Force and Laws of Motion

CSCE TUTORIAL

Force and Laws of Motion

Worksheet-1

 

  1. Which of the following has more inertia:
         (a)  a rubber ball and a stone of the same size?
         (b)  a bicycle and a train?
         (c)  a five rupees coin and a one-rupee coin?
  1. Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.
  1. Why do you fall in the forward direction when a moving bus brakes to a stop and fall backwards when it accelerates from rest?
  1. A constant force acts on an object of mass 5 kg for a duration of 2 s. It increases the object’s velocity from 3 m s–1 to 7 m s-1. Find the magnitude of the applied force. Now, if the force was applied for a duration of 5 s, what would be the final velocity of the object?
  1. A motorcar is moving with a velocity of 108 km/h and it takes 4 s to stop after the brakes are applied. Calculate the force exerted by the brakes on the motorcar if its mass along with the passengers is 1000 kg.
  1. A force of 5 N gives a mass m1 , an acceleration of 10 m s–2 and a mass m2 , an acceleration of 20 m s-2 . What acceleration would it give if both the masses were tied together?
  1. Explain why it is difficult for a fireman to hold a hose, which ejects large amounts of water at a high velocity.
  1. When a carpet is beaten with a stick, dust comes out of it. Explain.
  1. A stone of 1 kg is thrown with a velocity of 20 m s–1 across the frozen surface of a lake and comes to rest after travelling a distance of 50 m. What is the force of friction between the stone and the ice?
  1. An object of mass 100 kg is accelerated uniformly from a velocity of 5 m s–1 to 8 m s–1 in 6 s. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.
  1. How much momentum will a dumb-bell of mass 10 kg transfer to the floor if it falls from a height of 80 cm? Take its downward acceleration to be 10 m s–2 .

Class – 9 Motion

CSCE TUTORIAL

MOTION

Worksheet – 1

  1. Can the magnitude of the displacement be equal to the distance travelled by an object? Justify by giving an example.

 

  1. A farmer moves along the boundary of a square field of side 10 m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds from his initial position?

 

  1. What does the odometer of an automobile measure?

 

  1. The odometer of a car reads 2000 km at the start of a trip and 2400 km at the end of the trip. If the trip took 8 h, calculate the average speed of the car in km h–1 and m s–1. 

 

  1. A bus decreases its speed from 80 km h–1 to 60 km h–1 in 5 s. Find the acceleration of the bus.

 

  1. What is the nature of the distance-time graphs for uniform and non-uniform motion of an object? 

 

  1. What can you say about the motion of an object whose distance-time graph is a straight line parallel to the time axis?

 

  1. What can you say about the motion of an object if its speed-time graph is a straight line parallel to the time axis? 

 

  1. What is the quantity which is measured by the area occupied below the velocity-time graph?

 

  1. He brakes applied to a car produce an acceleration of 6 m s-2 in the opposite direction to the motion. If the car takes 2 s to stop after the application of brakes, calculate the distance it travels during this time.

 

  1. A trolley, while going down an inclined plane, has an acceleration of 2 cm s-2. What will be its velocity 3 s after the start?

 

  1. A stone is thrown in a vertically upward direction with a velocity of 5 m s-1. If the acceleration of the stone during its motion is 10 m s–2 in the downward direction, what will be the height attained by the stone and how much time will it take to reach there?

 

  1. Abdul, while driving to school, computes the average speed for his trip to be 20 km h–1. On his return trip along the same route, there is less traffic and the average speed is 30 kmh–1 What is the average speed for Abdul’s trip?

 

  1. A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 m s-2, with what velocity will it strike the ground? After what time will it strike the ground?

 

  1. State which of the following situations are possible and give an example for each of these:

          (a) an object with a constant acceleration but with zero velocity

          (b) an object moving in a certain direction with an acceleration in the perpendicular direction. 

 

  1. An artificial satellite is moving in a circular orbit of radius 42250 km. Calculate its speed if it takes 24 hours to revolve around the earth.

वाक्य अभ्यास

CSCE TUTORIAL

वाक्य अभ्यास

  1. ‘जो परिश्रम करेगा, वह सफल होगा-अर्थ के आधार पर वाक्य का कौन-सा भेद है?
  • (क) संदेहवाचक
  • (ख) विधानवाचक
  • (ग) संकेत वाचक
  • (घ) विस्मयवाचक

 

  1. ‘जैसी नीयत होती है अल्ला भी वैसी ही बरकत देता हैं अर्थ की दृष्टि से वाक्य भेद क्या होगा?
  • (क) इच्छावाचक
  • (ख) आज्ञावाचक
  • (ग) निषेधवाचक
  • (घ) संकेतवाचक

 

  1. ‘लड़का परसों सुबह मुँह अँधेरे बेलों में से पके खरबूजे चुन रहा था’ वाक्य अर्थ की दृष्टि से किस प्रकार का वाक्य है?
  • (क) विधानवाचक
  • (ख) संदेहवाचक
  • (ग) इच्छावाचक
  • (घ) विस्मयवाचक

 

  1. ‘आज वह बाजार में सौदा बेचने चली गई; हाय रे पत्थर दिल!’ वाक्य अर्थ की दृष्टि से किस वर्ग में आएगा?
  • (क) विधानवाचक
  • (ख) विस्मयवाचक
  • (ग) इच्छावाचक
  • (घ) संदेहवाचक

 

  1. ‘शायद उन्हें मेरी बात बुरी लग गई होगी’ वाक्य में अर्ध की दृष्टि से कौन-सा भेद है?
  • (क) निषेधवाचक
  • (ख) आज्ञावाचक
  • (ग) संदेहवाचक
  • (घ) संकेतवाचक

 

  1. ‘अनेक बार देखा कि केवल थोड़ी दूर के बाद कोई ऊँची चढ़ाई नहीं है’ अर्थ की दृष्टि से वाक्य का प्रकार बताइए।
  • (क) विधानवाचक
  • (ख) संदेहवाचक
  • (ग) आज्ञावाचक
  • (घ) निषेधवाचक

 

  1. ‘ल्हाटू एक नायलॉन की रस्सी लाया था’ वाक्य अर्थ के आधार पर किस प्रकार का वाक्य है?
  • (क) विस्मयवाचक
  • (ख) संदेहवाचक
  • (ग) इच्छावाचक
  • (घ) विधानवाचक

 

  1. निम्नलिखित वाक्यों को निर्देशानुसार परिवर्तित कीजिए-
  • उसके व्यवहार को कौन नहीं जानता?                                       विधान वाचक
  • उसने अपना काम पूरा कर लिया।                                            प्रश्नवाचक
  • हाथी बहुत बड़ा है।                                                                विस्मयादिबोधक
  • कल मैं विद्यालय नहीं जाऊँगा ।                                                संदेह वाचक
  • वह कक्षा में प्रथम आया।                                                          विस्मयादिबोधक
  • उसने किसी से बात नहीं की।                                                    विधान वाचक
  • अर्चना अपना पाठ याद कर रही है।                                            आज्ञा वाचक
  • आज बहुत ठंड है।                                                                   निषेधवाचक
  • वह मान जाएगा।                                                                      निषेधवाचक
  • तुम आ गए हो।                                                                         विस्मयादिबोधक
  • शायद आज मामा जी आएँगे।                                                      प्रश्नवाचक
  • वीरेश प्रतिदिन व्यायाम करता है।                                               आज्ञावाचक
  • तुम्हारा मित्र आज विद्यालय नहीं जाएगा।                                      प्रश्नवाचक
  • वह दिल्ली जाएगा।                                                                   प्रश्नवाचक
  • अपनी-अपनी आस्थानुसार नित्य प्रार्थना करनी चाहिए।                   आज्ञा वाचक
  • उसने कोई उपाय नहीं छोड़ा।                                                    विधान वाचक
  • वर्षा आएगी।                                                                           संदेह वाचक

विराम चिह्न

CSCE TUTORIAL
विराम चिह्न

लिखते समय रुकने वाले स्थानों को प्रकट करने के लिए कुछ विशेष चिह्न लगाने पड़ते हैं, उन्हीं चिह्नों को विराम-चिह्न कहते हैं।

ये तेरह हैं-

  1. पूर्ण विराम (Full Stop) ( I )
  2. अल्प विराम (Comma) (.)
  3. अर्ध विराम (Semicolon) (;)
  4. प्रश्नवाचक चिह्न (Mark of Interrogation)(?)
  5. विस्मय वाचक-चिह्न (Mark of Exclamation)(!)
  6. उप विराम / अपूर्ण विराम (Colon)(:)
  7. निर्देशक-चिह्न (Dash) _
  8. विवरण – चिह्न (Sign of Following) (:-)
  9. लाघव – चिह्न (Sign of Abbreviation) (•)
  10. योजक-चिह्न (Hyphen) (-)
  11. कोष्ठक (Brackets) ( )
  12. उद्धरण चिह्न (Inverted Comma) (” “) (‘ ’)
  13. त्रुटि पूरक (^)
(अभ्यास कार्य)

निम्नलिखित वाक्यों में उचित विराम-चिह्न लगाइए–

  1. स्त्री- बस, आप इस मुकदमे को ले लें I मैं आपको तीन हज़ार रुपए रोज़ दूँगीI
  2. मेरा बचपन ! क्या यह हाल की बात है?
  3. उन चार चेहरों के आठ- आठ जोड़ी दाँत I आहा ! मानो धूप में रखे आईने की तरह चमक उठते I
  4. जब तक अलाव जलते रहेंगे ; तब तक बची रहेगी आग , बची रहेगी सामूहिकता, बचा रहेगा खुलकर कह- सुन सकने का चलन I
  5. हम कर्मशील बनें I हमारी कारीगरी बढ़े, तभी हमारा भाग्योदय होगा I
  6. उसने उनके कान में जाकर कहा – “उठो मियाँ, उठो जागो ,जागने का वक़्त हैI”
  7. हाँ, देख लेना तुम I ताना मार रहे हो, लेकिन मैं दिखा दूँगा ;धन को कितना तुच्छ समझता हूँ I
  8. धन के लिए माँ -बाप, भाई- बंधु सबसे अलग यहाँ पड़ा हूँ , न जाने अभी कितनी सलामियाँ देनी पड़ेंगी , कितनी खुशामद करनी पड़ेगी ?
  9. अब कहाँ जाओगे ? यहीं सो रहो I और बातें हों , तुम तो कभी आते भी नहीं I
  10. मालिक जी जैसे सेवा व्रती निश्छल व्यक्ति भगवान की याचना अनुग्रह से ही मिलते हैं बिनु हरि कृपा मिलिए नहीं संता
  11. यह सब तो हुआ पर मालिक जी को जैसे गुरुमंत्र ही मिल गया अगर पीड़ा है तो आशा भी है
  12. उन्होंने निष्कर्ष दिया ज़्यादती उनकी है गलती हमारी मैंने पूछा गलती कौन सी
  13. उसके साथ कुछ मिठाई नमकीन बिस्कुट मौसमी फल जैसे सेब अमरूद केला संतरा यानी कि जी खोल कर स्वागत होता
  14. उन दिनों फ़ोटो नहीं खींची जाती थी भला यह कैसे कहा जा सकता है बात है कितनी पुरानी विधान बाबू का बचपन अभी तीस पैंतीस साल पहले की ही तो बात है
  15. मुझे क्या परेशानी होगी चल तो तुम रहे हो दिन में दस बीस मील गरम रेत पर मैं तो मज़े से बैठा हूँ कंधे पर
  16. आचार्यों ने कहा सेवा देने की चीज़ है लेने की नहीं सेवा लेने के अधिकारी बच्चे असहाय और वृद्ध हैं
  17. माताजी ने कहा सब ठीक ठाक होना चाहिए वरना बीच अंतरिक्ष में चलान कर दूँगा
  18. गुरुदेव हमारी तो बड़ी आफ़त है तमाम भले लोग आते हैं और कहते हैं उस बेचारे बेक़सूर को क्यों फँसा रहे हैं ऐसा तो चंद्रलोक में कभी नहीं हुआ
  19. कौन कहता है आप अकेली हैं महारानी आप तो गीता पढ़ती हैं फिर यह निराशा कैसी
  20. स्वराज्य प्राप्ति से बढ़कर है स्वराज्य की स्थापना के लिए भूमि तैयार करना स्वराज्य की नींव का पत्थर बनना




Social Science

Chapterwise Notes, Worksheets and Assignments

Geography

Chapter 1: Resources and Development

                 Resources and Development MCQ

                 Resources and Development Important Questions

Chapter 2: Forest and Wildlife Resources
Chapter 3: Water Resources
Chapter 4: Agriculture
Chapter 5: Minerals and Energy Resources
Chapter 6: Manufacturing Industries
Chapter 7: Lifelines of National Economy

Economics

Chapter 1: Development
Chapter 2: Sectors of the Indian Economy
Chapter 3: Money and Credit
Chapter 4: Globalisation and the Indian Economy
Chapter 5: Consumer Rights

 

History

Chapter 1: The Rise of Nationalism in Europe
Chapter 2: Nationalism in India
Chapter 3: The Making of a Global World
Chapter 4: The Age of Industrialisation
Chapter 5: Print Culture and The Modern World

Political Science

Chapter 1: Power Sharing
Chapter 2: Federalism
Chapter 3: Democracy and Diversity
Chapter 4: Gender, Religion and Caste
Chapter 5: Popular Struggles and Movements
Chapter 6: Political Parties
Chapter 7: Outcomes of Democracy
Chapter 8: Challenges to Democracy

 

 

 

Ch-3 Pair of Linear Equations in Two Variables

CSCE TUTORIAL

                                                                               Chapter 3                                                                                  Assignment-1

Pair of Linear Equations in two variables

Class – X                                                                                                                                                Mathematics

 

Q-1. The pair of linear equations 3x + 5y = 3 and 6x + ky = 8 do not have a solution if k=

a) = 5                    b) = 10                    c) ≠10                              d) ≠ 5

 

Q-2. The solution of the equation x + y = 5 and x − y = 5 is

a) (0,5)                     b) (5,5)                   c) (5,0)                            d) (10 ,5)

 

Q-3. The pair of linear equations x = 0 , x = −5 has

a) One solution                    b) two solution                    c) infinite no. of solution             d) no solution

 

Q-4. For what value of ‘k’ do the equations 3x – y + 8 = 0 and 6x – ky + 16 = 0 represent coincident lines

a) 1/2                     b) −1/2                      c) 2                                        d) -2

 

Q-5. For what value of ‘k’ for which the system of equations 4x + ky + 8 = 0 and 2x + 2y + 2 = 0 has a unique solution?

 

Q-6. In how many points do the lines represented by the equations x − y = 0 and x + y = 0 intersect?

 

Q-7. Find the value of (x + y) if  3x − 2y = 5 and 3y − 2x = 3.

 

Q-8. Sum of two numbers is 35 and their difference is 13, find the numbers.

 

Q-9. Find the value of ‘p’ for which the pair of linear equations 2px + 3y = 7 and 2x + y = 6 has exactly one solution.

 

Q-10. Do the equations y = x and y = x + 3 represent parallel lines?

 

Case study

  1. The alumni meet of two batches of a college- batch A & batch B were held on the same day in the same hotel in two separate halls “Rose” and “Jasmine”. The rents were the same for both the halls. The expense for each hall is equal to the fixed rent of each hall and proportional to the number of persons attending each meet. 50 persons attended the meet in “Rose” hall, and the organisers had to pay ₹ 10000 towards the hotel charges. 25 guests attended the meet in “Jasmine” hall and the organizers had to pay ₹ 7500 towards the hotel charges. Denote the fixed rent by ₹ x and proportional expense per person by ₹ y.
  2. Represent algebraically the situation in hall “Rose”.
  3. Represent algebraically the situation in hall “Jasmine”.
  4. What is the fixed rent of the halls?
  5. Find the amount the hotel charged per person.

 

Q-2.  Draw the graphs of 2x − 3y + 6 = 0 and 2x + 3y − 18 = 0. Find the ratio of areas of triangles formed by the given lines with X-axis and            Y-axis.

 

Q-3. Determine graphically the vertices of the triangle, the equations of whose sides are given below   2y − x = 8; 5y − x = 14; y − 2x = 1

Resources and Development Notes

CSCE TUTORIAL

Class – X                                                                                                                                                                                    Geography

Resources and Development

 

Resource

Everything available in our environment that can be used to satisfy our needs, which is technologically accessible, economically feasible and culturally acceptable can be termed as resource.

 

Types of Resource

Resources can be classified on the basis of origin, exhaustibility, ownership and the status of development.

On the basis of origin, resources are of two types, biotic resources and abiotic resources.

Biotic resources are obtained from biosphere and have life, i.e.; human beings, livestock, flora and fauna, fisheries etc.

Abiotic resources are composed of non-living things, e.g., rocks and metals.

 

On the basis of exhaustibility, resources are renewable and non-renewable.

Renewable resources can be renewed or reproduced by applying physical, chemical or mechanical process e.g. solar energy, wind energy, forest, water, wildlife, etc.

These resources can be further sub divided into two forms, i.e., flow or continuous resources and biological resources.

Non-renewable resources are formed through long geological time period and cannot be renewed easily, e.g., minerals, metals and fossil fuels. These resources may further divided as recyclable and non-recyclable.

 

On the basis of ownership, resources are individual, community owned, national and international resources.

Individual resources are owned privately by individuals, e.g. plantation, pasture land, farmland, etc.

Community owned resources are equally accessible to all the members of the community e.g., grazing ground, burial grounds, etc.

National resources are under the control of nation, eg. canal, roadways, railways, etc.

International resource are international institutions which regulate some resources like the oceanic resources beyond 200 nautical miles of the Exclusive Economic Zone belong to open ocean which cannot be used by any country without the permission of international institutions.

On the basis of the status of development, resources are potential, developed, stocks and reserves.

 

Potential resources are those resources which are found in a region, but not yet have been utilised.

Developed resources are surveyed and their quality and quantity is determined for utilization e.g., coal and petroleum.

Stock Material in the environment which have the potential to satisfy human need but human being do not have appropriate technology to access these are known as stock, e.g. hydrogen

Reserves are subset of stock which can used by technical know-how, but their use has not been started, e.g. river water

 

Development of Resources

Resources are vital for human survival and for maintaining quality of life. But over utilization of resources has led to the serious global problems like global warming, ozone layer depletion. environmental pollution and land degradation.

 

An equal distribution of resources therefore, is essential for a sustained quality of life and global peace. This can be achieved through sustainable development and resource planning.

 

Sustainable Development

 

Sustainable economic development means ‘development should take place without damaging the environment, and development in the present, should not compromise with the needs of the future generations.

 

Rio De Janeiro Summit, 1992

  • The first International Earth Summit was held in Rio De Janeiro in June 1992.
  • The summit addressed the problems of environmental protection and socio-economic development.
  • Leaders of more than 100 countries signed the Declaration on Global Climate Change and Biological Diversity. They also adopted Global Forest Principles and Agenda 21.

 

Agenda 21

  • It is a declaration signed at the United Nations Conference on Environment and Development (UNCED) in 1992 at Rio De Janeiro, Brazil.
  • It aims to combat environmental damage, poverty, disease through global co-operation, etc. It also aims that every local government should draw its own local Agenda 21.

 

Resource Planning

 

  • Planning is the widely accepted strategy for judicious use of resources.
  • Resource planning is essential for sustainable development in India because some regions are rich in one resources but are deficient in other resources.
  • There are some regions which can be considered self-sufficient in terms of availability of resources and there are some regions which have acute shortage of vital resources. e.g. Jharkhand and Madhya Pradesh.

 

Resource Planning in India

  • Complex process of resource planning in India divided into three stages, e.g., identification and inventory of resources, planning for resource development, matching the resource development plans with overall national development plans.
  • India has made concerted efforts for achieving the goals of resources planning right from the First Five Year Plan launched after Independence.

 

Resources and Colonisation

  • Rich natural resources of colonies were the main attractions for foreign invaders.
  • Technological development of the colonising countries helped them to exploit resources of colonised regions.
  • India has experienced by colonisation that the availability of resources as well as the technology and quality of human resource are needed for proper development.

 

Conservation of Resources

  • Resources are vital for any developmental activity. To overcome the problems of irrational consumption and over-utilisation of resources resource conservation at various levels is important.
  • At international level, resource conservation advocated in 1968 at Club of Rome and in 1987, the Brundtland Commission Report extensively mentioned the necessity of resources

 

Land Resources

Land is a very important natural resource. It a limited, so, it needs to be used with careful

planning.

Indian’s geographical area comprises of variety relief features i.e. 43 per cent plain land area for agriculture and industries, 27 per cent plates which source of mineral, fossil fuels and forest and 30 per cent of mountains.

 

Land Utilisation

Land resource are used for the many purposes such as Forests, Land not available for cultivation, Other uncultivated land, Fallow lands, Net sown area

 

Land Use Pattern in India

The use of land is determined by physical factors like climate, soil type, topography etc as well as human factors like population density, technological capability and culture and traditions, etc. Total geographical area of India is 3.28 million km. Out of this, the land under permanent pasture has decreased. In India, land use data is available for only 93 per cent of total area.

Between 1960-61 and 2014-2015 major changes took place in land use pattern in India.

For example,

  • Most of the other than current fallow lands are of poor quality and their cost of cultivation is very high. The pattern of net sown area varies greatly from one state to another.
  • Forest area in India is far lower than the desired 33% of geographical area.
  • Waste land includes rocky, arid and desert areas and land put to other non-agricultural uses includes settlements, roads, railways, industry, etc.

Dragline, Mining, Coal Mining, Machine

Land Degradation and Conservation Measures

  • It is a common problem associated with land resources which is accelerated today because of human activities like deforestation, overgrazing and mining.
  • Natural factors like water and wind cause erosion of top soil.
  • Mineral processing is also responsible for land degradation.
  • Measures to reduce land degradation are afforestation, controlled grazing, stabilization of and dunes etc.

 

Soil as a Resources

Soil is a living system and supports different types of living organisms.

It takes millions of years to form soil upto a few an in-depth relief, parent rock or bed rock, climate, vegetation and other forms of life and time are important factors in the formation of soil.

 

Classification of Soil

There are various types of soils found in India such as Alluvial, Black, Red and Yellow, Laterite, Arid, Forest and Mountain soils.

 

Alluvial soils

Alluvial soil is the most widespread soil in India, which has been deposited by three important Himalayan River systems i.e. the Indus, the Ganges and the Brahmaputra.

 

Black Soils

Black soil is also known as black cotton soil or regur soil. The factors that are important for the

formation of black soil are climatic condition along with parent rock material. It is found in the Deccan trap (Basalt) region and is made up of lava flows.

 

Red and Yellow Soils

It is red in colour due to diffusion of iron particles into crystalline and metamorphic rocks in low rainfall areas of the Deccan plateau (Eastern and Southern parts).

  • It is found in parts of Odisha, Chhattisgarh, Southern parts of Middle Ganga Plain and along the piedmont zone of the Western Ghats.

 

Laterite SoilsRed earth or soil background Tropical laterite soil or red earth background. More Africa photos: http://tonytremblay.com/sylvie/afrique.jpg laterite soil stock pictures, royalty-free photos & images

  • The word laterite has been derived from the Latin word ‘later ’ which means brick.
  • Laterite Soil develops in tropical and sub-tropical climate with alternative wet and dry season.
  • It is found mostly in Western Ghats region of Maharashtra, Odisha, some parts of West Bengal and North-East regions.

 

 

 

Arid Soils

  • Arid Soil is found in dry areas. In some areas, common salt is obtained in this soil due to evaporation of water.
  • It can be useful for cultivation only with suitable irrigation methods as in case of Western Rajasthan.

 

Forest Soils

Forest soil is found in hilly and mountainous areas where sufficient rain forests are available

It is found in lower parts of valleys particularly on the river terraces

The balance is disturbed due to natural and human causes.

 

Soil Erosion and Soil Conservation

  • Soil erosion is the removal of the soil cover and subsequent washing down of top soil.
  • The process of soil formation and erosion go on simultaneously and there is a balance between the two processes.
  • The balance is disturbed due to natural and human causes.
  • Erosion through wind, glacier and water are natural causes.
  • Erosion due to deforestation, overgrazing, construction and mining, etc. are Human causes.
  • Contour ploughing, terrace farming, strip cropping, shelter belts can prevent soil erosion.

 

 

Practice Multiple Choice Questions based on this chapter Click here

Ch – 1 Real Numbers Most important questions

CSCE TUTORIAL

Class – X                                                                                                                                                                                  Maths

Real Numbers

Worksheet – 1

 

  1. Express 98 as a product of its primes.
  2. Find the largest number that will divide 398, 436 and 542 leaving remainders 7, 11, and 15 respectively.
  3. If the HCF of 408 and 1032 is expressible in the form 1032 × 2 + 408 × p, then find the value of p.
  4. HCF and LCM of two numbers is 9 and 459 respectively. If one of the numbers is 27, find the other number.
  5. Find HCF and LCM of 13 and 17 by prime factorisation method.
  6. Find LCM of numbers whose prime factorisation are expressible as 3 × 52and 32 × 72.
  7. Find the LCM of 96 and 360 by using fundamental theorem of arithmetic.
  8. Find the HCF (865, 255) using Euclid’s division lemma.
  9. Find the largest number which divides 70 and 125 leaving remainder 5 and 8 respectively.
  10. Three bells toll at intervals of 9, 12, 15 minutes respectively. If they start tolling together, after what time will they next toll together?
  11. Two tankers contain 850 liters and 680 liters of petrol. Find the maximum capacity of a container which can measure the petrol of each tanker in the exact number of times.
  12. The length, breadth, and height of a room are 8 m 50 cm, 6 m 25 cm and 4 m 75 cm respectively. Find the length of the longest rod that can measure the dimensions of the room exactly.
  13. Three alarm clocks ring at intervals of 4, 12 and 20 minutes respectively. If they start ringing together, after how much time will they next ring together?
  14. In a school, there are two Sections A and B of class X. There are 48 students in Section A and 60 students in Section B. Determine the least number of books required for the library of the school so that the books can be distributed equally among all students of each Section.
  15. There are 104 students in class X and 96 students in class IX in a school. In a house examination, the students are to be evenly seated in parallel rows such that no two adjacent rows are of the same class.
         (a) Find the maximum number of parallel rows of each class for the seating arrangement.
         (b) Also, find the number of students of class IX and also of class X in a row.
         (c) What is the objective of the school administration behind such an arrangement?
  1. Dudhnath has two vessels containing 720 ml and 405 ml of milk respectively. Milk from these containers is poured into glasses of equal capacity to their brim. Find the minimum number of glasses that can be filled.
  2. Amita, Sneha, and Raghav start preparing cards for all persons of an old age home. In order to complete one card, they take 10, 16 and 20 minutes respectively. If all of them started together, after what time will they start preparing a new card together?
  3. If two positive integers x and y are expressible in terms of primes as x = p2q3and y = p3q, what can you say about their LCM and HCF. Is LCM a multiple of HCF? Explain.
  4. Find the largest number, which divides 615 and 963, leaving the remainder 6 in each case.
  5. If the HCF of 408 and 1032 is expressible in the form 1032m – 408 x 5, find m.