Chapter: Relations and Functions
① Let A and B be two nonempty sets. Then, the Cartesian product of A and B is the set denoted by (A×B), consisting of all ordered pairs (a, b) such that a ∈ A and b ∈ B.
∴ A × B = {(a, b): a ∈ A and b ∈ B }.
② If A = ϕ or B = ϕ (empty sets), we define A × B = ϕ
③ B × A = {(b, a) : b ∈ B and a ∈ A} and A × A = {(a,b):a,b ∈ A}.
OBJECTIVE: To draw the graph of a quadratic polynomial and observe.
(i) The shape of the curve when the coefficient of x² is positive.
(ii) The shape of the curve when the coefficient of x² is negative.
(iii) Its number of zeroes.
MATERIAL REQUIRED
Cardboard, graph paper, ruler, pencil, eraser, pen, adhesive.
Summary:
‘Fire and Ice’ is a short poem by Robert Frost. In this poem, the poet says that people knit two croaking notions about the destruction of the world. Some say it will end in fire while others say it will end in ice. According to the poet experience about human desire, he mentions that the ‘fire’ stands for desire, greed, avarice or lust. The more you try to satisfy them, the more they grow. There is no end to it. They spread rapidly like fire and engulf your whole life. One becomes selfish and sometimes cruel also. On the other hand, ‘ice’ according to the poet, stands for hatred, coldness and rigidity. One becomes insensitive and indifferent towards the feelings of others. The poet says that both fire and ice are growing with such a rapid speed that the world will soon perish either way, in fire or in ice. The poem, very artistically, underpins the philosophy that if we don’t control our emotions and let them rule us then they would bring the world to a catastrophic end.
Fill in the blanks with suitable words.
1. _________ are the substances obtained from petroleum and natural gas.
2. Petroleum is obtained from dead remains of living organisms, that is why it is called a ________ fuel.
3. Kerosene is used in ______ aircrafts.
4. In India, ________ gas has been found in Tripura, Rajasthan, Maharashtra and in the Krishna Godavari delta.
Geography: Our Environment
Fill in the blanks with suitable words:
1. The uppermost layer over the earth's surface is called the ________.
2. The innermost layer is the core with a radius of about ________ km.
3. Any natural mass of mineral matter that makes up the earth's crust is called a _____.
Fill in the blanks with suitable words.
1. The first animal to be tamed was the wild ancestor of the _______.
2. Some of the earliest plants to be domesticated were _____ and barley.
3. Archaeologists have found in Burzahom (in present-day Kashmir) people built ____-houses, to protect them from winter season.
4. In Neolithic age, usually tools were ________ to give a fine cutting edge.
Fill in the blanks with suitable words.
1. ____ regulate the exchange of gases and the loss of water vapour from the leaves.
2. Who won the Nobel Prize for his work on photosynthesis?
3. ____are stacks of thylakoid membrane.
4. Photosynthesis occurs in which organelle of the cell?
5. Iodine can be used to test the presence of____.
Topics Covered: Work, Power and Energy
Q1: A bullet is fired from a rifle, If the rifle recoils freely, then the kinetic energy of the rifle will be:
(a) same as that of bullet
(b) more than that of bullet
(c) less than that of bullet
(d) none of these
Q2: A body of mass 2 kg, initially at rest, is acted upon simultaneously by two forces, one of 4N and the other of 3N, acting at right angles to each other. The work done by the body after the 20s is
(a) 500 J
(b) 1250 J
(c) 2500 J
(d) 5000 J
Q1: Which of the following does NOT characterise business activity?
(a) Production of goods
(b) Presence of risk and services
(c) Sale or exchange of goods and services
(d) Salary or wages
Q2: Which of the broad categories of industries covers oil refinery and sugar mills?
(a) Primary
(b) Secondary
(c) Tertiary
(d) None of them
Q3: Which of the following cannot be classified as an auxiliary to trade?
(a) Mining
(b) Insurance
(c) Warehousing
(d) Transport
Salts/Compounds Colour
1. Potassium dichromate, K₂Cr₂O₇ Orange
2. Potassium permanganate, KMnO₄ Violet
3. Ferric tetra-oxide, Fe₃O₄ Black
4. Ferrous sulphate, FeSO₄.7H₂O Green
5. Ferric sulphate, Fe₂(SO₄)₃ Yellow
6. Ferric hydroxide, Fe(OH)₂ Green
