Class 12 | Determinants | Lecture no.4B | JEE (Mains& Advanced) / Board exams

Application in solving system of Linear equations CRAMERS RULE

conceptual guidance in following topics (JEE mains & advanced).....
Sets representation Union intersection complement of sets their algebraic properties Powerset
Relation Types of relations equivalence relations one-one into onto functions the composition of functions
Complex numbers as ordered pairs of reals Representation of complex numbers & their representation in a plane Argand diagram Algebra of complex numbers modulus and argument (or amplitude) square root of a complex number Triangle inequality Quadratic equations in real & complex number system and their solutions The relation between roots and coefficients nature of roots the formation of quadratic equations with given roots
Algebra types of matrices matrices of order two and three Properties of determinants evaluation the area of triangles using determinants Adjoint and evaluation of inverse of a square matrix using determinants elementary transformations Test of consistency solution of simultaneous linear equations in two or three variables using determinants & matrices
The fundamental principle of counting Permutation as an arrangement and combination as selection
Binomial theorem for a positive integral index General term and middle term Properties of Binomial coefficients & simple applications
Arithmetic & Geometric progressions insertion of arithmetic Geometric means The relation between A.M. and G.M. Sum up to n terms of special series Arithmetico Geometric progression
Real-valued functions algebra of functions polynomials rational trigonometric logarithmic & exponential functions inverse functions Graphs of functions Limits continuity & differentiability
Differentiation of the sum difference product & quotient of two functions trigonometric inverse trigonometric logarithmic exponential composite & implicit functions Rolle’s & Lagrange’s Mean Value Theorems
Applications of derivatives monotonic increasing and decreasing functions Maxima minima tangents and normals
Integral as an antiderivative Fundamental integrals involving algebraic trigonometric exponential logarithmic functions Integration by substitution by parts by partial fractions Integration using trigonometric identities Integral as limit of a sum Evaluation of simple integrals
Fundamental Theorem of Calculus evaluation of definite integral determining areas of the regions bounded by simple curves in standard form
Ordinary differential equations, their order & degree Formation of differential equations method of separation of variables homogeneous & linear differential equations
Cartesian system of rectangular coordinates in a plane distance formula section formula locus & its equation translation of axes the slope of a line parallel & perpendicular lines intercepts of a line on the coordinate axes Various forms of equations of a line intersection of lines angles between two lines conditions for concurrence of three lines Distance of a point from a line equations of internal & external bisectors of angles between two lines coordinates of the centroid orthocentre & circumcentre of a triangle equation of the family of lines passing through the point of intersection of two lines Circles conic sections Standard form of equation of a circle general form of the equation of a circle its radius and centre equation of a circle when the endpoints of a diameter are given points of intersection of a line & a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent Sections of cones equations of conic sections (parabola ellipse and hyperbola) in standard forms condition for y = mx + c to be a tangent and point (s) of tangency
Coordinates of a point in space the distance between two points Section formula direction ratios & direction cosines the angle between two intersecting lines Skew lines the shortest distance between them & its equation Equations of a line & a plane in different forms the intersection of a line & a plane coplanar lines
Addition subtraction multiplication & division of vectors Vector’s Components in 2D & 3D space
Scalar products & vector products triple product Calculation of mean mode median variance standard deviation & mean deviation of ungrouped and grouped data Probability of events multiplication theorems addition theorems Bayer’s theorem Bernoulli trials Binomial & probability distribution
Identities of Trigonometry and Trigonometric equations Inverse trigonometric functions Heights and Distances

various ALL INDIA BOARD & STATE BOARDS exams preparation like CBSE / ISC / ICSE / DELHI / IB / SSC / HSC / HARYANA / UTTAR PRADESH / BIHAR / MAHARASHTRA / WEST BENGAL / PUNJAB / NIOS / ANDHRA PRADESH / ASSAM / CHHATISGARH / GOA / GUJARAT / HIMACHAL PRADESH / JAMMU & KASHMIR / JHARKHAND / KARNATAKA / KERALA / MADHYA PRADESH / MANIPUR / MEGHALAYA / MIZORAM / NAGALAND / ORISSA / RAJASTHAN / TAMIL NADU / TRIPURA boards