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NEST Syllabus Maths 2018 | *NEST Maths Syllabus* 2018 | National Entrance Screening Test Syllabus Maths 2018 | NEST 2018 Syllabus Maths | *NEST 2018* Maths Syllabus | National Entrance Screening Test 2018 Syllabus Maths

**NEST Syllabus Maths Algebra**

Algebra of complex numbers, addition, multiplication, conjugation, polar representation,

properties of modulus and principal argument, triangle inequality, cube roots of unity,

**NEST Syllabus Maths geometric interpretations.**

Quadratic equations with real coefficients, relations between roots and coefficients,

formation of quadratic equations with given roots, symmetric functions of roots.

Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic

means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.

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NEST Syllabus Maths Integral calculus

**NEST Syllabus Maths Logarithms and their properties.**

Permutations and combinations, Binomial theorem for positive integral index, properties of

binomial coefficients. Matrices as a rectangular array of real numbers, equality of matrices,

addition, multiplication by a scalar and product of matrices, transpose of a matrix,

determinant of a square matrix of order up to three, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric

matrices and their properties, solutions of simultaneous linear equations in two or three variables.

Addition and multiplication rules of probability, conditional probability, Bayes Theorem,

independence of events, computation of probability of events using permutations and

**NEST Syllabus Maths Trigonometry**

Trigonometric functions, their periodicity and graphs, addition and subtraction formulae,

formulae involving multiple and sub-multiple angles, general solution of trigonometric

equations.

Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle, inverse trigonometric functions (principal value only).

**NEST Syllabus Maths Analytical geometry**

Two dimensions - Cartesian coordinates, distance between two points, section formulae, shift

of origin. Equation of a straight line in various forms, angle between two lines, distance of a

point from a line. Lines through the point of intersection of two given lines, equation of the

bisector of the angle between two lines, concurrency of lines. Centroid, orthocentre, incentre

and circumcentre of a triangle.

Equation of a circle in various forms, equations of tangent, normal and chord. Parametric

equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle

through the points of intersection of two circles and those of a circle and a straight line.

Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and

eccentricity, parametric equations, equations of tangent and normal. Locus Problems.

Three dimensions - Direction cosines and direction ratios, equation of a straight line in space, equation of a plane, distance of a point from a plane.

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**NEST Syllabus Maths Differential calculus**

Real valued functions of a real variable, into, onto and one-to-one functions, sum, difference,

product and quotient of two functions, composite functions, absolute value, polynomial,

rational, trigonometric, exponential and logarithmic functions.

Limit and continuity of a function, limit and continuity of the sum, difference, product and

quotient of two functions, L’Hospital rulefor evaluation of limits of functions.

Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions. Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial,

rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.

Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative, tangents and normals, increasing and decreasing functions, maximum and

minimum values of a function, Rolle’s Theorem and Lagrange’s Mean Value Theorem.

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NEST Syllabus Maths Integral calculus

Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their properties, Fundamental Theorem of Integral Calculus.

Integration by parts, integration by the methods of substitution and partial fractions,

application of definite integrals to the determination of areas involving simple curves.

Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations.

**NEST Syllabus Maths Vectors**

Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations.

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