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.

What is carpel ? Write the function of its various parts.

A 10 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 12 cm. The distance of the object from the lens is 18 cm. Find the nature, position and size of the image formed.

Write the essential function performed by ozone at the higher levels of the Earth’s atmosphere ? How is it produced ? Name the synthetic chemicals mainly responsible for the drop of amount of ozone in the atmosphere. How can the use of these chemicals be reduced ?

What are solar cells ? Explain the structure of solar panel. List two principal advantages associated with solar cells.

The electrons in the atoms of four elements A, B, C and D are distributed in three shells having 1, 3, 5 and 7 electrons respectively in their outermost shells. Write the group numbers in which these elements are placed in the Modern Periodic Table. Write the electronic configuration of the atoms of B and D and the molecular formula of the compound formed when B and D combine.

How does the metallic character of elements vary on moving from

- left to right in a period,
- from top to bottom in a group

of the Modern Periodic Table ? Give reason for your answer.

List any three observations which posed a challenge to Mendeleev’s Periodic Law.

How do nerve impulses travel in the body ? Explain.

Why is the use of iodised salt advisable ? Name the disease caused due to deficiency of iodine in our diet and state its one symptom.

What is hydrotropism ? Design an experiment to demonstrate this phenomenon.

Consider the given circuit and find the current flowing in the circuit and potential difference across the 15 Ω resistor when the circuit is closed.

Calculate the equivalent resistance of the following network :

A teacher provided acetic acid, water, lemon juice, aqueous solution of sodium hydrogen carbonate and sodium hydroxide to students in the school laboratory to determine the pH values of these substances using pH papers. One of the students reported the pH values of the given substances as 3, 12, 4, 8 and 14 respectively. Which one of these values is not correct ? Write its correct value stating the reason.

What would a student report nearly after 30 minutes of placing duly cleaned strips of aluminium, copper, iron and zinc in freshly prepared iron sulphate solution taken in four beakers ?

What is observed when a pinch of sodium hydrogen carbonate is added to 2 mL of acetic acid taken in a test tube ? Write chemical equation for the reaction involved in this case.

After examining a prepared slide under the high power of a compound microscope, a student concludes that the given slide shows the various stages of binary fission in a unicellular organism. Write two observations on the basis of which such a conclusion may be drawn.

List in proper sequence four steps of obtaining germinating dicot seeds.

List four precautions which a student should observe while preparing a temporary mount of a leaf peel to show stomata in his school laboratory.

The current flowing through a resistor connected in a circuit and the potential difference developed across its ends are as shown in the diagram by milliammeter and voltmeter readings respectively:

- What are the least counts of these meters ?
- What is the resistance of the resistor ?

Describe Economic Hardships Faced By Europe In 1830s?

Describe the serious problem faced by the modern part of Hanoi in 1903.

How had the printing press created a new culture of reading in Europe ? Explain with examples.

How had Charles Dickens depicted the terrible effects of industrialisation on peoples lives and characters ? Explain with examples.

Describe any three main features of ‘Alluvial soil’ found in India.