syntax highlighting, color code to make XML easier to read and understand.

Free XML editors

  1. XML look top
  2. XML mind standard Edition
  3. Peter’s XML editors

CBSE Sample Papers for Class 12 Informatics Practices Paper 5 8

(d) (i) private void ClearFormBTNActionPerformed(javax.swing.event.ActionEvent evt)
{
NameTF.setText (" ") ;
FatherNameTF.setText (" ") ;
MotherNameTF.setText (" ") ;
AddressTF.setText (" ") ;
FemaleRB.setSelected(true) ;
IntermediateCB.setSelected(false) ;
GraduateCB.setSelected(false);
PostGraduateCB;setSelected(false) ;
}
(ii) void ProCheckQual ification ( )
{
if (PostGraduateCB.isSelected ( ) )
{
GraduateCB.setSelected(true) ;
IntermediateCB.setSelected(true) ;
}
else if (GraduateCB.isSelected ( ) )
{
IntermediateCB.setSelected(true) ;
}
else
IntermediateCB.setSelected(true) ;
}
(iii) void ProConvertCase ( )
{
String Name = NameTF.getText ( ) ;

NameTF.setText(Name.tollpperCase( ) ) ;
String Fname = FatherNameTF.getText( ) ;
FatherNameTF.setText(Fname.toUpperCase( ) ) ;
String Mname = MotherNameTF.getText( ) ;
MotherNampTF.setText(Mname.tollpperCase( ) ) ;
String add = AddressTF.getText( ) ;
AddressTF.setText(add.toUpperCase( ) ) ;
}

Answer 5.

(a) SELECT* FROM PRODUCT WHERE Product_name LIKE ’B%’ ;

(b) If a column in a row has no value, then column is said to be null, or to contain a null.
(c) (i) I. i. EmpNo ii. Name

II. Primary key is EmpNo as it will be unique for each employee of the company.
(ii) Output of the above queries :

CBSE Sample Papers for Class 12 Informatics Practices Paper 5 10

(d) (i) SELECT * FROM BANK WHERE Transaction IS NULL ;
(ii) ALTER TABLE BANK ADD Address VARCHAR(30) ;
CBSE Sample Papers for Class 12 Informatics Practices Paper 5 11

Answer 6.

(a) (i) CREATE TABLE SUPPLIERS
(
Product_id INT(4),
Product_Name CHAR(10),
Quantity I NT (10),
Price DECIMAL (7,2),
Phone CHAR (10)
) ;

(ii) I. Primary, Foreign
II. Candidate keys: Cust_ID, Account_No

A candidate key can be defined as a column or set of columns, in a table that can uniquely identify any database record without referring to any other data.

(b) (i) ALTER TABLE TRANSACTION ADD Tran_Type VARCHAR (15) ;
(ii) SELECT Cust_ID, Cust_Name, Account_No, Tran_ID, Amount
FROM CUSTOMER. TRANSACTION
WHERE CUSTOMER.Cust_ID=TRANSACTION.Cust_ID AND Amount>5000.00 ;
CBSE Sample Papers for Class 12 Informatics Practices Paper 5 14

Answer 7.
(a) Front-end of an information system This is the user interface that the users see and which is responsible for interacting with the user. The front-end is responsible for receiving user’s queries, requests etc., and passing it over to the back-end.

(b) E-Business offers following benefits to the customers :

  1. Improved speed of response
  2. Cost savings
  3. Improved efficiency and productivity
  4. Improved customer service.

CBSE Sample Papers for Class 12 Informatics Practices Paper 5 16

We hope the CBSE Sample Papers for Class 12 Informatics Practices Paper 5 help you. If you have any query regarding CBSE Sample Papers for Class 12 Informatics Practices Paper 5, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4

NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4.

Board CBSE
Textbook NCERT
Class Class 9
Subject Maths
Chapter Chapter 14
Chapter Name Statistics
Exercise Ex 14.4
Number of Questions Solved 6
Category NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4

Question 1.
The following number of goals were scored by a team in a series of 10 matches
2, 3, 4, 5, 0, 1, 3, 3, 4, 3.
Find the mean, median and mode of these scores.
Solution:
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4 img 1
(iii) Mode Arranging the given data in ascending order, we have 0, 1,2, 3, 3, 3, 3, 4, 4, 5.
Here, 3 occurs most frequently (4 times)
∴ Mode = 3

Question 2.
In a mathematics test given to 15 students, the following marks (out of 100) are recorded
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60
Find the mean, median and mode of this data.
Solution:
(i) Mean
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4 img 2
(ii) Median Arranging the given data in descending order, we have 98, 96, 62, 60, 54, 52, 52, 52, 48, 46, 42, 41,40, 40, 39
Number of observations (n) = 15 which is odd.
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4 img 3
(iii) Mode Arranging the data in descending order, we have 98, 96, 62, 60, 54, 52, 52, 52, 48, 46, 42, 41,40, 40, 39.
Here, 52 occurs most frequently (3 times).
∴ Mode = 52

Question 3.
The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95
Solution:
Number of observations (n) = 10which is even.
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4 img 4
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4 img 5
According to question, median = 63
∴ x + 1 = 63 ⇒ x = 63 – 1 = 62
Hence, the value of x is 62.

Question 4.
Find the mode of 14, 25,14, 28,18,17,18,14, 23, 22,14 and 18.
Solution:
The given data is,
14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18
Arranging the data in ascending order, we have
14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28
Here, 14 occurs most frequently (4 times).
∴ Mode = 14

Question 5.
Find the mean salary of 60 workers of a factory from the following table
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4 img 6
Solution:
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4 img 7
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4 img 8
Hence, the mean salary is ₹ 5083.33.

Question 6.
Give one example of a situation in which
(i) the mean is an appropriate measure of central tendency.
(ii) the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.
Solution:
(i) Mean marks in a test in mathematics,
(ii) Average beauty

We hope the NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4 help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3

NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3.

Board CBSE
Textbook NCERT
Class Class 9
Subject Maths
Chapter Chapter 14
Chapter Name Statistics
Exercise Ex 14.3
Number of Questions Solved 9
Category NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3

Question 1.
A survey conducted by an organisation for the cause of illness and death among the women between the ages 15-44 (in years) worldwide, found the following figures (in %)
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 1
(i) Represent the information given above graphically.
(ii) Which condition is the major cause of women’s ill health and death worldwide?
(iii) Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause.
Solution:
(i) We draw the bar graph of this data in the following steps. Note that, the unit in the second column is percentage.

  1. We represent the causes (variable) on the horizontal axis choosing any scale, since width of the bar is not important but for clarity, we take equal widths for all bars and maintain equal gaps in between. Let on cause be represented by one unit.
  2. We represent the female fatality rate (value) on the vertical axis. Here, we can choose the scale as 1 unit = 4%.
  3. To represent our first cause i.e, reproductive health conditions, we draw & rectangle bar with width 1 unit and height 31.8 units.
  4. Similarly, other heads are represented leaving a gap of 1 unit in between two consecutive bars.

Now the graph is drawn in figure.
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 2
(ii) From graph, we observe that ‘reproductive health conditions’ is the major cause of women’s ill health and death world wide because it has maximum percentage among the causes i.e.,31.8%.

Question 2.
The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 3
(i) Represent the information above by a bar graph.
(ii) In the classroom discuss, what conclusions can be arrived at from the graph.
Solution:
(i) We draw the bar graph of this data, note that the unit in the second column is number of girls per thousand boys.
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 4
We represent the section on the horizontal axis choosing any scale, since width of the bar is not important but for clarity, we take equd widths for all bars and maintain equal gaps in between. Let on section be represented by one unit.
We represent the number of girls per thousand boys on the vertical axis.
Now, the graph is drawn in figure.
We represent the number of girls per thousand boys on the vertical axis. Here, we can choose the scale as 1 unit = 100.
Now, the graph is drawn in figure

(ii) From graph, we observe that scheduled tribe (ST) number of girls is major section in different sections of Indian society, because it has maximum number of girls per thousand boys i.e., 970.

Question 3.
Given below are the seats won by different political parties in the polling outcome of a state assembly elections
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 5
(i) Draw a bar graph to represent the polling results.
(ii) Which political party won the maximum number of seats?
Solution:
We draw the bar graph of this data, note that the unit in the second column is seats won by political party.
(i) We represent the political party on the horizontal axis choosing any scale, since width of the bar is not important but for clarity, we take equal widths for all bars and maintain equal gaps in between. Let on political party be represented by one unit.
(ii) We represent the seats won on the vertical axis. Here, we can choose the scale as 1 unit = 10
Now, the graph is drawn in figure
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 6
Party ‘A’ Won the maximum number of seats. i.e, 75.

Question 4.
The length of 40 leaves of a plant measured correct to one millimetre and the obtained data is represented in the following table
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 7
(i) Draw a histogram to represent the given data.
(ii) Is there any other suitable graphical representation for the same data?
(iii) Is it correct to conclude that the maximum number of leaves 153 mm long and Why?
Solution:
(i) We know that, the areas of the rectangles are proportional to the frequencies in a histogram. Now, we get the following modified table by given data
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 8
Now, we draw the histogram for given data
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 9
(ii) Frequency polygon.
(iii) No, because the maximum number of leaves have their lengths lying in
the interval 145-153.

Question 5.
The following table gives the lifetimes of 400 neon lamps
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 10
(i) Represent the given information with the help of a histogram.
(ii) How many lamps have a lifetime of more 700 h?
Solution:
(i) Here, we will make a modified table by given data.
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 11
Now, we draw the histogram for above table
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 12
(ii) 184 lamps have a life time of more than 700 h i.e.,74 + 62 + 48 = 184.

Question 6.
The following table gives the distribution of students of two sections according to the marks obtained by them
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 13
Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.
Solution:
Here, we make modified tables by given data.
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 14
Now, required frequency polygon curves are
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 15

Question 7.
The runs scored by two teams A and B on the first 60 balls in a cricket match are given below
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 16
Represent the data of both the teams on the same graph by frequency polygons.
Solution:
First make the class intervals continuous.
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 17
Now, draw a frequency polygon curve
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 18

Question 8.
A random survey of the number of children of various age groups playing in a park was found as follows
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 19
Draw a histogram to represent the data above.
Solution:
We know that, the areas of the rectangles are proportional to the frequencies in a histogram. Here, the widths of the rectangles are varying. So, we need to make certain modifications in the lengths of the rectangles, so that the areas are again proportional to the frequencies.

  1. Select a class interval with the minimum class size. The minimum class size is 1.
  2. The lengths of the rectangles are then modified to be proportionate to the class size

Now, we get the following table
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 20
So, the correct histogram with varying width is given below.
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 21

Question 9.
100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 22
(i) Draw a histogram to depict the given information.
(ii) Write the class interval in which the maximum number of surnames lie.
Solution:
(i) We know that, the areas of the rectangles are proportional to the frequencies in a histogram. Here, the widths of the rectangles are varying. So, we need to make certain modifications in the lengths of the rectangles. So that the areas are again proportional to the frequencies.

  1. Select a class interval with the minimum class size. The minimum class size is 2.
  2. The lengths of the rectangles are then modified to be proportionate to the class size 2.

Since we have calculated these lengths for interval of 2 letters in each case, we may call these lengths as ‘proportion of surnames per 2 mark ‘ interval’.
So, the correct histogram with varying width is given below.
Here, we make a modified table by given data with minimum class size 2.
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 23
NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 img 24
(ii) The class interval in which the maximum number of surnames lie is 6-8.

We hope the NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3 help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3, drop a comment below and we will get back to you at the earliest.