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# VIT Engineering Entrance Examinations VITEEE 2018 Mathematics Sample Question Paper

Name of the University : VIT, Vellore
Exam : VITEEE-2018 – VIT Engineering Entrance Examinations
Document Type : Sample Question Papers
Category or Subject : Mathematics

## VIT Engineering Entrance Exam Mathematics Question Paper

** VITEEE-2018 is a Common Entrance Exam and Eligible candidates can select the courses offered at VIT Vellore Campus, Chennai Campus, VIT-Bhopal and VIT-AP on the day of Counselling as per the order of merit and availability.

Related / Similar Question Paper : VITEEE 2020 Sample Questions

## Questions Pattern

** All Questions will be of Multiple Choice Question (MCQ)
** Part –I – Physics
** Part-II – Chemistry
** Part-III-Mathematics / Biology
** Part-IV – English

## Sample Questions Mathematics

1. If A is a non-singular matrix and ( )( ) [ ] then is
A) [0]
B) I
C) 2I
D) 6I

2. The amplitude of the complex number z= -1=i3/2
A) 1/6
B) 1/3
C) 21/3
D) 4/3

3. The eccentricity of ellipse 4×2+9y2-16x=20 is
A) 5/3
B) 2/3
C) 4/3
D) 3

4. If ¯ ¯ are unit vectors and ? is the angle between ¯ and ¯ then is equal to
A) 1
B) | 1¯2¯|
C) 0
D) |a+b|

5. The image of the point (1 2 4 ) 2x+5y+2=0 in the plane is
A) (3 2 4 )
B) (3 -4 2)
C) (-3 -4 -2)
D) ( 3 -4 -2)

6. [1+sinx – 8 is equal to
A) 0
B) e
C) 1
D) p

7. log (sin2x) dx
A) (1/2 )
B) (2e )
C) (1/6 )
D) (loge 2 )

8. The general solution of the differential equation 2x+dy/dx-y=3 is
A) y = 2x-1
B) x2+y2=1
C) y=cex-1+x2
D) y2 = cex2+1-6

9. A die is thrown 100 times. Getting an even number is considered as a success , the variance of number of successes is
A) 50
B) 25
C) 10
D) 100

10. In the set of integers under the operation a*b = a+b -ab the identity element is
A) 0
B) 1
C) a
D) b

## Syllabus Mathematics

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, non-homogeneous 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 Latus-rectum – 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.

## Selection Of VITEEE Question Paper

** Candidates are requested to give utmost attention during VITEEE Question paper selection (PCME / PCBE)

PCME :
** Candidates appearing in PCME (Physics/Chemistry/Mathematics/English) is eligible for all the B.Tech. Degree programmes, as per the VITEEE ranking

PCBE :
** Candidates who have studied Physics, Chemistry and Biology are eligible for B.Tech. Bio-engineering and B.Tech.Biotechnology programmes. They are also eligible for B.Tech. Computer Science and Engineering (Spec. in Bioinformatics) and Electronics and Communication with spl. in Biomedical Engineering but after joining, registering Mathematics as bridge course is mandatory.