Current Affairs 10th Class

 Areas Related to Circles      

• A circle is a closed curve in a plane drawn in such a way that every point on this curve is at a constant distance (r units) from a fixed point O inside it.

The fixed point O is called the centre of the circle and the constant distance r is called the length of radius of the circle.  

• Circumference of a circle:

The perimeter of a circle is called its circumference. The length of the thread that winds tightly around the circle exactly once gives the circumference of the circle. Circumference\[=2\pi r=\pi d\], where r = radius and d = diameter. Here \[\pi \] (Pi) is a constant.   Note: The approximate value of n is taken as\[\frac{22}{7}\]or 3.14. However n is not a rational number. It is an irrational number and is defined as the ratio of circumference of a circle to its diameter.  

• Area of a circle:

Area of a circle with radius r units is equal to\[\pi {{r}^{2}}sq\]units.  

• Area of a ring:

The region enclosed between two concentric circles of different radii is called a ring. Area of path formed\[=(\pi {{R}^{2}}-\pi {{r}^{2}})sq.\] units       \[=\pi ({{R}^{2}}-{{r}^{2}})sq.units\]       \[=\pi (R+r)(R-r)sq.units\]      

• Length of an arc of a circle:

Let A and B be any two points on a circle. The length of the thread that will wrap along this arc from A to B is the length of AB written as\[\overset\frown{AB}\]? In a circle of radius r, we have \[\frac{l(\overset\frown{AB})}{Circumference}=\frac{{{x}^{o}}}{{{360}^{o}}}or\,l(\overset\frown{AB})=\frac{2\pi r{{x}^{o}}}{{{360}^{o}}}\]  

• Area of a sector:

A sector of a circle is the region enclosed by an arc of a circle and two radii to its end points. Area of sector \[=\frac{{{x}^{o}}}{{{360}^{o}}}\times \pi {{r}^{2}}\]where x is sector angle and r is radius of circle.  

• Segment of a circle:

A segment of a circle is the region enclosed by an arc of the circle and its chord. Area of minor setment \[\text{AXB}=\]area of sector OAXB - area of \[\Delta \text{OAB}\] Area of major segment AYB = area of circle - area of minor segment AXB      

  Surface Area and Volume      

• A right circular cylinder is a solid generated by the revolution of a rectangle about one of its sides.

(i) Volume\[(V)=\pi {{r}^{2}}h\]     (ii) Curved surface area (C.S.A.) \[=2\pi \,rh\]          (iii) Base area\[=\pi \,{{r}^{2}}\]        (iv) Total surface area (T.S.A.) \[=2\pi \,r(h+r)\]

• Hollow cylinders:  

                                            (i) Volume of material \[=\pi h({{R}^{2}}-r)\]                        (ii) Curved surface area \[=2\pi h(R+r)\]                                              (iii) Total surface area \[=2\pi (R+r)(h+R-r)\]

• Right circular cone: If a right angled triangle is revolved about one of the sides containing the right angle, the solid thus generated is called a right circular cone.

(i) \[l=\sqrt{{{h}^{2}}+{{r}^{2}}}\] (ii) \[volume=\frac{1}{3}\pi {{r}^{2}}h\] (iii) \[C.S.A.=\pi rl=\pi r\sqrt{{{h}^{2}}+{{r}^{2}}}\] (iv) \[T.S.A.=\pi r(l+r)\]    

• Sphere: A sphere is the locus of a point which moves in space in such a way that its distance from a fixed point remains constant.
• (i) Volume\[=\frac{4}{3}\pi {{r}^{3}}\]
• (ii) Surface area\[=4\pi {{r}^{2}}\]

 

• Hemisphere: A plane through the centre of a sphere cuts it into two equal parts. Each part is called a hemisphere.

(i) Volume\[=\frac{2}{3}\pi {{r}^{3}}\] (ii) Curved surface area\[=2\pi {{r}^{2}}\] (iii) Total surface area\[=3\pi {{r}^{2}}\]   Volume and surface area of a frustum of a cone: When a cone is cut by a plane parallel to its base, the portion between the plane and the base is called frustum of the cone. (i) \[V=\frac{\pi h}{3}[{{R}^{2}}+{{r}^{2}}+Rr]\] (ii) \[L.S.A=\pi l[R+r]\] (iii) \[T.S.A=\pi [{{R}^{2}}+{{r}^{2}}+l(R+r)]\] Where, \[l=\sqrt{{{h}^{2}}+{{(R-r)}^{2}}}\]      

 Statistics      

• Statistics: The science of collection, organization, presentation, analysis and interpretation of numerical data is called statistics.

 

• Raw data: The collection of actual information used to make logical inferences is called raw data.

 

• Frequency table: The table in which raw data is condensed and presented is called the frequency table.

 

• Measure of central tendency: the tendency in the data to be concentrated around a certain single value that represents the whole set of data is called a measure of central tendency or average.

 

• Series: While 'preparing a frequency distribution table, classes can be considered in two ways- (i) inclusive or discrete series and (ii) Exclusive or continuous series.

 

• Discrete series: The series in which the class intervals are so fixed that the upper limit of the class is included in the same class interval is called the continuous series.

 

• Rule to convert a discrete (or discontinuous) series into a continuous series.

(i) Find the adjustment factor. i.e. \[\frac{1}{2}\][lower limit of second class – upper limit of first class] (ii) Subtract the adjustment factor from the lower limit of a class and add it to the upper limit of each class. (iii)  The series obtained is the exclusive series  

• Arithmetic mean of raw data (when frequencies are not given): The arithmetic mean of raw data is obtained by adding all the values of the variables and dividing the sum by the total number of values that are added.

 

• If \[{{x}_{1}},{{x}_{2}},.....{{x}_{n}},\]where ‘n’ is the total number of value, then arithmetic mean

\[(\overline{x})=\frac{{{x}_{1}}+{{x}_{2}}+.....+{{x}_{n}}}{n}=\frac{1}{n}\sum\limits_{i=1}^{n}{{{x}_{i}}}\]

• Direct method (when frequencies are given) o finding arithmetic mean: If \[{{x}_{1}},{{x}_{2}},.....,{{x}_{n}}\]are the ‘n’ variables with corresponding frequencies \[{{f}_{1}},{{f}_{2}},.....,{{f}_{n}}\]respectively, then the arithmetic mean is given by

 

• \[\bar{x}=\frac{{{f}_{1}}{{x}_{1}}+{{f}_{2}}{{x}_{2}}+.....+{{f}_{n}}{{x}_{n}}}{{{f}_{1}}+{{f}_{2}}+....{{f}_{n}}}=\sum\limits_{i=1}^{n}{\frac{{{f}_{i}}{{x}_{i}}}{{{f}_{i}}}}\]

 

• Properties of arithmetic mean:

(a) The algebraic sum of deviations from mean is zero; i.e. if \[{{x}_{1}},{{x}_{2}},.....{{x}_{n}}\]are ’n’ observations, then \[\sum\limits_{i=1}^{n}{({{x}_{i}}-\bar{x})}=0\] (b) If each observation of a data is increased by 'a', then the mean is increased by 'a'; i.e., if \[\bar{x}\]is the mean of \[{{x}_{1}},{{x}_{2}},....,{{x}_{n}}\], then the mean of \[{{x}_{1}}+a,{{x}_{2}}+a,....,{{x}_{n}}+a\]is \[\bar{x}+a\]. (c) If each observation of a data is decreased by 'a', then the mean is decreased by 'a'; i.e., if the mean of \[{{x}_{1}},{{x}_{2}},....,{{x}_{n}}\]is \[\bar{x}\], then the mean of \[{{x}_{1}}-a,{{x}_{2}}-a,....,{{x}_{n}}-a\]is \[\bar{x}-a\]. (d) If each observation of a data is multiplied by a non-zero number, 'a', then the mean of the new observations is the product of 'a' and\[\bar{x}\], i.e., if \[{{x}_{1}},{{x}_{2}},....,{{x}_{n}}\]are 'n' observations whose mean is\[\bar{x}\], then the mean of \[{{x}_{1}}a,{{x}_{2}}a,....,{{x}_{n}}a\]is \[\bar{x}a\]. (e) If each observations is \[\frac{{\bar{x}}}{a}\]; i.e., if the mean of ‘n’ observations \[{{x}_{1}},{{x}_{2}},....,{{x}_{n}}\]is \[\bar{x}\]then the mean of the more...

 Probability      

• Random experiment: An experiment in which all possible outcomes are known and the exact outcome cannot be predicted in advance is called a random experiment.

e.g., (1) Tossing a coin. (2) Rolling an unbiased die.  

• Sample space:

The set S of all possible outcomes of a random experiment is called the sample space. e.g., (1) In tossing a coin, sample space (S) = {H,T}.  

• (2) In rolling a die, sample space (S) = {1, 2, 3, 4, 5, 6}.

 

• Probability: Probability is a concept which numerically measures the degree of certainty of the occurrence of events.

                                   

• Definition of probability: in a random experiment, let S be the sample space arid let E be an event. Then probability of occurrence of \[E=P(E)=\frac{n(E)}{n(S)}\],where  

n(E) is the number of elements favorable in E and n(S) is the number of distinct elements in S. Note :  1. \[0\le P(E)\le 1\]

If \[P(E)=1\], The event E is called a certain event and if \[P(E)=0\], the event E is called an impossible event.

 

• Types of events:

 

• (i) Simple event or elementary event: An event is called a 'simple event; if it is a single- ton subset of the sample space's'.

e.g.. When a coin is tossed, sample space S = {H,T} Let A = {H} = The event of occurrence of head and B = {T}= The event of occurrence of tail. Then 'A' and 'B' are simple events.   (ii) Mixed event or compound event: A subset of the sample space 'S' which contains more than one element is called a compound event. e.g.. When a die is thrown, sample space S = {1, 2, 3, 4, 5, 6}. Let A = {1,3,5} = The event of occurrence of odd number and B = {5,6} = The event of occurrence of a number greater than 4. Then, A' and 'B' are compound events.   (iii) Sure event: If a random experiment 'E' has a discrete sample space 'S’; then 'S' itself is an event (E = S) called the sure or certain event of 'E'. e.g.. Getting a head or a tail in a single toss of a coin is a sure event. The probability of a sure event (or certain event) is 1.   (iv) Impossible event: The empty subset \['\phi '\]of 'S' \[(E=\{\})\]is called the impossible event or null event of 'E'. e.g.. Getting a head and a tail. both in a single toss of a coin is an impossible event. The probability of an impossible event is 0.   (v) Complementary event: For a random event more...

 Light Reflection and Refraction  

• Light: It is a form of energy which when reflected by objects falls on the eyes and enables us to see the objects. Light propagates as electromagnetic waves. It does not require a medium for its propagation.

 

• The speed of light in free space or vacuum is\[3\times {{10}^{8}}\,m\,{{s}^{-1}}\].All colours of light travel with different speeds. The speed of light in a medium is less than that in vacuum.

 

• Reflection: The bouncing back of light rays incident on a surface in the opposite direction in the same medium is called reflection of light.

 

• Reversibility of light: If a ray of light is reversed, it always retraces its previous path. Object and image positions are interchangeable.

 

• Refraction: The bending of light rays when they pass from one optical medium to another is called refraction of light.

 

• Refractive index: The refractive index of a single medium is measured with respect to air or

   \[vacuum{{.}_{air}}{{\mu }_{medium}}=\frac{\sin i}{\sin r}\] \[\text{The refractive index of a medium}\,{{\mu }_{m}}=\] \[\frac{\text{velocity of light in vacuum or air}}{\text{velocity of light in medium}}=\frac{c}{c'}\]  

• Different colours travel with different velocities in a medium. Velocity of light is maximum for red and minimum for violet in a medium.

 

• All colours travel with the same velocity in vacuum (air).

 

• The refractive index is minimum for red and maximum for violet.

 

• When a light ray passes from one medium into another, the frequency remains constant but the velocity and wavelength change.

 

• Principal focus and focal length: Light can pass through a lens from either directions. Therefore, a lens has two principal foci which are situated at equal distances from the optical centre, one on either side of the lens. These are called first focal point \[{{F}_{1}}\] and the second focal point\[{{F}_{2}}\].The focal length of a lens is the distance between the optical centre and principal focus of the lens.

 

• Power of lens

The power of a lens is defined as the reciprocal of its focal length. The S.I. unit is diopter. The power of a converging lens is positive and that of a diverging lens is negative.  

• Magnification

The linear magnification is defined as the ratio of the size of the image to the size of the object. \[\therefore \]\[\text{Magnification}(M)=\frac{v}{u}=\frac{\text{height of the object}\,\text{(I)}}{\text{height of the}\,object\,(O)}\]

  The Human Eye and the colourful World    

• The Human Eye

 

• The human eye is made of structures like cornea, iris, lens and retina, which allow refraction to take place and form images. Because of the presence of two eyes we have a binocular (3-D) vision..

 

• Persistence of vision It is a phenomenon where the brain continues to sense the image, even after the object has been removed. This illusion continues for a very short time (appr. 1/16th of a second).

 

• Power of accommodation of the eye

 

• The ability of an eye to focus the distant and nearby objects on the retina by changing the focal length of its lens is called the power of accommodation of the eye.

 

• Defects of vision are (i) Myopia (ii) Hypermetropia (iii) Astigmatism and (iv) Presbyopia

 

• Prism

A homogeneous, transparent and refracting medium bounded by two triangular bases and three lateral surfaces inclined to each other at an angle is called a prism.  

• Dispersion of light

The phenomenon of the splitting of light into its component colours due to the differences in the refractive indices with the wavelength is called dispersion of light.  

• Refraction of light through a prism

When a ray of light passes through a glass prism, refraction (or bending), of light occurs both, when it enters the prism as well as when it leaves the prism. Since the refracting surfaces of the prism are not parallel, therefore, the emergent ray and incident ray are not parallel to one another. The angle between incident ray and emergent ray is called angle of Deviation. The refractive index of the prism \[\mu =\frac{\sin {{i}_{1}}}{\sin {{r}_{1}}}=\frac{\sin {{i}_{2}}}{\sin {{r}_{2}}}\]  

• Atmospheric refraction and optical phenomena The refraction of light caused by the earth's atmosphere having air-layers of varying optical densities is called atmospheric refraction. Some of the optical phenomena in nature which occur due to the atmospheric refraction of light are twinkling of stars and advanced sunrise and delayed sunset.

 

• Scattering of Light

Light is scattered when it falls on various types of suspended particles in its path. Depending on the size of the particles, the scattering can be of white sunlight as such or of the coloured lights which make up the white sunlight.  

• Tyndall Effect is the scattering of light by particles in its path to make them visible.

 

• The sky is blue due to the scattering of blue component of the white sunlight by air molecules present in the atmosphere.

more...

  Electricity    

• Every atom as a whole is electrically neutral. Its total positive charge is equal to its total negative charge. Charges are produced by loss or gain of electrons.

 

• Charges in motion and current: Charges in motion constitutes current electricity. An electric current is the rate of flow of electric charge through a given cross section of a conductor. Charge flows from higher potential to lower potential. By convention the flow of charges is taken as the flow of positive charges. Negative charges flows from lower potential to higher potential.

 

• Electric potential: at a point in a field is the amount of work done in bringing a unit positive charge from infinity to that point along any arbitrary path.

 

• A positive charge in an electric field moves from higher potential to lower potential, while a negative charge moves from lower potential to higher potential.

 

• Potential difference: The amount of work done in moving a unit positive charge from a point of low potential to a point of high potential between the two points..

 

• Ohm's law: The current flowing through a metallic conductor is proportional to the potential difference applied between its ends, provided its temperature remains constant.

 

• Resistance: The property by virtue of which a conductor opposes the flow of charge in it is known as resistance. The resistance of a conductor depends directly on its length, inversely on its area of cross-section and also on the material of the conductor.

 

• Resistors in series

(i) Current in each resistor is the same. (ii) Potential difference across each resistor is different and is proportional to the resistance. (iii) Equivalent resistance of the arrangement is\[\text{R}={{\text{R}}_{1}}+{{\text{R}}_{2}}+{{\text{R}}_{3}}\]. Effective resistance is greater than any individual resistance. (iv) If 'n' wires, each of resistance R, are Connected in series, the effective resistance is nR.  

• Resistors in parallel

(i) Currents in the resistors are in proportion to the reciprocals of resistances. (ii) Potential difference across each resistor is the same. (iii) Equivalent resistance of the arrangement is \[\frac{1}{R}=\frac{1}{{{\text{R}}_{1}}}+\frac{1}{{{\text{R}}_{2}}}+\frac{1}{{{\text{R}}_{3}}}\]Effective resistance is less than any individual resistance. (iv)If 'n' wires each of resistance R, are connected in parallel, the equivalent resistance is R/n.  

• Heating effects of electric current: The heat produced is proportional to the square of the current, the resistance of the wire and the time for which the current flows.

 

• Electric power Power is the rate of doing work or the rate at which energy is produced or consumed. The electrical energy produced or consumed more...

 Magnetic Effects of Electric Current  

• Magnetic field and field lines: The space surrounding a magnet in which magnetic force is exerted is called a magnetic field. The magnetic field lines are the lines drawn in a magnetic field along which a north magnetic pole would move. The magnetic field lines always begin from the N-pole of a magnet and end on the S-pole of the magnet. The strength of magnetic field is indicated by the degree of closeness of the field lines. If the field lines are closer together, the magnetic field is the strongest.

 

• Magnetic field due to a current carrying conductor: The patterns of various magnetic fields or shapes of field lines produced by a current carrying conductor like straight wire, circular loop and solenoid are given below.

 

• Magnetic field due to a current through a straight conductor: The magnetic field lines around a straight conductor (straight wire) carrying current are concentric circles whose centres lie on the wire.

 

• Magnetic field due to a current through a circular loop: The magnitude of magnetic field produced by a current-carrying circular loop (or a circular wire) at its centre is directly proportional to the current passing through the circular loop (or the circular wire), and inversely proportional to the radius of the circular loop (or the circular wire).

 

• Magnetic field due to a current in a solenoid: The magnetic field produced by a current- carrying solenoid is similar to the magnetic field produced by a bar magnet.

 

• Force on a current carrying conductor in a magnetic field: A magnet exerts a mechanical force on a current-carrying wire, and if the wire is free to move, this force can produce a motion in the wire.

 

• Electric motor: An electric motor is a rotating device that converts electrical energy to mechanical energy.

 

• Electromagnetic induction:

The phenomenon in which an electric current is induced in a circuit because of a changing magnetic field or the motion of the circuit in a magnetic field is called electromagnetic induction. The process of electromagnetic induction has led to the construction of generators for producing electricity at power stations.

• Electric Generator: An electric generator works on the principle that when a straight conductor is moved in a magnetic field, then current is induced in the conductor.

 

• Direct current and Alternating current: If the current flows in one direction only, it is called direct current. If the current reverses direction after equal intervals of time, it is called alternating current.

 

• Domestic Electric Circuits: Usually there are two separate circuits in a house, the lighting circuit with more...

 Sources of Energy    

• Sources of energy

A source of energy is the one which can provide adequate amount of energy in a convenient form over a long period of time.  

• Renewable sources of energy

Sources of energy which are being produced continuously in nature and are inexhaustible are called renewable sources of energy. The renewable sources of energy are: solar energy, wind energy, hydro energy, bio fuels (wood, biogas), hydrogen, energy from oceans and geothermal energy.  

• Non-renewable sources of energy

Sources of energy which have been accumulated in nature over a very, very long period of time and cannot be quickly replaced when exhausted are called non-renewable sources of energy. Some important non-renewable sources of energy are fossil fuels, coal, petroleum and natural gas.  

• Fossil fuels

Fuels that originated from the remains of dead plants and animals are called fossil fuels. Fossil fuels were formed from organic matter by complex processes over millions of years.  

• Coal

The types of coal in the order of formation are\[\text{peat}\to \text{lignite}\to \text{bituminous}\to \text{anthracite}\]. Coal is used primarily as a fuel, mainly in thermal power plants. The burning of coal produces gases like \[C{{O}_{2}},CO,S{{O}_{2}}\]and\[N{{O}_{2}}\].  

• Petroleum

Petroleum or crude oil is not used directly. It is utilised in the form of its products. The products obtained from fractional distillation are fuel oil, diesel, kerosene, petrol and petroleum gas. Asphalt, paraffin wax and lubricating oil are obtained by fractionating the residual oil. Pollution caused by burning petrol is more difficult to control than that by coal.  

• Natural gas

Natural gas is the cleanest fossil fuel. It consists mainly of methane which gives\[C{{O}_{2}}\]and water on burning. Natural gas is used for cooking and heating. It is also used as a fuel in thermal power plants. Compressed natural gas is used as a fuel in vehicles.  

• Alcohol as fuel

Ethanol burns in air to produce heat, carbon dioxide and water. Ethane, for the purpose of being used as a fuel, is produced by the fermentation of plant sugars with the help of yeast. Although it has a low calorific value than petrol, it has many advantages.  

• Energy from biomass

Biomass means any organic matter from which we can get energy on a renewable basis.  

• Solar energy

The energy obtained from the sun is called solar energy. Solar constant = 1.4 kilowatt per square metre  

• Energy from wind and tides

Wind is caused by the uneven heating of the earth's surface by the sun and is an important source of energy. Waves are produced more...

 Chemical Reactions and Equations    

• Chemical reactions

  A chemical reaction is a process in which substances undergo change to produce new substances with new properties. The substances which take part in a chemical reaction are known as reactants. The new substances formed during a chemical reaction are known as products.  

• The important characteristics of chemical reactions are: evolution of a gas, formation of a precipitate, change in colour, change in temperature, and change in state.

 

• Chemical equations

A chemical equation is a short hand representation of a chemical reaction using symbols and formulae of the substances involved in the reaction.  

• A balanced chemical equation is the one which contains equal number of atoms of each element on both sides of the equation.

 

• Types of chemical reactions

The reaction in which two or more substances combine to produce a single substance is known as synthesis reaction or combination reaction.  

• The reaction in which a compound is broken down into two or more simpler substances is known as decomposition reaction.

 

• A reaction in which an atom or a group of atoms present in a molecule is displaced by another atom is known as displacement reaction.

 

• A reaction in which two compounds exchange their ions to form two new compounds is known as double displacement reaction.

 

• Double displacement reactions are also called double decomposition reactions or metathesis reactions.

 

• Reactions in which heat is given out along with the products are called exothermic reactions.

 

• Reactions in which heat is absorbed by reactants to form products are called endothermic reactions.

 

• Oxidation and reduction reactions

Oxidation is defined as the addition of oxygen or removal of hydrogen to a substance.  

• Oxidation is also defined in terms of metals and non-metals as the addition of non-metallic element (or removal of metallic element).

 

• Reduction is addition of hydrogen or removal of oxygen to a substance.

 

• Reduction is also defined in terms of metals and non-metals as the addition of metallic element (or removal of non-metallic element).

 

• The substance which oxidizes substances is known as an oxidizing agent.

 

• The substance which reduces substances is known as a reducing agent.

 

• In redox reactions, oxidation and reduction reactions occur simultaneously.