# WB JEE

WB JEE (West Bengal Board of Exam)

## West Bengal Joint Entrance Examinations Board (WB-JEE)

The West Bengal Joint Entrance Examinations Board was formed in the year 1962 for the purpose of holding Common Entrance Examinations for the Undergraduate Level Engineering Courses in the State of West Bengal. The endeavour of the Board has always been directed towards enhancement of transparency in conducting Common Entrance Examinations for various professional Undergraduate and Postgraduate level courses in the State through effective state-of-the-art technology. Online application and admission through e–Counselling is operational for the undergraduate level Engineering and Medical courses of the State.

## WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

## JEM 2012 - SYLLABUS

## MATHEMATICS

**Algebra**

**A.P., G.P., H.P. : **Definitions of A. P. and G.P.; General term;
Summation of first n-terms; A.M.and G.M.; Definitions of H.P. (only 3 terms) and
H.M.; Finite arithmetico-geometric series.

**Logarithms :**Definition; General properties; Change of base.

**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.

**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 ax^{2}+bx+c
(a,b,c are rational numbers and a≠0).

**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). Combinations of n different things
taken r at a time (r ≤ n). Combination of n things not all different. Basic
properties.

Problems involving both permutations and combinations.

**Principle of Mathematical Induction : **Statement of the principle.
Proof by induction for the sum of squares, sum of cubes of first n natural
numbers, divisibility properties like 2 2n – 1 is divisible by 3 (n ≥ 1), 7
divides 3^{2n+1}+2 ^{n+2}(n ≥ 1).

**Binomial theorem (positive integral index) :**Statement of the theorem,
general term, middle term, equidistant terms, properties of binomial co-efficients.

## WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

## JEM 2012 - SYLLABUS

## PHYSICS

**Mechanics & General properties of matter**

(i) Units and dimensions : Units of measurement, system of units, fundamental
and derived units, S I units, dimensional analysis. Methods of
measurement: Vernier scale, screw gauge, analysis of errors, significant
figures.

(ii) Scalars and vectors: Addition, subtraction, multiplication of vectors.

(iii) Kinematics in one, two and three dimensions, projectiles, uniform circular
motion,centripetal force, centrifigual force, relative velocity.

(iv) Dynamics: Newton's laws of motion; inertial frames, uniformly accelerated
frame (pseudoforces), conservation of linear momentum, rocket motion, centre of
mass, impulsive forces, friction.

(v) Work, Power and Energy , conservative and non-conservative forces,
conservation of energy, collision(elastic and inelastic)

(vi) .Rotational motion : Torque, angular momentum and conservation of angular
momentum, moment of inertia, radius of gyration, moment of inertia of objects
with simple geometrical shapes, rotational kinetic energy and rolling on
horizontal surface.

**Gravitation: **Laws of gravitation, gravitational field and potential,
acceleration due to gravity and its variation, escape velocity, Kepler's laws
and planetary motion, motion of satellites, Geostationary orbit.

**Elasticity: **Hooke's law, elastic modulii, Poisson's ratio, elastic
energy. Hydrostatics and fluid mechanics: Pressure in a fluid, Pascal's law,
Archimedes' principle, hydraulic press.

**Surface energy and surface tension, capillary rise. **Viscosity,
streamline and turbulent motion, critical velocity, Reynold's number, Stoke's
law, Bernoulli's theorem.

**Vibrations: **Simple Harmonic Motion, equation of motion, damped and
forced vibrations, resonance, superposition of SHM.

**Wave motion: **Elastic waves, longitudinal and transverse waves.
progressive waves, superposition of waves: interference, stationary waves,
beats, vibration of strings, air columns, velocity of elastic waves in different
media, Doppler effect.

## WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

## JEM 2012 - SYLLABUS

## CHEMISTRY

**Atoms, Molecules and Chemical Arithmetic:**

Dalton’s atomic theory; Gay Lussac’s law of gaseous volume; Avogadro’s
Hypothesis and its applications. Atomic mass; Molecular mass; Equivalent weight;
Valency; Gram atomic weight; Gram molecular weight; Gram equivalent weight and
mole concept; Chemical formulae; Balanced chemical equations; Calculations
(based on mole concept) involving common oxidation-reduction, neutralization,
and displacement reactions; Concentration in terms of mole fraction, molarity,
molality and normality. Percentage composition, empirical formula and molecular
formula; Numerical problems.

**Atomic Structure: **Concept of Nuclear Atom – electron,
proton and neutron (charge and mass), atomic number; Rutherford’s model and its
limitations; Extra nuclear structure; Line spectra of hydrogen atom.
Quantization of energy (Planck’s equation E = hv); Bohr’s model of hydrogen atom
and its limitations, Sommerfelds modifications (elementary idea); The four
quantum numbers, ground state electronic configurations of many electron atoms
and mono-atomic ions; The Aufbau Principle; Pauli’s Exclusion Principle and
Hund’s Rule.

**Uncertainty principle; **The concept of atomic orbitals,
shapes of s, p and d orbitals (pictorial approach)

**Radioactivity and Nuclear Chemistry
**Radioactivity – α-, β-, γ-rays and their properties; Artificial
transmutation; Rate of radioactive decay, decay constant, half-life and average
life period of radio-elements; Units of radioactivity; Numerical problems.
Stability of the atomic nucleus – effect of neutron–proton (n/p) ratio on the
modes of decay, group displacement law, radioisotopes and their uses (C, P, Co
and I as examples) isobars and isotones (definition and examples), elementary
idea of nuclear fission and fusion reactions.

**The Periodic Table and Chemical Families**

## WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

## JEM 2012 - SYLLABUS

## BIOLOGY

**Unit of Life : **Definition of life, Cell as the basic unit of life.
Cell theory, Prokaryotic and Eukaryotic cell – structure and differences.

**Ultrastructure and functions of cellular components : **Cell wall,
Plasma membrane, Plastid, Endoplasmic reticulum, Golgi bodies, Mitochondria,
Ribosomes, Lysosomes, Nucleus, Centrosomes, Cilia, Flagella.

**Microscopy : **Components and principles of Simple and Compound
Microscope; Electron Microscope : Basic functional principles.

**Physical and chemical principles involved in maintenance of life processes
:**Diffusion, Osmosis, Absorption, Osmoregulation. Biomolecules :
Classification and structural properties of carbohydrates, lipids, aminoacids,
proteins and nucleic acids.

**Carbohydrates :** Monosaccharides, digosaccharides, and polysaccharides
(starch, glycogen, cellulose).

**Proteins :**Simple (albumins, globulins, collagen) and conjugated
proteins (only examples).

**Nucleic acids : **Structure of DNA, RNA, types of RNA.

**Enzymes : **Definition & properties, Examples; Mechanism of Action,
Allosterism and Regulation. Chromosomes and Cell Division : Morphology of
chromosomes; Euchromatin and Heterochromatin. Nucleic acid as genetic material
(Examples: Bacterial Transformation and Viral Transduction). Brief idea of
Polytene chromosomes:Cell cycle and phases (excluding control mechanism).
Characters of malignant cell; Process & significance of Meiosis.

**Genetics : **Laws of Heredity : (Monohybrid and dihybrid crosses;
Mendel’s laws). Back cross, Test cross, Linkage, Crossing over, Sex linked
inheritance – Colour blindness, Haemophilia. Mutation – Definition and Types;
Replication of DNA, Transcription and Translation (Brief idea).

**Origin, Evolution and Diversity of Life :** Haldane and Oparin’s concept
on origin of life. Modern concept of Natural selection, Biological Species
concept. Human evolution – an outline.

**Taxonomy and Classification :** Definition; Importance of Taxonomy,
Binomial Nomenclature, Law of Priority (Homonym & Synonym).

**Concept of Biodiversity :** Definition of Biodiversity ; Genetic
diversity; Species diversity and Ecosystem diversity. Five kingdom
classification (only distinct characters).Salient features of major animal phyla
with common examples, classification of Chordates (up to Sub Class) with
distinctive characters only.

**Population Biology :**Concept of population growth (logistic and
exponential) and population control.

## WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

## JOINT ENTRANCE EXAMINATION, 2012 (JEM-2012)

**Applications are invited from Indian Citizens for admission to
undergraduate courses in Engineering / Technology /Architecture/Medical*/Dental*
and Pharmacy in Universities/Colleges in West Bengal for the academic session
2012- 2013, on the basis of a JOINT ENTRANCE EXAMINATION, to be conducted by the
"WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD". **

## Scheme of Examination:

Option |
Availability of Courses for admissionthrough “JEM-2012” |
Subjects to be appeared in JEM-2012 |
Type ofapplication form to be used |

1 | Engineering & Technology / B.Arch. / Dairy Technology/Agricultural Engineering / Pharmacy |
Mathematics, Physics & Chemistry | ‘E’ |

2 | Medical* / Dental* / Pharmacy | Biological Sciences, Physics & Chemistry |
‘M’ |

3 | Engineering & Technology/B. Arch./Dairy Technology / Agricultural Engineering / Pharmacy / Medical* / Dental* |
Mathematics, Physics & Chemistry and Biological Sciences |
‘C’ |

## West Bengal Joint Entrance Examinations Board 2011

West Bengal Joint Entrance Examination Board -2011. Answers Key & Solution
Hints Declared by Aakash Institute Delhi. Click given below to download answer
keys.

## JOINT ENTRANCE EXAMINATION, 2011 (JEM-2011)

**Applications are invited from Indian Citizens for admission to undergraduate
courses in Engineering / Technology / Architecture/Medical/ Dental and Pharmacy
in Universities/Colleges in West Bengal for the academic session 2011-2012, on
the basis of a JOINT ENTRANCE EXAMINATION, to be conducted by the "WEST BENGAL
JOINT ENTRANCE EXAMINATIONS BOARD". **

## Eligibility Criteria :

The applicant must be a citizen of India and should have passed the H.S.(10+2) or its equivalent examination. The general candidates must have to secure at least 50% marks in Physics, Chemistry and Mathematics or Biology taken together (40% for SC/ST candidates) and at least 30% marks in English (for all categories). In addition, candidates must secure at least pass marks in the subjects individually including vernacular (or any other fifth subject) as mentioned below: B.E/B.Tech./B.Arch :Physics, Chemistry, Mathematics, English and vernacular or any other fifth subject. M.B.B.S/B.D.S. : Physics, Chemistry, Biology, English and vernacular or any other fifth subject.

**PHARMACY: **Physics, Chemistry, Mathematics or Biology, English and
vernacular or any other fifth subject. For MBBS and BDS courses : In addition to
the aforesaid eligibility criteria, the general candidates must have to secure
at least 50% marks in Physics, Chemistry and Biological Sciences taken together
(40% for SC/ST) in the Joint Entrance Examination, W.B. Candidates appearing in
the qualifying examination in 2011 will be allowed to sit for JEM-2011
provisionally and their admission, if merit listed, will be subjected to
satisfying the minimum requirements of eligibility as specified above.

##

WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

SYLLABUS FOR JEM

## CHEMISTRY

**Atoms, Molecules and Chemical Arithmetic :**

Dalton’s atomic theory; Gay Lussac’s law of gaseous volume; Avogadro’s
Hypothesis and its applications.

Atomic mass; Molecular mass; Equivalent weight; Valency; Gram atomic weight; Gram molecular weight; Gram equivalent weight and mole concept; Chemical formulae; Balanced chemical equations; Calculations (based on mole concept) involving common oxidation-reduction, neutralization, and displacement reactions; Concentration in terms of mole fraction, molarity, molality and normality.

Percentage composition, empirical formula and molecular formula; Numerical problems.

**Atomic Structure:
**Concept of Nuclear Atom – electron, proton and neutron (charge and
mass), atomic number; Rutherford’s model and its limitations; Extra nuclear
structure; Line spectra of hydrogen atom.

Quantization of energy (Planck’s equation E = h*v*); Bohr’s model of
hydrogen atom and its limitations, Sommerfelds modifications (elementary
idea); The four quantum numbers, ground state electronic configurations of
many electron atoms and mono-atomic ions; The Aufbau Principle; Pauli’s
Exclusion Principle and Hund’s Rule.

Uncertainty principle; The concept of atomic orbitals, shapes of *s, p*
and d orbitals (pictorial approach)

**Radioactivity and Nuclear Chemistry:**

Radioactivity **– α-, β-, γ-**rays and their properties; Artificial
transmutation; Rate of radioactive decay, decay

constant, half-life and average life period of radio-elements; Units of
radioactivity; Numerical problems.

Stability of the atomic nucleus – effect of neutron–proton (n/p) ratio on the modes of decay, group displacement law, radioisotopes and their uses (C, P, Co and I as examples) isobars and isotones (definition and examples), elementary idea of nuclear fission and fusion reactions.

**The Periodic Table and Chemical Families:
**Modern periodic law (based on atomic number); Modern periodic table based on
electronic configurations, groups (Gr. 1–18) and periods. Types of
elements-representative (s-block and p-block), transition (d-block) elements and
inner transition (f-block / lanthanides and actinides) and their general
characteristics. Periodic trends in physical and chemical properties–atomic
radii, valency, ionization energy, electron affinity, electronegativity,
metallic character, acidic and basic characters of oxides and hydrides of the
representative elements (up to Z = 36). Position of hydrogen and the noble gases
in the periodic table; Diagonal relationships.

**Chemical Bonding and Molecular Structure:
**Valence electrons, the Octet rule, electrovalent, covalent and coordinate
covalent bonds with examples; Properties of electrovalent and covalent
compounds. Limitations of Octet rule (examples); Fajan’s Rule.

Directionality of covalent bonds, shapes of poly-atomic molecules (examples);
Concept of hybridization of atomic orbitals (qualitative pictorial approach) :
sp, sp^{2}, sp^{3} and dsp^{2}.

Molecular orbital energy diagrams for homonuclear diatomic species – bond order and magnetic properties.

Valence Shell Electron Pair Repulsion (VSEPR) concept (elementary idea) – shapes of molecules. Concept of resonance (elementary idea), resonance structures (examples). Elementary idea about electronegativity, bond polarity and dipole moment, inter- and intra- molecular hydrogen bonding and its effects on physical properties (mp, bp and solubility); Hydrogen bridge bonds in diborane.

Double salts and complex salts, co-ordination compounds (examples only), co-ordination number (examples of co-ordination number 4 and 6 only).

**Gaseous state:
**Measurable properties of gases. Boyle’s Law and Charles Law, absolute scale
of temperature, kinetic theory of gases, ideal gas equation – average, root mean
square and most probable velocities and their relationship with temperature.

Dalton’s Law of partial pressure, Graham’s Law of gaseous diffusion. Deviations from ideal behavior.

Liquefaction of gases, real gases, van der Waal’s equation; Numerical problems.

##

WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

SYLLABUS FOR JEM

## BIOLOGICAL SCIENCES

**Unit of Life : **Definition of life, Cell as the basic unit of life.
Cell theory, Prokaryotic and Eukaryotic cell – structure and differences.

**Ultrastructure and functions of cellular components : **Cell wall,
Plasma membrane, Plastid, Endoplasmic reticulum, Golgi bodies, Mitochondria,
Ribosomes, Lysosomes, Nucleus, Centrosomes, Cilia, Flagella.

**Microscopy : **Components and principles of Simple and Compound
Microscope;

**Electron Microscope : **Basic functional principles.

**Physical and chemical principles involved in maintenance of life processes
:**Diffusion, Osmosis, Absorption, Osmoregulation.

**Biomolecules : **Classification and structural properties of
carbohydrates, lipids, aminoacids, proteins and nucleic acids.

**Carbohydrates : **Monosaccharides, digosaccharides, and polysaccharides
(starch, glycogen, cellulose).

**Proteins :**Simple (albumins, globulins, collagen) and conjugated
proteins (only examples).

**Nucleic acids : **Structure of DNA, RNA, types of RNA.

**Enzymes : **Definition & properties, Examples; Mechanism of Action,
Allosterism and Regulation.

**Chromosomes and Cell Division : **Morphology of chromosomes; Euchromatin
and Heterochromatin.Nucleic acid as genetic material (Examples: Bacterial
Transformation and Viral Transduction).

Brief idea of Polytene chromosomes:Cell cycle and phases (excluding control
mechanism). Characters of malignant cell; Process & significance of Meiosis.

**Genetics : **Laws of Heredity : (Monohybrid and dihybrid crosses;
Mendel’s laws). Back cross, Test cross, Linkage, Crossing over, Sex linked
inheritance – Colour blindness, Haemophilia.

Mutation – Definition and Types; Replication of DNA, Transcription and
Translation (Brief idea).

**Origin, Evolution and Diversity of Life :**Haldane and Oparin’s concept
on origin of life. Modern concept of Natural selection, Biological Species
concept.

Human evolution – an outline.

**Taxonomy and Classification : **Definition; Importance of Taxonomy,
Binomial Nomenclature, Law of Priority (Homonym & Synonym).

**Concept of Biodiversity : **Definition of Biodiversity ; Genetic
diversity; Species diversity and Ecosystem diversity. Five kingdom
classification (only distinct characters).Salient features of major animal phyla
with common examples, classification of Chordates (up to Sub Class) with
distinctive characters only.

**Population Biology :**Concept of population growth (logistic and
exponential) and population control.

**Ecosystem : **Concept of ecosystem and Biosphere, Wetland.. Brief idea
of Ecological pyramids, Energy flow, Biogeochemical cycle (concept only).

**Environmental pollution : **Air, water and noise pollution – sources
effects and probable control strategies; Biomagnification and Bioaccumulation.
Cause of Dyslexia, Minamata and Etai etai diseases. Green house effect, BOD,
COD, Acid rain and Ozone hole.

##

WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

SYLLABUS FOR JEM

## MATHEMATICS

**Algebra**

A.P., G.P., H.P. :Definitions of A. P. and G.P.; General term; Summation of first n-terms; A.M.and G.M.; Definitions of H.P. (only 3 terms) and H.M.; Finite arithmetico-geometric series. Logarithms :Definition; General properties; Change of base.

**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.

**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).

**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).

Combinations of n different things taken r at a time (r ≤ n). Combination
of n things not all different. Basic properties.

##

WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

SYLLABUS FOR JEM

## PHYSICS

**Mechanics & General properties of matter
**(i) Units and dimensions : Units of measurement, system of units,
fundamental and derived units, S I units, dimensional analysis. Methods of
measurement: Vernier scale, screw gauge, analysis of errors, significant
figures.

(ii) Scalars and vectors: Addition, subtraction, multiplication of vectors.

(iii) Kinematics in one, two and three dimensions, projectiles, uniform circular motion,centripetal force, centrifigual force, relative velocity.

(iv) Dynamics: Newton's laws of motion; inertial frames, uniformly accelerated frame (pseudoforces), conservation of linear momentum, rocket motion, centre of mass, impulsive forces, friction.

(v) Work, Power and Energy , conservative and non-conservative forces, conservation of energy, collision(elastic and inelastic)

(vi) .Rotational motion : Torque, angular momentum and conservation of angular momentum, moment of inertia, radius of gyration, moment of inertia of objects with simple geometrical shapes, rotational kinetic energy and rolling on horizontal surface.

**Gravitation: **Laws of gravitation, gravitational field and
potential, acceleration due to gravity and its variation, escape velocity,
Kepler's laws and planetary motion, motion of satellites, Geostationary
orbit.

**Elasticity: **Hooke's law, elastic modulii, Poisson's ratio, elastic
energy.

## ANSWERS & HINTS for WBJEE - 2010 by Aakash Institute &
Aakash IIT-JEE

(MULTIPLE CHOICE QUESTIONS)

**West Bengal Joint Entrance Examination (WBJEE) For the Admission Of First
Year Engineering 2010.**

**Download WBJEE 2010 Answer Keys:**

**West Bengal Joint Entrance Exam 2010**

Joint Entrance Examination, 2010 (JEM-2010)

Eligibility: The applicant must be a citizen of India and should have passed the H.S.(10+2) or its equivalent examination. The general candidates must have to secure at least 50.00% marks in Physics, Chemistry and Mathematics or Biology taken together (40.00% for SC/ST candidates) and at least 30.00% marks in English (for all categories). In addition, candidates must secure at least pass marks in the subjects individually including vernacular (or any other fifth subject) as mentioned below:

**B.E/B.Tech./B.Arch : **Physics, Chemistry, Mathematics, English and vernacular or any other fifth subject.

**M.B.B.S/B.D.S. : **Physics, Chemistry, Biology, English and vernacular or any other fifth subject.

## Solutions And Answer Keys To WB-JEE 2009 By Aakash Institute

# Click Here To Download

**WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD**

**JOINT ENTRANCE EXAMINATION, 2009 (JEM-2009)**

**WEST
BENGAL JOINT ENTRANCE EXAMINATIONS BOARD
AQ-13/1, SECTOR – V,
SALT LAKE CITY,
KOLKATA – 700 091.**

** WB JEM NOTIFICATION
WBJEE 2009 WEST BENGAL JOINT ENTRANCE EXAMINATION
FOR ADMISSION TO PROFESSIONAL DEGREE COURSES
[MEDICAL/ENGINEERING / PHARMACY] – 2009**

**Details
of Engineering Examination
**