Underemployment continues to be rampant in the rural areas. Suggest any three ways through which employment for rural people can be generated.

Why was the period of 1848 considered as phase of the revolution of the Liberals in Europe? Explain.

Highlight the reasons for the growth of nationalist tensions in the Balkan region before the First World War.

‘The challenge of sustainable development requires control over industrial pollution.’ Substantiate the statement with examples.

Explain with examples the accommodative experience of Belgium for peace and harmony.

‘Democracy is based on the idea of deliberation and negotiation’. Examine the statement.

‘Respect and equal treatment of women are necessary ingredients of a democratic society’. Examine the statement.

Describe the role of technology in promoting globalisation process.

How does valency of an element vary across a period?

A lens produces a magnification of -0.5. Is this a converging or diverging lens? If the focal length of the lens is 6 cm, draw a ray diagram showing the image formation in this case.

A girl was playing with a thin beam of light from a laser torch by directing it from different directions on a convex lens held vertically. She was surprised to see that in a particular direction, the beam of light continues to move along the same direction after passing through the lens. State the reason for her observation. Draw a ray diagram to support your answer.

On entering in a medium from air, the speed of light becomes half of its value in air. Find the refractive index of that medium with respect to air?

A glass slab made of a material of refractive index n_{1} is kept in a medium of refractive index n_{2}. A light ray is incident on the slab. Draw the path of the rays of light emerging from the glass slab, if (i) n_{1} > n_{2} (ii) n_{1} = n_{2} (iii) n_{1} < n_{2}

Write the smallest number which is divisible by both 306 and 657.

Find a relation between x and y if the points A(x, y), B(–4, 6) and C(–2, 3) are collinear.

Find the area of a triangle whose vertices are given as (1, –1) (–4, 6) and (–3, –5).

The probability of selecting a blue marble at random from a jar that contains only blue, black and green marbles is 1/5. The probability of selecting a black marble at random from the same jar is 1/4 . If the jar contains 11 green marbles, find the total number of marbles in the jar.

Find the value(s) of k so that the pair of equations x + 2y = 5 and 3x + ky + 15 = 0 has a unique solution.

The larger of two supplementary angles exceeds the smaller by 18°. Find the angles.

Sumit is 3 times as old as his son. Five years later, he shall be two and a half times as old as his son. How old is Sumit at present ?

Prove that 2 + 5√3 is an irrational number, given that √3 is an irrational number.

Using Euclid’s Algorithm, find the HCF of 2048 and 960.

Two right triangles ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC. If AC and BD intersect at P, prove that AP × PC = BP × DP.

Diagonals of a trapezium PQRS intersect each other at the point O, PQ ∥ RS and PQ = 3RS. Find the ratio of the areas of triangles POQ and ROS.

In Figure, PQ and RS are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting PQ at A and RS at B. Prove that ∠AOB = 90º.

Find the ratio in which the line x – 3y = 0 divides the line segment joining the points (–2, –5) and (6, 3). Find the coordinates of the point of intersection.

In Figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 15 cm, find the area of the shaded region. (Use π = 3.14)

In Figure, ABCD is a square with side 2√2 cm and inscribed in a circle. Find the area of the shaded region. (Use π = 3.14)

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 20 cm and the diameter of the cylinder is 7 cm. Find the total volume of the solid. (Use π = 22/7)

For what value of k, is the polynomial f(x) = 3x^{4} – 9x^{3} + x^{2} + 15x + k completely divisible by 3x^{2} – 5 ?

Find the zeroes of the quadratic polynomial 7y^{2} – 11y/3 – 2/3 and verify the relationship between the zeroes and the coefficients.

Write all the values of p for which the quadratic equation x^{2} + px + 16 = 0 has equal roots. Find the roots of the equation so obtained.

Amit, standing on a horizontal plane, finds a bird flying at a distance of 200 m from him at an elevation of 30°. Deepak standing on the roof of a 50 m high building, finds the angle of elevation of the same bird to be 45°. Amit and Deepak are on opposite sides of the bird. Find the distance of the bird from Deepak.

A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm^{3} of iron has approximately 8 gm mass. (Use π = 3.14)

Which term of the Arithmetic Progression –7, –12, –17, –22, ... will be –82 ? Is –100 any term of the A.P. ? Give reason for your answer.

How many terms of the Arithmetic Progression 45, 39, 33, ... must be taken so that their sum is 180 ? Explain the double answer.

In a class test, the sum of Arun’s marks in Hindi and English is 30. Had he got 2 marks more in Hindi and 3 marks less in English, the product of the marks would have been 210. Find his marks in the two subjects.

The absolute refractive index of Ruby is 1.7. Find the speed of light in Ruby. The speed of light in vacuum is 3 × 10^{8} m/s.

On heating blue coloured powder of copper (II) nitrate in a boiling tube, black copper oxide, O_{2} and a brown gas X is formed.

- Identify the type of reaction and the gas X.
- Write balanced chemical equation of the reaction.
- Write the pH range of aqueous solution of the gas X.

(a) While diluting an acid, why is it recommended that the acid should be added to water and not water to the acid ?

(b) Dry hydrogen chloride gas does not change the colour of dry litmus paper. Why ?

How is sodium hydroxide manufactured in industries ? Name the process. In this process a gas X is formed as by-product. This gas reacts with lime water to give a compound Y, which is used as a bleaching agent in the chemical industry. Identify X and Y and write the chemical equation of the reactions involved.

What are amphoteric oxides ? Give an example. Write balanced chemical equations to justify your answer.

What is a homologous series of carbon compounds ? Give an example and list its three characteristics.

List in tabular form three distinguishing features between autotrophic nutrition and heterotrophic nutrition.

(a) What is translocation ? Why is it essential for plants ?

(b) Where do the substances in plants reach as a result of translocation ?

What is transpiration ? List its two functions.