JEE SYLLABUS
Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.
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Monday, October 22, 2007
CH. 2. THEORY OF EQUATIONS
JEE SYLLABUS
Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.
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Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.
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STUDY GUIDE CH.3 PROGRESSIONS
JEE SYLLABUS
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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I started study of Mathematics(9 Jan 2008). The conceptual portion is very limited in TMH book. But the first problem in the examples itself is complicated. Every problem thereon is a complicated problem.
In Mathematics and Physics, the conceptual portion is going to be limited but the problems are going to be complicated. One has to sit down and do all the problems in examples and exercises to develop the sharp brain that can discover the structure in the problem given in the examination.
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.
------------------
I started study of Mathematics(9 Jan 2008). The conceptual portion is very limited in TMH book. But the first problem in the examples itself is complicated. Every problem thereon is a complicated problem.
In Mathematics and Physics, the conceptual portion is going to be limited but the problems are going to be complicated. One has to sit down and do all the problems in examples and exercises to develop the sharp brain that can discover the structure in the problem given in the examination.
STUDY GUIDE CH. 5 PERMUTATION AND COMBINATION
JEE SYLLABUS
Permutations and combinations,
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JEE Question 07
The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is
(A) 360 (B) 192 (C) 96 (D) 48
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JEE question
The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0, 0), (0, 21) and (21, 0), is
(A) 133 (B) 190
(C) 233 (D) 105
answer B
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Permutations and combinations,
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JEE Question 07
The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is
(A) 360 (B) 192 (C) 96 (D) 48
-------------------------------
JEE question
The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0, 0), (0, 21) and (21, 0), is
(A) 133 (B) 190
(C) 233 (D) 105
answer B
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CH. 6. BINOMIAL EQUATION
JEE SYLLABUS
Binomial theorem for a positive integral index, properties of binomial coefficients.
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Binomial theorem for a positive integral index, properties of binomial coefficients.
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Study Guide Ch. 7 MATRICES
JEE SYLLABUS
Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, 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.
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Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, 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.
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CH. 8 DETERMINANTS
JEE SYLLABUS
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.
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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.
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STUDY GUIDE CH. 10. PROBABILITY
JEE SYLLABUS
Addition and multiplication rules of probability, conditional probability, independence of events, computation of probability of events using permutations and combinations.
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Addition and multiplication rules of probability, conditional probability, independence of events, computation of probability of events using permutations and combinations.
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STUDY GUIDE CH.11 ELEMENTARY TRIGONOMETRY
JEE SYLLABUS
Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles,
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Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles,
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CH. 12. APPLICATION OF TRIGONOMETRY, TRIANGLES
JEE SYLLABUS
Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle,
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Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle,
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Study Guide Ch. 13. TRIGONOMETRIC EQUATIONS
JEE SYLLABUS
general solution of trigonometric equations.
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JEE Question
Let F(x) be an indefinite integral of sin^2 x.
Statement - 1
The function F(x) satisfies F(x +Pi) = F(x) for all real x.
Because
Statement - 2
sin^2 (x+ Pi) = sin^2 x for all real x.
(A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for statement – 1
(B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is Not a correct explanation for Statement – 1.
(C) Statement – 1 is True, Statement – 2 is False
(D) Statement – 1 is False, Statement – 2 is True
answer D
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JEE 2007 Paper I
The number of solutions of the pair of equations
2sin²θ - cos2θ = 0
2cos²θ - 3sinθ = 0
in the interval [0,2π] is
(A) zero
(B) one
(C) two
(D) four
Answer: C
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general solution of trigonometric equations.
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JEE Question
Let F(x) be an indefinite integral of sin^2 x.
Statement - 1
The function F(x) satisfies F(x +Pi) = F(x) for all real x.
Because
Statement - 2
sin^2 (x+ Pi) = sin^2 x for all real x.
(A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for statement – 1
(B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is Not a correct explanation for Statement – 1.
(C) Statement – 1 is True, Statement – 2 is False
(D) Statement – 1 is False, Statement – 2 is True
answer D
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JEE 2007 Paper I
The number of solutions of the pair of equations
2sin²θ - cos2θ = 0
2cos²θ - 3sinθ = 0
in the interval [0,2π] is
(A) zero
(B) one
(C) two
(D) four
Answer: C
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CH. 14 INVERSE OF TRIGONOMETRIC FUNCTIONS
JEE SYLLABUS
inverse trigonometric functions (principal value only).
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JEE 2007 Paper II
Let (x,y) be such that Sin‾¹(ax) + Cos‾¹(y)+Cos‾¹(bxy) = π/2
Match the statements in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.
Column I --------------------- Column II
(A) If a = 1 and b = 0,------(p) lies on the circle
then (x, y)----------------- x² + y² = 1
===================================================
(B) If a = 1 and b = 1, ----(q) lies on
then (x, y)----------------- ( x²-1)(y²-1) =0
===================================================
(C) If a = 1 and b = 2,-----(r) lies on y = x
then (x, y)
===================================================
(D) If a = 2 and b = 2,-----(s) lies on
then (x, y)------------------ (4x²-1)(y²-1) = 0 ===================================================
Solution
(A) : (p)
(B) : (q)
(C) : (p)
(D) : (s)
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inverse trigonometric functions (principal value only).
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JEE 2007 Paper II
Let (x,y) be such that Sin‾¹(ax) + Cos‾¹(y)+Cos‾¹(bxy) = π/2
Match the statements in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.
Column I --------------------- Column II
(A) If a = 1 and b = 0,------(p) lies on the circle
then (x, y)----------------- x² + y² = 1
===================================================
(B) If a = 1 and b = 1, ----(q) lies on
then (x, y)----------------- ( x²-1)(y²-1) =0
===================================================
(C) If a = 1 and b = 2,-----(r) lies on y = x
then (x, y)
===================================================
(D) If a = 2 and b = 2,-----(s) lies on
then (x, y)------------------ (4x²-1)(y²-1) = 0 ===================================================
Solution
(A) : (p)
(B) : (q)
(C) : (p)
(D) : (s)
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STUDY GUIDE TMH MATHEMATICS CH.15. CARTESIAN SYSTEM
JEE SYLLABUS
Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin.
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Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin.
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STUDY GUIDE CH.16. CIRCLES AND SYSTEMS OF CIRCLES
JEE syllabus
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.
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JEE Question
Tangents are drawn from the point (17, 7) to the circle x^2 + y^2 = 169.
Statement - 1
The tangents are mutually perpendicular.
Because
Statement - 2
The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x^2 + y^2 = 338.
(A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for statement – 1
(B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is Not a correct explanation for Statement – 1.
(C) Statement – 1 is True, Statement – 2 is False
(D) Statement – 1 is False, Statement – 2 is True
answer A
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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.
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JEE Question
Tangents are drawn from the point (17, 7) to the circle x^2 + y^2 = 169.
Statement - 1
The tangents are mutually perpendicular.
Because
Statement - 2
The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x^2 + y^2 = 338.
(A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for statement – 1
(B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is Not a correct explanation for Statement – 1.
(C) Statement – 1 is True, Statement – 2 is False
(D) Statement – 1 is False, Statement – 2 is True
answer A
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CH. 17. PAIR OF STRAIGHT LINES
JEE SYLLABUS
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.
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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.
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Study Guide TMH Mathematics Ch. 18. CONIC SECTIONS (PARABOLA, ELLIPSE, HYPERBOLA)
JEE SYLLABUS
Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal.
Locus Problems.
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Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal.
Locus Problems.
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Ch. 19. THREE DIMENSIONAL GEOMETRY
JEE Syllabus
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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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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Study Guide Ch.20 VECTOR ALGEBRA
JEE Syllabus
Vectors
Addition of vectors, scalar multiplication, scalar products, dot and cross products, scalar triple products and their geometrical interpretations.
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JEE Question 2007
If a, b, c be unit vectors such that a + b + c = 0. Which one of the following is correct?
(A) a × b = b × c = c × a = 0
(B) a × b = b × c = c × a is not equal to 0
(C) a × b = b × c = a × c is not equal to 0
(D) a × b, b × c, c × a are mutually perpendicular
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Vectors
Addition of vectors, scalar multiplication, scalar products, dot and cross products, scalar triple products and their geometrical interpretations.
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JEE Question 2007
If a, b, c be unit vectors such that a + b + c = 0. Which one of the following is correct?
(A) a × b = b × c = c × a = 0
(B) a × b = b × c = c × a is not equal to 0
(C) a × b = b × c = a × c is not equal to 0
(D) a × b, b × c, c × a are mutually perpendicular
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Study Guide TMH Mathematics Ch.21. FUNCTIONS
JEE syllabus
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.
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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.
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Ch.22. LIMITS AND CONTINUITY
JEE Syllabus
Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, l'Hospital rule of evaluation of limits of functions.
Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions.
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Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, l'Hospital rule of evaluation of limits of functions.
Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions.
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Study Guide Ch. 23. DIFFERENTIATION
JEE Syllabus
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.
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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.
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Ch. 24 APPLICATIONS OF DERIVATIVES
JEE Syllabus
Geometrical interpretation of the derivative, tangents and normals, increasing and decreasing functions, maximum and minimum values of a function, applications of Rolle's Theorem and Lagrange's Mean Value Theorem.
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Geometrical interpretation of the derivative, tangents and normals, increasing and decreasing functions, maximum and minimum values of a function, applications of Rolle's Theorem and Lagrange's Mean Value Theorem.
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Study Guide TMH JEE Mathematics Ch. 25 INDEFINITE INTEGRALS
JEE Syllabus
Integration as the inverse process of differentiation, indefinite integrals of standard functions,
Integration as the inverse process of differentiation, indefinite integrals of standard functions,
Study Guide Ch.26. DEFINITE INTEGRALS
JEE Syllabus
definite integrals and their properties, application of the 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.
-------------------
JEE question
If f″(x) = − f(x) and g(x) = f′(x) and F(x) = [f(x/2)]^2 + [g(x/2)]^2 and given that F(5) = 5 then F(10) is equal to
(A) 5
(B) 10
(C) 0
(D) 15
answer A
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definite integrals and their properties, application of the 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.
-------------------
JEE question
If f″(x) = − f(x) and g(x) = f′(x) and F(x) = [f(x/2)]^2 + [g(x/2)]^2 and given that F(5) = 5 then F(10) is equal to
(A) 5
(B) 10
(C) 0
(D) 15
answer A
-----------------
Study Guide TMH JEE Mathematics Ch. 27 DIFFERENTIAL EQUATIONS
JEE syllabus
Formation of ordinary differential equations, solution of homogeneous differential equations, variables separable method, linear first order differential equations.
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JEE question
The differential equation dy/dx = [SQRT(1-y^2)]/y
determines a family of circles with
(A) variable radii and a fixed centre at (0, 1)
(B) variable radii and a fixed centre at (0, –1)
(C) fixed radius 1 and variable centres along the x-axis
(D) fixed radius 1 and variable centres along the y-axis
answer C
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Formation of ordinary differential equations, solution of homogeneous differential equations, variables separable method, linear first order differential equations.
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JEE question
The differential equation dy/dx = [SQRT(1-y^2)]/y
determines a family of circles with
(A) variable radii and a fixed centre at (0, 1)
(B) variable radii and a fixed centre at (0, –1)
(C) fixed radius 1 and variable centres along the x-axis
(D) fixed radius 1 and variable centres along the y-axis
answer C
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