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# Science

## Mathematics ### History of Department

History: The Deparment of mathematics as part of the Inter Arts Course started along with the inception of Jai Hind college in the year 1948-1949.Prof. Balwani who was a founder member and Vice Principal was the first HOD.

Mathematics at the TY level was revived  in the year 1996. Some of the highlights since 1996 are:  ### Faculty

Mathematics Department Jr College

Staff

 Name of Teacher Designation Qualifications Area of specialization Ms. Manjiri V. Sane HOD M.Sc., M.Phil, DHE Mr Ajay Kumar Panigrahy Lecturer M.Sc. B.Ed. Ms. Jasmina Desai Lecturer M.Sc. B.Ed Ms. Soniya Kanherikar Lecturer M.Sc. B.Ed Ms. Radhika T Lecturer M.Sc. B.Ed Mr Shaikh Mohd.Shakir Lecturer M.Sc. B.Ed Mr Oza Praful Dilip Lecturer M.Sc. B.Ed Mr Sakpal Surendra Krishna Lecturer M.Sc. B.Ed  ### Syllabus

XI  Science

Paper – I

1. Trigonometric [ Angle & its measurement , Identities , Compound & multiple angle , Factorization formulae , Properties of triangle , Inverse trigonometric function  ]

2. Plane Co-ordinate Geometry [ Locus & shift of origin , Straight line – equation of line , Angle between two lines , perpendicular distance & family of lines ]

3. Vectors [ Introduction & definition of vectors , Algebra of vectors & product of vectors ]

4. Solution pf Linear Equation of One & Two Variable

5. Determinant [ Determinant of order 3 (expansion & properties) , Application ]

6. Matrices [ Definition & types of matrices , Algebra of matrices ]

7. Statistics  [Measures of dispersion , Bivariate frequency distribution ]

Paper – II

1. Sets , Relations & Functions [Review , Power set , Cartesian production , Relations ,   Functions ]

2. Logarithms [ Laws of logarithm with proof , Change of base , Numerical problems ]

3. Complex numbers  [(a + i b)  form , algebra of complex nos. , square root of Complex nos. , Argand diagram ]

4. Quadratic Equations [ Nature of roots , sum & product of roots , formation of   quadratic equation , Symmetric function of roots & cube root of unity ]

5. Sequences & Series [ G.P , H.P , A.M , G.M & H.M , Series ]

6. Permutation & Combination [Factorial notation , Fundamental principle of counting , Permutation & Combination ]

7. Mathematical Induction & Bionomial Theorem [Principle Mathematical Induction & its application Binomial Theorem for n N & for any index ]

8. Limits [Algebraic  limits & trigo. Limits ]

9. Derivatives [Definition of derivatives , Derivatives of sum , difference , multiplication & Quotient ]

10. Integration [Definition of integration , Rules of integration

a. b. =  c. d. If then, , a ≠ 0.  ]

XII  Science

Paper – I

1. Mathematical Logic [Statement & logical connectives , Statement pattern & logical equivalence ,   & Application of logic ]

2. Matrices [Inverse of a matrix , Solution of linear equations ]

3. Vectors [Collinearity & co-planarity of vectors , section formula , Scalar triple        product , Application of vectors ]

4. Three Dimensional Geometry [ Direction cosines & ratios , Line  & Plane ]

5. Linear Programming Problems [Linear programming problem , Simplex method ]

6. Probability [Types of events , Addition theorem , Conditional probability & Probability distribution of a random variable]

7. Pair of Straight Lines [Pair of lines passing through origin , Pair of lines not passing through origin]

8. Circle [Definitions , tangent & normal ]

9. Conics [Equation of conics , Tangents & Normals ]

Paper – II

1. Limits & Continuty [Standard limits, Infinite limits , Continuity of a function at a point, Algebra of continuous function , continuity on interval ]

2. Differentiation [Derivative of first principle , relation between continuity & differentiability , composite function , inverse function , log function Implicit function , parametric function , second order derivative]

3. Application Derivatives [Geometric applications , rate of change , rate measure , approximation &   Maxima & minima]

4. Integration [Infinite integrals , Definite integral]

5. Application of Definite Integration [Area & Volume ]

6. Differential Equation [Formation of differential equation , solution of first & first degree differential equations , Application of differential equation ]

7. Numerical Methods [Finite differences , Interpolation , Numerical integration ]

8. Boolean Algebra [Boolean algebra as an algebraic structure algebra , Principle of duality , Boolean function & Switching circuits & Application of Boolean algebra to switching circuits]

XI Commerce

Paper 1

(1) Sets , Relations & Functions [ Revision of sets, subset, Union, intersection, Compliment of set Definition of power set, ordered pair, Cartesian product of two sets , Relation & Functions, Domain, Co-domain , Range,  Types  of  Functions, Composite Function, Inverse function. Graphs of  sin x, cos x, tan x, | x |, ex ,e-x , log x ]

(2) Logarithms [ Laws of logarithm with proof , Change of base ,  Numerical problems ]

(3) Complex Numbers  [ Introduction , Definition, Real and Imaginary parts, Modulus of complex  Number. Complex conjugate of complex number. Algebra of complex numbers.]

(4) Quadratic Equations [ Nature of roots , Sum and Product of roots , Formation of Quadratic Equations,  Symmetric functions of roots. Cube roots Unity ]

(5) Trigonometric [ Angle & its measurement , Identities , Compound & multiple angle ,   Factorization formulae , Inverse trigonometric function  ]

(6)  Determinant [ Determinant of order 3 (expansion & properties) ,  Application ]

(7)  Plane Co-ordinate Geometry [ Locus & shift of origin , Straight line – equation of line , Angle between two lines , perpendicular distance ]

Paper II

(1) Partition Values [ Quartiles, Deciles, and Percentiles for ungrouped and grouped  data. ]

(2) Measures of Dispersion [ Range, Mean Deviation about Mean, Median Mode, Quartile  Deviation, Standard Deviation, Variance ]

(3) Moments [Moments about ‘A’ raw moments and central moments. Relation between raw moments and central moments. Relation between  moments about ‘A’ and central moments Sheppard’s correction for central moments.]

(4) Skewness & Kurtosis [ Introduction of skewness, positive, negative skewness, Karl Pearson’s Pearsonian, Bow1ey’s oefficient of skewness. Introduction of kurtosis, types of kurtosis and coefficient of kurtosis.]

(5) Bivarite  Frequency Distribution  &  Correlation [ Tabulation of Bivariate data, frequency distribution, conditional and marginal frequencies and correlation ,Scatter Diagram, Covariance, Karl Pearson’s correlation coefficient , Spearman’s Rank correlation ]

(6) Permutation & combination [Factorial notation , Fundamental principle of counting , Permutation & Combination ]

(7) Probability [Types of events , Addition theorem , Conditional probability ]

(8) Random Variable & Probability Distribution [Probability Distribution , expected value and variance of random variable. Probability Distribution of random variable:Probability; mass function, probability density function; Cumulative distribution]

(9) Commercial Arithmetic [Commission Brokerage, Discount, Present worth, Sum Due, Discount, Insurance,  Meaning, Premium, claim, loss, Policy value, Property value.]

XII Commerce

Paper 1

(1)Mathematical Logic [Statement & logical connectives , Statement pattern & logical equivalence , & Venn – diagram ]

(2) Matrices [Algebra of matrices , Inverse of a matrix , Solution of linear equations ]

(3) Limits & Continuty [Standard limits, Infinite limits , Continuity of a function at a point, Algebra of continuous function , continuity on interval ]

(4) Differentiation [Derivative of first principle , composite function , inverse function , log function Implicit function , parametric function , second order derivative]

(5) Application Derivatives [approximation , error , increasing & decreasing function ,  Maxima & minima]

(6)Integration [Infinite integrals , Definite integral]

(7) Differential Equation [Formation of differential equation , solution of first & first degree differential equations , Application of differential equation ]

Paper 1I

(1) Theory of Attributes  [ Dichotomy, order of classes and class frequencies, Relation between class frequencies, Conditions for consistency of data, Independence of Attributes & Association of Attributes ]

(2) Regression Equation [Definition, meaning and types of regression , Method of least squares, lines of regression

(3) Numerical Methods [Finite differences , Interpolation , Numerical integration ]

(4) Probability Distribution [ Binomial distribution & Poisson distribution ]

(5) Linear Programming Problems [Linear programming problem , graphical method ]

(6)Assignment Problem & Sequencing

(7) Vital Statistics [ Measurement of mortality & life table ]

(8) Index Numbers [ Types & construction of index numbers & cost of living index numbers ] 