MATHEMATICS
చెన్నై:సుప్రీంకోర్టు ఉత్తర్వులు బేఖాతర్..మధురైలో జోరుగా జల్లికట్టు|తెలుగు రాష్ట్రాల్లో భోగి సంబరాలు|విజయవాడ: ఏ కన్వెన్షన్ సెంటర్లో సంక్రాంతి సంబరాలు|విజయవాడ: దుర్గమ్మను దర్శించుకున్న హీరో బాలకృష్ణ, హీరోయిన్ శ్రియ, దర్శకుడు క్రిష్|గోదావరి జిల్లాలో జోరుగా కోడిపందాలు|సంప్రదాయ కోడిపందాలనే నిర్వహిస్తున్నాం- రఘురామకృష్ణంరాజు|కృష్ణా జిల్లా కొమరవోలులో హీరో బాలకృష్ణ సంక్రాంతి సంబరాలు|రంగారెడ్డి: పెద్దఅంబర్పేట్ ఔటర్ రింగ్రోడ్డు దగ్గర ఆర్టీఏ తనిఖీలు|వరంగల్ అర్బన్: ఐనవోలులో వైభవంగా మల్లన్న జాతర|జమ్మూకశ్మీర్: శ్రీనగర్లో రెండు బ్యాంకుల్లో అగ్నిప్రమాదం
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MATHEMATICS
1. Determinants and Matrices
(i) Determinants - Order.
I.1Minors - Cofactors
I.2.Expansion.
I.3.Properties of determinants
I.4.Simple problems using properties of determinants
(ii) Matrices - Cramer's Rule
2. Boolean Algebra
2.1.Boolean algebra as an algebraic structure, principle of duality, Boolean function. Switching circuits, application of Boolean algebra to switching circuits.
3. Conics
3.0.As a section of a cone. Definition of Foci, Directrix, Latus Rectum. PS = ePL where P is a point on the conics, S is the focus, PL is the perpendicular distance of the point from the directrix.
3.0.As a section of a cone. Definition of Foci, Directrix, Latus Rectum. PS = ePL where P is a point on the conics, S is the focus, PL is the perpendicular distance of the point from the directrix.
3.0.As a section of a cone. Definition of Foci, Directrix, Latus Rectum. PS = ePL where P is a point on the conics, S is the focus, PL is the perpendicular distance of the point from the directrix.
3.0.As a section of a cone. Definition of Foci, Directrix, Latus Rectum. PS = ePL where P is a point on the conics, S is the focus, PL is the perpendicular distance of the point from the directrix.
(i) Parabola
(ii) Ellipse
(iii) Hyperbola
4. Inverse Trigonometric Function
4.1. Inverse Trigonometric Function
5. Calculus
(i) Differential Calculus
(i) Differential Calculus
(ii) Integral Calculus
6. Correlation and Regression
6.1.Definition and meaning of correlation and regression coefficient.
6.2.Coefficient of Correlation by Karl Pearson.
6.3.Rank correlation by Spearman’s (Correction included).
Lines of regression of x on y and y on x.
7. Probability
7.1.Random experiments and their outcomes.
7.2.Events: sure events, impossible events, mutually exclusive events, independent events and dependent events.
7.2.Events: sure events, impossible events, mutually exclusive events, independent events and dependent events.
Definition of probability of an event.
Laws of probability: addition and multiplication laws, conditional probability (excluding Baye’s theorem).
Laws of probability: addition and multiplication laws, conditional probability (excluding Baye’s theorem).
8. Complex Numbers
8.1.Argument and conjugate of complex numbers.
8.1.Argument and conjugate of complex numbers.
8.2.Sum, difference, product and quotient of two complex numbers
8.3.Additive and multiplicative inverse of a complex number.
8.4Simple locus question on complex number;
8.5.Triangle inequality.
8.6.Square root of a complex number.
8.7.Demoivre’s theorem and its simple applications.
8.8.Cube roots of unity: 1,?,?2 ; application problems.
9. Differential Equations
9.1.Differential equations, order and degree.
9.2.Solution of differential equations.
9.3.Variable separable.
9.4.Homogeneous equations and equations reducible to homogeneous form.
9.5.Linear form
10. Vectors
10.1.Scalar (dot) product of vectors.
10.2.Cross product - its properties - area of a triangle, collinear vectors.
10.3.Scalar triple product - volume of a parallelopiped, co-planarity.
10.3.Scalar triple product - volume of a parallelopiped, co-planarity.
10.3.Scalar triple product - volume of a parallelopiped, co-planarity.
10.4.Proof of Formulae (Using Vectors) - Sine rule.
10.4.1.Cosine rule
10.4.2.Projection formula
10.4.3.Area of a ? = ½ ab sin C
11. Co-ordinate Geometry in 3-Dimensions
(i) Lines - Cartesian and vector equations of a line through one and two points.
I.1.Coplanar and skew lines.
I.1.Coplanar and skew lines.
I.2.Conditions for intersection of two lines.
I.3.Shortest distance between two lines.
(ii) Planes - Cartesian and vector equation of a plane.
(ii) Planes - Cartesian and vector equation of a plane.
II.1.Direction ratios of the normal to the plane.
II.2.One point form.
II.3.Normal form.
II.4.Intercept form.
II.5.Distance of a point from a plane.
II.6.Angle between two planes, a line and a plane.
II.7.Equation of a plane through the intersection of two planes
12. Probability
12.1.Baye’s theorem;
12.2.theoretical probability distribution,
12.3.probability distribution function;
12.4.binomial distribution - its mean and variance.
13. Discount
13.1.True discount;
13.1.True discount;
13.2.banker's discount;
13.3.discounted value;
13.4.present value;
13.5.Cash Discount
13.6. Bill of Exchange
14. Annuities
14.1. Meaning
14.1. Meaning
14.2.formulae for present value and amount;
14.3.deferred annuity
14.4.applied problems on loans
14.5.sinking funds
14.6.scholarships. NOTE: Annuity due is required to be covered.
15. Linear Programming
15.1.Introduction
15.2.definition of related terminology such as constraints
15.3.objective function
15.4.optimization
15.5.iso profit
15.6.iso cost lines
15.7. advantages of linear programming; limitations of linear programming;
15.8.application areas of linear programming
15.9.different types of linear programming (L.P.)
15.10.problems, mathematical formulation of L.P problems
15.11.graphical method of solution for problems in two variables
15.12.feasible and infeasible regions, feasible and infeasible solutions
15.12.feasible and infeasible regions, feasible and infeasible solutions
15.13.optimum feasible solution.
16. Application of derivatives in Commerce and Economics
16.1.Cost function
16.2.average cost
16.3.marginal cost
16.4.revenue function and break even point.
17. Index numbers and moving averages
17.1.Price index or price relative.
17.2.Simple aggregate method.
17.3.Weighted aggregate method.
17.4. Simple average of price relatives - Weighted average of price relatives (cost of living index, consumer price index).