Differential Equations : Formulation and solution of differential equations of the forms.
1) dy / dx = ƒ(x).g(y)
2) dy / dx = ƒ(y/x)
3) dy / dx = (ax+by) / (cx+dy)
4) dy / dx = (a1x+b1y+c1 ) / (a2x+b2y+c2 ), (a1/a2 = b1/b2)
5) dy / dx + p(x)y = Q(x)
6) d²y / dx² + p1dy/dx + p2y = 0 with p1 and p2 constants.
7) d²y/dx² = ƒ(x)
Permutation and combination : Permutation of n different things taken r at a time (r≤n). Permutation of n things not all different. Permutation with repetitions (circular permutation excluded).
Quadratic Equations : Quadratic equations with real coefficients; Relations between roots and coefficients; Nature of roots; Formation of a quadratic equation, sign and magnitude of the quadratic expression ax2+bx+c (a,b,c are rational numbers and a≠0).
Complex Numbers: Definition and properties of complex numbers; Complex conjugate; Triangle inequality; Square root of complex numbers; Cube roots of unity; D’Moivre’s theorem (statement only) and its elementary applications.
Logarithms :Definition; General properties; Change of base.
SYLLABUS FOR WEST BENGAL JOINT ENTRANCE EXAMINATION MATHEMATICS
ALGEBRA
