THEORY EXAMINATION (SEM–II) 2016-17 ELEMENTARY MATHEMATICS - II

This examination paper is for Applied Mathematics / Engineering Mathematics, carrying 70 marks and divided into three main sections.
It tests the student's skills in Calculus, Differential Equations, Vector Algebra, 3D Geometry, and Probability.

SECTION – A (7 × 2 = 14 Marks)

This section consists of very short answer questions on:

Basic integration

Order & degree of differential equations

Unit vectors

Direction ratios & direction cosines

Magnitude of vectors

Standard integrals

Formula of a line parallel to a vector

These questions require definitions, formulas, and small evaluations.

SECTION – B (3 × 7 = 21 Marks)

This part contains medium-length questions where students must solve any three. Topics include:

Area of triangle in 3D using coordinates

Solving first-order differential equations

Evaluation of integrals

Vector equations of planes

Showing collinearity of vectors

This section checks calculation ability and vector/differential equation understanding.

SECTION – C (3 × 7 = 21 Marks)

Students must attempt any two questions. These include:

Part 3:

Evaluation of integrals

Logarithmic integration

Area enclosed by a circle

Part 4:

Verifying solutions of differential equations

General solutions of first-order differential equations

Part 5:

Projection of vectors

Vector cross product

Angle between two vectors

This section assesses advanced calculus and vector operations.

Part 6:

Vector equation of a line

Intercept form of plane

Angle between planes

Part 7:

Conditional probability

Probability with known conditions

Checking independence of events

This section focuses on 3D geometry and probability theory.