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.
