SHAPERS' Institute of Mathematics
INDEX NUMBERS
Index Number :An Index number shows how a quantity charges over a period of time.Price Index : The Price Index shows how the price of something changes over a period of time.
Note: The base value is the price to compare all the other prices to be compared.
Weighted Index Number : An Index number can include a number of different items. The index number must take into account the proportions of the different items. These are called veightings. the final number is called a weighted Index number.
Retail Price Index (RPI): It looks at how people spend their income. The RPI is based on the results of a analise on expenditure of a number of households.
RPI provides or measures the change in the cost of an representative basket of goods and services. It was started in 1987 and this acts as a base year.
CONIC SECTION
General Equation of a conic section is of the form: Ax^2 + Bxy +Cy^2 +Dx +Ey +F= 0CIRCLE: A circle is a collection of points (x,y) in a coordinate plane, such that each point is equidistant from a fixed point (h,k) which is known as the center .For circles the coefficients for x^2 and y^2 terms in the terms in the general quadratic relationship are equal . Equation of a circle in standard form is as follow: (x-h)^2 + (y-k)^2 = r^2where (h,k) is the center point and r is the radius of the circle.Observations: (i) The conic section will be a circle since the x^2 and y^2 terms have the same sign and equal coefficients.(ii) the eccentricity of a circle is zero (e=0).(iii) a circle can be drawn with a compass or one thumbtack and a string. ELLIPSE: An Ellipse is also a collection of points (x,y) in a coordinate plane. It is very similar to a circle, but some what " out of round" or oval. For an ellipse, the x^2 and y^2 terms have unequal co efficients , but the same sign (A not equal to C, and AC greater than 0) .PARABOLAS: A parabola has an equation that contains only one squared term. If the x^2 term is excluded, then the graph will open in an x -direction.If the y^2 term is excluded, then the graph will open in a y-direction. Only graphs whihc open in the y- direction are quardratic functions, thus those whihc open in th ex- direction are quardratic relations. Parabolic functions have the general equation:y =ax^2 + bx + cHYPERBOLA: An Hyperbola has two symmetric , disconnected branches.Each branch approaches diagonal asymptotes. Hyperbolas can be detected by the opposite signs of the x^2 and y^2 terms.WHY DO WE FALL ILL
1. Our body's well-being is dependent on the proper functioning of its cells and tissues.2. All our body parts and activities are greatly interconnected.
3. when we are healthyl we are able to perform our physical, mental and social functions.
4. A person suffering from a disease is in a state of discomfort.
5. Being in poor health is different from being diseased.
6. Depending on their duration, diseases may be classified as acute or chronic.
7. During infection, the body's activated immune system sends specialized cells to destroy the microbes, causing infammation, with associated lacal effects.
8. The symptoms of a disease depend ont the target organ infected by the microbe.
9. Sexual contact causes the spread of diseases like AIDS ans syphilis from the infected peson to a helthy one. AIDS virus can also spread through blood get the power of visual impact on your side on to transfussions, use of infected needles or during pregnancy and breast-feedign by an infected mother.
10. It is desirable to prevent a disease than to treat it completely.
CIRCLES
1. Prove that Equal chord of a circle subtend equal angles at the centre.2. Prove that the perpendicular from the centre to a chord bisects the chord.
3. Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centers is 4 cm. Find the length of the common chord.
4. If two equal chords of acircle intersect within the circle. Prove that the line joining the point of intersection to the center makes equal angles with the chords.
5. A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.
6. Two circles intersect at two points A and B. AD and AC are diameter to the two circles. Prove that B lies on the line segment DC.
7. If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal.
8. Prove that angles made in the same segments of a circe are equal.
IMPROVEMENT IN FOOD RESOURCES
1. Which of one of the following nutrients is not available in fertilizers: a. nutrients b. phosphorous c. iron d. potassium2. The science of growing vegetables , fruits and ornamental plants is called:a. floriculture b. horticulture c. agriculture d. animal husbandary
3. What are the advantages of organic farming?
4. Differentiate between mixed cropping and inter-croping?
5. Give difference between Rabi and Kharif crop?
6. What is hybridization?
7. what are the components of cattle feed?
8. Define the White Revolution?
9. What is green manuring?
10. What are the main practices involved in keeping of animals or animal husbandry?
NUMBER SYSTEM
1. Natural Numbers: counting numbers are called natural numbers.
Example: 1,2,,3,4,…………….. are natural numbers.
2. Whole Numbers: All counting numbers and 0 form the set of whole numbers. Example: 0,1,2,3,,4,………… are whole numbers
3. Integers: All counting numbers, zero and negative of counting numbers form the set of integers.
……….,-3,-2,-1,0,1,2,3,…………. integers Set of positive integers: {1,2,3,4,5,…………}= natural numbers; Set of negative integers:{-1,-2,-3,-4,………..} ; Set of non-negative integers:{0,1,2,,3,4,5,….}= whole numbers
4. Rational Numbers: A Number in the form of a/b where a & b are integers and b?0. Terminating (or finite) decimals: 17/4= 4.25, 21/5= 4.2 Non-terminating Periodic Fractions: 16/3=5.3333, 15.23232323,14.28764876 Non-terminating non-periodic fractions: 5.2731687143725186……..
Note: Terminating and non-terminating periodic decimal fractions belong to Rational numbers.
5. Irrational Numbers: Fractions that are non-terminating, non-periodic fractions are called Irrational numbers. Example: v2,v3,p, etc
6. Even Numbers: A counting number divisible by 2 is called an even number. Thus 0,2,4,6,8,10,12,…….. are even numbers.
7. Odd Numbers: A counting number not divisible by 2 is called an odd number. Thus:1,3,5,7,9,11,13,15,………. etc. are odd numbers
8. Prime Numbers: A counting number which has exactly two factors, namely itself and 1. Thus:2,3,5,7,11,13,17,………. etc. are Prime numbers
Example: 1,2,,3,4,…………….. are natural numbers.
2. Whole Numbers: All counting numbers and 0 form the set of whole numbers. Example: 0,1,2,3,,4,………… are whole numbers
3. Integers: All counting numbers, zero and negative of counting numbers form the set of integers.
……….,-3,-2,-1,0,1,2,3,…………. integers Set of positive integers: {1,2,3,4,5,…………}= natural numbers; Set of negative integers:{-1,-2,-3,-4,………..} ; Set of non-negative integers:{0,1,2,,3,4,5,….}= whole numbers
4. Rational Numbers: A Number in the form of a/b where a & b are integers and b?0. Terminating (or finite) decimals: 17/4= 4.25, 21/5= 4.2 Non-terminating Periodic Fractions: 16/3=5.3333, 15.23232323,14.28764876 Non-terminating non-periodic fractions: 5.2731687143725186……..
Note: Terminating and non-terminating periodic decimal fractions belong to Rational numbers.
5. Irrational Numbers: Fractions that are non-terminating, non-periodic fractions are called Irrational numbers. Example: v2,v3,p, etc
6. Even Numbers: A counting number divisible by 2 is called an even number. Thus 0,2,4,6,8,10,12,…….. are even numbers.
7. Odd Numbers: A counting number not divisible by 2 is called an odd number. Thus:1,3,5,7,9,11,13,15,………. etc. are odd numbers
8. Prime Numbers: A counting number which has exactly two factors, namely itself and 1. Thus:2,3,5,7,11,13,17,………. etc. are Prime numbers
AREA AND VOLUME
1.The sum of circumferences of two circles is 132 cm. If hte radius of one circle is 14 cm, find the radius of the second circle.
2. What is the surface area of the solid hemisphere of radius 5 cm.
3. Two cubes each with 12 cm edge are joined end to end. Find the surface area of the resulting cuboid.
4. Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9 cm.
5. A cone is divided into two parts by drawing a plane throught the mid-point of its axis, parallel to its base. Compare the volumes of the two parts.
6. solid spheres of diameter 6 cm are dropped into a cylindrical beaker containing some water and are fully submerged. If the diameter of the beaker is 18 cm and the water rises by 40 cm, find the number of solid spheres dropped in the water.
7. Two circles touch internally, the sum of their is 116 sq.cm, and the distance between their centers is 6 cm. Find the radii of the circles?
8. A cone, a hemisphere and a cylinder stand on equal bases and have the same height.Show that their volumes are in the ratio 1:2:3 ?
9. If the perimeter of a semi-circular protector is 36 cm. Find the diameter of the protector.
10. how many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter.
2. What is the surface area of the solid hemisphere of radius 5 cm.
3. Two cubes each with 12 cm edge are joined end to end. Find the surface area of the resulting cuboid.
4. Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9 cm.
5. A cone is divided into two parts by drawing a plane throught the mid-point of its axis, parallel to its base. Compare the volumes of the two parts.
6. solid spheres of diameter 6 cm are dropped into a cylindrical beaker containing some water and are fully submerged. If the diameter of the beaker is 18 cm and the water rises by 40 cm, find the number of solid spheres dropped in the water.
7. Two circles touch internally, the sum of their is 116 sq.cm, and the distance between their centers is 6 cm. Find the radii of the circles?
8. A cone, a hemisphere and a cylinder stand on equal bases and have the same height.Show that their volumes are in the ratio 1:2:3 ?
9. If the perimeter of a semi-circular protector is 36 cm. Find the diameter of the protector.
10. how many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter.
TRIANGLE AND QUARTILATERAL
1. Sum of three angles of a triangle is 180.
2. in a triangle sum of any two sides is greater than its third side.
3. in right angled tringle : (hyp)^2 = (Base)^2 + (Perpendicular)^2
4. The line joining the vertex with the midpoint of opposite side is called median
5. a point where the medians meed is called cetroid.
6. In an isosceles triangle the altitude from the vertex bisect the base.
7. diagonals of parallelogram bisect each other.
8. Diagonals of rectangle are equal and bisect each other
9. Diagonals of square are equal and bisect each other at right angle.
10. Diagonals of rhombus bisect each other at right angle.
WORK AND ENERGY
WORK: When force is exerted on an object and object is
displaced, work is said to be done.
LAW OF
CONSERVATION OF ENERGY
Electric consumption in
households is measured in kWh and generally called unit. Therefore, 1 unit of
electricity is equal to 1kWh.
Energy = Power X time
LINEAR EQUATIONS IN TWO VARIABLES
1. If (2, 3) and (4, 0) lie on the graph of equation ax + by = 1. Find value of a and b. Plot the graph of equation obtained.
2. Two years later a father will be eight years more than three times the age of the son. Taking the present age of father and son as x and y respectively
(a) Write a linear equation for the above and draw its graph.
(b) From the graph find the age of father when son’s age is 10 years.
3. Solve the linear equation for ‘x’ : 2x= 5y-3 .
4. A juice seller in a marriage party has a cylindrical vessel with base radius 25 cm and height 40 cm full of juice. He gives the same in small glasses of radius 5 cm and height 10 cm. How many oranges are required for the bigger vessel to fill it completely if to fill one small glass two oranges are required.
5. Give the geometric representations of 2x + 9 = 0 as an equation:
(1) in one variable
(2) in two variables
6. If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.
7. The cost of a notebook is two-third of the cost of a pen. Write a linear equation in two variables to represent this statement.
8. Write four solutions for each of the following equations:
(i) 2x + y = 7
(ii) πx + y = 9
(iii) x = 4y
9. The taxi fare in a city is as follows: For the first kilometre, the fares is Rs 10 and for the subsequent distance it is Rs 7 per km. Taking the distance covered as x km and total fare as Rs y, write a linear equation for this information, and draw its graph.
10. Draw a graph of linear equation 3x + 2y = 12.
Area under Curve- 10+2
1. Find the area of the region enclosed by the parabola x2 = y, the line y = x +2 and the x – axis.
3. Find area bounded by curves x, y : y = x2 and y = | x | .
4. Using method of integration find the area of the triangle ABC, coordinates of whose vertices are A (2, 0), B (4, 5) and C (6, 3).
5. Find the area of two regions x, y : y 2 = 4 x, 4 x2 + 4 y 2 = 9 .
6. Find the area of the circle x2 + y2 = 15 exterior to the parabola y2 = 6x
Atoms and Molecules
TRIANGLE AND QUARTILATERAL
1. Sum of three angles of a triangle is 180.
2. in a triangle sum of any two sides is greater than its third side.
3. in right angled tringle : (hyp)^2 = (Base)^2 + (Perpendicular)^2
4. The line joining the vertex with the midpoint of opposite side is called median
5. a point where the medians meed is called cetroid.
6. In an isosceles triangle the altitude from the vertex bisect the base.
7. diagonals of parallelogram bisect each other.
8. Diagonals of rectangle are equal and bisect each other
9. Diagonals of square are equal and bisect each other at right angle.
10. Diagonals of rhombus bisect each other at right angle.
3. in right angled tringle : (hyp)^2 = (Base)^2 + (Perpendicular)^2
4. The line joining the vertex with the midpoint of opposite side is called median
5. a point where the medians meed is called cetroid.
6. In an isosceles triangle the altitude from the vertex bisect the base.
7. diagonals of parallelogram bisect each other.
8. Diagonals of rectangle are equal and bisect each other
9. Diagonals of square are equal and bisect each other at right angle.
10. Diagonals of rhombus bisect each other at right angle.
WORK AND ENERGY
WORK: When force is exerted on an object and object is
displaced, work is said to be done.
Work = Force x Displacement Or, W = F x s
Where, W is work; ‘F’ is force and ; ‘s’ is displacement.
If force, F = 0 ; work done : W = 0 x s = 0
If displacement, s = 0 ; Work done: W = F x 0 = 0
Thus, there are two conditions for work is considered done –
(i). Force should act on the
object. (ii). Object must be
displaced.
In the absence of any one of the
above two conditions, work done will be equal to zero, that is work is not
considered as done.
SI unit of work:
The SI unit of Force is Newton
(N) and the SI unit of displacement is meter (m).
Therefore by substituting the SI
units of Force and displacement in the expression, W = F x s we get : W = N x
m.
The SI unit of work is joule and
is denoted as ‘J’, which is named after an English physicist James Prescott
Joule.
The 1 joule of work done is equal
to 1N x 1 m. Or, 1 joule = Nm
Direction of Force - Positive and
negative work:
When force is applied in the
direction of displacement, the work done is considered as positive. i.e. W = F x s
When force is applied in opposite
direction of displacement, the work done is considered as negative. i.e. W = – F x s = – Fs
For example: when engine works to accelerate or move the
vehicle, the work done is positive. But when brakes are applied to stop a
moving vehicle, i.e. work done against the direction of displacement of the
vehicle, the work done is considered as negative.
ENERGY: Energy is the capacity of doing work.
An object which can do more work
is said to have more energy and vice versa. For example, a motorcycle has more
energy than a bicycle.
SI unit of energy –
Since energy is capacity of doing
work, therefore, the SI unit of energy is same as of work.
Thus, the SI unit of energy is
joule and is denoted by ‘J’.
Larger unit of energy is kilo
joule and is denoted by kJ. 1kJ = 1000 J
Forms of Energy: There are many forms of energy, such as kinetic
energy, potential energy, mechanical energy, chemical energy, electrical
energy, etc.
KINETIC
ENERGY: Kinetic
energy is the energy possessed by an object because of motion. For example, a
fast moving pebble can injure a person or break glass pane of window, energy of
moving vehicle, a fast moving wind can damage many house, or wind can move
blades of wind mill, etc.
POTENTIAL ENERGY: Energy possessed by an object
because of its position is called potential energy. For example; when a stone
is kept at a height, it possesses some energy because of its height. Because of
this potential energy, object kept at a height falls over the ground.
A stretched rubber band possesses
some energy because of its position. Because of that energy, when the stretched
rubber band is released it acquires its original position by movement. A
stretched catapulted possesses potential energy because of its stretched string
and is able to do some work.
A stretched bow possesses energy
because of its position of stretched string.
LAW OF
CONSERVATION OF ENERGY
According to Law of conservation
of energy; energy can neither be created nor be destroyed rather the form of
energy can be converted from one form to another form.
POWER: Rate of doing work is called
power. For example; a more powerful engine can do more work in less time, such
as an aeroplane covers more distance in less time than a car consequently aeroplane is more powerful than a car.
SI unit of power:
The SI unit of power is watt
named after James Watt, the inventor of steam engine, and is denoted by ‘W’. 1 W = 1 J s –1
The bigger unit of power is kilo
watt and is written as kW.
1 kilowatt = 1000 watt Or, 1 kW = 1000 W Or, 1kW = 1000 J s –1
The average power can be
calculated after dividing total work done by total time taken.
COMMERCIAL UNIT OF ENERGY
Since joule is very small thus,
large quantity of energy is expressed in kilo watt hour and is written as kWh.
If a machine uses 1000 joule of
energy in one second and the machine runs for one hour, then it is said that
the machine will consume energy 1kWh.
1 kWh = 1 kW x 1 h Or, 1kWh = 1000 joule x 3600 s; Or, 1 kWh = 3600000 joule Or, 1kWh = 3.6 x 106 joule
Electric consumption in households is measured in kWh and generally called unit. Therefore, 1 unit of electricity is equal to 1kWh.
Electric consumption in households is measured in kWh and generally called unit. Therefore, 1 unit of electricity is equal to 1kWh.
Energy = Power X time
Thus, by knowing any two of
three, third can be calculated using the expression Energy = power x time.
If an electric appliance consumes
1000 joule of energy in one second and runs for one hour, it will consume 1unit
of electricity, i.e. 1kWh of electricity.
LINEAR EQUATIONS IN TWO VARIABLES
1. If (2, 3) and (4, 0) lie on the graph of equation ax + by = 1. Find value of a and b. Plot the graph of equation obtained.
2. Two years later a father will be eight years more than three times the age of the son. Taking the present age of father and son as x and y respectively
(a) Write a linear equation for the above and draw its graph.
(b) From the graph find the age of father when son’s age is 10 years.
3. Solve the linear equation for ‘x’ : 2x= 5y-3 .
4. A juice seller in a marriage party has a cylindrical vessel with base radius 25 cm and height 40 cm full of juice. He gives the same in small glasses of radius 5 cm and height 10 cm. How many oranges are required for the bigger vessel to fill it completely if to fill one small glass two oranges are required.
5. Give the geometric representations of 2x + 9 = 0 as an equation:
(1) in one variable
(2) in two variables
6. If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.
7. The cost of a notebook is two-third of the cost of a pen. Write a linear equation in two variables to represent this statement.
8. Write four solutions for each of the following equations:
(i) 2x + y = 7
(ii) πx + y = 9
(iii) x = 4y
9. The taxi fare in a city is as follows: For the first kilometre, the fares is Rs 10 and for the subsequent distance it is Rs 7 per km. Taking the distance covered as x km and total fare as Rs y, write a linear equation for this information, and draw its graph.
10. Draw a graph of linear equation 3x + 2y = 12.
Area under Curve- 10+2
1. Find the area of the region enclosed by the parabola x2 = y, the line y = x +2 and the x – axis.
2. Using method of integration, find the area bounded by the curve |x| + |y| = 1.
3. Find area bounded by curves x, y : y = x2 and y = | x | .
4. Using method of integration find the area of the triangle ABC, coordinates of whose vertices are A (2, 0), B (4, 5) and C (6, 3).
5. Find the area of two regions x, y : y 2 = 4 x, 4 x2 + 4 y 2 = 9 .
Atoms and Molecules
- Atoms
are the building blocks of all the matter around us.
- Atoms
are so small in size, that they cannot be seen even under the most powerful light
microscope.
- The
size of an atom is indicated by its radius, which is called atomic radius.
- Atomic
radius is measured in nanometers (nm). 1 nm = 10-9 m
Element-Any substance that contains only one kind
of an atom is known as an element. Because atoms cannot be created
or destroyed in a chemical reaction, elements such as phosphorus (P4)
or sulfur (S8) cannot be broken down into simpler substances by
these reactions.
Compounds-Elements combine to form chemical
compounds that are often divided into two categories.(i)ionic (ii)Covalent
Atomic
mass – According to Dalton’s atomic
theory, each element has a characteristic atomic mass.
One atomic
mass unit is a mass unit equal to exactly one-twelfth (1/12th)
the mass of one atom of carbon – 12.
The relative
atomic mass of the atom of an element is defined as the average mass
of the atom, as compared to 1/12th the mass of one carbon-12
atom.
Molecule –
A molecule is the smallest particle of an element or a compound that is capable
of an independent existence and show all the properties of that substance.
The number of
atoms constituting a molecule is known as its atomicity. Thus the
atomicity of hydrogen is 2, sulphur is 8, ozone is 3, phosphorus is 4, etc.
Molecular
mass – The relative molecular mass of a
substance is the average mass of its molecule as compared with the mass of a
carbon-12 atom taken as 12 units.
- The
molecular mass of a substance is the sum of the atomic masses of all the atoms
in a molecule of the substance.
Formula
unit mass – An ionic compound is made up of an extremely large
number of cations and anions. e.g. Sodium chloride is made up of a large (but
equal) number of Na+ and Cl- ions so the actual
formula of sodium chloride should be (Na+Cl-)n but
for simplicity we represent it by NaCl. So NaCl is the simplest formula of
sodium chloride and not its actual formula.
The formula
unit mass of a substance is the sum of the atomic masses of all atoms
in a formula unit of a compound.
- e.g.
formula unit mass of NaCl is 23 x 1 + 35.5 x 1 = 23 + 35.5 = 58.5u.
A mole is
defined as the amount of a substance that contains as many particles (atoms,
molecules or ions) of the substance as there are atoms in exactly 12 g of
carbon-12.
In other words, a
mole of a substance is that amount of the substance that contains 6.022 x 1023particles
of the substance.
- The
atomic mass of an element expressed in grams is called gram atomic mass of
the element.
- The
molecular mass of a substance expressed in grams is called gram
molecular mass of the substance.
- Gram
atomic mass or gram molecular mass also represents molar mass of the substance.
- The
mass of 1 mole of a substance is called molar mass of the
substance.
1 mole = 6.022 x 1023 particles
= Gram atomic mass (or gram molecular mass)
Q1 State law of conservation of mass.
Ans The
mass can neither be created nor destroyed in a chemical reaction.
Q2 State law of constant proportion.
Ans A pure chemical compound always consists of the
same elements that are combined together in a fixed proportion by mass.
Q3 Write name and symbol of first 20
elements of the periodic table.
Ans Atomic
number Name of the
element Symbol
1
Hydrogen
H
2
Helium
He
3
Lithium
Li
4
Beryllium
Be
5
Boron
B
6
Carbon
C
7
Nitrogen
N
8
Oxygen
O
9
Fluorine
F
10
Neon
Ne
11
Sodium
Na
12
Magnesium
Mg
13
Aluminium
Al
14
Silicon
Si
15
Phosphorous
P
16
Sulphur
S
17
Chlorine
Cl
18
Oxygen
O
19
Potassium
K
20
Calcium
Ca
Q4 Define atomic mass unit.
Ans: The mass of one twelfth (1/12) of the mass of one
atom of carbon taken as 12.
Q5 What are molecules?
Ans: Molecules represents a group of two or more
atoms(same or different) chemically bonded to each other and held tightly
by strong attractive forces.
Molecules are of two types
(a) Molecules of elements
(b) Molecules of compound
Q6 What do you mean by molecular mass?
Ans: The average relative mass of the molecule as
compared to the mass of carbon takrn as 1u.
Q7 Write the relationship between
number of moles and atomic mass.
Ans: Number of moles=given
mass/gram atomic mass
Q8 Why are chemical reactions according to
law of conservation of mass?
Ans: In all chemical reactions, there is only
exchange of reactants taking place when products are formed. Since there
is no loss or gain of mass, the chemical reactions are according to law
of conservation of mass.
Q9 What is basic difference between atoms
and molecules?
Ans: Atoms except those of noble or inert gas
elements cannot exist of their own. However ,all molecules can have
independent existence.
Q10 The atomic mass of an element is in
fraction .What does it mean?
Ans: If the atomic mass of an element is in
fraction, this mean that it exists in the form of isotopes. The atomic
mass is the average atomic mass and is generally fractional.
Q11 What is the difference between the
mass of molecule and molecular mass?
Ans: Mass of a molecule is that of a single
molecule also known as its actual mass. But molecular mass is the mass of
Avagadro’s number of molecules.
Q12 Where do we use the words mole and mol?
Ans: In the text part we use the word mole while
as a unit ,we call it mol.
Q13 How many moles are present in 11.5 g
of sodium?
Ans: Gram atomic mass of Na =23g
23g
of Na represents = 1 mol
11.5g of Na represents=
(1mol)*(11.5g)/23.5g)=0.5 mol
Q14 Explain why the number of atoms
in one mole of hydrogen gas is double the number of atoms in one mole of
helium gas?
Ans: Hydrogen gas is a diatomic in nature(H2) while
helium gas is monoatomic (He).As a result, the number of atoms in one
mole of hydrogen(2*NA )are expected to be double as compared to number of
atoms in one mole of helium(NA)
Q15An element Z forms an oxide with
formula Z2O3. What is its valency?
Ans:Valency of Z=3
Q16The valency of an element A is 4 .
Write the formula of its oxide.
Ans: The formula of its oxide is A2O4 or
AO2.
Q17 An element X has valency 3 while
the element Y has valency 2.Write the formula of the compound between X
and Y
Ans: X2Y3
Q18 What are ions?
Ans: Ions are of two types
(a) cations - positively charged
(b) anions - negatively charged
Q19 Which postulate of Dalton’s
Atomic theory is the basis of law of conservation of mass?
Ans: “ Atoms can neither be created nor
destroyed during a physical or a chemical change”
Q20 Write the formulae of sodium oxide and
aluminium chloride
Ans: Sodium oxide = Na2O
Aluminium chloride =AlCl3
Q21 Find out the ratio by mass of
the combining elements in the following compounds(a) MgCO3
(b) CH3OH (c) CaCl2
Ans: (a) MgCO3 ------ Mg :C:O
= 24:12:48 = 2:1:4
(b) CH3OH ------ C : H : O
=12:4:16 =3:1:4
(c)
CaCl2 ----------- Ca :Cl
= 40:71
Q22 Define atomicity of the molecule.
Ans: Atomicity of the molecule is the number of
atoms present in the molecule.
Q23 What is the atomicity of
oxygen,ozone,neon and sulphur?
Ans : Oxygen O2 = 2
Ozone O3 = 3
Neon Ne =1
Sulphur S8 =8
Q24 What is wrong with the statement '1
mol of hydrogen'
Ans: The statement is not correct.We must always
write whether hydrogen is in atomic form or molecular form. The correct
statement is : 1mole of hydrogen atoms or one mole of hydrogen
molecules .
Q25 The atomic mass of an element is in
fraction. What does it mean?
Ans: If the atomic mass of an element is in fraction, this mean that it exists in the form of isotopes. The atomic mass is the average atomic mass and is generally fractional.
Sequence and Series
1. The ratio of the sums of n terms of two A.P is (7n +1): (4n +27).find the ratio of their 11th terms.
2. IF a , b, c are in AP. Prove that 1/bc, 1/ac,1/ab are also in AP.
3. If p,q,r are in AP.show that pth,qth,and rth terms of any GP are in GP.
4. Sum the following series up to n terms 7 + 77 + 777 +..........................
5. If b is the GM between a and c P.T (a2 + b2) (b2 + c2) = (ab + bc) 2
6. Find the sum of the series 12 + 42 + 72 +………...
7. A ball is dropped from a height of 48 m and rebounds two- third of the distance it falls .if it continues to fall and rebounds in this way how far it travels before coming to rest.
8. There are n A.M between 1 and 23 such that the ratio of last mean to the first mean is 7:1. Find the value of n.
9 . If S1, S2, S3 are the sums of first n natural numbers, their squares and their cubes respectively, show that 9 S2 = S3 (1 + 8S1).
10. Find the sum of the series upto n terms
13 + 13+ 23 + 13+23+33 +…………
1 1+3 1+3+5
11. If the ratio of the A.M. And G.M. of two nos. a and b be m:n , then find the ratio between the two numbers
DIVERSITY IN LIVING ORGANISMS
1.
What do you mean by
bio diversity?
Solution: Bio-diversity means
the existence of a wide variety of species or other taxa of plants, animals and
micro-organisms in a natural habitat within a specific environment.
2.
Why do we classify organisms?
Solution:
1.
Identification is not possible without any system of
classification.
2. Classification helps in bringing out similarities and dissimilarities amongst organisms.
3. Relationships are built up with the help of classification. They indicate the evolutionary pathways.
4. Organisms of other localities and fossils can be studied only with the help of a system of classification.
5. It is not possible to study every organism. Study of one or two organisms gives sufficient idea about other members of the group.
2. Classification helps in bringing out similarities and dissimilarities amongst organisms.
3. Relationships are built up with the help of classification. They indicate the evolutionary pathways.
4. Organisms of other localities and fossils can be studied only with the help of a system of classification.
5. It is not possible to study every organism. Study of one or two organisms gives sufficient idea about other members of the group.
6. Other branches of biology depend upon proper
identification of the organism which is possible only through a system of classification.
3.
Give three examples of the range of
variations that you see in life-forms around you.
Solution:
(i) Size. It
varies from microscopic organisms (e.g., bacteria, size 0.5—5.0 um) to very
large sized animals (e.g., Blue whale, 30 meters long) and trees (e.g., Redwood
tree, height 100 metres).
(ii) Life Span. May fly lives for one day, most mosquitoes for a few days while some Pine trees live for thousands of years.
(iii) Colour. Jelly fish and many worms are colourless. Birds, butterflies and flowers are variously coloured brightly.
(ii) Life Span. May fly lives for one day, most mosquitoes for a few days while some Pine trees live for thousands of years.
(iii) Colour. Jelly fish and many worms are colourless. Birds, butterflies and flowers are variously coloured brightly.
4.
Which do you think is a more basic
characteristic for classifying organisms?
(a) The place where they live.
(a) The place where they live.
(b) The kind of cells they are made of. Why?
Solution:The kind of cells. Habitat is a place
where diverse types of organisms live together. It cannot be used for
classifying organisms. Cells have specific structure, prokaryotic in monerans
and eukaryotic in the remaining organisms. Organisms are unicellular in
protista and multi cellular in others. A cell wall is absent in animals. Cell
wall contains chitin in fungi and cellulose in plants. Plastids occur in plant
cells. They are absent it animal cells.
5.
What is the primary characteristic on
which the first division of organisms is made?
Solution: Type of cell, prokaryotic (genetic
material or nucleoid free in cytoplasm) and eukaryotic (genetic material
enclosed in nucleus).
6.
On what basis are plants and animals put
into different categories?
Solution:
1.Shape. Animals
have a definite shape while plants have less definite shape.
2.Branching. Animals are unbranched (exception sponges), while plants are generally branched.
3.Growth. Animals stop growing after reaching a certain size. Plants continue to grow till death.
4. Locomotion. Animals can move from place to place (exception corals, sponges) while plants are fixed.
5.Nutrition. Animals eat readymade food while plants manufacture their own food.
6.Reserve Food. It is glycogen in animals and starch in plants.
7. Cell Wall. Animal cells do not have a covering of wall while individual plant cells are surrounded by cell walls.
8.Excretory Organs. They are present in animals but absent in plants.
9. Sense Organs and Nervous System. They are found in animals but not in plants.
2.Branching. Animals are unbranched (exception sponges), while plants are generally branched.
3.Growth. Animals stop growing after reaching a certain size. Plants continue to grow till death.
4. Locomotion. Animals can move from place to place (exception corals, sponges) while plants are fixed.
5.Nutrition. Animals eat readymade food while plants manufacture their own food.
6.Reserve Food. It is glycogen in animals and starch in plants.
7. Cell Wall. Animal cells do not have a covering of wall while individual plant cells are surrounded by cell walls.
8.Excretory Organs. They are present in animals but absent in plants.
9. Sense Organs and Nervous System. They are found in animals but not in plants.
7.
Which organisms are called primitive and
how are they different from the so-called advanced organisms?
Solution:Primitive organisms are those organisms
which have simple ancient body design with only basic characteristics of the
group. There has been little change over a long period of time. Specializations
are fewer. Advanced organisms are more recent organisms. They are also called
higher organisms because they possess several specializations. They have more
complex structure and some new characteristics along with the basic ones.
8.
Will advanced organisms be the same as
complex organisms? Why?
Solution: Yes. Advancement is based on development
of specializations. Specialization occurs where there is more elaboration and
hence more complexity
9.
What is the criterion for classification
of organisms as belonging to kingdom Monera or Protista?
Solution: Cell structure is used as a criterion
for placing an organism in monera or protista. In monera the cells are
prokaryotic. Membrane bound cell organelles are absent. In protista the cells
are eukaryotic. Membrane bound cell organdies are present. Protista contains
only unicellular eukaryotes. Monera may have unicellular or multi cellular
forms.
10.
In which kingdom will you place an
organism which is single-celled, eukaryotic and photosynthetic?
Solution: Protista.
11.
In the hierarchy of classification,
which grouping will have the smallest number of organisms with a maximum of
characteristics in common and which will have the largest number of organisms?
Solution:
(i)
Small number (one) with maximum common characteristics –
Species
(ii)
Largest number -
Kingdom.
12.
Which division among plants has the
simplest organisms?
Solution: Thallophyta.
13.
How do gymnosperms and angiosperms
differ from each other?
Solution:
Gymnosperms
|
Angiosperms
|
1. Sporophylls. They are aggregated to form
cones.
|
Sporophylls are
aggregated to form flowers.
|
2. Seeds. The seeds are naked.
|
They are produced by fruit
wall.
|
3. Microspores and Megaspores.The microspores and megaspores
are produced by male and female cones.
|
They are produced in the same
or two different types of flowers.
|
4. Vascular Tissues. Xylem lacks vessels and
phloem lacks companion cells.
|
Xylem contain vessels and
phloem contains companion cells.
|
5. Ovules. The ovules are not contained in
the ovary.
|
The ovules are enclosed in the
ovary.
|
6. Endosperm. it is haploid.
|
It is triploid.
|
14.
How do annelid animals differ from
arthropods?
Solution:
Annelids
|
Arthropods
|
1. Appendages. They are unjointed.
|
Appendages are jointed.
|
2. Circulation. Blood flows inside blood
vessels (closed circulatory system).
|
Blood flows through large
sinsues or spaces (open circulatory system).
|
3. Cocelom. True coelom is well -
developed.
|
True coelom is small. Instead,
blood filled with body cavity called haemocoel is present.
|
4. Chitinous Exoskeleton. A chitinous exoskeleton
is absent.
|
A chitinous exoskeleton is
present.
|
5. Excretory Organs. They are nephridia.
|
Excretory organs are green
glands and malpighian tubules.
|
15.
How would you choose between two
characteristics to be used for developing a hierarchy in classification?
Solution:
The character which is of fundamental importance, generally
present in larger number of organisms, as a change in body design, is used in
raising a higher category The character of lesser importance, generally present
in smaller number of individuals is used for raising lower category.
16.
Explain the basis for grouping organisms
into five kingdoms.
Solution:
Four criteria have been used
for grouping of organisms into five kingdoms -
(i) Procaryotic and eukaryotic nature
(ii) Unicellular and multi cellular nature
(iii) Nutrition
(iv) Ecological life style.
(i) Procaryotic and eukaryotic nature
(ii) Unicellular and multi cellular nature
(iii) Nutrition
(iv) Ecological life style.
17.
How are the criteria for deciding
divisions in plants different from the criteria for deciding the subgroups
among animals?
Solution: Body design of plants is quite different
from that of animals. Plants are anchored. They require organs for fixation and
absorption. Plants are autotrophic. Reproductive organs, mechanical tissues and
conducting tissues have evolved in higher plants. In animals the requirement is
mobility for obtaining food and other necessities. Their evolution has occurred
towards greater mobility, protection, increased efficiency in obtaining food
and care of young ones. Therefore, criteria for deciding divisions or subgroups
are different for plants and animals.
18.
Define Evolution?
Solution: Evolution is a complex
process by which the characteristics of living organisms change over
generations to generations and the traits are passed from one generation to the
next. One of the main reason for diversity in bio-life is to attributed to
evolution.
19.
What is Symbiotic?
Give example of organisms which exhibit this relationship:
Solution: some fungal species
live in mutually dependent relationship with blue green algae. Such
relationships are called symbiotic. These symbiotic life forms are called
lichens. In lichens the fungal component is called the mycobiont and the algal
component is known as the phycobiont.
20.
Why bryophytes are
called the amphibians of the plant kingdom:
Solution: Beyophytes are known
as amphibians of the plant kingdom because these plants can live in soil but
are dependent on water for sexual reproduction .Usually they are found in humid
and damp areas.
21. What are the general characteristics found in all
animals:
Solution:
1.
All
animals are multi-cellular , eukaryotic and heterotrophic
2.
All
animals exhibit locomotion
3.
Most
of the animals have sense organs and nervous system
4.
Nutrition
is generally ingestive
5.
Reproduction
is generally sexual
22. What is osculum:
Solution: The body of sponge is
porous and the pores are called ostia. Single large opening or pore is called
the osculum.
DIVERSITY
IN LIFE ORGANISMS
1.
Explain the basis for grouping
organisms into five kingdoms.
2.
How do annelid animals differ from
arthropods?
3.
How do peripheral animals differ
from coelenterate animals?
4.
How are pteridophytes different
from the phanerogams?
5.
Which organisms are called
primitive and how are they different from the so-called advanced organisms?
6.
Which do you think is a more basic
characteristic for classifying organisms?
(a) The place where they live.
(b) The kind of cells they are made of. Why?
(a) The place where they live.
(b) The kind of cells they are made of. Why?
7.
Give three examples of the range of
variations that you see in life-forms around you.
8.
What are gymnosperms? Give two
characteristics.
9.
How many chambers do the heart of
fish, amphibians and mammals have?
10. What
are the two adaptive features of birds? What is the scientific name of ostrich?
11. What
are vertebrates? Name four sub groups of vertebrates.
12. Give
any two reasons why mosses are found in moist and humid places.
NATURAL RESOURCES
1. The atmosphere of the earth is heated by radiations
which are mainly
(a) Radiated by the sun
(b) Re-radiated by land
(c) Re-radiated by water
(d) Re-radiated by land and water.
2. If there were no atmosphere around the
earth, the temperature of the earth will
(a) Increase
(b) Go on decreasing
(c) increase during day and decrease
during night .
(d) Be unaffected
3. What would happen, if all the oxygen
present in the environment is converted to ozone?
(a) We will be protected more
(b) It will become poisonous and kill
living forms .
(c) Ozone is not stable, hence it will
be toxic
(d) It will help harmful sun
radiations to reach earth and damage many life forms.
4. One of the following factors does not
lead to soil formation in nature
(a) The sun
(b) Water
(c) Wind
(d) Polythene bags .
5. The two forms of oxygen found in the atmosphere are
(a) Water and ozone
(b) Water and oxygen
(c) Ozone and oxygen .
(d) Water and
carbon-dioxide
1.
Why
is the atmosphere essential for life?
2.
Why
is water essential for life?
3. How
are living organisms dependent on the soil? Are organisms that live in water
totally independent of soil as a resource?
4. You
have seen weather reports on television and in news paper. How do you think we
are able to predict the weather?
5.
We know that many human activities lead to
increasing levels of pollution of air, water bodies and soil. Do you think that
isolating these activities to specific and limited areas would help in reducing
pollution?
6.
Write
a note on how forests influence the air, soil and water resources.
7.
What
is ‘Water Cycle’ ? Explain the process of water cycle.
8.
Write
a short note on ‘Nitrogen Fixation’
9.
Explain
the ‘Nitrogen Cycle
10.
Discuss the consequences of the increase in the concentration of Carbon Dioxide and other Green House
gases in the atmosphere
ATOMS AND
MOLECULES
Atom: It
is the smallest particle of an element which may or may not have independent
existence. The atoms of certain elements such as hydrogen, oxygen, nitrogen,
etc .do not have independent existence whereas atoms of helium, neon, argon,
etc. do have independent existence. Thus we can say that all elements are
composed of atoms.
IUPAC (International Union of Pure and Applied
Chemistry) approves names of
elements. Many of the symbols are the first one or two letters of the
element’s name in English. The first letter of a symbol is always written as a
capital letter (uppercase) and the second letter as a small letter (lowercase).
For example : (i) hydrogen, H (ii)
aluminium, Al and not AL (iii) cobalt, Co and not CO.
Symbols of some elements are formed from the first
letter of the name and a letter, appearing later in the name. Examples are: (i)
chlorine, Cl, (ii) zinc, Zn etc.
Other symbols have been taken from the names of elements
in Latin, German or Greek. For example, the symbol of iron is Fe from its Latin
name ferrum, sodium is Na from natrium, potassium is K from kalium. Therefore,
each element has a name and a unique chemical symbol.
Molecule: A molecule is the
smallest or the simplest structural unit of an element (or) a compound which
contains one (or) more atoms. It retains the characteristics of an element. A
molecule can exist freely and it is a combined form of bonded units whereas an
atom is a singular smallest form of non bonded unit.
Molecules are of two types, namely homo atomic molecules
and hetero atomic molecules.
Homo atomic molecules: These are the molecules which are made up of atoms of the same element. For example hydrogen gas consists of two atoms of hydrogen (H2).Similarly oxygen gas consists of two atoms of oxygen (O2).
Homo atomic molecules: These are the molecules which are made up of atoms of the same element. For example hydrogen gas consists of two atoms of hydrogen (H2).Similarly oxygen gas consists of two atoms of oxygen (O2).
HETERO ATOMIC MOLECULES : The hetero atomic
molecules are made up of atoms of different elements. They are also classified
as diatomic, triatomic, or polyatomic molecules depending upon the number of
atoms present. H2O, NH3, CH4, etc., are the
examples for hetero atomic molecules.
Atomicity: The number of atoms
present in one molecule of an element is called the atomicity of an element.
Depending upon the number of atoms in one molecule of an element, molecules are
classified into monoatomic, diatomic, triatomic or poly atomic molecules
containing one, two, three, or more than three atoms respectively.
Mono atomic molecules:
Helium (He) Neon (Ne) Metals
Di atomic molecules: Hydrogen H2 Chlorine Cl2
Tri atomic molecules: Ozone (O3)
Poly atomic molecules: phosphorous P4 Sulphur S8
Atomicity = Molecular Mass/Atomic mass
Isotopes ⇒ These are the atoms of same element with same atomic number (Z) but different mass number (A). Example (17Cl35,17Cl37 )
Isobars ⇒ These are the Atoms of the different element with same mass number but different atomic number. Example (18Ar40, 20Ca40 )
Isotones ⇒ These are the atoms of different elements with same number of neutrons Example : (6C13, 7N14 )
WHAT IS AN ION? : An ion is a charged particle and can be negatively or positively charged.
A negatively charged ion is called an ‘anion’ and the positively charged ion, a ‘cation’. For example, sodium chloride (NaCl). Its constituent particles are positively charged sodium ions (Na+) and negatively charged chloride ions (Cl–). Ions may consist of a single charged atom or a group of atoms that have a net charge on them. A group of atoms carrying a charge is known as a polyatomic ion e.g. Calcium oxide (Ca+2 O-2) RELATIVE ATOMIC MASS : Relative atomic mass of an element is the ratio of mass of one atom of element to the1/12th part of mass of one atom of carbon. Relative atomic mass is a pure ratio and has no unit. If the atomic mass of an element is expressed in grams, it is known as gram atomic mass.
Di atomic molecules: Hydrogen H2 Chlorine Cl2
Tri atomic molecules: Ozone (O3)
Poly atomic molecules: phosphorous P4 Sulphur S8
Atomicity = Molecular Mass/Atomic mass
Isotopes ⇒ These are the atoms of same element with same atomic number (Z) but different mass number (A). Example (17Cl35,17Cl37 )
Isobars ⇒ These are the Atoms of the different element with same mass number but different atomic number. Example (18Ar40, 20Ca40 )
Isotones ⇒ These are the atoms of different elements with same number of neutrons Example : (6C13, 7N14 )
WHAT IS AN ION? : An ion is a charged particle and can be negatively or positively charged.
A negatively charged ion is called an ‘anion’ and the positively charged ion, a ‘cation’. For example, sodium chloride (NaCl). Its constituent particles are positively charged sodium ions (Na+) and negatively charged chloride ions (Cl–). Ions may consist of a single charged atom or a group of atoms that have a net charge on them. A group of atoms carrying a charge is known as a polyatomic ion e.g. Calcium oxide (Ca+2 O-2) RELATIVE ATOMIC MASS : Relative atomic mass of an element is the ratio of mass of one atom of element to the1/12th part of mass of one atom of carbon. Relative atomic mass is a pure ratio and has no unit. If the atomic mass of an element is expressed in grams, it is known as gram atomic mass.
e.g., Gram atomic mass of hydrogen = 1g ; Gram atomic mass of carbon = 12g
Gram atomic mass of nitrogen = 14g ; Gram atomic mass of oxygen = 16g
Atomic mass is expressed in atomic mass unit (amu). One atomic mass unit is defined as 1/12th part of the mass of one atom of carbon.
Chemical Formulae: The chemical formula is a symbolic representation of a compound of its composition.
Valency : The combining power (or capacity) of an element is known as its valency. Valency can be used to find out how the atoms of an element will combine with the atom(s) of another element to form a chemical compound.
RELATIVE MOLECULAR MASS : The relative molecular mass of an element or a compound is the ratio of mass of one molecule of the element or a compound to the mass of 1/12 th part of mass of one atom of carbon. Relative Molecular mass is a pure ratio and has no unit. If the molecular mass of a given substance is expressed in gram, it is known as gram molecular mass of that substance.
Molecular mass is the sum of the masses of all the atoms present in one molecule of the compound or an element.
Problem: Find the gram molecular mass of water (H2O)
Solution: 2(H) = 2 x 1 = 2 and 1(O) = 1 x 16 = 16 ; Gram molecular mass of H2O = 2 + 16 = 18g
Problem: Find the gram molecular mass of carbon dioxide
Solution: (CO2) 1(C) = 1 x 12 = 12 and 2(O) = 2 x 16 = 32 ; Gram molecular mass of CO2 = 12 + 32 = 44 g
MOLE CONCEPT
While performing a reaction, to know the number. of atoms (or) molecules involved, the concept of mole was introduced. The quantity of a substance is expressed in terms of mole.
Definition of mole : Mole is defined as the amount of substance that contains as many specified elementary particles as the number of atoms in 12g of carbon-12 isotope.
One mole is also defined as the amount of substance which contains Avogadro number (6.023 x 1023) of particles.
Avogadro number: Number of atoms or molecules or ions present in one mole of a substance is called Avogadro number. Its value is 6.023 x 1023.
Therefore, one mole of any substance = 6.023 x 1023 particles may be atoms, molecules, ions
For e g. One mole of oxygen atoms represents 6.023 x 1023 atoms of oxygen and 5 moles of oxygen atoms contain 5 x 6.023x1023 atoms of oxygen.
Number of moles = given mass/ atomic mass
Calculate the number of moles in (i) 81g of aluminium ii) 4.6g sodium (iii) 5.1g of Ammonia (iv) 90g of water (v) 2g of NaOH
Solution: (i) Number of moles of aluminium = given mass of aluminium / atomic mass of aluminium = 81/27 = 3 moles of aluminium
Calculate the mass of 0.5 mole of
iron
Solution: mass = atomic mass x number of moles = 55.9 x 0.5 = 27.95 g
Calculation of number of particles when the mass of the substance is given:
Number of particles =( Avogadro number x given mass)/gram molecular mass
Problem: Calculate the number. of molecules in 11g of CO2
Solution: gram molecular mass of CO2 = 44g
Number of molecules = (6.023 x 1023 x 11) / 44 = 1.51 x 1023 molecules
Calculation of mass when number of particles of a substance is given:
Mass of a substance = (gram molecular mass x number of particles)/6.023 x 1023
Problem: Calculate the mass of 18.069 x 1023 molecules of SO2
Solution: Gram molecular mass SO2 = 64gm
The mass of 18.069 x 1023 molecules of SO2 = (64x18.069 x 1023)/ (6.023 x 1023) = 192 g
Do yourself: (a) Calculate the mass of glucose in 2 x 1024 molecules (b) Calculate the mass of 12.046 x 1023 molecules in CaO
Calculation of number of moles when you are given number of molecules:
Problem: Calculate the number moles for a substance containing 3.0115 x 1023 molecules in it.
Solution: Number of moles = [Number of molecules/(6.023 x 1023)]
= ( 3.0115 x 1023)/( 3.0115 x 1023) =0.5 moles
Do yourself: (a) Calculate number of moles in 12.046x 1022 atoms of copper (b) Calculate the number of moles in 24.092 x 1022 molecules of water.
Problem: Calculate the number of aluminium ions present in 0.051 g of aluminium oxide. (Hint: The mass of an ion is the same as that of an atom of the same element. Atomic mass of Al=27 u)
Solution: Mass of the 1 mole of Al2 O3 = 2x27 + 3x16 = 102gm
The number of ions present in 102 gm of aluminium oxide = 6.023 x 1023 ion
The number of ions present in 0.051g of aluminium oxide= (6.023 x 1023 ion x 0.051g)/ 102 gm = 6.023 x 1023 ion x0.0005 = 3.0115 x 1020 ions In Al2 O3, Aluminium and oxygen are in ratio 2:3
So, The number of aluminium ions present(Al3+) in 0.051g of aluminium oxide = 2 x 3.0115 x 1020 ions =6.023 x 1020 ion
PRISM:
Co-ordinate Geometry
Solution: mass = atomic mass x number of moles = 55.9 x 0.5 = 27.95 g
Calculation of number of particles when the mass of the substance is given:
Number of particles =( Avogadro number x given mass)/gram molecular mass
Problem: Calculate the number. of molecules in 11g of CO2
Solution: gram molecular mass of CO2 = 44g
Number of molecules = (6.023 x 1023 x 11) / 44 = 1.51 x 1023 molecules
Calculation of mass when number of particles of a substance is given:
Mass of a substance = (gram molecular mass x number of particles)/6.023 x 1023
Problem: Calculate the mass of 18.069 x 1023 molecules of SO2
Solution: Gram molecular mass SO2 = 64gm
The mass of 18.069 x 1023 molecules of SO2 = (64x18.069 x 1023)/ (6.023 x 1023) = 192 g
Do yourself: (a) Calculate the mass of glucose in 2 x 1024 molecules (b) Calculate the mass of 12.046 x 1023 molecules in CaO
Calculation of number of moles when you are given number of molecules:
Problem: Calculate the number moles for a substance containing 3.0115 x 1023 molecules in it.
Solution: Number of moles = [Number of molecules/(6.023 x 1023)]
= ( 3.0115 x 1023)/( 3.0115 x 1023) =0.5 moles
Do yourself: (a) Calculate number of moles in 12.046x 1022 atoms of copper (b) Calculate the number of moles in 24.092 x 1022 molecules of water.
Problem: Calculate the number of aluminium ions present in 0.051 g of aluminium oxide. (Hint: The mass of an ion is the same as that of an atom of the same element. Atomic mass of Al=27 u)
Solution: Mass of the 1 mole of Al2 O3 = 2x27 + 3x16 = 102gm
The number of ions present in 102 gm of aluminium oxide = 6.023 x 1023 ion
The number of ions present in 0.051g of aluminium oxide= (6.023 x 1023 ion x 0.051g)/ 102 gm = 6.023 x 1023 ion x0.0005 = 3.0115 x 1020 ions In Al2 O3, Aluminium and oxygen are in ratio 2:3
So, The number of aluminium ions present(Al3+) in 0.051g of aluminium oxide = 2 x 3.0115 x 1020 ions =6.023 x 1020 ion
PRISM:
Ø Volume = Area of base x Height
Ø L.S.A = Perimeter of base x Height
Ø T.S.A = L.S.A + 2(Area of base)
Co-ordinate Geometry
Q. 1. The centre of the circle is (-1, 6) and one end of a diameter is (5, 9), find the coordinates of the other end.
Q. 2. If (3, 0), (2, a) and (b, 6) are the vertices of a triangle ABC whose centroid is (2, 5). Find the values of a and b.
Q. 3. If A(-1, 3), B(1, -1) and C(5, 1) are the three vertices of a triangle ABC, find the length of median through B.
Q. 4. If (3, 2), (4, 4) and (1, 3) are the mid-points of the sides of a triangle, find the coordinates of the vertices of the triangle.
Q. 5. Using section formula show that (4, -11), (5, 3), (2, 15) and (1, 1) are the vertices of a parallelogram.
Q. 6. In what ratio is the line segment joining the points (-2, -3) and (3, 7) divided by the y-axis? Also find the coordinates of the point of division.
Q. 7. Find the point which represents the three-fourths of the distance from (3, 2) to (-5, 6).
Q. 8. Find the coordinates of the centre of circle, the coordinates of the end points of whose diameters are (-5, -2) and (7, -6). Also find the radius of the circle.
Q. 9. In what ratio does the point (3, 12) divide the line segment joining the points (1, 4) and (4, 16) ?
Q. 10. Find the coordinates of the points of trisection of the line segment joining the points (4, -8) and (7, 4).
Q. 11. Find the coordinates of a point which divide the segment AB in the ratio 3:5 internally, where A and B are (4, -1) & (7, 4) respectively.
Q. 12. Find the coordinates of point on the line joining A(3, -4) and B(-2, 5) that is twice as far from A as from B.
Q. 13. The mid-point of the line segment joining (3p, 4) and (-2, 2q) is (2, 2p + 2). Find the values of p and q.
Q. 14. Find the coordinates of a point whose distance from (3, 5) is 5 units and that from (0, 1) is 10 units.
Q. 15. An equilateral triangle has one vertex at (3, 4) and another at (-2, 3). Find the coordinates of the third vertex.
Differential Equations, Mathematics: XII
1. What is the order and degree of the differential equation whose solution is y = cx+ c2 - 3c3/2 + 2, where c is a parameter.
2. Verity that the function is a solution of the corresponding diff. eq. x + y = tan-1 y ; y2y1 + y2 + 1 = 0
3. Form the differential equation representing the family of ellipses having foci on x – axis and centre at the origin.
4. Form the diff. eq of the family of circles touching the x axis at origin.
5. Solve the diff eq.ex tan y dx + (1 - ex)Sec2 y dy = 0
|
6. Solve Cos æ dy ö =a, ; y = 1 when x = 0
è dx ø
7. Solve. x 2 - y2dx+2xy dy = 0
8. Solve: x2dy + y(x + y)dx = 0 for y = 1, x = 1
9. Find the particulars solution of diff . Equation.(1+x 2 dy +2xy dx =Cotx dx
10. Find the particular solution of diff. equation
x dy y - x + xy Cot x = 0
dx
METAL AND NON-METALS
OCCURRENCE OF METALS AND NON METALS :-
•Out of the 92 naturally occurring elements 70
are metals and about 22 are non metals. Some elements show properties
of both metals and non metals. They are called metalloids.
•Only some metals like gold, silver, platinum
etc are found in the free state. Most metals are found in the combined states
as oxides, sulphides, carbonates, silicates etc.
•Some non metals are found in the free state
like helium, neon, argon etc. and some are found in free and combined states
like sulphur, phosphorus etc.
METALLURGY :-
•Metallurgy:-is science of extraction of metals
from their ores and their purification.
•Minerals:-are naturally occurring substances
containing one or more elements or their compounds.
•Ore:-is a mineral from which one or more metals
can be extracted profitably.
•Metallurgical processes:-consists of three main
steps. They are :-i) Concentration of the ore ii) Reduction iii) Refining
•Concentration of the ore:-is the removal of
impurities from the ore.
•Reduction:-the process of obtaining the metal
from its compound.
•Refining:-is the process of purification of the
impure metals to obtain the pure metal.
PHYSICAL PROPERTIES OF METALS AND NON
METALS:-
METALS
•Metals are solids (except mercury).
•Metals are hard (except sodium, potassium etc.
•Metals have metallic lustre.
•Metals have high melting points and
bolilingpoints.
•Metals are malleable ( can be made into
thin sheets).
•Metals are ductile (can be made into
thin wires).
•Metals are good conductors of heat and
electricity.
•Metals are sonorus(produces sound).
NON METALS
•Non metals may be solids, liquids or gases.
•Non metals which are solids are brittle
(diamond is the hardest).
•Non metals do not have lustre some have a dull
luster.
•Non metals have low melting points.
•Non metals are not malleable.
•Non metals are not ductile.
•Non metals are bad conductors of heat and
electricity (except graphite).
•Non metals are not sonorous
CHEMICAL PROPERTIES OF METALS AND NON
METALS:-
a) REACTION WITH OXYGEN:-
Metals react with oxygen to form metallic
oxides. These oxides are basic oxides because they react with water
to form bases. Eg. Magnesium burns in air to form magnesium oxide.
Magnesium reacts with water to form magnesium hydroxide.
2 Mg + O2-- MgO
MgO+ H2O -- Mg(OH)2
Non metals react with oxygen to form non
metallic oxides. These oxides are acidic oxides because they react
with water to form acids.
Eg. Sulphurburns in air to form sulphurdioxide.
Sulphurdioxide reacts with water to form sulphurous acid.
S + O2- SO2
SO2+ H2O---à H2SO3
b) REACTION WITH WATER:-
Metals react with water to form metal hydroxides
and hydrogen.
Eg. Sodium reacts with water to form sodium
hydroxide and hydrogen.
2 Na + 2 H2O
2 Na OH + H2
Magnesium reacts with water to form magnesium
hydroxide and hydrogen.
Mg + H2O Mg(OH)2+ H2
Non metals do not react with water.
c) REACTION WITH ACIDS:-
Metals react with acids to form metallic salts and hydrogen.
Eg. Zinc reacts with dilute hydrochloric acid
to form zinc chloride and hydrogen.
Zn + 2 HCl --------------- ZnCl2+ H2
Most non metals do not react with acids.
Some non metals like sulphur reacts with
concentrated nitric acid to forn sulphur dioxide, nitrogen dioxide and water.
S + 4
HNO3 ----------- SO2+ 4 NO2+2
H2O
d) Metals replace metals:-
A more reactive metal replaces a less reactive
metal from its salt solution.
Eg. Magnesium replaces copper from copper sulphate
solution to form magnesium sulphateand copper.
Mg + CuSO4---------------- MgSO4+ Cu
Zinc replaces copper from copper sulphate solution
to for zinc sulphate and copper.
Zn + CuSO4------------------ ZnSO4 + Cu
Iron replaces copper from copper sulphate solution
to form iron sulphate and copper
Fe + CuSO4---------- FeSO4+ Cu
Based on the reactivity of metals, they can be
arranged in the decreasing order of their activity.
5) Activity series of metals :-
The arranging of metals in the decreasing order of
their reactivity is called activity series of metals.
In decreasing order
Potassium
Sodium
Magnesium
Aluminium Decreasing
Zinc order of
Iron reactivity
Lead
Copper
Silver
Gold
6) NOBLE METALS :-
Metals like gold, silver, platinum etc. retain
their lustre because they do not react with air, water or acids. So they are
called noble metals.
Gold dissolves in aqua regia. Aqua regia is a
mixture of concentrated nitric acid and concentrated hydrochloric acid in the
ratio 1:3.
Pure is 24 carat gold. It is very soft and cannot
be used for making ornaments. So it is mixed with some silver or copper to make
it hard.
7) USES OF METALS :-
Iron :-is used for making pins, nails, nuts, bolts,
tools,
machines, construction of buildings, bridges etc.
Aluminium :-is used for making utensils, wires,
furniture, parts of aircrafts, vehicles, machines, for packing food
and medicines etc.
Copper :-is used for making wires, vessels,
electric gadgets etc.
Gold :-is used for making jewellery, coins medals
etc
Silver :-is used for making jewellery. Coins,
medals etc.
Platinum :-is used for making jewellery, electric
gadgets, plugs in vehicles etc.
Sodium :-compounds are used as common
salt, chemicals etc.
Calcium :-compounds are used for making cement,
glass etc.
8) Uses of non metals:-
Sulphur:-is used for making sulphuric acid, salts
of metals etc.
Oxygen:-is used for respiration by living things,
burning of fuels etc.
Nitrogen:-is used for making ammonia which is used
for making fertilizers.
Hydrogen:-is used for making ammonia which is used
for making fertilizers, as fuel in rockets, for welding etc.
Chlorine:-is used to kill germs in water.
Iodine:-is used as tincture iodine which is an
antiseptic
9) CORROSION:-
The surface of some metals gets corroded when
exposed to moist air for a long time. This is called corrosion.
Prevention of corrosion of metals:-
The corrosion of metals can be prevented
by:-
i) Applying oil or grease.
ii) Applying paint
iii) Galvanisation ( coating of metals with non
corrosive metals like zinc)
iv) Electroplating ( coating of metals with non
corrosive metals like chromium tin by passing
electricity)
v) Alloying ( Eg. When iron is alloyed with
chromium and nickel, it forms stainless steel which is resistant to corrosion)
MOTION
1. If a body starts from rest, what can be said about the acceleration of body?
(a)
Positively accelerated (b) Negative
accelerated
(c) Uniform accelerated (d) None of the above
(c) Uniform accelerated (d) None of the above
2. What does slope of position time graph give?
(a) speed (b) acceleration (c)
uniform speed
(d) Both (a) and (c) depending upon the type of graph.
(d) Both (a) and (c) depending upon the type of graph.
3. A boy throws a stone upward with a velocity of 60m/s.
(a) How long will it
take to reach the maximum height (g = -10m/s2)?
(b)
What is the maximum height reached by the ball?
(c) How long will it take
to reach the ground?
4. Which of the following statements is correct?
(a) speed distance are scalar, velocity and displacement are vector
(b) speed distance are vector, velocity and displacement are vector
(c) speed and velocity are scalar, distance and velocity are vector
(d) speed and velocity are vector, distance and displacement are scalar
(a) speed distance are scalar, velocity and displacement are vector
(b) speed distance are vector, velocity and displacement are vector
(c) speed and velocity are scalar, distance and velocity are vector
(d) speed and velocity are vector, distance and displacement are scalar
5. A car travels at a speed of 40km/hr for two hour and then at 60km/hr for three hours. What is the average speed of the car during the entire journey?
6. A body is dropped from a height of 320m. The acceleration due to the gravity is 10m/s2?
(a) How long does
it take to reach the ground?
(b) What is
the velocity with which it will strike the ground?
7. Calculate the acceleration and distance of the body moving with 5m/s2 which
comes to
rest
after travelling for 6sec?
8. Drive
the Equation: S = ut + ½ at2 graphically?
SURFACE
AREA OF CUBE, CUBOID AND CYLINDER
1)
Find the Total Surface Area of
a Cylinder having height 10 cm diameter 14 cm
2)
Three cubes each of side 5 cm are joined
end to end. Find the surface area of the resulting cuboids.
3)
The inner diameter of the
Cylindrical well is 3.5 m and 10 m deep
find its Inner Curved Area
4)
Find the lateral surface
area of a closed cylindrical patrol storage tank that is 4.2 m in diameter
and 4.5 m high.
5)
The surface area of a cuboid is 1300cm2
if its breadth is 10cm and height is 20cm , find its length
6)
The curved surface area of a cylinder is
216 π . If its height is 18 cm then what will be its radius?
7)
What will be the edge of a cube? If its
surface area is 324 sq cm .
8)
A rectangular box 14 cm long, 10 cm wide
and 5 cm high is to be made with card-board. Find the area of card-board to
make that box?
CO-ORDINATE GEOMETRY
1. The centre of the circle is (-1,
6) and one end of a diameter is (5, 9), find the coordinates of the other end.
2. If (3, 0), (2, a) and (b, 6) are
the vertices of a triangle ABC whose centroid is (2, 5). Find the values of a
and b.
3. If A(-1, 3), B(1, -1) and C(5,
1) are the three vertices of a triangle ABC, find the length of median through
B.
4. If (3, 2), (4, 4) and (1, 3) are
the mid-points of the sides of a triangle, find the coordinates of the vertices
of the triangle.
5. Using section formula show that
(4, -11), (5, 3), (2, 15) and (1, 1) are the vertices of a parallelogram.
6. In what ratio is the line
segment joining the points (-2, -3) and (3, 7) divided by the y-axis? Also find
the coordinates of the point of division.
7. Find the point which represents
the three-fourths of the distance from (3, 2) to (-5, 6).
8. Find the coordinates of the
centre of circle, the coordinates of the end points of whose diameters are (-5,
-2) and (7, -6). Also find the radius of the circle.
9. In what ratio does the point (3,
12) divide the line segment joining the points (1, 4) and (4, 16) ?
10. Find the coordinates of the
points of trisection of the line segment joining the points (4, -8) and (7, 4).
11. Find the coordinates of a point
which divide the segment AB in the ratio 3:5 internally, where A and B are (4,
-1) & (7, 4) respectively.
12. Find the coordinates of point
on the line joining A(3, -4) and B(-2, 5) that is twice as far from A as from
B.
13. The mid-point of the line
segment joining (3p, 4) and (-2, 2q) is (2, 2p + 2). Find the values of p and
q.
14. Find the coordinates of a point
whose distance from (3, 5) is 5 units and that from (0, 1) is 10 units.
15. An equilateral triangle has one
vertex at (3, 4) and another at (-2, 3). Find the coordinates of the third
vertex.
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