Shambhu Nath Srivastava

Name Hon’ble Mr. Justice Shambhu Nath Srivastava
Address 24/1, Strachy Road, Civil Lines. Allahabad  
Administrative Judge for the District Aligarh
Source Bar
Posting Allahabad
Date of Birth 05/09/1945
Initial Joining 14/02/2002
Joining at Allahabad 14/02/2002
Date of Retirement 04/09/2007
Graduated M.A. LL.B.
Enrolled as an Advocate on 01.11.1968.
Practised at Allahabad High Court since 1968.
Worked as Senior Standing Counsel. Govt. of India, Allahabad High Court.
Served as Senior Standing Counsel. Govt. of India, Allahabad High Court.
Elevated as permanent Judge on 14/02/2002.
E-Mail ID : [email protected]


VITEEE 2017 Mathematics Syllabus


1. Matrices and their Applications

Adjoint, inverse – properties, computation of inverses, solution of system of linear equations by matrix inversion method.

Rank of a matrix – elementary transformation on a matrix, consistency of a system of linear equations, Cramer’s rule, nonhomogeneous equations, homogeneous linear system and rank method.

Solution of linear programming problems (LPP) in two variables.

2. Trigonometry and Complex Numbers

Definition, range, domain, principal value branch, graphs of inverse trigonometric functions and their elementary properties.

Complex number system – conjugate, properties, ordered pair representation.

Modulus – properties, geometrical representation, polar form, principal value, conjugate, sum, difference, product, quotient, vector interpretation, solutions of polynomial equations, De Moivre’s theorem and its applications.

Roots of a complex number – nth roots, cube roots, fourth roots.

3. Analytical Geometry of two dimensions

Definition of a conic – general equation of a conic, classification with respect to the general equation of a conic, classification of conics with respect to eccentricity.

Equations of conic sections (parabola, ellipse and hyperbola) in standard forms and general forms- Directrix, Focus and Latusrectum – parametric form of conics and chords. – Tangents and normals – Cartesian form and parametric form- equation of chord of contact of tangents from a point (x1 ,y1) to all the above said curves.

Asymptotes, Rectangular hyperbola – Standard equation of a rectangular hyperbola.

4. Vector Algebra

Scalar Product – angle between two vectors, properties of scalar product, and applications of dot product. Vector product, right handed and left handed systems, properties of vector product, applications of cross product.

Product of three vectors – Scalar triple product, properties of scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors.

5. Analytical Geometry of Three Dimensions

Direction cosines – direction ratios – equation of a straight line passing through a given point and parallel to a given line, passing through two given points, angle between two lines.

Planes – equation of a plane, passing through a given point and perpendicular to a line, given the distance from the origin and unit normal, passing through a given point and parallel to two given lines, passing through two given points and parallel to a  given line, passing through three given non-collinear points, passing through the line of intersection of two given planes, the distance between a point and a plane, the plane which contains two given lines (co-planar lines), angle between a line and a plane.

Skew lines – shortest distance between two lines, condition for two lines to intersect, point of intersection, collinearity of three points.

Sphere – equation of the sphere whose centre and radius are given, equation of a sphere when the extremities of the diameter are given.

6. Differential Calculus

Limits, continuity and differentiability of functions – Derivative as a rate of change, velocity, acceleration, related rates, derivative as a measure of slope, tangent, normal and angle between curves.

Mean value theorem – Rolle’s Theorem, Lagrange Mean Value Theorem, Taylor’s and Maclaurin’s series, L’ Hospital’s Rule, stationary points, increasing, decreasing, maxima, minima, concavity, convexity and points of inflexion.

Errors and approximations – absolute, relative, percentage errors – curve tracing, partial derivatives, Euler’s theorem.

7. Integral Calculus and its Applications

Simple definite integrals – fundamental theorems of calculus, properties of definite integrals.

Reduction formulae – reduction formulae for ∫ sinn x dx and ∫ cosnn x dx, Bernoulli’s formula.

Area of bounded regions, length of the curve.

8. Differential Equations

Differential equations – formation of differential equations, order and degree, solving differential equations (1st order), variables separable, homogeneous and linear equations.

Second order linear differential equations – second order linear differential equations with constant co-efficients, finding the particular integral if f(x) = emx, sin mx, cos mx, x, x2.

9. Probability Distributions

Probability – Axioms – Addition law – Conditional probability – Multiplicative law – Baye’s Theorem – Random variable – probability density function, distribution function, mathematical expectation, variance

Theoretical distributions – discrete distributions, Binomial, Poisson distributions- Continuous distri butions, Normal distribution.

10. Discrete Mathematics

Functions – Relations – Basics of counting.

Mathematical logic – logical statements, connectives, truth tables, logical equivalence, tautology, contradiction.

Groups-binary operations, semi groups, monoids, groups, order of a group, order of an element, properties of groups.

Vellore Institute of Technology

Vellore Institute of Technology:

                  VIT (Vellore Institute of Technology) is one of the most popular and prestigious University in India which was established in the 1984. It was declared as a deemed University under the Act of UGC. VIT has its campuses situated at Vellore and Chennai. It provides numerous UG courses, PG courses, and Integrated and research programs.

Programs offered by Vellore Institute of Technology:

Let us check few important and unique courses offered at both Vellore and Chennai campus. The University offers 20 UG courses, 34 PG courses, 4 integrated programmes and four research programs.

UG courses in Vellore Campus:

  • Bio-Medical Engineering
  • Mechanical ( Specialization in Automobile, in Chemical process and in Energy Engineering)
  • Computer science and Engineering with specialization in Bioinformatics.
  • Other usual courses available in all engineering colleges

UG Courses in Chennai campus:

  • All usual courses like Civil Engineering, Computer Science Engineering, Electrical and Electronics Engineering, etc.,

PG Courses in Vellore campus:

  • Tech Computer Science and Engineering with specialization in cloud computing
  • Tech Computer Science and Engineering with specialization in Big data analysis
  • Tech Automotive Engineering in collaboration with ARAI, Pune
  • Tech Energy and Environmental Engineering
  • Tech CAD/CAM

PG Courses in Chennai campus:

  • Tech Mechatronics
  • Tech Structural Engineerning

Integrated courses offered:

  • Tech software Engineering (5 years course)
  • Sc Biotechnology (5 years course)

Fee structure:

Let us check out the Annual fees for few of the popular courses.

M.Tech Software Engineering:

For Scholarship category 1: INR 96,000 per annum

For Scholarship category 2: INR 1,59,000 per annum

For Scholarship category 3: INR 1,92,000 per annum

M.Tech CAD/CAM/ M.Tech Energy and Enviromental Engineering/ M.Tech Biomedical Engineering:

For Scholarship category 1: INR 1,50,000 per annum

For Scholarship category 2: INR 2,30,000 per annum

M.Tech Manufacturing Engineering/ M.Tech Communication Engineering/ M.Tech Nanotechnology:

For Scholarship category 1: INR 2,60,000 per annum

For Scholarship category 2: INR 2,96,000 per annum

M.Tech Embedded systems/ M.Tech Computer Science and Engineering with specialization in cloud

computing/ M.Tech Power Electronics and Drives:

For Scholarship category 1: INR 1,90,000 per annum

For Scholarship category 2: INR 2,99,000 per annum


B.E/B.Tech Programs:

Group A: Biotechnology, Civil, Chemical, Mechanical with spec in energy engineering, IT, EEE, E&I

Total fees to be paid per annum: INR 1,76,000

Group B: Mechanical Engineering, CSE, E&C, Mechanical in spec with automotive Engineering.

Total fees to be paid per annum: INR 1,98,000


             VITEEE (Vellore Institute of Technology Engineering Entrance Examination) is a national level

engineering entrance examination conducted by Vellore Institute of Technology for the admission to the

B.Tech programs in VIT campuses (Vellore and Chennai).

Eligibility criteria for this exam:

  • Candidate must be an Indian citizen to take part in the exam.
  • Candidate must have either completed or appearing for the qualifying examination conducted by State board, CBSE or ICSE board.
  • Candidates must have secured at least 60% of marks in all the major subjects such as Physics, Chemistry, Biology and Mathematics.
  • Candidates should not be more than 22 years.

Exam pattern:

Mode of examination: Online or offline mode

Total duration of the exam: 2 hours 30 minutes

Students can either choose Mathematics or Biology during the slot booking of VITEEE. According to the choice of subjects, question booklet differs for all the students. All subjects will be carrying 40 marks each. No negative marks are applicable for the incorrect attempts. Students who are in merit lists are called for the VIT counselling session, and admitted to their desirable courses according to their ranks and seat availability.

Placements in VIT:

                     Nowadays, this is a common question among students that which is the best college to provide “On campus” facility for the students. VIT is one of the famous institutes for placing maximum of its students in its campus drives. It has proved to be a consistent topper for placement records among all the private institutes of India. Most of the MNCs such as Wipro, Microsoft, Google, Oracle, Honda, Intel, Accenture, etc., have appointed many of the students from VIT for the past several years.

Facilities in VIT campus:

  • Hostels and Dining facility:

                   VIT provides best Hostel and dining facilities which provides students affordable food services within the campus.

  • Placement facilities:

               As mentioned above, VIT stands in the leading position among all the private Engineering institutions in placing numerous numbers of students every year.

  • Sports Facilities:

           VIT provides all facility regarding sports. It gives its full support for the students who are excellent in sports. It provides special training for those students and helps in building up their confidence and competitive spirit.

  • Conference Facility:

             VIT often conducts symposiums/ workshops/ National and international conferences which provides students a great exposure in every fields. VIT campus has numerous conference halls and Auditoriums for this purpose. Few of them are:


  1. Anna Auditorium with a capacity of 1800 persons
  2. M.Channa Reddy Auditorium which can occupy 469 persons
  3. Kamaraj Auditorium which occupies 128 persons

    Conference halls:

  1. Rajaji Hall with capacity of 120 people
  2. Seminar hall at CDMM block which can occupy 120 people
  3. Navalar Neduchezian Hall which can occupy 38 people

Smart classrooms:

             VIT has enabled a new facility called Smart classroom with hi-tech equipments which allows the faculties to conduct classes very easily just through single click of a button. This is a very special learning environment with a projector, computer and a touch screen white board. This touch screen board serves also as a electronic board where everything written can be saved for the future reference.

               Right now, there are two smart classrooms inside the VIT campus. More smart classrooms are planned to be derived in the near future for the welfare of the students of VIT. Thus, VIT University has dedicated itself to provide education through modern and innovative techniques. It is a cosmopolitan campus with students from all over the country. Thus, studying at VIT gives you a guaranteed success to your life and career.