Can you provide me Syllabus of the mathematics for MBA Entrance IP University because i am going to take part in the entrance exam of IP University?

[prince karak]

Here i am giving you syllabus of the mathematics for MBA Entrance IP University as below:-

Mathematics - Syllabus for PUC-I/XI Std. or equiv.

ALGEBRA
1. THEORY OF INDICES AND LOGARITHMS
• Recapitulation of theory of Indices - problems
• Laws of logarithms (with proof) - problems

2. PROGRESSIONS
• Recapitulation of sequences of real numbers, finite and infinite sequences as mappings.
• Definition of infinite series, A.P., G.P., H.P,. nth term of an AP, GP, HP, sum to n terms of
an AP, GP (with proof) - problems
• Sum to infinity of a G.P. when the common ratio r is such that -1 < r < 1. Recurring decimal
numbers - problems.
• A.M., G.M., H.M. of two numbers a and b. Proofs of G2 = AH and A P G P H , where A, G H are the
A.M., G.M., and H.M. respectively of any two numbers a and b. To insert n arithmetic means, n
geometric means and n harmonic means between any two given numbers - problems

3. MATHEMATICAL INDUCTION
• Principle of mathematical induction. Problems on induction including Sn, Sn2, Sn3

4. THEORY OF EQUATIONS
• Recapitulation of quadratic equations and the formula for the roots of a quadratic equation.
• The equation x2 + 1 = 0 and introducing complex numbers, square roots, cube roots and fourth
roots of unity.
• The relations between the roots and coefficients of a quadratic equation, a cubic equation and
a biquadratic - equation. Solutions of quadratic, cubic and biquadratic equations given certain
conditions and given that the roots are in A.P., G.P., H.P. - problems.
• Symmetric functions of the roots of quadratic, cubic and biquadratic equations - problems.
• Proofs of (i) irrational roots of a polynomial equation occur in conjugate pairs, (ii) complex
roots of a polynomial equation occur in conjugate pairs - Problems of solving equations given an
irrational root and given a complex root - problems.
• Solution of a standard cubic equation X3 + 3HX + G = 0 by Cardan's method only - problems.

5. PERMUTATIONS AND COMBINATIONS
• Definition of linear permutation, derivation of the formula for nPr from first principles.
Formula for the number of permutations when some things are alike of one kind, etc. - problems
• Circular permutation - formula - problems.
• Definition of combination, derivation of the formula for nCr, from first principles. Proofs of
nCr = nCn-r and
nCr-1 + nCr = n+1Cr - problems
6. BINOMIAL THEOREM
• Statement and proof of Binomial theorem for a positive integral index by induction. To find the
middle terms, terms independent of x and term containing a definite power of x - problems.
• Binomial coefficients - problems.

7. PARTIAL FRACTIONS
• Rational fractions, proper and improper fractions, reduction of an improper fraction into a sum
of a polynomial and a proper fraction - problems
• Rules for resolving a proper fraction into partial fractions. - problems

8. ELEMENTS OF NUMBER THEORY AND CONGRUENCES
• Divisibility - Definition and properties of divisibility, statement of Division Algorithm.
• Greatest Common Divisor (G.C.D.) of any two integers, using Euclid,s Algorithm., to find the
G.C.D. of any two integers. To express the G.C.D. of two integers a and b as ax + by for integers
x and y - problems
• Relatively prime numbers, prime numbers and composite numbers, the number of positive divisors
of a number and sum of all positive divisors of a number - statements of the formulae without
proof - problems.
• Proofs of the following properties
(1) The smallest divisor > 1 of an integer > 1 is a prime number.
(2) There are infinity of primes.
(3) If c and a are relatively prime and c|ab then c|b
(4) If p is prime and p|ab then p/a or p|b
(5) If there exist integers x and y such that ax + by = 1 then (a,b) = 1
(6) If (a,b) = 1, (a,c) = 1 then (a, bc) = 1
(7) If p is prime and a is any integer then either (p,a) = 1 or p | a
(8) The smallest positive divisor of a composite number "a" does not axceed a
• Congruence modulo m - Definition, Proofs of the following properties
(1) "Lmode m" is an equivalence relation
(2) a L b (mod m) => a ExLbEx (mod m) and ax L bx (mod m)
(3) If c is relatively prime to m and ca Lcb (mod m) then a L b (mod m) - cancellation law
(4) If a L b (mod m) and n is a positive divisor of m then a L b (mod n)
(5) a L b (mod m) => a and b leave the same remainder when divided by m
• Conditions for the existence of the solution of linear congruence ax L b (mod m) (statements
only). to find the solution of ax L b (mod m) - problems
ANALYTICAL GEOMETRY AND CALCULUS
9. COORDINATE GEOMETRY
• Coordinate system in a plane (cartesian)
• Distance formula, section formula, mid-point formula, centroid of a triangle, area of a
triangle - Derivations, problems
• Locus of a point, problems
• Straight lines, slope of a line m = tanq where q is the angle made by the line with the
positive x-axis, slope of the line joining any two points, general equation of a line. Derivation
and problems
• Conditions for parallelism and perpendicularity of two lines - problems
• Various forms of the equation of a straight line : slope - point form, slope - intercept form ,
two point form, intercept form, Normal form - Derivations - problems
• Angle between two lines, point of intersection of two lines, condition for concurrency of three
lines, Length of the perpendicular from the origin and from a point to a line, Equation of the
inernal and external bisector of the angle between two lines - Derivations, problems
• Pair of lines - Homogeneous equation of second degree, general equation of second degree,
derivations of (1) condition for pair of lines, (2) condition for a pair of parallel lines,
perpendicular lines and distance between the pair of parallel lines, (3) condition for a pair of
coincident lines (4) angle and point of intersections of a pair of lines - problems.

10. CALCULUS
• Functions of a real variable, types of functions, periodic functions, functional value -
problems.
• Limit of a function - definition, statements of the algebra of limits - problems
• Standard limits (with proofs)
(1) lim x -> a, x^n - a^n
x - a =n a^(n-1) when n is rational


(2) lim q -> 0, sin q = 1 when q is radians
q

(3) lim q -> 0, (tan q)/q= 1 when q is radians


(4) Statements of the limits
(i) lim n->infinty (1+ 1/n)^n = e
(ii) lim x->0 (1 + x)^ 1/x = e
(iii) lim x->0 loge (1 + x) /x = 1
(iv) lim x->0 e^x - 1 / x = 1
(v) lim x->0 a^x - 1 / x = loge a
Problems on these limits
Evaluation of limits if
lim x -> 0 f (x) / g (x) OR 0/0 form

lim n -> h f (n) / g (n) OR infinity/infinity form
where degree of f(n) O degree g (n) problems

TRIGONOMETRY
11. MEASUREMENT OF ANGLES AND TRIGONOMETRIC FUNCTIONS
• Radian measure - Definition. Proofs of
(i) p radians = 1800
(ii) 1 radian is constant
(iii ) s = rq where q is in radians
(iv) Area of the sector of a circle given by A=1/2 r2q where q is in radians - problems
• Trigonometric functions - definitions.
• Trigonometric ratios of an acute angle.
• Trigonometric identities (with proofs), problems
• Trigonometric functions of standard angles, problems.
• Trigonometric functions of allied angles, compound angles, multiple angles, submultiple angles
and Transformation formulae (with proofs) - problems.
• Heights and distances - Angle of elevation, angle of depression, problems.
• Graphs of Trigonometric functions

12. RELATIONS BETWEEN SIDES AND ANGLES OF A TRIANGLE
• Sine rule, Cosine rule, Tangent rule, Half-angle formulae, area of a triangle, projection rule
(with proofs) - problems.
• Solution of triangles given
(i) three sides
(ii) two sides and the included angle
(iii) two angles and a side
(iv) two sides and the angle opposite to one of these sides . Problems.