বীজগণিত (Algebra)

বীজগণিত (Algebra)

Surds and Indices :   Fundamental laws of Surds and Indices, simple applications.

Arithmetic Progression : (A.P.):    Definition of A.P., Common difference, General term, Summation of first n terms. Sum of first n-natural numbers, A.M.

Geometric Progression : (G. P.):  Definition of G.P., Common ratio, General term, Summation of first n-terms, G.M.

Logarithms :  Definition, General properties of logarithms.

Complex numbers : Complex numbers in the form a + ib, Real and imaginary parts of a complex number, Geometrical representation of complex numbers, Complex Conjugate, Modulus and Argument of a complex number, Algebra of complex numbers, (fundamental operations). Triangle inequality | $\left| {{Z_1} + {Z_2}} \right| \le \left| {{Z_1} + {Z_2}} \right|$  and also $\left| {{Z_1}{Z_2}} \right| = \left| {{Z_1}} \right|\left| {{Z_2}} \right|$ . Cube roots of unity and their properties.

Theory of Quadratic Equations :   Quadratic equations with real coefficients. Fundamental theorem of Algebra (Statement only). Roots, relations between roots and coefficients of a quadratic equation, Nature of roots, formation of quadratic equation, common root  ax2 + bx + c.  (a, b, c are rational numbers).

Permutation and Combination : Defination of Permutation. Permutation of n different things taken $r( \le n)$ at a time; Permutation of n things, not all different; Permutation with repetitions (circular permutation excluded).

  Definition of Combination; Combination of n different things taken r at a time; Combination of n things when things are not all different; Basic properties.