# NUCAT 2024 Syllabus: Check Section-wise Exam Syllabus Here

NITTE University Common Admission Test 2024 ( NUCAT )

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NUCAT 2024 syllabus: The NUCAT 2024 syllabus is essential in preparing for the NUCAT exam. To effectively prepare for NUCAT 2024, candidates need to have a thorough understanding of the examination syllabus. This includes key topics from subjects such as Chemistry, Physics, and Maths. Detailed information on the NUCAT 2024 syllabus can be found on this page. Currently, the NUCAT application form 2024 is available. The direct link to apply for the exam is updated here.

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1. NUCAT 2024 Syllabus

## NUCAT 2024 Syllabus

 SYLLABUS: I PUC PHYSICS UNIT-I Chapter 1: PHYSICAL WORLD Physics: Scope and excitement of physics, Physics-technology and society Mention of fundamental forces in nature - Nature of physical laws. Chapter 2: UNIT OF MEASUREMENT Unit of measurement - System of units - SI units - Fundamental and derived units - Length, mass and time measurements - Accuracy and precision of measuring instruments. Errors in measurement; Significant figures. Dimensions of physical quantities - Dimensional analysis and its applications: (a) Checking of dimensional consistency of equations and (b) Deducing relation among physical quantities.   UNIT-II Chapter 3: MOTION IN A STRAIGHT LINE Position and frame of reference - Definitions of path length and displacement - Definitions of average speed and average velocity, instantaneous speed and instantaneous velocity and uniform and non-uniform motion. Uniformly accelerated motion. Position-time graph, Velocity-time graph: To show that area under the velocity time curve is equal to displacement. Kinematic equations for uniformly accelerated motion. Derivation of v = v o + at , x = v o + 1⁄2 at 2 and v 2 = v o 2 + 2ax using v-t graph - Relative velocity. Elementary concepts of differentiation and integration for describing motion. Chapter 4: MOTION IN A PLANE Scalars and vectors, Position and displacement vectors, Equality of vectors, Multiplication of a vector by real number. Addition and subtraction of two vectors: Triangle method and parallelogram method. Unit vector, Resolution of a vector, Rectangular components. Resultant of two concurrent vectors. Scalar and vector product of two vectors with examples. Motion in a plane with constant acceleration. Projectile motion: Derivations of equation of path, time of flight, maximum height and horizontal range, of a projectile. Uniform circular motion: Derivation of centripetal acceleration.   UNIT-III Chapter 5: LAWS OF MOTION Aristotle’s fallacy, Newton’s first law of motion, Concept of inertia and force. Concept of momentum - Newton’s second law of motion: Derivation of F= ma and definition of SI unit of force. Impulse, impulsive force and examples - Newton’s third law of motion, Identification of action and reaction pairs with examples in everyday life. Law of conservation of linear momentum: Statement and proof in the case of collision of two bodies. Condition for the equilibrium of a particle under the action of concurrent forces. Friction: Static and kinetic friction - Laws of friction - Rolling friction - Methods of reducing of friction. Dynamics of uniform circular motion: Derivation of maximum speed of a car moving on banked circular road and discuss in the case of level circular road by taking θ = 0.   UNIT-IV Chapter 6: WORK, ENERGY AND POWER WORK: Definition of Work: W = F. d and discussion of various cases - Work done by a constant force and by a variable force. Kinetic energy - Work-energy theorem: Statement and proof in the case of rectilinear motion under constant acceleration. Concept of potential energy - Principle of conservation of mechanical energy: Statement and illustration in the case of freely falling body. Conservative and non-conservative forces with examples. Potential energy of a spring - Mention of expression V(x) = kx 2/2. POWER: Definition and derivation of power P = F.v COLLISIONS: Elastic and inelastic collisions - Collisions in one dimension: Derivation of loss of kinetic energy in completely inelastic collisions - Derivation of final velocity of masses undergoing elastic collision. Collisions in two dimensions.   UNIT-V Chapter 7: SYSTEMS OF PARTICLES AND ROTATIONAL MOTION Definitions of a rigid body, translatory motion and rotatory motion - Centre of mass of a two-particle system. Mention of expression for position coordinates of centre of mass of (a) n-particle system (b) a rigid body and (c) a uniform thin rod. Definition of angular velocity and mention of the relation v = rw.Definitions of angular acceleration and moment of a force-torque - Angular momentum (l) of a particle: Derivation of dl/dt = τ. Equilibrium of rigid body: Mention of conditions for mechanical equilibrium of a rigid body. Definitions of the moment of inertia and radius of gyration. Theorems of parallel and perpendicular axes: Statement and explanation. Mention of expressions for a moment of inertia of simple geometrical objects. Kinematics of rotational motion about a fixed axis: Mention of the equation of rotational motion. Comparison of linear and rotational motion. Principle of conservation of angular momentum: Statement and illustrations.   UNIT-VI Chapter 8: GRAVITATION Kepler’s laws (three laws) of planetary motion: Statement and explanation. Universal law of gravitation: Statement and explanation. Acceleration due to gravity of earth: Derivation of relation between g and G. Variation of acceleration due to gravity with altitude (height) and depth: Derivation of acceleration due gravity at a point (a) above and (b) below the surface of earth. Gravitational potential energy: Derivation of gravitational potential energy. Escape speed: Definition and derivation of expression for escape speed from the principle of conservation of energy. Earth satellites: Derivation of orbital speed of earth satellite - Geostationary and polar satellites.   UNIT-VII Chapter 9: MECHANICAL PROPERTIES OF SOLIDS Elasticity and plasticity - Elastic behavior of solids - Stress and strain - Hooke’s law: Stress–strain curve. Elastic moduli; Definitions and expressions of Young’s modulus, Bulk modulus and Shear modulus of rigidity. Poisson’s ratio - Elastic energy. Chapter 10: MECHANICAL PROPERTIES OF FLUIDS Pressure: Definition - Derivation of pressure at a point inside a liquid - Gauge pressure. Pascal’s law: Statement and its applications (hydraulic lift and hydraulic brakes). Streamline flow: Equation of continuity - Turbulent flow - Critical speed. Bernoulli’s principle; Statement - Explanation of Bernoulli’s equation - Illustration of Bernoulli’s principle in the case of (a) blood flow and heart attack (b) dynamic lift of a ball and aerofoil. Viscosity: Definition and mention of expression for coefficient of viscosity. Stoke’s law. Reynolds’s number: Mention of expression - Classification of nature of flow on the basis of Reynolds’s number. Surface tension: Surface energy and surface tension - Angle of contact - Applications of surface tension ideas to drops, bubbles, capillary rise and action of detergents. Chapter 11: THERMAL PROPERTIES OF MATTER Temperature and heat, Thermal expansion of solids: linear, area and volume expansion of solids – Thermal expansion of liquids: Anomalous expansion of water, Thermal expansion of gases: Derivation of αV = 1/T for ideal gas. Specific heat capacity: Definition of heat capacity and specific heat capacity - Molar specific heat capacity at constant pressure and Molar specific heat capacity at constant volume. Principle of calorimetry - Change of state ; melting, fusion, melting point, regelation, boiling point, sublimation point - Latent heat ; Latent heat of fusion and vapourisation. Heat transfer: Conduction and thermal conductivity, Convection: Sea breeze and land breeze, Radiation: Newton’s law of cooling. Stefan’s law - Qualitative ideas of black body radiation. Wien’s displacement law - Greenhouse effect.   UNIT-VIII Chapter 12: THERMODYNAMICS Thermal equilibrium - Zeroth law of Thermodynamics: Statement and explanation. Heat, internal energy and work - First law of thermodynamics: Statement and explanation, Isothermal process: Derivation of work-done in isothermal process. Adiabatic process: Mention of the expression PVγ = constant, for adiabatic process. Heat engines: Schematic representation and efficiency. Refrigerators (Heat pumps): Schematic diagram and coefficient of performance. Second law of thermodynamics: Kelvin-Planck statement and Clausius statement. Reversible and irreversible processes. Carnot’s engine; Carnot cycle and efficiency.   UNIT-IX Chapter 13: KINETIC THEORY Equation of state of a perfect gas - Kinetic theory of an ideal gas: Derivation of P =(1/3)mnv̅ 2 Kinetic interpretation of temperature ; Mention of expression for average kinetic energy of a molecule in terms of absolute temperature - Definition of rms speed of gas molecules. Degrees of freedom - Law of equipartition of energy: Statement and application to specific heat capacities of monatomic, diatomic and polyatomic gases - Concept of mean free path.   UNIT-X Chapter 14: OSCILLATIONS Periodic & oscillatory motion: Definitions of Period & Frequency, Displacement as a function of time. Periodic functions. SIMPLE HARMONIC MOTION: Definition, equation, graphical representation of displacement with time, Phase. Mention of expressions for velocity and acceleration - Force law for simple harmonic motion : F(t) = −kx(t). Energy in simple harmonic motion: Derivations of kinetic energy, potential energy and total energy. Oscillations due to a spring - Restoring force & force constant - Mention of expression for time period. Simple pendulum: Derivation of expression for time period - Qualitative ideas of damped, forced and free oscillations - Resonance. Chapter 15: WAVES Wave motion: Longitudinal and transverse waves, Mention of displacement relation in a progressive wave- Amplitude and phase - Wavelength and angular wave number - Period, frequency and angular frequency. Speed of traveling wave: Mention of expression for velocity of wave: v = λv. Mention of expression for speed of transverse wave on a stretched string v = √T/μ Speed of a longitudinal wave(sound) ; Newton’s formula and Laplace’s correction. Qualitative explanation of principle of superposition of waves. Reflection of waves at rigid and open boundary. Standing waves and normal modes: Theory, extension to stretched string and air columns - Fundamental mode and harmonics - Theory of beats. Doppler Effect: Explanation of the phenomenon. Derivation of apparent frequency in the case of (a) moving source and stationary observer, (b) moving observer and stationary source and (c) both source and observer moving.
 SYLLABUS: II PUC Chemistry UNIT-I Solid State Classification of solids based on different binding forces: molecular, ionic, covalent and metallic solids, amorphous and crystalline solids (elementary idea). Unit cell in two dimensional and three dimensional lattices, calculation of density of unit cell, packing in solids, packing efficiency, voids, number of atoms per unit cell in a cubic unit cell, point defects, electrical and magnetic properties. Band theory of metals, conductors, semiconductors and insulators and n and p type semiconductors.   UNIT-II Solutions Types of solutions, expression of concentration of solutions of solids in liquids, solubility of gases in liquids, solid solutions, Raoult's law, colligative properties - relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass, Van't Hofffactor.   UNIT-III Electrochemistry Redox reactions, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical cells, Relation between Gibbs energy change and EMF of a cell, conductance in electrolytic solutions, specific and molar conductivity, variations of conductivity with concentration, Kohlrausch's Law, electrolysis and law of electrolysis (elementary idea), dry cell-electrolytic cells and Galvanic cells, lead accumulator, fuel cells,corrosion.   UNIT-IV Chemical Kinetics Rate of a reaction (Average and instantaneous), factors affecting rate of reaction: concentration, temperature, catalyst; order and molecularity of a reaction, rate law and specific rate constant, integrated rate equations and half-life (only for zero and first order reactions), concept of collision theory (elementary idea, no mathematical treatment), activation energy, Arrhenius equation.   UNIT-V Surface Chemistry Adsorption - physisorption and chemisorption, factors affecting adsorption of gases on solids, catalysis: homogenous and heterogenous, activity and selectivity of solid catalysts; enzyme catalysis, colloidal state: distinction between true solutions, colloids and suspension; lyophilic, lyophobic, multi-molecular and macromolecular colloids; properties of colloids; Tyndall effect, Brownian movement, electrophoresis, coagulation, emulsion - types of emulsions.   UNIT-VI General Principles and Processes of Isolation of Elements Principles and methods of extraction - concentration, oxidation, reduction - electrolytic method and refining; occurrence and principles of extraction of aluminium, copper, zinc and iron.   UNIT-VII p-Block Elements Group -15 Elements: General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; Nitrogen preparation properties and uses; compounds of Nitrogen: preparation and properties of Ammonia and Nitric Acid, Oxides of Nitrogen (Structure only); Phosphorus - allotropic forms, compounds of Phosphorus: Preparation and properties of Phosphine, Halides and Oxoacids (elementary idea only). Group 16 Elements: General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties, dioxygen: preparation, properties and uses, classification of Oxides, Ozone, Sulphur -allotropic forms; compounds of Sulphur: preparation properties and uses of Sulphur- dioxide, Sulphuric Acid: industrial process of manufacture, properties and uses; Oxoacids of Sulphur (Structures only). Group 17 Elements: General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; compounds of halogens, Preparation, properties and uses of Chlorine and Hydrochloric acid, interhalogen compounds, Oxoacids of halogens (structures only). Group 18 Elements: General introduction, electronic configuration, occurrence, trends in physical and chemical properties uses.   UNIT-VIII d and f Block Elements General introduction, electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the first row transition metals – metallic character, ionization enthalpy, oxidation states, ionic radii, colour, catalytic property, magnetic properties, interstitial compounds, alloy formation, preparation and properties of K 2Cr 2O 7 and KMnO 4. Lanthanoids - Electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction and its consequences. Actinoids - Electronic configuration, oxidation states and comparison with lanthanoids.   UNIT-IX Coordination Compounds Coordination compounds - Introduction, ligands, coordination number, colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds. Bonding, Werner's theory, VBT, and CFT; structure and stereoisomerism, importance of coordination compounds (in qualitative analysis, extraction of metals and biological system).   UNIT-X Haloalkanes and Haloarenes. Haloalkanes: Nomenclature, nature of C–X bond, physical and chemical properties, optical rotation mechanism of substitution reactions. Haloarenes: Nature of C–X bond, substitution reactions (Directive influence of halogen in monosubstituted compounds only). Uses and environmental effects of - dichloromethane, trichloromethane, tetrachloromethane, iodoform, freons, DDT.   UNIT-XI Alcohols, Phenols and Ethers Alcohols: Nomenclature, methods of preparation, physical and chemical properties (of primary alcohols only), identification of primary, secondary and tertiary alcohols, mechanism of dehydration, uses with special reference to methanol and ethanol. Phenols: Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophillic substitution reactions, uses of phenols. Ethers: Nomenclature, methods of preparation, physical and chemical properties, uses.   UNIT-XII Aldehydes, Ketones and Carboxylic Acids Aldehydes and Ketones: Nomenclature, nature of carbonyl group, methods of preparation, physical and chemical properties, mechanism of nucleophilic addition, reactivity of alpha hydrogen in aldehydes, uses. Carboxylic Acids: Nomenclature, acidic nature, methods of preparation, physical and chemical properties; uses.   UNIT-XIII Amines Amines: Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary, secondary and tertiary amines. Diazonium salts: Preparation, chemical reactions and importance in synthetic organic chemistry.   UNIT-XIV Biomolecules Carbohydrates - Classification (aldoses and ketoses), monosaccahrides (glucose and fructose), D-L configuration oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen); Importance of carbohydrates. Proteins -Elementary idea of - amino acids, peptide bond, polypeptides, proteins, structure of proteins - primary, secondary, tertiary structure and quaternary structures (qualitative idea only), denaturation of proteins; enzymes. Hormones - Elementary idea excluding structure. Vitamins - Classification and functions. Nucleic Acids: DNA and RNA.   UNIT-XV Polymers Classification - natural and synthetic, methods of polymerization (addition and condensation), copolymerization, and some important polymers: natural and synthetic like polythene, nylon polyesters, bakelite, rubber. Biodegradable and non-biodegradable polymers.   UNIT-XVI Chemistry in Everyday life Chemicals in medicines - analgesics, tranquillizers antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihist amines. Chemicals in food - preservatives, artificial sweetening agents, elementary idea of antioxidants. Cleansing agents- soaps and detergents, cleansing action.
 SYLLABUS: I PUC Mathematics UNIT-I SETS AND FUNCTIONS 1. Sets Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of the set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and intersection of sets. Difference of sets. Complement of a set, Properties of Complement sets. 2. Relations and Functions Ordered pairs, Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the reals with itself (upto R × R × R). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain and range of a function. Real valued function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions 3. Trigonometric Functions Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin2x + cos2x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin(x + y) and cos(x + y) in terms of sinx, siny, cosx and cosy. Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x. General solution of trigonometric equations of the type sinθ = sinα, cosθ = cosα and tanθ = tanα. Proofs and simple applications of sine and cosine formulae.   UNIT-II ALGEBRA 1. Principle of Mathematical Induction Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications. 2. Complex Numbers and Quadratic Equations Need for complex numbers, especially √−1 , to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system, Square-root of a Complex number. 3. Linear Inequalities Linear inequalities, Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Solution of system of linear inequalities in two variables - graphically. 4. Permutations and Combinations Fundamental principle of counting. Factorial n. Permutations and combinations derivation of formulae and their connections, simple applications. 5. Binomial Theorem History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, general and middle term in binomial expansion, simple applications. 6. Sequence and Series Sequence and Series. Arithmetic Progression (A.P.), Arithmetic Mean (A.M.), Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P. Arithmetic and geometric series, infinite G.P. and its sum, geometric mean (G.M.). Relation between A.M. and G.M. Sum to n terms of the special series : ∑n , ∑ n 2 and ∑ n 3.   UNIT-III COORDINATE GEOMETRY 1.Straight Lines Brief recall of 2-D from earlier classes, shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axes, point-slope form, slope-intercept form, two-point form, intercepts form and normal form. General equation of a line. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line. 2. Conic Sections Sections of a cone: Circles, ellipse, parabola, hyperbola, a point, a straight line and pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle. 3. Introduction to Three-dimensional Geometry Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.   UNIT-IV CALCULUS 1. Limits and Derivatives Derivative introduced as rate of change both as that of distance function and geometrically, The intuitive idea of limit. lim x→0 loge(1+x)/x, lim x→0e x−1/x. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.   UNIT-V MATHEMATICAL REASONING Mathematically acceptable statements. Connecting words/phrases - consolidating the understanding of “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied by”, “and”, “or”, “there exists” and their use through a variety of examples related to real life and Mathematics. Validating the statements involving the connecting words - the difference between contradiction, converse and contrapositive.   UNIT-VI STATISTICS AND PROBABILITY 1.Statistics Measure of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances. 2. Probability Random experiments: outcomes, sample spaces (set representation). Events: Occurrence of events, ‘not’, ‘and’ & ‘or’ events, exhaustive events, mutually exclusive events. Axiomatic (set theoretic) probability, connections with the theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’, & ‘or’ events.
 SYLLABUS: II PUC Mathematics UNIT-I RELATIONS AND FUNCTIONS 1. Relations and Functions Types of relations: Reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations. 2. Inverse Trigonometric Function Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.   UNIT-II ALGEBRA 1. Matrices Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication. Non- commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries). 2. Determinants Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.   UNIT-III CALCULUS 1. Continuity and Differentiability Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concepts of exponential, logarithmic functions. Derivatives of loge x and e x. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second-order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretations. 2. Applications of Derivatives Applications of derivatives: Rate of change, increasing/decreasing functions, tangents and normals, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations). 3. Integrals Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type – ∫dx/(x 2±a 2), ∫dx/√x 2±a 2, ∫dx/√a 2−x 2, ∫dx/ax 2+bx+c, ∫dx/√ax 2+bx+c, ∫(px+q)/ax 2+bx+c dx, ∫(px+q)/√ax 2+bx+cdx, ∫ √a 2 ± x 2dx, ∫√x 2−a 2dx, ∫ √ax 2 + bx + cdx and ∫(px + q)√ax2 + bx + cdx to be evaluated. Definite integrals as a limit of a sum. Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals. 4. Applications of the Integrals Applications in finding the area under simple curves, especially lines, arcs of circles/parabolas/ellipses (in standard form only), area between the two above said curves (the region should be clearly identifiable). 5. Differential Equations Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type – (dy/dx) + Py = Q , where P and Q are functions of x or constants (dx/dy) + Px = Q , where P and Q are functions of y or constants.   UNIT-IV VECTORS AND THREE DIMENSIONAL GEOMETRY 1. Vectors Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors, scalar triple product. 2. Three dimensional geometry Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.   UNIT-V LINEAR PROGRAMMING Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constrains).   UNIT-VLINEAR PROGRAMMING Introduction, related terminology such as constraints, objective function, optimization, differenttypes of linear programming (L.P.) problems, mathematical formulation of L.P. problems,graphical method of solution for problems in two variables, feasible and infeasible regions,feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints). UNIT-VIPROBABILITY Multiplications theorem on probability. Conditional probability, independent events, totalprobability, Baye’s theorem. Random variable and its probability distribution, mean and varianceof haphazard variable. Repeated independent (Bernoulli) trials and Binomial distribution. Multiplications theorem on probability. Conditional probability, independent events, total probability, Baye’s theorem. Random variable and its probability distribution, mean and variance of haphazard variable. Repeated independent (Bernoulli) trials and Binomial distribution.

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The duration of the NUCAT exam is usually 2 hours. The exam can be taken at home or at the exam centre. The technical requirements to take the test online are as follows:

• Computer CPU: i3 Processor or equivalent (higher always recommended)
• Computer RAM: 4 GB (higher is always recommended)
• Operating Sys

...more

D

Dhanya B

Contributor-Level 10

NUCAT 2024 will be a total of 120 marks asked from Physics, Chemistry and Mathematics. 40 questions are asked from each subject. Only multiple-choice questions are asked in NUCAT 2024.

D

Dhanya B

Contributor-Level 10

## 1 Institutes accepting NUCAT

B.Tech. in Computer Science and Engineering
• 4.2

Placements

4.0

Infrastructure

4.2

Faculty & Course Curriculum

4.1

Crowd & Campus Life

4.5

Value for Money

4.1
(18)
• |
• Total Fees: ₹ 3.86 Lakh
• |
• 4 years
• |
• Full Time

## Upcoming B.Tech Exam Dates

27 Feb '24: SAT Deadline for Changes, Regular Cancellation, and Late Registration for March Test
28 Feb '24: GAT 2024 phase 2 last date for payment of the allotment fee
15 Feb '24 - 29 Feb '24: LPU NEST 2024 Entrance Examination Dates - Current Schedule II
Feb '24: AMIE Exam 2024 Summer Application last date
8 Feb '24 - 11 Mar '24: WBJEE JELET 2024 application form dates