Theory Examination (Semester-II) 2015-16 ELEMENTARY MATHEMATICS-II

This question paper evaluates a student’s understanding of algebra, coordinate geometry, vectors, inequalities, permutations & combinations, and 3-D geometry.
It is divided into three sections: short answers, descriptive problems, and long analytical questions.

SECTION – A (10 × 2 = 20 Marks)

This section contains ten brief questions asking for short computations or definitions.
Topics include:

Complex number simplification

Linear inequality solution

Binomial coefficient equality

nᵗʰ term of an arithmetic progression

Slope of a line from two points

Dot product of vectors

Proving magnitudes of two vectors

Equation of a circle with given center and radius

Direction cosines of a line given three angles

Equation of a plane with given intercepts

This section checks speed, accuracy, and basic formula knowledge.

SECTION – B (5 × 10 = 50 Marks)

Students must attempt any five detailed questions involving algebraic methods, coordinate geometry, and vector geometry.

Topics include:

Graphical solution of a system of linear inequalities

Total arrangements of the word INDEPENDENCE and special cases

AP with given first term, last term, and sum

Equation of a line with given point and intercept conditions

Circle through three given points

Ellipse properties: eccentricity, foci, latus rectum

Area of a parallelogram using vector method

This section tests intermediate-level problem solving and geometric reasoning.

SECTION – C (2 × 15 = 30 Marks)

Students must attempt any two long-answer questions requiring deeper mathematical analysis.

Topics include:

Perpendicular Distances from Origin

Using geometry & trigonometry to prove 4p2+p′2=a24p^2 + p'^2 = a^24p2+p′2=a2

Angle Between Two Vectors

Using dot product formula

Shortest Distance Between Two 3-D Lines

Using vector form of skew lines and distance formula

This section evaluates conceptual clarity, multi-step reasoning, and 3-D geometry skills.