Chapter 2 What is polynomial ? "An expression that contains different power of same variable in algrebaic form " . Example : P(x) = 2x + 5 , P(y) = y 2 + 5y + 6 What is the Degree Of polynomial ? " Degree of polynomial is the highest power of variable in given polynomial. " For Example : P(x) = 2x + 5 has one as the highest power of x , so degree of polynomial is 1 similarly P(y) = y 2 + 5y + 6 is 2 as the highest power of y , degree polynomial. Linear Polynomial : Polynomial having degree '1' Quadratic Polynomial : Polynomial having degree '2' Cubic Polynomial : Polynomial having degree '3' Zeroes of a polynomial : A real number K is said to be zero of polynomial , If P(K) = 0 Example : P(x) = x + 5 For x = -5 ⇒ P(-5) = 0 So , -5 is the zero of the polynomial. Geometrical meaning Of zeroes : If we plot or draw any polynomial on x-y plane, and the curve cuts the x-axis at ...

Chapter 1 Euclid Division Algorithm: Given positive integers a and b , there exist unique integers q and r satisfying a = bq + r , 0 ≤ r < b How to find HCF and LCM using Euclid's Algorithm I) 135 and 225 let a = 225 , b = 135 Apply Euclid's Algorithm till remainder becomes zero , the corresponding divisor will be the HCF 225 = 135 × 1 + 90 135 = 90 × 1 + 45 90 = 45×2 + 0 So , HCF = 45 . I) 455 and 42 let a = 455 , b = 42 Apply Euclid's Algorithm till remainder becomes zero , the corresponding divisor will be the HCF 445 = 42 ×10 + 35 42 = 35 × 1 + 7 35 = 7×5 + 0 So , HCF = 7 . Fundamental theorem of Arithmetic: "Every Composite number can be expressed as a product of primes and this factorizaion is unique." Example : Let's take a composite number '12' It can be written as factorization of prime numbers. i.e. 12 = 2 ×2 ×3 and this factorization is unique. this is the fundamental the...

IIT JEE Examination In this article , you will get to know about the process of examination to get the admission in IIT(Indian Institute of Technology). Admission to various undergraduate programs across IITs is carried out through the Joint Entrance Examination (Advanced) [JEE (Advanced)]. At present, there are twenty three IITs across the country. Through JEE (Advanced), IITs offer admission into undergraduate courses leading to a Bachelors, Integrated Masters, Bachelor-Master Dual Degree in Engineering, Sciences, or Architecture. The Joint Entrance Examination (Advanced)[JEE (Advanced)] will be conducted by the seven Zonal Coordinating IITs under the guidance of the Joint Admission Board. Examination Pattern: The examination consists of two papers (Paper 1 and Paper 2) of three hours duration each. Note : i) Appearing in both the papers is compulsory ii) Candidate who wish to appear for JEE (Advanced) are required to write / have written the JEE (Main) of that year...

Physics General Dimensions and Units : General Units and dimensions Dimensional analysis Least count Significant figures Measurement: Methods of measurement Error analysis for physical quantities pertaining to the following experiments: Vernier calipers Screw gauge (micrometer) Determination of g using simple pendulum Young’s modulus - elasticity of the material Surface tension of water by capillary rise and effect of detergents Specific heat of a liquid using calorimeter Focal length of a concave mirror and a convex lens using u-v method Speed of sound using resonance column Verification of Ohm’s law using voltmeter and ammeter Specific resistance of the material of a wire using meter bridge and post office box Mechanics Kinematics Kinematics in one and two dimensions (Cartesian coordinates only), projectiles Uniform circular motion Relative velocity Newton’s laws of motion Inertial and uniformly accelerated frames of reference Static and dynamic friction; K...

Chemistry General Topics Concept of atoms and molecules; Dalton’s atomic theory; Mole concept; Chemical formulae; Balanced chemical equations; Calculations (based on mole concept and stoichiometry) involving common oxidation-reduction, neutralisation, and displacement reactions; Concentration in terms of mole fraction, molarity, molality and normality. States of Matter: Gases and Liquids Gas laws and ideal gas equation, absolute scale of temperature; Deviation from ideality, van der Waals equation; Kinetic theory of gases, average, root mean square and most probable velocities and their relation with temperature; Law of partial pressures; Diffusion of gases. Intermolecular interactions: types, distance dependence, and their effect on properties; Liquids: vapour pressure, surface tension, viscosity Atomic Structure Bohr model, spectrum of hydrogen atom; Wave-particle duality, de Broglie hypothesis; Uncertainty principle; Qualitative quantum mechanical picture of hydrogen atom:...

Mathematics Algebra Complex Number: Algebra of complex numbers, addition and multiplication of complex number conjugation of complex number polar representation properties of modulus and principal argument triangle inequality cube roots of unity geometric interpretations Quadratic equations : Quadratic equations with real coefficients relations between roots and coefficients formation of quadratic equations with given roots symmetric functions of roots Progression: Arithmetic, geometric and harmonic progressions (AP , GP , HP) Arithmetic, geometric and harmonic means(AM , GM ,HM) Sums of finite arithmetic and geometric progressions Infinite geometric series sums of squares and cubes of the first n natural numbers Logarithms and their properties Permutations and combinations Binomial theorem for a positive integral index, properties of binomial coefficients Matrices Matrices as a rectangular array of real numbers Equality of matrices Addition, multiplication by a...

For free study material for nda maths : NDA maths free study material NDA maths Free mock test paper NDA Examination pattern In this examinaton , there are two papers. Paper I is 'Mathematics' and Paper II is 'General Ability Test'. Each paper duration is 2.5 hours. But paper I is 300 marks and Paper II is 600 marks. Subject Duration Maximum Marks Mathematics (Paper I) 2.5 hr 300 General Ability Test (Paper II) 2.5 hr 600 Note : 1. The Papers in all the subjects will consist of objective type qustions only .It means all the questions will be multiple choice question 2. There is also a minimum qualifying marks for each paper. 3.The Question papers(test booklets) of mathematics and part “B” of general ability test wil be set BILINGUALLY in Hindi as well as english NDA Examination Syllabus Paper I (Mathematics) 1. Algebra a) SET ( Concept of set, operations on sets, Venn di...