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LEGISLATURE Legislature of the Union which is called Parliament , consists of President and two Houses, known as Council of States (Rajya Sabha) and House of the People (Lok Sabha). Each House has to meet within six months of its previous sitting. A joint sitting of two Houses can be held in certain cases. RAJYA SABHA The Constitution provides that the Rajya Sabha shall consist of 12 members to be nominated by the President from amongst persons having special knowledge or practical experience in respect of such matters as literature, science, art and social service; and not more than 238 representatives of the States and of the Union Territories. Elections to the Rajya Sabha are indirect; members representing States are elected by elected members of legislative assemblies of the States in accordance with the system of proportional representation by means of the single transferable vote, and those representing Union Territories are chosen in such manner as P

INDIA, a Union of States, is a Sovereign Socialist Secular Democratic Republic with a parliamentary system of government. The Republic is governed in terms of the Constitution, which was adopted by Constituent Assembly on 26 November 1949 and came into force on 26 January 1950. The Constitution which envisages parliamentary form of government is federal in structure with unitary features. The President of India is constitutional head of executive of the Union. Article 74(1) of the Constitution provides that there shall be a Council of Ministers with the Prime Minister as head to aid and advise President who shall in exercise of his functions, act in accordance with such advice. Real executive power thus vests in Council of Ministers with Prime Minister as head. Council of Ministers is collectively responsible to the House of the People (Lok Sabha). Similarly, in states, Governor is head of executive, but it is the Council of Ministers with Chief Minister as head in whom re

Characteristics of square numbers 1. A square cannot end with an odd number of zeros 2. A square cannot end with an odd number 2, 3, 7 or 8 3. The square of an odd number is odd 4. The square of an even number is even. 5. Every square number is a multiple of 3 or exceeds a multiple of 3 by unity. Ex. 4 × 4 = 16 = 5 × 3 + 1 5 × 5 = 25 = 8 × 3 + 1 7 × 7 = 49 = 16 × 3 + 1 6. Every square number is a multiple of 4 or exceeds a multiple of 4 by unity. Ex. 5 × 5 = 25 = 6 × 4 + 1 7 × 7 = 49 = 12 × 4 + 1 7. If a square numbers ends in ‘9’, the preceding digit is even. Ex. 7 × 7 = 49 ‘4’ is the preceding even numbers 27 × 27 = 729 ‘2’ is the preceding even numbers. Characteristics of square roots of numbers 1. If a square number ends in ‘9’, its square root is a number ending in’3’ or ‘7’. 2. If a square number ends in ‘1’, its square root is a number ending in’1’ or ‘9’. 3. If a square number ends in ‘5’, its square root is a number ending in’5’

Problems: 1. If a number when divided by 296 gives a remainder 75, find the remainder when 37 divides the same number. Method: Let the number be ‘x’, say ∴x = 296k + 75, where ‘k’ is quotient when ‘x’ is divided by ‘296’ = 37 × 8k + 37 × 2 + 1 = 37(8k + 2) + 1 Hence, the remainder is ‘1’ when the number ‘x’ is divided by 37. 2. If (2^32)+1 is divisible by 641, find another number which is also divisible by ‘641’. Method:                                           NOTE:^-POWER OF NUMBER Consider 2^96+1 = (2^32)^3 + 1^3 = (2^32 +1)(2^64-2^32 +1) From the above equation, we find that 296+1 is also exactly divisible by 641, since it is already given that 232+1 is exactly divisible by ‘641’. 3.3. If m and n are two whole numbers and if m^n = 25. Find n^m, given that n ≠ 1 m^n = 25 = 5^2 ∴m = 5, n = 2 ∴n^m = 2^5 = 32 4.A number when successively divided by 9, 11 and 13 leaves remainders 8, 9 and 8 respectively. Method: The least number that satisfies the conditio

Number System Test of divisibility: 1. A number is divisible by ‘2’ if it ends in zero or in a digit which is a multiple of ‘2’i.e. 2,4, 6, 8. 2. A number is divisible by ‘3’, if the sum of the digits is divisible by ‘3’. 3. A number is divisible by ‘4’ if the number formed by the last two digits, i.e. tens and units are divisible by 4. 4. A number is divisible by ‘5’ if it ends in zero or 5 5. A number is divisible by ‘6’ if it divisible by ‘2’ as well as by ‘3’. 6. A number is divisible by ‘8’ if the number formed by the last three digits, i.e, hundreds tens and units is divisible by ‘8’. 7. A number is divisible by ‘9’ if the sum of its digit is divisible by ‘9’ 8. A number is divisible by ‘10’ if it ends in zero. 9. A number is divisible by ‘11’ if the difference between the sums of the digits in the even and odd places is zero or a multiple of ‘11’. LCM: LCM of a given set of numbers is the least number which is exactly divisi

1. H.C.F. and L.C.M. of Decimals Step 1 Make the same number of decimal places in all the given numbers by suffixing zero(s) if necessary. Step 2 Find the H.C.F./L.C.M. of these numbers without decimal. Step 3 Put the decimal point (in the H.C.F./L.C.M. of step 2) leaving as many digits on its right as there are in each of the numbers 2. L.C.M. and H.C.F. of Fractions L.C.M = L.C.M. of the numbers in numerators/H.C.F. of the numbers in denominators H.C.F. = H.C.F. of the numbers in numerators/L.C.M. of the numbers in denominators 3. Product of two numbers = L.C.M. of the numbers  x H.C.F. of the numbers 4. To find the greatest number that will exactly divide x, y and z. Required number = H.C.F. of x, y and z. 5. To find the greatest number that will divide x, y and z leaving remainders a, b and c, respectively. Required number = H.C.F. of (x – a), (y – b) and (z – c). 6. To find the least number which is exactly divisible by x, y and z. Required number = L.C.M. o

Common Factor A common factor of two or more numbers is a number which divides each of them exactly. For example, 4 is a common factor of 8 and 12. Highest common factor Highest common factor of two or more numbers is the greatest number that divides each one of them exactly. For example, 6 is the highest common factor of 12, 18 and 24. Highest Common Factor is also called Greatest Common Divisor or Greatest Common Measure. Symbolically, these can be written as H.C.F. or G.C.D. or G.C.M., respectively Methods of Finding H.C.F. I. Method of Prime Factors Step 1 Express each one of the given numbers as the product of prime factors. [A number is said to be a prime number if it is exactly divisible by 1 and itself but not by any other number, e.g. 2, 3, 5, 7, etc. are prime numbers] Step 2 Choose Common Factors. Step 3 Find the product of lowest powers of the common factors. This is the required H.C.F. of given numbers. Illustration 1 Find the H.C.F. of 70 and 90. Solu

ADDITION AND SUBTRACTION (SHORT-CUT METHODS): The method is best illustrated with the help of following example: Illustration 2 54321 – (9876+8976+7689) = ? Step 1 Add 1st column:                                                           54321                                                             9876                                                             8967                                                             7689                                                           27789 6+7+9 = 22 To obtain 1 at unit’s place add 9 to make 31. In the answer, write 9 at unit’s place and carry over 3. Step 2 Add 2nd column: 3+7+6+8=24 To obtain 2 at tens place add 8 to make 32. In the answer, write 8 at ten’s place and carry over 3. Step 3 Add 3rd column: 3 + 8 + 9 + 6 = 26 To obtain 3 at hundred’s place, add 7 to make 33. In the answer, write 7 at hundred’s place and carry over 3. Step 4 Add 4th column: 3 + 9 + 8 + 7 = 27 To obtain 4 at thousand’s p

NUMBER SYSTEMS In Hindu Arabic System, we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 called digits to represent any number. This is the decimal system where we use the numbers 0 to 9. 0 is called insignificant digit. A group of figures, denoting a number is called a numeral. For a given numeral, we start from extreme right as Unit’s place, Ten’s place, Hundred’s place and so on. We represent the number 309872546 as shown below: 6-units 4-Tens 5-Hundreds 2-Tounsands 7-Ten thousand 8-Lacs 9-Ten lacs(million) 0-Crocres 3-Ten croces We read it as “Thirty crores, ninety- eight lacs, seventy-two thousands five hundred and forty-six.” In this numeral: The place value of 6 is 6 ×1 = 6 The place value of 4 is 4 ×10 = 40 The place value of 5 is 5 ×100 = 500 The place value of 2 is2 ×1000 = 2000 and so on. The face value of a digit in a numbers is the value itself wherever it may be. Thus, the face value of 7 in the above num

Astronomy and space science. If you go to the country,far from city lights,you can see about 3,000 stars on a clearnight.If your eyes were bigger,you could see many more stars.With a pair of binoc-ulars,an optical device that effectively enlarges the pupil of your eye by about 30times,the number of stars you can see increases to the tens of thousands.With amedium-sized telescope with a light-collecting mirror 30 centimeters in diameter,you can see hundreds of thousands of stars.With a large observatory telescope,millions of stars become visible. It would seem that when it comes to observingthe universe, the larger the instrument, the bet-ter. This is true up to a point, but there are lim-its—limits not imposed by technology but bynature itself.Surrounding Earth is a life-sustaining atmos-phere that stands between our eyes and the radi-ation that falls upon Earth from outer space.This radiation is comprised of a very broad spec-trum of energies and wavelengths. Collectively,they a

Principles of Spectroscopy Interaction of radiation and matter If matter is exposed to electromagnetic radiation, e.g. infrared light, the radiation can be absorbed, transmitted, reflected, scattered or undergo photoluminescence. Photoluminescence is a term used to designate a number of effects, including fluorescence, phosphorescence, and Raman scattering.   Electromagnetic Spectrum Type of Radiation Frequency :Range (Hz):Wavelength Range:Type of Transition Gamma-rays 1020-1024 <10-12 m nuclear X-rays 1017-1020 1 nm-1 pm inner electron Ultraviolet 1015-1017 400 nm-1 nm outer electron Visible 4-7.5x1014 750 nm-400 nm outer electron Near-infrared 1x1014-4x1014 2.5 mm-750 nm outer electron molecular vibrations Infrared 1013-1014 25 mm-2.5 mm molecular vibrations Microwaves 3x1011-1013 1 mm-25 mm molecular rotations, electron spin flips* Radio waves <3x1011 >1 mm >1 mm TYPES OF OPTICAL INSTRUMENTS • Spectroscope: uses human eye as a detector • Spectrogr

Solid-state physics is the study of rigid matter , or solids , through methods such as quantum mechanics , crystallography , electromagnetism, and metallurgy . It is the largest branch of condensed matter physics . Solid-state physics studies how the large-scale properties of solid materials result from their atomic -scale properties. Thus, solid-state physics forms a theoretical basis of materials science . It also has direct applications, for example in the technology of transistors and semiconductors . Solid materials are formed from densely packed atoms, which interact intensely. These interactions produce the mechanical (e.g. hardness and elasticity ), thermal , electrical , magnetic and optical properties of solids. Depending on the material involved and the conditions in which it was formed, the atoms may be arranged in a regular, geometric pattern ( crystalline solids , which include metals and ordinary water ice ) or irregularly (an amorphous solid such as common

A nuclear reaction is considered to be the process in which two nuclear particles (two nuclei or a nucleus and a nucleon) interact to produce two or more nuclear particles or ˠ-rays (gamma rays). Thus, a nuclear reaction must cause a transformation of at least one nuclide to another. Sometimes if a nucleus interacts with another nucleus or particle without changing the nature of any nuclide, the process is referred to a nuclear scattering, rather than a nuclear reaction. Perhaps the most notable nuclear reactions are the nuclear fusion reactions of light elements that power the energy production of stars and the Sun. Natural nuclear reactions occur also in the interaction between cosmic rays and matter. Nuclear reactors are devices to initiate and control a chain nuclear reaction, but there are not only manmade devices. The world’s first nuclear reactor operated about two billion years ago. The natural nuclear reactor formed at Oklo in Gabon, Africa, when a uranium-ri

Nuclear Stability is a concept that helps to identify the stability of an isotope. To identify the stability of an isotope it is needed to find the ratio of neutrons to protons. To determine the stability of an isotope you can use the ratio neutron/proton (N/Z). Also to help understand this concept there is a chart of the nuclides, known as a Segre chart. This chart shows a plot of the known nuclides as a function of their atomic and neutron numbers. It can be observed from the chart that there are more neutrons than protons in nuclides with Z greater than about 20 (Calcium). These extra neutrons are necessary for stability of the heavier nuclei. The excess neutrons act somewhat like nuclear glue. Atomic nuclei consist of protons and neutrons, which attract each other through the nuclear force , while protons repel each other via the electric force due to their positive charge. These two forces compete, leading to various stability of nuclei. There are only certain com

adiation Most general definition is that radiation is energy that comes from a source and travels through some material or through space. Light, heat and sound are types of radiation. This is very general definition, the kind of radiation discussed in this article is called ionizing radiation . Most people connect the term radiation only with ionizing radiation, but it is not correct. Radiation is all around us. In, around, and above the world we live in. It is a natural energy force that surrounds us. It is a part of our natural world that has been here since the birth of our planet. We should distinguish between: Non-ionizing radiation . The kinetic energy of particles ( photons, electrons, etc. ) of non-ionizing radiation is too small to produce charged ions when passing through matter. The particles (photons) have only sufficient energy to change the rotational, vibrational or electronic valence configurations of target molecules and atoms. Sunlight, radio waves