In Figure, ABCD is a rectangle. Find the values of x and y.

Find the sum of first 8 multiples of 3.

Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, –3). Hence find m.

Two different dice are tossed together. Find the probability:

An integer is chosen at random between 1 and 100. Find the probability that it is:

Find all zeroes of the polynomial (2x^{4} – 9x^{3} + 5x^{2} + 3x – 1) if two of its zeroes are (2 + √3) and (2 – √3).

If A(–5, 7), B(–4, –5), C(–1, –6) and D(4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides.

A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 km/h from the usual speed. Find its usual speed.

Prove that the area of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonal.

Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.

If 4 tan θ = 3, evaluate

If the area of two similar triangles are equal, prove that they are congruent.

If tan 2A = cot (A - 18°), where 2A is an acute angle, find the value of A.

Find the area of the shaded region in Figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm. [Use π = 3.14]

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Figure. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm. Find the total surface area of the article.

A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

The table below shows the salaries of 280 persons:

Calculate the median salary of the data.

A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete total journey, what is the original average speed?

A motor boat whose speed is 18 km/hr in still water takes 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7 : 15. Find the numbers.

Prove that

The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find:

As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. [Use √3 = 1.732]

The mean of the following distribution is 18. Find the frequency f of the class 19 - 21.

The following distribution gives the daily income of 50 workers of a factory.

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

Describe steps taken to clean up London during nineteenth century.

Describe any three major problems faced by Indian cotton weavers in nineteenth century.

Describe the impact of ‘Rinderpest’ on people’s livelihoods and local economy in Africa in the 1890s.

Distinguish between the themes of ‘Pride and Prejudice’ and ‘Jane Eyre’ novels written by Jane Austen and Charlotte Bronte respectively.

“The ‘Print Revolution’ had transformed the lives of people changing their relationship to information and knowledge.” Analyse the statement.

How has the ever increasing number of industries in India made worse position by exerting pressure on existing fresh water resources? Explain.

“Dense and efficient network of transport is a pre-requisite for local and national development.” Analyse the statement.

Describe any three provisions of amendment made in ‘Indian Constitution’ in 1992 for making ‘Three-Tier’ government more effective and powerful.

"Three factors are crucial in deciding the outcome of politics of social divisions." Elaborate upon the statement.

How is the issue of sustainability important for development? Explain with examples.

Distinguish the service conditions of organised sector with that of unorganised sector.

Why is cheap and affordable credit important for the country’s development? Explain any three reasons.

How can consumer awareness be spread among consumers to avoid exploitation in the market place? Explain any three ways.

Describe the role of different religious groups in the development of anti-colonial feelings in Vietnam.

Describe the explosive conditions prevailed in Balkans after 1871 in Europe.

Why was Congress reluctant to allow women to hold any position of authority within the organisation? How did women participate in Civil Disobedience Movement? Explain.

How did Non-Cooperation movement start with participation of middle class people in the cities? Explain its impact on the economic front.

Compare ‘intensive subsistence farming’ with that of ‘commercial farming’ practiced in India.

“The Government of India has introduced various institutional and technological reforms to improve agriculture in the 1980s and 1990s.” Support this statement with examples.

Why is the economic strength of a country measured by the development of manufacturing industries? Explain with examples.

Describe major functions of political parties.

Do democracies lead to peaceful and harmonious life among citizens? Clarify.

“Democracy stands much superior to any other form of government in promoting dignity and freedom of the individual.” Justify this statement.

How has foreign trade been integrating markets of different countries? Explain with examples.

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