MATHEMATICS (Gen./Subsidiary)
Total number of questions 17 .Answer any Eight questions selecting at least one from each groups. QNo. 1 will be objective and compuslory
GROUP-A
Ordinary Differential Equations
Degree and order of a differential equation, Equation of first order and first degree, Equations in which the variables are separable, Homogeneous equations, Linear equations and equations reducible to the linear form.
Exact differential equations, First order higher degree equation solvable for x, y. p, Clairaut's form and singular solutions. Orthogonal trajectories, Linear differential equations of second order with constant coefficients Complementary functions and particular Integrals 4 Qn.
GROUP-B
Analytical Geometry of two Dimensions:
Standard Equations of Parabola Ellipse and Hyperbola and their properties.1 Qn.
Reduction of the general equation of second degree into standard forms Equations of tangents and normals Analytical :
Geometry of three Dimension:
Direction Cosines, The plane, The straight, the shortest distance between two skew-straight lines, Sphere. 1 Qn1
Cone, Cylinder, Central conicoids (includmg Ellipsoid). Conjugate drameter, Paraboloids 1 Qn.
GROUP -C
Statics ;
Analytical condition of equilibrum of coplanar forces : 1 Qn.
Dynamics:
Velocities and acceleraton s along radial and trasverse directions, and along tangential, normal directions Simple harmonic motion, Elasitc Sting : 1Qn.
Motion on smooth and rough Plane, Motion in a resisting medium, Motion of praticle of varying mass : 1 Qn.
GROUP-D
Advanced Calculus
Continuity; sequential continuity. Properties of continuous Functions. Uniform continuity, Chain rule of differential ability: 1Qn
Mean value theorems and their geometrical inter pretations, Darboux's intermediate value theorem for derivaties, Taylor's theorem with various forms of remainders : 1 Qn.
Limit and continuity of functions of two variables, Partial differential, Change of variables, Euler's theorem on homogeneous functions : 1 Qn.
Talor's theorem for functions of two variables, Maxima, Minima and saddle points of functions of two variables, Lagrange's multiplier method: 1 Qn.
