Your roadmap · आपका रोडमैप
- 1
Admission & first meetingप्रवेश और पहली मुलाकातEnquire at your nearest NDSS centre, meet the teacher, fix the batch time and get your study material.
- 2
Part 1 of the syllabusपाठ्यक्रम भाग 1Unit-wise coaching with notes and doubt classes.
Unit 1: Matrices and RankUnit 2: Eigenvalues and Cayley-Hamilton TheoremUnit 3: First Order Differential Equations
- 3
Part 2 of the syllabusपाठ्यक्रम भाग 2Unit-wise coaching with notes and doubt classes.
Unit 4: Two-Dimensional Geometry (Conics)Unit 5: Three-Dimensional Geometry
- 4
Unit tests & assignmentsयूनिट टेस्टRegular tests in the university / board pattern.
- 5
Semester 2 exam (university / board)विश्वविद्यालय / बोर्ड परीक्षाPrevious papers and full revision before the exam.
- 6
Online tests & resultऑनलाइन टेस्ट और रिज़ल्टTake the tests online; your marks and result show in your student login and at the centre.
सिलेबस · पाठ्यक्रम
1 subject · 5 chapters · 26 topics
01Unit 1: Matrices and Rank
5 टॉपिक+
- Types of matrices
- Elementary operations
- Rank, echelon and normal forms
- Inverse by elementary operations
- Consistency of systems of linear equations
02Unit 2: Eigenvalues and Cayley-Hamilton Theorem
5 टॉपिक+
- Characteristic equation
- Eigenvalues and eigenvectors
- Properties of eigenvalues
- Cayley-Hamilton theorem
- Diagonalisation
03Unit 3: First Order Differential Equations
6 टॉपिक+
- Formation of differential equations
- Variables separable and homogeneous equations
- Exact equations and integrating factors
- Linear and Bernoulli equations
- Equations of first order and higher degree
- Clairaut's equation and singular solutions
04Unit 4: Two-Dimensional Geometry (Conics)
5 टॉपिक+
- General equation of second degree
- Classification of conics
- Tracing of conics
- Polar equation of a conic
- Tangent and normal
05Unit 5: Three-Dimensional Geometry
5 टॉपिक+
- Plane and straight line
- Sphere
- Cone
- Cylinder
- Central conicoids (introduction)
About this course
आप यह कर पाएँगे
- Find the rank of a matrix and test consistency of linear systems
- Find eigenvalues and eigenvectors and apply the Cayley-Hamilton theorem
- Solve first-order differential equations of standard types including Clairaut's form
- Identify and trace conics from the general second-degree equation
- Solve problems on planes, lines, spheres, cones and cylinders in three dimensions
यह किसके लिए है
- B.Sc Mathematics students of Semester 2 (UP State Universities, NEP 2020)
- Students preparing for end-semester theory papers of Mathematics
आपको क्या चाहिए
- Class 12 Mathematics (matrices, determinants, differential equations, 3D geometry)
Online tests & result
Practice and unit tests online; marks and result show in your student login and at the centre.
Student login →
सवाल
Which syllabus does this subject follow?
It follows the B.Sc Mathematics Semester 2 syllabus of the UP State Universities (NEP 2020 common minimum syllabus). Where your own university's syllabus differs, the centre follows your university syllabus.
How are students assessed at the centre?
Through unit-wise multiple-choice tests, a final test paper and doubt-clearing sessions that follow the university examination pattern.
Will this help in the semester examination?
Yes. Units are taught in the university order with solved numericals and exam-pattern questions.
