Vec<strong>to</strong>r spaces, Linear independence basesDimensions of a finitely generated space.Lineartransformation. Matrices and theiroperations. Row & column reduction Echelonform, Rank and nullity of a linear transfoamation.System of linear equations.2. Differential Calculus - Convergenceof sequences and series; Limit and continuity offunctions. Differentiability, Mean Value theorem.Taylor's theorem. Expansion in Taylor's andMaclauries Series, Maxima and Minima,successive differentiation. Leibnitz's theorem.Functions. of several variables Partial derivatives,transformation. Eular's theorem.jacobian.3. Integral Calculus - Integration ofrational , irrational and transcendental functions.Definite integrals; Double and tripe integrals, Betaand Gamma functions.4. Differential Equations - Ordinarydifferential equations of first and higher degreeHomogeneous equations of first degree Integratingfac<strong>to</strong>rs; Linear differential equations with constantco-efficients. Complimentary functions andperticular integrais, Linear differential equationswith variable co-efficients.5. Vec<strong>to</strong>r Analysis - Algebra of vec<strong>to</strong>rs ,Double and triple products (Scalar and Vec<strong>to</strong>rs ), Differentiation of vec<strong>to</strong>rs, Directional direvativesGradient divergence and curl and their elementaryproperties. Integratioin of vec<strong>to</strong>r functions alongcurves.6. Statistics - Statistical population andrandom sample Collection, and presentation ofdata measures of loca<strong>to</strong>n dispersion Momentsand shepard's corrections, cummulants. Measuresof skewness and kur<strong>to</strong>sis.PAPER - II1. Analytical Geometry- Directioncosines, plane and straight line, sphere cone andcylinder. Tangent planes and normal lines.2. Advanced Calculus -Tangents andNormals. Asymp<strong>to</strong>tes Curvature and Tracing ofconics. Determination of areas, lengths surfacesand volumes (Cartesian and polar curves)3. Real Analysis - Least upper bound andgreatest lower bounds of sets; limit point of a set. Bolzanoweirstrass theorem. open and closedsets and their porperties, Metric spaces. Cauchysequences and complete metric spares . Compactsets and Heine-Borel theorem.4. Boolean Algebra - Difinition andproperties. Demorgan's Laws. Switching circuits.Boolean fuctions conjunctive and disjunctiveforms.5. Mechanics - Equilibrium of three forces,friction. New<strong>to</strong>n's second law of motion, impulsiveforce. kinetic energy of particles angular velocity,tragential and normal velocity and acclerationprojectiles on horizontal and inclined planesCollis<strong>to</strong>n of elastic bodies, Direct and boliqueimpacts.(20)6. Partial Differential Equations - Partialdifferential equations of first order, Standardsforms, Linear partial differential equations of higherdegree with constant co-efficients. Laplace,diffusion and vibration equation. Simple cases ofsolutions of these equations as boundary valueproblems.14-;kaf=dh bathfu;jhbathfu;jh fo"k;ksa ds iz'ui= dsoy vaxzsthesa gksaxs- vr,o ikB~;Øe dsoy vaxzsth esa gh eqfnzrgS A¼ifjf'k"V ,d iSjk 4 ¼?k½ ns[ksa½14.MECHANICALENGINEERINGPAPER - I1. Statics and Dynamics :Analysis of framed structures, method ofsections. Simple harmonic motions, simple andcompound pendulum, work, energy , power,Gyroscopic motion.2. Theory of Machines :Higher and lower pairs, inversions, steeringmechanisms, Hooks joint, velocity andacceleration of links inertia-forces, Cams,Conjugate action of gearing and interference , geartrains , epicyclic gears, Belt drives, brakes ,dynamometers, Fly wheels, Governors Balancingof rotating and reciprocating masses. Free forcedand damped vibratiions for a single degree offreedom. critical speed and whirling of shafts.3. Mechanics of solids:Stess and strain in two dimensions, Mohr'scircle. Theories of failure . Deflection of beams,Buckling of columns. Combined bending and<strong>to</strong>rsion. Castigliano's theorem, Thin cylinders,closed coil helical springs, leaf springs.4. Manufacturing Science : Taylor'sequation. Machinability Unconventional machiningmethods including EDM, ECM and ultrasonicmachining . Use of laser and plasmas. Surfaceroughness, gauging compara<strong>to</strong>rs, jigs and Fixtures.5. Production Management :Work simplification, work sampling. Valueengineering . Line balancing , ABC analysis.Economic order quantity including finite porductionrate Graphical and simplex methods for linearprogramming , transporation model, elementaryqueuing theory Quality control and its usesinproduct designs Use of X, R,σ, p and C charts.PAPER - II1. TheromodyamicsApplications of the first and second laws ofthermodynamics. Detailed analysis of thermodynamic cycles & their limitations.2. Fluid MechanicsContinuity momentum and energyequations, Velocity distribution in laminar andturbulent flow. Dimensional analysis. Boundarylayer on a flat plate; Adiabatic and insentropic flow,Mach number.3. Heat transfer :Critical thickness of insulation . Conductionin the presence of heat source. Heat transfer <strong>from</strong>fins. Momentum and energy equations forboundary layer on a flat plate. Dimentionlessnumbers. Free and forced convection . Boilingand condensation. Nature of radiant heat, Stafan-Boltzmann law, Configuration. fac<strong>to</strong>r, Logarithmicmean temperature difference Heat exchangereffectiveness.4. Energy ConversionCombustion phenomenon in C.I. and S.I.engines, Carburation and a<strong>to</strong>misation.Classification of of hydraulic turbines, specificspeed, Impulses and Reaction turbines, velocitytringles, diagram efficiency, open and closed cycle, Gas turbine plants, Nuclear power and MHDsystems, Solar' thermal systems.5. Environmental ControlVapour, Compression, absorption and airrefrigeration systems. Properties andcharacteristics of important refrigerants . Use ofPsychromatric chart and comfort chart. Estimationof cooling and heating loads. Calculation of supplyair, state and rate. Summer & winter, Air-Conditioning plants . layout.15-n'kZu'kkL=iz'u i= izFkerRoehekalk ,oa KkuehekalkmEehnokjksa ls Kku ehekalk ,oa rRoehekalkds fuEufyf[kr ik'pkR; rFkk Hkkjrh; fl)kUrksals voxr gksus dh vk'kk dh tk,xh &¼v½ ik'pkR; &vuqHkookn] cqf)okn] ijh{kkokn]HkkSfrdokn] izR;;okn] oLrqokn] vFkZfØ;kokn]rkfdZd Hkkookn ,oa vfLrRookn¼vk½ Hkkjrh;] izek ,oa izek.k] lR; ,oa Hkze dsfl)kUr] lŸkk ds fl)kUr] Hkkjrh; n'kZu dsizeq[k laiznk;ksa ¼vkfLrd ,oa ukfLrd½ ds fo'ks"klanHkZ esaØe'k%
iz'u i= f}rh;lkekftd jktuSfrd n'kZu ,oa/keZn'kZu1- n'kZu'kkL= dk Lo:i] thou] foKku ,oalaLd`fr ls mldk laca/k2- ¼d½ fuEufyf[kr okn % iztkra=] lek<strong>to</strong>kn]Qklhokn] lkE;okn ,oa loksZn;¼[k½ jktuSfrd dk;Zokgh dh iz.kkfy;ka ,oamuds igyw] lafo/kkuokn] Økafr] vkradokn,oa lR;kxzg3- ijaijk] ifjorZu ,oa vk/kqfudrk ¼Hkkjrh;lkekftd O;oLFkk ds fo'ks"k lanHkZ esa½4- ¼d½ /keZn'kZu dk Lo:i ,oa {ks=¼[k½ bZ'oj dk Lo:i ,oa mlds vfLrRo dsizek.k¼x½ /kkfeZd vuqHko dk Lo:i rdZ fnO;vuqHkwfr ,oa jgL;okn5- ¼d½ v'kqHk ,oa iki dh leL;k¼[k½ ca/ku vkSj eks{k izkfIr ds ekxZ¼x½ /keksZa dh ,drk ,oa fo'o O;kidrk]/kkfeZd lfg".kqrk ,oa /keZfujis{krk15.PHILOSOPHYPAPER - IOn<strong>to</strong>logy , & EpistemologyCandidates will be expected <strong>to</strong> be familiarwith the following Western and Indian theories ofEqistemology and On<strong>to</strong>logy -(a) Western - Empiricism, Rationalism,Critical philosophy, Materialism, Idealism, Realism,Pragmatism, Logical positivism and Existentialism.(b) Indian : Prama and pramanas .Theoriesof truth and error,Theories of Reality with specialreference <strong>to</strong> main systems (orthodox andheterodox ) of Indian Philosophy)PAPER - IISocio-Political Philoscophy andphilosophy of Religion.1. Nature of Phillosophy, its relation withlife, science and culture.2. (a) the following <strong>to</strong>pics ; Damocracy,Socialism. Fascism, Communism and Sarvodaya.(b) Methods and aspects of politicalaction - Constitutionism, Revolution, Terrorismand Satyagrah.3. Tradition , Change and modernity (withspecial reference <strong>to</strong> Indian social order)4. (a) Natural land scope of philoscophy ofreligion.(21)(b) Nature of God and proofs of God'sexistence.(c) Nautre of religious experience; reason,revelation and mysticism.5. (a) Problem of evil and sin(b) Bondage and Liberation (Moksa) andpaths for the realisation of Liberation.(c) Unity , and universality of religions :religious <strong>to</strong>lerance and secularism.16-HkkSfrdhiz'u i= izFke;kaf=dh] rkih; HkkSfrdh] rjaxvkSj nksyu rFkkHkkSfrd&izdkf'kdh;kaf=dh &laj{kh cy &{ks= vkSj fLFkfrt ÅtkZ]xq:Roh; foHko vkSj ,d leku xksyh; dks'k rFkk,d leku xksys ds dkj.k bldh rhozrk] th dkekiu] xzgksa dh xfr vkSj dsiyj ds fu;e] í
Change language